Strojniški vestnik Journal of Mechanical Engineering VOL 71 ▪ NO 9-10 ▪ Y 2025 Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief: Miha Brojan International Editorial Board Co-Editor-in-Chief: Matevž Zupančič Hafiz Muhammad Ali, King Fahd U. of Petroleum & Minerals, Saudi Arabia Section Editors: Josep M. Bergada, Politechnical University of Catalonia, Spain Domen Šeruga, Structural Design Anton Bergant, Litostroj Power, Slovenia Matej Borovinšek, Mechanics Matej Borovinšek, University of Maribor, Slovenia Dominik Kozjek, Mechatronics Filippo Cianetti, University of Perugia, Italy Simon Klančnik, Production Engineering Peng Cheng, Virginia State University, USA Jaka Tušek, Process Engineering Franco Concli, University of Bolzano, Italy Luka Lešnik, Power Engineering J.Paulo Davim, University of Aveiro, Portugal Joško Valentinčič, Additive Manufacturing Igor Emri, University of Ljubljana, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Editorial Office: Soichi Ibaraki, Kyoto University, Department of Micro Engineering, Japan University of Ljubljana, Faculty of Mechanical Engineering Julius Kaplunov, Brunel University, West London, UK SV-JME, Aškerčeva 6, 1000 Ljubljana, Slovenia Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Phone: +386 (0)1 4771 137 Simon Klančnik, University of Maribor, Slovenia info@sv-jme.eu, http://www.sv-jme.eu Jernej Klemenc, University of Ljubljana, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Technical Editor: Pika Škraba Dominik Kozjek, University of Ljubljana, Slovenia Guest Editors of this Special Issue: Peter Krajnik, Chalmers University of Technology, Sweden Matej Vesenjak, Luka Lešnik, Matej Borovinšek, Simon Klančnik Janez Kušar, University of Ljubljana, Slovenia Luka Lešnik, University of Maribor, Slovenia Print: Grafika Gracer d.o.o. printed in 490 copies Edgar Lopez, University of Istmo, Mexico President of Publishing Council: Trung-Thanh Nguyen, Le Quy Don Technical University, Vietnam Mihael Sekavčnik Vladimir Popović, University of Belgrade, Serbia University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Franci Pušavec, University of Ljubljana, Slovenia Mohammad Reza Safaei, Florida International University, USA Vice-President of Publishing Council: Silvio Simani, University of Ferrara, Italy Matej Vesenjak Marco Sortino, University of Udine, Italy University of Maribor, Faculty of Mechanical Engineering, Slovenia Domen Šeruga, University of Ljubljana, Slovenia Founders and Publishers: Jaka Tušek, University of Ljubljana, Slovenia University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Branko Vasić, University of Belgrade, Serbia University of Maribor, Faculty of Mechanical Engineering, Slovenia Arkady Voloshin, Lehigh University, Bethlehem, USA Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association Founding Editor: Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia ISSN 0039-2480, ISSN 2536-2948 (online) © 2025 with Authors; CC BY and CC BY-SA General information: Strojniški vestnik – Journal of Mechanical Engineering is published in 6 double issues per year. 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Contents Strojniški vestnik - Journal of Mechanical Engineering Volume 71, (2025), Number 9-10 Ljubljana, September-Oktober 2025 ISSN 0039-2480 Published every two months 268 Editorial: Special Issue of the Faculty of Mechanical Engineering, University of Maribor — 30 Years of Excellence in Engineering Research Matej Vesenjak, Luka Lešnik, Matej Borovinšek, Simon Klančnik Process and Thermal Engineering Additive Manufacturing 271 Numerical Solving of Dynamic Thermography Inverse 318 Fusion Behavior of Pure Magnesium During Selective Laser Problem for Skin Cancer Diagnosis Based Melting on non-Fourier Bioheat Model Snehashis Pal, Matjaž Finšgar, Jernej Vajda, Uroš Maver, Ivan Dominik Horvat, Jurij Iljaž Tomaž Brajlih, Nenad Gubeljak, Hanuma Reddy Tiyyagura, Igor Drstvenšek Power Engineering Production Engineering 284 Numerical Investigation of Erosion Due to Particles in a Cavitating Flow in Pelton Turbine 328 Advancing Intelligent Toolpath Generation: A Systematic Luka Kevorkijan, Matjaž Hriberšek, Luka Lešnik, Aljaž Review of CAD–CAM Integration in Industry 4.0 and 5.0 Škerlavaj, Ignacijo Biluš Marko Simonič, Iztok Palčič, Simon Klančnik Production Engineering Process and Thermal Engineering 294 Removal of Inclusions and Trace Elements 337 Comparison of 1D Euler Equation Based from Al-Mg-Si Alloys Using Refining Fluxes and 3D Navier-Stokes Simulation Methods Uroš Kovačec, Franc Zupanič for Water Hammer Phenomena Nejc Vovk, Jure Ravnik Mechanics Process and Thermal Engineering 301 Effect of Presetting and Deep Rolling on Creep of Torsion Spring Bars 349 Analysis of Gas Flow Distribution in a Fluidized Bed Vinko Močilnik, Nenad Gubeljak, Jožef Predan Using Two-Fluid Model with Kinetic Theory of Granular Flow and Coupled CFD-DEM: A Numerical Study Mechanics Matija Založnik, Matej Zadravec 309 Integrated Design, Simulation, and Experimental Validation Mechanics of Advanced Cellular Metamaterials Nejc Novak, Zoran Ren, Matej Vesenjak 357 Fatigue of Triply Periodic Minimal Surface (TPMS) Metamaterials – a Review Žiga Žnidarič, Branko Nečemer, Nejc Novak, Matej Vesenjak, Srečko Glodež Strojniški vestnik Journal of Mechanical Engineering ography Inverse Problem Ignacijo Biluš: Numerical n Turbine ON THE COVER ents from Al-Mg-Si Alloys d Deep Rolling on Creep of This Special Issue features a selection of articles spanning applied fluid mechanics, advanced materials and metamaterials, ulation, and Experimental h, Nenad Gubeljak, Hanuma ium during selective laser manufacturing science, and biomedical modelling. The collected works integrate experimental, numerical, and review-based nt Toolpath Generation: A Navier-Stokes Simulation approaches to address contemporary challenges in mechanical engineering. Beyond showcasing the scientific excellence achieved luidized Bed Using Two- : A Numerical Study dež: Fatigue of Triply at the Faculty of Mechanical Engineering, University of Maribor, this publication also celebrates the Faculty’s enduring mission — to connect knowledge, innovation, and human creativity in shaping a sustainable and technologically advanced future. The cover image depicts the Dean’s chain, part of the Faculty’s insignia. The photograph symbolizes the Faculty’s long-standing commitment to excellence, innovation, and the integration of scientific knowledge in building a sustainable and technologically advanced society. www.sv-jme.eu/ Image courtesy: Assist. Prof. dr. Gregor Harih, Faculty of Mechanical Engineering, University of Maribor SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 267 VOL 71 ▪ NO 9-10 ▪ Y 2025 Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Editorial Special Issue of the Faculty of Mechanical Engineering, University of Maribor — 30 Years of Excellence in Engineering Research Matej Vesenjak ‒ Luka Lešnik ‒ Matej Borovinšek ‒ Simon Klančnik Faculty of Mechanical Engineering, University of Maribor, Slovenia tajnistvo.fs@um.si Abstract This editorial introduces the Special Issue of the Strojniški vestnik - Journal of Mechanical Engineering dedicated to the 30th anniversary of the Faculty of Mechanical Engineering as an independent member of the University of Maribor, and the 50th anniversary of the University of Maribor. The Faculty of Mechanical Engineering is one of the most successful members at the University of Maribor and is recognised for its excellence in education, research and collaboration with industry. Its history of development, from its early beginnings in 1959 to becoming an internationally active and research-driven institution, reflects a continuous commitment to technological progress and societal impact. The Special Issue presents a selection of articles covering applied fluid mechanics, advanced materials and metamaterials, manufacturing science, and biomedical modelling. The collected works combine experimental, numerical, and review-based approaches to address contemporary challenges in mechanical engineering. This publication not only highlights the scientific excellence achieved at the Faculty of Mechanical Engineering, University of Maribor, but also celebrates its enduring mission to connect knowledge, innovation and human creativity in shaping a sustainable and technologically advanced future. Keywords applied fluid mechanics, computational fluid dynamics (CFD), hydropower systems, advanced materials, metamaterials, triply periodic minimal surfaces (TPMS), biomedical modelling, inverse bioheat problem, intelligent toolpath generation, artificial intelligence in manufacturing Highlights ▪ Special Issue marks 30 years of Faculty of Mechanical Engineering and 50 years of the University of Maribor. ▪ The contributions cover applied fluid mechanics, materials, manufacturing, and biomedical modelling. ▪ The issue showcases cutting-edge research and technological innovation in mechanical engineering. ▪ It reflects the Faculty’s long-standing link between academia and industry and celebrates engineering creativity and multidisciplinary collaboration. 1 INTRODUCTION encourage students to participate actively in various project-based activities, providing them with valuable theoretical knowledge and The Faculty of Mechanical Engineering is one of the most practical experience, an excellent foundation for their future careers. successful members of the University of Maribor, recognised for We place great importance on collaboration with national its achievements in education, research, professional and artistic institutions, especially the Faculty of Mechanical Engineering, endeavours. One of our key priorities is to strengthen the connection University of Ljubljana. Although both Faculties differ in their between academia and industry, and to co-create technological dynamics, strengths and challenges, we share a common vision, progress that drives social transformation. With our broad spectrum demonstrating that engineering truly knows no boundaries. of knowledge and experience, we continue to preserve tradition It is an honour to commemorate our anniversary with the while, simultaneously, embracing the trends of modern society. publication of this Special Issue of the Journal of Mechanical The planned renewal of infrastructure across the technical Faculties Engineering, which, for more than 70 years, has shaped and will undoubtedly contribute to the highest quality of research and advanced the field of mechanical engineering and related disciplines educational activities in the future. significantly, while promoting its recognition and excellence The origins of mechanical and textile engineering studies continuously. in Maribor date back to 1959, when the Technical College was Looking ahead, our Faculty will continue to embrace modern established. In 1973, it evolved into the Higher Education Technical technologies, development, and unexplored potentials that represent Institution, and, in 1975, it became part of the newly founded limitless sources of new opportunities for engineering creativity University of Maribor, which is celebrating its 50th anniversary optimistically. The word technology originates from the Greek word this year. In 1985, the Higher Education Technical Institution was »techne«, meaning the art or skill of making and building. At the renamed to the Faculty of Technical Sciences, and in 1995, it was Faculty of Mechanical Engineering, University of Maribor, we will reorganised into four independent Faculties of the University of continue to build ideas that advance technological progress skilfully, Maribor, one of which is the Faculty of Mechanical Engineering, while nurturing the art of building and maintaining a positive celebrating its 30th anniversary this year. working environment, and valuing- human relationships — the true Our Faculty places great emphasis on international cooperation, added value behind every achievement. which we enrich continuously through numerous projects and We will foster connectivity and openness, strengthen collaborations with researchers from around the world. We also interdisciplinary academic networks, and encourage diverse 268 DOI: 10.5545/sv-jme.2025.09-10.ed Editorial perspectives that can lead to new insights and innovative solutions. In loading, and clarifies fabrication and material dependent performance doing so, we will continue writing stories of success, innovations and trade-offs. progress, bringing science closer to life and creating a better future. Expanding the metamaterials perspective, the work of Novak et al. [8] provided a comprehensive review of cellular metamaterials, covering two decades of research progress. The article highlights 2 SELECTED ARTICLES OVERVIEW how advanced fabrication methods, such as additive manufacturing and explosive compaction, enable the design of foams, TPMS This issue brings together a compact but diverse collection of lattices, and hybrid auxetic structures with tailored mechanical contributions spanning applied fluid mechanics, advanced materials properties. The validated computational models are emphasised as and metamaterials, manufacturing science, and biomedical modelling. indispensable tools for optimising graded and hybrid designs. Their The papers collected here share a common thread: rigorous modelling insights underline the transformative potential of metamaterials for combined with targeted experiments or comprehensive literature crash absorption, biomedical implants and defence applications. synthesis, all aimed at solving pressing engineering problems with Manufacturing and process planning received critical attention in practical relevance. Simonič et al [9], a systematic literature review on intelligent toolpath In the area of hydraulic and turbomachinery flows, Vovk and generation. Mapping the evolution from Industry 4.0 towards human- Ravnik [1] compared 1D Euler-based and full 3D Navier–Stokes centric Industry 5.0, the authors spotlight AI/ML-driven feature approaches to the water-hammer problem, showing how simplified recognition, STEPNC interoperability prospects, and the urgent models, if validated carefully, remain powerful engineering tools. On need to broaden realworld validation and SME-focused adoption the other hand, the 3D viscous simulations reveal detailed cavitation strategies. dynamics and interactions with protective devices such as dynamic Finally, the experimental–numerical study by Močilnik et al. [10] combination air valves. Complementing this, Kevorkijan et al. [2] examined how pre-setting and deep-rolling sequences affect creep presented a CFD study of particle-driven erosion in Pelton turbine and long-term torque stability in torsion spring bars. Their combined runners: using Lagrangian particle tracking and the Finnie abrasion FEM and long-duration tests identified a narrow process window model, they quantify when sediment loading becomes critical, and (around moderate pre-setting levels) that balances the enhanced where real-world wear is likely to occur, offering insights for design elastic range with acceptable creep. The results can be applicable and maintenance in sediment-prone hydropower plants. directly to suspension component design and production. Fluid and process engineering are also addressed in the Taken together, this issue underscores the strength of contribution by Založnik and Zadravec [3], who investigated gas multidisciplinary engineering in terms of robust numerical tools, flow distribution in fluidised beds using both the Two-Fluid Model thoughtfully designed experiments and careful literature synthesis, enhanced by the Kinetic Theory of Granular Flow (TFM-KTGF) which contribute to progress across domains. We thank the authors and coupled CFD-DEM simulations. Their results, validated for their excellent work and the reviewers for their constructive against the experimental data, revealed that common geometric assessments, and hope that the readers will find both inspiration and assumptions for gas distribution plates underestimate particle effects practical ideas to advance their own projects. on flow distribution significantly. While CFD-DEM offers detailed particle-level resolution, the TFM-KTGF approach emerged as a computationally efficient alternative for large-scale systems Bridging numerical analysis and healthcare, Horvat and Iljaž [4] 3 CONCLUSION addressed an important diagnostic challenge: they solved the inverse The articles presented in this Special Issue illustrate the broad scope dynamic-thermography bioheat problem for skin tumours using a and scientific excellence of the contemporary engineering research non-Fourier (dual-phase-lag) model and a boundary-element solution conducted at the Faculty of Mechanical Engineering, University strategy coupled with Levenberg–Marquardt optimisation. Their of Maribor. They demonstrate collectively how fundamental results showed robust retrieval of the tumour parameters (notably the understanding, advanced modelling, and innovative experimentation diameter and thermal relaxation time) even with noisy data, pointing contribute to addressing practical challenges in engineering science, to promising improvements in non-invasive early-detection methods. from fluid dynamics and materials development to manufacturing Materials and structural topics are reported in the paper of intelligence and biomedical applications. Kovačec et al. [5], which presented a systematic industrial trial of This collection also symbolises the shared values of curiosity, rotary flux injection, to remove inclusions and alkali and alkaline- creativity and collaboration that have defined the Faculty of earth trace elements from Al–Mg–Si melts, demonstrating an Mechanical Engineering throughout its 30-year history within the effective salt-flux formulation that supports higher scrap fractions University of Maribor. As we celebrate this milestone alongside without compromising cleanliness. the University’s 50th anniversary, we reaffirm our commitment to Continuing within the field of metallic materials, Pal et al. [6] advancing engineering knowledge and fostering connections that investigated the melting behaviour of magnesium during additive bridge academia, industry and society. Looking ahead, the Faculty manufacturing using experimental testing. The study focused on will continue to support multidisciplinary research, collaboration, understanding melt-pool dynamics, solidification characteristics, cultivate new generations of engineers, and contribute to shaping a and potential defect formation mechanisms, which are critical sustainable and technologically advanced future. for improving print quality and structural integrity of magnesium components. The results contribute to optimising process parameters References and advancing the use of lightweight magnesium alloys in 3D printing applications. [1] Vovk, N., Ravnik, J. Comparison of 1D Euler equation based and 3D Navier-Stokes simulation methods for water hammer phenomena. Stroj Vestn-J Mech E 71 337- In a materials-oriented review, Žnidarič et al. [7] synthesised the 348 (2025) DOI:10.5545/sv-jme.2025.1340. latest knowledge on fatigue behaviour of triply periodic minimal [2] Kevorkijan, L., Hriberšek, M., Lešnik, L., Škerlavaj, A., Biluš, I. Numerical surface (TPMS) metamaterials. The review highlighted why TPMS investigation of erosion due to particles in a cavitating flow in Pelton turbine. Stroj geometries often outperform conventional lattices under fatigue Vestn-J Mech E 71 284-293 (2025) DOI:10.5545/sv-jme.2025.1351. SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 269 Editorial [3] Založnik, M., Zadravec, M. Analysis of gas flow distribution in a fluidized bed [10] Močilnik, V., Gubeljak, N., Predan, J. Effect of presetting and deep rolling on creep using two-fluid model with kinetic theory of granular flow and coupled CFD-DEM: of torsion spring bars. Stroj Vestn-J Mech E 71 301-308 (2025) DOI:10.5545/ A numerical study. Stroj Vestn-J Mech E 71 349-356 (2025) DOI:10.5545/sv- sv-jme.2025.1407. jme.2025.1365. [4] Horvat, I. D., Iljaž, J. Numerical solving of dynamic thermography inverse problem Acknowledgement Gratitude is extended to all the authors for their for skin cancer diagnosis based on non-Fourier bioheat model. Stroj Vestn-J Mech valuable scientific contributions, and to the reviewers for their constructive E 71 271-283 (2025) DOI:10.5545/sv-jme.2025.1368. and timely evaluations, which ensured the high quality of this Special Issue. [5] Kovačec, U., Zupanič, F. Removal of inclusions and trace elements from Al- Appreciation is also due to the Editorial Board and editorial team of the Journal Mg-Si alloys using refining fluxes. Stroj Vestn-J Mech E 71 294-300 (2025) of Mechanical Engineering for their continuous support and professional DOI:10.5545/sv-jme.2025.1371. collaboration. Special recognition is given to the Faculty of Mechanical [6] Pal, S., Finšgar, M., Vajda, J., Maver, U., Brajlih, T., Gubeljak, N., Tiyyagura, H.R., Engineering, University of Maribor, for its commitment to research excellence, Drstvenšek, I. Fusion behaviour of pure magnesium during selective laser melting. innovation and education throughout its 30-year history, and to the University Stroj Vestn-J Mech E 71 318-327 (2025) DOI:10.5545/sv-jme.2025.1381. [7] of Maribor for fostering an environment that encourages academic and Žnidarič, Ž., Nečemer, B., Novak, N., Vesenjak, M., Glodež, S. Fatigue of triply periodic minimal surface (TPMS) metamaterials – A review. Stroj Vestn-J Mech E technological advancement. Acknowledgement is also made to colleagues, 71 357-368 (2025) DOI:10.5545/sv-jme.2025.1369. research groups and students, whose enthusiasm, creativity and dedication [8] Novak, N., Ren, Z., Vesenjak, M. Integrated design, simulation, and experimental continue to shape the Faculty’s success. Recognition is likewise extended to validation of advanced cellular metamaterials. Stroj Vestn-J Mech E 71 309-317 our industrial and academic partners, particularly the Faculty of Mechanical (2025) DOI:10.5545/sv-jme.2025.1363. Engineering of the University of Ljubljana, for their fruitful collaboration and [9] Simonič, M., Palčič, I., Klančnik, S. Advancing intelligent toolpath generation: A shared vision. This Special Issue is dedicated to all who have contributed to systematic review of CAD-CAM integration in industry 4.0 and 5.0. Stroj Vestn-J the development, reputation and excellence of the Faculty of Mechanical Mech E 71 328-336 (2025) DOI:10.5545/sv-jme.2025.1370. Engineering, University of Maribor — past and present. 270 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Numerical Solving of Dynamic Thermography Inverse Problem for Skin Cancer Diagnosis Based on non-Fourier Bioheat Model Ivan Dominik Horvat − Jurij Iljaž University of Maribor, Faculty of Mechanical Engineering, Slovenia jurij.iljaz@um.si Abstract This paper presents numerical solving of the inverse bioheat problem to estimate four skin cancer parameters; diameter, thickness, blood perfusion rate and thermal relaxation time, based on the thermal response on the skin surface obtained by dynamic thermography and numerical skin cancer model, which can greatly enhance dynamic thermography diagnostics. To describe the heat transfer inside biological tissue and thermal behavior during the dynamic thermography process as realistic as possible, the non-Fourier dual-phase-lag bioheat model was used, as well as skin cancer model has been composed of multilayered healthy skin, embedded skin tumor and subcutaneous fat and muscle. Boundary element method has been used to solve a complex non-Fourier bioheat model to simulate dynamic thermography based on the skin cancer model and guessed searched parameters to obtain the thermal response on the skin surface during the cooling and rewarming phase using a cold air jet provocation, which is needed for the solution of the inverse bioheat problem. The inverse problem has been solved by optimization approach using the hybrid Levenberg-Marquardt optimization method, while the measurement data has been generated numerically with known exact tumor parameters and added noise, to evaluate the accuracy and sensitivity of the solution. Inverse problem solution has been tested for two different thermal responses; absolute temperature and temperature difference response, as well as for two different tumor stages; early stage or Clark II and later stage or Clark IV tumor. All important tumor parameters were successfully retrieved, especially the diameter and relaxation time, even for the high level of noise, while the accuracy of obtained parameters is slightly better using absolute temperature response. The results demonstrate the robustness of the method and a promising way for early diagnosis. The findings contribute to improving bioheat modeling in biological tissues, solving inverse bioheat problems and advancing dynamic thermography as a non-invasive tool for early skin cancer diagnosis. Key words numerical modeling, dynamic thermography, inverse problem, non-Fourier bioheat transfer, dual-phase-lag model, boundary element method, Levenberg-Marquardt optimization Highlights ▪ Non-Fourier dual-phase-lag model improves the heat transfer simulation in skin cancer. ▪ Dynamic thermography with cold air jet detects tumors during cooling and rewarming. ▪ Levenberg–Marquardt algorithm estimates tumor diameter, thickness, perfusion rate, and relaxation time. ▪ Tumor parameters are estimated robustly even with high noise in thermography temperature data. 1 INTRODUCTION cancer, gynecology, kidney transplantation, heart treatment, fever screening, brain imaging, dentistry, cryotherapy, forensic medicine, In recent years due to the development of infrared (IR) cameras, thermography has become an invaluable tool in science and laser treatments, burn diagnostics to dermatology [8–17]. engineering for many heat transfer problems and applications where Medical IR thermography is based on the principle of bioheat measuring or monitoring of the temperature is important. IR camera transfer govern by blood perfusion, metabolic activity, tissue detects thermal radiation emitted from the observed object, which conductivity and heat exchange with the environment. Therefore, is then converted into electrical signals to produce thermal images a physiological or pathological change of the tissue is reflected or thermograms. The advantage of this technique is that it measures in the change of the tissue temperature or thermal contrast on its or records the temperature in a contactless manner for the observed surface that can be easily observed with the IR camera. Therefore, object compared to a thermocouple, which must be in direct contact the deviation of the surface temperature can signal inflammation, and measures only at one point [1–3]. Of course, the disadvantage of infection, neurological, vascular or metabolic dysfunction and even it is that it can only measure the temperature at the surface and you malignancy due to the higher blood perfusion rate compared to the have to accurately define various parameters like the emissivity of the surrounding healthy tissue [2,8,18–20]. Thermography is especially surface, surrounding temperature, relative humidity etc. to measure effective in detecting lesions near tissue surface, like skin cancer. surface temperature accurately in an absolute manner. However, Skin cancer cells differ from normal cells by growing larger due to the obtained thermal image can still be used in the relative manner, their rapid and uncontrolled division. This fast-paced growth requires meaning that thermography is mostly used and effective to detect more energy to maintain cellular functions, a process referred to temperature changes based on the recorded temperature contrast of as metabolism. To meet this increased energy demand, the body the object surface for various scientific and industrial applications initiates angiogenesis, where new blood vessels form from existing [2,4–7]. For its advantage of recording thermal contrast image in non- ones. Melanoma lesions are, therefore, warmer than the surrounding invasive manner and the ability to screen larger areas it also found healthy skin, a key indicator used in diagnostic [21–24]. Because its way in various medical application from diagnostic of breast medical IR thermography can identify small temperature differences, DOI: 10.5545/sv-jme.2025.1368 271 Process and Thermal Engineering it can also detect the growth of new blood vessels or metabolic [20,42–45]. Strąkowska et al. [19,20] uses simplified one-dimensional changes associated with tumor development meaning it can also (1D) multilayered skin model to evaluate blood perfusion rate and be a valuable tool for drug or treatment evaluation [25]. The most thermal parameters of the skin tissue based on the temperature dangerous form of skin cancer is melanoma that can easily spread to response of active thermography. Luna et al. [46] used a simple 2D other soft tissues, for which is fatal and responsible for about 75 % numerical model composed of tumor and healthy surrounding skin of all skin cancer-related deaths [18]. According to Clark et al. [26] to identify thickness and blood perfusion rate of the tumor based on and Breslow [27], there is a direct correlation between the survival the static thermography information. Similar model has been used by rate and invasiveness or depth of the melanoma. Clark classified Partridge and Wrobel [47,48] to estimate blood perfusion parameters melanoma into five levels from I to V, which is still used nowadays. of the skin tumor, size and position using steady-state skin temperature Clark I and II represent an early stage with more than 72.2 % survival profile, as well as, Fu et al. [49] to estimate the size and position of rate, for which an early detection or diagnostic is very important the circular tumor or multiple tumors using meshless generalized factor to improve the survival in patients with malignant melanoma finite difference method combined with a hybrid optimization [26]. algorithm. Bhowmik and Repaka [42] upgraded the skin cancer Currently, the detection of melanoma mainly relies on a subjective model to 3D multilayered one to estimate tumor diameter, thickness, asymmetry, border, color, diameter, evolution (ABCDE) test [28] blood perfusion rate and metabolic heat generation. Bhowmink et al. performed visually by dermatologists, general practitioners or primary [50] also included thermally significant blood vessels into their 3D care physicians. The ABCDE test provides a qualitative guideline, and multilayered skin tumor model to evaluate the effect of blood vessels it requires a trained specialist to distinguish malignant lesions from on finding the position and size of the tumor. Cheng and Herman benign nevi. Moreover, the ABCDE approach has a relatively high [43] used simplified 2D multilayered skin tumor model to investigate false-alarm probability and moderate detection probability [29]. Since numerically what type of cooling approach would give the highest a false negative can lead to metastasis and death, excisional biopsies temperature contrast between the skin tumor and healthy skin during are routinely performed even on lesions that are non-cancerous [30]. the recovery phase of dynamic thermography. Çetingül and Herman For these reasons, medical IR thermography, especially dynamic [33,44] used a more realistic 3D multilayered skin lesion model to thermography, is an emerging promising new technique offering a evaluate model parameter and tumor shape sensitivity on dynamic fast, painless, non-invasive and radiation-free method for early skin thermography temperature contrast. Similar model has also been cancer diagnosis with high sensitivity and specificity that can achieve used by Bonmarin and Gal [51] on investigating lock-in dynamic rates of up to 99 % [2,18,31]. thermography for detection of early-stage melanoma, as well as Medical IR thermography can be done in two ways, first as a static Iljaž et al. [52] to solve inverse bioheat problem to evaluate tumor or passive and secondly as dynamic or active thermography. Static size, blood perfusion rate and metabolic heat generation based on thermography obtains the thermal contrast image or thermograms dynamic thermography thermal contrast. Later they improve the skin of the skin or tissue under the steady-state condition, while dynamic tumor model by including thermoregulation of the blood perfusion thermography uses thermal stimulus of the tissue by controlled rate to simulate dynamic thermography [53] and solve inverse cooling or heating and observing thermal response of the tissue during bioheat problem to evaluate several tumor parameters [45]. All the the recovery period [17–19,31–34]. Static thermography relies on the mentioned models to supplement dynamic or static thermography are natural temperature difference between a tissue and its surroundings, based on the Pennes bioheat model that has significant limitations, with focus on detection of abnormal temperature variations, which including the assumption of uniform blood perfusion, the neglect may indicate underlying health concerns. Despite being the most of blood flow direction and countercurrent heat exchange, and the used measurement strategy, it is in certain ways limited. Factors treatment of arterial blood as a constant value [54]. A major drawback such as bone structure, distribution of blood vessels, recent food or of the Pennes model is the assumption of infinite heat propagation beverage intake, patient positioning, time of day and hormonal cycles speed, which disregards thermal lag effects that become critical in can all affect accuracy of this measurement strategy [17,31,35,36]. conditions with large heat fluxes in a relatively short period of time Feasibility in routine medical practice is further reduced by strict especially in inhomogeneous biological structures [55–59]. In those measurement protocols that have been proposed and the need for scenarios, Fourier-based bioheat models generally tend to fail in fully temperature-controlled rooms where the patient has to acclimatize capturing the process of heat propagation. [17,37]. On the other hand, dynamic thermography can provide To address the limitations of traditional bioheat transfer models, quantitative data about investigated tissue, by transient behavior of non-Fourier models have been developed to account for thermal lag the tissue due to the thermal stimulus and increased thermal contrast and microscale heat transfer effects. Maybe the most important non- due to the changed rate of bioheat transfer during recovery phase. Fourier bioheat model is the dual-phase-lag (DPL) model [60,61] There are also various ways of stimulating the observed tissue, some introducing a relaxation time for heat flux and temperature gradient of them using conductive heat transfer, electromagnetic radiation and has been used in many bioheat transfer applications, like laser or convective heat transfer [17,31]. The most common used thermal irradiation during hyperthermia treatment, brain tissue heating stimulus is cooling the tissue with cold gel packs or cold metal disk during laser ablation and nano-cryosurgery [62–64]. DPL model can [19,38–40], and convection cooling using cold air jets [18,33,41]. describe more complex bioheat transfer considering many effects Research shows that dynamic thermography has multiple advantages that classical Pennes model cannot describe, however, it has not been over static one. First, the temperature contrast during the recovery used so extensively due to the hyperbolic behavior of the model and phase is increased, making the diagnostic process more accurate, its complexity to solve it numerically, as well as unknown tissue as well as more information about the tissue properties or deep relaxation times. The most important research has been done by Liu lesion can be retrieved. Secondly, there is no need for the patient to and Chen [65] investigated the DPL model in a bi-layer spherical acclimatize or to have a special temperature-controlled room, making tissue domain, using experimental data to estimate relaxation times the examination period much shorter [17–19,29,31]. and demonstrating that the DPL model better captures non-Fourier Focusing on skin cancer or skin disease diagnosis, medical IR thermal behavior compared to classical bioheat transfer models, thermography can reach its full diagnostic value potential when paired particularly in scenarios involving rapid thermal processes and with accurate bioheat modeling to solve direct and inverse problems finite thermal wave propagation. Similar Zhang et al. [66] used 272 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering the DPL model to study non-Fourier heat conduction in biological [44] concluded that the shape of the tumor has little effect on the tissues during pulsed laser irradiation. Kishore and Kumar [67] temperature response on the skin surface during the rewarming tried to estimate thermal relaxation parameters numerically in laser- period and that most important parameters are average volume and irradiated living tissue. All these papers still use very simple tissue thickness. Therefore, the tumor is represented by cylindrical shape models, usually composed out of single or double layer as 1D or 3D where diameter and thickness represent its effective values. The axisymmetric problem and constant thermal relaxation parameters. surrounding healthy tissue has also been modeled with cylindrical The literature review highlights that most existing thermography- shape with the lesion in the center, as can be seen from Fig. 1 based skin cancer models rely on the classical Pennes bioheat showing the whole computational domain of the model. Because of equation, which assumes uniform perfusion, constant arterial the cylindrical geometry of the domain and skin tumor, as well as conditions, and infinite heat propagation speed. Such assumptions adiabatic boundary conditions at the side, the bioheat problem has neglect tissue heterogeneity, blood flow direction, and thermal lag, been treated as an axisymmetric one. This reduces the computational leading to limitations when modeling rapid transient processes in cost due to the computational mesh dimension reduction, which is multilayered biological tissues. Although the non-Fourier dual-phase- very important for inverse problem solving. Discretization of an lag bioheat model has been introduced in other biomedical contexts, axisymmetric computational domain needed for the numerical it has not been extensively applied to skin cancer thermography, simulation, is therefore done with only 2D cross sectional particularly for inverse problem formulations and the estimation of discretization along the rotational axis, as shown in Fig. 2. This multiple tumor parameters in realistic geometries. drastically reduces the number of computational elements and nodes, In this study, these gaps are addressed by applying a non-Fourier speeding up the computational time. dual-phase-lag bioheat model in an axisymmetric multilayered skin The dimension of the tumor for Clark II and Clark IV has tumor domain and formulating the inverse problem using a boundary been chosen based on our previous work [45,52,68] and for both element method solver combined with a Levenberg–Marquardt examples are gathered in Table 1 together with the layer thicknesses optimization approach. The paper is organized as follows: Section that have been taken from [42–45,53]. The size of computational 2 introduces the model geometry, governing equations, boundary domain diameter D has been evaluated based on the comparison of conditions, and numerical implementation, as well as describes the temperature contrast from the dynamic thermography simulation, inverse problem formulation and optimization framework. Section aiming to reduce the effect of adiabatic boundary conditions at the 3 presents the results and discussion, and Section 4 concludes the side. The appropriate and chosen domain diameter is D = 40 mm, work with key findings. Overall, this work contributes to the field while the height of the skin model is the sum of the heights of all of mechanical engineering by advancing thermal modeling of layers and is H = 11.6 mm. heterogeneous biological tissues and providing a more rigorous framework for non-invasive diagnostics using dynamic thermography. 2.1.2 Non-Fourier DPL Model In the wave theory of heat conduction, the heat flux and the 2 METHODS AND MATERIALS temperature gradient, are assumed to occur at different times. In 1990, Tzou [60] introduced the DPL model with the aim of 2.1 Skin Cancer Model eliminating the precedence assumption in the Cattaneo–Vernotte An axisymmetric multilayered numerical model of skin cancer is model. It allows either the temperature gradient (cause) to precede the developed based on our previous work [45,53,68], work of Çetingül heat flux (effect) or the heat flux (cause) to precede the temperature and Herman [44], Cheng and Herman [43] and Bhowmik and Repaka gradient (effect) in the transient process. This can be mathematically [42]. The novelty here is that the model uses non-Fourier DPL represented by [60]: bioheat governing equation proposed by Tzou in 1990 [60] making qr,t  q   T r,t T , (1) it more general and adapted to the complex bioheat behavior, tissue non-homogeneity and other effects by adjusting the relaxation where q is the heat flux, r an arbitrary space vector, t the physical time parameter. The model presented here is used for dynamic time, λ the thermal conductivity, T = T(r,t) the temperature, ∇ is thermography simulation by getting the tumor thermal response. the nabla operator, τq relaxation time of the heat flux and τT is the The most common thermal stimulus for dynamic thermography relaxation of the temperature gradient. Relaxation time of the is cooling the tissue by applying cold gel packs, metal blocks, water heat flux can be also written as τq = α/C2, where α is the thermal immersion, alcohol sprays and even Peltier devices to control the diffusivity and C the thermal wave speed. For the case of τT >   τq, the cooling temperature [17,19,38,39,69,70]. The disadvantage of these temperature gradient established across a material domain is a result cooling techniques is that we cannot monitor or record the thermal of the heat flux, implying that the heat flux vector is the cause and the contrast or response during the cooling period, which can give us temperature gradient is the effect. For τT < τq, heat flux is induced by additional information about the investigated tissue [68]. Therefore, the temperature gradient established at an earlier time, implying that in this paper we are proposing to use convective cooling approach the temperature gradient is the cause, while the heat flux is the effect. by temperature adjustable airflow like Ranque-Hilsch vortex tube In a local energy balance, the energy conservation of bioheat [18,41]. This way, we can monitor thermal response of the tissue transfer is described as [71]: during the cooling and rewarming period of dynamic thermography revealing more information about the investigated tissue, which is  q   bwbcb (Tb T )  q T m  c , (2) needed for successful solving of the inverse problem. t where ρ is the tissue density, c the specific heat of the tissue, ρb 2.1.1 Geometry the blood density, cb the specific heat of the blood, wb the blood perfusion rate, qm the metabolic heat generation and Tb the arterial Skin cancer model is composed of six distinct layers, each with its blood temperature. The first term on the left-hand side represents own thermophysical properties; epidermis, papillary dermis and heat conduction or diffusion, second term the heat exchange between reticular dermis representing the skin, subcutaneous fat, muscle blood and tissue due to blood perfusion that acts like temperature and tumor, making model more realistic. Çetingül and Herman dependent heat source, the third term the heat generation due to SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 273 Process and Thermal Engineering Fig. 1. Computational domain of the axisymmetric multilayered skin tumor model; a) isometric view with named tissues and b) cross sectional view with dimensions and boundary names the metabolic activity and the term on the right-hand side the heat where n represents the normal vector. By applying definition of the accumulation. The heat exchange between the arterial blood flow and heat flux given by Eq. (3) to the equilibrium condition, it can be the tissue proposed Pennes in 1948 [72] who assumed that it happens rewritten in the following form: on the capillary level due to the large interface area. Therefore, the blood perfusion rate represents the volumetric blood flow rate   T T i i  i  qi    T ,i      t q,i  n  through the capillary network and small arterioles per tissue volume   t i  and is non-directional.   Ti1  q   Applying first-order Taylor series expansion of the Eq. (1), while  i1 Ti1  T ,i1       i 1 ( t q ,i 1  n , )   t i 7 1  neglecting higher-order terms, we can rewrite the definition of the heat flux as: which is complex and not easy to implement. For the example when τq,i = τq,i+1 and τT,i = τT,i+1 the equilibrium condition can be rewritten in qr  q  r   T r r,t  ,t  q ,t    T  ,t      . t T  t  (3)  the form −λi∇Ti·ni = −λi+1∇Ti+1·ni+1 which is well known equilibrium Implementing Eq. (3) to the Eq. (2) yields the (type I) DPL condition in heat transfer. equation of bioheat transfer [61,68]: 2  qc T  c T 2.1.3 Boundary Conditions      t qwb bc2 b t Because the bioheat problem has been treated as axisymmetrical, the tissue temperature and other field functions like heat flux has been T 2T  2 T  wbbcb (T T t b  )  qm , (4) transformed from classical cartesian coordinate system to cylindrical where heat conductivity of the tissue and metabolic heat generation one which does not depend on the angle; T(x,y,z,t) → T(r,z,t), and assumed to be constant; λ = const. and qm = const. The first term on where r represents the radial distance from the center and z the depth the left-hand side of the Eq. (4) represents the hyperbolic term that from the top of domain. captures thermal inertia due to the finite speed of heat propagation, To simulate dynamic thermography, it is essential to define which is otherwise not present in the bioheat models using Fourier appropriate initial and boundary conditions for the computational law of heat conduction. The second term on the left-hand side is domain. For the bottom section of the domain, Dirichlet boundary the energy storage term from the classical heat conduction, that is condition is applied. This choice is based on the assumption that now extended to account for the delayed effect of blood perfusion the muscle tissue is thick enough to preserve body core temperature on heat transfer. The first term on the right-hand side represents throughout both the cooling and warm-up phases. Therefore, at the classical heat conduction, while the second term, which is the mixed- bottom we prescribed the following condition: derivative term dramatically alters the fundamental characteristics of T (r, z,t)  Tbc , z  H , 0  r  D / 2, 0  t  tsim , (8) heat propagation, by removing the wave behavior of the hyperbolic where Tbc is the body core temperature and tsim = tcool + twarm is the type of equation becoming parabolic in its nature. In the case of τq = 0 total simulation time, which is composed of the cooling time tcool, and τT = 0 or τq = τT, the DPL model reduces to the classical Pennes and the warm-up time twarm. The body core temperature can vary equation. between 36.5 °C to 37.5 °C and has chosen to be Tbc = 37 °C, as this The non-Fourier DPL bioheat model given by Eq. (4) is written is considered to be the average core body temperature of a healthy for each layer or tissue of the skin cancer model, assuming constant person at rest [17,44,52]. material properties and parameters. Equilibrium and compatibility On the sides of the domain we prescribed adiabatic boundary conditions have to be prescribed at the interface between two adjoint condition, based on the assumption that there are no side effects that tissues to describe the bioheat transfer in the whole computational will influence the thermal contrast of the lesion: domain. The compatibility condition at the interface is: r z t T T t T t q( , , ) ( , , ) , , / , , i s,   i1 s, , (5)  0 r z t  0 0  z  H r  D 2 0  t  t r sim (9)  where indices i and i + 1 represent adjoint layers and s position vector To simulate cooling with the cold air jet and rewarming period, we of the interface boundary. This condition represents that there is no prescribed Robin boundary condition as: contact resistance between the layers. While equilibrium condition represents the conservation of energy and is written as: qr z t  T , ,  r, z,t    T r, z,t  T , r  qi s,t  ni  qi1 s,t  ni1, (6) z  0, 0  r  D / 2, 0  t  tsim , (10) 274 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering where α represents the heat transfer coefficient of the cooling where Nu is the Nusselt number and db the representative artery air jet during the cooling time or the heat transfer coefficient to diameter of the tissue. the environment during the rewarming time, and T∞ denotes the The thermal relaxation time τq for all layers, except the tumor and temperature of the cooling jet or ambient temperature. During the epidermis, was determined based on Eq. (11) by prescribing Nusselt cooling phase, the heat transfer coefficient was set to α = 50 W/(m2K) number to Nu = 4.93 and artery diameter to db = 1.5 mm, representing and the temperature of the cold air jet to T∞ = 5 °C. After cooling time tcool, the cold air jet is removed, and rewarming occurs due to average value for the skin and muscle. metabolic heat production, blood perfusion and heating from the For tumor layer we assigned a higher τq value than the other tissues environment. In the rewarming phase, the heat transfer coefficient to reflect its increased perfusion rate and structural inhomogeneity is reduced to α = 10 W/(m2K), and the ambient temperature is set to [75], therefore, we set it to τq = 3.0 s for the tumor. In contrast, the T∞ = 22.4 °C which is the same condition used for the steady-state epidermis, which lacks blood vessels and is more uniform than other simulation and is based on the following work [33,45,52,68]. tissue layers, was given a lower thermal relaxation time. We set τq for The total simulation time has been set to tsim = 80 s, with the the epidermis to τq = 0.3 s, assuming that despite its homogeneity, it cooling phase lasting tcool = 30 s and the rewarming phase twarm = 50 s. still introduces some thermal resistance due to delayed heat transfer. The choice of a 30 s cooling phase is based on the work of Godoy The values for τT were selected based on the stability criteria for DPL et al. [73] that used a rewarming duration of twarm = 120 s. We deliberately opted for relatively short cooling and rewarming times presented by Quintanilla and Racke [76]. In this study, τT was chosen compared to other studies [42,52], as our primary focus is to examine to be half of τq, with τT /τq = 1/2, in order to satisfy the stability limits the thermal behavior of tissue under highly transient conditions, and commonly associated with higher-order Taylor series expansions. to shorten the examination period of the dynamic thermography. The values chosen for the τq and τT for each tissue are also gathered The initial temperature condition T(r,z,t = 0) was set to the steady- in Table 1. state solution of the bioheat problem, determined by the boundary The arterial blood temperature needed for governing equation conditions specified with Eq. (8) to Eq. (10). This approach assumes is assumed to be as equal as defined body core temperature; that the patient has already acclimated to the conditions in the Tb = Tbc = 37.0 °C. examination room. 2.1.4 Model Parameters 2.1.5 Solver and Discretization Material properties for each tissue layer can vary a lot and are not Presented multilayered skin cancer model based on the non-Fourier determined exactly as stated by Çetingül and Herman [44]. Therefore, DPL bioheat equation to simulate dynamic thermography is highly the material properties have been taken as an average value found in non-linear and numerically difficult to solve. For this reason, we the literature and can also be found in the work of other authors [33,42- wrote our own solver based on the subdomain BEM approach using 45,52]. For tumor with different stages, we assumed and prescribed elliptic axisymmetric fundamental solution and quadratic elements, the same material properties, due to the lack of more precise data; which has been tested on bench-mark problems of other authors [77– therefore, stage differs only with the size of the tumor as suggested 79]. A detailed description of the solver and numerical discretization by Clark [26]. Table 1 gathers the material properties like density, of non-Fourier DPL model with the treatment of equilibrium specific heat, blood perfusion rate, relaxation times etc., used in the condition at the interface can be found in our previous work [68]. presented skin tumor model together with the tissue dimensions. Relaxation times τq and τT needed for the non-Fourier DPL The maximum number of non-linear steps for dynamic thermography bioheat model remains challenging to define exactly due to the lack simulation and inverse bioheat problem was set to lmax = 20, with a of experimental data, significant variability and ongoing debate. For maximum error tolerance of ε = 1·10−8. processed meat, these values are estimated to be τq = 14 s to 16 s and To discretize computational domain, we used our own 2D τT = 0.043 s to 0.056 s, while for muscle tissue from cow have shown structured mesh generator with the representative spatial element size values τg = 7.36 s to 8.43 s and τT = 14.54 s to 21.03 s [65,74]. The of ∆r = ∆z = 0.5 mm, with minimal number of 2 elements in z direction relaxation times τq and τT in this work were determined based on the in each layer. A non-uniform mesh was used with an expansion factor expressions provided in the generalized DPL model by Namakshenas of ζ = 1.1 in both spatial directions from the center. The reason for et al. [59] that is based on the tissue porosity as well. However, in this work the influence of porosity is taken into account through using own mesh generator is due to the inverse problem solving, effective tissue properties instead. The relaxation times τq and τT can where diameter and thickness of the tumor is changing during the be estimated using the following expressions [59]: optimization process where generation of a new mesh must be done.   For the Clark II example, the computational mesh consists of 360 1   bc b q  , (11) computational cells and 1517 computational nodes, while for the    G   (1  ) Clark IV example the mesh includes 442 computational cells and c  tb  1855 nodes and is presented in Fig. 2. The difference in mesh density  1     bc b T , (12) between these two examples is because of different tumor sizes,    G   generating different element sizes for tumor discretization, which (1  )   where c  = tρb  affects the size of the structured mesh for the whole computational tb c/ρbcb represents the stored energy of the tissue relative domain. Presented mesh density has been confirmed to be adequate to that of the blood, while λtb = λ/λb denotes the thermal conductivity of the tissue compared to the blood. G is the coupling factor between following a mesh sensitivity study. Similar, by time step sensitivity the tissue and blood, defined as [59]: analysis, we define the time step needed to describe the transient behavior of the model. For time discretization of tsim = 80 s a constant G 4  b Nu   d 2 bwbcb , time step of ∆t = 0.5 s has been taken. b (13) SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 275 Process and Thermal Engineering Table 1. Tissue dimensions and material properties of the skin cancer model Layer d [mm] h [mm] ρ [kg/m3] cp [J/(kg K)] λ [W/(mK)] wb [s−1] qm [W/m3] τq [s] τT [s] Epidermis – 0.1 1200 3589 0.235 – – 0.30 0.15 Papillary Dermis – 0.7 1200 3300 0.445 0.0002 368.1 2.28 1.14 Reticular Dermis – 0.8 1200 3300 0.445 0.0013 368.1 2.46 1.23 Fat – 2.0 1000 2674 0.185 0.0001 368.3 2.16 1.08 Muscle – 8.0 1085 3800 0.510 0.0027 684.2 2.22 1.11 Blood – – 1060 3770 – – – – – Tumor Clark II 2.0 0.44 1030 3852 0.558 0.0063 3680 3.00 1.50 Tumor Clark IV 2.5 1.1 1030 3852 0.558 0.0063 3680 3.00 1.50 ∆T. Therefore, this paper covers four different inverse problems, to evaluate the feasibility of early skin cancer diagnosis and solution sensitivity regarding to type of the recorded thermal image. 2.2.1 Measurement Data Dynamic thermography measurements have been generated numerically by solving direct bioheat problem with known searched parameters and by adding a measurement noise to simulate more realistic measurement data and not to commit inverse crime. First test example uses early stage (Clark II) skin tumor with the following searched parameters; d = 2.0 mm, h = 0.44 mm, wb = 0.0063 s−1, τq = 3.0 s, and the second one the later stage (Clark IV) tumor with the following searched parameters; d = 2.5 mm, h = 1.1 mm, wb = 0.0063 s−1, τq = 3.0 s, that has already been introduced in Section 1 and gathered in Table 1. These parameters are written here again due to clarity, because they represent the exact Fig. 2. 2D computational mesh representing axisymmetric cylindrical domain values of the considered inverse problems. for Clark IV example Thermal response during the dynamic thermography has been recorded in two ways, first as an absolute temperature value and second as the temperature difference. Fig. 3 shows the absolute 2.2 Inverse Bioheat Problem temperature response of simulated dynamic thermography for Clark When the numerical simulation of certain processes or phenomena II and Clark IV tumor, while Fig. 4 and 5 show the temperature is needed, we are talking about direct problem. For example, the difference response. As can be seen, the temperature contrast or simulation of dynamic thermograph is direct bioheat problem, where difference between the tumor temperature and surrounding healthy skin is increased during the cooling phase by almost two times, we must prescribe governing equation of the process, geometry, all compared to the steady-state conditions. This is the advantage of material or model properties and boundary conditions describing dynamic thermography. The temperature spatial profile is the same the process. These problems are well-posed, meaning that they have regarding the absolute or temperature difference response, while the a unique and stable solution that can be obtained using established transient behavior is different, as can be seen from Fig. 3 and 4. For numerical or analytical methods. However, when certain parameters, better understanding, Fig. 5 is simulating the processed IR image such as material properties, boundary conditions or internal sources, at the end of the cooling phase together with the tumor dimension, are unknown and must be estimated from indirect measurements, where enhanced contrast of dynamic thermography is obtained. It we encounter what is known as inverse problem. Inverse problems can be observed that early-stage tumors produce lower temperature seek to determine unknown inputs based on observed outputs. Their contrast than later-stage ones meaning it can be harder to detect and solution depends on the mathematical model used and is often diagnose. sensitive to measurement noise or model inaccuracies, which can Measurement data obtained at the surface of the skin z = 0 for lead to instability or non-uniqueness of the solution, characteristics position p and time t can be written as: that make inverse problems ill-posed by nature [42,45–47,52,80,81]. Tabs ,s , p,t = T (rp ,0,tt ), (14) To solve inverse problem an optimization approach has been used. The inverse problem is transformed to optimization process by Ts , p ,t  T (rp ,0,tt ) T (D / 2,0,tt ), (15) objective function that measures the difference between simulated where index s represents simulation, rp the radial position of the temperature response and actual measurement data. The solution of measurement points and tt the time of the measurement taken. the inverse problem is represented by the minimum of the objective Measurement data resolution is very important for successful function. A well-posed inverse problem should have only one global parameter estimation, as it needs to describe the temperature response minimum; otherwise, the solution is not unique, making parameter adequately. The measurement points have been taken in the radial estimation unreliable [42,45,52]. range of rp∈ [0 mm, 5 mm] at np = 6 equally spaced points meaning This paper covers two test examples; Clark II and Clark IV, to that the distance between two measurement points is δr = 1 mm. evaluate their important properties based on two different thermal While for the time measurement the data has been taken during responses of the tissue, first the absolute temperature; Tabs, and cooling, as well as rewarming period of dynamic thermography; second the temperature difference regarding to the healthy skin; tt∈ [0 s, 80 s] at intervals of δt = 1 s generating nt = 81 time measurement 276 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering points. We notice that this measurement resolution is fine enough last two cases, the measurement data does not follow numerical to capture tissue temperature response and to be able to evaluate model anymore and therefore no inverse crime is committed. Because tumor parameters. Finer resolution did not increase the accuracy of the noisy measurement data are generated randomly, we generated the searched parameters, while coarser resolution, especially in time three different measurement sets for each test example and noise domain, increased the error in the estimated parameters. level, except for the exact one. This way we can also analyze how To mimic real measurement data a white noise has been added to the randomness of the added white noise affects the inverse solution. the generated measurement data as: For a clear presentation Fig. 6 shows the generated measurement Tabs ,m, p ,t  Tabs ,s , p ,t Terr , data compared to the simulated dynamic thermography response or (16) exact data for Clark II and Clark IV test example. As can be seen,  the level of noise can affect the temperature response for the Clark II Tm, p,t  Ts , p,t  Terr , 2 more than for Clark IV, which makes solving inverse problem more (17) difficult and poor accuracy to be expected for early-stage tumor. where η represents a random number; η ∈ [−1, 1], index m stands for measurement data and ∆Terr the temperature uncertainty level. 2.2.2 Objective Function The second term on the right-hand side represents the temperature deviation or noise. Modern IR cameras can obtain noise equivalent Objective function measures the difference between simulated temperature difference (NETD) value of less than 30 mK. Therefore, temperature response of dynamic thermography by guessed searched we investigate test examples under three levels of uncertainty; 0 mK, parameters and generated measurement data in our case. Therefore, 25 mK and 50 mK [45,52]. The first one represents exact measurement the objective function for the absolute temperature response can be data, while the last two represent low and high level of noise. In the defined as: Fig. 3. Simulated absolute temperature response Tabs,s at the skin surface for Clark II and Clark IV tumor during dynamic thermography: a) transient response for tumor position r = 0 and healthy skin at position r = D/2, and b) radial temperature distribution at the end of cooling phase t = 30 s Fig. 4. Simulated temperature difference response ∆Ts at the skin surface for Clark II and Clark IV tumor during dynamic thermography: a) transient response of maximal temperature difference measured at the center of the tumor, b) radial temperature difference distribution at the end of cooling phase t = 30 s SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 277 Process and Thermal Engineering nt np In this work, the LM optimization algorithm is chosen because it 2 F1(y) Tabs ,s , p ,t (y) Tabs ,m, p ,t  , (18) balances the advantages of the steepest descent and Gauss-Newton t1 p1 methods, making it well-suited for nonlinear least-squares problems and for the temperature difference or temperature contrast as: [45,84]. nt np 2 The optimization problem is formulated as: F2 (y) Ts , p ,t (y)  Tm, p,t  , (19) t1 p1 find y*  arg minF (y), (20) y where indices 1 and 2 stand for the absolute and temperature difference where y* represents the minimum of the objective function and thermal response, respectively, F(·) is the objective function value, solution of the inverse problem. The optimization is performed y is the vector of unknown parameters, indices t and p correspond iteratively, updating the unknown parameter values using: to the time and location of temperature measurements, while nt and y n k 1  yk  vsk  F (yk 1)  F (yk ), (21) p represent the number of observed time points and measurement locations. Vector y is defined as y = {yj; j = 1, ..., n} = {d, h, wb, τq}, where s represents the search direction, β is the step size, and where n = 4 is the number of searched parameters. indices k and v denote iteration and trial step indices, respectively. LM algorithm finds the search direction at each iteration step as the 2.2.3 Levenberg-Marquardt Algorithm solution to the equation system: J tr  J I s J trk k  k  k   k  f (yk ), (22) Deterministic optimization methods work faster and require fewer evaluations compared to stochastic methods [49] like particle swarm where J represents the Jacobian matrix, µ is a damping parameter, optimization (PSO) [82], design of experiment (DOE), differential I the identity matrix and f(·) represents the residual vector; evolution (DE) [83] or simulated annealing (SA), when objective F(y) = ftr(y)·f(y) → f(y) = {fi; i = 1, ..., m}, where m = ntnp. In each function is smooth and computational cost for direct problem is high. iteration step the Jacobian matrix and damping parameter must be Fig. 5. Simulated temperature difference ∆Ts contour at the skin surface, simulating the IR image at the end of the cooling phase for; a) Clark II and b) Clark IV tumor, while blue line represents tumor diameter Fig. 6. Representation of numerically generated measurement data of temperature difference response ∆Tm for Clark II and Clark IV tumor using 0 mK, 25 mK and 50 mK level of noise: a) transient response at the center of the tumor, and b) radial response at the end of cooling phase t = 30 s 278 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering calculated and updated. The Jacobian matrix is evaluated numerically 2.2.4 Starting Point using first-order finite difference scheme as: To test the stability of the inverse solution depending on the initial J fi fi (y j  y j )  fi (y j ) i , j   , (23) guess, we have chosen three different starting point of optimization y j y j process. Table 2 is gathering the different initial guesses for the where indices i and j represent the row and column of matrix J, and optimization process for Clark II and Clark IV example. One starting ∆y point is close to the exact solution, while other two are more off. j represents the change of parameter j, which has been taken as 1 % of its value; ∆yj = 0.01yj. Once the search direction sk is known the solution can be updated using Eq. (21) where the descent criteria is checked; F(yk+1) < F(y 3 RESULTS AND DISCUSSION k). The step size is taken as β0 = 1 for the first trial, as the search direction Results of the inverse bioheat problem are presented in tables, which is also controlled by the damping parameter µ. If the descent criteria are the most appropriate to show the estimated value of the searched is not met, the step size is then reduced by βv+1 = βv /2. parameters. For better representation of results accuracy, the relative The damping parameter is updated by equation: error for certain parameters is highlighted with the gray color in the tables where intensity reflects its level. This section covers the   1  3  k 1  k max  ,1 (2 k 1) 3  , (24) analysis of the starting point, measurement noise and randomness of the measurement data using the absolute temperature response, while where θ represents the gain ratio as: at the end the effect of thermal response type is presented. F (y  k )  F (yk ) k  1 , (25) Z (0)  Z ( 3.1 Starting Point vsk ) where Z(·) represents a linear Taylor expansion of the objective The analysis of the starting point has been carried out first to evaluate function. For the first iteration step, the damping parameter has been its effect on the solution of the inverse problem and stability of the chosen to be µ0 = 10−5max(Jtr·J). optimization process. Table 3 shows the solution of the inverse To stop the optimization algorithm, we used three stopping criteria problem together with the relative error regarding the starting point where only one of them has to be fulfilled: for Clark IV tumor using absolute temperature response. The solution k > k for the exact measurement data; 0 mK, coincidence with the exact max , (26) data and does not depend on the starting point. Solution of the inverse J trk  f y problem also does not depend strongly on the starting point for the k     1, (27) noisy measurement data; however, there can be a slight difference y but negligible. The average objective function value reached for the k 1  yk   2  yk   2 , (28) exact measurement data was 1.39·10−9 K2 in 12 optimization steps. where kmax represents the maximum number of iterative steps and ε1 While for the noisy measurement data the objective function value and ε2 the tolerance for the gradient and step size, respectively. The increased to 2.65·10−2 K2 for the 25 mK noise and to 1.07·10−1 K2 maximum number of iterative steps has been chosen to be kmax = 50, for the 50 mK with the average number of optimization steps 10, while the tolerance for the second and third criteria has been taken as because the measurement data does not follow the numerical model ε exactly due to the noise. Similar observation and conclusion have 1 = ε2 = 10−8. been made using different set of measurement data, Clark II example Table 2. Different starting points for the optimization process and temperature difference response, and is therefore omitted here. At this point, we can conclude that solution of the inverse bioheat Example y0 d [mm] h [mm] wb [s−1] τq [s] problem using LM algorithm does not depend on the initial guess 1 2.3 0.60 0.0080 3.5 or starting point making optimization method stable, as well as that Clark II 2 1.9 0.50 0.0060 2.8 convergence of the optimization process is fast. 3 1.7 0.30 0.0050 1.5 1 2.4 0.90 0.0090 3.7 3.2 Measurement Noise and Data Clark IV 2 2.6 1.20 0.0060 2.8 Here, we would like to evaluate how the level of measurement noise 3 1.8 0.70 0.0050 1.7 and randomness of generating the measurement data set affects Table 3. Solution of the inverse problem for Clark IV example using different starting points and absolute temperature response; F1(y), together with relative error Solution Relative error ΔTerr y0 d [mm] h [mm] wb [s−1] τq [s] d [%] h [%] wb [%] τq [%] Exact 2.50000 1.10000 0.006300 3.00000 1 2.50002 1.09995 0.006300 3.00002 0.00 0.00 0.01 0.00 0 mK 2 2.50001 1.09996 0.006300 3.00001 0.00 0.00 0.00 0.00 3 2.50002 1.09996 0.006300 3.00001 0.00 0.00 0.00 0.00 1 2.50889 1.11174 0.006188 2.97513 0.36 1.07 1.78 0.83 25 mK 2 2.50997 1.09994 0.006230 2.97529 0.40 0.01 1.11 0.82 3 2.50909 1.11072 0.006191 2.97496 0.36 0.97 1.73 0.83 1 2.51047 1.00056 0.006691 3.03187 0.42 9.04 6.21 1.0 50 mK 2 2.51011 1.00098 0.006691 3.03156 0.40 9.00 6.21 1.05 3 2.51019 1.00031 0.006694 3.03156 0.41 9.06 6.25 1.05 SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 279 Process and Thermal Engineering Table 4. Solution of the inverse problem for Clark II example using different measurement data set of absolute temperature response; F1(y), together with relative error Solution Relative error ΔTerr y0 d [mm] h [mm] wb [s−1] τq [s] d [%] h [%] wb [%] τq [%] Exact 2.00000 0.44000 0.006300 3.00000 1 2.00000 0.43494 0.006380 2.99436 0.00 1.15 1.26 0.19 25 mK 2 2.00000 0.43730 0.006314 2.96224 0.00 0.61 0.22 1.26 3 2.00000 0.44054 0.006271 3.03409 0.00 0.12 0.46 1.14 1 2.01886 0.43046 0.006178 3.03609 0.94 2.17 1.93 1.20 50 mK 2 2.00000 0.46098 0.006174 2.91235 0.00 4.77 2.00 2.92 3 2.00000 0.42768 0.006426 2.95631 0.00 2.80 2.00 1.46 the solution. Because, it has been shown that the solution does not insight on the accuracy of the inverse solution and its dependency. depend on the starting point, we set starting point 3 for all our further Table 5 shows the obtained inverse solution for Clark II and Clark IV calculations. Table 4 shows the obtained results for Clark II example examples using statistical indicators for noisy measurement data of using absolute temperature response and different data sets for 25 mK absolute temperature response, together with the mean error. and 50 mK noise level together with relative error. As can be seen, As can be seen from Table 5 for Clark II the diameter can be the solution varies on the randomness of the noise or measurement determined very accurately regarding the noise level, while the data set and the relative error of the solution increases by increasing accuracy of other parameters is in the same range of less than 1 % the level of noise. Diameter of the tumor d can be determined very for low noise level and increases to 2 % to 3% for high noise level. accurately, while other parameters have the same level of error, The COV also shows the deviation of the estimated parameters that however, still under 5 %, meaning a good estimation or retrieval of coinciding with the average error and increases by increasing level the searched parameters. Similar findings have also been found for of noise, meaning that these parameters will be hard to evaluate in Clark IV example and are therefore omitted here. real experimental setup. Similar conclusion can be made for Clark From this small analysis, we can conclude that the solution of the IV example that shows good evaluation of tumor diameter and better inverse problem depends on the level of the noise and randomness evaluation of relaxation time than for Clark II example, while the of the generated measurement data set. Therefore, it is important to error for tumor thickness and blood perfusion rate is slightly higher generate or record more than one measurement data set to evaluate but still in the same range, less than 5 %. This shows that relaxation the deviation of the solution. time can be easily obtained for later stage tumor. Because inverse problem solution depends on the randomness Findings coincide with the findings of our previous work [45], of the measurement data, it is better to use statistical indicators like where diameter can be determined very accurately even for the mean value, deviation and coefficient of variation (COV). We are noisy measurement data, regarding the stage of the tumor. And also, well aware that three different solutions are too small sample size that blood perfusion rate and thickness show lower accuracy and to make accurate statistical analysis, however, it can still give us the interdependence. Table 5. Solution of the inverse bioheat problem for Clark II and Clark IV example under noisy Table 6. Solution of the inverse bioheat problem for Clark II and Clark IV example under noisy measurement data sets of absolute temperature response; F1(y), showing the mean value, measurement data sets of temperature difference response; F2(y), showing the mean value, deviation, COV and mean relative error deviation, COV and mean relative error ΔT d [mm] h [mm] wb [s−1] τq [s] d [mm] h [mm] w [s−1] τq [s] ΔT b err Exact 2.00000 0.44000 0.006300 3.00000 err Exact 2.00000 0.44000 0.006300 3.00000 Mean value 2.00000 0.43759 0.006321 2.99690 Mean value 2.00045 0.45606 0.006094 2.98212 Deviation 0.00000 0.00281 0.00005 0.03599 25 mK Deviation 0.00079 0.01779 0.000302 0.08330 Clark COV [%] 0.00 0.64 0.86 1.20 25 mK Clark COV [%] 0.04 3.90 4.95 2.79 II Error [%] 0.00 0.63 0.65 0.86 II Error [%] 0.02 4.31 4.55 2.16 Mean value 2.00629 0.43971 0.006260 2.96825 Mean value 2.02638 0.42853 0.006277 2.93446 Deviation 0.01089 0.01848 0.000144 0.06273 50 mK Deviation 0.03468 0.04114 0.000690 0.18607 COV [%] 0.54 4.20 2.30 2.11 50 mK COV [%] 1.71 9.60 10.99 6.34 Error [%] 0.31 3.25 1.98 1.86 Error [%] 1.32 6.59 8.54 5.32 ΔT d [mm] h [mm] wb [s−1] τq [s] err Exact 2.50000 1.10000 0.006300 3.00000 ΔT d [mm] h [mm] wb [s−1] τq [s] err Exact 2.50000 1.10000 0.006300 3.00000 Mean value 2.50510 1.11683 0.006204 2.98604 Mean value 2.50208 1.07415 0.006387 2.99885 Deviation 0.01363 0.01486 0.00001 0.01856 25 mK Deviation 0.00561 0.01426 0.000134 0.01172 Clark COV [%] 0.54 1.33 0.21 0.62 25 mK Clark COV [%] 0.22 1.33 2.10 0.39 IV Error [%] 0.47 1.53 1.52 0.63 IV Error [%] 0.17 2.35 1.79 0.31 Mean value 2.50793 1.08020 0.006355 3.00681 Mean value 2.52163 1.09922 0.006311 3.06237 Deviation 0.01973 0.06984 0.000308 0.02167 50 mK Deviation 0.03057 0.07763 0.000486 0.06745 COV [%] 0.79 6.47 4.85 0.72 50 mK COV [%] 1.21 7.06 7.70 2.20 Error [%] 0.66 4.24 3.30 0.47 Error [%] 1.15 4.98 5.44 2.42 280 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering 3.3 Type of Thermal Response dynamic thermography scenario, allowing recording of temperature response during both cooling and rewarming phases. To solve the Table 6 shows the obtained solution of the inverse problem using inverse bioheat problem, a hybrid LM optimization algorithm has temperature difference response for both test examples. Comparing been implemented that was combined with direct bioheat problem of results to the one from Table 5, where absolute temperature response simulating dynamic thermography using BEM. has been used, we can draw the same conclusion of estimating The results showed that solution of the inverse problem does not unknown parameters. Accuracy of tumor diameter and relaxation depend on the initial guess making LM algorithm robust, accurate time is still better from the blood perfusion rate and tumor thickness, and efficient for this type of inverse problem. All four parameters especially for Clark IV. The relative error of the estimated parameters can be retrieved exactly only for the measurement data that follows based on the temperature difference response is higher than the numerical model exactly. However, this is not possible in real life results based on the absolute temperature response, especially for the problem. The parameters can be still retrieved very accurately even early-stage tumor. This means it is better to use absolute temperature under higher level of measurement data noise, especially the diameter response to diagnose early-stage tumor. However, using temperature and thermal relaxation time for both examples using absolute difference response shows that accuracy of the parameters is better temperature response. Blood perfusion rate and tumor thickness for later stage tumor. These findings coincidence with our previous exhibit slightly higher estimation error but remain within acceptable work [45]. Nevertheless, early-stage diagnosis is still possible using bounds. The accuracy of the estimated parameters is lower when temperature difference response and good accuracy of estimated using temperature difference response, however, this is practically parameters can be obtain by keeping the level of measurement noise more feasible, because the temperature contrast does not depend low. strongly on the body core temperature or boundary condition at the From the analysis done on the solution of inverse bioheat problem, bottom of the numerical model. For Clark II example, all parameters we can conclude that all searched parameters can be successfully were estimated with relative errors below 5 % for lower level of evaluated even for high level of measurement noise, especially tumor measurement noise, demonstrating strong potential for early-stage diameter and relaxation time where relative error of the obtained skin cancer diagnosis. parameters is less than 5 %. Based on this study, it is better to Overall, this study confirms that dynamic IR thermography, determine unknown parameters using absolute temperature response combined with non-Fourier bioheat modeling and inverse analysis, is than temperature difference, especially for an early-stage tumor. a promising tool for non-invasive skin cancer assessment. The ability However, from the practical point of view, temperature difference to estimate not only geometric properties but also physiological such response is preferred because it does not depend strongly on the as blood perfusion and thermal relaxation time provides insight into prescribed body core and surrounding temperature, making it more tumor size, stage, and invasiveness. general and still accurate enough. Future work will focus on developing this approach even further in the field of numerical simulations, solving inverse problems, statistical assessment of the approach, as well as on the experimental 4 CONCLUSIONS validation of the proposed model and real-time implementation This paper presents a numerical framework for the non-invasive strategies. skin cancer diagnosis using dynamic IR thermography, supported by improved skin cancer model and inverse problem analysis, to estimate References tumor diameter, thickness, blood perfusion rate and thermal relaxation [1] Wilson, A.N., Gupta, K.A., Koduru, B.H., Kumar, A., Jha, A., Cenkeramaddi, L.R. time. A novel contribution of this work lies in the integration of the Recent advances in thermal imaging and its applications using machine learning: non-Fourier DPL bioheat model into a multilayered, axisymmetric A review. 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Evaluation of hardening performance of cooling media by using Ključne besede numerično reševanje, dinamična termografija, inverzni inverse heat conduction methods and property prediction. Stroj Vestn-J Mech E problem, nefourierov prenos toplote, DPL model, metoda robnih elementov, 56 77-83 (2010). Levenberg-Marquardt optimizacija SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 283 Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Numerical Investigation of Erosion Due to Particles in a Cavitating Flow in Pelton Turbine Luka Kevorkijan1 − Matjaž Hriberšek1 − Luka Lešnik1 − Aljaž Škerlavaj2 − Ignacijo Biluš1 1 University of Maribor, Faculty of Mechanical Engineering, Slovenia 2 Scotta Turboinštitut, Slovenia ignacijo.bilus@um.si Abstract Erosion of Pelton turbine components due to cavitation and particle-laden flow is a major challenge in hydropower applications, particularly in sediment-rich river environments. This study presents a numerical investigation on how solid particles contribute to the erosion of a Pelton runner. Computational fluid dynamics (CFD) simulations were conducted using ANSYS CFX 2023 R2, incorporating a Lagrangian particle tracking approach and the Finnie abrasion model to predict erosion patterns under varying sediment concentrations. The results indicate that, under normal sediment conditions, particle erosion does not significantly contribute to blade tip damage. However, under extreme sediment loading, the predicted erosion patterns closely match real-world observations, particularly at the blade tip. Keywords Pelton turbine, solid particle erosion, cavitation, CFD simulation Highlights ▪ Numerical CFD analyzis was used to evaluate erosion in Pelton turbine runners. ▪ Particle erosion is negligible under normal sediment conditions but significant under extreme loading. ▪ Erosion patterns predicted by simulations align with real-world turbine wear. 1 INTRODUCTION turbines are conventionally designed for operation within normal operating limits. When operating outside these limits, i.e. within Multiphase flows occur in wide range of devices in process and temporary operating limits, the operating time is limited according energy engineering. In some cases, their occurrence is intentional due to the process taking place between the phases in the flow, such to IEC 60609 standard [6]. If a turbine is operating in temporary as in spray coating (spray towers), preparation of suspensions in the operating limits in such a regime that pressure drops below vapor pharmaceutical and food industries (fluidized bed devices, mixing pressure, cavitation can occur. Cavitation can cause erosion of turbine reactors), distillation, drying, air conditioning (air conditioning and components, independent of other erosion causes. Another challenge ventilation systems), combustion in thermal machines (thermal power arises in rivers with suspended sediments, where the flowing water plants, internal combustion engines), coating removal (sandblasting), carries solid particles, which can cause additional erosion, termed and many other processes [1]. abrasion. However, multiphase flow can also arise unintentionally as a To improve turbine design with respect to erosion phenomena, consequence of natural phenomena or engineering process, for or to predict erosion in existing turbine designs, computational fluid example, solid particles in emissions during combustion (combustion dynamics (CFD) simulations coupled with erosion models are often in internal combustion engines, thermal power plants, fires), utilized. In the past, various modelling approaches for cavitating sediments in river flows (flow through hydraulic turbine machines) flow have been adopted, and several cavitation erosion models and sand particles in wind flow (wind erosion in deserts). have been developed. Research in this field remains ongoing, with In general, multiphase flows are classified into stratified and recent efforts focused on phenomenological models applied to a dispersed types, with flows containing solid dispersed phases, such range of engineering applications. Leclercq et al. [7] developed a as particles in liquid flow, being a special case of the latter. Due to the cavitation erosion model based on earlier work by Fortes-Patella et frequent occurrence of such flows in process and energy devices, the al. [8] in which all cavitation collapses are considered by projecting interaction of particles with the walls of the devices is of significant cavitation erosion potential from interior cells to the wall using a engineering interest. These interactions can result in material discrete formulation. Implemented in Code_Saturne, this model was loss from the wall surface, commonly referred to as abrasion. A successfully applied to predict cavitation erosion on a NACA65012 particularly relevant issue is the damage to the flow components of hydrofoil. Schenke and van Terwisga [9] proposed a continuous turbine machines operating in rivers polluted with sediments [2]. formulation for the projection of cavitation potential to walls, while In 2023, approximately 750 million people worldwide still Melissaris et al. [10] later improved the model by considering energy lacked access to electricity [3]. In the preceding year, 4300 TWh focusing during cavity collapse. Using this improvement, they were of electricity worldwide was produced in hydropower plants, able to predict more spatially focused cavitation erosion patterns in accounting for about 15 % of total global electricity production. the case of a KCD-193 model propeller. Arabnejad et al. [11] further Annual growth of production was 2 %, with projections suggesting advanced modeling by considering two different mechanisms, both an increase of 4 % by 2030 [4]. pressure waves and microjets, depending on the distance from the As further adoption of hydraulic turbines to produce electricity is wall at which cavity collapse occurs. These complex models have pursued, several engineering challenges have emerged [5]. Hydraulic been successfully used to predict erosion for various cases; however, 284 DOI: 10.5545/sv-jme.2025.1351 Power Engineering open questions remain regarding modeling assumptions, particularly literature, indicating the need to better understand abrasion of Pelton the cavitation collapse driving pressure [12]. injectors, particularly for full scale Pelton turbine injectors, which In addition to above presented complex models, simpler models has recently been analyzed by Liu et al. [31]. have been developed and successfully applied to predict cavitation In general, abrasion of turbine components is prevalent also on erosion in different hydraulic systems. These simpler models are turbine runners, specifically rotor blades. Kumar and Bhingole often applied to complex geometries or cases in which change in [32] conducted a CFD study of a combined effect of cavitation geometry needs to be considered. Such was the study by Brunhart et al. [13], where it has been determined that for the cavitation and particle erosion on Kaplan turbine, with varying particle size erosion prediction within a diesel fuel pump, where dynamic mesh and concentration and determined that larger particles and larger was adopted, good agreement with experiment was obtained using concentrations of particles produced more abrasion on the runner. an erosion indicator based on the recorded maximum of the squared Similarly, effects of particle concentration and diameter on abrasion total time derivative of pressure. Santos et al. [14] used three erosion characteristics obtained by CFD simulations on a Pelton turbine indicators to predict cavitation erosion in gasoline direct injection runner have been studied by Li et al. [33], where they concluded (GDi) injector, where again dynamic mesh was adopted in the that the diameter of the particles mainly effected the distribution of simulation. For the prediction of cavitation erosion in Pelton turbine, predicted abrasion regions and concentration mainly influenced the Jošt et al. [15] adopted criteria previously proposed by Rossetti et intensity of abrasion. Han et al. [34] also considered cavitation to al. [16], which relate material damage to presence of water vapor in have an influence on particle abrasion of Pelton runner, which they contact with the wall, rapid reduction in volume of this water vapor predicted using the Finnie [17] model. They concluded that cavitation and the volume fraction of air mixed with the water (and water has a clear influence on particle abrasion development, especially due vapor) in the observed region. Based on this approach, Jošt et al. [15] concluded that damage of the observed Pelton rotor blades is not the to its effect on motion of smaller particles at the jet interface (air- result of cavitation erosion as the collapses are too slow. liquid interface) [34]. Table 1 summarizes the mechanisms of erosion Erosion of material due to particles has long been a topic of and highlights the studies where erosion was modelled specifically in investigation of a distinct branch of engineering research – tribology. the case of Pelton runner. It stems from early research of contact forces due to friction by physicists such as Coulomb and later Hertz. Due to previously Table 1. Summary of studies of erosion modelling highlighting which erosion mechanism was mentioned industry applications in which multiphase flows and modelled subsequent abrasion occur, research into particle abrasion focused Reference Mechanism of erosion on experimental studies to obtain empirical predictive models of Leclercq et al. [7] Cavitation collapse abrasion. Such early study was conducted by Finnie [17], in which basic Melissaris et al. [10] Cavitation collapse parameters that influence abrasion were determined, notably the Arabnejad et al. [11] Cavitation collapse influence of the particle impact angle on abrasion. Similarly, Bitter Brunhart et al. [13] Cavitation collapse [18,19] identified different influencing parameters and proposed Santos et al. [14] Cavitation collapse an empirical abrasion model, following by Grant and Tabakoff Rossetti et al. [16] Cavitation collapse conducted studies [20,21] of abrasion in helicopter turbines and Finnie [17] Particle impact proposed a particle wall rebound model alongside their own abrasion Bitter [18,19] Particle impact model. Ahlert [22] proposed another abrasion model based on Ahlert [22] Particle impact experimental investigation of particles impacting AISI 1018 steel Oka, Okamura and Yoshida [24,25] Particle impact sample. For AISI 4130 steel Forder et al. [23] conducted similar Det Norske Veritas society [26] Particle impact study and applied the abrasion model to predict abrasion in control Peng and Cao [28] Particle impact valve using CFD simulations. Later multiple models have been Messa, Mandelli and Malavasi [30] Particle impact proposed, with increasing complexity with respect to number of Liu et al. [31] Particle impact. parameters considered, such as studies by Oka et al. [24] and Oka Kumar and Bhingole [32] Particle impact and cavitation collapse and Yoshida [25] and by Det Norske Veritas society (DNV) [26]. Over time adoption of empirical abrasion models in CFD has increased, Li et al. [33] Particle impact Gnanavelu et al. [27] used this approach to reduce the number of Han et al. [34] Particle impact experiments needed in their study of abrasion. These empirical abrasion models have been applied to predict In the present study, we investigated numerically, whether the particle abrasion in different hydraulic systems by using CFD cause of erosion of Pelton runner, found in the previous study by Jošt simulations of flows containing solid particles, where particles are et al. [15], could be due to solid particles present in the water flow. considered as points and are tracked in Lagrangian frame. Peng For this purpose, we extended the modelling of flow through Pelton and Cao [28] studied abrasion of pipe bends in piping found in oil turbine by including Lagrangian particle tracking and applying Finnie industry, by comparing multiple abrasion models used in numerical abrasion model within ANSYS CFX 2023 R2 [17]. Two particle simulations with experimental results, they concluded that McLaury concentrations were considered, one for regular river conditions and model [29] in conjunction with the Grant and Tabakoff particle-wall rebound model [20,21] was the most accurate in predicting abrasion one for the case of heightened presence of particles, for example due due to particles in liquid flow. Messa et al. [30] conducted a numerical to the extreme weather phenomena. Unlike previous studies, such as study of abrasion in Pelton turbine injectors, where they applied the the one by Han et al. [34], we considered fully transient behavior of model by Oka et al. [24] and Oka and Yoshida [25] to predict abrasion the flow including particle motion and Pelton rotor rotation. For this of the nozzle seat and needle for different needle openings and needle purpose, a sliding mesh approach was adopted, specifically a rotating vertex angles. They found enhanced abrasion for low openings mesh was used for the rotor region. With this approach we managed and lower needle vertex angles. Many similar analyzes exist in the to avoid using a simplification to steady-state. SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 285 Power Engineering 2 METHODS AND MATERIALS Table 2. Chemical composition of sediment 2.1 Case Description Element Spectrum 1 Spectrum 2 Element Spectrum 1 Spectrum 2 O 45.43 48.21 K 2.42 0.58 A Pelton runner from previous study is considered [15], where a C 13.68 16.17 Mg 0.87 - numerical simulation of the existing prototype-scale Pelton turbine Si 17.12 28.55 Na 0.54 0.44 was conducted for the case of cavitating flow. The purpose of that Al 6.32 0.83 Cl - 0.11 study was to determine if cavitation could be the cause of erosion on the blade tip observed after prolonged operation as shown in Fig. 1. Ca 9.29 3.42 Ti 0.33 0.18 The authors [15] concluded that cavitation alone could not explain Fe 3.67 1.51 Mn 0.32 - the erosion in the region of the blade tip. The main question then Total 100 100 arose, whether that damage could be the result of turbine operating in a river laden with sediments (solid particles). 2.2 Mathematical Model The presence of sediment particles was confirmed by electron microscope imaging of the river water sample and both size and An incompressible, turbulent, multiphase flow of water jet with chemical composition of sediment particles were determined. cavitation and solid particles is considered. Multiphase flow of liquid Sediment particles were found to be in range between 30 µm and 80 water and due to cavitation water vapor contained within a jet, which µm and are visible on an electron microscope image shown in Fig. 2. forms an interface with respect to surrounding gas (air), is modelled It was then found that sand particles, which are agglomerated using a homogeneous mixture approach. Mixture density (ρ) and to form a sediment particle, are silica particles (SiO2). Chemical mixture viscosity (μ) are determined by mixing rule as: composition of sediment for a wider sampling region Spectrum 1  ll vv gg , (1) and a sampling point Spectrum 2 (elongated particle visible in Fig. 2) is shown in Table 2, where Oxygen (O) and Silicone (Si) have the  ll vv gg , (2) highest fraction of all elements present in sediment sample for both where φl is liquid volume fraction, φv is the vapor volume fraction sampling regions Spectrum 1 and Spectrum 2. and φg is gas volume fraction. Similarly, ρl and ρv are liquid and a) b) Fig. 1. Damage of a Pelton rotor blade tip (in red bracket) after prolonged operation: a) view of the back side of the blade, view of the front side of the blade vapor density respectively and ρg is gas density. Finally, μl and μv are liquid and vapor dynamic viscosity respectively, while μg is gas dynamic viscosity. The governing equations of cavitating flow can then be written, the continuity equation as:  u  0, (3) t and momentum equation as: u  uu  p   S ( ) t M , 4 where Eqs. (3) and (4) are written for the mixture of liquid and vapor phases which share the same velocity u and pressure p. In Eq. (4) τ is mixture shear stress tensor and SM is the momentum source term accounting for the presence of particles. Since the multiphase flow is considered as a mixture of two phases, an additional equation for transport of vapor volume is needed: v m vu  , (5) t  Fig. 2. Electron microscope image of the river sediment with two sampling positions l to determine chemical composition indicated as Spectrum 1 and Spectrum 2 286 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Power Engineering where m is the interface mass transfer rate due to cavitation, for to drag force and virtual mass force can be written in the form of which a cavitation model by Zwart et al. [35] was adopted in this particle acceleration as: study: dv 18l CDRep u v 1     l  Du dv  , (10) dt  2     3r F nuc 1v v 2 pv  p d  p p 24 2  p  Dt dt   e , if p  p R v m  B 3  where ν is the particle velocity, ρv is the particle density, dp is the l    , (6) particle diameter and the particle Reynolds number Rep is defined as: F 3vv 2 p  pv  c , if p  p  R 3  v  R pde  p u - v B l p , (11)  where Fe is the evaporation coefficient with a recommended value l The drag coefficient CD is calculated using the Schiller Naumann of 50 [35], Fc is the condensation coefficient with a recommended correlation [40]: value of 0.01, rnuc is the nucleation site volume fraction with a default value of 5×10−4 and RB is the bubble radius upon which the model is  1 0.15Re0.687  p  derived, with a recommended value of 10−6 m [35]. From Eq. (6) it is C 24 , if Rep 1000 D   Rep . (12) evident that the mass transfer rate was considered negative in the case  of evaporation, when pressure p is bellow vapor pressure pv, which  0.44, if Rep 1000 was 1300 Pa for water. Likewise, in Eq. (6) the mass transfer rate is Since the volume fraction of the particles in particle-laden flow positive in the case of condensation, when the pressure p is above is low, interactions between particles are neglected. However, vapor pressure pv. interaction of particles with the wall must be considered as it is Although more advanced turbulence models (hybrid Reynolds- one of the boundary conditions. For this, Hard Sphere Model is averaged Navier-Stokes and large Eddy simulation (RANS/LES), adopted, where particles are considered as nondeformable during and large Eddy simulation (LES)) have recently been used in the their collision with the wall. Rebound of particles from the wall is studies of turbulent, cavitating flows [36], even for some engineering then described with two coefficients of restitution, one in wall normal applications [37,38], RANS two-equation models still represent a good direction: balance between accuracy and calculation times for most engineering v e n applications, like a Pelton turbine. Therefore, in this study turbulence n = ,2 , (13) vn,1 was modelled using a RANS approach, specifically the k – ω SST and one in tangential direction: two-equation turbulence model was used. Two additional transport equation are introduced, one for the turbulent kinetic energy k: v e t t = ,2 , (14) v  k   t ,1      ku      t   k  Gk Yk  St k , (7) where vn,1 and vn,2 are particle velocities in the wall normal direction  k   before and after rebound respectively, and vt,1 and vt,2 are particle and one for the specific turbulence dissipation rate ω: velocities in the wall tangential direction before and after rebound respectively. Particle velocity in both directions after rebound (vn,2          u      t     G Y t  D  S , (8) and vt,2) are calculated for the known coefficients of restitution (en    and et), which were determined by using Grant and Tabakoff model [19], where coefficients of restitution are given as functions of where Gk and Gω are production terms for the turbulent kinetic particle impact angle γ as: energy and the specific turbulence dissipation rate respectively, Yk and Yω are the dissipation terms for the turbulent kinetic energy and en  0.993 -1.76 1.56 2  0.49 3 , (15) for the specific turbulence dissipation rate respectively, σk and σω are et  0.988 1.76 1.56 2  0.49 3. (16) the turbulent Prandtl numbers for k and for ω respectively, Sk and Sω are the source terms. Since the k – ω scale-adaptive simulation model To predict erosion of the wall due to impacting particles, we used (SST) is a blended turbulence model, consisting of standard k – ε and an empirical model by Finnie [17], which gives the erosion rate as: standard k – ω model, an additional term cross-diffusion term Dω is n  v  introduced in Eq. (8) due to reformulation of k – ε model for blending ER    f  , (17)  vwith k – ω model. RANS approach results in additional turbulent 0  viscosity μl, which is in the case of k – ω SST model written as: where ν0 is the empirical reference velocity with a value of 3321 m/s for steel, n is the velocity exponent with a value of 2.4 and f (γ) is an k 1  impact angle function, given as: t  , (9)   1 SF  max  , 2  * a   1 2 1  cos  ; if tan  1  f     3 3  . (18) where α* is the turbulent viscosity damping coefficient, a1 is a model  constant with value of 0.31 [39], S is the strain rate magnitude and     n2 1 sin 2 3si  , if tan   3 F2 is the second blending function. A detailed description of the turbulent model used is available in [39]. Particles represent a discrete phase for which Lagrangian tracking 2.3 Boundary Conditions and Physical Properties is adopted within previously described continuous phase (mixture Based on the previously described sediment analyzis, solid silica of two continuous phases) which was considered in Eulerian frame. particles with density ρp = 2650 kg/m3 of sizes between 30 µm and In our study drag force and virtual mass force were considered, 80 µm were considered in numerical simulation. To account for the gravity effects (buoyancy) were neglected as the inertia of the flow, varying size of particles we used the Rosin-Rammler particle size due to high fluid velocity, had a dominant influence on the motion distribution, where the mass fraction of particles above a certain of particles. Then, an additional motion equation for particles due particle diameter dp is defined as: SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 287 Power Engineering    d    was realized by prescribing their number rate and mass flow rate.  p      d   R e e    This is presented in Table 4 for both particle loading scenarios.  , (19) where de is the size constant and χ is the size distribution parameter. We considered a particle distribution with de= = 50 μm and χ = 1.1. The resulting cumulative mass fraction distribution is shown in Fig. 3. Fig. 4. Boundary conditions marked by colors: green – inlet, blue – outlet, red – no-slip wall, purple – symmetry and yellow – opening Table 4. Particle injection definition at the inlet Particle loading Volume fraction Number rate Mass flow rate Fig. 3. Rosin-Rammler particle size distribution used in numerical simulation, scenario [%] [s–1] [kg/s] represented with a cumulative mass fraction over particle diameters Normal 0.006 2.81794e+7 0.048875 Varying shape of particles was not considered in numerical Heavy 0.06 2.81794e+8 0.48875 simulations; therefore, particles were assumed to be spherical. Two different cases of particle loading of the flow were considered, At the outlet, static pressure was prescribed with a value of one for the regular river flow where volume fraction of particles 101,300 Pa for continuous phase, and particles are given the escape is 0.006 % and one for heightened particle loading scenario where boundary condition by default. Same conditions were prescribed for volume fraction of particles is 10 times higher, resulting in volume the opening boundary condition. fraction of particles of 0.06 %. Properties of liquid water, water vapor To reduce computational demands, symmetry boundary condition and air are presented in Table 3. was used at symmetry plane as shown in Fig. 4. For particles, however, this symmetry plane represented a wall, the fact that only half of the full volume (domain) was considered was accounted Table 3. Properties of continuous phases (liquid water, water vapor and air) used in numerical simulation for when calculating particle inlet number rate and mass flow rate presented in Table 4. Material Density [kg/m3] Dynamic viscosity [Pa s] Remaining surfaces (rotor blades and hub) were treated as no- Liquid water 999.18 0.00114029 slip walls for the continuous phase and solid walls with a rebound Water vapor 0.02308 9.86e-6 boundary condition for particles. Air 1.185 1.83e-5 2.4 Mesh and Numerical Setup Boundary conditions were defined as shown in Fig. 4. For the To further reduce the computational demands, we considered only 5 liquid jet flow, velocity components were prescribed as a function rotor blades in the geometrical model for the meshing, since mesh of coordinates over the nozzle area, which were determined with around the blades require refinement resulting in higher mesh cell previous numerical simulation of flow through the injector [15] density. We used the mesh from the previous study [15], where a for the mean velocity magnitude of 105.233 m/s and 5 % turbulent mixed hexahedral and tetrahedral mesh with 10.75 million cells intensity at the inlet. For the particles entering the domain with the was used. The mesh is presented in Fig. 5. The mesh consisted of jet, zero-slip velocity condition was used while injection of particles two main regions, stationary and rotating. Rotating region of mesh Fig. 5. Mesh showing: a) full mesh, b) detailed view of the blade region on the symmetry plane, and c) detailed view around a single blade at cross-section 288 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Power Engineering was prescribed mesh rotation, such that 0.1° of rotor rotation was loading scenario. In Figs. 6 and 7 we observe jet (green) impacting achieved per time step, and in total 27° of rotor rotation was achieved Pelton rotor blades shown at different times, with visible cavitation during the simulation. (magenta) shown as iso-surface with 20 % volume fraction of vapor Since the simulation was fully transient, a second order backward and sand particles (black) for a normal particle loading scenario and Euler transient scheme was adopted and for the advection terms heavy particle loading scenario, respectively. Rotor blade on which high resolution scheme was used. Within each time step maximum subsequent erosion is studied is highlighted with orange color. At the 10 iterations were performed, however a residual target of 1e-4 was beginning in a) the blade is yet to come in contact with the jet, in achieved before this limit. following moments b) through e) it passes through the jet, particles in the jet impact the blade and in f) finally jet is cut-off by next passing blade 3 RESULTS AND DISCUSSION The difference in particle loading is clearly shown and discernible when comparing Figs. 6 and 7. Due to the modelling approach taken First, we present the results for the flow of sand particles in water in this work, jet development and cavitation development are not jet impacting Pelton rotor blades, which is shown in Fig. 6 for the influenced by particles, therefore they are identical for both particle normal particle loading scenario and in Fig. 7 for the heavy particle loadings, as seen when comparing Figs. 6 and 7. Fig. 6. Impact of jet with particles on Pelton rotor blade at different times for normal particle loading scenario Fig. 7. Impact of jet with particles on Pelton rotor blade at different times for heavy particle loading scenario SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 289 Power Engineering Fig. 8. Erosion on the front side of the Pelton rotor blade: a) real operating blade, b) normal particle loading scenario simulation, and c) heavy particle loading scenario simulation Particle motion follows the motion of the water jet. Attached and heavy loading scenarios two distinct erosion zones are formed cavitation pocket behind the second blade, visible at time t = on the front side of the blade. One is at the tip of the blade and is 0.0114 s on Figs. 6 and 7, redirects the particles around it. Within more pronounced in the heavy particle loading scenario. Second one the simulated time, the second blade of five blades considered in is in the middle of the blade bucket and is again more pronounced this simulation passes through the impacting water jet carrying sand in the heavy particle loading scenario. The difference between the particles completely. As the second blade passes through the jet, erosion zone B pattern in Fig. 8 can be explained by larger number particles entrained in the jet impact the back side of the blade as well. of particles in the flow in the heavy particle loading scenario. Due This is why erosion prediction results will be presented only for the second blade, since particle erosion is expected to occur on both to larger number of particles, which take up more configurations the front and the back side of the blade. Particle erosion on the front in space (in the water jet), they produce a more spread-out pattern. side of the blade is shown in Fig. 8, where contour of time integral These results of erosion patterns for the front side of the blade are of Eq. (17) is shown for both particle loading scenarios. Two distinct also in general agreement with reference lab-scale experimental erosion zones are marked as A – blade tip region, and B – blade investigation of Pelton bucket by Umar et al. [41], where they also bucket. Difference in the pattern of zone B is observed, for heavier observed two distinct erosion zones (one around the blade splitter particle loading case (Fig. 8c) a more spread-out pattern emerges. and one in the middle of the bucket). Direct comparison is however Presented simulation results show that the extent of abrasion is limited, by different Pelton geometry, operating parameters and higher in the heavy particle loading case, while in both normal sediment concentration. Fig. 9. Erosion on the back side of the Pelton rotor blade: a) real operating blade, b) normal particle loading scenario simulation , c) heavy particle loading scenario simulation 290 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Power Engineering Similarly, we present erosion on the back side of the blade in Fig. equation modelling approach adopted in this study, several algebraic 9. Three distinct erosion zones are marked as A – blade mid-bucket cavitation models exist. For an overview of different cavitation region, B – blade bucket edge, and C – blade tip region. On the blade models, we refer the reader to Folden and Aschmoneit [44]. of real operating Pelton rotor, three erosion zones can be identified, (Fig. 9a), one in the middle of the bucket, one at the edge, splitting the blade in two halves, and one around the blade tip. All three regions 4 CONCLUSIONS are observed in the case of the simulation with the heavy particle loading, however, for the normal particle loading condition only the This study presents a numerical investigation into the erosion of region in the middle of the bucket (Fig. 9b) region marked with A is Pelton turbine rotor due to solid particles in a cavitating flow. By predicted. In general, it is observed that the extent of erosion is less extending previous research that focused on cavitation-induced on the back of the blade than on the front side. erosion, we incorporated Lagrangian particle tracking and employed Since from the previous study a research question was whether the Finnie abrasion model [17] to assess the effects of sediment-laden particles could be the cause of blade tip damage, a detailed view of water on turbine blades. Our findings indicate that, under normal river the blade tip is shown in Fig. 10. Results of simulation with heavy conditions, particle-induced erosion is not a significant contributor particle loading only are shown in Fig. 10a), as in the normal particle to the observed blade tip damage but can cause erosion of the blade loading no erosion of the tip was predicted (Fig. 9). Under normal bucket. However, under heavy sediment loading scenario, as a result particle loading of the river, tip damage observed after operation of of extreme weather phenomena, erosion predictions closely align a real Pelton rotor as seen in Fig. 10b), can’t be attributed to particle with real-world observation on an actual operating Pelton rotor, erosion. However, under heavy loading conditions, particle erosion suggesting that heavy particle concentrations can lead to substantial could cause damage to the tip, simulation results for these conditions material loss, particularly at the blade tip. show good agreement. Erosion rate is highest at the tip and the The results highlight the necessity of considering both cavitation spreads out with lower intensity, and black lines in Fig. 10 indicate and particle erosion when evaluating turbine durability in sediment- the extent of erosion spread. rich environments. Future work could focus on refining erosion Finally, we give brief discussion of model sensitivity to different models by incorporating particle shape effects, varying material parameters or modelling scenarios. Particles were assumed properties, and exploring mitigation strategies such as optimized to be spherical, however real river sediment particles come in blade coatings or operational adjustments to minimize erosive wear. different shapes. An example of idealized non-spherical shape is a superellipsoid, for which Wedel et al. [42] found that Lagrangian Nomenclature tracking gives better particle motion than by using simpler shape α* turbulent viscosity damping coefficient, [-] factors, indicating the complexity of this problem. This difference γ impact angle, [°] in particle motion could then be reflected in the erosion pattern at χ size distribution parameter, [-] the wall. The influence of particles on erosion could also be due to φl liquid volume fraction, [-] irregular shape of particles, for example angular particles are known φv vapor volume fraction, [-] to be more erosive. Yasser, Zhou and El- Emam [43] conducted φg gas volume fraction, [-] detailed computational fluid dynamics - discrete element method μ mixture viscosity, [Pa s] (CFD-DEM) simulations of different angular particles and spherical μl liquid dynamic viscosity, [Pa s] μv vapor dynamic viscosity, [Pa s] particles in pipe elbow and found that particles with fewer corners μg gas dynamic viscosity, [Pa s] (but therefore sharper edges) produced more erosion, while pattern ω specific turbulence dissipation rate, [s−1] of erosion was more localized. In addition to that, even for spherical ρ mixture density, [kg/m3] particles different drag models exist. Likewise, there are several ρl liquid density, [kg/m3] approaches to model cavitation and within the vapor transport ρg gas density, [kg/m3] Fig. 10. 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Shape matters: Numerična raziskava erozije zaradi delcev v kavitirajočem toku Lagrangian tracking of complex nonspherical microparticles in superellipsoidal approximation. Int J Multiphase Flow 158 104283 (2023) DOI:10.1016/j. skozi Peltonovo turbino ijmultiphaseflow.2022.104283. Pozetek Erozija komponent Peltonove turbine zaradi kavitacije in toka [43] Yasser, E., Zhou, L., El-Emam, M.A. Numerical analysis of particle shape influence on erosion and flow behavior in a 90-degree elbow pipe under Solid-Liquid flow. z delci predstavlja velik izziv pri hidroenergetskih sistemih, zlasti v rekah, Adv Powder Technol 36 104928 (2025) DOI:10.1016/j.apt.2025.104928. bogatih s sedimenti. V tej študiji je predstavljena numerična raziskava vpliva [44] Folden, T.S., Aschmoneit, F.J. A classification and review of cavitation models with trdnih delcev na erozijo rotorja Peltonove turbine. Simulacije računalniške an emphasis on physical aspects of cavitation. Phys Fluids 35 081301 (2023) dinamike tekočin (CFD) so bile izvedene z uporabo programa ANSYS CFX DOI:10.1063/5.0157926. 2023 R2, pri čemer sta bila vključena Lagrangev pristop sledenja delcev in Finniejev model abrazije za napovedovanje erozijskih vzorcev pri različnih Acknowledgements The authors wish to thank dr. Dragica Jošt for her koncentracijah sedimentov. Rezultati kažejo, da pri običajnih pogojih assistance in the transfer and explanation of the previous case, as well as her sedimentacije erozija zaradi delcev ne prispeva bistveno k poškodbam konic kind openness for discussion. Additionally, we thank the Slovenian Research lopatic. Vendar pa pri ekstremni obremenitvi s sedimenti napovedani erozijski Agency (ARRS) for its financial support in the framework of Research Program vzorci tesno ustrezajo dejanskim opazovanjem, zlasti na konici lopatice. P2-0196 in Power, Process, and Environmental Engineering. Ključne besede Peltonova turbina, erozija zaradi trdnih delcev, kavitacija, CFD računalniška dinamika tekočin SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 293 Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Removal of Inclusions and Trace Elements from Al-Mg-Si Alloys Using Refining Fluxes Uroš Kovačec1,2, Franc Zupanič1 1 University of Maribor, Faculty of Mechanical Engineering, Slovenia 2 Impol 2000 d.d., Slovenia franc.zupanic@um.si Abstract The cleanliness of aluminium alloys has a decisive effect on their properties and performance. In this work, the melts of several Al-Mg-Si alloys (6xxx series) were refined using rotary flux injection (RFI) of the salt fluxes in the industrial environment. A typical charge consisted of 25 % to 30 % external scrap, 45 % to 50 % internal scrap, and 20 % to 30 % primary aluminium. During injection, the entire melt volume was mixed uniformly. The melt was filtered using a porous ring filtration apparatus. The fraction and type of non-metallic inclusions were determined using light and scanning electron microscopy. The contents of alkali and alkaline-earth metals were determined using optical emission spectroscopy. The reduction of alkali and alkaline earth metals and the fraction of non- metallic inclusions were used to evaluate the process efficiency and the flux selection for the regular production. An analysis of more than 100 industry charges confirmed that the flux selected after the experimental trials, consisting of a mixture of MgCl2, KCl, NaCl and CaF2, was effective in regular production. Keywords aluminium, refinement, flux, cleanliness, non-metallic inclusion, rotary injection, alkali element Highlights ▪ Alloys were produced with an increased fraction of scrap. ▪ Melt cleaning was carried out using several salt fluxes. ▪ Systematic testing in an industrial environment using a rotary flux injection (RFI) system. ▪ Determination of non-metallic inclusions using porous disc filtration apparatus. ▪ Optimal removal of non-metallic inclusions and alkali elements by complex fluxes. 1 INTRODUCTION While preparing an aluminium alloy for casting, non-metallic inclusions can come into the melt from several sources. Metallic Al-Mg-Si alloys, which belong to the 6xxx series, are used widely oxides on the scrap, debris from the furnace lining and agglomerates in the automotive, aerospace, and construction industries, due to of borides in Al-Ti-B grain refiners represent the exogenic inclusions. their excellent combination of properties. They have medium to high The interaction of the melt with the surroundings, e.g., oxidation strength, good corrosion resistance, and excellent weldability [1]. with air or reduction of water vapor, can lead to the formation of They also have low density, and can be produced at moderate cost. endogenic inclusions. The reaction with moisture forms aluminium They are suitable for extrusion processes, making them appropriate oxide, introducing hydrogen into the melt simultaneously, resulting for manufacturing structural profiles and components, but they can be in several harmful effects [7]. Besides non-metallic inclusions, the deformed using other forming technologies. An essential advantage amounts of undesired alkali or alkaline earth elements, such as Na of Al-Mg-Si alloys is their ability to undergo precipitation hardening, and Ca, increase with repeated recycling. enhancing their mechanical properties considerably, such as strength One of the most important approaches to improving the and hardness, while preserving ductility and toughness [2]. Compared cleanliness of aluminium melts is the application of solid salt fluxes to other aluminium alloys, they offer a balanced combination of [8]. Solid salt fluxes are mixtures of inorganic compounds, mainly strength, ductility, fatigue and corrosion resistance, making them chlorides and fluorides. They are used when processing molten metal, versatile for various applications. including aluminium recycling, dross treatment and molten metal The production of primary aluminium is highly energy-intensive; treatment. Salt fluxes are also added to ensure high metal recovery thus, the use of aluminium scrap instead of primary aluminium can and decrease oxidation and metal losses [9]. Additionally, salt fluxes save up to 95 % of energy [3]. Therefore, it is imperative for the new are used to treat both primary and secondary molten aluminium, to alloys to be produced with an ever-higher addition of aluminium remove impurities such as alkali and alkaline earth metals and oxides [10]. Chloride and fluoride fluxes in aluminium refining can lead to scrap. The scrap fraction represents about 25 % of aluminium harmful gaseous emissions, including organochlorine compounds production in 2025, and is expected to rise to 50 % by 2050 [4]. For and toxic solid slags, which can have a negative impact on the environmental conservation and cost reduction, it is desirable that environment and workers’ safety [11]. The effect can be reduced recycled alloys retain their properties, even after multiple recycling considerably by appropriate measures in the melting plant and the use cycles. However, in real life, different adverse effects arise when the of the minimum necessary quantity of fluxes, reducing the emissions scrap fraction is increased [5]. Oxides, paintings and other coatings to the surroundings. can cover the surface of scrap, being a source of non-metallic Fluxes can be introduced to aluminium melts using several inclusions and residual elements for newly manufactured alloys, methods. They can be added by manual application. The powder worsening their properties gradually [6]. fluxes are sprinkled onto the surface of the molten aluminium and 294 DOI: 10.5545/sv-jme.2025.1371 Production Engineering stirred into the melt using a tool. Some fluxes, like degassing or grain The compositions of the salt fluxes were selected based on their refining, are plunged to the bottom of the melt; they are typically in melting points, reactivity for removing alkali and alkaline earth the form of tablets or briquettes. The powdered or granulated fluxes elements, density, and their ability to reduce surface tension between can be injected with an inert gas, such as argon or nitrogen. They the aluminium melt and the molten fluxes. The starting point was can also be added by a rotary degasser, which is one of the most the ternary diagram KCl‒NaCl‒MgCl2 [15]. The primary agent for effective methods. A rotary degasser injects the flux into the melt removing alkali elements is MgCl2. Its melting point is too high while stirring, ensuring thorough mixing [4]. Generally, each method (714 °C) to be added alone in the Al-melt, because its viscosity is can be used for the introduction of different types of fluxes (cover, too high at 750 °C. Thus, Salt#1, 40 % KCl, was added to achieve dross or melt cleaning fluxes). It depends on the technology which the eutectic composition, with the eutectic temperature of 467 °C, is used in a specific aluminium cast shop. However, each technology much lower than the temperature of the alloy melt. The second has a preferred type of flux. Rotary flux injection (RFI) typically uses composition, Salt#2, corresponded to the compound KCl MgCl2, granulated fluxes. having a slightly higher melting point of 487 °C. Salt#3 lies close to Most experiments on applying salt fluxes using RFI are conducted the center of the KCl-NaCl-MgCl2 phase diagram, having as low a in a laboratory environment [12,13]. There has been no systematic melting temperature as 390 °C. Adding NaCl additionally decreases research in an industrial environment yet. Some articles report the melting temperature, viscosity and the cost of fluxes because of general principles about mechanisms and applications [14]. This its much lower price. The Salt#4 had a ternary composition, located work investigates the application of several compositions of solid salt fluxes systematically on the type and amounts of non-metallic close to the binary diagram KCl‒MgCl2 (KCl + MgCl2 ≈ 95 %) with inclusions and residual alkali and alkaline earth elements in Al-Mg-Si up to 3 % NaCl and up to 3 % CaF2, keeping the melting temperature alloys using RFI. The analyzes were done using up-to-date industrial at around 430 °C. The primary role of CaF2 is to reduce the surface equipment and advanced laboratory techniques, such as porous disc tension between the Al-melt and the fluxes, allowing easier separation filtration apparatus (PoDFA), spectral chemical analysis, light and of both phases. electron microscopy and microchemical analysis. The main goal of In each charge, one of the fluxes given in Table 2 was added to the the research was to test different types of fluxes, and then, according melt. The experimental tests were carried out using fluxes produced to the experimental results, select the optimal flux for regular by the Hoesch Group and Pyrotek Incorporation, Germany, in the production. form of granulates up to 3 mm mesh size. The solid salt fluxes (15 kg to 25 kg; 1 kg t‒1 melt) were added into a melt using an RFI system (STAS, France) with a feeding rate of 120 kg/h. It is of the utmost 2 METHODS AND MATERIALS importance that the flux is dispersed uniformly in the melt, with as small droplets as possible. The optimal position of the rotor and Several Al-Mn-Si alloys were tested, mainly EN AW 6082, EN rotation speed were determined using a mesh-less flow model [16] AW 6182, and EN AW 6063. They varied slightly in chemical and experimental testing of the RFI system in the casting furnace. composition. However, all compositions fit inside the tolerances Uniform mixing of the melt can be achieved with the rotor angle of given in Table 1. No specific differences were observed in the 45° and the rotation speed of 410 min‒1, using a graphite impeller behavior of these alloys in the molten state. with a 400 mm diameter. During mixing, argon was used for the degassing, with a flow rate of 200 L/min. Table 1. Range of chemical compositions of the investigated Al-Mn-Si alloys (in wt.%) After fluxing, the melt was grain refined with AlTi3B1 feeding Si Fe Cu Mn Mg Cr Zn Ti Pb Zr wire, to achieve 0.025 wt.% to 0.030 wt.% Ti in the melt. The melt 1.20 0.05 0.55 0.80 0.12 0.00 was then transferred to the degassing unit (Siphon Inert Reactor 0.25 0.2 0.05 0.05 1.30 0.1 0.70 0.90 0.15 0.15 (SIR), Hycast, Norway) and filtered using a 50 pores per inch ceramic foam filter (CFF). Finally, the alloy was cast into billets with hot-top, Several charges were melted in a 50 t multi-chamber gas furnace air-slip technology [17]. The diameter of the billets was 279 mm. (SMS-Hertwich Engineering GmbH, Germany). A typical charge The alloy cleanliness was tested using different methods. The consisted of 25 % to 30 % external scrap, 45 % to 50 % internal scrap primary method was PoDFA by ABB, Switzerland [18]. A sample and 20 % to 30 % primary aluminium. The final temperature achieved of the molten metal was taken from the melt 30 min after finishing in the melting furnace was 750 °C. The melt (26.5 t) was transferred the flux injection and filtered through a porous refractory disc to to a one-chamber casting furnace (Sistem Teknik, Turkey), where the capture the inclusions. The sample was then prepared by grinding required chemical composition was achieved by adding clean master and polishing. The captured inclusions were analyzed using a light alloys. microscope (Axio Observer, Zeiss, Germany) and a scanning electron The next step was cleaning and refining the melt by using several microscope (SEM Jeol JSM 6610LV, Jeol, Japan) equipped with an solid salt fluxes (Table 2). The temperature in the casting furnace energy dispersive spectrometer (EDS) to determine their type and during flux treatment was 750 ±10 °C. content. This method provided both qualitative and quantitative data on the inclusions. The quantitative value is obtained by measuring Table 2. Chemical composition of the fluxes (mole and weight fraction in %) the area of the inclusions, which is then divided by the mass of the Designation Chemical composition filtered melt. Thus, the unit was mm2/kg. Salt#1 60 % MgCl2, 40 % KCl (weight 54 % MgCl2, 46 % KCl) The chemical analysis of the alloy, including the contents of alkali Salt#2 51 % MgCl2, 49 % KCl (weight 45 % MgCl2, 55 % KCl) elements (Na, Ca), was carried out using Spectro S101, SPECTRO 36 % to 40 % MgCl2, 21 % to 26 % KCl, Analytical Instruments GmbH, Germany. The light microscopy (LM) Salt#3 26 % to 31 % NaCl, 1 % to 3 % CaF2 and scanning electron microscopy (SEM) samples were ground (weight 33 % MgCl2, 26 % KCl, 39 % NaCl, 2 % CaF2) mechanically using SiC papers with granulations 320 to 4000 and 30 % to 35 % MgCl2, 60 % to 65 % KCl, 1 % to 3 % NaCl, 1 % to polished using 9 mm, 6 mm and 3 mm diamond paste. The EDS Salt#4 3 % CaF2 (weight 27 % MgCl2, 68 % KCl, 3 % NaCl, 2 % CaF2) analyzes were carried out using polished samples, while LM required chemical etching with Weck’s reagent, consisting of 2 g KMnO4, 1 g SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 295 Production Engineering NaOH, and 50 mL of distilled water. The grain size of the cast billets Therefore, much meticulous work is required to obtain adequate was determined according to Standard ASTM E112-24 [19]. results. 3 RESULTS AND DISCUSSION 3.1 Microstructure The alloys solidified in the metallic mold. Without a grain refiner addition, columnar grains of the aluminium solid solution α-Al would grow from the mold walls towards the billet center. The solidification front pushes non-metallic inclusions and alloying elements to the billet center, strongly reducing the alloy’s ductility, toughness and malleability. The addition of an effective grain refiner induces heterogeneous nucleation of the α-Al grains throughout the melt, causing the formation and growth of equiaxed crystal grains, which have a typical dendritic morphology. Fig. 1 shows a typical microstructure in the as-cast condition, at lower magnification. It consists of dendritic equiaxed grains of the aluminium solid solution, with a linear intercept length of 200 ±30 μm. Such a small and uniform grain size was obtained by adding the AlTi3B1 grain refiner. Small equiaxed grains prevent stronger macrosegregations of the alloying elements, allow more uniform distribution of the non- metallic inclusions and provide improved mechanical properties. Only extremely large non-metallic inclusions can be observed in such micrographs. The grain refiner contains particles of Al3Ti and TiB2. Only a small part of the particles causes the heterogeneous nucleation of α-Al crystal grains. Undissolved and inactive TiB2 particles often form agglomerates, which constitute part of the non-metallic inclusions. Fig. 2. Microstructure of an Al-Mg-Si cast billet: a) backscattered electron image, and b) EDS-spectrum of the oxide inclusion 3.2 Non-Metallic Inclusions Using the PoDFA method, non-metallic inclusions in the melt become concentrated in the filter. Thus, it is possible to identify their types and quantities more easily, even with LM. SEM is used when identification with a light microscope is insufficient. Figure 3 shows a typical light micrograph of non-metallic inclusions before and after melt treatment with fluxes. There are several types of inclusions. The Spinel comes from the furnace lining, while the TiB2 was part Fig. 1. The grain structure of an Al-Mg-Si cast billet of the Al-Ti-B grain refiner present in the scrap. On the other hand, (light micrograph,, depicting each grain in a different color) Al4C3 is formed by the reaction of Al melt with organic substances [21], and MgO with the dissolved magnesium and oxygen from the Several processes occur during the solidification of Al-Mg-Si atmosphere. alloys. These processes lead to the formation of several other Table 3 gives the results of the quantitative PoDFA analysis. The phases. The fractions of these phases are typically no more than a agglomerated TiB2 particles, arising from the grain refiner debris few per cent [20]. Figure 2a shows a SEM micrograph, revealing (GF) in the scrap, present the largest fraction of the non-metallic the dendritic shapes of the aluminium solution grain α-Al. Other inclusions. Thus, the results for all inclusions and the inclusions phases are located in the interdendritic regions. We identified Al2Cu, without grain refiner debris are given separately. The inclusion Mg2Si and α-Al(Mn,Fe)Si phases, which are typical constituents of fraction was always higher before the melt treatment, indicating the Al-Mg-Si alloys [2]. Oxide non-metallic inclusion Al2O3 was efficiency of the fluxes. identified with EDS analysis (Fig. 2b). It is challenging to find Figure 4 shows the fractions of the non-metallic inclusions after oxide particles, because they appear dark in the backscattered melt treatment in dependence on their fraction before melt treatment. electron images, such as shrinkage porosity, gas porosity and Mg2Si. Fig. 4a indicates the effect of individual fluxes. Still, Fig. 4b shows 296 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Production Engineering Fig. 3. Light micrographs of non-metallic inclusion in PoDFa filter; a) before, and b) after melt treatment with fluxes Table 3. Contents of non-metallic inclusions, determined using PoDFA Total before [mm2/kg] Total after [mm2/kg] Reduction [%] Without GF before [mm2/kg] Without GF after [mm2/kg] Reduction [%] Salt#1 1.05 0.37 64.76 0.69 0.32 53.62 Salt#1 0.58 0.29 50.00 0.32 0.14 56.25 Salt#1 0.34 0.05 86.01 0.26 0.04 86.59 Salt#2 2.76 0.75 72.94 2.18 0.50 76.91 Salt#2 1.39 0.34 75.18 1.04 0.20 80.48 Salt#3 0.78 0.10 87.50 0.64 0.01 98.60 Salt#3 1.80 0.14 92.16 1.20 0.20 83.18 Salt#3 1.88 0.69 63.40 1.35 0.50 62.84 Salt#4 3.13 1.11 64.56 2.00 0.62 69.00 Fig. 4. Inclusions determined using PoDFa; a) the effect of different fluxes (average values from Table 3), b) effectiveness irrespective of the flux type that the amount of non-metallic inclusion after melt treatment the melt surface, depending on their density (Stoke’s law). However, depends strongly on the initial fraction, and that, in each case, the the added fluxes could also stay in the aluminium melt, increasing reduction of non-metallic inclusions was about 70 %. Due to the the fraction of non-metallic inclusions [22]. The PoDFA analysis did small number of experiments and additional variables occurring not confirm their presence. In industrial practice, the melt is filtered in the industrial environment, the scattering was relatively high just before casting to reduce the fraction of non-metallic inclusions (R2 ≈ 0.75). Nevertheless, the complex salt mixture Salt#3 was the [23]. However, the melt should contain as few inclusions as possible most efficient (Fig. 4a). One of the reasons can be the presence of before filtering, because they can block the filter. CaF2, which reduces the surface tension and makes the removal of redundant fluxes easier [4]. However, removing inclusions does not 3.3 Removal of Trace Elements depend primarily on the melt treatment with fluxes. The holding time can contribute to better removal of inclusions, because they can One of the main functions of fluxes is to remove undesirable trace have sufficient time either to sink to the furnace bottom or float to elements. Trace elements are typically present in tiny quantities, e.g., SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 297 Production Engineering in ppm (parts per million), which is equivalent to 10‒4 %, but can allowed content of Ca is 20 ppm, the effectiveness of all fluxes was deteriorate the mechanical and other properties of aluminium alloys satisfactory. Nevertheless, Salt#3 was selected to be used in industrial substantially [24]. Among them, alkali (Li, Na, K, Rb, Cs and Fr) and applications for the Al-Mg-Si alloys. alkaline earth (Be, Mg, Ca, Sr, Ba and Ra) are very often present in Al-alloys. Mg is one of the most important alloying elements in Al- Mg-Si alloys. The chemical analyzes of all the investigated charges showed that the contents of all the aforementioned elements, except for Na and Ca, were negligible, often below their detection limits. Thus, they could not be used to evaluate the efficiency of the fluxes. Even the maximum contents of Na and Ca were very low, namely, seven ppm (7×10‒4 %) and 14 ppm (14×10‒4 %), respectively. Table 4. Contents of Na and Ca using spectroscopic analysis Na Na Na Ca Ca Ca before after reduction before after reduction [ppm] [ppm] [%] [ppm] [ppm] [%] Salt#1 3.1 2.2 29.0 9.8 4.6 53.1 Salt#1 4.1 2.5 39.0 9.4 5.4 42.6 Salt#1 2.1 1.1 47.6 8.5 4.1 51.8 Salt#1 2.9 1.6 44.8 10.6 3.7 65.1 Salt#1 2.7 1.7 37.0 14.0 5.2 62.9 Salt#1 3.9 1.8 53.9 13.7 4.3 68.6 Salt#2 2.0 2.0 0.0 7.5 2.0 73.3 Salt#2 7.0 2.0 71.4 11.0 3.7 66.4 Salt#3 3.0 2.7 10.0 12.0 1.9 84.2 Salt#3 2.0 1.0 50.0 5.0 1.0 80.0 Salt#3 2.7 0.3 89.1 14.0 0.29 97.9 Salt#4 3.0 1.3 56.7 11.0 3.0 72.7 Fig. 5. The effect of different fluxes on the removal of; a) an alkali element, Na, and b) an alkaline earth element, Ca The results are depicted in Table 4 and Fig. 5. The Salt#3 and Salt#4 removed Na the most effectively. Since the overall content 3.4 Analysis of the Actual Charges of Na was very low, the effect was not very pronounced (Fig. 5a). On the other hand, it can be seen easily that the Salt#3 was the most The industrial trials presented above can be considered experimental, potent in removing Ca from the melt (Fig. 5b). because different fluxes were added to Al-Mg-Si alloys in order to Chloride salt MgCl2 plays the most crucial role in removing Na select a composition which removes non-metallic inclusions and and Ca. In the melt, the following chemical reactions take place [25]: trace elements effectively from the aluminium melt, and is also cost friendly. After selecting Salt#3, it has been used in regular production. MgCl2 (l) + 2[Na] → 2NaCl (l) + [Mg], (1) This part shows the analysis of more than 100 charges of just MgCl2 (l) + [Ca] → CaCl2 (l) + [Mg], (2) one alloy EN AW 6182, which is produced in large quantities, where (l) means the liquid state, and the parentheses [] the dissolved so the number of charges is statistically relevant. The chemical element in the Al-melt. analysis was taken after the melting of the alloy and after casting. The free energies of reactions in Eqs. (1) and (2) are hugely The only possibility of removing Na and Ca was by melt treatment negative (ΔG0), having a very high equilibrium reaction constant Kp, using the selected flux. All the other treatments can contribute to an that can be calculated using Eq. (3). increase in these two elements. In many of the investigated charges, the initial contents of Na and Ca were much higher than during the G0  RT ln(Kp ), (3) experiments. The highest contents of Na and Ca were 27 ppm and where R is the gas constant and T is the absolute temperature. 73 ppm, respectively, thus representing tougher conditions for their The actual reaction constant for the reaction in Eq. (1) is calculated removal. as: In Fig. 6a, only two charges with less than five ppm Na are a2  a shown, indicating the final content of Na below its detection limit. K  NaCl Mg , (4) a 2 All the other charges (50 charges) contained more than five ppm. MgCl  a2 Na The maximum content of Na in the cast billets was three ppm. It where a stands for activity. Due to the low values of Na and Mg, was higher only in three charges, suggesting inappropriate handling activities can be replaced by their concentrations. of the melt in these cases. Only charges with nine or more ppm Ca The reaction takes place all the time as K < Kp. With the addition were selected (70 charges) for the analysis (Fig. 6b). The Ca-content of the flux in the range of 1 kg per 1 t melt, and the amounts of Na was higher than six ppm only in five charges, showing the efficiency and Ca typical in the industry practice, the reactions do not stop, and of the Ca removal. It is to be stated that the data for Fig. 6 were can cause a considerable decrease of Na and Ca in the melt. shown only for charges having a higher content of Na and Ca. The Figure 5 shows clearly that the amounts of Ca and Na are thermodynamic considerations using Eq. (4) indicate that the final practically independent of the initial content in the investigated content of harmful trace elements should be independent from their range. It is obvious that the flux Salt#3 can decrease the quantity initial content. However, the results of the chemical analyzes in Fig. of Ca below two ppm, very often below one ppm. 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International West Conshohocken. • The fractions and types of non-metallic inclusions were deter- [20] Engler, O., Schröter, T., Krause, C. Formation of intermetallic particles during mined by analyzing the sample after filtering through a porous solidification and homogenisation of two Al-Mg-Si alloys. Mater Sci Technol 39 ceramic filter. 70-84 (2023) DOI:10.1080/02670836.2022.2102279. SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 299 Production Engineering [21] Mendoza-Duarte, J.M., Estrada-Guel, I., Garcia-Herrera, J.E., Perez-Bustamante, Author Contribution Uroš Kovačec: Conceptualization, Data curation, R., Arcos-Gutiérrez, H., Martinez-García, A. et al. Aluminum carbide formation Investigation, Writing – original draft; and Franc Zupanič: Conceptualization, in Al-graphite composites: In situ study and effects of processing variables and Methodology, Writing – review & editing, Supervision. sintering method. Mater Today Commun 38 108396 (2024) DOI:10.1016/j. mtcomm.2024.108396. [22] Majidi, O., Shabestari, S.G., Aboutalebi, M.R. Study of fluxing temperature in AI-Assisted Writing The AI tool Grammarly was used to prepare this molten aluminum refining process. J Mater Process Technol 182 450-455 (2007) manuscript for grammar and language editing. All the content and DOI:10.1016/j.jmatprotec.2006.09.003. conclusions remain the responsibility of the authors. [23] Kvithyld, A., Syvertsen, M., Bao, S., Eriksen, U.A., Johansen, I., Gundersen, E., Akhtar, S., Haugen, T., Gihleengen, B.E. Aluminium filtration by bonded particle filters. Light Metals (2019) 1081-1088 DOI:10.1007/978-3-030-05864-7_132. Odstranjevanje vključkov in elementov v sledovih [24] Casari, D., Ludwig, T.H., Merlin, M., Arnberg, L., Garagnani, G.L. The effect of Ni iz zlitin Al-Mg-Si z rafinacijskimi talili and V trace elements on the mechanical properties of A356 aluminium foundry alloy in as-cast and t6 heat treated conditions. Mater Sci Eng A 610 414-426 Povzetek Čistoča aluminijevih zlitin ima odločilen vpliv na njihove lastnosti (2014) DOI:10.1016/j.msea.2014.05.059. in uporabnost. V industrijskem okolju smo rafinirali taline več Al-Mg-Si [25] Utigard, T. Thermodynamic considerations of aluminum refining and fluxing. zlitin (serija 6xxx) s solnimi talili, ki smo jih vnašali v talino z rotacijskim Sahoo, M., Pinfold, P. (eds.), Extraction, Refining, and Fabrication of Light Metals. Pergamon (1991) Amsterdam 353-365 DOI:10.1016/B978-0-08-041444- vpihovanjem. Običajni vložek je bil sestavljen iz 25 % do 30 % zunanjega 7.50034-2. odpada, 45 % do 50 % notranjega odpada in 20 % do 30 % primarnega [26] Wang, J., Xie, Y., Xie, S., Chen, X. Optimization of aluminum fluoride addition in aluminija. Talina je bila med vpihovanjem talil enakomerno premešana in aluminum electrolysis process based on pruned sparse fuzzy neural network. ISA nato je bila filtrirana skozi porozni obročasti filter. Za opredelitev deleža in Transactions 133 285-301 (2023) DOI:10.1016/j.isatra.2022.06.039. vrste nekovinskih vključkov smo uporabili svetlobno mikroskopijo in vrstično [27] Babič, M., Kovačič, M., Fragassa, C., Šturm, R. Selective laser melting: A elektronsko mikroskopijo. Z optično emisijsko spektroskopijo je bil izmerjen novel method for surface roughness analysis. 70 12 (2024) DOI:10.5545/sv- delež alkalijskih in zemljoalkalijskih kovin. Zmanjšanje deleža alkalijskih jme.2024.1009. in zemljoalkalijskih kovin ter deleža nekovinskih vključkov je bilo merilo za [28] Van, A.-L., Nguyen, T.-C., Bui, H.-T., Dang, X.-B., Nguyen, T.-T. Multi-response optimization of gtaw process parameters in terms of energy efficiency and quality. ovrednotenje učinkovitosti rafinacije in za izbiro rafinacijskega sredstva za 70 11 (2024) DOI:10.5545/sv-jme.2023.890. redno proizvodnjo. Analiza več kot sto industrijskih vložkov je potrdila, da je bilo izbrano talilo, sestavljeno iz zmesi MgCl2, KCl, NaCl in CaF2, učinkovito Received: 2025-04-24, revised: 2025-07-04, accepted: 2025-07-17 tudi pri redni proizvodnji. as Original Scientific Paper 1.01. Ključne besede aluminij, rafinacija taline, talilo, čistoča, nekovinski vključek, rotacijsko vbrizgavanje, alkalijski element Data Availability The data supporting this study’s findings are available from the corresponding author upon reasonable request. 300 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Effect of Presetting and Deep Rolling on Creep of Torsion Spring Bars Vinko Močilnik − Nenad Gubeljak − Jožef Predan University in Maribor, Faculty of Mechanical Engineering, Slovenia nenad.gubeljak@um.si Abstract This study investigates the creep behavior of torsion spring bars by combining experimental testing and numerical modeling. Experimental investigations were performed on torsional specimens subjected to different presetting levels and deep rolling surface treatments, showing different effects on stress relaxation at a constant torsion angle. Finite element method (FEM) simulations incorporating elasto-visco-plastic material behavior successfully reproduced the time-dependent deformation observed experimentally. Material parameters for the FEM model were derived from experimental data. The findings show that a two-stage presetting process combined with intermediate deep rolling results in higher residual compressive stresses in the surface layers compared to a single-stage presetting process. Although this method aims to mitigate creep under constant loading conditions, its effectiveness is limited. A reduction in creep strains is only observed up to a presetting level of approximately 4.3 %; above this threshold, creep strains increase significantly and loading capacity decreases. Keywords creep; torsion bar; FEM analyzis; presetting, deep rolling; torque, twist angle Highlights ▪ The material parameters for the FEM model were derived from experimental creep data. ▪ The experimental measured tensile creep data can be used to numerical simulation of creep torque. ▪ The optimal life is within a narrow range of prestressing and rolling-induced residual stresses. 1 INTRODUCTION on the applied elastic-plastic preset torque [3]. The study analyzed how presetting the twist angle affects fatigue life under various strain Torsion bars are commonly used in suspension systems to absorb road surface irregularities and shocks in both wheeled and tracked conditions. Presetting causes plastic deformation at the outer surface, vehicles. To increase the elastic (linear) operating range, torsion bars while the core remains elastic, leading to compressive residual are strain-hardened—preset in the direction of subsequent torsional stresses. Increasing the preset torque allows for a larger twist angle loading—to introduce compressive stresses into the surface layers. but reduces fatigue life. Experiments showed that fatigue life strongly An additional component of compressive stress is introduced into the depends on the ratio between preset load and fatigue loading range. surface layers through the deep rolling process. Perenda et al. [4] highlighted the significant influence of residual Previous investigation shows that the stress state of a torsion stresses on the fatigue life and load capacity of torsion bars. Deep bar under torsional loading by analyzing the effects of various rolling induces compressive stresses in the subsurface, which distributions of residual and applied stresses, using the Drucker- suppress crack formation. Presetting overstrains and hardens the bar, Prager criterion to assess the actual stress condition [1]. The increasing residual shear stresses and material yield strength, thereby findings indicate that the fatigue limit is maintained as long as the enhancing load capacity. The study simulated various sequences of combined principal stresses remain within the safe zone. However, deep rolling and presetting using mapping and FE analyzis on a cut- increasing compressive residual stresses near the surface can alter out model, with results validated by measured residual stresses. their distribution in depth and potentially shift the principal stress Residual stresses were measured on the surface of a round amplitude outside the safe zone as defined by the Drucker-Prager specimen during torsional presetting, specifically in the principal criterion. directions of +45° (compressive) and −45° (tensile) [5]. These stresses In [2], a dynamic explicit simulation was used to analyze the follow a linear distribution in the elastic range and become nonlinear residual stresses induced by the deep rolling process on a high- once the material exceeds its elastic limit. Initial residual stresses strength steel torsion bar. A three-dimensional simulation of a were introduced by surface cold rolling, which plastically deforms a representative section effectively replicated the residual stress shallow surface layer. This process induces anisotropic strain due to profile generated during deep rolling. The final stress magnitude is material flow in both axial and circumferential directions, resulting in significantly influenced by the process input parameters. Additionally, a helical lattice structure and differing stress values in each direction. the depth distribution of these residual stresses is strongly dependent Torsional characteristics derived from converted tensile data (σ–ε to on the dimensions of the extracted model. Therefore, it is crucial τ–γ) showed slight deviations from direct torsion test results. Residual to carefully choose modeling assumptions and simplifications, as stresses were analytically calculated based on both datasets and they directly affect the accuracy of the simulation results. The finite compared. Additionally, FEM simulations using ABAQUS Release element model developed for the deep rolling process provides a 2025, based on tensile properties, confirmed the analytical results. solid foundation for future numerical studies. Blum et al. [6] were compared experimental results on creep It was an established model for fatigue lifetime prediction where kinetics and microstructural evolution with the predictions of a the torsion-bar springs show different fatigue behavior depending simple, spatially homogeneous plastic deformation model. The model DOI: 10.5545/sv-jme.2025.1407 301 Mechanics describes the development of the dislocation structure as well as the fatigue tests and the Skelton model. In [15], the authors use the creep kinetics. same approach when considering creep in the case of a press fit load Kolev et al. [7] were introduced a new expression for the creep capacity study. law aiming to study in detail the behavior of simple structures using a This article investigates the creep behavior of torsion bars for generalized creep law with separable variables. The new expression, two levels of presetting, specifically 4.3 % and 5.1 % surface shear based on experimental data, combines the primary, secondary, and strain. For each case, creep was comparatively evaluated for both tertiary regions of the creep curve. The relaxation functions for manufacturing technologies, Technology A and Technology B. The bending and torsion depend solely on the maximum stress in the creep of the torsion bars was assessed through experimental testing cross-section that occurs on the outer surface. and FEM numerical simulation. In [8], the main objective is to derive exact closed-form expressions for torsional and flexural creep in isotropic materials, based on generally accepted constitutive laws. The Norton–Bailey, 2 METHODS AND MATERIALS Prandtl–Garofalo, and Naumenko–Altenbach–Gorash laws permit a closed-form solution. A partial generalization of the Norton–Bailey The final geometry of the torsion bar is produced using a suitable law is also solved in closed form. Stress relaxation was studied for material and appropriate mechanical properties. The manufacturing structural elements subjected to torsional and flexural loads. The process involves rolling, hardening, tempering, and mechanical structures examined—such as a beam in bending, a bar in torsion, cutting. This is followed by deep rolling, which smooths the surface and a coil spring—demonstrate the fundamental characteristics of and introduces significant compressive residual stresses into the nonlinear creep. Closed-form solutions, using common creep models, surface layers of the torsion bar. In addition to inducing compressive provide a deeper understanding of the inherent effects in structural residual stresses, deep rolling also improves corrosion resistance and elements and support the design process. surface wear characteristics. Several authors have investigated biaxial loading with torsion and After deep rolling, the process of increasing the elastic operating axial force on cylindrical specimens. range—known as presetting—is carried out. During presetting, the Šeruga at al. [9] developed a software tool for predicting creep torsion bar is strain-hardened by controlled multiple transitions into damage in thermo-mechanically loaded components. It enables the plastic region of the material under torsional loading [4]. This master curve determination using time-temperature parameters and establishes a new, higher elastic limit. Upon unloading, residual calculate creep damage based on Robinson’s rule and simple time torsional deformation remains, along with significant residual integration. The software also allows separate evaluation of fatigue stresses. In the surface layers, these residual stresses are compressive, and creep damage. The article presents commonly used time- while in the core of the torsion bar, they are tensile. The compressive temperature parameters, a fast and user-friendly method for master surface stresses enhance the cyclic fatigue strength, which is critical curve generation, and an example of creep damage calculation using since torsion bars are designed for a defined service life with a real data with a simple temperature-stress history [9]. limited number of load cycles. The torsion bar manufactured in this Makabe and Socie [10] analyzed the fatigue crack growth in way is intended to be loaded with a unidirectional torsional moment, precracked torsion specimens and find that friction of the crack in the same direction as the presetting. surfaces prevented shear mode crack growth. Yang and Kuang [11] The introduction of residual stresses through deep rolling enhances examined the crack paths and growth rates of S45 steel specimens the cyclic endurance of the torsion bar, while the presetting process under various combinations of torsional and constant axial loads. They tends to reduce its service life. It has been shown that performing reported that the crack propagation angle was approximately 45° for presetting after deep rolling reduces the compressive residual stresses different load amplitudes. Static tension combined with axial force at the surface [4,5]. The number of loading cycles until failure and cyclic torsion accelerated crack growth and reduced service life, depends on the degree of presetting as well as the load magnitude while compressive axial force combined with torsion significantly during testing or in actual use of the torsion bar [3]. In addition to increased service life without affecting the crack propagation angle. reducing service life, increased presetting also leads to larger creep or They also found that the crack propagation direction depended on the yielding strains of the torsion bar under constant load. alternating stress amplitude and was independent of the mean stress. To stabilize creep, a slightly modified manufacturing process Tanaka et al. [12] tested hollow lead-free solder samples under has been adopted in practice. It has been shown that maintaining torsional and combined torsional and compressive axial loads. They sufficiently high compressive stresses on the surface during the found that the crack initially propagated in the direction of maximum production of the torsion bar is crucial. This modified process shear stress and later in the direction perpendicular to the maximum involves partial presetting before deep rolling, followed by final principal stress. Numerous microcracks formed between individual presetting after deep rolling. This approach helps preserve a relatively phases within the material’s lattice, which later coalesced into a high level of compressive residual stresses on the surface of the single crack. torsion bar [4] and reduces creep. Grigoriev at al. [13] investigated that grinding kinematics play The first process, referred to as Technology A, consists of deep a key role in the efficiency of creep-feed grinding. Paper examines rolling followed by presetting the torsion bar into the plastic region. non-traditional parameters—such as removal area, force ratios, The second process, referred to as Technology B, involves partial and depth-to-diameter ratio—through three case studies on turbine presetting into the plastic region, then deep rolling, and finally final blades, gears, and broaches using low-speed vitrified alumina wheels. presetting [2]. Though experimental details are omitted, practical guidelines for improving productivity and quality are provided. 2.1 Material Properties and Manufacturing Technology Nagode and Fajdiga [14] investigate that the isothermal strain-life method, commonly used for low-cycle fatigue, is fast and typically Torsion bars were manufactured from high-strength, fine-grain spring based on elastic finite element analyzis. Adapted for variable steel grade 150VCN (according to EN 10027-1:2016 [16] 50CrV4, temperatures using a Prandtl-type operator, it assumes stabilized W. Nr. 1.8159). Figure 1 shows tensile tests results.The chemical hysteresis loops and neglects creep. Reversal point filtering is composition (in weight %) and mechanical properties are listed in examined, and the method is compared with thermo-mechanical Tables 1 and 2, respectively [3]. Material has high yield strength Re 302 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics and ultimate tensile strength (UTS) Rm more than 2000 MPa. The The torsion specimen shown in Fig. 2b had a diameter of d = 10 material used was hot-rolled, forged, and soft annealed during the mm, with a root-split section and a calculated effective length of l = manufacturing process. The final shape and properties were achieved 250 mm. The surface of the bar was polished to a roughness of Ra through the following mechanical processes: programmed turning, = 0.2 μm. The torsion bars were hardened using a dedicated process milling, and polishing. to achieve a target hardness of 54 ±1 HRC. Surface rolling and pre- setting were carried out as described in [4]. Table 1. Chemical composition in weight % of the used material, as specified in [4] C Si Mn Ni Cr Mo V Cu S P Actual 0.44 0.28 0.56 1.41 0.87 0.26 0.11 0.12 0.002 0.009 val. Min. 0.42 0.17 0.5 1.3 0.8 0.2 0.1 0 0 0 Max. 0.5 0.37 0.8 1.8 1.1 0.3 0.18 0.25 0.002 0.009 Figure 1 presents the engineering and true stress-strain curves for the material in its tempered condition. The engineering curve was obtained through tensile testing at ambient temperature, while the true curve was derived by calculation. The yield strength was determined using the following expression:  f  1  , (1) and logarithmic strain: ε' = ln(1+ε), (2) Fig. 1. True and engineering curves where σf is the true stress [MPa], σ engineering stress [MPa], ε engineering strain [-], and ε' true strain [-]. Table 2. Average mechanical properties of the torsion bar for different loading ratio R = σmin / σmax Yield strength, UTS, Poisson, Torsion elastic Shear modulus, Modulus, Tensile fatigue limit Tensile fatigue limit Torsion fatigue limit Re [MPa] Rm [MPa] ν [-] limit, τe [MPa] G [GPa] E [GPa] R = 0, [MPa] R = –1, [MPa] R = –1, [MPa] 1442 2010 0.3 800 80 193 1200 800 520 a) b) Fig. 2. Setup for creep tension testing with; a) elongation measurement, and b) torsion bar specimen Fig. 3. Time dependent properties of the used material SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 303 Mechanics A creep test under constant stress was performed on the material. bar preparation methods are considered in this study: Technology Figure 2a shows the setup for creep tension testing with elongation A, involving a single presetting after deep rolling, and Technology measurement on the INSTRON 1255 servo-hydraulic testing B, which uses a two-step presetting process with intermediate deep machine. In Figure 1, points 1, 2, and 3 indicate the locations where rolling. stress relaxation was measured. Three tensile specimens were loaded In the diagram shown in Fig. 4, points 1 and 2 indicate the to specific stress levels and then held under constant plastic strain. preparation and testing parameters of the torsional specimens. For Plastic strain was measured using an extensometer, and the moment both points, the two technologies, Technology A and Technology B when the target stress was reached was defined as time zero. Figure 3 were applied. The diagram reflects the results of long-term torsional illustrates the dependence of creep strain rate on time under constant testing, thereby indirectly accounting for creep behavior as well. stress. The three stress levels considered were 1778 MPa, 1928 MPa, Table 3 presents the preparation parameters of the specimens used and 2037 MPa. The parameters A, n, and m were experimentally in the torsional creep tests. The symbols in the table represent: gps [%] determined for use in ABAQUS finite element simulations. shear strain on the surface of the torsion specimen at presetting, fps [°]  twist angle of the torsion specimen at presetting, gapp [%] shear strain   A ntm , (3) on the surface of the torsion specimen at application or at testing, where ε is uniaxial equivalent creep strain rate; σ uniaxial equivalent fapp [°] twist angle of the torsion specimen at application or testing, deviatoric stress, and A, n, m are constants determined experimentally and T0 [Nm] initial torque. at room temperature. Table 3. Preparation of torsion specimens (DR – Deep rolling; P – Presetting) 2.2 Torsion Specimen Preparation torque The specimens were manufactured using the same technological Point gps fps gapp fapp Initial Technology [%] [°] [%] [°] T0 [Nm] process as that used for standard torsion bar production. The final 1 4.3 123 1.5 43 206 A (DR – P) shape and properties were achieved through programmed turning, 1 4.3 123 1.5 43 206 B (P – DR – P) milling, and polishing of the torsion bar body to a surface roughness 2 5.1 146 1.9 54.4 237 A (DR – P) of 0.2 μm. The geometry of the specimen is shown in Fig. 2b. 2 5.1 146 1.9 54.4 237 B (P – DR – P) In Figure 4 provides a recommended presetting level for achieving optimal service life during torsion bar production, depending on Figure 5 illustrates the preparation parameters for torsional the magnitude of the load applied during testing or actual use [3]. specimens used in creep testing. The points labeled 1-A, 1-B, In the diagram, the presetting shear strain (γₚₛ) and the applied shear 2-A, and 2-B correspond to the positions in the diagram in Fig. 4, strain (γₐₚₚ) represent the surface strain on the torsion bar. The upper representing the respective technological preparation methods A curve denotes the elastic limit, while the lower curve corresponds and B. Each of these marked points indicates the starting point for to the high-cycle fatigue limit. The area between these two curves measuring the time-dependent torque during creep at a constant twist represents the optimal service life range for torsion bars. Red lines angle. within this area are isolines indicating constant service life. After the torsional specimens were prepared through deep rolling and presetting, they were loaded to a twist angle of either 43° (initial torque T0 = 206 Nm) or 54° (T0 = 237 Nm), respectively. The change in torque over time due to creep was then measured and recorded. 2.3 Tors ion Test Method During the presetting phase, the torsion bar must be deliberately overloaded in a controlled manner into the plastic region, while measuring both torque and twist angle. A dedicated torsional loading device was designed for this purpose, as shown in Fig. 6. On one end of the tested torsion specimen, a clamping sleeve is connected to a WATT DRIVE gear unit, type FUA 65A 101LA4 BR20 FL, 3 kW, 10 min⁻¹. The gear is driven by an electric motor, with speed regulated by a V2500 frequency control unit from the same manufacturer. On the opposite side of the gear’s hollow shaft, a SIMODRIVE incremental encoder (Siemens, Germany) is installed, Fig. 4. Lifetime optimum zone of the torsion bar [3] offering an angular measurement resolution of 5000 pulses per revolution. The service life of a torsion bar is influenced by the degree of Torque is measured using a DF-30 (500 Nm) torque sensor presetting and the intensity of the cyclic torsional loading during from Lorenz Messtechnik. For data acquisition and visualization, operation. Additionally, presetting introduces creep, which results in the torque sensor and incremental encoder are integrated into a vehicle settling under a constant load. In practice, a presetting surface measurement chain consisting of Spider-8 universal PC measuring shear strain of γₚₛ = 4.3 % is generally considered an acceptable upper electronics and the Catman EASY software, both from HBM. limit, beyond which both service life and creep behavior remain within acceptable bounds. However, in some cases, presetting beyond 4.3 % may be required, though this leads to a significant increase in 2.4 FEM Simulation creep. The finite element analyzis of the stress–strain state was Experimental results have shown that, in terms of minimizing conducted using the SIMULIA Abaqus 2025 software suite [17]. A creep, it is more favorable to perform presetting in two stages with comprehensive three-dimensional simulation of a torsion spring was intermediate deep rolling. As outlined in the introduction, two torsion performed, employing a single-layer discretization of finite elements 304 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics Fig. 5. Preparation of torsion specimens with presetting Fig. 6. Presetting device [3] along the spring’s axial direction. Eight-node brick elements simulation of key physical phenomena, including material yielding, (C3D8) were utilized throughout the model. Appropriate boundary the development of residual stresses due to preloading, and long- conditions were imposed on the free end surfaces of the thin, single- term stress relaxation effects attributable to creep. In the linear layer configuration to ensure well-posedness of the problem and to elastic regime, the material was defined by a Young’s modulus of enable the accurate determination of stress–strain responses under 193 GPa and a Poisson’s ratio of 0.3. The yield strength was specified torsional loading. This modeling strategy significantly reduced the as 1442 MPa, with strain hardening extending to 2010 MPa. Time- computational complexity and numerical size of the model, thereby dependent material behavior was modelled using a creep formulation enabling rapid and efficient numerical simulations, while still that incorporated experimentally determined hardening parameters: capturing the complete stress–strain field that would be observed A = 1.6248×10−35, n = 9.47, and m = −0.9. The final simulation in a full-length spring model. The material analyzed in this study is employed a total of 47.630 C3D8 elements within the single-layer isotropic and homogeneous spring steel. Therefore, it was essential model, achieving a high-fidelity representation of the stress–strain to determine the key material parameters through experimental field in the torsion spring. testing in order to accurately describe its elastic–plastic and additional viscoelastic behavior. Similar approach was applied in the research study [18] where analyzes the evolution patterns of damage 3 RESULTS AND DISCUSSIONS parameters concerning sheet metal and corresponding temperatures. Possible applications are described in testing of in special off-road Figure 7 displays the measured torque values at a constant twist angle vehicles and their parts [19]. as a function of time for all four torsion bar cases. The measured The material behavior was characterized using an elastic–plastic– data in the graphs are approximated using an analytical logarithmic visco-plastic constitutive model. This allowed for the accurate function, given by Eq. (4). Table 4 summarizes the constants a and b SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 305 Mechanics for each of the four torsional moment measurements. The analytical testing, the largest relaxation was observed at point 2 for Technology function in Eq. (4) describes the experimental results with a mean B, despite the fact that Technology B was designed to reduce torsion coefficient of determination of R² = 0.98. bar relaxation. Using the diagram in Fig. 4, the service life of a Sudden drops observed in the torque measurements due to creep cyclically loaded torsion bar can be estimated as a function of the are attributed to the fact that the measured decrease in torque is applied surface shear strain and the surface presetting shear strain. smaller than the resolution of the measurement system. The upper region of the diagram corresponds to low-cycle fatigue, while the lower region corresponds to high-cycle fatigue. Within the hatched area, lines indicate constant service life. By locating the operating point on the diagram—point 1 or 2 in our case—it is possible to estimate the expected service life of the torsion bar. Fig. 8. Prediction of relative time dependent torque drop; ΔT is torque drop Table 5. Relative torque drop in 18 weeks at a constant twist angle and estimated lifetime Relative torque drop in Estimated lifetime, Fig. 4 Point Initial torque T0 [Nm] 18 weeks [%] [cycles] 1-A 206 1.39 200,000 1-B 206 1.19 200,000 2-A 237 2.64 < 40,000 2-B 237 7.05 < 40,000 A comprehensive three-dimensional simulation of a torsion spring was performed, employing a single-layer discretisation of finite elements along the spring’s axial direction, as shown in Fig. 9. Figure 10 presents the results of the FEM analyzis performed to simulate Fig. 7. Time dependent torque measured at a constant twist angle; a) 1-A and 1-B, and b) 2-A and 2-B the specimen preparation process, which includes both presetting and creep. Fig. 10a illustrates the residual stresses at point 2 after the Table 4. Constants a and b for Eq. (4) presetting step, while Figs. 10b and c depict the applied stresses at point 3, captured before and after the creep process, respectively. The Point a b locations of points 2 and 3 are marked in Fig. 5 for reference. 1-A –0.24313 216.53131 1-B –0.21623 207.14633 2-A –0.56792 239.46698 2-B –0.56792 245.73548 T t   a  ln t   b, (4) where T(t) is dependent torque, t time and a, b are constants. Figure 8 illustrates the relative torque drop over time. The curves represent the predicted torque reduction as a function of the specimen preparation technology, based on Eq. (4). For comparison, the torque drop predicted by FEM simulation is also shown for case 1-A. The most significant creep is observed at point 2 using Technology B, with a torque drop exceeding 7 %. In contrast, much smaller creep is observed at point 1, where Technology B results in less creep than Technology A. The results of the creep analyzis for the torsion bars are summarized comparatively in Table 5. After 18 weeks of creep Fig. 9. Finite element model, mesh and interaction constraints 306 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics a) b) c) Fig. 10. The Von Mises stresses obtained from the FEM analyzis at points 2 and 3, as marked in Fig. 5, a) residual stresses after presetting at Point 2, b) applied stresses at point 3, and c) aplied stresses at Point 3 a) b) Fig. 11. a) Von Mises, and b) Shear stress distribution across section of torsion bar calculated using FEM analyzis at point 1, point 2 and point 3 from Fig. 5 Figure 11 illustrates the distribution of Von Mises and shear The FEM numerical simulations accurately captured the time- stresses across the cross-section of the torsion bar, as determined dependent stress relaxation behavior observed in the experiments, by FEM analyzis. Curve 1 represents the stresses introduced during demonstrating the capability of the model to reflect real material presetting, while Curve 2 shows the residual stresses remaining responses over time. Furthermore, the results validated the after unloading. Curve 3 depicts the stresses under the applied load, application of visco-plastic material models for simulating long- including the additional creep stresses accumulated over a period of term deformation processes. The simulations also provided strong 18 weeks. Measurement points 1, 2, and 3 correspond to the locations support for the experimental findings, confirming the reliability and identified in Fig. 5. consistency of the observed phenomena. In conclusion, a balanced presetting rate combined with an optimized deep-rolling sequence can significantly affect the long- 4 CONCLUSIONS term performance and dimensional stability of torsion bars. Excessive This study investigated the creep of torsion bars subjected to different presetting should be avoided as it leads to undesirable creep effects manufacturing processes involving presetting and deep rolling. that compromise component reliability. Future work should include Two technological approaches were compared: Technology A (deep a more detailed parametric study of the visco-plastic behavior under rolling followed by presetting) and Technology B (partial presetting, different temperature and loading conditions, and an analyzis of the deep rolling and final presetting). interaction between fatigue and creep. Experimental results showed, that at moderate levels of presetting (4.3 % shear strain), Technology B resulted in lower torque release References over time compared to Technology A, confirming the advantage of maintaining high surface compressive stresses via intermediate [1] Močilnik, V., Gubeljak, N., Predan, J. Effect of residual stresses on the fatigue behaviour of torsion bars. Metals 10 1-16 (2020) DOI:10.3390/met10081056. deep rolling. At higher presetting levels (5.1 % shear strain), creep [2] Perenda, J., Trajkovski, J., Žerovnik, A., Prebil, I. Residual stresses after deep increased significantly regardless of the process used. However, rolling of a torsion bar made from high strength steel. J Mater Process Technol Technology B resulted in an even higher creep rate than Technology 218 89-98 (2015) DOI:10.1016/j.jmatprotec.2014.11.042. A, likely due to the redistribution of internal stresses caused by [3] Močilnik, V., Gubeljak, N., Predan, J. Model for fatigue lifetime prediction of excessive plastic deformation. torsion bars subjected to plastic Pre-setting. Tech Gazette 18 537-546 (2011). SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 307 Mechanics [4] Perenda, J., Trajkovski, J., Žerovnik, A., Prebil, I. Modeling and experimental Acknowledgement Authors gratefully acknowledges the support of the validation of the surface residual stresses induced by deep rolling and Pre-setting Slovenian Research and Innovation Agency (ARIS) conducted through the of a torsion bar. Int J Mater Form 9 435-448 (2016) DOI:10.1007/s12289-015- research programme P2-0137 “Numerical and Experimental Analyzis of 1230-2. Mechanical Systems”. In addition, this paper has been written to mark [5] Močilnik, V., Gubeljak, N., Predan, J. Surface residual stresses induced by the 30th anniversary of the Faculty of Mechanical Engineering and 50th torsional plastic pre-setting of solid spring bar. Int J Mech Sci 92 269-278 (2015) DOI:10.1016/j.ijmecsci.2015.01.004. anniversary of the University of Maribor. [6] Blum, W., Eisenlohr, P., Breutinger, F. Understanding Creep-a Review. Metall Mater Received: 2025-05-26, revised: 2025-07-21, 2025-08-17, Accepted: 2025- Trans 33 291-303 (2002) DOI:10.1007/s11661-002-0090-9. [7] Kobelev, V. Relaxation and creep in twist and flexure. Multidiscip Model Mater 08-27 as Original Scientific Paper 1.01. Struct 10 304-327 (2014) DOI:10.1108/MMMS-11-2013-0067. [8] Kobelev, V. Some basic solution for nonlinear creep. Int J Solids Struct 51 3372- Data availability Data supporting the findings of this study are available 3381 (2014) DOI:10.1016/j.ijsolstr.2014.05.029. from the corresponding author upon reasonable request. [9] Šeruga, D., Fajdiga M., Nagode M. Creep damage calculation for thermo mechanical fatigue. Stroj Vestn-J Mech E 57 371-378 (2011) DOI:10.5545/sv- Author contribution Vinko Močilnik: Conceptualization, Metodology, jme.2010.108. Computational Analyzis, Measurements, Validation, Writing – Original Draft; [10] Makabe, C., Socie, D.F. Crack growth mechanisms in precracked torsion fatigue Nenad Gubeljak: Conceptualization, Metodology, Computational Analyzis, specimens. Fatigue Fract Eng Mater Struct 24 607-615 (2001) DOI:10.1046/ j.1460-2695.2001.00430.x. Validation, Writing – Review and Editing; Jožef Predan: Conceptualization, [11] Yang, F.P., Kuang, Z.B. Fatigue crack growth for a surface crack in a round bar Metodology, Computational Analyzis, Validation, Writing – Original Draft. under multi-axial loading condition. Fatigue Fract Eng Mater Struct 28 963-970 (2005) DOI:10.1111/j.1460-2695.2005.00929.x. Vpliv prednapetja in globokega valjanja [12] Tanaka, K., Kato, T., Akinawa, Y. Fatigue crack propagation from a precrack under na lezenje paličaste torzijske vzmeti combined torsional and axial loading. Fatigue Fract Eng Mater Struct 28 73-82 (2005) DOI:10.1111/j.1460-2695.2005.00861.x. Povzetek Prispevek obravnava obnašanje lezenja torzijskih vzmetnih palic [13] Grigoriev, N.S., Starkov, K.V., Gorin, A.N., Krajnik, P., Kopač, J. Creep-Feed Grinding: s kombinacijo eksperimentalnega testiranja in numeričnega modeliranja. An overview of kinematics, parameters and effects on process efficiency. Stroj Eksperimentalne raziskave so bile izvedene na torzijskih vzorcih, ki so bili Vestn-J Mech E 60 213-220 (2014) DOI:10.5545/sv-jme.2013.1547. podvrženi različnim stopnjam prednapenjanja in različnim površinskim [14] Nagode, M., Fajdiga, M. Thermo-mechanical modelling of stochastic stress-strain obdelavam z globokim valjanjem, pri čemer so se pokazali različni učinki states. Stroj Vestn-J Mech E 52 74-84 (2006). [15] Močilnik, V., Gubeljak, N., Predan, J. Time dependent load capacity of the press na sproščanje napetosti pri konstantnem kotu zasuka. Simulacije z metodo fit. Tech gasette 19 434-441 (2025) DOI:10.31803/tg-20250115224222. končnih elementov (MKE), ki vključujejo elasto-visko-plastično obnašanje [16] EN 10027-1:2016. Designation systems for steels - Part 1: Steel names, materiala, so uspešno reproducirale časovno odvisno deformacijo, ki smo European Committee For Standardization, Brussels. izmerili tudi med eksperimentom. Materialni parametri za model MKE so bili [17] Simulia Abaqus 13.0. Dassault Systems, Vélizy-Villacoublay. izpeljani iz eksperimentalnih podatkov. Ugotovitve kažejo, da dvostopenjski [18] Wu, D., Li, D., Liu, X., Li, Y., Wang, Y. i Liu, S. Temperature dependence of meso postopek prednastavitve v kombinaciji z vmesnim globokim valjanjem constitutive parameters for advanced high-strength steel. Trans FAMENA 48 87- povzroči višje preostale tlačne napetosti v površinskih plasteh v primerjavi z 102 (2024) DOI:10.21278/TOF.484063324. [19] enostopenjskim postopkom prednastavitve. Čeprav je cilj te metode ublažiti Stodola, J., Stodola, P. Accelerated Reliability Tests Of Characteristics Of Off- Road Vehicles And Their Parts. Trans FAMENA 48 31-44 (2024) DOI:10.21278/ lezenje pri konstantnih pogojih obremenitve, ugotavljamo, da je njena TOF.482049422. učinkovitost omejena. Zmanjšanje deformacij lezenja je opaziti le do stopnje prednastavitve približno 4,3 %; nad tem pragom se deformacije lezenja znatno povečajo in vzmet zgublja na nosilnosti. Ključne besede lezenje, torzijska palica, metoda končnih elementov (MKE), prednapenjanje, globoko valjanje, torzijski moment, kot vzvoja 308 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Integrated Design, Simulation, and Experimental Validation of Advanced Cellular Metamaterials Nejc Novak − Zoran Ren − Matej Vesenjak University of Maribor, Faculty of Mechanical Engineering, Slovenia n.novak@um.si Abstract Cellular metamaterials offer supreme properties for engineering, medicine, and defence, but their transition to industrial use faces design, fabrication, and characterisation challenges. This review provides an overview of 20 years of advancements in cellular structures, from open-cell foams to triply periodic minimal surfaces (TPMS), presenting novel fabrication techniques (e.g., explosive compaction for UniPore structures) and demonstrating validated computational models for optimising graded auxetic and hybrid TPMS lattices. The study indicates that porosity and base material primarily govern energy absorption, with closed-cell foams and TPMS outperforming other geometries. Additive manufacturing enables spatially graded designs with tailored mechanical properties. This work accelerates the development of next-generation metamaterials for crash absorption, blast protection, and biomedical devices. Keywords cellular structures, metamaterials, experimental testing, computational simulations, mechanical properties Highlights ▪ Modern metamaterials are set to revolutionise engineering, transportation, medicine, and sports. ▪ Design, fabrication, modelling, and characterisation of cellular structures are covered. ▪ The article offers a comparative analyzis of mechanical responses of various cellular structures. ▪ Validated computational models are crucial for optimising metamaterial design. 1 INTRODUCTION As the use of cellular structures grows, it is essential for engineers, material scientists, and commercial entities to understand Modern engineering faces dual challenges: escalating material costs their behavior under various loads to optimise performance through and stringent sustainability requirements. Cellular metamaterials— customised designs. Combining different base materials with tailored engineered porous structures with tunable mechanical, thermal, and internal structures can achieve unique mechanical and thermal acoustic properties—have emerged as a transformative solution. properties [7]. Advanced additive manufacturing enables the creation These materials leverage hierarchical architectures spanning nano- of complex cellular metamaterials designed for specific applications to macro-scales to achieve unprecedented performance-to-weight through computational simulations and topological optimisation [8]. ratios, making them indispensable for aerospace (impact-absorbing The mechanical properties of cellular (meta)materials depend components), biomedical (tissue scaffolds), and defence (blast- on factors like relative density (porosity), base material (metal or resistant panels) applications [1,2]. Cellular materials excel in non-metal), morphology (pore size and shape), topology (pore mechanical and thermal properties and enable multifunctionality. distribution) and fillers [1]. The most important factor is relative They serve as structural components (cores for sandwich panels, density, which is calculated as the ratio of the bulk density of the enhancing stiffness and damping [3]), functional systems (heat foam to the solid density of the material, while the porosity is then exchangers, acoustic isolators, and fluid filters [4]) and energy determined by subtracting relative density from 1. In general, the absorbers (crashworthy fillers in automotive and protective gear [5]). higher the porosity, the lower the mechanical properties, which can Despite their potential, widespread deployment is hindered by also be analytically calculated using the empirical equations given fabrication limitations (traditional methods like powder foaming) in [4]. Careful selection of these parameters and proper fabrication lack precision for complex geometries), knowledge gaps (incomplete can yield desired mechanical, damping, and thermal properties data on shear/dynamic behavior and graded porosity effects), [4,5]. Detailed geometry and mechanical behavior of fabricated design barriers (absence of standardised guidelines for application- structures can be evaluated using CT scanning [9]. High-quality 3D specific optimisation) and scepticism towards new materials. data acquisition is crucial for building precise digital twins, which However, advanced fabrication technologies, such as additive aid in developing new cellular structures with advanced material manufacturing, are overcoming these hurdles. All of the additive engineering techniques. manufacturing technologies offer precise control over cell shape, Standard mechanical tests like compression, tension, and bending size, and distribution on a certain level of the scale, depending on are well-documented, but data on shear and dynamic testing are the printing accuracy. These methods surpass traditional methods limited. Recent studies have explored cellular structures’ dynamic like melt/powder foaming and replication techniques in terms of and impact behavior, but a detailed analyzis of functionally graded fabrication accuracy and adaptability, while in some cases, the costs porosity is still needed [10–12]. Specifically designed internal and fabrication speed are still in favour of the traditional methods structures can optimise mechanical responses for applications in [6]. They also enable the integration of digital twins using three- safety, defence, and crashworthiness [13]. dimensional (3D) models obtained from computed tomography (CT) In general, the cellular metamaterial’s unit cell size is in the range for iterative design.. of millimetres, while also micro-architected cellular structures and DOI: 10.5545/sv-jme.2025.1363 309 Mechanics nano-lattices with unit cell sizes below 1 µm have been developed, due to their unique properties. In the furniture industry, polymeric driven by the need to control band gaps in phononic metamaterials open-cell foams are commonly used for sofa cushions, foam [14,15]. These structures offer unique properties like tailorable mattresses, and car seats because they can be easily compressed and stiffness and auxetic behavior. However, further research is then naturally return to their original shape. Additionally, they are needed on their mechanical behavior, fabrication optimisation, and employed in acoustic and soundproofing applications. Metal open- biocompatibility for medical applications [16]. cell foams, produced through methods like investment casting, are This review systematically investigates the design, fabrication, and valued for their lightweight and high-strength properties, making mechanical behavior of cellular metamaterials under various loading them suitable for use in automotive, aerospace, and other engineering conditions, with a focus on their specific energy absorption (SEA) fields [17]. The mechanical properties of open-cell foams can be capabilities and its relationship to the base material, geometry and further enhanced by introducing fillers, such as polymers, into the loading conditions. Understanding these relationships and the distinct cellular structure. Additionally, open-cell foams can be used as fillers deformation mechanisms of cellular metamaterials is crucial, as it for foam-filled tubes [18]. This adaptability and multifunctionality enables the tailored design of high-performance cellular materials make open-cell foams necessary in modern engineering and design. for diverse engineering applications. This study’s significance lies in The impact of the base material on the mechanical properties of providing critical insights for optimising metamaterial design, which open-cell foams is well-documented, with numerous empirically is essential for advancing fields such as automotive crashworthiness, established relationships linking the base material and cell aerospace impact resistance, and biomedical engineering. In morphology to the properties of the cellular material. The metals and summary, there is a clear need for more research on detailed alloys used for metal foams must also be lightweight to retain the geometry characterisation and the development of digital twins advantage of low relative density over conventional solid materials. to create new geometries and optimised fabrication processes. The Therefore, the most commonly used metals for cellular materials group at the University of Maribor is working to address these gaps include aluminium, magnesium, titanium, and their alloys. in metamaterials research. The influence of cell morphology on the mechanical properties of regular and irregular open-cell materials has been extensively studied using representative unit cells. However, since the geometry of 2 METHODS AND MATERIALS fabricated open-cell foams often deviates from geometric regularity, The following section categorises (meta)materials based on their many researchers have also examined the cell morphology of these topology and manufacturing processes. Figure 1 illustrates the fabricated foams [19]. The mechanical behavior of open-cell foam progression from primitive to advanced geometries over the last two can be further enhanced by introducing polymer fillers into the decades in the research group at the University of Maribor. cellular structures [18]. The geometry and properties of cellular metamaterials presented in Fig. 1 are provided in the next paragraphs. The fabrication methods 2.2 Closed-cell Foams are given as follows: investment casting (IC), (aluminium), selective electron beam melting (SEBM) (titanium), powder bed fusion (PBF) Closed-cell foam’s interconnected, sealed cells provide higher (stainless steel), photopolymerisation (VAT) (photopolymer), gas stiffness and water resistance, are suitable for shock absorption and injection (GI) (aluminum), powder metallurgy (PM) (aluminium), thermal insulation (Fig. 1a). Powder metallurgy is a standard method explosive compaction (EC) (copper). for producing closed-cell aluminium foams [20]. This involves heating a precursor (aluminium, silicon, and titanium hydride) within 2.1 Open-cell Foams a mould, allowing it to expand and fill the cavity. After cooling, the foam is extracted and sectioned. The mechanical behavior of these Open-cell foams are materials characterised by an interconnected foams has been thoroughly investigated under free and laterally network of pores, which allow air or fluids to pass through (Fig. 1b). constrained compression, and it was proved that the behavior These foams are highly versatile and are used in various applications of the cell material could be adequately described with a single, F ig. 1. Research of cellular metamaterials in recent years: from primitive to advanced cellular geometry; a) closed-cell foams, b) IC, C) SEBM, d) PBF, e) VAT, f) GI, g) PM, and h) EC 310 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics geometrically uniform cell [21]. Applications include ex-situ and periodicity in three orthogonal directions [38,39]. They partition in-situ foam-filled tubes, where the latter, produced directly within space into interconnected domains without enclosed voids, leading to the tube, demonstrates enhanced stiffness due to improved bonding unique topological characteristics. This makes them highly suitable [22]. Furthermore, closed-cell foam can be integrated into auxetic for applications ranging from tissue and structural engineering to aluminium alloy panels to improve their mechanical performance thermal management and fluid transport [38,40]. Their optimised [22]. thermal and electrical conductivity and controlled fluid permeability make them promising candidates for advanced heat exchangers, 2.3 UniPore Structure filters, and catalytic reactors. The ability to precisely control the The UniPore structure, characterised by longitudinal pores, is geometric parameters of TPMS through additive manufacturing fabricated by explosively welding thin-walled inner tubes within opens up new avenues for designing materials with tailored functional an outer tube (Fig. 1h) [23]. This process involves densely packing properties. the outer tube with smaller diameter inner tubes along its length, resulting in a uniform porous cross-section. However, variations in collision angles during welding due to the inner tubes’ curvature can 3 DESIGN AND CHARACTERISATION lead to inconsistent interface formation, a phenomenon supported by Cellular metamaterials are engineered materials with cellular computational simulations [24]. structures that exhibit unique mechanical, thermal, acoustic, or To address these limitations, a novel UniPore fabrication method electromagnetic properties not found in conventional materials. has been recently developed [25]. This approach utilises rolling thin metal foil with acrylic spacer bars, followed by explosive Their design involves careful selection of the unit cell geometry, compaction. This technique ensures a stable collision angle, similar size, arrangement, and constituent material to achieve the desired to conventional explosive welding, leading to more uniform welding macroscopic behavior. This often entails intricate topologies like interfaces. The production process, demonstrated with copper, allows lattices, honeycombs, or triply periodic minimal surfaces, which are for the use of various metallic foils. Notably, this method offers carefully examined using CT scanning. These can be optimised using flexibility in tailoring external dimensions, pore size, internal wall computational methods like finite element analyzis and topology thickness, and porosity to meet specific application requirements. optimisation to tailor properties like stiffness, strength-to-weight ratio, energy absorption, and wave propagation characteristics. The 2.4 Advanced Pore Morphology (APM) Foam ability to precisely control the microarchitecture allows for creating materials with unprecedented functionalities, opening doors for Advanced Pore Morphology (APM) foam, a hybrid cellular material applications in diverse fields ranging from aerospace and automotive featuring interconnected, sphere-like closed-cell pores within a to biomedical engineering and soft robotics. solid outer skin, was pioneered at Fraunhofer IFAM in Bremen, A critical aspect of metamaterial design and research involves Germany (Fig. 1g) [26]. This unique structure offers a balance of developing and validating robust computational models, essential for high surface area and structural integrity, making it attractive for accurately predicting their behavior. These models, often employing applications requiring energy absorption and thermal management. techniques like finite element analyzis, must be rigorously validated The fabrication begins with the compaction and rolling of an AlSi7 against experimental data to ensure reliability. The complexity of alloy combined with a TiH2 foaming agent, yielding an expandable these models can vary significantly, with simplifications tailored to precursor. This precursor is subsequently granulated and subjected the specific geometry of the metamaterial and the intended application to thermal decomposition of the TiH2 in a continuous belt furnace, of the simulation. For instance, simplified models might be used for resulting in spherical foam elements. The internal structure of APM preliminary design studies. In contrast, more detailed models are foam has been extensively characterised [9,27], revealing its tailored necessary to predict complex phenomena like non-linear deformation pore distribution and connectivity. Notably, APM elements have or dynamic response accurately. Moreover, these validated numerical demonstrated efficacy as filler material in foam-filled tubes [28,29], models can serve as powerful tools for parametric studies, allowing enhancing their mechanical performance under impact loading. researchers to explore the influence of geometric variations and material properties on the overall performance of the metamaterial, 2.5 Predesigned Structures thereby accelerating the design and optimisation process. Advanced fabrication techniques, particularly additive manufacturing, enable the creation of complex, pre-designed cellular 3.1 Experimental Testing structures with tailored mechanical properties (Fig. 1d) [6,30,31]. This includes the development of three-dimensional auxetic cellular Experimental characterisation of cellular metamaterials has materials, such as those built from interconnected inverted tetrapods predominantly focused on compression testing, revealing a [32,33] and chiral auxetic designs [34]. Inverted tetrapod structures characteristic mechanical response: an initial elastic region, followed are constructed by stacking unit cells in layers, resulting in a layered by a plateau phase denoting progressive cell collapse, and finally, 3D auxetic architecture [35]. These structures, along with chiral a densification regime. To gain deeper insights into deformation auxetic designs based on the 10th eigenmode of a regular cubic unit mechanisms, micro-computed tomography (μCT) has been employed cell [36], are typically modelled using computer aided design (CAD) to visualise and quantify internal structural changes during the software and fabricated using additive manufacturing technologies. compression of closed-cell aluminium foams [41]. This technique has The mechanical performance of these auxetic structures can be facilitated detailed analyzes of pore collapse and crack propagation, further enhanced by incorporating polymeric fillers [37], offering a contributing to a fundamental understanding of foam behavior under route to multi-functional materials. load [42]. Furthermore, triply periodic minimal surfaces (TPMS) represent Beyond compression, extensive studies have investigated the a class of periodic cellular materials with significant potential in mechanical response of various closed-cell foams under diverse diverse engineering applications. TPMS are intricate 3D topologies loading conditions, including bending [43–47]. Similarly, Advanced that minimise surface area within defined boundaries and exhibit pore morphology (APM) foams and APM-filled tubes have been SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 311 Mechanics subjected to both compression [28] and bending tests [29], with in-situ The only observable discrepancy occurs at the initial stages of the geometric analyzis conducted to track deformation evolution [48]. HSR response, where the computational model fails to capture the The influence of loading rate on mechanical behavior has also initial stress peak observed experimentally. This stress peak, a direct been of considerable interest. High-strain-rate compression testing, consequence of the impact-induced collision in the experimental utilising the split Hopkinson pressure bar (SHPB) apparatus, has been setup, represents a transient phenomenon characteristic of the used to assess the dynamic response of closed-cell aluminium foams initial impact phase. However, as demonstrated by the subsequent [49]. Studies employing powder guns have further extended the correlation between experimental and simulated data, this initial investigation of high-strain-rate behavior to both open-cell [43] and peak does not significantly influence the overall global deformation closed-cell foams [50] as well as auxetic structures [33,51], revealing behavior of the foam [33]. The use of this simplified model allows rate-dependent phenomena such as inertial effects and material for efficient simulations while still retaining the overall mechanical strengthening. response of the closed-cell foam. Furthermore, three-point bending tests have been instrumental in evaluating the flexural performance of foam-filled tubes [29,44,45], providing data on bending stiffness, energy absorption, and failure modes. Recent investigations have also explored the shear response of open-cell foams [52] and auxetic cellular structures [53], contributing to a more comprehensive understanding of their anisotropic mechanical behavior. The combined use of these experimental techniques, complemented by advanced imaging and analyzis, allows for a thorough characterisation of the mechanical behavior of cellular metamaterials, providing critical data for the design and optimisation of these materials for diverse engineering applications. 3.2 Homogenised Computational Models For computational modelling of closed-cell foam behavior, a simplified yet practical approach employed within Abaqus finite element (FE) software involves a homogenised material model, Fig. 2. Comparison between the computational and experimental results under Q-S at loading specifically the crushable foam model with volumetric hardening. velocity 0.01 mm/s and HSR at loading velocity 250 m/s Leveraging the axial symmetry of the experimental specimens, axisymmetric boundary conditions were applied, significantly Under quasi-static loading, the specimen exhibits a uniform reducing computational cost while maintaining accuracy. An explicit deformation pattern, indicative of a homogeneous stress distribution solver was utilised to capture the dynamic nature of foam deformation throughout the sample (Fig. 3). In contrast, HSR loading induces a [50]. distinct shift in the deformation mode, characterised by localised The crushable foam constitutive model parameters were deformation concentrated at the impact interface between the loading determined through an optimisation algorithm, where the plate and the specimen. This localisation signifies the influence computational response was iteratively matched to the experimental of inertial effects and stress wave propagation at high strain rates, quasi-static (Q-S) compression data (Figs. 2 and 3). This optimisation leading to a non-uniform deformation profile. The observed ensured that the model accurately represented the foam’s behavior difference in deformation patterns highlights the significant impact of under low strain rate conditions. Subsequently, the optimised loading rate on the material’s mechanical response. material model was employed for high strain rate (HSR) simulations, This can be further used to develop modern crash absorbers, where demonstrating a remarkable agreement with experimental HSR data the validated FE models enable the development of new foam-filled (Fig. 2). auxetic panels with a tailored response, where different geometries, The difference between the experimental and computational sheet thicknesses, densities and distributions of the foams can be results across quasi-static and high-strain rate regimes is noteworthy. virtually tested before fabrication. The deformation behavior of that Fig. 3. Comparison between the Q-S and HSR deformation responses of closed-cell foam modelled with homogenised computational model (PEEQ - equivalent plastic strain) 312 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics Fig. 4. Comparison of deformation behaviour of: a) empty, and b) foam-filled crash absorber [55] kind of absorber is shown in Fig. 4b, where the crash absorber is relationships and deformation patterns, to quasi-static experimental filled with Polyurethane (PU) foam. This will hopefully lead to the data from reference [59] for each analyzed geometry and relative application of modern crash absorption systems on newly built roads density. Furthermore, the computational deformation behavior is or blast protection elements in buildings [54]. validated through comparisons with experimental observations recorded by high-definition video cameras. Figure 5 illustrates the 3.3 Discrete Computational Models comparative deformation behavior of diamond TPMS lattices with varying relative densities, demonstrating a high correlation between Discrete computational models, while demanding higher experimental and computational results. computational resources than homogenised models, provide a more Volume finite elements could also be employed for the accurate representation of metamaterial deformation behavior. Beam discretisation of open-cell foams. Achieving an accurate geometric finite elements are predominantly employed for strut-based cellular representation of fabricated aluminium open-cell foam samples structures, such as open-cell foams and auxetic designs [11,56,57]. necessitates high-resolution micro-computed tomography (μCT) This approach allows for a detailed analyzis of individual strut scans. These high-resolution scans are crucial for capturing the deformation and interaction. intricate geometric details of the foam‘s porous structure and enabling The generation of TPMS lattice computational models is precise segmentation of the metallic phase from the void space. This facilitated by shell finite elements, utilising the MSLattice code precise segmentation is essential for generating reliable volume finite [58] to define the fundamental lattice geometry. Subsequently, element meshes and critical for accurate computational modelling of meshing is performed using PrePoMax software, and boundary the foam‘s mechanical behavior. conditions are defined within the LS-PrePost environment. Inverse parametric computational simulations are conducted to refine material parameters to account for manufacturing imperfections, particularly plate thickness variations. This indirect incorporation of 4 OPTIMISATION AND DEVELOPMENT OF NEW GEOMETRIES imperfections enhances the model’s fidelity. Validated computational models provide a powerful platform for The validation of these discrete TPMS lattice models involves developing and optimising novel metamaterials. For instance, comparing their mechanical response, specifically stress-strain topology optimisation techniques have been employed to generate Fig. 5. Comparison between a) computational, and b) experimental results in case of TPMS structures modelled with shell finite elements SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 313 Mechanics new auxetic geometries [60]. These studies used a 2D plane stress demonstrated a high correlation with the computational predictions state simplification to model the auxetic structure, focusing on a [61], confirming the model’s accuracy and predictive capabilities. single unit cell of the periodic structure as the optimisation domain. Building upon existing 3D conventional chiral unit cell designs To further reduce the computational cost, only one-quarter of this [57,62], novel 3D axisymmetric chiral structures exhibiting negative unit cell was modelled, with the remaining portion represented and zero Poisson’s ratios have been developed. This innovation by appropriate double symmetry boundary conditions. This involves mapping the conventional tetra-chiral unit cell into an simplification is justified by the prevalence of double symmetry in axisymmetric space, resulting in a new class of 3D axisymmetric many existing auxetic structures, including re-entrant hexagons, chiral architectures (ACS structures). These structures are fabricated symmetric chiral designs, and sinusoidal ligament configurations. using additive manufacturing techniques (Fig. 7), enabling the precise Triply periodic minimal surface (TPMS) lattices, inherently realisation of complex geometries. mathematical designs, benefit significantly from advanced Experimental compression tests were conducted to validate the fabrication methods. These methods enable the creation of graded or computational modelling of these axisymmetric chiral structures. hybrid structures, where diverse TPMS geometries are strategically The resulting experimental data was used to refine and validate the computational models. Subsequently, these validated models were combined to enhance topological features and achieve desired employed to evaluate the performance of new axisymmetric chiral properties. To accurately predict the mechanical behavior of additively structures featuring graded cell configurations. manufactured uniform TPMS lattices made of stainless steel 316L The analyzis revealed that these newly developed axisymmetric under quasi-static and dynamic loading, a FE computational model structures demonstrate significantly enhanced mechanical was developed in LS-DYNA. This validated model was then used to properties compared to conventional 3D chiral structures (the SEA simulate the performance of a newly designed hybrid TPMS cellular is comparable to structures made of titanium and much higher than lattice featuring spatially varying gyroid and diamond cells in both in structures made of copper). This improvement is attributed to the longitudinal (the diamond and gyroid cells are on top of each other) optimised geometry and graded cell arrangements, offering potential and radial (the diamond and gyroid cells are concentric) directions advantages in applications requiring tailored mechanical responses. (Fig. 6). Experimental validation of the fabricated hybrid lattices a) b) Fig. 6. Comparison between the computational and experimental results for: a) linear, and b) radial hybrid TPMS lattices [61] a) b) Fig. 7. Design of the: a) axisymmetric auxetic structure, and b) comparison between the computational and experimental results under quasi-static (QS) and dynamic (DYN) loading conditions [57] 314 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics 5 CONCLUSIONS AND OUTLOOK crashworthiness. In aerospace applications, lightweight structures with high SEA are desirable for impact resistance and vibration This review systematically examined cellular metamaterials‘ design, damping. By leveraging the insights gained from experimental fabrication, and mechanical behavior across quasi-static and dynamic and computational analyzes, researchers can optimise the design loading regimes. Figure 8 illustrates the SEA up to 50 % strain for these structures under compression loading to facilitate a comparative of cellular metamaterials to meet the stringent demands of various analyzis of energy absorption capabilities. engineering applications, driving innovation in transportation, In Figure 8, darker shading corresponds to specimens with lower construction, and biomedical engineering. porosity within each analyzed group of cellular structures, while Future research directions encompass expanded shear and high- lighter shading indicates higher porosity specimens. A clear trend strain-rate testing protocols for anisotropic metamaterials and emerges: porosity and base material significantly influence SEA integrating thermal/electrical conductivity into TPMS designs for capacity. Lower porosity structures and stiffer base materials (e.g., innovative applications. We also envisage that we will accelerate high Young‘s modulus alloys) exhibit superior SEA. the discovery of novel architectures using machine learning and AI- Notably, closed-cell foams, TPMS structures, and UniPore driven optimisation. structures exhibit consistently high SEA values at 50 % strain, Computational simulations have emerged as an indispensable suggesting their suitability for applications requiring efficient energy tool for the preliminary evaluation of novel cellular designs and for dissipation within this strain range. However, a key distinction arises gaining a deeper understanding of the complex deformation behavior with UniPore structures, where densification initiates at 50 % strain exhibited by various cellular structures. This article has showcased (Fig. 8). Consequently, the SEA reported for UniPore structures at a spectrum of computational approaches, ranging from simplified this strain level represents their total SEA capacity, limiting their and computationally efficient homogenised models to intricate and applicability in higher strain scenarios. In contrast, closed-cell foams time-intensive discrete models employing volume finite elements to (Fig. 8) and other analyzed cellular structures exhibit densification represent the entire cellular architecture. at significantly higher strain levels, enabling them to achieve greater The ongoing advancement of computational power and software total SEA capacity beyond 50 % strain. This demonstrates that capabilities heralds a significant evolution in computational while UniPore structures provide good energy absorption at low modelling. Specifically, the implementation of mesoscale modelling strain, closed-cell foams and TPMS structures outperform UniPore approaches holds immense promise, enabling the incorporation of structures at strains >50 % due to delayed densification. fabrication defects and microstructural features into simulations. This Furthermore, the observed differences in SEA capacity can be enhanced level of detail will lead to more precise virtual prediction attributed to the distinct deformation mechanisms exhibited by these capabilities, allowing researchers to accurately anticipate the structures. Closed-cell foams, for example, undergo progressive cell deformation behavior of cellular metamaterials under diverse loading wall buckling and crushing, leading to sustained energy absorption conditions. Consequently, the optimisation of their mechanical over a wider strain range. TPMS structures, with their complex response will become more efficient and reliable, facilitating the interconnected geometries, exhibit a combination of bending, development of high-performance cellular materials tailored to stretching, and buckling, contributing to their high SEA and controlled specific engineering applications. deformation behavior. UniPore structures, with their unidirectional Furthermore, the integration of machine learning and artificial pore channels, primarily deform through axial compression, leading intelligence techniques into computational modelling workflows to rapid densification and limited energy absorption at higher strains. will further accelerate the design and optimisation process. These Understanding these deformation mechanisms and their influence techniques can be used to perform parametric studies, predict trends, on SEA capacity is crucial for the tailored design of cellular structures and optimise geometries based on the simulation results. The use of for specific applications. For instance, materials with high SEA at these techniques will lead to faster development times and higher- high strain rates are essential for occupant protection in automotive performing materials. F ig. 8. Comparison of SEA for different cellular metamaterials made from different base materials (Ti-titanium, Cu-copper, Al-aluminium, SS-stainless steel) SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 315 Mechanics This work lays the foundation for the design of multifunctional [20] Duarte, I., Vesenjak, M., Vide, M.J. Automated continuous production line of parts, metamaterials with application-specific performance characteristics. Metals (Basel) 9 (2019) 531 DOI:10.3390/met9050531. 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Mater Des Process Ključne besede celične strukture, metamateriali, eksperimentalno Commun 3 205 (2021) DOI:10.1002/mdp2.205. testiranje, računalniške simulacije, mehanske lastnosti SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 317 Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Fusion Behavior of Pure Magnesium During Selective Laser Melting Snehashis Pal1,2 − Matjaž Finšgar1 − Jernej Vajda3 − Uroš Maver3 − Tomaž Brajlih2 − Nenad Gubeljak2 − Hanuma Reddy Tiyyagura4 − Igor Drstvenšek2 1 Faculty of Chemistry and Chemical Engineering, University of Maribor, Slovenia 2 Faculty of Mechanical Engineering, University of Maribor, Slovenia 3 Faculty of Medicine, University of Maribor, Slovenia 4 Institute of Optoelectronics, Military University of Technology, Poland snehashis.pal@um.si. Abstract This study examined the melting behavior and flowability of pure magnesium during selective laser melting. The potential to increase product density was also investigated. Various combinations of manufacturing parameters were considered. The laser power was gradually increased in different machine runs, with different scanning speeds for each run to vary the energy density (ED). The laser power ranged from 10 W to 75 W, and the scanning speed ranged from 100 mm/s to 800 mm/s. Lower laser powers resulted in poor melting, while higher laser powers produced better melting, with significant differences even when the ED was the same. High EDs between 3.50 J/mm² and 4.30 J/mm² led to a lack of melting at low laser power and to an unstable melt pool with significant spattering at high laser power. In contrast, moderate EDs in the range of 1.40 J/mm² to 2.90 J/mm² resulted in better density at high laser power. Higher scanning speeds helped to avoid the formation of a dense smog cloud and provided sufficient energy in a short time with the aid of higher laser power. Therefore, increasing both laser power and scanning speed improved melting performance and increased product density. The relative product density ranged from 80 % to 96.5 %. Reducing the layer thickness from 50 µm to 25 µm at a laser power of 40 W resulted in the formation of a well-formed melt pool in some areas and significant melt spattering in others, which led to a deterioration in density. Keywords magnesium, melt pool, laser power, scanning speed, layer thickness, support structure, laser powder bed fusion Highlights ▪ The fusion and pore formation of Mg during the selective laser melting process were investigated. ▪ Higher energy density (ED) may cause a lack of melting than lower ED due to the high smog formation. ▪ Higher scanning speed with higher laser power can avoid the smog cloud and perform better fusion. ▪ Reducing the layer thickness from 50 µm to 25 µm led to improved melting or massive spattering. 1 INTRODUCTION provides a protective environment for the manufacturing process and enables in-situ alloying, which is crucial when working with reactive Lightweight materials are essential for a range of applications, particularly in the automotive, aerospace, and electronics industries materials like magnesium. It can transform complex computer-aided [1,2]. Reducing component weight can significantly improve design (CAD) models into single or multiple products, supporting overall performance and fuel efficiency [3]. In medical implants, customization and intricate designs [21]. Selective laser melting especially for orthopedic applications, lightweight and biodegradable (SLM), also known as laser powder bed fusion (LPBF), is one of materials are vital [4,5]. Their lightness aids patient mobility, the most popular metal AM technologies for manufacturing metal while biodegradability eliminates the need for a second surgery by products [22]. allowing the implant to dissolve naturally in the body over time SLM uses an inert gas to reduce the oxygen content in the process [6,7]. Magnesium (Mg) and its alloys are increasingly favored due to chamber, requiring a continuous flow of this gas to maintain the their properties, which meet these stringent requirements [8,9]. Mg desired oxygen levels [23]. In this process, a laser melts the metal is not only very light but also offers promising biodegradability and powder track by track and layer by layer [24,25]. The powder high biocompatibility [10,11]. Mg and Mg-alloys allow regulation particles, typically with diameters of several dozen micrometers, of mechanical and corrosive properties, making them suitable build up the product layer by layer, with each layer usually being 20 for biomedical applications [12]. Furthermore, the mechanical to 100 micrometers thick [26,27]. Rapid heating, melting, mixing, and properties of magnesium alloys are similar to those of bone, which is solidification occur during the fusion process in SLM [28,29]. Using advantageous for orthopedic implants [13]. Mg in SLM presents significant challenges due to its low melting and Despite these benefits, Mg has certain drawbacks, such as a boiling points and high flammability [30]. Rapid heating can lead lower melting point and higher reactivity to oxygen and moisture to vaporization and combustion of Mg [2]. The small temperature compared to other metals [14,15]. In various applications, proper difference between the melting and boiling points causes the melt handling and alloying are required to address these challenges pool to become unstable [31]. Additionally, the lightweight nature of [16,17]. Traditional manufacturing processes have limitations in this Mg poses a problem as it can be easily carried away by inert gas, regard [18]. However, additive manufacturing (AM) processes offer leading to material loss and the formation of smog that obstructs much greater flexibility than conventional methods [19,20]. AM the laser’s operation [16]. These issues significantly affect the SLM 318 DOI: 10.5545/sv-jme.2025.1381 Additive Manufacturing process, as material loss from the action zone and smog formation conductivity and a very high coefficient of thermal expansion hinder the laser’s ability to function effectively [32]. (CTE of 26 × 10⁻⁶ K⁻¹), large thermal stresses and volume changes To address these challenges, this study investigated the occur during the SLM process, causing the part to shrink, bend, and interactions between the laser and Mg, as well as the thermophysical eventually self-destruct. Therefore, three types of support structures properties of the melt pools and solidification during the SLM were used to hold the samples firmly. As shown in Fig. 1, fabrication manufacturing process. There are several results in the literature of the specimens began with 2 mm high supports. In this study, a on the density of Mg-alloys fabricated by SLM, but only a few support structure typically used for the fabrication of stronger studies focus on improving the density of pure Mg products. To our materials such as Ti-6Al-4V and AlSi10Mg was employed (see Fig. knowledge, and according to the report by Zeng et al. [33], there is 1a). This support beam has a smaller diameter neck that facilitates no literature in which a relative density of 98 % was achieved for Mg separation of the fabricated part from the support beams. Twenty-five parts produced by the SLM process. Therefore, in this study, the laser (5 × 5) support beams were placed under the 6 mm × 6 mm base of powers and scanning speeds were initially selected based on previous the cubes. studies by Hu et al. [34] and Yang et al. [5]. Hu et al. [34] obtained the best relative height density of 96.13 % at a high energy density (ED) with a laser power and scanning speed of 90 W and 100 mm/s, respectively. On the other hand, Yang et al. [5] obtained useful results Cubic sample at laser powers and scanning speeds between 20 W to100 W and 100 mm/s to 900 mm/s. Therefore, this study started with a scanning speed of 100 mm/s and a laser power of 10 W to keep the ED within a suitable range. Observations and analyses from this initial phase served as a basis for selecting different combinations of laser power and scanning speed to further investigate these phenomena and Z Neck Z Y achieve better metallurgical properties. Support This comprehensive approach aimed to optimize the SLM process a) Y beams X b) X for Mg, focusing on understanding and mitigating issues related Contour scanning Core to rapid heating, material loss, and smog formation. By exploring scanning the effects of different combinations of laser powers and scanning speeds, the study sought to enhance the metallurgical properties of Cubic sample the produced components, paving the way for more effective use of Mg in SLM processes. 2 METHODS AND MATERIALS Z 2.1 Material Y Y Z c) X Support beams d) X The samples were produced using pure magnesium powder from Fig. 1. Supports and scanning patterns; a) support beams with necks, b) cylindrical support Nanografi Nano Technology (Germany), and the manufacturing beams, c) samples with different orientations, and d) scanning pattern characteristics were analyzed. The spherical powder particles ranged in size from 35 µm to 50 µm, with 5 % of the particles outside this In this study, the effects of laser parameters at different layer range. After production by centrifugal atomization, the powder was thicknesses and their melting properties with existing supports were packaged in an inert gas environment. The powder was unsealed to investigated. The manufacturing process is costly due to the use of fill the filling chamber after the oxygen concentration was reduced to argon and the risk that the failure of a single sample can cause the less than 0.01 % using argon. failure of several samples in the same build. If one sample fails, it can hinder the movement of the recoater, requiring the entire process to be 2.2 Machining Chamber stopped and restarted from the beginning. This research aimed to find The manufacturing behavior was studied using the Arrow Metal a solution to the manufacturing problem when supports are present, Printing – LMP200 SLM machine supplied by Dentas, Slovenia. as supports are often necessary for the actual production of the part. It Argon was used to reduce the oxygen content in the chamber and is easier to remove samples from the build plate and prepare a smooth to keep the O2 level below 10 ppm during sample production. An build plate again than to produce samples without support. Therefore, O2 sensor monitored and automatically adjusted the O2 level by in addition to analyzing melting properties, the effect of support, adding argon to the machining chamber when it exceeded 10 ppm. including different support designs, is also examined and reported in As magnesium is very light, the processing environment contained this article. Mg powder and its fumes. To remove these, the chamber gases Since the support beam with a neck was not able to prevent the were circulated and passed through a filter at a flow rate of 280 L/ piece from bending, cylindrical beams were used, as shown in Fig. min. Before production runs began, the laser system was calibrated 1b. The beams had diameters of 0.4 mm, with a 6 × 6 array of beams and a sensor monitored the current laser power. To maintain heat under the 6 mm × 6 mm base of the cubes. Although this support conduction and the material bond between the build plate and the structure was sufficient to prevent most specimens from bending, support, the build plate was made of magnesium. some specimens still bent or detached from the supports after a few layers were fabricated. 2.2 Support Structure As some specimens bent and moved away from the cylindrical support beams, the orientation of the specimens was changed, as Several cubic test specimens measuring 6 mm × 6 mm × 6 mm were shown in Fig. 1c. However, this orientation increased the bottom produced for each test condition. As magnesium has good thermal surface area, leading to a more uneven surface at the start of SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 319 Additive Manufacturing fabrication. Although this support structure held the part firmly in densities, higher laser powers were selected to analyze their effects. place, the uneven shape and surface formation of the specimens led However, scanning speed can also have a significant influence. to the decision in this study to align the cubic specimens so that their Therefore, in the second step of the study, the most effective scanning base surface remained horizontal. Ultimately, cylindrical support speeds were combined with the increased laser powers. Although beams are best suited to hold the part when the base of a cubic sample scanning speeds of 400 mm/s, 600 mm/s, and 800 mm/s at 40 W is horizontal. resulted in good densities, 400 mm/s, 500 mm/s, and 600 mm/s were chosen at laser powers of 55 W, 65 W, and 75 W, respectively, due to 2.3 Scanning Patterns the high ED induction. The scanning pattern consisted of four successive contours and Table 1. Manufacturing parameters in the first step of the study a checkerboard core scanning pattern, as shown in Fig. 1d. As the area to be scanned for each layer was approximately 6 mm × 6 mm, Laser Scanning Hatch Layer Product Relative Sample ED four sub-squares were scanned in a checkerboard arrangement. power speed spacing thickness density density number [J/mm2 ] [W] [mm/s] [mm] [mm] [g/cm3] [%] Each square was scanned with multiple laser scan tracks, with a 50 % overlap between tracks. The diameter of the laser spot was 70 I-1 10 100 0.035 0.050 2.86 - - µm; therefore, the hatch spacing was 35 µm. A larger hatch spacing I-2 10 200 0.035 0.050 1.43 - - resulted in a lower product density. Two consecutive scanning I-3 10 300 0.035 0.050 0.95 - - tracks were scanned in opposite directions. The scanning tracks I-4 10 400 0.035 0.050 0.71 - - were rotated by 60° for successive layers during manufacture. The I-5 20 150 0.035 0.050 3.81 - - Yb:glass fiber laser was always focused perpendicular to the powder I-6 20 200 0.035 0.050 2.86 - - bed using a telecentric F-theta lens. The telecentric F-theta lens I-7 20 300 0.035 0.050 1.90 - - combines the flat-field focusing of a conventional F-theta lens with I-8 20 400 0.035 0.050 1.43 - - the vertical positioning of a telecentric lens for object space, ensuring I-9 30 200 0.035 0.050 4.29 - - the emerging laser beam is always perpendicular to the target surface I-10 30 300 0.035 0.050 2.86 - - across the entire scan field. I-11 30 400 0.035 0.050 2.14 - - Since the diameter of the laser spot is 70 µm and the laser moves I-12 30 500 0.035 0.050 1.71 - - at high speed during scanning, which is typical for the SLM process, the space between successive hatches must be considered when I-13 40 300 0.035 0.050 3.81 - - measuring the ED. Therefore, the ED [J/mm²] can be defined as I-14 40 400 0.035 0.050 2.86 1.65 94.91 defined in Eq. (1), where P, v, and h denote the laser power [W], I-15 40 600 0.035 0.050 1.90 1.61 92.68 scanning speed [mm/s], and hatch distance [mm], respectively. I-16 40 800 0.035 0.050 1.43 1.39 80.18 ED P  . (1) Table 2. Manufacturing parameters in the second step of the study v  h Laser Scanning Hatch Layer Product Relative Sample ED power speed spacing thickness density density number [J/mm2 ] 2.4 Manufacturing Parameters [W] [mm/s] [mm] [mm] [g/cm3] [%] II-1 55 400 0.035 0.050 3.93 - - Laser power, scanning speed, and layer thickness were varied to II-2 65 500 0.035 0.050 3.71 - - investigate their effects on the fusion of pure Mg and the potential II-3 75 600 0.035 0.050 3.57 - - for sample fabrication. As Mg has low melting and boiling points, the experiments began with low laser power combined with four different scanning speeds. Thus, the ED varied with scanning speed, In the second step of the study, a large amount of smoke and while laser power remained constant. Subsequently, the laser power smog was observed when using high laser power and relatively was gradually increased from 10 W to 40 W, as shown in Table 1, low scanning speed. The lower scanning speed resulted in a high and combined with four different scanning speeds. Consequently, ED. Consequently, the samples were not produced satisfactorily. the ED also changed, ranging from 0.95 J/mm² to 4.29 J/mm². The Therefore, higher scanning speeds were used in the third step of the ED played a significant role in the melting process of Mg and was study to reduce the ED, while the laser power remained the same as therefore considered an important fabrication parameter. The hatch in the previous step. These parameters are listed in Table 3. distance and layer thickness were kept constant in the initial stage Table 3. Manufacturing parameters in the third step of the study of the study at 35 µm and 50 µm, respectively. Three samples were fabricated for each testing condition. Laser Scanning Hatch Layer Product Relative Sample ED The most important factor in determining the useful range of power speed spacing thickness density density number [J/mm2 ] [W] [mm/s] [mm] [mm] [g/cm3 parameters is the density of the samples. The proportion of smog ] [%] formation is also considered. With some parameters, a higher III-1 55 700 0.035 0.050 2.24 1.65 94.96 density product can be achieved, but smog formation can cause III-2 65 700 0.035 0.050 2.65 1.67 95.95 deterioration in melting at higher scan ranges. A high level of smog III-3 75 750 0.035 0.050 2.86 1.68 96.51 in the processing chamber causes the laser rays to be reflected more strongly by the airborne powder particles. Increased vapor also Higher laser powers and their adjustable scanning speeds did absorbs more of the laser energy, which ultimately prevents the laser not yield improved results. Therefore, the optimal laser power and beams from reaching the powder bed. scanning speeds identified in previous studies were used in the fourth After observing and analyzing the fusion behavior and density step of the study, where a lower layer thickness was selected. As results in the first step of the study, the laser power was increased in 800 mm/s at a laser power of 40 W resulted in low product density, the second step while maintaining the scanning speeds listed in Table a reduced scanning speed of 700 mm/s was chosen for this step, 2. Since higher laser power led to better fusion results and product as shown in Table 4. These parameters were selected to observe 320 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Additive Manufacturing the effects of different layer thicknesses and the laser absorption As a result, some plate formation and shifting were observed, as characteristics of the powder bed and its top surface. shown in Fig. 2. The plates were shifted by the recoater movement. With a further increase in scanning speed, sintering among the powder Table 4. Manufacturing parameters in the fourth step of the study particles occurred. Consequently, soft cubic samples were formed at Laser Scanning Hatch Layer Product Relative scanning speeds of 400 mm/s and 500 mm/s. These were destroyed Sample ED power speed spacing thickness density density during powder removal and detachment from the support structures. number [J/mm2] [W] [mm/s] [mm] [mm] [g/cm3] [%] Eventually, an increase in scanning speed resulted in better melting. IV-1 40 400 0.035 0.025 2.86 1.54 88.66 IV-2 40 500 0.035 0.025 2.29 1.55 89.34 Scan IV-3 40 600 0.035 0.025 1.90 1.55 89.16 areas IV-4 40 700 0.035 0.025 1.63 1.55 89.04 2.5 Analysis of Product Properties The densities were measured on samples that were well fused and capable of providing accurate results. When ethanol was used as a liquid, Archimedes’ principle was applied to determine the densities. The weight of each sample was measured in air and then while immersed in the liquid, with an error margin of ±0.0001 g, to calculate the density. The measurement was performed six times to improve the accuracy of the results. Three-dimensional images of the solid and pore zones of the materials were obtained using a ZEISS Xradia 620 Versa nano-computed tomography (nano-CT) scanner (Germany). The porosity of the samples was also observed with a scanning electron microscope (SEM) from Carl Zeiss (Germany), after the samples had been ground 1 mm from the vertical surface and then polished. Departed part 3 RESULTS AND DISCUSSION Powder spreading direction Fig. 2. A photograph during scanning 3.1 Effect of Lower Laser Powers The powder particles were not well fused at the low laser powers of A large amount of smog was observed in the processing chamber 10 W and 20 W, even though the energy density was sufficient at during laser scanning. Although the smog was not detected by any lower scanning speeds. At a laser power of 30 W, the particles were sensor, only the observations made during production are discussed adequately fused at scanning speeds of 200 mm/s and 300 mm/s; here. Smoke and particle detectors could provide more quantitative however, some layers were distorted and delaminated, as shown in results and better control over the melting process. Therefore, it can Fig. 2. With a further increase in scanning speed to 400 mm/s and be assumed that this smog also affects the amount of laser power 500 mm/s at 30 W laser power, fusion did not occur. Therefore, the reaching the powder bed. The smog formed from evaporated and samples fabricated using 10 W to 30 W laser power were unsuitable combusted materials and powder particles [37,38]. As Mg has a low for further studies such as density and porosity measurements. melting point and is prone to oxidation, it evaporated and burnt There are several possible reasons for these results with 10 W significantly. In addition, due to the cyclone effect above the action to 30 W laser powers. The main reasons may be the low absorption zone and the significantly low mass of Mg, the powder particles of laser rays by the powder bed and the obstruction of the rays by were easily lifted and mixed into the cyclone, as schematically the dense smog cloud. In laser–material interaction, most laser rays represented in Fig. 3d. Moreover, powder explosions occurred in the are typically reflected from the top surface of the powder layer [35]. powdered zone due to the expansion of inter-particle inert gas [37]. Furthermore, magnesium is a shiny grey metal, which increases this Consequently, a dense cloud formed above the action zone, with a reflection. The process is illustrated by the schematic diagram in high probability of impeding the laser from reaching the powder bed. Fig. 3a. Therefore, although the power was sufficient, only a small At this point, higher laser power could escape this smog cloud. As a fraction of the laser rays was absorbed by the powder bed. After result, higher scanning speeds led to the formation of soft cubes at entering the powder bed, the rays are reflected multiple times within 30 W laser power. it [36]. The reflection and absorption are shown schematically in Fig. A further increase in laser power to 40 W enabled the fabrication 3b. However, the low laser power of 10 W to 20 W was not sufficient of some samples, whereas the lowest scanning speed of 300 mm/s did to heat and melt the powder particles. not produce any samples. At higher scanning speeds, however, some As the laser power increased to 30 W, the laser rays were sufficient good cubes were formed with measurable densities. The laser power to raise the temperature of the powder bed above 650 °C and melt of 40 W delivered sufficient energy into the powder layer for good the powder. Scanning speeds of 200 mm/s and 300 mm/s at 30 W fusion to begin, as shown in Fig. 3c. As discussed, the lower scanning laser power allowed enough time to melt the particles. Although speed did not allow sufficient time to move forward to avoid the melting occurred due to the greater number of laser rays penetrating smog cloud. When the scanning speed increased to 400 mm/s, better the powder layer, as shown in Fig. 3b, the melt pool did not form melting occurred. Gradually increasing the scanning speed to 500 sufficiently to agglomerate the layers and scan tracks. Therefore, it mm/s and 600 mm/s resulted in better melting than at 300 mm/s, even can be assumed that some areas were melted while others were not. though the energy density was higher at the lower scanning speed. SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 321 Additive Manufacturing Laser beam Laser beam Reflecting ray Reflecting ray Top surface Top surface Powder particle Powder particle Penetrated ray Penetrated ray Scanning layer Scanning layer a) No fusion occurrence Preceding layer b) Partial fusion occurrence Preceding layer Laser beam Reflecting ray Top surface Powder particle Scanning layer Heat affected zone c) Preceding layer d) Melt pool occurrence Fig. 3. Fusion characteristics; a) fusion with low laser power, b) fusion with medium laser power, c) melt pool formation with high laser power, and d) smog formation However, the product density decreased at higher scanning speeds particles in the subsequent layer at that location, resulting in a higher from 400 mm/s to 800 mm/s due to the significantly lower energy powder layer height. Consequently, the subsequent layer could not density. fuse well or form a uniform melt pool, as shown in the SEM images There is also a possibility of high ED formation in the melt pool in Fig. 4. This led to insufficient bonding with the previous layer and at a low scanning speed of 300 mm/s, which may cause instability in the formation of a pore. To observe this phenomenon, the sample the melt pools and result in melt spattering [39], as shown in Fig. 3d. fabricated with 60 W laser power, 700 mm/s scanning speed, 0.035 Additionally, trapped gas bubbles and metal vapor caused explosions mm hatch spacing, and 0.050 mm layer thickness is shown in Fig. 4. in the melt pools [40]. This resulted in significant metal splashes, Figure 4 shows that some layers are affected by the phenomena causing the action zones to lose material. Conversely, the splashed described above. These layers are significantly influenced by highly material fell onto the scan area and created some bumpy zones. irregular melt pool and pore formation. Several of these layers are The loss of material in one area led to an accumulation of powder marked by two parallel lines in Fig. 4. These pores also influenced Pores in a layer 50 µm (a layer) Balling Connected pore between layers 50 µm Connected pores 50 µm A layer Connected pores in a layer a) 200 µm b) 40 µm Fig. 4. Common pore characteristics of the samples; a) overall pore formation, with some layers exhibiting high pore content, and b) higher magnification image of the pores in a layer with high pore content 322 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Additive Manufacturing pore formation in subsequent layers. Some pores extended across the lowest density was selected. This can provide an indication of the several layers, forming connected pores between them. Additionally, melting mechanism, even if the product was not well manufactured. part of the last scanned layer may exhibit uneven areas due to the Therefore, this sample was analyzed with nano-CT scanning and is deposition of spattered particles and the formation of spheres caused shown in Fig. 5. The light grey and dark grey areas represent the by the balling effect, as shown in Fig. 4a. As a result, this part had to solid and porous regions, respectively. Successive images are taken at be removed and displaced from the specific manufacturing location intervals of 5 µm through the vertical direction, which is the build-up by the recoater movement. Ultimately, the combination of 40 W laser direction of the sample. Examining these images, it can be seen that power and 300 mm/s scanning speed produced disorganized samples. the pores are interconnected. It is also clear that they have irregular Therefore, density was not determined for samples produced with shapes, and their sizes vary accordingly. these manufacturing parameters. Based on the pores of sample I-16 and the consolidated patches, Comparing the effects of laser power between samples I-5 and certain melting characteristics of this sample can be determined. This I-13, it can be seen that despite the same high ED of 3.81 J/mm², indicates that the track was not laid down evenly throughout. There no melting occurs in I-5, while high temperatures and significant are occasional fluctuations in the melt pools of the track [25]. The spattering of molten metal occur in I-13. The heating rate (scanning pores also varied in size in each direction. Consequently, the density speed) played an important role in the fusion mechanisms. Since the varied both between the layers and between the tracks. For example, ED was very high, there is a high probability that strong vaporization the three strips -1, -2, and -3 marked in Fig. 5 can be considered to began at the top of the powder bed. After the onset of vaporization, investigate their melting properties. The width of the stripes is 100 µm, the penetration of the laser beam decreased due to obstruction by the and these stripes can be visualized in all images. However, the region vapor cloud, resulting in insufficient melting of sample I-5. When the in strip-1 has a higher density than the region in strip-3, indicating scanning speed was increased at the same ED, the laser left the action that fusion was better in some areas, while in others less material zone after supplying higher energy in less time. This allowed for a was obtained, and pores were formed. Although this is one possible higher probability of melting and a greater energy content in the melt cause for such melting properties and the formation of porosity, other pools. Therefore, a high ED led to high temperatures and a reduction factors may also contribute. It is an inherent characteristic of SLM in the viscosity of the melt pools, resulting in spattering of molten that some action zones melt well and form a good melt pool, while metal in sample I-13. To investigate these phenomena in more detail, others may suffer from lack of melting or spattering of molten metal. the part with the lowest density was analyzed using a nano-CT scan This can also be influenced by the different size distribution of the and explained with the help of Fig. 5. powder particles and the varying powder packing from place to place. Comparing samples I-1, I-6, I-10, and I-14, which have the same The shape of a melt pool can be understood from any dot (with ED (2.86 J/mm²) but different laser powers (10 W, 20 W, 30 W, and a small surrounding area) placed on a figure panel in Fig. 5. For 40 W), it can be observed that while 10 W to 30 W could not produce example, a red dot is placed on each panel representing the same a good sample, 40 W resulted in the highest density. Even the scan area. Since the following images represent the 5 µm above in significantly low ED of 1.43 J/mm² was sufficient to fabricate a good the build direction, the same area or location shows the variation sample with a laser power of 40 W. In contrast, the same ED of 1.43 of the melt pool in the vertical direction. However, the red dot J/mm² and higher EDs could not produce a sample when the laser originated from a pore area that eventually filled with material as powers were below 40 W. It is therefore clear that lower laser powers it moved in the vertical direction. Similarly, one can visualize and perform worse due to insufficient absorption of the laser rays by the examine the pore and solid zones, which provides insight into the powder bed. Here, a good sample refers to one that is well formed melting properties. As mentioned earlier, these porosities result from with a cubic structure and whose product density can be measured, evaporation, combustion, material loss, material spattering, and laser while other samples are not well formed or fused and do not form a shielding by smog [32]. On the other hand, a large number of round cube. patches of solid material in the cross-section of the sample match the Since I-16 has the lowest product density among the well-formed section size of the powder particles and could indeed be unmelted samples, this research has taken this sample into account to study the powder particles. Better stabilization of the melt pools is required to formation and behavior of melt pools. To investigate the effects of the maximize density. A higher laser power may be preferable to achieve laser parameters and the formation of melt pools, the product with the desired melt pool properties. Metal Strip-1 Pore Dot Strip-2 Strip-3 100 µm 100 µm 100 µm 100 µm 100 µm 100 µm 100 µm 100 µm 100 µm 100 µm Fig. 5. Nano-CT scanned images showing pores and metallic zones SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 323 Additive Manufacturing 3.2 Effects of High Laser Powers powder bed, which drew in many Mg powder particles and formed a protective shield. This shield prevented the laser from penetrating the As the increase in laser power supported an improved fusion process powder layer. Many sparks were observed with the increased number during manufacturing and resulted in higher product density, the of powder particles in the cyclone, as shown in Fig. 3d. It can be laser power was further increased in the second stage of the study. assumed that the laser struck the particles and caused the sparks. As However, since scanning speed significantly affects the fusion a result, the amount of melting was insufficient to form a good melt process, the speeds were selected based on findings from the previous pool. Additionally, the formation of smoke, the vaporization of the study. High ED also led to increased fume and smog generation metal, and the removal of powder particles caused metal loss from in the manufacturing chamber. Therefore, to maintain the ED, a the action zone [38]. Consequently, the density decreased, and the scanning speed of 400 mm/s to 600 mm/s was chosen for the second samples were damaged during production. stage. It was observed that higher laser power produced better melt pools; for example, 40 W was more effective than 30 W, although both generated considerable smog. Additionally, although increased 3.3 Effects of High Laser Powers with Higher Scanning Speeds vaporization from the top of the powder bed is possible, the resulting Since lower scanning speeds combined with higher laser powers vapor also impedes effective laser penetration. Therefore, higher resulted in a high ED, the scanning speed was increased in the third laser power at the outset can lead to excessive energy deposition. step of the study. As a result, the samples were well prepared, as The proportion of laser rays reaching the powder bed decreases as shown in Fig. 6a. Additionally, the densities of the samples increased vaporization begins. Accordingly, higher laser power can result in this step, as shown in Fig. 6b. When the laser power was lowest at in improved melt pool formation. With this in mind, a higher laser 55 W (in sample III-1) in the third step, the resulting density was low power was selected for further investigation. (1.62 g/cm³). However, when the laser power was increased to 65 W The densities of some samples in the second stage are lower and the scanning speed was kept constant at 700 mm/s, the resulting than those prepared with 40 W laser power for samples I-14 to I-16, density in sample III-2 increased to 1.63 g/cm³. In sample III-3, and some are not well fabricated. Therefore, the densities of these which was fabricated with a higher laser power (75 W) and scanning samples cannot be reported. The second stage of the experiment speed (750 mm/s), the density was even higher. showed strong smog formation in the fabrication chamber. The smog Since a high ED occurred in sample II-1 due to the lower reflected the laser rays even above the intended scanning layer. As a scanning speed compared to sample III-3, a large amount of smog result, insufficient energy was delivered in many areas, which also was generated. When the scanning speed was increased at the same contributed to a high level of pore formation. However, due to the laser power, the ED decreased, and fusion and melt pool formation high laser power, a significant amount of Mg was burnt and vaporized. improved. This resulted in successful sample fabrication with high As previously mentioned, this also created a cyclone above the density. The smog and fumes were much lower compared to the 1.74 Cubic samples Build-tray 1.72 1.70 Sample Sample Sample 1.68 III-1 III-2 III-3 1.66 1.64 1.62 1.60 1.58 1.56 1.54 1.52 1.50 1.48 1.46 1.44 1.42 1.40 Speed [mm/s] 700 700 750 a) b) Power [W] 55 65 75 Fig. 6. Samples and density results in the third step of the study; a) photograph of the cubic samples on the build tray; and b) densities a) 200 µm b) 200 µm Fig. 7. Difference in porosity; a) sample fabricated with a laser power of 70 W and a scanning speed of 750 mm/s; and b) sample fabricated with a laser power of 80 W and a scanning speed of 800 mm/s 324 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Density [g/cm3] Additive Manufacturing second step of the study. However, increasing the laser power from step was within the optimal range, smog formation was low. This 55 W to 65 W improved the quality of the melt pools, as indicated by was due to the uniform effects on the top of the powder layer. As the increase in density. This was confirmed by SEM examinations of the layer thickness decreased, the total energy input to the powder other samples produced with a laser power of 70 W and a scanning layer increased, which also increased the thermal energy in the melt speed of 750 mm/s, and with a laser power of 80 W and a scanning pools. This led to a lower viscosity of the melt, resulting in instability speed of 800 mm/s, while keeping the other parameters constant. of the melt pools and spattering of molten metal [39]. Therefore, the The SEM images of the vertical cross-sections of these samples are action zone lost more material than the previous samples produced at shown in Fig. 7. 50 µm. As a result, the overall density of the samples decreased. The SEM images in Fig. 7 clearly show that the quality of the melt The melting mechanism and the effects of smog can be visualized pools improved as the laser power increased, reducing gaps between by examining pore formation in one of the samples, which was tracks and decreasing pores. Therefore, higher laser power combined produced with a layer thickness of 25 µm. Fig. 8b to d shows the with a slightly higher scanning speed helped to melt the powder more nano-CT images of sample IV-1, which are vertical cross-sectional effectively and form a better melt pool in sample III-3 compared to planes arranged sequentially at intervals of several hundred sample II-3. As the EDs in the third step of the study were within an micrometers. The proportion of pores is visible in these images, appropriate range, less fume and smog were observed. indicating that they contain a low, medium, and high proportion of pores, respectively. The density therefore varied significantly within 3.4 Effect in Decreasing the Layer Thickness the same scanning layer. In some areas, there was good fusion and stabilized melt pool formation, while in others there was low laser By reducing the layer thickness to 25 µm, the density results were energy or an unstable melt pool with high thermal energy. The smog slightly lower than those for samples with a higher layer thickness obstructed the laser, resulting in low energy deposition on the powder of 50 µm. In the fourth step of the study, the densities were almost bed. As the energy decreased, evaporation also decreased, causing the the same for all samples, as shown in Fig. 8. Smog formation was laser to fall onto the powder bed. When the melt pools accumulate almost identical to that of samples fabricated with the same laser higher energy, the viscosity of the melt may decrease, which can power (40 W) in the first step of the study, except at the lowest lead to destabilization of the melt pools. This can eventually result in scanning speed (300 mm/s). As the scanning speed in the fourth spattering and material loss. 1.74 1.72 Edge of the sample 1.70 1.68 1.66 Metal 1.64 1.62 1.60 Sample Sample Sample Sample 1.58 IV-1 IV-2 IV-3 IV-4 Pore 1.56 1.54 1.52 1.50 1.48 1.46 1.44 1.42 1.40 Speed [mm/s] 400 500 600 700 a) b) 100 µm Power [W] 40 40 40 40 Metal Pore Metal c) Pore 100 µm d) 100 µm Fig. 8. Densities and porosities of the sample fabricated in the fourth step of the study; a) densities; b) low-porosity site; c) medium-porosity site, and d) high-porosity site SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 325 Density [g/cm3] Additive Manufacturing 4 CONCLUSIONS [15] Persaud-Sharma, D., Mcgoron, A. Biodegradable magnesium alloys: A review of material development and applications. J Biomim Biomater Tissue Eng 12 25-39 This article investigates and describes the melting properties (2012) DOI:10.4028/www.scientific.net/JBBTE.12.25. of magnesium during selective laser melting. The following [16] Gray, J.E., Luan, B. Protective coatings on magnesium and its alloys - A critical characteristics are observed and demonstrated using density review. J Alloys Compd 336 88-113 (2002) DOI:10.1016/S0925-8388(01)01899- measurements, as well as images from nano-CT scans and SEM of 0. the samples. [17] Kiani, F., Wen, C., Li, Y. Prospects and strategies for magnesium alloys as Low laser power is insufficient to melt the powder particles and biodegradable implants from crystalline to bulk metallic glasses and composites-A connect the layers and tracks, even when the ED is the same as with review. Acta Biomater 103 1-23 (2020) DOI:10.1016/j.actbio.2019.12.023. [18] DebRoy, T., Wei, H.L., Zuback, J.S., Mukherjee, T., Elmer, J.W., Milewski, higher laser power. At the same ED, the scanning speed must be J.O., et al. Additive manufacturing of metallic components - Process, increased, which is the main advantage in melting the powder and structure and properties. 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Influence of local heat powder bed. flow variations on geometrical deflections, microstructure, and tensile properties of Ti-6Al-4 V products in powder bed fusion systems. J Manuf Process 65 382- A high ED causes melt pool instability due to the explosion of 396 (2021) DOI:10.1016/j.jmapro.2021.03.054. melt pools and spattering, resulting in insufficient material and [21] Pal, S., Gubeljak, N., Hudák, R., Lojen, G., Rajťúková, V., Brajlih, T., et al. Evolution the formation of voids or the inability to form a product. Although of the metallurgical properties of Ti-6Al-4V, produced with different laser reducing the layer thickness enables better melting in some areas, in processing parameters, at constant energy density in selective laser melting. other areas there is instability in the melt pools, which also worsens Results Phys 17 103186 (2020) DOI:10.1016/j.rinp.2020.103186. the overall density. 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Formal analysis, Investigation; Hanuma Reddy Tiyyagura: Conceptualization, [36] Tolochko, N.K., Mozzharov, S.E., Yadroitsev, I.A., Laoui, T., Froyen, L., Titov, V.I., et Formal analysis, Investigation, Writing—review and editing, Supervision; Igor al. Balling processes during selective laser treatment of powders. Rapid Prototyp J 10 78-87 (2004) DOI:10.1108/13552540410526953. Drstvenšek: Conceptualization, Formal analysis, Investigation, Writing—review [37] Yadav, P., Rigo, O., Arvieu, C., Le Guen, E., Lacoste, E. In situ monitoring systems and editing, Supervision. of the SLM process: On the need to develop machine learning models for data processing. Crystals 10 524 (2020) DOI:10.3390/cryst10060524. [38] Shan, X., Pan, Z., Gao, M., Han, L., Choi, J.P., Zhang, H. Multi-physics modeling of Proces spajanja čistega magnezija melting-solidification characteristics in laser powder bed fusion process of 316L med selektivnim laserskim taljenjem stainless steel. Materials 17 946 (2024) DOI:10.3390/ma17040946. [39] Li, Z., Li, H., Yin, J., Li, Y., Nie, Z., Li, X., et al. A Review of spatter in laser powder Abstract V raziskavi smo proučevali obnašanje taljenja čistega magnezija bed fusion additive manufacturing: in situ detection, generation, effects, and in pretočnost njegove taline med selektvinim laserskim taljenjem. Raziskali countermeasures. Micromachines 13 1366 (2022) DOI:10.3390/mi13081366. smo tudi vpliv različnih kombinacij procesnih parametrov na povečanje [40] Yu, G., Gu, D., Dai, D., Xia, M., Ma, C., Chang, K. Influence of processing gostote izdelka. Moč laserja smo postopoma povečevali in pri tem spreminjali parameters on laser penetration depth and melting/re-melting densification during selective laser melting of aluminum alloy. Appl Phys A Mater Sci Process hitrosti skeniranja za vsako serijo izdelkov, s čimer smo vplivali na vnos 122 891 (2016) DOI:10.1007/s00339-016-0428-6. energije v talilni process (ED). Moč laserja se je gibala od 10 W do 75 W, hitrost skeniranja pa od 100 mm/s do 800 mm/s. Z nižjimi močmi laserja Acknowledgements The authors thank the Slovenian Research Agency nismo dosegli zadovoljivega taljenja materiala, medtem ko so višje moči for funding the research (Grant Nos. GC-0007 P2-0118, P2-0137, P2-0157 laserja povzročile boljše taljenje, z znatnimi razlikami tudi pri enakih vnosih J1-2470, J1-2471, J1-4416, J7-4636, J7-50226, J7-50227, J1-60015 and J7- energije - ED. Visoka energijska gostota - ED med 3,50 J/mm² in 4,30 J/mm² 60120). The project is co-financed by the Republic of Slovenia, the Ministry of je povzročila pomanjkljivo taljenje pri nizki moči laserja oziroma nestabilen Education, Science and Sport, and the European Union through the European talilni bazen z znatnim pršenjem materiala pri visoki moči laserja. Nasprotno Regional Development Fund. pa so zmerne ED v območju od 1,40 J/mm² do 2,90 J/mm² povzročile boljšo gostoto pri visoki moči laserja. Višje hitrosti skeniranja so pomagale preprečiti Received 2025-05-09, revised 2025-09-16, 2025-10-13, accepted 2025- nastanek gostega oblaka smoga in s pomočjo večje laserske moči zagotovile 10-13 as Original scientific paper 1.01. zadostno energijo v kratkem času. Zato je povečanje tako laserske moči kot hitrosti skeniranja izboljšalo učinkovitost taljenja in povečalo gostoto vzorca. Data availability The data that support the findings of this study are Relativna gostota vzorcev se je gibala od 80 % do 96,5 %. Zmanjšanje available from the corresponding author upon reasonable request. debeline plasti s 50 µm na 25 µm pri laserski moči 40 W je na nekaterih območjih povzročilo nastanek dobro oblikovanega bazena taline, na drugih Author contribution Snehashis Pal: Conceptualization, Methodology, pa znatno brizganje taline, kar je povzročilo poslabšanje gostote. Formal analysis, Investigation, Visualization, Writing—original draft; Matjaž Finšgar: Formal analysis, Investigation, Writing—review and editing; Ključne besede magnezij, talilni bazen, moč laserja, hitrost skeniranja, Jernej Vajda: Formal analysis, Investigation; Uroš Maver: Formal analysis, debelina plasti, nosilna struktura, lasersko taljenje praškastega sloja SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 327 Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Advancing Intelligent Toolpath Generation: A Systematic Review of CAD–CAM Integration in Industry 4.0 and 5.0 Marko Simonič − Iztok Palčič − Simon Klančnik University of Maribor, Faculty of Mechanical Engineering, Slovenia marko.simonic@um.si Abstract This systematic literature review investigates advancements in intelligent computer-aided design and computer-aided manufacturing (CAD–CAM) integration and toolpath generation, analyzing their evolution across Industry 4.0 and emerging Industry 5.0 (I5.0) paradigms. Using the theory–context– characteristics–methodology framework, the study synthesizes 51 peer-reviewed studies (from 2000 to 2025) to map theoretical foundations, industrial applications, technical innovations, and methodological trends. Findings reveal that artificial intelligence (AI) and machine learning dominate research, driving breakthroughs in feature recognition, adaptive toolpath optimization, and predictive maintenance. However, human-centric frameworks central to I5.0, such as socio-technical collaboration, remain underexplored. High-precision sectors (aerospace, biomedical) lead adoption, while small and medium enterprises (SMEs) lag due to resource constraints. Technologically, AI-driven automation and STEP-NC standards show promise, yet interoperability gaps persist due to fragmented data models and legacy systems. Methodologically, AI-based modeling prevails (49 % of studies), but experimental validation and socio-technical frameworks are sparse. Key gaps include limited real-time adaptability, insufficient AI training datasets, and slow adoption of sustainable practices. The review highlights the urgent need for standardized data exchange protocols, scalable solutions for SMEs, and human-AI collaboration models to align CAD–CAM integration with I5.0’s sustainability and resilience goals. By bridging these gaps, this work provides a roadmap for advancing intelligent, human-centered manufacturing ecosystems. Keywords CAD–CAM integration, Industry 4.0, Industry 5.0, toolpath optimization, AI, theory–context–characteristics–methodology (TCCM) Highlights ▪ Artificial Intelligence drives CAD–CAM integration but lacks human-centric focus. ▪ High-precision sectors lead; SMEs face adoption barriers. ▪ Interoperability and lack of standardized AI datasets hinder progress. ▪ Review reveals the need for sustainable, scalable solutions. 1 INTRODUCTION communication bottlenecks, inconsistencies in toolpath generation, and rework cycles that undermine efficiency [11,12]. By improving The manufacturing sector has undergone radical transformation data exchange protocols [13,14], standardizing file formats, and through Industry 4.0 (I4.0), characterized by cyber-physical systems incorporating real-time feedback from manufacturing constraints, (CPS), internet of things (IoT), and data-driven automation. These organizations can bridge the CAD–CAM gap and accelerate the technologies have revolutionized production efficiency, enabling transition from digital designs to production-ready components [11]. real-time monitoring, predictive maintenance, and adaptive Various approaches have been developed to automate numerical workflows [1,2]. By integrating robotics, cloud computing, and control (NC) code generation directly from CAD models, aiming to artificial intelligence (AI), I4.0 has minimized downtime, optimized streamline the transition from design to manufacturing. Traditional resource use and reduced operational costs [3,4]. methods typically rely on geometry-based feature recognition Building on this foundation, Industry 5.0 (I5.0) emphasizes [15] and rule-based process planning [16], wherein the system human-machine collaboration and sustainability, prioritizing extracts manufacturing features (e.g., holes, pockets, slots) from ethical resource allocation and workforce upskilling alongside 3-dimensional (3D) CAD geometry, maps them to corresponding technological advancement [5]. This paradigm shift leverages AI machining operations, and then generates toolpaths and tool selection not to replace human expertise, but to augment it, fostering agile, data. Knowledge-based systems further enhance this pipeline by socially responsible manufacturing ecosystems [5]. Computer-aided incorporating predefined machining rules and best practices [17], engineering (CAE) plays a crucial role in this aspect. It enables enabling semi-automated decision-making for process parameters product design validation [6], process simulation and optimization. such as spindle speed, feed rate, and cutting depth. Post-processors This reduces the need for physical prototyping and minimizes costly then translate these planning outputs into machine-specific G-code design errors [7]. (or equivalent) formats, ensuring compatibility with diverse computer Despite the advancements in CAE and integrated design numerical control (CNC) equipment. While these workflow-oriented workflows, a significant disconnect often persists between computer- techniques have significantly reduced programming time and manual aided design (CAD) and computer-aided manufacturing (CAM) intervention, they often demand expert tuning [18] and may lack [8]. CAD tools focus on creating detailed, precise models, yet these flexibility when confronted with complex geometries or evolving models do not always seamlessly translate into manufacturable production requirements [19]. In recent years, however, AI has begun instructions for CAM systems [9,10]. This disparity can lead to to complement these conventional strategies, leveraging deep neural 328 DOI: 10.5545/sv-jme.2025.1370 Production Engineering networks [20] and reinforcement learning (RL) [21] to automate details the data sources, selection criteria, and analytical processes, feature recognition, optimize toolpaths, and continuously refine CAD providing sufficient information for replication and validation by assumptions in real time [22]. By incorporating AI modules at critical other researchers. points of the CAD to CAM workflow, manufacturers can achieve adaptive, self-improving systems [23] that further streamline NC 2.1 Research Design and Analytical Framework code generation and reduce the need for extensive human oversight [24], ultimately closing the design-to-production gap [25]. The SLR follows a clear, step-by-step process rooted in proven Recent contributions further illustrate this evolution. CAD-Coder review protocols [35]. It employs the TCCM framework, delivering introduces an open-source vision–language model fine-tuned to a well-rounded analysis of the literature while staying true to the generate editable CAD code (CadQuery Python) directly from visual study’s goals [36]. With a spotlight on CAD–CAM integration, the input [26]. Similarly, CAD-based automated G-code generation for review digs deepest into the Theoretical and Methodological angles, drilling operations demonstrates an application program interface exploring how challenges are defined, tackled, and resolved. This lens (API)-driven approach that extracts geometric parameters from CAD sheds light on practical strategies, tools, and techniques, pinpointing models and automatically generates CNC code for drilling tasks overlooked areas and opening doors to fresh methodological without dedicated CAM software [27]. Complementing these, the approaches [35]. AutoCAD to G-code converter outlines a workflow for converting Compared to alternatives like PRISMA, which prioritize reporting AutoCAD designs directly into CNC-compatible G-code [28]. Those transparency [37], TCCM offers a theory-driven and context- strategies range from AI-driven CAD code generation to lightweight sensitive structure [36]. This is particularly valuable for research API-based tooling. of interdisciplinary domains like CAD–CAM integration, where Despite the growing body of literature on the evolution of solutions depend on synergies between theoretical foundations, manufacturing technologies and the integration of AI in CAD–CAM contextual constraints (e.g., industry-specific requirements), system workflows [29–31], there remains a lack of comprehensive research characteristics (e.g., scalability), and methodological rigor. The synthesizing the specific challenges and opportunities in bridging the inclusion of the Methodology dimension allows us to systematically CAD–CAM disconnect, particularly in the context of I4.0 and I5.0 assess how problems are framed, investigated, and resolved in paradigms. Recent studies have explored individual aspects, such as existing research, identifying gaps in methods (e.g., underuse of AI-driven NC code generation or feature recognition [32,33], yet these AI-driven optimization) and opportunities for methodological efforts are often narrow in scope, limited by the time span of analysis, innovation. or constrained to specific methodologies. Furthermore, the rapid adoption of human-machine collaboration and sustainable practices 2.2 Data Sources and Study Selection in I5.0 underscores the need for an updated, holistic understanding of how these advancements influence design-to-production integration. This review is based on a comprehensive and systematic search of Consequently, a systematic literature review (SLR) is essential to academic and industry-related literature to ensure broad coverage consolidate and analyze the existing research landscape. This study of relevant studies in the domains of CAD/CAM integration, AI in proposes an SLR of over 50 studies published in the last two decades, manufacturing, and CNC toolpath optimization. The selected sources employing the theory–context–characteristics–methodology (TCCM) include peer-reviewed journal articles, conference papers, and book framework [34], to systematically analyze critical gaps, emerging chapters, along with a curated set of industry reports and white papers trends and understudied areas that could enhance the CAD and CAM to capture practical implementations of emerging technologies. interoperability in modern manufacturing ecosystems shaped by I4.0 and I5.0. Given this focus, the study aims to address the following 2.2.1 Data Sources research questions: 1. Theory: Which theoretical models or frameworks guide the To maintain academic rigor and reliability, the following key integration of CAD and CAM in I4.0/5.0 settings? databases were utilized: 2. Context: In which industrial or organizational contexts is CAD– • Scopus – for its extensive indexing of engineering and AI-related CAM integration most frequently examined, and what contextual publications. factors shape these efforts? • Web of Science – providing a broad range of peer-reviewed 3. Characteristics: Which key technical or organizational features studies in advanced manufacturing (e.g., AI-based tools, knowledge-based systems) facilitate or • Google scholar & ResearchGate – used selectively to retrieve impede CAD–CAM interoperability, and how do they evolve literature, such as industry reports and white papers, ensuring under I4.0 and I5.0 paradigms? coverage of real-world implementations and emerging trends. 4. Methodology: Which research methods are used to investigate CAD–CAM integration, and how do these methodological choices 2.2.2 Search Strategy affect the reliability, scalability, and reproducibility of results? A structured search strategy was employed, using Boolean operators to refine results and ensure the retrieval of high-quality studies. The primary search terms used included: CAD–CAM integration, 2 METHODS AND MATERIALS Industry 4.0, Industry 5.0, AI in manufacturing, NC code generation, This section outlines the methodology employed to conduct SLR of feature recognition, toolpath optimization, and human-machine studies addressing CAD–CAM integration within the paradigms of collaboration. I4.0 and I5.0. The approach is designed to systematically identify and To enhance relevance, secondary qualifiers such as sustainability, synthesize relevant research, ensuring a comprehensive analysis of interoperability, and systematic review were incorporated. The theoretical frameworks, contextual factors, technical characteristics, research was limited to studies published between January 2000 and and methodological trends. The TCCM framework was selected as March 2025, ensuring a focus on recent advancements while covering the analytical lens due to its ability to structure multidimensional historical developments in AI-driven manufacturing. In addition research inquiries and uncover gaps in literature. This section to direct search results, the reference lists of selected articles were SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 329 Production Engineering also reviewed to identify further relevant studies, helping to ensure a This structured approach enabled both qualitative syntheses, to comprehensive literature base. identify thematic trends, theoretical orientations, and methodological patterns, and basic quantitative summaries, such as publication year 2.2.3 Inclusion and Exclusion Criteria distribution and research domain coverage. Data management and visualization were supported using Microsoft Excel and Python, To maintain focus and relevance, inclusion and exclusion criteria while Zotero was used for literature organization and InstaText were defined as follows: assisted in refining the academic writing style. The detailed and • Inclusion Criteria: traceable extraction process supports transparency and replicability • Studies published between 2000 and 2025, reflecting more of the review. than two decades of advancements in CAD–CAM integration. • Research addressing CAD–CAM workflows, interoperability, or automation in the context of I4.0 or I5.0. 3 RESULTS OF THE SYSTEMATIC LITERATURE REVIEW • Studies incorporating AI, knowledge-based systems, or other innovative approaches to bridge the CAD–CAM gap. This section summarizes the results of the reviewed literature • Peer-reviewed articles, conference proceedings, or authoritative on CAD–CAM integration in the context of I4.0 and I5.0. The reviews offering empirical or theoretical insights. analysis follows standardized framework, to ensure a structured and • Exclusion Criteria: comprehensive review. In addition to presenting the evidence, the • Studies unrelated to manufacturing or CAD–CAM processes key patterns, challenges and opportunities are discussed, considering (e.g., pure software development without manufacturing the research objectives. applications). • Non-English publications or those lacking sufficient 3.1 Overview of Included Studies methodological detail. This SLR includes a total of 51 peer-reviewed studies published • Duplicates or redundant publications from the same research between 2002 and 2025. Although the search covered the entire group with no significant new contributions. period from 2000 to 2025, the earliest relevant study in this period was published in 2002. The overview shows the development of 2.3 Data Extraction and Analysis academic interest in CAD–CAM integration in the context of I4.0 Data extraction was conducted manually using a standardized Excel and I5.0. Figure 1 shows the number of articles and conference template aligned with the TCCM framework. In addition to capturing papers published per year as well as a 3-year moving average trend the four core dimensions, the template included several other line representing the overall progression of publications. descriptive and analytical fields to support a comprehensive review. As can be seen from Fig. 1, the volume of publications remained Specifically, the following elements were recorded for each study: relatively low and stable between 2002 and 2015, averaging around • Bibliographic details: Paper title, authors, year of publication, one to two publications per year. From 2016 onwards, a modest keywords, journal/conference name. increase can be observed, with more consistent growth after • Research context: Study aim/goals, research goals. 2018. The number of studies peaked in 2024 with a total of eight • Analyzed dimensions: publications, indicating increased research attention and relevance of • Theory: Theoretical models or conceptual frameworks CAD–CAM integration in recent years. The 3-year moving average, underlying CAD–CAM integration (e.g. systems theory, CPS). marked with a black dashed line in Fig. 1, confirms this upward trend • Context: Industrial settings (e.g., automotive, aerospace), and signals continued momentum in this area. organizational factors, or sustainability considerations. In terms of dissemination channels, articles dominate the literature • Characteristics: Technical features (e.g., AI algorithms, file and account for most publications, while conference papers have also formats) or organizational factors influencing interoperability. gained visibility in recent years, particularly from 2019 onwards. • Methodology: Research approaches (e.g., case studies, This indicates a growing interest in disseminating preliminary or simulations, experiments) and their reported limitations. applied research results via academic conferences, possibly reflecting • Analytical fields: identified gaps, suggested future research the increasing pace of technological innovation and industry directions and main findings. involvement. Fig. 1. Annual distribution of articles and conference contributions with a trend line 330 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Production Engineering 3.2 Theoretical Foundations are used to enhance CPS and digital twins by predicting toolpaths. Similarly, knowledge-based engineering (KBE) frameworks integrate Integrating theoretical foundations into CAD–CAM research is with high-level standards like STEP-NC (a semantic computer crucial to guide system design, enable model-driven automation and navigated control (CNC programming protocol) to support feature- ensure scalability across industrial applications. In the era of I4.0 driven toolpath generation. Optimization approaches like non- and more recently I5.0, theory played a central role in aligning smart dominated sorting genetic algorithms (NSGA-II), particle swarm manufacturing technologies with broader technical, organizational optimization (PSO), and gravitational search algorithms (GSA) are and societal goals. To evaluate the conceptual basis of current widely used for machining parameter tuning. Geometric modeling research, each study in this review was assessed based on its stated or concepts such as function representation (FRep) and voxel-based implied theoretical basis. Based on a thematic analysis, the identified techniques further reinforce CAD–CAM correctness and accuracy. theories were grouped into six overarching categories, which are Such synergies reinforce the impact of each theory and promote summarized in Table 1. These categories reflect the main conceptual innovative CAD–CAM solutions tailored to I4.0 and I5.0 demands. approaches underlying CAD–CAM integration research over the past These foundations also overlap with I5.0’s focus on human- 25 years. centeredness, sustainability and resilience. ML and AI support sustainability through predictive maintenance that reduces waste, Table 1. Theoretical Foundations in CAD–CAM Integration while CPS improve resilience by enabling adaptive manufacturing Category Description Examples/Applications systems. However, the limited presence of human-centered theories, ML & AI Use of ML algo- ANN for process modeling [38] such as cognitive ergonomics or socio-technical systems, suggests rithms for prediction, DL for toolpath recognition [39] that CAD–CAM research has not yet fully embraced I5.0’s focus classification, or RL for CNC control [21] on human–machine collaboration, indicating a potential area for optimization tasks GANs for toolpath generation[40] theoretical expansion. These categories reflect the main conceptual Optimization Swarm-based and NSGA-II for multi-objective optimization approaches underlying CAD–CAM integration research over the past algorithms evolutionary algo- [41] 25 years, and their temporal distribution is illustrated in Fig. 2. rithms applied to PSO for toolpath adaptation [42] improve machining GA for machining time reduction [43] outcomes GSA for tool selection [44] 3.3 Application Contexts Feature/ Utilization of CAD Feature-based machining [45] The studies examined were conducted in a variety of industrial, Knowledge- features, KBE, and Knowledge-based process planning [45] technical and organizational contexts, reflecting the broad Based rule-based decision CAD/CAM integration for orthopedic/ applicability of CAD–CAM integration solutions. Analyzing the Systems systems dental workflows [46] contextual focus of the individual studies provides insight into where CPS/Digital Digital representa- Digital twins for predictive maintenance and how such technologies are used and tested. Based on the content Twins tions of physical [47] systems for control Multi-agent systems [48] analysis, three main dimensions were identified: industry domains, and maintenance CPS for smart manufacturing [49] enterprise types, and technological environments, each depicting High-Level Abstractions of STEP-NC for feature-based programming unique facets of application environments. These are summarized in Programming low-level CNC code [50] Table 2. / Standards through semantic Modular robotic machining [51] While Table 2 summarizes the three primary contextual frameworks AM programming standards [52] dimensions (industry domain, enterprise type, and technological Geometric / Theories improving Voxelization for complex surfaces [53] environment) it is also important to recognize several recurring Mathematical geometric modeling Adaptive isocurves [54] challenges in CAD–CAM integration identified across the reviewed models and toolpath FRep for CAD/CAM correctness [55] studies. accuracy In this context, computer aided process planning (CAPP) systems play a pivotal role in bridging the gap between CAD and CAM. Taken together, these six categories reflect the various theoretical The reviewed studies include manual programming inefficiencies, foundations that have shaped research into CAD–CAM integration. such as time-consuming G-code authoring and limited reusability In practice, these theoretical categories often merge into hybrid of strategies [58]; discontinuities in CAD–CAM-CNC integration, approaches. For instance, ML methods such as artificial neural where data loss or misalignment occurs between design, planning, networks (ANNs) and generative adversarial networks (GANs) and execution stages [40]; and a lack of feedback and adaptivity, Fig. 2. Annual distribution of studies by theoretical category, with legend showing overall category share SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 331 Production Engineering reflected in the absence of closed-loop control or learning capabilities and Toolpath optimization (23.5 %) highlights a strong focus on in conventional systems [62]. intelligent, adaptive systems capable of self-learning and real-time Toolpath optimization is the most prominent technical theme, decision-making. For instance, optimization techniques such as self- appearing in over 40 % of the reviewed studies. It reflects the supervised DL and evolutionary optimization are increasingly used to ongoing challenge of generating efficient and adaptable machining automate toolpath generation and process parameter tuning, reducing paths, often in connection with precision manufacturing, AI-driven reliance on manual interventions. planning, and CNC automation—key elements of I4.0. Table 3. Distribution of representative studies across CAD–CAM integration characteristics Table 2. Application contexts of CAD–CAM integration by dimensions Characteristic Share of Description Dimension Category / Focus area Description / Notes theme studies Aerospace, Automotive, Common use cases include 5-axis Self-supervised DL with voxel-based RNNs [58] Tooling, Die/Mold, machining, dental restoration, ANN for adaptive toolpath generation [38] % Medical, Dental, Orthotics, orthotic insole production, etc. AI & ML Evolutionary optimization & simulation models [41] 31.4 Industry 16 studies Micromachining [10,46,56] Contrastive self-supervision for feature domains Focused on toolpath accuracy, segmentation [63] Precision manufacturing freeform surface machining, CNC Voxelization, and B-spline interpolation for smooth optimization [54] toolpaths [64] Advanced CNC setups, digital twins, Deep graph RL for adaptive toolpath optimization Large enterprises/labs Toolpath robotic systems, smart factories [50] [59] 23.5 % optimization 12 studies Enterprise Evolutionary algorithms for parameter optimization type Rapid tooling, low-batch Small & medium [44] manufacturing, focus on ease of enterprises (SMEs) PSO variants for tool movement constraints [42] setup and cost-effectiveness [57] Hybrid/ Semi-automated Matlab for trajectory analysis [56] Focused on automating or enhan cing 25.5 % Traditional CAM integrated Strategic frameworks for integrated manufacturing legacy workflows (e.g., manual environments architectures [60] 13 studies G-code, static toolpaths) [58] Feature STL (stereolitography)-based feature extraction & Studies leveraging interconnected 7.8 % Technol- Integrated CAD, CAM, CAE, recognition & segmentation [65] design and manufacturing toolchains 4 studies ogical CAPP systems CAD parsing DNN on structured descriptors [39] [59] environ- Real-Time RL model for toolpath control [66] 5.9 % ments High-level programming Transition from G-code to semantic, systems & (e.g., STEP-NC) feature-based CNC programming [60] 3D vision for adaptive monitoring [61] 3 studies feedback Real-time optimization, digital Cloud-based/Adaptive Data models FRep–based CAD/CAM with topology optimization threads, feedback control, intelligent 5.9 % systems & inter- [55] machining [61] 3 studies operability Object oriented model for NC programming [67] The rise of cloud-based platforms, digital twins, and adaptive Meanwhile, Hybrid/integrated architectures (25.5 %) demonstrate control further supports I4.0 goals of connectivity, flexibility, and efforts to unify design, simulation, and execution through real-time responsiveness. frameworks like STEP-NC and MATLAB-based tools, reflecting Conversely, applications in dental and orthopedic manufacturing I4.0’s emphasis on CPS integration. However, underrepresented reflect I5.0 priorities, such as personalization and human–machine themes such as feature recognition & CAD parsing (7.8 %) and collaboration. Attention to SMEs also signals a push toward data models & interoperability (5.9 %) signal gaps in addressing accessible and scalable CAD–CAM solutions. Finally, interest in persistent challenges like dynamic CAD data translation and system high-level programming models like STEP-NC marks a shift from interoperability. Similarly, the limited focus on real-time systems & rigid G-code to more semantic and interoperable approaches. feedback (5.9 %) underscores the need for more empirical validation of adaptive monitoring and control mechanisms in physical 3.4 Characteristics of CAD–CAM Integration machining environments. The studies examined present a wide range of technical features and architectural implementations designed to improve CAD–CAM 3.5 Research Methodologies integration in the context of I4.0 and I5.0. This section analyzes The methodological foundations of the reviewed studies highlight the the functional and technological features reported in the selected interdisciplinary approaches to CAD–CAM integration, reflecting the literature, focusing on how the integration is realized, what types field’s experimental and computational complexity. Five overarching of automation are implemented and what elements contribute to the methodological categories emerged from the analysis (Table 4): adaptability, intelligence and efficiency of the system. (1) AI and ML modeling, (2) simulations and algorithm validation, To structure this analysis, the features have been grouped into six (3) STEP-NC and CPS system development, (4) experimental overarching themes based on their core function and implementation machining, and (5) reviews and analytical contributions. Table 4 strategy: AI and ML, toolpath optimization, feature recognition summarizes these approaches, their key techniques, applications, and and CAD parsing, real-time systems and feedback, data models & representative references. interoperability, and hybrid/integrated architectures. Table 3 provides AI and ML Modeling dominate the field, accounting for 49 % of a summary of the distribution of studies across these thematic studies (Figure 3). These works employ various DL architectures, categories, along with a selection of representative examples and such as ANN, CNN, RL, and generative models. Applications include methodologies that highlight key developments within each group. intelligent toolpath generation, feature recognition, and adaptive The distribution of studies reflects the field’s prioritization of AI- machining, underscoring the transformative role of data-driven driven automation and computational optimization to address CAD– intelligence in automating and optimizing digital manufacturing CAM integration challenges. The dominance of AI & ML (31.4 %) processes. Simulations and algorithm validation represent 21.6 % 332 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Production Engineering Fig. 3. Yearly distribution of studies by research methodology of methodologies. Techniques like PSO and numerical simulations 4 DISCUSSION are widely used to validate toolpath strategies, cutting parameters, and process control systems in virtual environments. These This SLR synthesizes more than two decades of research on CAD– approaches reduce reliance on physical prototyping by enabling CAM integration and intelligent toolpath generation through pre-testing of computational models. STEP-NC, CPS, and system the TCCM framework. The results reveal an evolution from the development (17.6 % of studies) focus on advancing interoperability automation-focused strategies of I4.0 toward I5.0’s emphasis on in manufacturing systems. Innovations include plug-and-produce human-centric and sustainable manufacturing. This transition mirrors automation frameworks, machine-interpretable NC code standards, wider industrial and societal demands for inclusivity, adaptability, and architectures validated in industrial robotic environments. and environmental accountability in production systems. These efforts aim to bridge gaps between design and execution AI and ML dominate the theoretical foundations, underpinning phases in CAD–CAM workflows. Experimental machining (5.9% advances in feature recognition, adaptive toolpath planning, and of studies) emphasizes practical validation through CNC machine predictive maintenance. However, theoretical models incorporating testing, toolpath design, and process reliability analysis. While human factors, socio-technical interaction, and sustainability are underrepresented, these works provide critical insights into the scarce, limiting alignment with I5.0 principles. While CPS and digital physical realities of CAM execution, such as parameter tuning twins offer strong potential for feedback-driven manufacturing, their and material behavior. Reviews and analytical contributions (5.9 industrial deployment remains limited, signaling a gap between %) remain scarce, highlighting a gap in meta-level synthesis and conceptual readiness and real-world integration. theoretical frameworks. Structured reviews and interdisciplinary From an application standpoint, adoption is concentrated in high- conceptual models are needed to unify fragmented advancements and precision industries, where geometric complexity and customization establish robust benchmarks for future research. needs justify investment in intelligent CAD–CAM workflows. Although SMEs show growing interest, financial constraints, Table 4. Overview of methodological approaches in CAD–CAM integration workforce training needs, and integration barriers hinder uptake. This calls for solutions that are scalable, cost-effective, and compatible Research Key techniques/ Example applications Refs. with diverse industrial infrastructures. Cloud-based adaptive systems approach methods and STEP-NC offer viable alternatives to conventional workflows, DL architectures Intelligent toolpath [20–22,30, but persistent interoperability issues slow adoption. AI and ML (ANN,CNN, RL), generation, feature 67,69,70, modeling regression, generative recognition, adaptive Technologically, AI-driven automation and optimization dominate 73,74] models machining CAD–CAM integration, with precision and efficiency as central Validating toolpath strate- objectives. Yet, unresolved interoperability challenges (rooted in Simulations PSO, GA, GSA, gies, cutting parameters, [42,44,55, fragmented data standards, proprietary formats, and insufficient and algorithm numerical simulations process control systems 68,69] CAD–CAM–CNC integration) limit seamless workflows. validation in virtual environments Sustainability-focused innovations, such as material efficiency New system archi- and energy optimization, are increasing but remain secondary to STEP-NC, tectures, plug-and- Industrial/robotic automation goals, indicating the need to embed environmental CPS, system produce frameworks, [47–52,70] machining environments metrics into core CAD–CAM strategies. development machine-interpretable Methodologically, the literature is led by AI/ML-based modeling, NC code standards followed by simulation-based validation and fewer experimental Practical testing Physical realities of CAM studies. While virtual and data-driven approaches accelerate design Experimental of CNC machines, execution, parameter [53,64,71] machining toolpath design, cycles, the lack of experimental verification, standardized datasets, tuning process reliability and consistent reporting weakens reproducibility and comparability. Structured reviews, Combining physical and virtual validation, and establishing shared Reviews, benchmarking Meta-level synthesis, benchmarks, would improve industrial credibility and scalability. conceptual, frameworks, theoretical framework [57] Key gaps persist across all TCCM dimensions: the shortage of and analytical interdisciplinary development contributions large, validated datasets; difficulties in freeform surface recognition; conceptual models limited cross-domain model generalizability; and the lack of robust solutions for real-time toolpath adaptation and force control. The slow adoption of STEP-NC, coupled with cybersecurity and SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 333 Production Engineering interoperability constraints, particularly affects SMEs and restricts effective human – machine collaboration while ensuring the scalability of advanced CAD–CAM solutions. scalability from small workshops to large enterprises. Addressing these gaps will require coordinated research and development efforts across four strategic areas: 1. Comprehensive, annotated, multimodal datasets. Datasets that 5 CONCLUSIONS integrate geometry, process parameters, sensor streams, and toolpath data are essential for developing robust AI models and Over the past two decades, CAD–CAM integration has advanced achieving semantic interoperability through asset administration significantly within the I4.0 and I5.0 paradigms, evolving from shells. However, most current studies depend on limited automation-focused solutions toward more adaptive, sustainable, or proprietary datasets, which hampers reproducibility and and collaborative manufacturing systems. The systematic mapping scalability. Progress is constrained by the absence of standardized provided by this review clarifies the field’s theoretical foundations, formats, low data variability, and intellectual property concerns. application contexts, technical innovations, and methodological Advancing the field will require open-access repositories, practices, highlighting where progress has been made and where harmonized CAD/CAM–sensor datasets, and the use of synthetic critical work remains. Key strategic directions emerging from this data generation to broaden coverage while safeguarding sensitive synthesis include: information. • Bridging research–practice divides by embedding socio-technical 2. Interpretable, transferable, and robust AI algorithms. Developing and sustainability considerations directly into CAD–CAM AI algorithms that combine interpretability, cross-domain solutions, ensuring they are deployable in diverse industrial transferability, and operational robustness is crucial for advancing contexts. CAD–CAM integration. Hybrid approaches that merge geometric • Expanding accessibility through scalable, cost-effective reasoning methods (e.g., voxelization) with simulation-informed integration strategies that address SME-specific constraints training and adaptive control can help bridge the gap between without sacrificing interoperability or performance. virtual optimization and real-world execution. However, many • Embedding sustainability as a core metric alongside productivity existing models remain opaque and narrowly specialized, and precision, ensuring material efficiency, energy optimization, which limits trust, adaptability, and scalability. Progress will and lifecycle awareness in CAD–CAM workflows. depend on the adoption of explainable AI techniques, domain- • Leveraging advanced AI and standards (interpretable models, adaptive learning strategies, and open-source, modular plug- STEP-NC, and OPC UA) to enable adaptive, interoperable, and and-play toolkits to facilitate seamless integration into diverse future-proof manufacturing ecosystems. manufacturing environments. While this review focuses on peer-reviewed literature, future 3. Practical implementation of standards. Effective CAD–CAM studies should combine industrial case evidence with academic integration depends on adopting and operationalizing existing research to capture region-specific practices, operational constraints, yet underutilized standards such as STEP-NC and OPC UA [72]. and emerging innovations. 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Int J Manuf Res 7 354 (2012) DOI:10.1504/ standardiziranih protokolov za izmenjavo podatkov, razširljivih rešitev za IJMR.2012.050101. malo serijsko proizvodnjo ter razvoj modelov sodelovanja med človekom in [72] Ji, T., Xu, X. Exploring the integration of cloud manufacturing and cyber-physical UI, ki bi CAD–CAM integracijo uskladili s trajnostnimi in odpornimi cilji I5.0. Z systems in the era of Industry 4.0 - an OPC UA approach. Robot Comput Integr Manuf 93 102927 (2025) DOI:10.1016/j.rcim.2024.102927. odpravljanjem teh vrzeli prispeva pregled k oblikovanju načrta za napredno, inteligentno in človeku usmerjeno proizvodno okolje. Acknowledgement The authors acknowledge the financial support from Ključne besede CAD–CAM integracija, Industrija 4.0, Industrija 5.0, the Slovenian Research Agency (Research Core Funding No. P2-0157). optimizacija poti orodja, umetna inteligenca (UI), teorija–kontekst– značilnosti–metodologija (TCCM) 336 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY-SA 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Comparison of 1D Euler Equation Based and 3D Navier-Stokes Simulation Methods for Water Hammer Phenomena Nejc Vovk − Jure Ravnik Faculty of Mechanical Engineering, University of Maribor, Slovenia jure.ravnik@um.si Abstract Water hammer phenomena in pipelines can induce significant transient pressure surges, leading to structural failures and operational inefficiencies. This study presents a comparative analyzis of two numerical approaches for simulating water hammer: a one-dimensional (1D) inviscid model with added friction based on the Euler equations and the method of characteristics, and a three-dimensional (3D) viscous model utilizing the Navier-Stokes equations in OpenFOAM. Benchmarking problems are solved first, then both methods are used to study a 3.4 km long DN400 pipeline subject to sudden pump failure by analyzing pressure surges, cavitation, and water column separation. The 1D model effectively predicts transient pressure waves and cavitation conditions with minimal computational cost, while the 3D model provides a detailed representation of multiphase flow dynamics, including cavitation bubble growth and collapse via the volume of fluid method. To mitigate adverse effects, a dynamic combination air valve is introduced, and its effectiveness in reducing pressure surges and cavitation is demonstrated. The results highlight the trade-offs between computational efficiency and accuracy in modelling water hammer events and underscore the importance of protective measures in pipeline systems. Keywords water hammer, cavitation, water column separation, CFD, Euler equation, Navier-Stokes equations, OpenFOAM, method of characteristics Highlights ▪ A 1D inviscid and 3D viscous simulation models were developed for water hammer simulations. ▪ The developed models were compared and used on an example of a 3.4 km long pipeline undergoing sudden pump failure. ▪ Advantages and disadvantages of inviscid versus viscous modelling are discussed. ▪ Results of simulation of cavitation bubble growth on a pipeline with and without a dynamic combination air valve are presented and compared. 1 INTRODUCTION systems and hydropower. Khan et al. [4] investigated hydropower penstocks, showcasing CFD’s role in modelling water hammer, The phenomenon of water hammer in pipelines, particularly during cavitation, and column separation. They performed transient CFD sudden flow blockages, has received significant attention in the field simulations for different load rejection conditions using Ansys CFX of hydraulic engineering. Water hammer is characterized by transient by modifying the URANS equations. pressure surges that occur when the flow of fluid is abruptly stopped The impact of pipe material properties on water hammer dynamics or altered, often leading to severe mechanical stress on pipeline has been studied extensively. Morvarid et al. [5] analyzed viscoelastic systems. pipe wall effects on pressure fluctuations using the method of Traditionally, water hammer analyzis has relied on one- characteristics and turbulence modelling. Protective systems like dimensional (1D) inviscid models based on the Euler equations hydropneumatic tanks were investigated by El-Hazek and Halawa with additional consideration of steady or unsteady friction and the [6], showing their effectiveness in damping pressure surges. method of characteristics [1]. These models provide a simplified Air entrainment has been explored as a mitigation strategy. Zhang representation of fluid dynamics, allowing for efficient simulations of et al. [7] demonstrated that air pockets can absorb pressure surges in pressure transients in pipelines and can include cavitation phenomena gravitational pipe flows. Additionally, Meng et al. [8] highlighted [2]. More recently, three-dimensional (3D) viscous models based the influence of flow velocity and pipe wall roughness, finding on the Navier-Stokes equations have been employed to provide a that higher velocities and roughness exacerbate pressure surges, more detailed representation of fluid behavior, including the effects underscoring their importance in pipeline design. of viscosity and turbulence. These models can simulate complex Nikpour et al. [9] emphasized the role of CFD in understanding interactions between fluid phases, such as cavitation bubble dynamics cavitation and its link to water hammer, crucial for preventing failures and water column separation. The choice between 1D and 3D models in hydraulic systems. They used Ansys Fluent and have shown often depends on the specific requirements of the analyzis, including CFD can be successfully employed in modelling of water hammer computational resources, desired accuracy, and the complexity of the phenomena. Ansys Fluent was also used by Han et al. [10] to show that system being studied. While 1D models are computationally efficient rapid valve closures amplify water hammer pressures, highlighting and suitable for preliminary assessments, 3D models offer a more the need for controlled valve operations. Zhang et al. [11] proposed comprehensive understanding of fluid dynamics in complex systems. a dynamic mesh simulation method to analyze transient behavior Numerical simulations of water hammer have been widely studied in pipelines with moving isolation devices, aiding in the design using computational fluid dynamics (CFD). Cao et al. [3] analyzed of resilient systems. Aguinaga et al. [12] proposed a mechatronic transient flow in pipelines, emphasizing its importance in urban water approach to control water hammer, integrating mechanical, electrical, DOI: 10.5545/sv-jme.2025.1340 337 Process and Thermal Engineering and hydraulic systems for better transient pressure management. Wu based on the observation that the solution of a first-order partial et al. [13] reviewed transient flow percussion theory, emphasizing its differential equation can be represented as a family of curves role in preventing water hammer in long-distance pipelines. Yang et (characteristics) in the domain of the independent variables. The al. [14] validated 3D CFD simulations as effective tools for analyzing method of characteristics is well suited for solving these equations valve-induced water hammer and its impact on pipeline integrity. as it can capture the shock waves and other discontinuities that arise The interaction between water hammer waves and centrifugal in the flow. When we combine the two equations with the Lagrange pumps has also been a subject of investigation. Zhang et al. [15] multiplier λ = ±ρc we obtain a system of two equations named C+ and explored the dynamic interactions between valve-closure water C−: hammer waves and pump components, revealing that these interactions can lead to substantial pressure variations and fluid- C vi , j1  vi1, j g H , 1 H  i j  i , j 2 fv2 1  i1, j : sgn(v induced forces on the pump. t c t D i1, j )  0, (4)   Malesinska et al. [16] analyzed the effects of sudden cross-section changes on water hammer, showing that abrupt geometry variations  vi , j1  vC i1, j g Hi , j  Hi , j 2 fv2 1 1 i 1, j :      sgn(v  0. (5) significantly influence transient pressure waves. Lupa et al. [17] t c t D i1, j ) reviewed water hammer impacts on hydraulic systems, highlighting The equations are discretized in space (∆x) and time (∆t), and the the importance of empirical validation for simulation reliability. solution is obtained by iterating through the grid points, where the In the present work we focus on the comparison of two methods time and position step are connected via ∆x = c∆t. The unknowns in for assessing flow conditions in a pipeline after a sudden discharge these equations are the flow velocity and piezometric head at location decrease: the 1D inviscid simulation with added friction model and i at time j+1: vi,j+1 and Hi,j+1. Piezometric head is calculated as the 3D viscous simulation. In the following subsections we present H = p/ρg+z. Fig. 1 shows the characteristics C+ and C− and the both methods and then apply them to the analyzis of a 3.4 km long intersections where we can calculate the values of the unknown pipeline, which experiences a sudden drop of discharge due to the fields. Index i denotes location along the pipe, index j denotes time. failure of the electrical grid to deliver power to the pumping station. The 1D solver is based on the method of characteristics and is capable of simulating water hammer in pipelines with various boundary conditions. The 3D model is implemented into OpenFOAM, [18], 3D Navier-Stokes solver, and supports cavitation and multiphase flow. By comparing the results we are able to identify the strengths and weaknesses of both methods. 2 METHODS 2.1 1D Solver When neglecting viscosity the Euler equation describes the momentum balance in the fluid system and at the same time the mass balance is described by the continuity equation. When taking the pipe Fig. 1. The characteristics C+ and C− deformation into account the mass conservation equation reads: Boundary conditions can be either known values of head or p  c2 v  0. (1) discharge. For example, if the discharge is known on the left side t x (i = 0), the boundary condition for head can be calculated from the Here the pressure wave speed is: Eq. (5) and reads: 1 v0, j1  v0 , c 1 D        (2)   Ee  ,  H  2  2  0, j1  H c 1, j  v0, j1  v f t 1, j  v1, j sgn(v with E the Young’s modulus, e the wall thickness, D the pipe diameter g D 1, j ).   and χ the compressibility. At the other side of the pipe (i = N) the head is known. If there is The law of conservation of momentum is established using the an open reservoir a there, then the head is equation to the elevation, force balance and reads as: and the discharge is calculated from the Eq. (4): v 1 p 2 fv2    sgn(v)  g sin , (3) HN 1, j1  zN 1, t  x D where sgn(v) is the sign of the velocity. The effect of viscosity is v v g H H 2 f t N  j  N j  ( v2 1, 1 , N 1, j  N , j )  N , j sgn(v c D N , j ). modelled with the Fanning friction coefficient f and the wall stress τw. The wall stress is calculated using the quadratic law of resistance as The friction factor is calculated from the steady state discharge. 1 Assuming known pipe length, the elevation difference between inlet w   fv2. 2 and outlet and the discharge of the friction factor can be calculated from Eq. (4). We developed the 1D model primarily to discover if conditions, 2.1.1 Method of Characteristics which would enable cavitation are present in the pipeline. Thus, when We solve the coupled Eqs. (1) and (3) using the method of pressure drops below the vapor pressure, we assume that cavitation characteristics, [19]. The method of characteristics is a numerical occurs. If the simulation continues beyond this time instant, the method for solving hyperbolic partial differential equations. It is cavitation is not modelled, but rather only the pressure is limited to 338 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering the vapor pressure. A detailed model of cavitation is implemented in equations for the mixture and introduces a volume fraction field to the 3D model. track the distribution of each fluid within the computational domain. The volume fraction field is a scalar field that represents the fraction 2.1.2 1D Model Validation of each phase in a given cell. The continuity equation is: To validate the 1D solver, we compared the results to the experimental m   mu  0, (6) data from the literature. The researchers [20,21] performed an t experiment by creating a pressure wave with a rapid valve closure. A 37.23 m long copper pipe (d = 22.1 mm) connected to two reservoirs where u is the flow velocity field and ρm the mixture density, was used. The pipe was installed so that it rises by 2.03 m in the flow calculated via the mixing rule from the liquid phase (index l) and gas direction. phase (index v) partial mass densities: The fluid flowed through the pipe at a speed of 0.3 m/s. The m v  1 l , (7) static pressure in the upstream reservoir was h = 32 m. A ball valve Here α is the gas phase volume fraction. Momentum conservation was installed at the end of the pipe, which closed in 0.009 s with is described by the Navier-Stokes equations: the help of a torsion spring. The propagation speed of the pressure waves is given as 1319 m/s. We used a time step of ∆t = 10−5 s and mu    muu  p  T  ft  , (8) a spatial step of ∆x = 1.319 cm using 2823 nodes. The friction factor was set to f = 0.009. In Figure 2 we compare the results of where p is the pressure and fσ = σκ∇α the source of momentum due to the simulations with our method and the experimentally measured surface tension between the gas and liquid phase, where σ = 0.07 N/m values [21] and numerical simulation with steady friction factor [20]. is the surface tension coefficient for water and water vapor and We find a good agreement, especially when the pressure wave arrives κ is the interface curvature [18]. Tensor T is the deviatoric part of first at the measurement point, as the error in pressure surge is less Cauchy stress tensor, which includes viscosity calculated using the than 2 %. This is the most important part for further calculations, as mixing rule, as well as the Reynolds stresses, arising from turbulence, the highest overpressure and the longest lasting under-pressure are measured at the first pressure wave in the pipeline. We notice that and need to be modelled. To close the system of equations, we use later in the simulation, the simulated wavefronts are sharper in our the Menter’s kOmegaSST turbulence model [29]. In the past, it has result compared to the experimental data. This is due to the use of been discussed, that standard two-equation turbulence models tend steady state friction factor, which does not account for the transient to overpredict the eddy viscosity in vapor-liquid mixture zones, nature of flow. Our results compare well with the numerical results of suppressing the natural unsteadiness of cavitation [30,31]. This has Wan et al. [20], who also used a steady state friction factor. The use of been solved by Reboud et al. [32], who introduced a correction an unsteady friction factor would improve the results, but this is not term for eddy viscosity, improving the modelling of phenomena the focus of our study. such as periodic vapor cloud shedding in turbulent cavitation flows [33]. Since our study focuses on pressure-wave propagation and column separation, rather than the detailed structure or dynamics of cavitation, we have not applied the Reboud correction. Moreover, the occurrence of periodic cavitation phenomena, such as cavity shedding, is not expected under the conditions considered in our simulations. The VoF method requires solving an additional equation for the volume fraction field α:    u  S   S  , (9) t where S+ and S− are source due to evaporation and condensation. To model turbulence, we chose the Menter kOmegaSST [29] turbulence model. Finally, we solve the energy equation, which includes the effects of phase change in the ST term: Tm E  km 1    1  E      T   Fig. 2. Comparison of the temporal development of the static head in the center of the pipeline t t c mu k  v m c mu , v,m where time zero corresponds to the moment when the valve starts to close  k      m  T     (mup 1 )  m ug 1  ST , (10)  mcp ,m  cv,m cv,m 2.2 3D Navier-Stokes Solver where Ek is the kinetic energy calculated as Ek = 1/2|u|2 and cp,m, For the 3D pressure surge calculations, we used the open-source cv,m the specific heats. The first term on the right-hand side includes software package OpenFOAM v11 [18], which allows simulations the thermal conductivity of the mixture, km, that incorporates the of multiphase fluid flows and includes models for cavitation. An molecular thermal conductivity as well as the turbulent thermal analyzis of the numerical results was carried out with the open-source conductivity. software package ParaView 5.12 [22]. We model cavitation using the Schnerr-Sauer et. al. [34] model, by To simulate multiphase flow, we employed the volume of fluid modifying the source terms S+ and S− in (9) as: (VOF) method [23–28], which is a numerical technique for capturing  3 1  2 max pv  p,0 the interface between two immiscible fluids. The VOF method S C   v , (11) Rb 3  models the interface by solving a single set of Navier-Stokes l SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 339 Process and Thermal Engineering the experimental traces display damped oscillatory tails after the   p p S  3 1  C    2 max  v ,0 c . (12) main impulse. The fact that Wang et al. observed the same repeatable Rb 3 l waveform across all BV2 valve closure cases strongly supports the Here Rb is the cavitation cloud diameter and pv is the vapor interpretation that these features are systematic instrumentation pressure. effects rather than random measurement noise. Further broadening of At last, the relation between pressure and density was computed the measured signal could also arise from the influence of elbows and using linear compressibility χ as fittings, which extend the effective propagation path and introduce partial reflections and scattering. Taken together, these structural and χm = αχv + (1−α)χl , (13) instrumental effects smear and lengthen the measured time history and compared with the rigid-wall model used here. dρm = χmdp (14) serves as the equation of state. In short, the comparison of the considered phenomena between 1D and 3D simulations goes as follows: • In 1D, no velocity profile develops, since velocity has one compo- nent that points downstream of the pipe. In 3D, we account for the viscosity, which, along with the no-slip boundary condition on the wall, develops a velocity profile. • In 1D, we solve for the wave propagation and do not account for cavitation that might occur as a result of sudden depressuriza- tion. In 3D, we model cavitation through extra terms in the energy equation. • In the 3D simulations we do not account for the deformation of the pipe walls. Fig. 3. Pressure head versus time for different mesh densities 2.2.1 3D Model Validation Wang et. al. [35] performed an experiment to investigate the water hammer phenomenon in a pipeline with a sudden valve closure. The pipeline is 5.692 m long, DN 40 and made of plexiglass. The Darcy-Weisbach friction factor of the system ranged between 0.034 and 0.055 (Fanning factor 0.0085 to 0.0138). In their study, multiple scenarios were investigated by varying the static pressures in Tank 1 and Tank 2. This approach allowed them to achieve different initial flow velocities corresponding to different static heads in the pipeline. For the purposes of comparison, we selected the case with an initial velocity of 1.148 m/s and a static head of 1.55 m in Tank 2. After closure, they measured the pressure head versus time. For the remaining details of the experimental apparatus, the reader is directed to the reference [35]. We recreated the experiment numerically using a 2D axisymmetric Fig. 4. Pressure head versus time for different time steps, for mesh with 7500 cells approach and compared different mesh densities (Fig. 3) and time steps (Fig. 4). We observe good convergence with both mesh density and time step, and the results are in agreement with the experimental 2.3 Pipeline Length data. The error in the prediction of the maximum pressure between simulation and experiment amounts to around 2 % for the coarse and The length of the pipeline is an important parameter in the water medium meshes, and 1.5 % for the fine mesh. The time step analyzis hammer analyzis. The longer the pipeline, the longer the time it shows that the solution does not change significantly when decreasing takes for the pressure wave to travel from the valve to the end of the the time step value tenfold. When the time step is decreased by a pipeline. This can result in higher pressure surges and longer duration factor of 100, numerical instability is observed. We attribute this to of underpressure. While for 1D simulations the pipeline length is the fact that for very small time steps approaching machine double- easily adjusted, for 3D simulations the computational cost increases precision limits, the transport phenomena become dominated by the with the length of the pipeline. Time step analyzis in the previous accumulation term. This term can reach disproportionately large section showed that good results are achieved when the pressure values due to the combination of very small time increments and wave does not travel more than one element within one time step, i.e. the accumulation of machine precision errors, which are of a similar time step is limited by the Courant-Friedrichs-Lewy (CFL) condition. magnitude to the time step itself. This sets the limit for the pipeline length in 3D simulations due to the The experimental pressure history, however, exhibits a computational effort required. substantially broader pulse following cavity collapse than predicted in our rigid-wall simulations. The duration of the experimental pulse is governed by the round-trip wave travel time 2L/ceff , where the 3 RESULTS effective wave speed ceff depends not only on fluid compressibility but also on the compliance of the pipeline and reservoir walls. These 3.1 The Pipeline elastic effects are absent from our rigid-wall model and therefore To test and compare the 1D and 3D approaches we simulate a shorten the simulated pulse relative to the experiment. In addition, pipeline with a length of L = 3408.45 m and a diameter of DN400, 340 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering which connects a pumping station and a reservoir and assumes an 3.2 1D Simulation Results electrical power failure, which stops the pump. The pipeline is made of 17 steel segments; its profile is shown in Fig. 5. The inner diameter In this section we present the results obtained using the developed of the pipe is 400.1 mm, the outer 406.4 mm, the wall thickness is 6.3 1D inviscid solver. We focus specifically on the time frame before mm. Height difference between the pumping station and the outlet cavitation occurs as the objective of this work is to identify the is z pump failure conditions that lead to cavitation. Detailed simulation 0 = 8.16 m. The Young’s modulus of E = 207·109 Pa is used. In normal operation we consider water (ρ = 999.84 kg/m3, χ = 4.54·10−10 including cavitation were done with the 3D viscous solver and Pa−1, ν = 1.005·10−6 m2/s) flowing at a rate of Q0 = 750 m3/h with an are presented in the next section. If cavitation does occur in the average velocity of v0 = 1.66 m/s. The pressure wave speed in these 1D simulation, we limit the pressure to vapor pressure and let the conditions, Eq. (2), is c = 1310 m/s, which gives a characteristic wave simulation continue. travel time of τ = L/c = 2.6 s. The friction factor is calculated for each pipe segment separately; the average is fave = 0.0067±2.79·10−5. 3.2.1 Grid Sensitivity Analyzis In Table 1 we show three sets of numerical parameters used in simulations. We compare the results of the simulations with the parameters A, B and C at time t = 3.4τ (Fig. 6). By calculating the relative difference between the head and velocity profiles we obtain the values shown in Table 1. The relative difference norm is calculated as:   2 f a 2  f b i i / f a )1 i  / , wh re i  2 i  e f is either head or velocity, i is the index of the node and a,b = A, B or a,b = B, C. We observe that the difference in results between numerical parameter sets B and C is very small, which shows that the numerical parameters do not affect the results. We use parameters B in all further simulations. Table 1. Time step, distance between nodes and the number of nodes used for sensitivity analyzis Fig. 5. A 17-segment pipeline profile with length of 3408.45 m Numerical Time step Δx = cΔt Number of Norm Norm parameters Δt [s] [cm] nodes head velocity We assume that electrical power supply fails, which stops the A 10−3 131 2627 pump. The discharge decreases from Q0 to Qmin = βQ0 in tstop. The B 10−4 13.1 26047 0.0413 0.0663 pressure wave travels from the pumping station to the reservoir, C 5·10−5 6.55 52067 0.0018 0.0029 where it reflects and travels back. At β = 0 the discharge is Qmin = 0 meaning that the power loss completely blocks the flow. This represents the worst-case scenario, as it results in the highest-pressure surges in the pipeline. For 0 < β < 1 the discharge is not completely blocked. We assume that between t0 and t = tstop linear upstream end discharge variation:   Q  Q t   Q t  0 (1  ) 0 1  t  t ( t stop )    stop  . (15)   Q0 t  tstop The pump manufacturers estimated the time in which the discharge stops after electrical power failure at tstop is 15 s to 20 s. To estimate the worst-case scenario, we make the following estimate. The pump is rotating at ω0 = 1488 rpm, has a moment of inertia of I = 3.614 kg/m2, its pump efficiency is η = 0.72 and has the electrical a) power of Pel = 132 kW and provides 40.2 m of pressure head. We first estimate the useful work P = ρgΔhQ0/η = 14 kW. This gives a normal operation torque of M0 = P/ω0 = 732 Nm. The pump stops when the kinetic energy of the rotating parts is converted to the potential energy of the water column. We assume that the average torque is half of the normal operation torque and write a differential equation for the angular acceleration: d P   . (16) dt 20I After integration up to time tstop we are able to estimate the time when the pump stops: t 2 2 0 I stop  1.5 s. (17) P b) This value serves as the worst-case scenario in the analyzis below. Fig. 6. a) Head, and b) velocity profile at t = 3.4 τ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 341 Process and Thermal Engineering a) b) c) d) e) f) g) h) Fig. 7. a), c), e), g) Absolute pressure, and b), d), f), h) flow velocity profiles for three stopping times and four-time instants: a), b) t = 0.5τ = 1.3 s , c), d) t = 1.5τ = 3.9 s ,e), f) t = 2.5τ = 6.5 s and g), h) t = 3.5τ = 9.1 s 342 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering 3.2.2 Discharge stops completely, β = 0 of the pipeline and travels back to the pump. In the case of a rapid We simulate the worst-case scenario, when the discharge stops interruption of the flow, we see that the water in the second half of the completely, β = 0 and consider three stopping times: tstop = 1.5 s, pipeline flows towards the pump and the pressure wave consequently which represent the worst case scenario, tstop = 15 s, which is the also moves towards the pump. When it reaches it at t = 2τ, it will cause pump manufactures estimate and t a sharp increase in pressure there. If we look at the pressure curve for stop = 25 s. Figure 7 shows absolute pressure and flow velocity profiles for four-time instances. At half tstop = 15 s, we can see that the pressure has now also fallen to the of the characteristic time, the pressure wave has travelled through vapor pressure in this case. In the case of tstop = 25 s, the pressure is half of the pipeline. In the case of a fast interruption of the flow, we still falling but has not yet reached the vapor pressure. Nevertheless, see that the flow has stopped in the first half of the pipeline and the the vapor pressure also occurs in this case, as can be seen from the pressure there has dropped to the vapor pressure. In the case of slow pressure curve at t = 2.5τ. At the same time, we see at t = 2.5τ that in interruption, the flow velocity in the first half of the pipeline only the case of tstop = 1.5 s the pressure in the part of the pipeline near the decreases, and the pressure drops, but not yet to the vapor pressure. pump has increased significantly, which is a result of the sudden stop At t = 1.5τ, the pressure wave has already been reflected from the end of the water flowing towards the pump. This phenomenon is greatly a) b) c) d) e) f) Fig. 8. Time traces of absolute pressure (left) and flow velocity (right) for three flow stopping times: a), b) tstop = 1.5 s, c), d) tstop = 15 s , e), f) tstop = 25 s SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 343 Process and Thermal Engineering attenuated in cases where the time for the flow to stop is longer, as it In Figure 9 we show the maximum absolute pressure that occurs occurs later when the water velocity decreases and then hits the pump in the pipeline as a function of the flow stop time tstop. We see that in at a much lower speed. the case of a very fast flow interruption, when the flow is interrupted Figure 8 shows the time histories of absolute pressure and before the pressure wave has travelled through the pipeline and flow velocity at the center of the pipeline and at the beginning of back, i.e. when tstop < 2τ = 5.2 s, a very large pressure increase occurs the pipeline near the pump. Green line denotes the values at the in the system. The increase corresponds to the Joukowsky pressure pumping station, orange the values at the middle of the pipeline. The ∆p = ρcv0 = 21.7 bar. If the flow is closed slower than 2τ = 5.2 s, results are shown up to 52 s, which is twenty characteristic times. the Joukowsky pressure is not reached. At about tstop = 4τ = 10.4 s The simulation results are shown for three flow stopping times, the maximum pressure drops and reaches the value of normal for tstop = 1.5 s, tstop = 15 s and tstop = 25 s. We notice considerable operation. Interestingly, if the stopping time corresponds to three differences in the progression. At a very fast stop, tstop = 1.5 s, the or four propagation times of the pressure wave through the system pressure wave travels back and forth along the pipeline and at the 4τ < tstop = 8τ, we see a further, smaller increase in the maximum selected location we observe a clear and distinct velocity fluctuation pressure. This is due to the interference between the propagating between positive values (flow from the pump to the end of the wave and the point at which the flow is interrupted. When pipeline) and negative values (flow back from the end of the pipeline interpreting this diagram, it must be emphasized that the maximum to the pump). The pressure behaves similarly, with the difference pressure in the system occurs after the moment when vapor pressure that in the part where the pressure drops, it quickly reaches the vapor has been reached in the system. Since the numerical model presented pressure and the growth of the water vapor column begins. The 1D in this section limits the pressure to vapor pressure and does not take simulation does not take cavitation into account, so the results in this cavitation into account, the values are too high. A more accurate part show a constant vapor pressure of 2337 Pa. When the flow stop 3D model, which is presented in the next section, shows that the is slower, there is interference between the pressure waves travelling maximum pressure is lower. back and forth along the pipeline and between the consequences of At the same time, in Fig. 9, we show the moment when the the slow decrease in velocity. In both cases, tstop = 15 s and tstop = 25 s pressure drops to vapor pressure depending on the time in which the the stopping time is longer than the characteristic time τ = 2.6 s. Due flow is interrupted. We note that regardless of whether the flow is to this interaction, we see that up to tstop there is no enormous increase interrupted very quickly (1.5 s) or slowly (45 s), the vapor pressure in pressure, but this increase is smaller. Even later, when a more is always reached. If the discharge reduction is very slow and lasts significant increase in pressure occurs, we see that the maximum longer than approximately 45 s, we see that pressure does not decrease pressure in the system is much lower than in the case of a rapid flow to vapor pressure and at the same time it does not increase anywhere interruption. in the pipeline. Given that the estimate of the flow interruption time obtained from the pump manufacturer indicates a time of about 20 s, it means that measures are needed in the proposed pipeline to mitigate the consequences of the formation of pressure waves due to the failure of the pump power supply. We see that the case when the flow is completely interrupted (β = 0) is the most demanding case from an engineering point of view, since vapor pressure occurs first in this case and the highest pressure achieved in the system is the highest. Therefore, the results at β = 0 can be considered as the worst possible scenario and if in a real system the pump allows some flow, this alleviates the situation. 3.3 3D Viscous Simulation Results 3.3.1 Reduced Length Pipeline a) The computational requirements for a 1D simulation of the full length (3.4 km) pipeline for 50 s using a million time steps are about 10 minutes on a single core. The computational requirements for a 3D simulation of the full-length pipeline are much higher, as the number of nodes in the 3D mesh would be at a minimum about 106 and the time step is limited by the CFL condition. The computational requirements for a 3D simulation of the full-length pipeline are about 1000 times higher than for a 1D simulation. This means that the computational requirements for a 3D simulation of the full-length pipeline are about 104 hours, which is prohibitive. To reduce the computational cost, we simulate a shorter pipeline (Lr = 120 m) with the same diameter (DN400) and the same discharge (Q0 = 750 m3/h) while at the same time at linearly reduced pressure drop. We calculated equivalent flow stopping times for the reduced pipeline so that their ratio to the characteristic time is the same as for the full-length pipeline, i.e. tstop,120 m/(Lr/c) = tstop,3400 m/τ. To capture b) the rapid transient dynamics of column separation and the subsequent Fig. 9. a) Maximal absolute pressure in the pipeline, and b) the moment when vapor pressure water hammer, a time discretization of at least one microsecond is reached versus flow stopping time tstop for different β was required, resulting in several million time steps for a full-length 344 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering pipeline simulation. By reducing the numerical pipeline length while Figure 13 shows the maximal length of the cavitation bubble and preserving equivalent stopping times, the total number of required the maximal absolute pressure for different pump stopping times. time steps was decreased, reducing computational time from several We see that the maximal length of the cavitation bubble is largest weeks to a few days per simulation. for the shortest pump stopping time and amounts to ≈ 0.55 m. The The results show that a large cavitation bubble forms behind maximal length of the cavitation bubble decreases with increasing the pump and due to energy lost for this process the pressure pump stopping time. The maximal absolute pressure is largest for the wave reaches smaller absolute pressure values as compared to the shortest pump stopping time and amounts to 7.4 bar. The maximal inviscid simulation results. Figure 10 shows the pressure curve just absolute pressure also decreases with increasing pump stopping downstream of the pump, for different pump stopping times. We time. The maximal absolute pressure is lower than in the inviscid find that the magnitude of the pressure surge is largest for stopping simulation, which is due to the energy lost for the cavitation process. time 1.5 s and amounts to 7.4 bar. We tested shorter stopping times as well and found similar maximal pressure surges for them. At a stopping time of 15 s we find that the magnitude of the pressure surge is lower and amounts to 6.3 bar. As the pump stopping time is further extended, the magnitude of the pressure surge decreases. We begin to observe the phenomenon when the pressure wave reflected from the outlet returns to the pump before cavitation occurs. The lower values of the pressure surge can be explained by analyzing the average velocity in the pipeline in Fig. 11. At the moment when the cavitation bubble collapses the flow velocity is lower in the case of longer pump stopping time. A long pump stopping time causes deceleration of the average water velocity in the pipeline, which can be seen in the enlarged image in Fig. 11. The pump stopping time can thus be interpreted as a relaxation rate, which determines the point in time when the cavitation bubble will start to grow. This is evident in Fig. 12, where the cavitation bubble length is shown. The cavitation Fig. 12. Length of cavitation bubble for different pump stop times bubble stops growing when the water velocity in the pipeline is zero. Fig. 13. Maximal length of cavitation bubble and maximal absolute pressure for different pump stopping times Fig. 10. Pressure time traces for different flow stopping times 3.3.2 Dynamic Combination Air Valve Simulation Both 1D and 3D simulations showed that in the case of sudden loss of electrical power supplying the pump a pressure surge occurs, vapor pressure is reached in the pipeline and cavitation occurs. One possible measure that could be taken to mitigate the consequences of the pressure surge and cavitation, is to install a dynamic combination air valve behind the pump outlet. The dynamic combination air valve opens when the pressure exceeds or is below a certain value and allows the water to flow out or air to be sucked into the pipeline. We simulate the pipeline with the dynamic combination air valve installed and compare the results with the case when the dynamic combination air valve is not installed. We study the use of ARI D-070 dynamic combination air valve [36] for which discharge versus pressure drop curves are available from the Fig. 11. Average flow speed for different flow stopping times manufacturer. The simulation domain is only the first 24 m of the SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 345 Process and Thermal Engineering pipeline with the dynamic combination air valve installed, details are in the analyzis of the pressure conditions downstream of the pump shown in Fig. 14. before the pressure surge is triggered, in Fig. 17. Here we can see the increase in pressure in the system, which is due to the ingress of air from the environment. The pressure rises above the saturation pressure, which prevents further growth of the cavitation bubble and causes its premature collapse. Fig. 15. Comparison of water vapor content in the pipeline with and without the dynamic combination air valve Fig. 14. Geometry of the 3D simulation domain with the dynamic combination air valve installed The boundary conditions used were defined as follows. The discharge at the inlet linearly had the turbulent flow profile shape and the discharge decreased to zero in the chosen flow stopping time tstop. No change in the pressure and the water vapor volume fraction was assumed to occur across the inlet surface. No slip boundary condition was used on the pipe wall. Wall functions were used for turbulent quantities. The flow velocity at the dynamic combination air valve is modelled based on the difference between the pressure in the pipeline and the atmospheric pressure:  K p Fig. 16. Pressure surge in the pipeline with and without the dynamic combination air valve atm  p u  , p  patm y |vent  a , (18)  0m / s, p  patm where K = 0.7 was calibrated based on the manufacturer’s pressure drop curve and ρa = 1.225 kg/m3 is the air density. The fluid volume fraction depends on the flow direction. When the pressure inside the pipeline exceeds the external pressure, the medium is water; when the external pressure is higher, air enters instead. The negative sign in front of K arises from the chosen coordinate system (see Fig. 14), where the inflow of air is defined in the negative y-direction. At this boundary, a zero pressure gradient is imposed. At the outlet, the pressure is fixed at p = 497,000 Pa, and outflow boundary conditions are applied to the velocity. In Figure 15 we show a comparison of pipelines with and without a dynamic combination air valve. The left Fig. 17. Pressure at the start of the pipeline, directly after the pump panel shows a comparison of the growth of the cavitation bubble. The right panel shows the entry of air through the dynamic combination air valve due to the pressure drop in the pipeline. The results are shown for an equivalent pump stop time t 4 CONCLUSIONS stop = 1.5 s. When the pump stops, we observe the growth of the cavitation bubble in both cases. We have developed and compared a 1D inviscid and a 3D viscous The ingress of air into the pipeline leads to an increase in the average numerical simulation tool to model the pressure surge and pressure pressure, so that the cavitation bubble collapses earlier in the case of drop in a pipeline subjected to a sudden suspension of flow. The using a dynamic combination air valve. main advantage of the inviscid simulation is that it can be performed The results of the pressure surge for the cases with and without with minimal computational resources for pipeline systems at an a dynamic combination air valve are shown in Fig. 16. The use of engineering level. It can correctly predict the pressure surge and the a dynamic combination air valve reduces the size of the pressure presence of the conditions that would lead to pressure dropping to surge by a third. The reason for the faster collapse of the cavitation vapor pressure. However, it does not model cavitation dynamics. bubble and thus the smaller size of the pressure surge can be found On the other hand, viscous 3D simulation is severely limited by 346 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering computational resources, making it impossible to simulate a pipeline [15] Zhang, W., Yang, S., Wu, D., Xu, Z. Dynamic interaction between valve-closure over its entire length. We have shown that with the necessary steps it water hammer wave and centrifugal pump. Proc Inst Mech Eng C-J Mech Eng Sci is possible to obtain good results for an equivalent short pipeline. The 235 6767-6781 (2021) DOI:10.1177/09544062211000768. main advantage of viscous simulations is the fact that it is possible to [16] Malesinska, A., Kubrak, M., Rogulski, M., Puntorieri, P., Fiamma, V., Barbaro G. Water hammer simulation in a steel pipeline system with a sudden cross section model water phase change and the influence of these changes on the change. J Fluids Eng 143 091204 (2021) DOI:10.1115/1.4050728. flow dynamics in a detailed 3D model. [17] Lupa, S.-I., Gagnon, M., Muntean, S., Abdul-Nour, G. The impact of water hammer This advantage becomes particularly clear when the case of on hydraulic power units. Energies 15 1526 (2022) DOI:10.3390/en15041526. simulation of the pipeline with a dynamic combination air valve. [18] Weller, H.G., Tabor, G., Jasak, H., Fureby, C. A tensorial approach to computational Such a simulation is not possible with an inviscid simulation but continuum mechanics using object-oriented techniques. Comp Phys 12 620-631 gives an important insight into the efficiency of such a valve as (1998) DOI:10.1063/1.168744. protection against pressure surges or cavitation. Our simulations have [19] Douglas, J.Jr., Russell, T.F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite shown that such a measure significantly alters the flow dynamics in element or finite difference procedures. SIAM J Numer Anal 19 871-885 (1982) the pipeline. The valve releases air into the system when the pressure DOI:10.1137/0719063. drops, which prevents the formation of a vacuum and consequently [20] Wan, W. Huang, W. Water hammer simulation of a series pipe system using prevents the pipe from flattening. At the same time, the valve allows the MacCormack time marching scheme. Acta Mech 229 3143-3160 (2018) air and water to be released from the pipeline at the moment when DOI:10.1007/s00707-018-2179-2. the pressure wave returns and the pressure rises. This reduces the [21] Bergant, A., Simpson, R.A., Vìtkovsky, J. Developments in unsteady pipe flow friction modelling. J Hydraul Res 39 (2001) 249-257 DOI:10.1080/00221680109499828. maximum pressure reached in the system and protects the pipeline [22] Ayachit, U., Geveci, B., Avila, L. The ParaView guide: Updated for ParaView version from rupture. 4.3, Technical report (2015). [23] Cazzoli, G., Falfari, S., Bianchi, G.M., Forte, C., Catellani, C. Assessment of the References cavitation models implemented in OpenFOAM® under DI-like conditions. Energy Proc 101 638-645 (2016) DOI:10.1016/j.egypro.2016.11.081. 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SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 347 Process and Thermal Engineering Data availability The data that support the findings of this study are prikazana validacija pristopov, nato obe metodi uporabimo za simulacijo available from the corresponding author upon reasonable request. 3,4 km dolgega cevovoda DN400, ki je izpostavljen nenadni okvari črpalke, kjer analiziramo tlačni udar s pretrganjem vodnega stoplca. 1D model Author contribution Nejc Vovk: Investigation, Writing - review & editing; Jure Ravnik: Methodology, Software, Supervision, Writing - original draft, Writing - učinkovito napoveduje prehodne tlačne valove in kavitacijske pogoje z review & editing. minimalnimi računskimi stroški, medtem ko 3D model zagotavlja podrobno študijo dinamike večfaznega toka, vključno z rastjo in kolapsom kavitacijskih mehurjev po metodi končnih volumnov. Za ublažitev neželenih efektov je Primerjava simulacij vodnega udara na podlagi predlagan kombinirani zračni ventil, za katerega smo dokazali učinkovitost pri 1D Eulerjeve enačbe in 3D Navier-Stokesove enačbe zmanjševanju tlačnega udara in kavitacije. Rezultati poudarjajo kompromise med računsko učinkovitostjo in natančnostjo pri modeliranju pojavov vodnega Povzetek Pojav vodnega udara v cevovodih lahko povzroči porast tlaka, kar udara in poudarjajo pomen zaščitnih ukrepov v cevovodnih sistemih. vodi do strukturnih okvar cevovodov. Ta študija predstavlja primerjalno analizo dveh numeričnih pristopov za simulacijo vodnega udara: enodimenzionalni Ključne besede vodni udar, kavitacija, pretrganje vodnega stolpca, (1D) neviskozni model z dodanim trenjem, ki temelji na Eulerjevih enačbah CFD, Eulerjeva enačba, Navier-Stokesove enačbe, OpenFOAM, metoda in metodi karakteristik, ter tridimenzionalni (3D) viskozni model, ki uporablja karakteristik. Navier-Stokesove enačbe v OpenFOAM simulacijskem okolju. Najprej je 348 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Analysis of Gas Flow Distribution in a Fluidized Bed Using Two-Fluid Model with Kinetic Theory of Granular Flow and Coupled CFD-DEM: A Numerical Study Matija Založnik - Matej Zadravec Faculty of Mechanical Engineering, University of Maribor, Slovenia matej.zadravec@um.si Abstract Fluidized bed systems are widely used in chemical and process engineering due to their excellent heat and mass transfer properties. Numerical modeling plays a crucial role in understanding and optimizing these systems, with the two-fluid model enhanced by the kinetic theory of granular flow (TFM-KTGF) and the coupled computational fluid dynamics-discrete element method (CFD-DEM) emerging as leading techniques. This study employs both models to simulate gas-solid interactions and evaluates their performance using a benchmark single-spout fluidized bed case validated against experimental data. Subsequently, the influence of particle presence on gas flow distribution through a non-uniform distribution plate is analyzed. The results show that the common assumption of proportional flow distribution based on the opening area fraction is inaccurate, particularly in the presence of particles. Both numerical models capture this behavior, with TFM-KTGF showing trends comparable to the coupled CFD-DEM approach but at significantly reduced computational cost. The findings highlight the importance of accounting for particle dynamics in distribution plate design and promote the TFM-KTGF approach as a promising alternative for large-scale simulations. Keywords fluidized bed, distribution plate, two-fluid model with kinetic theory of granular flow, coupled CFD-DEM, flow distribution Highlights ▪ Two models (TFM-KTGF and CFD-DEM) simulate gas-solid flow in fluidized beds. ▪ Models validated against experiments, showing good particle behavior prediction. ▪ Gas flow depends on particles, not just plate geometry. ▪ CFD-DEM captures local effects; TFM-KTGF is faster and predicts overall trends. 1 INTRODUCTION could successfully replicate key hydrodynamic features observed in the more computationally intensive coupled CFD-DEM approach. Fluidized bed systems are widely used in various industrial Similarly, Ostermeier et al. [5] compared both numerical models for applications due to their excellent heat and mass transfer gas-solid fluidized beds and reported consistent global trends between characteristics. Their applications range from chemical reactors and them. These findings highlight why the TFM-KTGF approach is drying processes to coating technologies and catalytic cracking. increasingly favored in both research and industry, offering reduced Despite these advantages, fluidized beds remain inherently complex computational times while maintaining comparable predictive systems, where interactions between the gas and solid phases must be accuracy. Additional studies have examined the capabilities and thoroughly understood to ensure efficient and stable operation [1,2]. limitations of both models through practical multiphase case studies With recent advances in computational modeling, the two-fluid of fluidized bed systems [6-9]. model with added kinetic theory of granular flow (TFM-KTGF) Flow distribution plays a crucial role in the proper functioning of and the coupled computational fluid dynamics-discrete element fluidized bed systems, directly influencing particle mixing and the method (CFD-DEM) have emerged as powerful tools for simulating effectiveness of heat and mass transfer. One of the most essential the complex behavior of fluidized bed systems. The TFM-KTGF components for ensuring optimal flow is the gas distribution plate approach treats both the gas and solid phases as interpenetrating (also referred to as the distributor), which governs the efficiency continua within the Eulerian-Eulerian framework, with kinetic of gas introduction into the particle bed. Numerous designs for theory of granular flow (KTGF) playing a key role in characterizing distribution plates have been proposed in the literature for various particle behavior and inter-particle interactions. In contrast, the applications [10,11]. A numerical analysis of gas flow distribution coupled CFD-DEM approach models the motion and interactions of across a distribution plate in a Wurster coater setup was performed individual particles in a Lagrangian framework, while the gas phase by Kevorkijan et al. [12], using the coupled CFD-DEM approach. is treated using computational fluid dynamics (CFD) in the Eulerian Their study revealed that both particle loading and inlet airflow rate framework. Although the coupled CFD-DEM approach provides significantly impact the uniformity of gas distribution across the a detailed resolution of particle dynamics, its complexity and high distribution plate. computational cost make it less practical for large-scale simulations Recent studies have further examined distributor performance, compared to TFM-KTGF [3]. pressure drop, and mixing efficiency in both industrial and laboratory Esgandari et al. [4] conducted a direct comparison between these systems, emphasizing that distributor geometry and particle two modeling approaches in fluidized single- and multi-spout bed properties critically influence hydrodynamic behavior inside the systems. Their study demonstrated that the TFM-KTGF approach system. Gonzalez-Arango and Herrera [13] used CFD to study how DOI: 10.5545/sv-jme.2025.1365 349 Process and Thermal Engineering the geometries of different gas-phase distributors inside the fluidized where the subscripts g and s denote the gas and solid phases, bed affect the pressure drop and particle mixing. Their findings respectively. Here, αi represents the volume fraction, ρi the density, highlight that both the physical design and material selection of vi the velocity, ps the solid pressure, τi the stress tensor, g the distribution plates can substantially impact system performance. The gravitational acceleration, and β the momentum exchange coefficient, optimization of a uniform distributor inside a fluidized reactor was which is computed using a drag model. The solid pressure and the carried out by Singh et al. [14] using CFD, providing an example of stress tensor of the solid phase are calculated as follows: the effective use of modeling tools for equipment optimization. Although distribution plates are often designed based on open ps  sss  2s 1 ess  2 s g0,sss , (5) area fractions, this geometric assumption neglects particle effects that can significantly modify local gas flow through resistance, clustering,  and particle-fluid interactions. While TFM-KTGF and coupled CFD- i    s vs  v T s    s vs , (6) DEM have been widely used to analyze fluidized bed hydrodynamics, where Θs is the granular temperature, ess is the restitution coefficient, few studies have investigated how particles influence gas distribution g0,ss is the radial distribution function, µs is the granular viscosity, and through non-uniform distribution plates. To address this gap, the λs is the bulk viscosity. The radial distribution function is a correction present study employs both TFM-KTGF and coupled CFD-DEM factor that accounts for the increased probability of particle collisions modeling to evaluate deviations from theoretical, area-based flow as the solid phase becomes dense. It is calculated using the following distributions and to provide insights for more accurate distribution equation: plate design. This approach improves our understanding of why 1 simplified assumptions sometimes fail in real-world applications,  especially when complex physical phenomena are involved. The g   s 0,ss  1 3  , (7)   analysis was conducted on a laboratory-scale fluidized bed equipped s ,max  where α with a distribution plate featuring non-uniform opening sizes, as s,max represents the packing limit. The granular viscosity, which is related to the particle motion and interactions, is calculated shown in Fig. 1. using the following expressions [15,16]: s  s ,kin  s ,col , (8)  sds   s s  2 s ,kin     ess  ess  sg  1 1 3 1      es  0,ss ( 6 3  5  , 9) s 4  s s ,col   ssdsg0,ss 1 ess   . (10) 5  where ds is the particle diameter. The bulk viscosity characterizes the material’s response to changes in pressure and stress and is calculated by the equation proposed by Lun et al. [17]: 4     s s  s sdsg (11) 0,ss 1 ess  . 3  Fig. 1. A distribution plate with non-uniform opening sizes in a laboratory-scale The granular temperature Θs is a parameter introduced into the fluidized bed system was used for the numerical analysis two-fluid model (TFM) through the KTGF. It quantifies the random fluctuations in particle velocity arising from collisions. The transport equation for the granular temperature is given as follows: 2 METHODS 3          2.1 Two-Fluid Model with Kinetic Theory of Granular Flow 2 t sss  ssvss    psI  In the TFM approach, both the gas and solid phases are treated as s  :vs  s s     , 1 ) s gs ( 2 independent continua, each governed by its own set of conservation where I is the identity tensor, κΘ is the diffusion coefficient, γ s Θ equations. For a non-reactive, transient, isothermal system composed s represents the collisional dissipation of energy, and ϕgs denotes the of spherical particles, the governing equations for mass and interphase energy transfer due to particle-gas interactions. The first momentum conservation are expressed as follows: term on the right-hand side of the granular temperature equation  corresponds to energy production; the second term represents the      v   t g g gg g 0, (1) diffusion of granular temperature; the third accounts for energy  dissipation due to particle collisions; and the final term describes   ss    ssvs   0, (2) the energy exchange between the gas and solid phases. The diffusion t coefficient is calculated using the following expression [15]:   g      t gvg  ggvgv 15d 12 g   ss s s  [1  2 4  3 s 4  4  3   1 3 5   gp g  ggg   vs  vg , (3) 16  sg0,ss  41 33 sg0,ss ], (13) 15    v      t s s s  ssvsvs where η is a dimensionless parameter calculated as:   sp ps  s  ssg   vg  vs , 1 (4)   1 ess . (14) 2 350 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering The collisional dissipation of energy represents the rate at which  energy is dissipated within the solid phase due to collisions between  K st Fn, t t min     l ,  Kus if s  0 particles. It is calculated using the following equation [17]: Fn,t ij ij   , (24)  Fn,tt max ij  Kus,0.001K stl  if s  0 121 e2   ss g 3 0,ss  s 2 s2 s d s . (15) s  s  st  stt , (25) Lastly, the interphase energy transfer is described by the following where Fn,t ij and Fn,(tt) ij are the normal forces acting on particle i at equation [18]: the current and previous time steps, ∆t is the time step size, s is the  contact overlap, and Kl and Ku are the loading and unloading contact gs  3s . (16) stiffnesses, determined by the particle properties as: In this work, the Syamlal-O’Brien drag model, which is based on the terminal velocity of particles, is employed [19]. The momentum  1 1 exchange coefficient β is calculated using the following equation:   for particle-particle contact 1 KL, p K 1 L, p  2 3 K  , (26) l  1 1  s gg  Re   C  s  for particle-wall contacts   vs  v , (17) 4v2 D v g r KL, p KL,w ,sds  r ,s  where vr,s is the terminal particle velocity, ds is the particle diameter, CD is the drag coefficient, and Res is the Reynolds number K K = l u , (27) for the solid phase. The drag coefficient, originally derived by Dalla e2 ss Valle [20], is calculated as follows: where subscripts 1 and 2 represent two contacting particles. The individual stiffnesses associated with a particle and a wall are 2   calculated as:   K C  4.8  l , p = EpL, (28) D  0.63 . (18) Re   s  Kl ,w = EwL, (29)  v   r ,s  where E is the Young’s modulus and L is the particle size. The The terminal particle velocity for the solid phase is calculated tangential contact force is modeled using the linear spring Coulomb using the following expression [21]: limit model. If the tangential force is assumed to be purely elastic, it v 2 can be calculated using the following equation: r ,s  0.5A  0.03Res  0.5 0.06Res   0.12Res 2B  A  A2 ,(19) with F ,t   ,tt ij,e Fij  K s , (30) A  4.14 g , (20) and where F ,(tt ) ij is the tangential contact force at the previous time step, Kτ is the tangential stiffness, and ∆sτ is the tangential overlap  for difference between two time steps. Since this model does not allow B 0.81.28 g  g  0.85   . 2.65 (21)  the tangential force to exceed Coulomb’s limit, the complete g for  g  0.85 expression is given as follows:  ,t 2.2 Coupled CFD-DEM F ,t F ij  min  F ,t ij e , Fn,t  ij,e (31) , ij,e , F ,t ij,e In the coupled CFD-DEM approach, the hydrodynamic behavior where µ is the friction coefficient. For a more detailed description of the gas within a gas-solid fluidized bed is modeled using CFD of the model, the reader is encouraged to consult the literature by to solve the conservation equations. The particles in the system are Walton and Braun [24] and Cundall and Strack [22]. modeled using the discrete element method (DEM), which governs The effect of fluid flow across the particle bed is modeled using their motion and interactions based on Newton’s second law of a two-way coupled CFD-DEM approach. The force Ff of motion [22]. In the CFD-DEM coupling, the solid volume fraction i consists drag and pressure contributions, as shown below: field is computed using a volumetric diffusion Lagrangian-Eulerian mapping, which smoothly distributes each particle’s volume to the Fp  Vpp, (32) surrounding cells while conserving the total solid phase volume. For particle i with mass m F 1 i, the following set of equations is solved: D  g Ap vg  vs,i (vg  vs,i ), (33) 2 m dv n i i Fc , (22) where V dt ij  F f i  F g i p is the particle volume, ∆p is the local pressure gradient, Ap j1 is the projected particle area in the direction of the flow, and vg − vs,i  ni is the relative velocity between particle i and the fluid. The Syamlal- I d i i  dt Mij, (23) O’Brien drag model was again used to calculate the momentum j1 where v exchange coefficient, as described in the equations shown above. i is the translational velocity of the particle, ωi is the angular velocity, Fc In both numerical models, the k − ω SST turbulence model was ij and Mij are the contact force and torque resulting from particle interactions with other particles and walls, Ff employed [25]. i is the force due to particle-fluid interactions, Fgi is the gravitational force, and Ii is the moment of inertia. Particle-particle and particle-wall 2.3 Model Validation interactions are described using a soft-sphere model, where normal The validation of both the TFM-KTGF and coupled CFD-DEM and tangential forces relative to the contact are modeled separately models was performed using a benchmark single-spout fluidized bed [23]. The normal contact force component is modeled using the case. The simulation results were compared with experimental data Hysteretic linear spring model [24], as shown below: reported by Van Buijtenen et al. [26]. In that study, particle velocities SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 351 Process and Thermal Engineering were measured using particle image velocimetry (PIV) and positron the coupled CFD-DEM approach at t = 6 s (Figs. 3a and d), t = 18 s emission particle tracking (PEPT) systems at two different heights: (Figs. 3b and e), and as a time-averaged profile (Figs. 3c and f). 0.05 m and 0.10 m from the bottom, as indicated by the red dashed lines in Fig. 2. Fig. 3. a), b) and c) Average particle velocity in the y direction obtained using the TFM-KTGF approach, and d) e) and f) coupled CFD-DEM approach at: Fig. 2. Schematic of the single-spout fluidized bed used for model validation, a) and d) t = 6 s, b) and e) t = 18 s, and c) and f) as a time-averaged result where the red dashed lines indicate the locations where particle velocities were measured Simulations were performed using two software packages: ANSYS It is evident that the particle velocities obtained using the TFM- Fluent [27] for hydrodynamics and ANSYS Rocky [28] for DEM. A KTGF approach exhibit a very uniform profile throughout the uniform numerical mesh consisting of 58,000 hexahedral elements simulation. This behavior arises from the nature of the TFM-KTGF was used for both models. The system under study contained 12,000 model, in which particles are treated as a continuum phase. In this spherical glass particles, each with a uniform diameter of 3 mm and a framework, there is no discrete mechanism driving the fluid to interact density of 2505 kg/m3. The restitution coefficients for all interactions with particles in a way that would cause substantial variations in the were set to 0.97, while the friction coefficients for particle-particle velocity profile over time. In contrast, the velocity profiles obtained and particle-wall interactions were set to 0.1 and 0.3, respectively, from the coupled CFD-DEM approach show a noticeable change consistent with previous studies [26,29,30]. as time progresses. This is because the direct interactions between particles and the airflow influence particle velocities, causing the Table 1. Simulation parameters used for the validation study profile to evolve dynamically over time. The time-averaged particle velocity profiles in y direction, along Parameter Value the length of the fluidized bed at heights of 0.05 m and 0.10 m from Material Glass the bottom, were compared with experimental data. The results are Number of particles, N 12000 shown in Fig. 4. Good agreement between the numerical model Particle diameter, ds 3 mm predictions and the experimental data is observed, particularly at the Particle density, ρs 2505 kg/m3 height of 0.05 m from the bottom. Both numerical models produced Restitution coefficient, ess 0.97 similar velocity trends, demonstrating the validity of both approaches Particle-particle friction coefficient, μp‒P 0.1 for simulating fluidized bed behavior. Particle-wall friction coefficient, μp‒w 0.3 Figure 5 shows the time-averaged particle velocity vectors Spout velocity, vsp 43.5 m/s obtained from PIV and PEPT measurements by Van Buijtenen et Background velocity, vbg 2.4 s al. [26], along with the corresponding results from this study. Good Total simulation time, t 20 s agreement was observed between both the TFM-KTGF and coupled CFD time step, ΔtCFD 10‒5 s CFD-DEM approaches and the experimental data. In the coupled CFD-DEM approach, intensive circulation patterns are clearly The spout and background velocities at the inlet were set to 43.5 visible, closely matching the experimental observations from PIV m/s and 2.4 m/s, respectively, with the pressure outlet set to ambient and PEPT. In contrast, the TFM-KTGF results show less pronounced pressure. All walls were assigned with no-slip boundary conditions. circulation. The slight differences observed between the PIV and The total simulation time for both models was set to 20.0 s, with a PEPT vector fields are attributed to challenges inherent in the CFD time step of 10−5 s, while the DEM time step was calculated experimental setup, as described by Van Buijtenen et al. [26]. automatically within ANSYS Rocky based on the hysteretic linear In summary, both the TFM-KTGF and coupled CFD-DEM spring model [31]. A summary of all simulation parameters used in approaches for simulating single-spout fluidized beds provide this study is presented in Table 1. satisfactory predictions of flow dynamics when compared with Figure 3 compares the particle velocity profiles in y direction at experimental results obtained using PIV and PEPT, despite different simulation times. Figures 3a, b and c show results from the slight deviations. Both models showed good agreement with the TFM-KTGF approach, while Figs. 3d, e and f present results from experimental particle velocity data, as shown in Fig. 3, confirming 352 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering Fig. 4. Time-averaged particle velocity profiles in y direction along the length of the single-spout fluidized bed system at heights of a) 0.05 m, and b) 0.10 m from the bottom Fig. 5. Time-averaged particle velocity vector fields in the single-spout fluidized bed system; a) velocity PIV [26], b) velocity PEPT [26], velocity TFM-KTGF, and d) velocity coupled CFD-DEM their reliability of these models for further analyses of flow manner while maintaining the computational framework of the two- distribution through a non-uniform distribution plate. fluid model. The interaction parameters, including restitution and friction coefficients for particle-particle and particle-wall contacts, 2.4 Flow Distribution Analysis were based on literature values [32] and are summarized in Table 3. The flow distribution analysis was conducted on the geometry of a laboratory-scale fluidized bed system with a non-uniform distribution plate, as shown in Fig. 6. The colored sections on the distribution plate (Fig. 6c) represent different groups of openings: cyan indicates 4 mm, magenta 3.5 mm, red 3 mm, blue 1 mm, and green 2 mm. To reduce computational cost and simulation time, the geometry was symmetrically reduced to a quarter section, while preserving the essential flow characteristics. As in the validation study, ANSYS Fluent [27] and ANSYS Rocky [28] were used to simulate multiphase flow using the TFM-KTGF and coupled CFD-DEM numerical models, respectively. Both approaches used the same numerical mesh, consisting of 1.5 million polyhedral elements. The simulations were performed with a total of 300 g of zeolite particles, with diameters ranging from 0.5 mm to 5 mm. The detailed particle size distribution is provided in Table 2, and the bulk particle density was set to 770 kg/m3. These values were selected Fig. 6. a) Laboratory-scale fluidized bed system, b) the simplified geometry, based on the work of Zadravec et al. [32] to reflect realistic conditions and c) distribution plate geometry used in the analysis in a laboratory-scale fluidized bed system. In the TFM-KTGF approach, where particles are represented as a continuous phase, the Air was introduced into the system through the bottom inlet particle size distribution was first determined using the population at volume flow rates ranging from 50 m3/h to 70 m3/h, increasing balance model (PBM). The discrete method was applied, in which in increments of 5 m3/h to examine the effect of inlet velocity on the overall particle size distribution is discretized into a finite number flow distribution. Ambient pressure was applied at the outlet, and of size classes. From this distribution, the Sauter mean diameter was symmetry boundary conditions were imposed on the cut planes to evaluated and used in the TFM-KTGF model. This ensures that the represent the quarter geometry. All other walls were assigned no-slip influence of the particle size distribution is captured in an averaged boundary conditions to accurately capture near-wall interactions. SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 353 Process and Thermal Engineering The total simulation time for each case was set to 5 s, with a CFD 3 RESULTS AND DISCUSSION time step size of 10−4 s, while the DEM time step was calculated automatically, as in the validation case [31]. This ensured sufficient To thoroughly examine the effect of particsles on airflow distribution temporal resolution to capture flow evolution and particle behavior through the fluidized bed distribution plate, multiple simulation cases throughout the system. were performed. These included simulations of the system without particles, to establish the baseline flow distribution in an empty Table 2. Zeolite particle size distribution geometry, and simulations with particles using the TFM-KTGF and Particle size [mm] 0.5 1.0 2.0 3.15 5.0 coupled CFD-DEM models to assess the influence of particles on Mass fraction [%] 0.5 0.8 3.5 77.3 17.9 flow distribution. The objective was to compare the simulation results with the Table 3. Restitution and friction coefficients used in this analysis theoretical flow distribution, which assumes that air distributes proportionally according to sthe opening fraction of each hole size Particle-Particle Particle-Wall group on the distribution plate. In other words, the flow rate through Restitution coefficient 0.1 0.5 each group of openings was assumed to correspond to its relative area Friction coefficient 0.6 0.5 fraction on the plate. Figure 7 compares the theoretical flow distribution, based on The complete set of parameters used in flow distribution the open-area fraction, with the simulation results under different simulations is summarized in Table 4. operating conditions. The solid lines represent the theoretical flow fractions for each group of openings, while the symbols and dashed Table 4. Simulation parameters used for the flow distribution study lines correspond to the simulation data at various inlet flow rates. Parameter Value Results are presented for both an empty system (without particles) and Material Zeolite a fluidized system (with particles), evaluated using two multiphase Total mass of particles, ms 300 g modeling approaches: TFM-KTGF and coupled CFD-DEM. The Particle diameter, ds Table 2 figure illustrates that the actual flow distribution deviates from the Particle density, ρs 770 kg/m3 theoretical prediction even in the absence of particles, with these Restitution coefficient Table 3 deviations becoming more pronounced when particles are introduced. Friction coefficient, μ Table 3 In particular, the system containing particles shows clear shifts in Inlet volume flow rate, V [50, 55, 60, 65, 70] m3/h the flow fractions through each opening group (e.g. 3 mm, 3.5 mm Total simulation time, t 5.0 s and 4 mm opening groups experience increased flow relative to the CFD time step, ΔtCFD 10−4 s geometric assumption, while the 1 mm and 2 mm groups exhibit reduced flow). Furthermore, increasing the inlet air flow rate slightly Fig. 7. Flow distribution through distribution plate openings of different sizes at various inlet air volume flow rates 354 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Process and Thermal Engineering alters the distribution, indicating that operating conditions influence TFM-KTGF approach treats the particle phase as a continuum, which how gas is channeled through the distributor. smooths out these details but still accurately represents the overall These findings highlight that particle interactions introduce behavior on a global scale. A key advantage of the TFM-KTGF additional resistance and non-uniformity in local flow paths that approach is its computational efficiency: in this study, it completed cannot be captured by geometric assumptions alone, emphasizing the the simulations approximately five times faster than the coupled importance of modeling approaches that explicitly account for the CFD-DEM approach on the same hardware, making it a practical particle phase. choice for larger systems. A broader overview of the flow distribution is presented in Fig. 8, where the flow fractions for each opening size group are averaged across all inlet air flow rates. The results again confirm a significant mismatch between the theoretical distribution and the actual simulated distribution, particularly in the presence of particles. Differences between the results obtained using the TFM-KTGF approach and those from the coupled CFD-DEM approach are also evident. These differences stem from the fundamental modeling approaches: TFM-KTGF treats the particle phase as a continuum, whereas the coupled CFD-DEM explicitly tracks individual particles. This distinction influences not only the flow predictions but also the computational performance of each model. From a computational perspective, the TFM-KTGF approach proved to be significantly more efficient. Because it does not resolve individual particle trajectories, it requires far fewer computational resources than the coupled CFD-DEM model, which solves the Fig. 8. Flow distribution through distribution plate openings of different sizes, averaged across all inlet air volume flow rate cases equations of motion for each particle. In our simulations, the TFM- KTGF model completed each run approximately five times faster While the coupled CFD-DEM approach captures particle-scale than the coupled CFD-DEM model on the same hardware. This effects with high fidelity, its computational cost makes applications substantial difference in computational time underscores the appeal to large or industrial-scale fluidized beds impractical with current of TFM-KTGF for large-scale simulations involving high particle resources. Conversely, the TFM-KTGF model, though efficient, counts. relies on a continuum treatment of the granular phase, which may smooth out local heterogeneities such as clustering or jet instabilities. These differences highlight that each model has inherent limitations, 4 CONCLUSIONS and their predictions should be interpreted within the context of In this study, we investigated gas flow distribution through a non- laboratory-scale systems. uniform distribution plate in a laboratory-scale fluidized bed system It should be emphasized that the present simulations were using two numerical approaches: TFM-KTGF and coupled CFD- performed for laboratory-scale geometries, and direct extrapolation DEM. Both approaches were employed to examine their behavior of the findings to full industrial-scale fluidized beds requires and predictive capability in a laboratory-scale fluidized bed. CFD- caution. Although the observed trends provide valuable guidance for DEM provides detailed particle behavior, capturing particle-fluid distributor plate design, additional validation at pilot or industrial interactions and heterogeneities, while TFM-KTGF efficiently scale would be necessary to fully confirm the transferability of these predicts global flow trends. Using both methods allows us to evaluate results. Future work should therefore focus on bridging the gap how particle effects influence gas distribution and to assess the between laboratory validation and industrial application. validity of the continuum assumptions in the TFM framework. Both models were validated against experimental data from a single-spout References fluidized bed and demonstrated satisfactory agreement in predicting [1] Daizo, K., Levenspiel, O. Fluidization Engineering, 2nd ed. Butterworth Publishers, particle velocity profiles and overall flow behavior. 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Fluidization, Solids Handling, and Processing, William Acknowledgements The authors would like to express their sincere Andrew Publishing, Westwood 209-235 (1999) DOI:10.1016/B978-081551427- gratitude to the professors, assistants, and colleagues at the Faculty of 5.50006-5. Mechanical Engineering, University of Maribor for their valuable support [12] Kevorkijan, L., Zadravec, M. Numerične simulacije toka tekočine in delcev v and constructive discussions throughout this work. We also gratefully granulatorju z lebdečim slojem. Anali PAZU 12 17-30 (2022) DOI:10.18690/ acknowledge the financial support provided by the Slovenian Research analipazu.12.1.17-30.2022. Agency (ARRS) under the framework of Research Program P2-0196: Power, [13] Gonzalez-Arango, D.I., Herrera, B. Evaluation of the flow distribution system influence on mixing efficiency in a fluidized bed for low-size Geldart B particles: Process, and Environmental Engineering. A case study using CFD. S Afr J Chem Eng 52 325-335 (2025) DOI:10.1016/j. sajce.2025.03.007. Received: 2025-04-23, Revised: 2025-09-09, Accepted: 2025-09-24 [14] Singh, R., Marchant, P., Golczynski, S. Modeling and optimizing gas solid as Original Scientific Paper 1.01. distribution in fluidized beds. Powder Technol 446 120145 (2024) DOI:10.1016/j. powtec.2024.120145. Data availability The data that support the findings of this study are [15] Syamlal, M., Rogers, W., O’Brien, T. MFIX Documentation: Theory Guide US Department of Energy, Morgantown (1993) DOI:10.2172/10145548. available from the corresponding author upon reasonable request. [16] Gidaspow, D., Bezburuah, R., Ding, J. Hydrodynamics of circulating fluidized beds, kinetic theory approach. 7th Fluidization Conference 75-82 (1992). Authors contribution Matija Založnik: Formal analysis, Investigation, [17] Lun, C., Savage, S., Jeffrey, D., Chepurniy, N. 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[27] ANSIS Inc. Ansys® Academic Research, Release 23.1, Help System, Solver s sklopljenim CFD-DEM pristopom a pri bistveno nižjih računskih časih. Theory, Multiphase Flow Theory, ANSIS (2023). Ugotovitve poudarjajo pomen upoštevanja dinamike delcev pri oblikovanju [28] ANSIS Inc. Ansys® Academic Research, Release 23.1, Help System, DEM-CFD distribucijskih plošč ter promovirajo uporabo TFM-KTGF kot obetavno Coupling Technical Manual, ANSIS (2023). alternativo za simulacije na velikih sistemih. [29] Jajcevic, D., Siegmann, E., Radeke, C., Khinast, J.G. Large-scale CFD-DEM simulations of fluidized granular systems. Chem Eng Sci 98 298-310 (2013) Ključne besede lebdeči sloj, distribucijska plošča, model dveh tekočin s DOI:10.1016/j.ces.2013.05.014. kinetično teorijo granularnega toka, sklopljen CFD-DEM, distribucija toka 356 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 © The Authors. CC BY 4.0 Int. Licencee: SV-JME Strojniški vestnik - Journal of Mechanical Engineering ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Fatigue of Triply Periodic Minimal Surface (TPMS) Metamaterials – a Review Žiga Žnidarič , Branko Nečemer, Nejc Novak, Matej Vesenjak, Srečko Glodež University of Maribor, Faculty of Mechanical Engineering, Slovenia ziga.znidaric@um.si Abstract A review of the fatigue behavior of triply periodic minimal surface (TPMS) metamaterials with consideration for their fabrication is presented in this paper. The review analyses the most common TPMS geometries used due to their mechanical characteristics. Production methods and the base materials used are presented with the key advantages and drawbacks. Furthermore, the mechanical characteristics of cellular structures with emphasis on TPMS geometries are described. Lastly, the state-of-the-art findings of their fatigue behavior are analyzed and explained. Based on the findings in this article, cellular geometries based on TPMS are superior to conventional cellular structures when comparing their fatigue life. Because of the smooth transitions between struts or surfaces, the stress distribution is much more uniform without stress concentration zones. Keywords cellular structures, TPMS metamaterials, production technologies, mechanical characterization, fatigue behavior Highlights ▪ The general characteristics of cellular structures, with focus on TPMS geometries, are explained. ▪ Fabrication techniques used to produce TPMS metamaterials are briefly introduced. ▪ Fatigue behavior of TPMS metamaterials is presented and compared. 1 INTRODUCTION metamaterials [5], they can be further categorized in more detail as shown in Fig. 2. Porosity or relative density are typically used Cellular structures are materials composed of solid edges or faces to describe metamaterials. Porosity refers to the fraction of the that are arranged in patterns to fit a certain space. They are inspired material’s volume that is made up of voids or pores, while relative by porous materials found in nature, such as bone, wood, coral and density compares the density of the cellular material to that of the honeycombs [1]. Their main benefits are high strength and excellent solid material [2,6]. Additionally, plateau stress, densification strain energy absorption at a relatively low weight. Due to these qualities, and energy absorption (SEA) are critical in characterizing the cellular materials are being analyzed and applied in industries like mechanical response of these materials [7]. They can achieve an aerospace, sports, automotive and medicine [2,3]. Cellular materials auxetic response with the right combination of cell topology and can be broadly categorized into three types. The first are open- morphology. This means that they have a negative Poisson’s ratio, so cell structures (Fig. 1b). The voids and pores inside the structures when a compressive force is applied, the material contracts laterally, are interconnected, meaning a fluid could flow freely through unlike typical materials that expand. This behavior leads to benefits the material. In contrast, closed-cell structures (Fig. 1c) feature such as increased stiffness, high energy absorption and enhanced isolated voids. The third category are honeycomb cellular structures, shear stiffness [8]. Geometries that exhibit this type of response are comprised of repeating cells in two dimensions that resemble the typically strut-based lattices and chiral structures. They are designed hexagonal pattern found in natural honeycombs (Fig. 1a) [4]. to be lightweight yet highly efficient in distributing forces. A negative However, due to the increasing number of newly engineered aspect of these types of structures is their sharp transitions in areas materials, designed to exhibit unusual or tunable mechanical, where their struts meet. This can negatively affect their mechanical acoustic or electromagnetic properties that are known as properties, especially whenever dynamic loads are applied [9–12]. a) b) c) Fig. 1. a) Honeycomb, b) open-cell and c) closed-cell cellular structures, reproduced from [4] DOI: 10.5545/sv-jme.2025.1369 357 Mechanics Another type of architected cellular structures that do not have this porosity and stiffness, making them ideal for lightweight structures drawback are TPMS geometries, which are usually geometrically or scaffolds in tissue engineering [27]. Additionally, their shapes more complex but offer highly efficient structural performance such and continuity influence local stress distributions and fatigue as compressive strength, elastic modulus and energy absorption due resistance. For example, smooth and continuous surfaces reduce to their smooth surface transitions [13,14]. stress concentrations, while sharp transitions act as fatigue crack Because of their unique properties, they have gained attention in initiation sites. Euler and Lagrange first studied the theory behind various applications, e.g. energy absorption, thermal management, minimal surfaces in a three-dimensional space. The name refers to fluid mixing and biomedical engineering [15–18]. With the proper surfaces with a mean curvature of zero at every point [31]. Meusnier production method, unit cell selection and grading, TPMS structures discovered the most primitive examples of this with the help of an were shown to closely mimic human bone’s mechanical properties, analytical approach to calculate the mean curvature of a catenoid such as strength, stiffness and porosity [19]. This makes them viable and helicoid [32]. These surfaces can be described using a general for manufacturing personalized bone implants [20,21]. Additionally, implicit equation of the form: these mechanical properties make them suitable for applications as f (x, y, z) = C. (1) energy absorbers, such as components designed to assure controlled deformation during a crash in the transport industry [22]. TPMS Equation (1) defines a surface in a three-dimensional space. For metamaterials are not only used in mechanical applications. Certain it to exhibit the mean-zero curvature and periodicity characteristic of geometries are being investigated for use in the static mixing of fluids. TPMS, the function must be expressed using specific trigonometric Their geometries enhance turbulence and mixing efficiency, making formulations. Some of the most common examples are presented them suitable for pH control and inline coagulation applications in Table 1. These trigonometric functions divide space into two in water treatment systems [23]. Some TPMS configurations are domains as the equation approaches zero. The resulting domains increasingly being integrated into heat exchangers. They improve can be identical in shape or differ from one another. By adjusting heat transfer efficiency due to their high surface area to volume ratio, the constants within the function, the topology of the surface can which leads to better heat transfer and thermal efficiency [17,24–27]. be modified, resulting in different TPMS configurations. Because these types of structures are fully defined with an equation, they allow for great freedom when modelling [32-34]. The first triply periodic minimal surfaces were described by Schwarz in 1865 [31] and Neovius in 1883 [35]. They are defined as continuous, non- self-intersecting structures that extend infinitely in three principal directions. They exhibit periodicity and crystallographic space group symmetry [36]. Using this definition, Alen Schoen built upon Schwarz’s foundational discoveries. The most common TPMS geometries with their implicit equations are presented in Table 1. The first surface model that fits these requirements is called Schwarz Primitive. It has two intertwined congruent labyrinths, each with the shape of an inflated tubular version of the simple cubic lattice [37]. If we replace the shape of the lattice with a diamond bond structure, we get the so-called Diamond surface [37]. The Gyroid was discovered by Alan Schoen in 1970 and is an infinitely connected triply periodic Fig. 2. Categorisation of cellular materials, reproduced from [28] minimal surface. It is an intermediate between the aforementioned Diamond and Schwarz Primitive surfaces. This geometry is found in In addition to the mechanical and thermal properties of TPMS butterfly wings and is widely used in fluid transport and mixing [27]. metamaterials, like other cellular materials, understanding their long-term mechanical performance under cyclic loading conditions Table 1. Common TPMS geometries and their corresponding equations remains essential [29]. Many of their main applications include bone implants and crash absorbers. These components are often Name Equation Model subjected to repeated mechanical loads. Under such conditions, fatigue behavior becomes a critical design consideration, since Schwarz failure may occur even before the loads reach the static mechanical Primitive cos(x) + cos(y) + cos(z) = 0 limits of the structure [30]. Fatigue analyzis of TPMS metamaterials is therefore vital in ensuring their long-term performance. Research on the fatigue behavior of cellular materials has slowly increased cos(x) · cos(y) · cos(z) ‒  Diamond over the past years. However, TPMS metamaterials only have a ‒ sin(x) · sin(y) · sin(z) = 0 handful of scientific publications that have analyzed their response under cyclic loading. This paper aims to review different types of TPMS geometries, production methods, and mechanical and fatigue sin(x) · cos(y) + sin(y) · cos(z) +  Gyroid properties to better understand their advantages and limitations. + sin(z) · cos(x) = 0 Lastly, outlines for future research are given. I-Wrapped cos(x) · cos(y) + cos(y) · cos(z) +  2 TPMS GEOMETRIES Package (I-WP) + cos(z) · cos(x) = 0 2.1 Most Common TPMS Geometries The design and geometries of TPMS structures can be tailored Lastly, the I-Wrapped Package (I-WP) was described by Alan for specific properties. They can be adjusted to achieve desired Schoen in 1970. It is characterized by its two to four self-intersecting 358 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics Schoenflies surfaces [37]. In engineering applications, TPMS variations can either mitigate or amplify local strain accumulation metamaterials are typically designed with relative density ranging during cyclic loads. from 0.1 to 0.5, and unit cell sizes commonly falling within the range In addition to their mechanical response, these geometrical of 1 mm to 6 mm, depending on the chosen manufacturing process choices also determine how TPMS structures can be produced. [38-41]. For example, sheet-based designs have thin walls needing higher resolutions to achieve smooth transitions when compared to skeletal- 2.2 TPMS Structure Generation based structures. Graded or multimorphology designs add further The above presented geometries are based on surfaces. To be able challenges, as variations in cell size and topology can prove too to test them and make physical specimens, they must be assigned challenging for certain manufacturing processes. Because of this, the a volume. There are two ways of generating a volumetric model next section presents the main technologies used to produce TPMS from the sheet-based geometries. In the first instance, a thickness is structures. assigned to the surface model. With altering the wall thickness, the relative density of the structure changes. These geometries are called a) b) sheet-based TPMS structures. The second method uses the implicit surfaces and divides the domain around them into two solids [42]. Depending on the chosen TPMS design, the resulting domains can be identical or different from one another. By adjusting the constant C in Eq. (1), it is possible to control the domains shape. Figure 3 shows how the resulting geometries differ, depending on which method was used to generate them. Further modifications made by changing the values in the implicit functions, while still retaining smooth transitions between cells can be made easily. The first modification that can be made is changing the relative density. As previously mentioned, it can be altered by changing the C constant. Suppose C is not constant, and we assign a function that changes its value depending on the location in the coordinate system. In that case, we c) can achieve graded structures with different relative densities and mechanical properties throughout their geometries [20]. Fig. 4. Designed models of gradient samples; a) in relative density, b) in heterostructure and c) in cell size. Reproduced from [40] 3 PRODUCTION TECHNOLOGIES OF TPMS STRUCTURES Because of their complexity, TPMS structures can only be produced with limited technologies. The most common and widespread is Fig. 3. Difference between: a) skeletal-TPMS metamaterials, additive manufacturing (AM). It enables the creation of complex and b) sheet-TPMS metamaterials, adapted from [43] geometries that are difficult or impossible to achieve with traditional methods. Even with the advancements in AM technologies, the Another type of grading can be achieved by changing the size porous features and complex geometries still represent a challenge of individual cells. This changes the surface area and pore sizes for layer-by-layer manufacturing [27]. while retaining a constant relative density. Liu et al. [40] described how this is achieved mathematically and is showcased in Fig. 4. It 3.1 Powder Bed Fusion – Laser Beam/Metals (PBF-LB/M) was observed that cell-size adjustments do not cause as substantial of a change in the mechanical properties of TPMS metamaterials as PBF-LB/M, sometimes referred to as selective laser melting (SLM), density gradients do. This is because larger cells negatively affect is a type of laser powder bed fusion (LPBF), which falls under the the mechanical properties, which is also where the geometries failed broader category of powder bed fusion (PBF) technologies. In PBF- in testing. The last method is cell type grading or multimorphology. LB/M fabrication, a high-power laser is used to fully melt metallic It is obtained by transitioning between different types of TPMS powders to create structures. Not all of the powder gets melted. The geometries while retaining smooth surface transitions. This is done remaining media supports the next layers [27]. With PBF-LB/M, by dividing the volume into different subdomains. If the equations both the size of the laser spot and material grain size influence the that describe the unit cells have the same value at the intersections of quality of the final product. The most commonly used materials in these domains, we can achieve a continuous surface connecting them PBF-LB/M manufacturing are Ti6Al4V and 316L stainless steel [44,45]. [46–49]. Metals are used instead of polymers for applications that Graded designs not only influence mechanical stiffness but also require greater strength. Another advantage of these two materials play a role in fatigue behavior, since density, cell-size or cell-type is their corrosion resistance and biocompatibility, making them SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 359 Mechanics excellent for use in medical fields as porous bone scaffolds [47,49]. results of different types of geometries [57]. An advantage of The aerospace industry is another sector that has been utilizing AM this production method is the possibility of reasonably quickly metamaterials made with PBF-LB/M for less demanding, lightweight constructing specimens from two or more other materials, creating components, with TPMS geometries slowly being integrated [50]. so-called interpenetrating phase composites (IPC) [58]. The manufacturing accuracy of TPMS structures with PBF-LB/M is influenced by the designed thickness and overhang angle, mainly because of unmelted material particles sticking to the surface [51]. 3.5 AM-assisted/Hybrid Casting These regions accelerate fatigue crack initiation and should be removed or minimized with post-treatments to improve fatigue life A newer way of manufacturing cellular structures is so-called hybrid [18,46]. casting. The first step in the process is creating an AM model of metamaterial samples using castable wax resin. The samples are 3.2 Powder Bed Fusion – Laser Beam/Polymers (PBF-LB/P) connected to each other with channels (Fig. 5a). A mold is then created with Ransom & Randolph “Platinum Investment & Binder” As the name suggests, PBF-LB/P works on the same principle as around the wax structure, followed by a burnout cycle (Fig. 5b and PBF-LB/M technologies, but this process only sinters or bonds the c). The resulting mold can be used to cast complex geometries such material together without fully melting it. Commonly used materials as TPMS structures. The process is described in more detail in the include semi-crystalline and amorphous polymers, ceramics, metals work of Singh et al. [59]. When TPMS structures made with this new such as Ti6Al4V and CoCr, and various polymer composites. The hybrid technology were compared with ones created with PBF, the resulting parts are somewhat porous, making them suitable for cast specimens exhibited a longer fatigue life. This improvement is vibration absorption [27]. They are also of a good enough quality to primarily attributed to smoother surfaces, reduced porosity and more be compared to the ideal geometries used in numerical tests. Their rounded geometrical transitions achieved by the casting process. mechanical characteristics are greatly influenced by the relative These microstructural and geometric advantages, in turn, result density and porosity of the sintered material [52]. The main advantage in less fatigue ratcheting and strain accumulation during cyclic of this method is the possibility of mixing different types of powder loading. The same authors have used this new process to embed the material, enhancing their mechanical properties, and achieving specimens within another material, creating IPCs [60]. Interestingly, controlled degradation [53]. they observed that the mechanical response of Al-ceramic and steel- Al interpenetrating phase composites considerably differs from the 3.3 Vat Photopolymerization – Photoinitiated (VPP-PI) performance of the base materials. This production method could significantly increase the availability of cellular structures and their A different approach to additive manufacturing is VPP-PI. It uses use in real-world applications, since casting enables the production of a photosensitive liquid material that cures layer by layer using many products at a lower cost. ultraviolet or another special light source [27]. The designs can be produced with high accuracy depending on the size of the light spot, and mechanical properties depend on the specimen’s geometry and post-curing time [54]. The main drawback of this technique is the limited number of materials that can be utilized, but this number is slowly growing with materials such as Biomed Amber making their appearance [55]. Instead of using a light spot to trace each layer, a screen can also be used to project an entire layer at once. This approach reduces build times while maintaining high precision. This a) b) c) d) process’s main limitation is the projection’s resolution, as the pixel Fig. 5. Schematic of the hybrid casting production process; size determines the print accuracy. Additionally, the build volume is a) additively manufactured wax resin samples, b) creation of mold used for casting, generally smaller than when using a laser due to the projection system c) casting of specimens, and d) cast specimens [27]. Despite these limitations, it is being used to produce and analyze complex TPMS geometries intended for use as electromagnetic absorbers in the field of high-temperature electromagnetic wave 4 MECHANICAL CHARACTERIZATION OF TPMS STRUCTURES absorption [56]. Although this method produces smoother surfaces, the limited material options restrict usability and research, even Mechanical characterization of TPMS structures is commonly though surface quality suggests potential improvements in fatigue performed under quasi-static loading; however, many of the observed life over powder-based approaches. mechanisms, such as buckling, densification and deformation mode (stretching- or bending-dominated), directly affect fatigue resistance. 3.4 Material Extrusion – Thermal Rheological Behavior/Polymers It is essential to analyze the structures across multiple orders of (MEX-TRB/P) magnitude to characterize cellular materials and understand their deformation behavior. At the macroscopic level, entire components Probably the most well-known additive manufacturing method or representative test samples typically comprise at least 5 to 7 cells is fused deposition modelling, or MES-TRB/P. This is most used (3 cells for 2D geometries [61]) in each direction are used in an in commercially available AM technologies. Material is melted analyzis. This scale allows for the statistical evaluation of mechanical and extruded layer by layer to build the desired part. This type of properties, such as elastic modulus, Poisson’s ratio and plateau stress. manufacturing is of lower precision than VPP-PI or PBF-LB/M, and When analyzing at the mesoscopic scale, the focus shifts to individual many support structures are needed, resulting in wasted material cells within the material. They are influenced by the geometry, choice and rough surface finishes [27]. Despite its limitations, MEX- of base material, and, in some cases, gases caught in the cells. The TRB/P offers an effective way of producing geometries quickly and last microscopic scale describes the base material from which the for a relatively low price from polylactic acid (PLA), acrylonitrile cellular structures are made. This includes chemical elements, pores butadiene styrene (ABS) or similar polymer materials and comparing and possible inclusions. When analyzing cellular materials, it is 360 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics Fig. 6. Properties and characteristics at different scales for cellular materials essential to understand the connections between the different orders Deformation velocity is another critical factor that influences the of magnitude to be able to examine the mechanical response. The mechanical response of cellular materials. Under quasi-static loading mechanisms at the micro and meso scales determine macroscopic conditions, where the deformation occurs at a very low strain rate, properties. For instance, global macroscopic deformation reflects materials typically have a homogeneous response throughout their the nominal strain observed in the material. In contrast, local entire volume. In this regime, the structures deform uniformly until macroscopic deformation corresponds to the global response at the local instabilities or imperfections cause the collapse of individual mesoscopic level or the deformation behavior of individual cells. The layers or regions. On the other hand, when the specimens are exact correlation between mesoscopic local strain and microscopic subjected to high-speed loading, such as impact or impulse, the global strain can be made, representing the base material strain [62]. material exhibits a different behavior [62]. It usually becomes stiffer, Properties, characteristics and testing methods at different scales for and the deformation localizes at the point of loading. Instead of a cellular materials are graphically presented in Fig. 6. uniform collapse, a localized deformation forms at the loading point, A typical compressive stress-strain response of cellular structures known as a so-called shock front [67]. This behavior is essential in can be divided into three distinct deformation stages, as illustrated in applications involving fast, dynamic loads where a lot of energy must Fig. 7. The initial elastic stage is known as the pre-collapse stage and be absorbed quickly, such as in a crash [62,68]. When subjected to a is characterized by a nearly linear response of the material. This is macroscopic load, static or dynamic, cellular structures can deform caused by the elastic deformation of cell walls in the material. When by a combination of bending, twisting or stretching [69]. If the struts the strain in the material reaches a point where it starts to deform support mainly axial loads and collapse by stretching, the geometry plastically, and the cells begin to buckle, bend or collapse, it enters the is referred to as stretching-dominated. In contrast, if the deformation so-called plateau stage. It is characterized by a significant increase in occurs primarily through bending of the struts or cell walls, the strain with minimal increase in stress, resulting in a nearly horizontal structure is considered bending-dominated. Most cellular solids, such stress-strain response. This phase is responsible for the material’s as metal foams, are bending-dominated. Consequently, they exhibit energy absorption capabilities. As the deformation increases, the lower strength and stiffness compared to stretching-dominated cellular structure becomes increasingly compressed and compact, geometries [70]. Another way of determining what mechanism leading to the densification stage. In this final phase, the collapsed is more prevalent in a geometry is by plotting their mechanical cell walls come in contact with each other, and the material acts more properties obtained from uniaxial tests using the Gibson–Ashby like a solid specimen. This results in a steep rise in the stress-strain scaling power law [2]: curve, so-called densification [63–66]. M  C n. (2) In this relation, M is the normalized mechanical property, and ρ is the relative density. The parameters C and n are obtained by fitting experimental data, with the exponent n in particular serving as an indicator of the dominant deformation mechanism [71]. If the value of n is below 2, then the geometry is stretching-dominated, while anything above is considered bending-dominated. Following this criterion, sheet-based TPMS metamaterials are stretching-dominated, while skeletal-based geometries are bending-dominated, with the exception being the skeletal gyroid [70]. Knowing these deformation mechanisms allows us to evaluate advanced cellular geometries such as TPMS, which offer unique mechanical advantages to conventional materials. As already mentioned, their properties are influenced by the manufacturing process, material selection and unit cell geometry. Unlike conventional strut-based geometries, their uninterrupted surfaces Fig. 7. Characteristic quasi-static compressive stress-strain curve for cellular materials enhance their mechanical efficiency under various loading conditions. Several studies have been conducted proving this fact [63–66]. They SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 361 Mechanics all concluded that TPMS structures outperform other designs when Rhombic dodecahedron subjected to compressive and tensile loads, with the Diamond and 0.14-0.38 12.4-112.8 0.54-6.34 [81] (strut-based) Gyroid sheet geometries outperforming other structures. Table 2 shows the mechanical properties of several cellular materials made from Ti6Al4V under quasi-static compressive loading. The base material was selected due to its excellent corrosion resistance, favorable strength-to-weight ratio and AM capabilities, making it common in the field of cellular structures. Structures made from materials with comparable properties can be expected to exhibit similar performance under equivalent conditions. Elastic modulus and strength of TPMS metamaterials are greatly influenced by the type of unit cell and base material selection. How the shape of the unit cell affects the elastic modulus is graphically presented in Fig. 8, which was prepared by the authors based on the data reported in the literature and summarized in Table 2. The results demonstrate that for Fig. 8. Graphical comparison of elastic modulus of different a given relative density, TPMS structures such as Gyroid and I-WP cellular structures made from Ti6Al4V achieve a significantly higher elastic modulus compared to strut- based lattices. Strut-based geometries generally show lower stiffness but can still offer comparable compressive strength depending 5 FATIGUE BEHAVIOR OF TPMS STRUCTURES on density. Open-cell foams exhibit the lowest strength values, confirming the superior load-bearing capacity of TPMS structures. When designing cellular structures, their fatigue behavior has become Using PBF-LB/M with Ti6Al4V alloy, Gain et al. [20] were able to a critical consideration, particularly for those that are intended to be closely mimic the elastic modulus, compressive strength and tensile used in load-bearing applications. As highlighted by Benedetti et al. strength of human cortical bone with graded TPMS metamaterials. A [82] in their literature review, the majority of fatigue design methods similar study was conducted by Wang et al. [21], where cubic, octet rely on experiments, which are time-consuming, expensive and able and TPMS gyroid lattice structures were fabricated to mimic natural to handle only selected architectures and materials. While there are bone. The gyroid structure was found to have the highest elastic theoretical approaches, they can result in inappropriate estimates of modulus and yield strength. the material parameters [83]. They did highlight, however, that with Porosity is another parameter influencing the mechanical the amount of numerical methods, machine learning algorithms characteristics of TPMS structures, and it was investigated by Cai et and data-driven approaches being developed in recent years, they al. [72]. Results comparing the different iterations showed that both could predict complex nonlinear relationships. Despite this promise, yield strength and modulus of elasticity decreased when porosity predictive modelling of TPMS fatigue life remains challenging. was increased. Another observation was that the failure mechanism Classical finite element analyzis can capture stress distributions, but changed. While low-porosity geometries broke down via buckling, it struggles to account for manufacturing defects, surface roughness high-porosity specimens endured micro-fractures under load. The and microstructural variability. This makes purely numerical introduction of functionally graded porosity with a varying density predictions unreliable without experimental calibration. By training across different regions of the structure was demonstrated to enhance on experimental datasets, data-driven methods, including machine mechanical strength and energy absorption capacity by Liu et al. [40], learning, could capture complex mechanisms and fatigue response. Zhang et al. [73] and Shi et al. [44]. This results from mitigating stress However, such models require large datasets and careful validation. concentrations and providing a more uniform load distribution. Since The integration of physics-based simulations with machine learning porosity influences crack initiation and propagation, these results link is therefore emerging as a promising direction. Reflecting these structural design and fatigue strength. Higher porosity often reduces challenges, Nečemer et al. [29] also noted that the fatigue performance fatigue life due to stress concentration and easier crack initiation. of cellular materials under cyclic loading remains underexplored and Several studies have emerged in recent years exploring possible requires further investigation. While TPMS metamaterials exhibit alternative designs and their advantages. Isotropy would be an substantial potential as lightweight structural materials, their fatigue excellent characteristic for load-bearing and energy-absorption behavior is still limited and warrants further investigation. They are implications, meaning the material has the same response under loads especially of interest because of their smooth transitions between in all orientations. Fu et al. [74] designed and tested such structures struts, avoiding stress concentrations which could promote better by performing Boolean operations. The new isotropic hollow cellular fatigue life. Most studies until now have focused on the impact of structures had a higher Young’s modulus and better energy absorption manufacturing and topology on their mechanical response [63–66]. properties than the original designs. In works [44,45], hybrid designs Even though these types of structures are being investigated for use have been shown to improve energy absorption efficiency and yield in applications where damage is a result of repetitive, low-intensity strength under both static and dynamic loading conditions. loads, only a handful of studies have been conducted [30]. In this section, relevant scientific articles on the fatigue behavior of TPMS Table 2. Compressive mechanical characteristics of common cellular and TPMS shapes made metamaterials are presented. from Ti6Al4V The defining characteristic of TPMS metamaterials is their Relative Compressive Elastic modulus topology, which dictates how they deform under loading. Different The shape of base cell Ref. density [-] strength E [GPa] types of TPMS unit cells have been evaluated for their fatigue Gyroid (TPMS) 0.1-0.4 16.44-275.17 1.21-10.60 [75-77] performance, stress distribution and failure mechanisms. This is presented in Table 3, where common TPMS and regular cellular I-WP (TPMS) 0.1-0.4 9.81-306.62 0.94-3.2 [77] structures are presented with their fatigue properties. Fatigue strength Diamond (strut-based) 0.13-0.4 21.00-118.80 0.4-6.5 [78,79] is the maximum stress a material can withstand for a specified Cubic (strut-based) 0.3-0.6 7.28-163.02 0.57-14.59 [80] number of loading cycles without failure, while the fatigue ratio, Foam (open-cell) 0.08-0.1 3.80-4.50 0.19-0.49 [81] or sometimes called fatigue endurance ratio, is the fatigue strength 362 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics Table 3. Fatigue properties of different metamaterials The shape of base cell Material Relative density [-] Ultimate cycles Fatigue strength [MPa] Fatigue ratio [-] Ref. Gyroid (TPMS) 316L 0.15 2∙106 9.1 0.35 [30] Gyroid (TPMS) 316L 0.15 2∙106 11.7 0.45 [30] Gyroid (TPMS) Ti6Al4V 0.31 106 14.3 0.18 [84] Diamond (TPMS) Ti6Al4V 0.31 106 18.4 0.17 [84] Schwarz Primitive (TPMS) Ti6Al4V 0.31 106 13.6 0.21 [84] I-WP (TPMS) NiTi / 106 2.08 0.33 [85] BCC (strut-based) NiTi / 106 1.88 0.34 [85] Cubic (strut-based) Ti6Al4V 0.37 107 75 0.48 [86] Rhombic dodecahedron (strut-based) Ti6Al4V 0.8 107 13.9 0.2 [86] divided by yield strength. It can be observed that there is a large failed under a 45° angle, aligning with the observations made by variation in fatigue ratios between Ti6Al4V and 316L Gyroid Yang et al. [30] under the same loading conditions. Importantly, they structures. This can be attributed to a number of factors, with highlighted a greater fatigue resistance compared to other AM porous the most influential being the high ultimate strength of Ti6Al4V materials. Even when loaded with stress levels as high as 60 % of their compared to 316L stainless steel. Others may include surface quality yield stress, some variants managed to exceed the usual threshold of of specimens, porosity, relative density and testing parameters. Yang 1∙106 cycles used for these types of AM materials. Another study et al. [30] investigated a Gyroid structure fabricated with PBF-LB/M comparing different geometries was conducted by Singh et al. and subjected to compression-compression cyclic fatigue. Their study [59]. They compared Gyroid and I-WP metamaterials made from concluded that TPMS geometries have a higher fatigue resistance AlSi10Mg using powder bed fusion (PBF). They were subjected than strut-based lattice structures, primarily due to their stretch- to load-controlled cyclic loading. They found that Gyroid designs dominated deformation mechanism. The failure analyzis showed that outperformed I-WP specimens. Overall, they had comparable or fatigue cracks formed at nodal intersections, leading to 45° diagonal lower fatigue ratcheting and higher stiffness. In particular, the Gyroid fracture bands. A similar result was achieved by Soro et al. [84] structures with 30 % relative density consistently demonstrated longer under tension-tension loading conditions for three different TPMS fatigue lives with lower comparable damage metrics. Overall, these geometries. They also outperformed regular strut-based lattices, with studies indicate that the fatigue performance of TPMS metamaterials fatigue cracks initiating at the surface, highlighting the importance of is largely determined by the topology and deformation mode, with post-treatment. Jiang et al. [87] performed experimental testing and stretching-dominated geometries such as Gyroid being better suited finite element analyzis (FEA) on four TPMS metamaterials (Gyroid, for compression and tension loading, while the Primitive geometry Diamond, I-WP, Schwarz Primitive) to evaluate their torsional and exhibits better fatigue life when subjected to bending loads. Bending- fatigue resistance. They found that the Schwartz Primitive shape dominated geometries, such as I-WP, on the other hand, tend to exhibits superior torsional and fatigue resistance. I-WP structures concentrate stresses at curved junctions, making them less efficient showed lower torsional fatigue resistance because of their bending- under loads and more prone to earlier fatigue failure. dominated deformation. This failure was initiated at the curved Mechanical performance, surface quality, and fatigue behavior junctions, with stress concentrations occurring in all four structures are all impacted by the manufacturing process used to produce during the compression process. These aligned closely with the specimens. Because of this, several publications were conducted to regions exhibiting larger strain. The same four TPMS geometries determine how the different technologies affect fatigue life. Tilton were analyzed by Bobbert et al. [88] under compression-compression et al. [89] investigated TPMS scaffolds fabricated with Ti6Al4V via loading. The change in loading conditions resulted in the Schwarz PBF. The process left behind unwanted surface characteristics like Primitive geometry having the shortest fatigue life, while all the other partially melted powder and their agglomerations. These unwanted specimens varied between 1∙105 cycles and 7∙105 cycles. The samples surface characteristics were initiation sites for fatigue failure. A Fig. 9. SEM micrograph of TPMS metamaterials with; a) 1.5 mm, and b) 2.5 mm unit cell size, adapted from [90] SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 ▪ 363 Mechanics similar study was done by Ren et al. [85], but with nickel-titanium studies, the absence of surface particles enhanced the fatigue as the base material. Similar results were achieved with unmelted resistance by reducing crack initiation zones. Similar results were or partially melted particles on the surface of the structures. Cracks achieved by Singh et al. [59]. They examined heat-treated AlSi10Mg appear at the root of powder particles attached to the surface. The TPMS structures fabricated with PBF. The process significantly I-WP lattice structure seemed to slightly benefit in avoiding powder improved the fatigue resistance compared to as-built structures. This adhesion. Even though AM has come a long way, it still has some was due to a slower fatigue damage accumulation in the heat-treated limitations. In a study by Emanuelli et al. [90], TPMS samples made samples. The most significant effect was seen in Gyroid 30 % density with PBF from β-Ti21S alloy were investigated. They concluded that geometries. These findings confirm that different heat treatments this material exhibits promising mechanical and biological properties effectively enhance the fatigue life of TPMS structures made with for femoral implants. However, its main drawback was poor AM methods. Other methods to improve the surface quality of printability, which impacted pore size and fatigue resistance. They specimens are chemical etching, shot peening, and sandblasting. also highlighted surface irregularities and agglomerations, pointed Araya-Calvo et al. [76] compared as-built and chemically etched out in Fig. 9, caused by unmelted material particles. Ti6Al4V structures and concluded that the post-treated samples Studies on possible post-treatment methods that would improve had an approximately 20 % improved fatigue resistance. They also surface quality, reduce stress concentrations, and eliminate demonstrated better biocompatibility and surface morphology. The manufacturing defects have been conducted to try to mitigate some effect of chemical etching is shown in Fig. 10. The as-built specimens of the inherent drawbacks of AM technologies. Liu et al. [91] studied show a significantly rough surface due to the adhesion of partially the impact of high isostatic pressing (HIP) and electropolishing melted powder particles. The post-treatment resulted in a smoother (ELP) on the fatigue life of diamond and gyroid TPMS structures. surface, which resulted in improved fatigue resistance. HIP is a process in which high pressures are applied at elevated An advantage of mechanical post-treatments such as shot peening temperatures to enhance the material’s ductility and improve and sandblasting is the compressive residual stresses they leave mechanical performance. This process resulted in a decline in surface behind on the surface, which was investigated by Jiang et al. [92] and roughness, reduced micro porosities, and released residual stresses in Was et al. [93]. These delay crack initiation and extend fatigue life. the Ti6Al4V specimens. Because of this, the fatigue ratio of bending- This was studied by Yang et al. [30] on sandblasted Gyroid structures. dominated TPMS structures improved from 0.11 to 0.26 and from The fatigue resistance increased from 0.35 for the as-built samples 0.59 to 0.69 for the stretching-dominated structures. As in previous to 0.45 for the sandblasted specimens. In addition to the residual Fig. 10. Comparison of a) b) c) as-built with d) e) f) chemically etched specimens, reproduced from [76] Table 4. Summary table of post-processes with their mechanisms and effect on fatigue life Post-processing method Mechanism Effect on fatigue life Reference Hot isostatic pressing (HIP) Removes microporosity, relieves residual Improved fatigue ratio from 0.11 to 0.26 (Gyroid) Liu et al. [91] (applied in combination with ELP) stress, improves ductility and from 0.59 to 0.69 (Diamond) Electropolishing (ELP) Reduces surface roughness, removes Improved fatigue ratio from 0.11 to 0.26 (Gyroid) Liu et al. [91] (applied in combination with HIP) powder particles and from 0.59 to 0.69 (Diamond) Slows fatigue damage accumulation, Heat treatment Improved fatigue life due to lower fatigue ratcheting Singh et al. [59] improves microstructure Improved fatigue resistance, Chemical etching Smooths surface, removes powder particles Araya-Calvo et al. [76] especially at lower stress levels Removes powder particles, introduces Sandblasting Fatigue resistance increased from 0.35 to 0.45 Yang et al. [30] compressive residual stress Removes powder particles, introduces Jian et al. [92], Shot peening Extended fatigue life because of delayed crack initiation compressive residual stress Was et al. [93] 364 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Mechanics stresses, the process removed partially melted powder particles, especially with grading strategies, hybrid geometries, and multi- reducing stress concentrations and crack initiation zones. Their results material integration. In conclusion, TPMS metamaterials represent show that surface treatments are a highly effective way of mitigating structurally efficient, customizable and application-specific cellular fatigue failure, especially when working with AM-fabricated TPMS materials that show promising results for use in fields such as structures. Table 4 summarizes the main post-processing methods biomedical engineering, energy absorption applications, and thermal investigated for TPMS structures. In it, the mechanisms by which management. each technique improves fatigue life are highlighted, and results are presented to provide a clearer overview. Among the potential applications of TPMS cellular structures, 7 SUGGESTIONS FOR FUTURE RESEARCH WORK the biomedical field has the most studies, particularly for use as bone scaffolds [94–96]. Slowly, they are also being considered for dental Despite significant research in the design and mechanical implants, as numerically investigated by Kök et al. [97]. Compared to characterization of TPMS metamaterials, not much emphasis has standard dental implants, they showed 15 % less stress-shielding and been placed on their fatigue behavior which is evident in the limited still complied with the number of cycles required by DIN EN ISO number of publications. Future work should firstly focus on achieving 14801, resulting in a 45 % reduction in weight. good reproductivity. This could be done by using specimens of similar size, relative density and production methods if possible. The results would give us a more general understanding of their properties and 6 CONCLUSIONS be a good foundation for analyzing more complex factors. After this a logical next step would be to analyze how different mean stresses and This review of recent studies confirms that TPMS structures are a strains affect their fatigue life. Most tests up to this point have been versatile class of cellular structures with a broad potential. Their uniaxial which is sufficient if the loads are mostly in one direction. continuous geometry based on mathematical equations offers With more complex spaces being filled with TPMS metamaterials, advantages in terms of mechanical properties, unit cell design, and multiaxial tests should be considered for future work. Outside factors tunability. Compared to traditional strut-based cellular structures, such as impacts could cause deformations and failure in directions they demonstrate superior mechanical performance under static not accounted for in uniaxial tests. Lastly, because these types and dynamic loads because of their smoother stress distribution, of structures can be utilized as fluid mixers and heat exchangers, especially in the Gyroid and Diamond unit cell shapes. They also studying the effects that temperature has on its fatigue life could mitigate failure caused by stress concentrations, which are common prove beneficial to prevent premature failure caused by temperature in strut-based designs. fluctuations. A general observation across the analyzed studies is that the mechanical properties of TPMS structures depend not only on the relative density and cell type but can also be significantly enhanced References by improving surface quality and reducing unit cell size. 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Povzetek Članek predstavlja celovit pregled obnašanja metamaterialov, zasnovanih na trojno-periodičnih minimalnih površinah (TPMS), pri Acknowledgement The authors acknowledge the financial support of the obremenitvah zaradi utrujanja, s posebnim poudarkom na vplivu tehnologije Research Core Funding (No. P2-0063), Basic Postdoc Research Project (No. njihove izdelave. V prispevku so podrobno analizirane različne geometrije Z2-50082) and Basic Research Project (No. J2-60049) from the Slovenian TPMS, ki so v zadnjih letih pridobile veliko pozornosti zaradi izjemnega Research and Innovation Agency. razmerja med trdnostjo in maso ter sposobnosti nadzora mehanskih lastnosti s prilagajanjem geometrijskih parametrov. Predstavljene so sodobne Received: 2025-04-25, Revised: 2025-09-05, Accepted: 2025-09-24 metode izdelave TPMS struktur s poudarkom na dodajalnih tehnologijah, as a Review Scientific Paper (1.02). kjer je za osnovni material privzeta titanova in jeklena zlitina. Za vsak material so navedene ključne prednosti, omejitve in vpliv proizvodnega Data Availability All data supporting the study’s findings are included in the procesa na končne mehanske lastnosti struktur. Poleg tega članek paper. obravnava mehanske značilnosti celičnih gradiv, pri čemer je poseben poudarek namenjen TPMS strukturam, ki zaradi svoje topologije omogočajo Author Contribution Žiga Žnidarič: Writing – original draft, Investigation; enakomerno porazdelitev napetosti in visoko absorpcijo mehanske energije. Branko Nečemer: Supervision and Resources; Nejc Novak: Supervision and V nadaljevanju so predstavljene najnovejše raziskave in ugotovitve glede Resources; Srečko Glodež: Conceptualization Writing – review & editing; vedenja TPMS metamaterialov pri utrujanju. Analiza kaže, da TPMS celične Matej Vesenjak: Writing – review & editing. strukture izkazujejo bistveno boljšo odpornost proti utrujanju v primerjavi s konvencionalnimi celičnimi metamateriali. Ključni razlog za to je njihova AI Assisted Writing AI tool ChatGPT was used for grammar and language gladka, zvezna geometrija brez ostrih robov ali stičnih točk, kar zmanjšuje editing, as well as picture editing. All content and conclusions remain the koncentracijo napetosti in omogoča bolj homogeno porazdelitev napetosti responsibility of the authors. skozi celotno strukturo. Na podlagi predstavljenih rezultatov lahko zaključimo, da TPMS metamateriali predstavljajo perspektivno smer razvoja naprednih lahkih konstrukcijskih materialov, ki združujejo visoko trdnost, odpornost proti utrujanju in prilagodljivost geometrije glede na specifične zahteve uporabe. Ključne besede celične strukture, TPMS metamateriali, proizvodne tehnologije, mehanska karakterizacija, obnašanje pri utrujanju 368 ▪ SV-JME ▪ VOL 71 ▪ NO 9-10 ▪ Y 2025 Contents 271 Ivan Dominik Horvat, Jurij Iljaž: Numerical Solving of Dynamic Thermography Inverse Problem for Skin Cancer Diagnosis Based on non-Fourier Bioheat Model 284 Luka Kevorkijan, Matjaž Hriberšek, Luka Lešnik, Aljaž Škerlavaj, Ignacijo Biluš: Numerical Investigation of Erosion Due to Particles in a Cavitating Flow in Pelton Turbine 294 Uroš Kovačec, Franc Zupanič: Removal of Inclusions and Trace Elements from Al-Mg-Si Alloys Using Refi ning Fluxes 301 Vinko Močilnik, Nenad Gubeljak, Jožef Predan: Effect of Presetting and Deep Rolling on Creep of Torsion Spring Bars 309 Nejc Novak, Zoran Ren, Matej Vesenjak: Integrated Design, Simulation, and Experimental Validation of Advanced Cellular Metamaterials 318 Snehashis Pal, Matjaž Finšgar, Jernej Vajda, Uroš Maver, Tomaž Brajlih, Nenad Gubeljak, Hanuma Reddy Tiyyagura, Igor Drstvenšek: Fusion Behavior of Pure Magnesium During Selective Laser Melting 328 Marko Simonič, Iztok Palčič, Simon Klančnik: Advancing Intelligent Toolpath Generation: A Systematic Review of CAD–CAM Integration in Industry 4.0 and 5.0 337 Nejc Vovk, Jure Ravnik: Comparison of 1D Euler Equation Based and 3D Navier-Stokes Simulation Methods for Water Hammer Phenomena 349 Matija Založnik, Matej Zadravec: Analysis of Gas Flow Distribution in a Fluidized Bed Using Two-Fluid Model with Kinetic Theory of Granular Flow and Coupled CFD-DEM: A Numerical Study 357 Žiga Žnidarič, Branko Nečemer, Nejc Novak, Matej Vesenjak, Srečko Glodež: Fatigue of Triply Periodic Minimal Surface (TPMS) Metamaterials – a Review https://www.sv-jme.eu/