Strojniški vestnik Journal of Mechanical s Engineering 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 Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www. sv-jme.eu Print: Grafex, d.o.o., printed in 310 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Branko Širok University of Ljubljana, Faculty of Mechanical Engineering, Slovenia International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, University of Engineering and Technology, Pakistan Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, UL, Faculty of Mechanical Engineering, Slovenia Franci Čuš, UM, Faculty of Mechanical Engineering, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Igor Emri, UL, Faculty of Mechanical Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, UL, Faculty of Mechanical Engineering, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, UM, Faculty of Mechanical Engineering, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, UL, Faculty of Mechanical Engineering, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, UL, Faculty of Mechanical Engineering, Slovenia Gorazd Lojen, UM, Faculty of Mechanical Engineering, Slovenia Thomas Lubben, University of Bremen, Germany Janez Možina, UL, Faculty of Mechanical Engineering, Slovenia George K. Nikas, KADMOS Engineering, UK José L. Ocana, Technical University of Madrid, Spain Miroslav Plančak, University of Novi Sad, Serbia Vladimir Popovič, University of Belgrade, Faculty of Mech. Eng., Serbia Franci Pušavec, UL, Faculty of Mechanical Engineering, Slovenia Bernd Sauer, University of Kaiserlautern, Germany Rudolph J. Scavuzzo, University of Akron, USA Arkady Voloshin, Lehigh University, Bethlehem, USA Vice-President of Publishing Council Jože Balič University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: Image presents visualization setup for cavitation monitoring. High-speed camera Fastec with Samyang manual lense was used. In-house build LED setup provided the necessary illumination. The sequence of frames captured during the experiment is visible in the back. It shows how cavitation is generated on the fast rotating rotor. Cavitation is visible in white on black rotor background. Image Courtesy: Tadej Stepisnik Perdih, Laboratory for Water and Turbine Machines, Faculty of Mechanical Engineering, University of Ljubljana ISSN 0039-2480 General information Strojniški vestnik - Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue). Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. 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Strojniški vestnik - Journal of Mechanical Engineering is available on http://www.sv-jme.eu, where you access also to papers' supplements, such as simulations, etc. Contents Strojniški vestnik - Journal of Mechanical Engineering volume 63, (2017), number 2 Ljubljana, February 2017 ISSN 0039-2480 Published monthly Papers Tadej Stepišnik Perdih, Brane Širok, Matevž Dular: Influence of Hydrodynamic Cavitation on Intensification of Laundry Aqueous Detergent Solution Preparation 83 Deng Li, Yong Kang, Xiaolong Ding, Xiaochuan Wang, Zhenlong Fang: Effects of Nozzle Inner Surface Roughness on the Performance of Self-Resonating Cavitating Waterjets under Different Ambient Pressures 92 Mohamed Charifi, Rabah Zegadi: Inverse Method for Controlling Pure Material Solidification in Spherical Geometry 103 Zhen Jia, Zhiren Han, Baoming Liu, Yong Xiao: Work Hardening of Non-Axisymmetric Die-Less Spinning 111 Mohamed Abdel-wahed, Tarek Emam: MHD Boundary Layer Behaviour over a Moving Surface in a Nanofluid under the Influence of Convective Boundary Conditions 119 Leilei Zhao, Changcheng Zhou, Yuewei Yu: Comfort Improvement of a Novel Nonlinear Suspension for a Seat System Based on Field Measurements 129 Duraisamy Kumar, Sadayan Rajendra Boopathy, Dharmalingam Sangeetha, Govindarajan Bharathiraja: Investigation of Mechanical Properties of Horn Powder-Filled Epoxy Composites 138 Strojniški vestnik - Journal of Mechanical Engineering 63(2017)2, 83-91 © 2017 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2016.3970 Original Scientific Paper Influence of Hydrodynamic Cavitation on Intensification of Laundry Aqueous Detergent Solution Preparation Tadej Stepišnik Perdih* - Brane Širok - Matevž Dular University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Washing machines are one of the most energy and water demanding domestic appliances. Over years, a significant effort of the scientific community has been invested into making laundry more "sustainable". Nevertheless, the preparation of detergent solution has been entirely overlooked step of laundering. The preparation of aqueous detergent solutions in the currently available washing machines takes up to 10 minutes. In this work, we propose a design of a special rotary hydrodynamic cavitation generator, which would impact this process. New detergent dissolution rates have been experimentally tested on the laboratory model washing machine using the designed cavitation generator. The dissolution rates have been determined from the measurements of the undissolved detergent after the specific time of treatment. Additionally, the influence of hydrodynamic cavitation on that process has been isolated and investigated. To do so, two flow regimes have been established: the regime with cavitation present and the regime where cavitation was not present. In order to evaluate cavitational intensity, pressure oscillations inside cavitation generator have been recorded. Results indicate that cavitation significantly increases the detergent dissolution rates. In the cavitation flow regime, more than 80 % of the detergent is dissolved in approximately 10 seconds. With no cavitation present, about 150 seconds are needed to dissolve the same amount of the detergent. Intensification of the process can be attributed to mechanical effects of cavitation. This research shows that use of the cavitation generators in the washing machines could lead to shorter washing programs and henceforth potential water and energy savings. Keywords: hydrodynamic cavitation, rotary cavitation generator, cavitational intensity, washing machines, aqueous detergent solution Highlights • Hydrodynamic cavitation was used to prepare aqueous detergent solution. • Special rotary hydrodynamic cavitation generator was designed. • Cavitation significantly improves detergent dissolution rates. • Cavitation generators could improve water and energy efficiency of washing machines. 0 INTRODUCTION Washing machines are among most common devices worldwide and at the same time one of biggest consumers of household energy [1]. One can assume that already a minor improvement in a laundry process or a washing machine production will have a globally non-negligible effect. Many advances in laundry technology and washing machines design are already reported in the literature. Teschler suggests the use of a variablespeed inverter electromotor [2]. Ivarsson et al. proposed sensors for fill and rinse control [3], which would reduce water and detergent consumption. Most of the energy in washing machine is used for water heating, therefore Persson investigated the use of hot-water circulation loop [4]. Drinking water consumption could be significantly reduced with use of recycled water [5] or rainwater [6] and lastly, improved detergent composition would make laundry less of an environmental threat, while maintaining washing performance [7]. Surprisingly, preparation of wash bath (aqueous detergent solution) is completely neglected by researchers. Our team aims to intensify the preparation of wash bath by utilizing cavitation and to our knowledge, this is the first research where cavitation is used for detergent solutions preparation. The use of cavitation is drawing great attention of researchers from various fields. Cavitation is a physical phenomenon characterized by formation, growth and subsequent collapse of bubbles in a bulk liquid. The collapses of bubbles create local "hot spots", releasing extreme amounts of energy [8]. If the bubble collapse occurs symmetrically, pressure shock waves are created, which propagate microscopic turbulence - a phenomenon known as microstreaming [9]. Moreover, when cavitation bubble is in a proximity of a solid surface, asymmetric bubble implosion takes place, which results in a formation of microjets [10]. These violent circumstances are being widely utilised to clean solid surfaces in different industries and medical and scientific laboratories for over 40 years [11] and [12]. On the other hand, the use of cavitation in textile engineering gained scientific attention only in recent years. Nevertheless, cavitation shows great potential for textile finishing and textile washing purposes. Vouters et al. [13] report, that with the use of cavitation, water consumption can be reduced by 20 % and energy consumption for 30 % with a rise of the quality of products by the same textile finishing treatment. In work of Gogate [14] one can additionally find an in-depth overview of other applications of cavitation phenomena for process intensification and reactor designs. Cavitation is also recognised as an efficient method to prepare solutions and emulsions for various purposes. Depending on the application, either chemical effects (such as temperature and pressure hot spots, free radical formation) or mechanical effects (such as high shear stress and turbulence, microjets and microstreaming) are harnessed [15]. Kentish et al. [16] used cavitation to prepare range of food grade emulsions, Sivakumar et al. [17] proposed cavitation as green technology for preparation of poorly water-soluble drugs in pharmacy and Hasanbeigi and Price [18] investigated how use of cavitation can optimise costs and reduce pollution in production of dyeing solutions in textile industry. Additionally, Patil and Pandit [19] showed that cavitation is energy efficient method to produce nano-suspensions and Sharma et al. [20] was investigating operating parameters of cavitation setup on the intensification of hydrogenation reactions. This paper is focused on basic research that aims to improve the efficiency of commercial washing machines by utilizing cavitation. More precisely, we have investigated the use of cavitation for aqueous detergent solution preparation in washing machines. Washing machines currently available on the market prepare the washing dissolution in the drum. Water from the supply network enters the machine and is led through the detergent tray to carry the detergent into the drum. There the detergent is mixed with clothes and the dissolution starts due to the rotation of the drum. The dissolution process consists of two steps: i) the interaction between the solute and the solvent molecules at the solid-liquid interface and ii) the diffusion of the solute molecules away from the interface to the bulk [21]. Since the dissolution is sequential it can take up to 10 minutes or even more, to prepare an adequate aqueous detergent solution in a washing machine. We assume this process would be accelerated if the detergent would be washed into a special bath, where it would be exposed to cavitation before it enters the drum. This could be a major improvement of washing machines operation by shortening laundry duration and potentially saving energy. Our goal was to determine to what extent hydrodynamic cavitation contributes to the dissolution time. 1 EXPERIMENTAL The experiments were conducted at the University of Ljubljana in the Laboratory for Water and Turbine Machines. For this purpose, special rotary hydrodynamic cavitation generator (RHCG) has been designed. The detergent dissolution rates were experimentally evaluated, for both cavitation and non-cavitation flow regime, on a model washing machine. In addition, standardised tests with a magnetic stirrer were performed as a reference. 1.1 Set-Up and Materials The experimental set-up (Fig. 1) was designed in a way to simulate an actual washing machine. Together with the rotary hydrodynamic cavitation generator, the experimental set-up consisted of a closed pressure tank, connection pipes and pressure (ABB 266 ast), flow (Bio-Tech: FCH-C-Ms-N) and temperature sensors (Fluke 51 II). Ports seen in Fig. 1 on the top of pressure vessel are used to fill the set-up with water and detergent. When operating, the mixture exits the vessel at the bottom, then it is led through RHCG, where it is exposed to cavitation. RHCG also serves as a pump. Water and detergent than flow through control valve and back to the pressure vessel. The RHCG was driven with a single-phase electromotor, which is already present in the most of the washing machines. Two sets of experiments have been conducted -one with cavitation present and one in non-cavitating flow regime (this was achieved by increasing the system pressure while the rotational frequency and Fig. 1. Experimental set-up the flow rate were not altered). The dissolution rate experiments have been performed in alignment to the standard IEC 60456: Clothes washing machines for household use - Methods for measuring the performance. The tank was filled with 2 litres of water at 23.5 °C. 11 grams of standard IEC-A detergent purchased from WFK Institute, Germany, was added to water and left to be treated by the generator for a specified time. The RHCG rotational speed was set to 7000 rpm, which established a flow rate of 11.3 l/ min. In the cavitation regime, the tank was open to atmospheric pressure (101 kPa). In an actual washing machine with implemented RHCG, this regime would correspond to the washing machine operation. The non-cavitating flow regime was achieved by closing the tank air valves and raising the static pressure (in the tank) to 253 kPa. Operating conditions are collected in Table 1. We used same method as Bilus et al. [22] for cavitation monitoring. A high-speed camera (Fastec HiSpec4 2G mono) was used in order to monitor cavitation presence. To evaluate cavitation intensity, pressure oscillations were recorded using hydrophone Reson TC4014. After treating the sample for the specified time (between 10 and 300 seconds -from approximately 1 to 30 sample passages through the RHCG), the detergent solution was poured through the textile filter, so that the undissolved detergent remained on the filter. Filter textile (100 % cotton, swiss pique knit, yarn count 17 tex, double threaded) complied with the IEC 60456 standard requirements. After the experiments, the filters were left to dry at ambient air for 24 h. The filters were weighed on the precision scale (Tehtnica Exacta EB 3600), prior and after the experiment and the percentage of detergent residues were recorded. We achieved the following uncertainties of the measured values: ±1 % for the flow rate, ±0.5 % for the system pressure and ±0.8 % for the medium temperature. Mass of the detergent was measured to ±0.01 g and dynamic pressure oscillations to ±2.6 %. 1.2 Test Section - Rotary Hydrodynamic Cavitation Generator (RHCG) The design of the rotary hydrodynamic cavitation generator follows the basic principles of high shear mixing devices [23], adjusted so that it also generates cavitation. The RHCG is an assembly of rotor and stator discs (Fig. 2) with special geometry inside the closed chamber. Both the rotor and the stator diameters have diameter 50 mm. They have 12 radial indentations, 3 mm deep (u) and 4 mm wide. Unindented area of the rotor disc has been machined in a way that the surfaces are angled at 8° (a), giving them a sharp edge. The stator surface has not been modified. The distance between the rotor and the stator was set to 1 mm (g). The whole assembly is illustrated in Fig. 3 and the details are given in Table 1. Fig. 2. a) Rotor and b) the stator of cavitation generator Water and the detergent enter the RHCG in the axial direction through the stator. The RHCG operation causes periodically repeating pressure drops inside the chamber, due to relative movement of the two shear layers that form between the rotor and the stator. These conditions are favourable for hydrodynamic cavitation, hence before exiting in the radial direction, the mixture passes cavitation zones. Due to the rotation of the rotor, also centrifugal force is exerted on the fluid, which maintains the flow through the reactor. Because of that design, the cavitation generator can also replace a water recirculation pump in a washing machine. Although acoustic cavitation is used in most of the aforementioned researches [13], [17], [18], [20], our device generates hydrodynamic cavitation. Its main advantages over acoustic cavitation are better potential for industrial and commercial scale applications, robust operation as well as improved energy efficiency [19] and [24] to [26]. In particular, the shear-induced cavitation generated with our device has proven to be even more effective than hydrodynamic cavitation generated on Venturi section, as it was showed by Zupanc et al. [27]. Fig. 3. Scheme of the cavitation generator assembly; water and detergent enter the RHCG in the axial direction through the stator; before exiting in the radial direction, the mixture passes cavitation zones Table 1. Operating conditions and cavitation generator geometry details Operating parameters Cavitating regime Non-cavitating regime p [kPa] 101 253 g [mm] 1 u [mm] 3 « [°] 8 /0 [min-1] 7000 2 RESULTS 24 experiments in the RHCG were performed in order to determine the detergent dissolution rate - at cavitating (p = 1.01 bar) and non-cavitating (p = 2.53 bar) flow regimes, both at the rotating frequency of 7000 rpm (/0). The lengths of exposure of the detergent to the RHCG were 10 s, 40 s, 70 s, 130 s and 300 s (this corresponds to approximately 1, 4, 7, 12 and 30 sample passages through the RHCG). 2.1 Cavitation Monitoring Fig. 4 represents the sequences of images captured with the high-speed camera. In Fig. 4a, the RHCG front view is presented with indicated (the dashed rectangle) the high-speed camera observation window. Fig. 4b shows images of the cavitating regime with Fig. 4. a) Top image shows RHCG frontal view with marked camera observation window; b) cavitating regime and c) the non-cavitating operation of the RHCG the system pressure 101 kPa. Fig. 4c was recorded at elevated pressure (253 kPa) and shows no presence of cavitation bubbles. The time difference between two frames is 0.1 ms. At atmospheric pressure, cavitation, which is seen as white clouds, can be clearly distinguished from the black painted rotor. We can notice, that cavitation is generated in two regions: the attached cavitation on the sharp edge of the rotor and the cavitation in stator indentations. This means that the most of the fluid flow is uniformly exposed to cavitation. When the system pressure is raised to 253 kPa (Fig. 4b), no cavitation is present. The high-speed camera images confirm, that we have successfully established the two flow regimes (cavitating and non-cavitating one), by only changing the system pressure (the rotating frequency, the fluid temperature, the geometry and the flow rate were not altered) - this is important as we are not allowed to alter the rotating frequency of the rotor, to achieve comparable measurements. The intensity of cavitation was evaluated by means of pressure oscillations. Bigger pressure amplitudes at bubble collapses represent higher cavitational intensity, [12], [15] and [22]. Fig. 5 shows pressure evolution recorded with the hydrophone, which was mounted exactly between the rotor and the stator. One can see that both amplitudes and gradients are higher for the cavitating regime in comparison to the non-cavitating regime. This means that detergent is exposed to much higher stresses when cavitation is generated in RHCG. 2.2 Detergent Dissolution Rate The results are shown in Fig. 6. Triangles mark results obtained under the cavitating regime and diamonds to the tests under the non-cavitating regime. For comparison also dissolution rates using magnetic stirrer were performed (circles in Fig. 6): the tests complied with the IEC-A detergent solubility test acquired from IEC 60456 standard. Power trend lines are added for easier interpretation. As expected, the dissolution rate is significantly improved when the RHCG is used in comparison to the magnetic stirrer. For the case when the solution is prepared with the magnetic stirrer, more than 35 % of the detergent remains undissolved after 300 seconds of operation. In the same time, with using the RHCG in the non-cavitating regime, only about 15 % of the detergent remains undissolved. The amount of the undissolved detergent after 300 seconds of the RHCG operation in cavitation regime is less than 5 %. The improved dissolution rate when using the RHCG can be attributed to intensified mixing. Similar to other rotating reactors used for mixing purposes [23] and [28] the RHCG operation establishes high Fig. 5. Pressure evolution in case of the a) cavitating regime and b) the non-cavitating regime Fig. 6. The measurements of the detergent dissolution rate; significant difference in the amount of undissolved detergent is observed between operation in cavitating regime versus non-cavitating and furthermore the measurements with magnetic stirrer according to ¡EC 60456 standard local turbulence levels inside the reactor chamber and enhances the solid-liquid mass transfer. This improves both steps of the dissolution process: the interactions between the solute (detergent) and the solvent (water) at the solid-liquid interface (first step), and especially the diffusion of the detergent to the bulk water (second step). Comparison of the results of the RHCG in cavitating and non-cavitating regimes furthermore indicates that cavitation has a substantial impact on the dissolution process. For objective assessment, ANOVA analysis of variance of the experiments was performed. The test confirms, that statistically significant difference with confidence level higher than 96 % exists between the cavitating and the non-cavitating regime (a < 0.04). Effect of cavitation on the dissolution process can be attributed to the violent collapses of cavitation bubbles. As evident from comparison of pressure evolution in Fig. 5, pressure pulsations in the cavitation regime increase for factor 2 in comparison to operation with no cavitation present. Henceforth high pressure pulsations and microjets due to cavitation [29] additionally increase the local turbulence and the detergent-water interaction and raising the dissolution rate. The difference in the amount of dissolved detergent is clearly demonstrated in Fig. 7. Images show two textile filters with detergent residues. The filter on the left belongs to the test where the detergent was exposed to the cavitation regime for 40 seconds, and the filter on the right corresponds to the test after the exposure to the non-cavitating regime for the same period of time (40 seconds). Fig. 7. The detergent residues on the textile filters for: a) the cavitation regime with 1.0 g of the detergent remained on the filter and b) the non-cavitation regime with 3.2 g of the detergent remained on the filter The difference in dissolution rates is especially evident in the initial stages of experiments. With the cavitation regime, approximately 80 % of the detergent is dissolved within the first few seconds of the RHCG operation. When the RHCG operates at the same rotation frequency but without cavitation, 150 seconds are required to dissolve the same amount of the detergent. The dissolution rates decrease with the passing time for both flow regimes. The trend can be described by a power law. A similar trend can also be recognised for dispersion kinetics of other dispersing machines such as a dissolver, a high-pressure homogenizer or a stirred media mill [30]. This is because the probability of successful solute-solvent interactions in the reactor is gradually decreasing. 3 CONCLUSIONS AND DISCUSSION Our work indicates, that the rotary hydrodynamic cavitation generator substantially improves the preparation of the detergent washing dissolution and thus the washing machine performance. Implementation of such a device would shorten the washing program in general. In addition, the RHCG could tackle other identified issues related to detergent solution, such as: i) improved mixture homogeneity, which would result in improved washing effect and in decrease water consumption, ii) improved detergent solution rinsing, due to break up of detergent agglomerates - Sauter et al. [31] used cavitation for de-agglomeration of nanoparticles and Parivnzadeh et al. [32] studied cavitation assisted cotton processing with softener. They argued, that the reason for enhanced treatment is cavitation de-agglomeration of softener. We predict that cavitation has a similar effect to detergent agglomerates and therefore a lower volume of water is required to rinse smaller detergent particles. Furthermore we assume that the implementation of the RHCG would have negligible if not beneficial effect on the energy consumption of the washing machines because: i) cavitation would assist the dissolution process and reduce the operating time for roughly 10 minutes, ii) the RHCG also operates as a pump and would replace the existing water circulation pump and iii) most of the energy required to generate cavitation is eventually transformed into heat, which, in case of washing machine, could be balanced by the reduction of the power consumption of electric water heaters. In addition to the detergent solution preparation, the RHCG or similar cavitation generators, could enhance other aspects of a washing machine operation. One example is a washing performance. Several research groups worldwide are studying ultrasonic textile cleaning. Leading mechanism of ultrasonic cleaning is in fact acoustically generated cavitation. Gallego-Juarez et al. [33] developed semi-industrial system for textile washing in liquid layers, where Gotoh et al. [34] and Uzun and Patel [35] used ultrasonic cavitation bath. They achieved comparable or better washing results than the horizontal-axis washing machine, causing less damage to the textile. Another important subject related to current development trends of laundering is microbial deactivation. High washing temperatures and aggressive detergents from the past are nowadays replaced by milder conditions: low temperatures and biodegradable detergents. Studies show, that various bacteria and fungi species are capable of surviving inside washing machines [36] and [37] under such circumstances. This could present a health risk [36], or development of malodour [37]. Researchers will be forced to find solutions for those problems. One more time harnessing cavitation may bring desired results. Use of cavitation for pathogen deactivation [38] and [39] and wastewater treatment is well developed [26] and [27]. Lastly, cavitation may have a potential to mitigate limescale. Limescale can cause serious issues to washing machine heat exchangers. Already a thin layer of scale reduces a heat exchanger efficiency and can lead to component failure. Review paper of Heath et al. [40] shows that cavitation/scale interaction is complex, but a lot of effort is invested in its research. In previous paragraphs, we pointed out what aspects of washing machines may be improved with cavitation in addition to wash bath preparation. 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D0l:10.5545/sv-jme.2016.3563 Original Scientific Paper Effects of Nozzle Inner Surface Roughness on the Performance of Self-Resonating Cavitating Waterjets under Different Ambient Pressures Deng Li123 - Yong Kang12* - Xiaolong Ding12 - Xiaochuan Wang12 - Zhenlong Fang12 1 Wuhan University, School of Power and Mechanical Engineering, China 2 Wuhan University, Hubei Key Laboratory of Waterjet Theory and New Technology, China 3 University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, United States The self-resonating cavitating waterjet (SRCW) has been widely used for many practical and industrial applications since the first recognition of its strong cavitation ability. To further improve the performance of SRCW under ambient pressures, the effects of nozzle inner surface roughness were experimentally studied by impinging the jets on pure aluminium specimens (1070A) at various standoff distances. The typical macroscopic appearances and mass losses of the eroded specimens were used to evaluate the performances of the jets issuing from six organ-pipe nozzles of different inner surface roughness values (0.8 pm, 1.6 pm, 3.2 pm, 6.3 pm, 12.5 pm, and 25 pm). The results show that nozzle inner surface roughness significantly influences the optimum standoff distance and the cavitation intensity, which greatly depends on the ambient pressure. Moreover, it is found that there is always an optimum surface roughness that can remarkably enhance the cavitation erosion capability under each ambient pressure. Specifically, at ambient pressures of 2 MPa and 4 MPa, the surface roughness of 6.3 pm causes the strongest cavitation intensity at standoff distances of 42 mm and 50 mm, respectively. While at ambient pressures of 6 MPa, 8 MPa, and 10 MPa, the surface roughness of 12.5 pm is the one that maximally enhances the intensity at standoff distances of 45 mm, 40 mm, and 35 mm, respectively. Furthermore, the enhanced cavitation intensity is found to improve the impingement power of the high-speed waterjet as well. The present study also helps to provide a guideline for determining the finishing accuracy of inner surface required in the fabrication of organ-pipe nozzles. Keywords: self-resonating cavitating waterjet, surface roughness, cavitation erosion, ambient pressure, organ-pipe nozzle Highlights • Erosion tests under ambient pressures were performed to study the effects of nozzle inner surface roughness on cavitation. • The macroscopic appearances and mass losses of eroded specimens were analysed. • Nozzle inner surface roughness affects the optimum standoff distance and the impingement power of the jet. • There is a preferred nozzle inner surface roughness value under each ambient pressure. 0 INTRODUCTION Cavitation is the formation of vapor bubbles in a liquid and happens when the local pressure is lower than the vapor pressure of the liquid [1]. It can be easily generated with high-speed waterjets. The collapse of cavitation bubbles near a solid boundary can cause very high amplitude and small duration impulsive loads and emits a large amplitude pressure wave, which subsequently leads to serious local damage [2]. Based on this feature, cavitating waterjet, which can be produced by creating a large number of bubbles in the periphery of the jet, has been proposed and is now being used in a wide spectrum of applications, such as cavitation peening, removal coating [3], cleaning [4], cutting [5], deep-hole drilling [6], and killing bacteria [7]. To enhance the cavitation intensity of the cavitating waterjet for better utilization, a considerable number of investigations related to the mechanism of cavitation and methods for promoting it have been conducted. In more specific terms, Bilus et al. [8] performed an experimental analysis of the structure dynamics of cavitation cloud and corresponding pressure fluctuations. They concluded that there is a strong interaction between pressure and cavitation cloud with two dominant frequency bands. Soyama [9] experimentally studied the effect of various types of nozzle geometries on the aggressive intensity of cavitation erosion. Based on a control volume concept, Zhou et al. [10] developed a novel lumped parameter model of cavitating orifice flow by using the computational fluid dynamic method. Furthermore, several self-resonating cavitating nozzles, named "Pulsef', "Pulser-Fed", "Laid-back Pulser", and "Organ-pipe", have been proposed and investigated by Johnson et al. [11]. Waterjets issuing from these nozzles have large-scale coherent structures and vortex rings in the shear layer, which can dramatically increase the cavitation intensity. A schematic diagram of the generation and working principles of SRCW is shown in Fig. 1 with the use of an organ-pipe nozzle, which is one of the most promising nozzles in applications due to its simple structure and strong cavitation ability [12]. Fig. 1. Schematic diagram of the operating principles of an SRCW issuing from an organ-pipe nozzle As is shown in the figure, an organ-pipe nozzle consists of an upstream area contraction (Df/Dc), a downstream area contraction (Dc /De), and a resonant chamber with a length of Lc and a diameter of Dc. When a high-speed flow is passing through the nozzle, pressure waves will be formed at the downstream area contraction because of the sudden changes of the flow velocity. These waves propagate upwards and then are reflected at the upstream contraction due to the change of impedance. At this time, the upstream and downstream contractions are excitation zones, which are the geometrical foundation for producing SRCWs. Then, the incident waves are superimposed on the reflected waves, and an acoustic resonance will finally be formed if the length of the chamber is designed to shape a standing wave [11] to [14]. The peak resonance can be achieved by matching the fundamental frequency of the organ-pipe nozzle with the critical jet structuring frequency. Moreover, the exact frequency of peak resonance depends on the end impedances; for instance, if both (Df/Dc)2 and (Dc /De)2 are large, the first model natural frequency of the chamber will occur when the wavelength in the fluid is approximately four times the chamber length Lc [13]. When an SRCW is produced, the energy content of the jet can be dramatically amplified, because the shear layer of the jet can be organized into large ring vortices emitted from the nozzle at a discrete frequency and could cavitate to form toroidal bubbles [14]. The formation, growth, and collapse of these bubbles could cause very high-pressure fluctuations that can be further enhanced by the self-resonance to several orders of magnitude higher, resulting in the greatly improved cavitation erosion capability of the jet [15]. These features make SRCWs especially suitable for deep-hole drilling, where high ambient pressures can prevent the formation of cavitation bubbles in conventional cavitating jets because of the low incipient cavitation numbers [16]. Furthermore, it has already been proven that SRCW has stronger cavitation erosion ability at relatively greater ambient pressures. To be more specific, Johnson et al. [17] experimentally claimed that the incipient cavitation numbers for SRCWs were generally two to six times higher than conventional cavitating waterjets under the same ambient pressure. Results of field trials conducted by Li et al. [18] revealed that the drilling rate in deep oil wells of high ambient pressures could be considerably improved from 10.1% to 31.5% with the use of SRCWs. Even though SRCW has many advantages over conventional cavitating jets under ambient pressure conditions, to the best of our knowledge, few investigations have been performed to understand the influence of nozzle inner surface roughness on the cavitation erosion capabilities of the jets. However, nozzle inner surface roughness is expected to affect the cavitation characteristics significantly. Based on a numerical investigation on the effects of wall roughness on cavitating flow, Echouchene et al. [19] concluded that wall roughness leads to higher shear stresses in the liquid and produces additional disturbance of the velocity and pressure. In addition, Chang et al. [20] experimentally found that the nozzle inlet surface roughness can affect the occurrence of cavitation much more than it affects hydraulic flip. Most importantly, in our most recent studies [21] and [22], it has been shown that the nozzle inner surface roughness can have dramatic effects on the axial pressure oscillations as well as the cavitation erosion intensity and efficiency of SRCW. As the strong cavitation ability under ambient pressures is one of the greatest advantages of SRCW, the purpose of this study is to further improve the aggressive intensity of cavitation erosion by investigating the effects of nozzle inner surface roughness. 1 RELATIONS BETWEEN SURFACE ROUGHNESS, TURBULENT FLOW, AND CAVITATION Turbulent flow occurs when the ratio of inertial force to viscous force exceeds a critical value, and its intensity can be measured by the Reynolds number (Re). In a turbulent flow, the violent and unsteady motions of the fluid particles make the flow highly irregular, which produces large pressure fluctuations in the fluid. When the local pressure drops below the vapor pressure, cavitation occurs and then disordered, and unstable eddies are formed in the fluid. The formed vortices have a tendency of pairing into vortex rings of many different length scales, which greatly impacts the flow behaviours, including energy dissipation and pressure pulsations [23]. Fig. 2 illustrates the structure of a fully turbulent viscous flow passing through a circular pipe of the rough inner surface. As shown in the figure, the flow structure can be divided into viscous sublayer region and turbulent core region. Though the thickness of the viscous sublayer is rather small (about 10 % of the boundary layer thickness), the viscous shear force in the layer plays a significant role on the turbulence properties, such as the convective heat transfer, momentum and mass exchange, and energy diffusion [24]. If the viscous sublayer is affected, cavitation, which is closely related to the turbulent characteristics, will be influenced as a result. turbulence and cavitation mentioned above, it can be deduced that once the turbulent flow is affected, the cavitation process will be influenced as well. This assumption is in accordance with one of the studies on the influence of surface roughness on turbulent flow, carried out by Nikuradse [25]. He demonstrated that the velocity distribution of the turbulent flow was dramatically dependent on the relative roughness. By means of experimental investigation, Li et al. [26] found that when the roughness height is more than five times the viscous sublayer thickness, the flow friction, which can cause large pressure drops in the fluid, begins to increase sharply. In contrast, when a highspeed liquid is flowing over the roughness elements, fluid separation tends to occur, which will promote the generation of cavities and thus the cavitation erosion intensity. A preliminary calculation (detail is shown in Section 3.2) has shown that the most commonly used surface roughness values (0.8*10-6 m ~ 25*10-6 m) are of the same order of magnitude with the thickness of viscous sublayer at high Reynolds numbers. So, combined with the previous related literature [19] to [22], it could be expected that nozzle inner surface roughness should put some effects on the cavitation erosion ability of SRCW. 2 EXPERIMENTAL SETUP AND PROCEDURES 2.1 Experiment Apparatus and Procedures Fig. 2. Schematic of flow structure of turbulent flow over rough surface Because of the practical limitations on surface machining, the inner surface of the nozzle is not ideally smooth but has enormous amounts of micro-irregularities called roughness elements. If the magnitude of roughness element height is similar to the viscous sublayer thickness, violent interactions between the roughness elements and the viscous sublayer will happen and thus significantly influence the turbulent flow. Based on the relations between A schematic diagram of the experimental setup for the cavitation erosion test under several ambient pressures is shown in Fig. 3. Pressured tap water was supplied from a plunger pump whose working pressure can be continuously regulated through the control table from 0 MPa to 60 MPa with a maximum flow rate of 120 l/min. Two bladder accumulators were applied to minimize the influence of pressure fluctuations of the pump on the experimental results. Specifically, one accumulator was installed near the pump, and the other one was positioned close to the nozzle being tested, as shown in Fig. 3. To remove the effects of pressure loss in the pipeline under different operating conditions, a pressure transducer (Model: BD DMP331P), which had been calibrated by the manufacturer, was installed immediately before the nozzle to make sure that the inlet pressure (Pi) of each test was consistent with the designed value of 25 MPa. The range and accuracy of the pressure transducer were 1 MPa to 40 MPa and ±0.05 %FS, respectively. And in each test, the shutter would not be removed until the value obtained by this transducer remained stable. Fig. 3. Schematic of experimental setup for erosion tests The tests were conducted in a high-pressure chamber made of stainless steel. The maximum design pressure of the chamber was 10 MPa, and the achievable standoff distance was 300 mm with a regulation precision of 0.5 mm. The chamber pressure (which is also the ambient pressure Pa ) was regulated and controlled by an electromagnetic relief valve, as shown in the figure. Standoff distance, S, was defined as the distance from nozzle exit to the impingement surface of the specimen. Preliminary tests had been performed to determine a proper range of the testing standoff distance, which was from 10 mm to 100 mm with an interval of 10 mm. During the process of each test, the chamber pressure was monitored by another pressure transducer of the same model. The erosion time for each test was 180 seconds, which was guaranteed by removing the shutter between the nozzle and the specimen in the chamber. The mass of each specimen was measured before and after each erosion test, and mass loss, Am, was defined as the difference between the two values. The specimen was measured on an electronic balance (Model: Sartorius BSA224S-CW) with a resolution of 0.1 mg and linearity of 0.2 mg. 2.2 Nozzles and Specimens In this experiment, all the organ-pipe nozzles had the same geometry with Df = 13 mm, Dc = 5 mm, De = 2 mm, and Lc = 18 mm, which were obtained based on the design principles of organ-pipe nozzle proposed by Chahine [14]. The inner surface roughness values of the six nozzles (shown in Fig. 4) were 0.8 ^m, 1.6 ^m, 3.2 ^m, 6.3 ^m, 12.5 ^m, and 25 ^m, respectively, which were achieved by changing the machining process on a high-precision digital controlled lathe [22]. These roughness values are the most commonly used in machining nozzles of similar size. Before the tests, the inner surface roughness of each nozzle was measured on a roughness measuring instrument (Model: Hommel-Etamic T800 RC) with a resolution of 1 nm to ensure the precise accuracy of the roughness values. The manufacturer was Metrology, and the measuring range was 0.1 ^m to 120 mm. Considering that pure aluminium is commonly used in cavitation erosion tests [22], [28], and [29], the same material was used as a specimen here. The chemical composition and physical properties of the specimen are listed in Tables 1 and 2, respectively. It should be noted that the surface of each specimen exposed to the impingement of the jets had been 95 Table 1. Chemical composition of specimen (mass%) Material Chinese standard Al Si Cu Mg Zn Mn Ti Fe Pure aluminium 1070A 99.70 <0.20 <0.03 <0.03 <0.07 <0.03 <0.03 0.000 ~ 0.250 Table 2. Physical properties of specimen . , . , , Density Elasticity modulus Tensile strength Material Chinese standard ^ px103 [kg/m3] £x109 [Pa] ^xioe [Pa] Offset yield strength ^0.2x106 [Pa] Vickers hardness tfvx109 [Pa] Pure aluminium 1070A 2.71 71 55 15 38 polished and measured on the mentioned roughness measuring instrument to ensure the uniformity of specimens. Fig. 4. The testing organ-pipe nozzles 3 RESULTS AND DISCUSSION Based on the previous related theoretical and experimental efforts [2], [22], and [28], the effects of nozzle inner surface roughness on the cavitating erosion intensity of SRCW were evaluated from the aspects of both the macroscopic appearances and the mass losses of the eroded specimens. 3.1 Macroscopic Appearances of the Eroded Specimens Fig. 5 shows the macroscopic appearances of the eroded specimens at an ambient pressure of 4 MPa and a standoff distance of 40 mm. These photographs are chosen and displayed because the appearances reveal the most obvious differences at these operating conditions. From the size of the pit and the distribution density of the dots as well as the size of the eroded area, one can have a visualized and preliminary understanding of the effects of nozzle inner surface roughness on the cavitation erosion performance of SRCW. As can be observed in the figure, all the eroded specimens have the typical appearance of cavitation erosion with a pit at the centre and a ring shape as the main erosion region composed of numerous small dots [28] to [30]. The pit is caused by the high-speed waterjet impingement of droplets, and the ring shape is created by a cavitation cloud. More specifically, when a cavitation bubble collapses to a boundary, microjets are formed during the process and subsequently a shock wave is generated at the moment of rebounding, resulting in the damage of materials most possibly through fatigue erosion [2]. It is clear that nozzle inner surface roughness significantly affects the cavitation ability. In more specific terms, the sizes of the pit in the centre are nearly the same with a diameter of about 4 mm for surface roughness values of 0.8 pm, 1.6 pm, and 3.2 pm. Moreover, the distribution of small dots composing the ring shape is somewhat scattered, and the general size is relatively small, meaning the cavitation abilities of these three nozzles are similar. Since the surfaces of these three nozzles are rather smooth, it should be reasonable to conjecture that this is because the mean height of the roughness elements is rather small compared with the viscous sublayer thickness under this condition. This is hydraulically smooth turbulent flow [25]. Therefore, the roughness elements can hardly protrude and interact with the viscous sublayer, and the turbulent behaviours of the high-speed flow cannot be affected nor can the cavitation ability. From Fig. 5, it can be observed that the macroscopic appearance of the specimen eroded by the jets from the nozzle of the inner surface roughness of 6.3 pm is the most apparent, with respect to both the pit at the centre and the dots composing the ring shape. The pit has a diameter of about 8 mm, which is twice that of the pits on the specimens eroded by the jets from the nozzles of surface roughness values below 3.2 pm. In addition, the general sizes of the dots are larger, and the distributions are more concentrated. This indicates that both the high-speed waterjet impingement and the cavitation intensity are dramatically enhanced. Moreover, the improved Ra=6,3 pm Ra=12,5 pm Ra=25 pm Fig. 5. Photographs of the eroded specimens at Pa = 4 MPa, S = 40 mm, and o = 0.190 cavitation intensity is most probably caused by the increased inner surface roughness, as it is the only variable between each erosion test. It can be deduced that the improved impingement ability of the highspeed waterjet is most likely to be induced by the enhanced cavitation intensity. To be more specific, the promoted cavitation produces more bubbles around the jet periphery, leading to a great reduction of the friction and interaction between the high-speed jet and the surrounding fluid [29]. As a result, the high-speed water jet contains more energy, which subsequently leads to a bigger size of the pit at the centre. With the surface roughness value increased to 12.5 ^m, the sizes of the pit and the small dot become smaller again, meaning a reduction of both the impingement of high-speed waterjet and the cavitation intensity. This phenomenon is more evident when the nozzle inner surface roughness is increased to 25 ^m. Under this condition, the pit is no longer a circle, indicating the jet beam is dispersed. The phenomenon suggests that surface roughness elements already violently interact with the high-speed flow through the viscous sublayer and put a disadvantageous effect on the cavitation erosion performance of SRCW. In contrast, it can be concluded that, under the current condition, surface roughness value of 6.3 ^m is a critical value for the nozzle to achieve the strongest cavitation intensity. Below this value, surface roughness has little effect on the cavitation erosion behaviours, while above the value surface roughness will reduce the cavitation intensity. 3.2 Cavitation Erosion Intensity Fig. 6 shows the mass loss of eroded specimen as a function of standoff distance with respect to various ambient pressures and values of nozzle inner surface roughness. Each curve experiences a peak at a distance where the maximum mass loss occurs. This distance is called the optimum standoff distance. This observation suggests that the existence of an optimum standoff distance is a common feature of SRCW, regardless of the nozzle inner surface roughness. The main reason 160 140 120 100 1 I f ž' i i 0— Ra=0.8|im A— Ra=3.2iim —X— Ra=1.6jim Ra=6.3jim —*—Ra= 12.5|jjn —s— Ra=25|jjn 1 1 1 1 —O— Ra=0. 8 pm Ra= 1. 6|im -A-Ra—3.2|_im -X-Ra=6.3|im —*—Ra=12.5|xm —9—Ra=25jim ; Standoff distance.? [mm] iPa=6MPa. o=0J16) StandetY distances [m :Pi!=8MPa, <¡=0.471 Fig. 6. Mass loss as a function standoff distance at different ambient pressures; a) Pa = 2 MPa, b) Pa = 4 MPa, c) Pa = 6 MPa, d) Pa = 8 MPa, e) Pa = 10 MPa for the occurrence of optimum standoff distance is that bubbles generated in the boundary or shear layer need a certain time to grow into sizes at which the collapse of cavitation clouds could produce destructive power for the specimens [2]. Therefore, analysing the optimum standoff distance is an important way to evaluate the effects of nozzle inner surface roughness on cavitation erosion. Moreover, the figure makes it possible to determine a proper range of standoff distances where strong cavitating capabilities can be achieved under different operating conditions. It is of great interest to note that even the nozzles have different values of surface roughness; the optimum standoff distance for each nozzle experiences the same tendency. More specifically, the optimum standoff distance first increases and then decreases with the increase of ambient pressure. This is in rough agreement with the experimental results obtained by Li et al. [18] and [31] who concluded that the optimum standoff distance should keep increasing with the increase of ambient pressure. The statement was that the increasing ambient pressure suppresses the bubbles. As a consequence, additional time was needed for the bubbles to grow, leading to an increase of the optimum standoff distance. Actually, this can also be used to explain the increased optimum standoff distance at ambient pressures below 6 MPa. Since a certain degree of ambient pressure has the ability to keep the bubbles from bursting, more cavitation bubbles will exist in the shear layer under this condition. Another reason for the increasing optimum standoff distance should be the largely reduced friction between the jet and the surrounding fluid, caused by the enormous cavitation bubbles generated in the free shear layer. However, when the ambient pressure exceeds 6 MPa, the convective heat transfer and momentum and mass exchange between the jet and the ambient liquid become so violent that the energy of the jet dissipates rapidly with increasing standoff distance [32], leading to the decrease of the optimum standoff distance. In contrast, at high ambient pressures, pressure fluctuations around the jet are largely attenuated, causing a decrease in the number of cavitation bubbles. As a result, cavitating erosion intensity is dramatically weakened, which is reflected as a reduction of the optimum standoff distance [11]. It is a fact that an optimum standoff distance under all ambient pressures exists regardless of nozzle surface roughness. However, the values of the optimum standoff distance are different. For example, at ambient pressure of 2 MPa, the optimum standoff distance for the nozzle with a roughness value of 6.3 ^m is around 45 mm, while for roughness values of 12.5 ^m and 25 ^m, it is about 35 mm. Furthermore, at ambient pressure of 2 MPa and 4 MPa, the optimum standoff distance of a nozzle with roughness value of 12.5 ^m is always the largest. Furthermore, at ambient pressure of 6 MPa, 8 MPa, and 10 MPa, the optimum standoff distance of a nozzle with a roughness value of 25 ^m is the largest. In contrast, if the maximum mass loss is considered, it can be found that a roughness value of 6.3 ^m is the best one at ambient pressures of 2 MPa and 4 MPa, while roughness value of 12.5 ^m takes its place to be the best one at pump pressures of 6 MPa, 8 MPa, and 10 MPa. Specifically, proper surface roughness can promote the generation of cavitation bubbles, which is in satisfying agreement with the results obtained by Numachi et al. [33], who experimentally demonstrated that surface roughness could advance cavitation inception. Similar evidence can also be obtained from the research performed by Chang et al. [20]. Despite the influence of surface roughness on the value of optimum standoff distance, it is observed that nozzle inner surface roughness also significantly affects the magnitudes of the mass losses of the specimens. As the figure illustrates that curves of roughness values of 0.8 ^m and 1.6 ^m are overlapped all the time, which means surface roughness below 1.6 ^m have little effect on the cavitation erosion intensity. This is consistent with the assumption that the chamber plays a dominating role when the surface is relatively smooth. It is interesting to note that the maximum mass loss caused by the roughness value of 3.2 ^m is a little larger than that caused by roughness values of 0.8 ^m and 1.6 ^m at lower ambient pressures (Fig. 6a and b). However, the difference between these curves diminishes gradually with increasing ambient pressure. After the ambient pressure has exceeded 6 MPa, the difference disappears (Fig. 6c and d). In addition, a surface roughness value of 25 ^m should be avoided in the fabrication of organ-pipe nozzles because it leads to the weakest erosion intensity. In order to provide a further discussion on the effects of nozzle inner surface roughness, the viscous sublayer thickness under each ambient pressure has been calculated and is shown in Table 3. It should be emphasized that only viscous sublayer thicknesses at nozzle chamber and exit were calculated because the velocity at nozzle inlet (U,) is nearly 2.37% the velocity at nozzle exit (Ue). The calculation process is shown below. The Bernoulli equation is [24]: p U2 p U2 _J_ + + + hf + h, (1) pg 2 g pg 2 g ' where p is the liquid density, g is the acceleration of gravity, hf is the fictional head loss, hj is the local head loss. hf =X--, f d 2 g h. = kU-, 1 2g ' (2) (3) where X is the friction coefficient, l is the length of the flow channel (here it is the nozzle length), d is channel diameter, u is flow velocity, and k is the local resistance coefficient. Under the sudden contraction condition, k can be expressed as: ( / . ^V *=1 2 1 - f AlL A (4) where Ax and A2 are the cross-section areas at the contraction. In Eq. (2), X, l, and u are rather small. So, it can be neglected during the calculation. When compared with Ue, U can also be neglected. Table. 3. Thickness of viscous sublayer under different conditions (in [pm,]) _Pa [MPa]_ Ra [um] _2_4_6_8_10 Chamber Exit Chamber Exit Chamber Exit Chamber Exit Chamber Exit 0.8 9.011 0.0965 9.630 0.101 10.015 0.106 10.353 0.112 11.210 0.120 1.6 9.011 0.104 9.630 0.109 10.015 0.115 10.353 0.121 11.210 0.129 3.2 0.627 0.113 0.675 0.118 0.702 0.125 10.353 0.134 11.210 0.140 6.3 0.679 1.170 0.732 1.220 0.761 1.290 0.793 0.145 0.866 0.154 12.5 0.741 1.060 0.798 1.104 0.830 1.168 0.864 1.231 0.944 1.311 25 0.817 0.944 0.881 0.984 0.916 1.041 0.954 1.097 1.041 1.168 By combining Eqs. (1), (3), and (4), different Ue for each of the five ambient pressures are obtained, which are 172.20 m/s, 164.54 m/s, 156.52 m/s, 148.05 m/s, and 139.06 m/s, respectively. For the viscous sublayer thickness, it can be obtained by [24]: 8, = 32.8d Re^' And Re is expressed by: _ ud Re = —, (5) (6) where v is the fluid kinematic viscosity coefficient. In terms of A, it depends on Re and can be calculated as follows [24]: ( d ^ For 104 < Re< 26.981-1 : = 2\g(Re>/Ä) - 0.8, (7) where A is the absolute surface roughness, here, it is the surface roughness value. For 26.981 -' A < Re < 41601 — 1 ( A ;/r=_21g 2.51 3.7d (8) For Re > 41601 — = 1.74 + 2lg—. 4Ä 2A (9) From Eqs. (5) to (9), ^ at each roughness value and each ambient pressure can be achieved, shown in Table 3. Moreover, the important parameter defining cavitation intensity is cavitation number, a, which can be expressed as: P. - P. a = - (10) K V where Pv is the vapor pressure of the liquid. From Table 3, it can be observed that the viscous sublayer thickness not only depends on the ambient pressure but also largely depends on the roughness value. And the sublayer thicknesses at chamber and exit are much different, particularly when the surface is relatively smooth, say 0.8 ^m and 1.6 ^m. The data also looks irregular. However, from the optimal surface roughness in Fig. 6, it seems that the viscous sublayer thicknesses at chamber and exit determine the erosion intensity respectively, depending on the surface roughness value. For example, at roughness values of 0.8 ^m and 1.6 ^m, the viscous sublayer thickness is around 10 ^m, which is much thicker than the roughness element. As a result, the roughness elements are totally covered by the viscous sublayer and can hardly influence the turbulence core. Thus, the cavitation erosion intensities are similar. When the viscous sublayer thickness at nozzle exit changes abruptly, the corresponding surface roughness results in the strongest cavitation erosion intensity. However, this is not applicable to the case of roughness value of 6.3 ^m and ambient pressure of 6 MPa. Under this case, a roughness value of 6.3 ^m is the one that causes the abrupt change, but roughness value of 12.5 ^m is the optimum. Even with this inconsistency, the curves of roughness values of 6.3 ^m and 12.5 ^m nearly experience the same tendency. However, due to the rather limited literature on the effects of nozzle inner surface roughness, it is currently very difficult to provide an explanation for this phenomenon. Further theoretical and mathematical investigations need to be performed. v It is also observed in the figure that at an ambient pressure of 4 MPa, each surface roughness can cause a greater mass loss around the optimum standoff distance compared to those under the other ambient pressures, meaning a certain degree of ambient pressure can enhance the cavitation erosion intensity of SRCW. The fact that the jet has the strongest cavitation erosion intensity at an ambient pressure around 5 MPa is in good agreement with the results obtained by Johnson et al. [11], demonstrating the reliability of our research. 4 CONCLUSIONS For the purpose of enhancing the cavitation intensity of SRCW under ambient pressures, the effects of nozzle inner surface roughness values were studied by means of erosion testing. Unfortunately, there is currently little literature on the effects of nozzle inner surface roughness. Further investigations need to be conducted to understand the interactions of surface roughness and cavitation. However, the present study brings light to some evidence: 1. Under the experimental conditions, nozzle inner surface roughness has dramatic effects on the cavitation erosion performance of SRCW, which seems to largely depend on the viscous sublayer thickness. Corresponding to each ambient pressure, an optimum roughness value for achieving the strongest cavitation intensity exists. 2. The optimal surface roughness almost occurs at the place where the viscous sublayer thickness at the nozzle exit changes abruptly. 3. The existence of an optimum standoff distance is a common feature of SRCW, and the surface roughness affects its exact value of the optimum standoff distance. 4. A certain ambient pressure enhances cavitation erosion intensity, which is another feature of SRCW regardless of nozzle inner surface roughness. 5 ACKNOWLEDGEMENTS This research is financially supported by the National Key Basic Research Program of China (No. 2014CB239203), the National Natural Science Foundation of China (No. 51474158) and the China Scholarship Council (No. 201406270047). 6 REFERENCES [1] Karadžič, U., Bulatovic, V., Bergant, A. (2014). Valve-induced water hammer and column separation In a pipeline apparatus. Strojniški vestnik - Journal of Mechanical Engineering, vol. 60, no. 11, p. 742-754, DOI:10.5545/sv-jme.2014.1882. [2] Kim, K.H., Chahine, G., Franc, J.P., Karimi, A. (eds.) (2014). Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction. Springer, Dordrecht, DOI:10.1007/978-94-017-8539-6. [3] Ciubotariu, C.R., Secosan, E., Marginean, G., Frunzaverde, D., Campian, V.C. (2016). 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Flow regimes of free jets and falling films at high ambient pressure. Chemical Engineering Science, vol. 55, no. 19, p. 4189-4208, D0I:10.1016/S0009-2509(00)00074-9. [33] Numachi, F., Öba, R., Chida, I. (1965). Effect of surface roughness on cavitation performance of hydrofoils-Report 1. Journal of Basic Engineering, vol. 87, no. 2, p. 495-502, D0I:10.1115/1.3650583. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)2, 103-110 © 2017 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2016.3805 Original Scientific Paper Inverse Method for Controlling Pure Material Solidification in Spherical Geometry Mohamed Charifi* - Rabah Zegadi University of Setif, Institute of Optics and Precision Mechanics, Algeria In this study, we present the control of the solidification process of a phase-changing, pure material described in one-dimensional spherical geometry. We used an inverse global descent method in which the gradient and the adjoint equation are constructed in continuous variables of time and space. The control variable is the temperature at the fixed boundary of the solid domain. For the desired solidification front, the control was determined using information on the heat flux deduced by heat balance. The numerical resolution was based on a finite difference method in a physical domain with a moving grid related to the evolving solidification front with time. The developed numerical model was validated using an exact built solution. The numerical results of the control problem are presented for both the exact and noisy data cases. For the noisy data, a regularization method was applied. In the case of the exactdata, a rapid control determination was achieved except for time steps near the end. The random errors effects in bruited data were considerably reduced by regularization. Keywords: phase change, interface solid/liquid, inverse problem, spherical geometry Highlights • Control of pure material solidification in spherical geometry was studied for a solidification planar front. • An inverse global method has been used to determine the temperature at the fixed boundary of the solid domain as a control. • The numerical resolution was based on the finite difference method in a physical domain with a moving grid. • The algorithm has enabled the rapid control determination with excellent accuracy. 0 INTRODUCTION Material phase change represents a major challenge in various fields (metallurgy, heat storage systems, food conservation, etc.). Each year, more than a billion tons of metals are solidified around the world, mainly ferrous alloys (steel, cast iron), and aluminium. Moreover, storing thermal energy methods used in the food and pharmaceutical industries and air conditioning are directly related to the melting and solidification phenomena. In the case of material solidification, the kinetics of the state change and, more specifically, the geometry of the interface phase transition and its evolution over time determine the structure and properties of the final state. The determination by direct measurement of the mobile interface is generally very difficult to achieve. Inverse methods are most commonly used to simulate such phenomena of phase change. The control of the solidification front of a material by simulation, in metallurgy, for example, enables modification of its mechanical properties (hardness, toughness or mechanical strength). These properties depend mainly on the parameters used in the simulation (temperature, heat flux, the geometry of the solid/liquid interface and its velocity evolution). It is, therefore, necessary to control the solid/liquid interface in order to obtain particular desired properties. The melting or solidification of pure substances and eutectic alloys are characterized by a well-defined melting temperature. The solid and liquid phases are well differentiated by a sharp interface. In the case of mixtures and non-eutectic alloys, the phase change spreads out over a temperature range where the solid and liquid phases coexist. This two-phase mushy region is limited by an interface with the liquid phase at the liquidus temperature and another interface with the solid phase at the solidus temperature [1]. Solid/liquid phase change problems have been widely discussed by several authors using either inverse or direct methods. Zabaras and Ruan [2] sequentially solved a one-dimensional inverse Stefan solidification problem. They used a deformable finite element method to calculate the position and the speed of displacement of the interface and information on the temperature measured by two or more sensors located within the solid phase. Zabrasand Kang [3] treated an iterative resolution numerical simulation of a freezing front control problem in a linear case. Samaï et al. [4] identified the position of the solidification front using an iterative descent method. Jiang and al. [5] solved an inverse problem by the conjugate gradient method using finite differences to determine the historic heat flux and the final temperature distribution. Tikhonov's zero order regularization method was introduced to stabilize the inverse solution. Hetmaniok and Slota [6] determined the boundary conditions in the process of binary alloy solidification when the temperature measurements at selected points of the cast are known. In this model of Stefan, the liquidus temperature varies with the concentration of the alloy component. Various direct methods were also used by some authors for determining the temperature at a fixed boundary, knowing the position of a mobile interface solid/liquid [7] or for evaluating the position of one or many mobile interfaces for a given temperature [8] to [10]. Other studies on phase change on materials (PCM) were treated using cylindrical or spherical coordinates [11] to [13], by fixing the mobile front in the presence of convection [14] and increasing energy storage [15]. The position of the solid/liquid interface can be directly determined experimentally using temperature measurements [16], optical monitoring [17], x-ray [18], ultrasound [19] and [20], eddy current [21], thermoelectric [22], and electrical resistance diagnostics. Although these experimental techniques are largely used for identifying the solid/liquid interface in a phase change problem, they remain expensive and difficult to implement. Moravč et al. treated experimentally the solidification conditions of cold worked high alloy tool steel in comparison to construction steels in quasi equilibrium state [23]. Steiner Petrovič and Šturm experimentally study the modification of a non-oriented electrical steel sheet entirely treated with antimony using a laser surface alloy [24]. Hriberšek et al. solved inverse problem for determining surface heat transfer coefficient between liquefied nitrogen and a plate of inconel 718. The design of the numerical simulation was validated experimentally [25]. Indirect identification or control of the solidliquid interface requires a simulation of the problem and its resolution. In the case of material solidification, the phase change problem can be resolved by inverse methods, usually validated by experimental data. From a theoretical perspective, the validation of a simulation (mathematical model used) can be done using exact solutions in particular situations instead of experimental data. In a solidification phase change process, the solid and liquid phases have different thermophysical properties. In the solid phase, the heat transfer is purely conductive. In the liquid phase, two heat transfer situations are possible. If the liquid phase is maintained at the phase change temperature as in our study case, the heat transfer is purely conductive. When the temperature of the liquid phase is greater than the phase change temperature, the heat transfer occurs by diffusion and natural convection. The purpose of this work is to control a pure material solidification by an optimization method formulated as an inverse problem of thermal conduction. We are interested in the control of the solid/liquid interface for a pure material in one-dimensional spherical geometry considering a planar front. The control variable used is the temperature at the fixed boundary of the solid domain. The given problem data are the initial state, the desired front (planar front) evolution, and the phase change temperature. With supplementary information on the heat flux at the front deduced from a heat balance, the inverse problem resolution can be made. The thermal system of our problem is governed by the conduction equation. We introduce for this resolution the least square criteria characterizing the difference between the dynamic behaviour of the system and the corresponding developed mathematical model. We then introduce the adjoint equation for evaluating the criteria gradient. The use of an iterative algorithm based on a conjugated gradient enables to find the optimal solution. We described the problem equation with space-and-time continuous variables and the procedure for finding the criteria gradient with the corresponding adjoint equation. The numerical resolution was undertaken using the conventional finite difference method with a mobile grid related to the considered physical domain. The time variable is then discretized according to the Crank-Nicolson unconditionally stable scheme. The exposed results concern the exact built solution and the noisy exact data. In order to guaranty the well-posed problem and a stable solution for the noisy data case, Tickonov's regularization method was used. 1 INVERSE PROBLEM FORMULATION The equations that govern the problem for the solid and the liquid phases are presented in the following. 1.1 Solid Phase In the solid phase, the temperature T(r,t) re[Sd(t),R] and the heat flux ^(t) penetrating the moving boundary Sd(t) in the time interval [0, f are obtained by the resolution of the following thermal conduction equations: dT(r, t) A d i 2 dT(r, t) pscs---s—I r - dt r dr ^ dr T (0, t ) = U (t ), = 0, (1) (2) T (Sd (t ), t ) = T Sd (t = 0) = So, T (r, 0) = T0(r ), dT çs (t ) = ^ dT(Sd (t ), t) dr (3) (4) (5) (6) 1.2 Liquid Phase In the liquid phase, the temperature T(r,t) re [0, .¿(t)] and the heat flux ^(t) penetrating the moving boundary Sd(t) in the time interval [0, tf] are obtained by the resolution of the following thermal conduction equations: dT(r, t) A, d ( 2 dT(r, t)N Pfif 2 -I r dt r dr ^ dr T (Sd (t ), t ) = Tf, dT (0, ? ) = 0 dr Sd (t = 0) = So, T (r, 0) = T0(r ), dT (Sd (t ), t) = 0, Ç(t ) = Xi dr (7) (8) (9) (10) (11) (12) where the variables r, t and T in their non-dimensional forms are defined as follows: * r * t'À r = R ' = ' where Trf. = T(0,0) - T(0, tf ). T =- T - T f (13) ref Remark: thereafter the symbol * will be omitted. During solidification, the heat balance (Stefan equation) at the solid/liquid interface can be expressed as: dS (t) 9p(t ) -9i (t) = 9l (t ) = PiL~ dt (14) In the case in which the liquid phase is maintained at the melting temperature Tf, the heat flux entering the solid is: 9 p (t) = 9, (t) = P'ld^. (15) To solve the direct problem, we need to determine T(r,t;U) and $s(t;U) from the data: {tf,S0, T0(r), Tf,Sd(t)} and from the U(t) control in the interval (0 < t< tf). If 0p(t) is the prescribed flux entering the solid at the front, the inverse problem to solved is to find the control U*(t) on [0,tf from the data set in order to obtain $s(t; U*) as close as possible to ^(t). Fixed boundary U(t) Fig. 1. Definition domain solidification process 1.3 Assumptions This simulation concerns a pure material where the following assumptions are usually admitted for this type of material: • The material in each phase is homogeneous and isotropic. • The thermo-physical properties (A, p, c) of the material are independent of temperature, but they are different form phase to phase. • The effect of natural convection in the liquid phase of the material is not taken into account (constant density). • No internal heat generation and all radiation effects are neglected. • The mould wall is considered very thin with no temperature gradient. Its thermal resistance can be neglected. 2 INVERSE RESOLUTION METHOD The introduced least squares criterion J is: J (U) = \'^wl(t )(ys (t;U)-yp (t ))2 dt. (16) The problem resolution consists in determining U*(t) with the conditions: U*eV ,Vt e [0, tf] such that: J(U*) = inf J(U) where V is the set of admissible solutions. A Ribiere-Polak conjugate gradient algorithm is used to calculate the time interval [0, tf] the iterates U(t) according to the following steps: 1. Determination of T (r, t; Un) and ^(t; Un) as solutions of the direct problem in the solid phase. 2. Evaluation of the criterion J( U*). 3. Resolution of the adjoint problem to calculate VJ"(t;U), the gradient of the criterion J with respect to U. 4. Solving the problem of variation to determine ST(r, t)d. 5. Determination of the iterates Un+1(t) using the following equation: Un+l(t) = Un(t)-endn, n = 1,2,3,... , (17) with the descent direction dn defined as: dn =VJ" (t;U) +andn-1, (18) jo"]VJ"dt and a =j Gateaux's directional derivative DSU(U) of the functional J at point U in the direction SU is defined by: (U) = Dro / (tf) = Mm J + ) - J ), (19) MO s 8 J(U) = 2jo'/w1(t) (ps(t;U) -pp (t)) 8ps(t;U) dt, (20) DSU J(U) =jyj(t;U)8U (t )dt. (21) 0 Using the definition of Gateaux's derivative and computing the variations, we obtain the variation problem where ST and 30 are solutions of the following variation equations: dST(r,t) _ 2 dST(r, t) d2ST(r, t) dt r dr dr2 ST (1, t ) = SU (t ), ST (Sd (t ), t) = 0, Sd (t = 0) = S0, ST (r,0) = 0, dST (Sd (t ), t ) 8
1000). Instead, the introduction of the weighting function wj(t) = t2 (Fig. 2a) allows the algorithm to converge more quickly after few iterations (n = 54). Consequently, the weighting function has an impact on the computation time and the number of iterations. The improved results over the considered entire thermal process interval depend on the initial guess. The latter must not be chosen arbitrarily. It must belong to the domain of admissible solutions and obey the laws of heat transfer.
Figs. 2a and b show that the control U(t) the flux at the fixed boundary are obtained with high precision after a few number of iterations on 95 % of the time horizon. At the remaining time, important errors appear as expected from these global optimization methods.
k
a)
b)
Fig. 2. a) Exact control and calculated and b) exact flux and calculated (no-noisy exact data)
3.2 Case of Noisy Exact Data
To simulate these errors and generate a data flux $p(t) close to reality, a white noise b(t) is added to the data 0p(t) with a 5 % maximal amplitude using the following relation:
Vp (t) = Vp (t)exact + b(tI
(36)
with b(t) = y(t)(0.05)$refi y(t) is a random variable with a uniform probability density over [-1, 1] and $ref is defined as:
Vref
Vp (tf ) exact + Vp (0) e 2
(37)
Fig. 3 shows that the inverse methods are susceptible to errors. The white noise added to the data $p(t) caused significant oscillations on the results. The relative error on the evaluated control U(t) is about 20 %. This is related to the ill-posed nature of the problem. Consequently, these results are not satisfactory. According to [26], in the case of noisy
a)
b)
Fig. 3. a) Exact control and calculated and b) exact flux and calculated (noisy exact data)
data, the computing stop criterion must satisfy the following condition:
| J (Un+1) - J (Un) \ 1 and no effect of this parameter on the boundary layer in the case of flat surface n = 0. Moreover, one can observe that the surface temperature is higher in the case of n > 1 than that in the case of n < 1, and the influence of the thickness parameter on the temperature changes by changing the value of n such that in the case of n > 1 the temperature Increases by the increase of the value of the thickness parameter and the opposite is true for n < 1.
In addition, the nanoparticles concentration increases by increasing the thickness parameter in the case of n > 1 and decreases in the case of n < 1. Figs. 5 to 7 show the effect of magnetic field parameter on the boundary layer velocity, temperature, and concentration respectively.
It is clear that the increase of the magnetic parameter decreases the velocity and the opposite is true for the temperature and nanoparticles concentration.
The effect of non-linear thermal radiation appears in the dimensionless system through the radiation parameter Rd and temperature ratio parameter 0w. The effects of the radiation parameter on the boundary layer temperature and concentration are exhibited in Figs. 8 and 9. It is clear that the effect of this parameter near the surface differs from its effect far from the surface such that the increasing of the radiation parameter near the surface decreases the temperature near the surface to a certain point at which the effect is reversed. In contrast, the increase of such parameter increases the temperature of the boundary layer.
In contrast, the effects of the temperature ratio on the boundary layer temperature and concentration are
Fig. 2. Influence of thickness parameter on the velocity
Fig. 5. Influence of magnetic parameter on the velocity
Fig. 3. Influence of thickness parameter on the temperature
Pr=6.2, Le=2, Nt= Nb= 0.1,
y =y2 y3 0.1, o-=0.5, Rd=l,
!', 0w=1.2
11-1.5, M-0.5
- li-l.O. M-0.5
\v n=0.5
M =0.5, 1, 1.5
(
Fig. 6. Influence of magnetic parameter on the temperature
Pr=6.2, Le=2, Nt= Nb= 0.1, yl=y2=y3=0.1, 1=0.5, Rd=l, 8w=1.2
\ • n~ . n= n= =1.5, M=0.5 =1.0, M=0.5 =0.5
y M =0.5, 1, 1.5
Fig. 4. Influence of thickness parameter on the concentration
Fig. 7. Influence of magnetic parameter on the concentration
shown in Figs. 10 and 11. The figures show that the increase of the temperature ratio decreases both the temperature and the concentration of the nanoparticles near the surface.
The effects of Biot numbers on the temperature and nanoparticles concentration are shown in Figs. 12 to 14. It is clear that the temperature and nanoparticle concentration both increase by the increase in thermal Biot number and concentration Biot number.
The effect of random motion of the nanoparticles within the fluid appears in this study through the Brownian motion parameter Nb. Referring to Figs. 15 and 16, one can observe that increasing Nb leads to an increase in the temperature and a decrease of the nanoparticles concentration. Moreover, one can observe that the impact of the random moving of particles on the concentration decreases by increasing the value of Brownian motion parameter for all values of the shape parameter n.
123
Pr=6.2, Le=2, Nt= Nb= 0.1,
yl=y2=y3=l, £1=0.5, M=0.5,
0w=1.2
i n-1.5
\ w n=1.0
11-0.5
VW ✓ Rd =0,1,2
Pr=6.2, Le=2, Nt= Nb=0.1,
s yl=y2=y3 = l, tr=0.5, M=0.5,
X V , Rd=l
\\ \\ - 11-1.5
\\\ ----- - 11=1.0
' , 6w-i, 1.5,2 11-0.5
Fig. 8. Influence of radiation parameter on the temperature
Pr=6.2, Le=2, Nt=Nb= 0.1,
; ■ \ yl=y2=y3=l, o=0.5, M=0.5,
\ Sw=1.2
^ \ ii=1.5
\\ V - 11=1.0
Vv- 11=0.5
Rd=0, 1,2
i
Fig. 9. Influence of radiation parameter on the concentration
0.4 r
Pr=6.2, Le=2, Nt= Nb= 0.1,
yl=y2=y3=l, 1=0.5, M=0.5,
Rd=l
V n=1.5
y \ ------- 11=1.0
\ v1 ii=0.5
\ \\ . Bw=\, 1.5,2
/■Sij ^ .. .
Fig. 11. Influence of temperature ratio parameter on the concentration
Pr=6.2, Le=2, Nt= Nb= 0.1,
y2=y3=l, a=0.5, M=0.5 Rd=l,
\ 0w=1.2
\ 11=1.5
\ \ n=1.0
\ \ , yl =0.1, 0.5, 1 11=0.5
(
Fig. 12. Influence of thermal ratio parameter on the temperature
Pr=6.2, Le=2, Nt= Nh= 0.1,
r2=y3=l,a=0.5,M=0.5 Rd=l,
0w=l .2, 11=0.5
\V ^ rl =0.1, 0.5, 1
Fig. 10. Influence of temperature ratio parameter on the temperature
i
Fig. 13. Influence of thermal ratio parameter on the concentration
The Thermophoresis parameter Nt is a dimensionless parameter that describes the response of the suspended particles to the force of the temperature gradient. Figs. 17 amd 18 show that the increase of this parameter leads to increasing the boundary layer temperature and nanoparticles concentration. Moreover, Fig. 18 shows that the effect of this phenomenon on the concentration is very clear in the case of n > 1. In addition, one can observe that
increasing the thermophoresis parameter leads to forming a concentrated zone of the nanoparticles near the surface.
The main objective of this work is to study the effects of convective condition with the thickness variation and the nonlinear thermal radiation on the boundary layer behaviour.
Table 2 presents the values of the skin friction, Nusselt number and the Sherwood number for linear
Pr=6.2, Le=2, Nt= Nb= 0.1,
i4=y2=l,o=0.5,M=0.5 Rd=l,
fw=1.2
V ■ n-1.5
\ V 11=1.0
> ' n-0.5
\\\ , y3 =0.1, 0.5, 1
'••Y
Pr=6.2, Le=2, Nb=0.1, M=0 5, Q=0.5.
A'' 7l==y2=y3 = l, o=0.5, Rd =i,ew=i.2
n= 1.5
' ------- n= =1.0
\w - n= =0.5
% ' ' Y Nt =0.1, 0.4, 0.8
Fig. 14. Influence of concentration Biot number on the concentration
Pr=6.2, Le=2, Nt=0.1, M= =0.5, o=0.5.
T1^2=r3=l,«=0.5,Rd= =l,0w=1.2
v1 - 11=1.5
\\ \ 1 -11=1.0
\\Y\1 11=0 5
f Nb =0.1, 0.4, 0.8
Fig. 15. Influence of Brownian motion parameter on the temperature
Fig. 17. Influence of thermophoresis parameter on the concentration
Fig. 18. Influence of thermophoresis parameter on the concentration
Pr=6.2, Le=2, Nt=0.1, M=0.5, o=0.5,
yl==yi=y3=l, o=0.5, Rd=l, 0W=1.2
^ V " ----- 11= 1.5
\ v ■ -n= =1.0
\ \ ' 1 11= =0.5
\ \\ ■ , Nb =0.1, 0.4, 0.8
0 2 4 6 8
f
Fig. 16. Influence of Brownian motion parameter on the concentration
and non-linear thermal radiation at three cases of shape parameter n. from the first look, one can observe that the skin friction and Sherwood number values increase with the increase of the shape parameter n. Such increasing of n decreases the values of the Nusselt number. Moreover, one can observe that the presence of thermal radiation increases the Nusselt
and Sherwood numbers. Finally, the values obtained in Table 2 indicate that the nonlinear modelling of the thermal radiation gives high values for Nusselt and Sherwood numbers. It is worth mentioning that the increasing of the skin friction and Nusselt number values to the increase of surface shear stress and the rate of heat transfer from the surface.
The effects of hydromagnetic flow on the skin friction, Nusselt number and Sherwood number are shown in Table 3. The observed results show that using hydromagnetic flow as a cooling medium increases skin friction, and decrease Nusselt number and Sherwood number. Consequently, the surface shear stress is increased, and the rate of heat transfer and rate of mass transfer is decreased by increasing the magnetic parameter M.
Table 4 shows the influence of thermal Biot number on the Nusselt and Sherwood Numbers. It is clear that the increase of the heat convective coefficient increases the heat flux and decreases the mass flux relative to the increasing and decreasing of the Nusselt and Sherwood Numbers, respectively. In contrast, the effect of concentration Biot number on
125
Table 2. Values of skin friction, Nusselt number and Sherwood number for linear and non-linear thermal radiation at Le=2, Pr = 6.2, Nt=Nb = 0.1, M=0.5, a=0.5, and y¡ = y2=y3 = 0.1
Rd n -/''(0) -6'(0) -f(0) C/x Nu Sh
0.5 1.2807 0.0439 0.0814 2.2183 0.0966 0.0705
1 1 1.0 1.2247 0.0411 0.0793 2.4495 0.0960 0.0793
1.5 1.1827 0.0383 0.0774 2.6446 0.0953 0.0866
0.5 1.2807 0.1099 0.0733 2.2183 0.0951 0.0635
0 1.0 1.2247 0.0943 0.0722 2.4495 0.0943 0.0722
1.5 1.1827 0.0834 0.0713 2.6446 0.0933 0.0797
0.5 1.2807 0.0308 0.0829 2.2183 0.0976 0.0718
1 1.0 1.2247 0.0294 0.0807 2.4495 0.0971 0.0807
1.5 1.1827 0.0282 0.0788 2.6446 0.0966 0.0881
Table 3. Values of skin friction, Nusselt number and Sherwood number for MHD flow at a= : 0.5, Le=2, Pr= : 6.2, Nt = Nb =0.1, ew =1.2, Rd=1
and Yi = y2=y3 = 1
M n -/"(0) -0'(0) -¿'(0) C/x Nu Sh
0.5 -1.2807 -0.2472 -0.2653 -0.0031 151.93 162.45
0.5 1.00 -1.2247 -0.2266 -0.2384 -0.0035 160.73 168.56
1.50 -1.1827 -0.2089 -0.2192 -0.0037 165.60 173.26
0.5 -1.5297 -0.2450 -0.2443 -0.0037 150.45 149.61
1 1.00 -1.4142 -0.2241 -0.2177 -0.0040 158.95 153.96
1.50 -1.3351 -0.2060 -0.1991 -0.0042 163.32 157.43
0.5 -1.9310 -0.2415 -0.2181 -0.0047 148.45 133.57
2 1.00 -1.7321 -0.2196 -0.1854 -0.0049 155.77 131.10
1.50 -1.5981 -0.2006 -0.1675 -0.0051 159.02 132.41
Table 4. Values of Nusselt number and Sherwood number for different values of thermal Biot number a=0.5, Le=2, Pr=6.2, Rd=1, 9w=1.2, M = 0.5, Nt=Nb = 0.1 and y1 = y3=1
Y2 n -e\0) -¿'(0) Nu Sh
0.50 0.08478 0.34525 0.26876 0.29900
0.1 1.00 0.07490 0.31222 0.24747 0.31222
1.50 0.06771 0.28563 0.23170 0.31935
0.50 0.20411 0.28636 0.64704 0.24799
0.5 1.00 0.18533 0.25829 0.61235 0.25829
1.50 0.17000 0.23725 0.58175 0.26525
0.50 0.24716 0.26528 0.78351 0.22974
1 1.00 0.22657 0.23839 0.74859 0.23839
1.50 0.20886 0.21915 0.71473 0.24502
Table 5. Values of Nusselt number and Sherwood number for different values of concentration Biot number Le=2, Pr = 6.2, Rd=1, 9w=1.2, M = 0.5, a=0.5, Nt=Nb = 0.1 and y1 = y2=1
Y3 n -e\0) -¿'(0) Nu Sh
0.50 0.24863 0.05885 0.78818 0.05096
0.1 1.00 0.22822 0.05719 0.75403 0.05719
1.50 0.21066 0.05630 0.72087 0.06295
0.50 0.24770 0.19088 0.78521 0.16530
0.5 1.00 0.22714 0.17631 0.75047 0.17631
1.50 0.20945 0.16585 0.71676 0.18543
0.50 0.24716 0.26528 0.78351 0.22974
1 1.00 0.22657 0.23839 0.74859 0.23839
1.50 0.20886 0.21915 0.71473 0.24502
the rate of heat and mass transfer is shown in Table 5. The effect of this number on the Nusselt number is low and limited, but it has a direct effect on the Sherwood number and the mass flux such that increasing the concentration Biot number increases the mass flux.
5 CONCLUSIONS
This study presents a mathematical model of a continuous moving non-flat surface over a hot
convective fluid subjected to nonlinear thermal radiation and magnetic field. Above the surface, there is a Nanofluid boundary layer with Brownian motion and thermophoresis effects. The heat and mass transfer characteristics of the boundary layer are the main concern of this study, and the following results are obtained:
• The values of the Nusselt and Sherwood numbers for non-linear thermal radiation model are high comparing with a linear model.
• Surface shear stress for the convex outer shape surface (n < 1) is higher than that in the case of concave outer shape surface (n > 1).
• The presence of convective conditions decreases surface heat flux and mass flux.
• The random motions of the nanoparticles and the thermophoresis force have direct and high influences on the concentration boundary layer, especially for the non-flat surface.
6 NOMENCLATURES
u velocity in the x direction [m/s], v velocity in the y direction [m/s], u kinematic viscosity [m2/s], a, b, ô constants [-], T temperature [°C], C concentration [mol/m3], Cp specific heat capacity [J/(kgK)], k thermal conductivity [W/(mK)], h convective heat transfer coefficient [-], km surface mass transfer coefficient [-], Db Brownian diffusion [m2/s], Dt thermophoresis diffusion [m2/s], qr heat flux [W/m2], p density of the base fluid [kg/m3], a electrical conductivity [s/m], B(x) strength of the magnetic field [kg/(s2m)], ax thermal diffusion [m2/s], a* Rosseland mean absorption coefficient [-], n, Z similarity variables [-], 8(n) dimensionless temperature [-], ^(n) dimensionless concentration [-], Boltzmann constant, [m2kg/(s2K)]
a*
a Pr
Le Lewis number, Le = u/ DB [-],
M
thickness parameter, a = Sy] ( temperature ratio, 6w = Tw / Tx Prandtl number, Pr = v/a [-]
magnetic field parameter, M = [-],
ap 4 aT3
Rd radiation parameter, Rd =-^ [-],
k a t D
Nb Brownian parameter, Nb = —B (Cw — C®
v
T D
thermophoresis parameter, Nt = —'-(Tw - T®) [-]
uT®
Nt
Yi Y2
thermal ratio, y1= h/k ,[ thermal Biot number,
h
Y2 = -
£
£ \ a(x+bf k
[-],
Y3 concentration Biot number, y, = I , " n1 [-]
specific heat capacity ratio, t =
(PO p (pC )f
[-]
7 REFERENCES
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[2] Hamad, M.A.A. (2011). Analytical solution of natural convection flow of a Nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer, vol. 38, no. 4, p. 487-492, D0l:10.1016/j.icheatmasstransfer.2010.12.042.
[3] Yacob, N.A., Ishak, A., Pop, I., Vajravelu, K. (2011). Boundary layer flow past a stretching/ shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a Nanofluid. Nanoscale Research Letters, vol. 6, 1-7, D0I:10.1186/1556-276X-6-314.
[4] Alsaedi, A., Awai, s M., Hayat, T. (2012). Effects of heat generation/absorption on stagnation point flow of Nanofluid over a surface with convective boundary conditions. Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, p. 4210-4223, D0I:10.1016/j. cnsns.2012.03.008.
[5] Elbashbeshy E.M.A., Emam T.G., and Abdel-wahed M.S. (2014). An exact solution of boundary layer flow over a moving surface embedded into a nanofluid in the presence of magnetic field and suction/injection. Heat and Mass Transfer, vol. 50, no. 1, p. 57-64, D0I:10.1007/s00231-013-1224-x.
[6] Abu Bakar N.A., Zaimi W.M.K.A.W., Abdul Hamid R., Bidin, B., Ishak, A. (2012). Boundary layer flow over a stretching sheet with a convective boundary condition and slip effect. World Applied Sciences Journal, vol. 17, p. 49-53.
[7] Ozturk, A., Kahveci, K. (2016). Slip flow of nanofluids between parallel plates heated with a constant heat flux. Strojniški vestnik - Journal of Mechanical Engineering, vol. 62, no. 9, p. 511-520, D0I:10.5545/sv-jme.2016.3188.
[8] Noghrehabadi A., Pourrajab R., Ghalambaz M. (2013).Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions. Heat and Mass Transfer, vol. 49, no. 9, p. 13571366, D0I:10.1007/s00231-013-1179-y.
[9] Rahman, M.M., Eltayeb, I.A. (2013). Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition. Meccanica, vol. 48, no. 3, p. 601-615, D0I:10.1007/s11012-012-9618-2.
[10] Ramesh, G.K., Gireesha B.J. (2014). Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Engineering Journal, vol. 5, no. 3, p. 991-998, D0I:10.1016/j.asej.2014.04.003.
[11] Nadeem, S., Haq, R.U. (2014). Effect of thermal radiation for megnetohydrodynamic boundary layer flow of a nanofluid past a stretching sheet with convective boundary conditions. Journal of Computational and Theoretical Nanoscience, vol. 11, n. 1-9, p. 32-40, D0I:10.1166/jctn.2014.3313.
[12] Chamkha, A.J., Rashad, A.M., RamReddy, C., Murthy, P.V.S.N. (2014). Viscous dissipation and magnetic field effects in a non-Darcy porous medium saturated with a nanofluid under convective boundary condition. Special Topics & Reviews
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in Porous Media, vol. 5, no. 1, p. 27-39, D0l:10.1615/ SpeciaITopicsRevPorousMedia.v5.i1.30.
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[14] Ibrahim, W., Shankar, B. (2013). MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions. Computers & Fluids, vol. 75, p. 1-10, D0I:10.1016/j. compfluid.2013.01.014.
[15] Hayat, T., Imtiaz, M, Alsaedi, A. (2014). MHD flow of nanofluid over permeable stretching sheet with convective boundary conditions, Thermal Science (On-line first), D0I:10.2298/ TSCI140819139H.
[16] Fang, T., Zhang, J., Zhong ,Y. (2012). Boundary layer flow over a stretching sheet with variable thickness. Applied
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[17] Elbashbeshy, E.M.A, Emam, T.G., Abdel-wahed, M.S. (2013). Flow and heat transfer over a moving surface with non-linear velocity and variable thickness in a nanofluid in the presence of thermal radiation. Canadian Journal of Physics, vol. 91, no. 2, p. 124-130, D0I:10.1139/cjp-2013-0168.
[18] Abdel-wahed, M.S., Elbashbeshy, E.M.A., Emam, T.G. (2015). Flow and heat transfer over a moving surface with non-linear velocity and variable thickness in a Nanofluid in the presence of Brownian motion. Applied Mathematics and Computation, vol. 254, p. 49-62, D0I:10.1016/j.amc.2014.12.087.
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Strojniški vestnik - Journal of Mechanical Engineering 63(2017)2, 129-137 © 2017 Journal of Mechanical Engineering. All rights reserved.
D0l:10.5545/sv-jme.2016.3719 Original Scientific Paper
Comfort Improvement of a Novel Nonlinear Suspension for a Seat System Based on Field Measurements
Leilei Zhao - Changcheng Zhou* - Yuewei Yu Shandong University of Technology, School of Transportation and Vehicle Engineering, China
This paper describes improved ride comfort of a novel nonlinear suspension for seat system based on field measurements. For the novel nonlinear suspension proposed, a rubber spring is used as its elastic element which has highly nonlinear characteristics to adapt various working conditions, and an asymmetrical damper is designed to yield asymmetric damping characteristics. Previous seat models were not very suitable for the system; thus, a nonlinear mathematical model was built to describe it better. Then, based on field measurements, the model parameters were identified, and the suspension damping coefficients were tuned under the practical constraints, to achieve satisfactory ride comfort to the greatest extent possible. Finally, the bench test was carried out, and the results show that, after the coefficients tuning, the seat vertical frequency-weighted root mean square (RMS) acceleration values are decreased by about 10 % and 8 % under the driving conditions on the highway and the gravel road, respectively, which proves the damping coefficients tuned are workable. The novel nonlinear suspension and the method of the damping coefficients tuning provide a valuable reference for further improving ride comfort to better protect the driver's health.
Keywords: ride quality; road conditions; nonlinear suspension; coefficients tuning Highlights
• A rubber spring is used as an elastic element of seat suspension.
• A nonlinear mathematical model of seat suspension system.
• Integrated optimization of damping coefficients.
• Field measurements.
0 INTRODUCTION
Seat suspension is an essential component of trucks. The design of seat suspension has significance for comfort improvement [1] to [3]. Prolonged exposure to occupational vibrations leads to some diseases for drivers [4] and [5]. Reducing the vibration transmitted from vehicle to the driver has become a key issue [6] and [7]. To reduce the vibration, various seat suspension systems use a wide variety of springs as the elastic component, including the coil spring, the air spring, and the rubber spring, etc.
Due to the good nonlinear characteristics of the rubber spring, it is widely used as the elastic element of vehicle suspension systems, especially in rail vehicle suspensions and in chassis suspensions of commercial vehicles. For example, to improve the service life of the rubber spring for rail vehicle suspensions, Luo et al. researched the fatigue design method of rubber springs [8]. Luo presented an evaluation method of the creep behaviours of the rubber suspension for railway vehicles [9]. Sebesan et al. analysed the broad application prospects of the rubber suspension on the railway vehicles [10]. Pang et al. analysed the mechanical properties of the rubber suspension for heavy vehicles using the finite element method [11]. Many research efforts on the modelling and designs
of the vibration isolation system using rubber springs have been made. Thaijaroen and Harrison studied the dynamic behaviours of rubber isolators using a simulation model with six parameters [12]. Sun et al. investigated the modelling method and the parameter acquisition method of a rubber isolator [13]. In their paper [14], they presented a model to describe the hysteretic characteristics of a rubber isolator. Ren et al. studied the effects of the temperature and the pressure on the shear stiffness of the rubber spring [15].
In recent years, the rubber spring has been applied to the seat suspension. For example, Zhou et al. investigated a seat suspension system with a type of rubber spring embedded with metal splints [16]. The dynamic characteristics of the seat suspension should be matched according to the road conditions of vehicles [17] to [19]. The common methodology is to use a passive seat suspension system model to optimize the results, which could be approached by the single degree-of-freedom (DOF) vibration isolation system [20] and [21]. To facilitate the dynamic analysis of vehicles equipped with the rubber spring, Berg presented a rubber spring model with five parameters [22]. Shi and Wu presented a nonlinear model with fractional derivatives for rubber springs of railway vehicle suspensions [23].
*Corr. Author's Address: Shandong University of Technology, School of Transportation and Vehicle Engineering, China, greatwall@sdut.edu.cn
129
These above studies about the designs of the vibration isolation system using rubber springs have significant relevance to the seat suspension. However, these previous models were not very suitable for the seat suspension system with a nonlinear hollow rubber spring and an asymmetrical damper with bushings, which will be optimized in this paper.
The objective of this work is to present a nonlinear mathematical model for a novel seat suspension system which employs a hollow rubber spring as the elastic element and improves its ride comfort by optimal design based on field measurements. According to the field measurements, the damping coefficients were tuned. In the end, by bench test, the optimal matching results were validated.
1 SEAT SYSTEM MODEL
The driver's seat analysed in this study is a new seat, which was tested for use in a heavy truck. The suspension seat was configured as a typical scissor system. It employs a hollow rubber spring and a hydraulic damper. They were mounted between the scissor structure on the seat pan and the seat frame. The hollow rubber spring, as shown in Fig. 1, is used as the elastic element of the seat suspension system, which has highly nonlinear characteristics to adapt the various working conditions.
Fig. 1. The hollow rubber spring
A good and simple mathematical model would enable us to make reasonable indicative predictions of seat performance, and related models exist. The paper [25] provided a linear model of a seat suspension system with the damper mounting bushings. The paper [16] presented a nonlinear model of seat suspension system with the polynomial fitting the stiffness characteristics of the rubber spring, but the damper has linear damping. In this study, the seat dynamic properties are known to be non-linear, and the damper mounting bushings and friction in various seat components cannot be neglected, especially in response to low magnitude vibration. Thus, the previous models of seat suspension systems were not
expected to be sufficient to simulate the driver's seat used in this study.
The assumptions made in formulating the model are as follows. Assumption 1: The elastic deformation of the seat frame could be ignored for this simplified model, and the driver is replaced by a matching block while removing the seat cushion. Assumption 2: The hollow rubber spring stiffness is considered to be nonlinear, while its damping is considered to be constant. Assumption 3: The asymmetric damping characteristics of the seat damper are simplified to be different constants in compression and rebound. Assumption 4: The Coulomb friction Ff within the linkage mechanism and the rubber spring is assumed to possess ideal properties. Assumption 5: The dynamic properties of the damper mounting bushings are characterized by equivalent linear stiffness while neglecting the damping coefficients.
A vertical dynamic model of the seat system was created on the basis of the assumptions, as shown in Fig. 2. Cs represents the rubber spring damping, m represents the effective mass; Kb1 and zb1 represent the upper bushing stiffness and vertical displacement, respectively; Kb2 and zb2 represent the lower bushing stiffness and vertical displacement, respectively; zs represents the seat pan vertical displacement; q represents the vertical displacement input. Although the model is relatively simple, it can capture the major dynamic properties of seat suspension systems, including the seat vertical acceleration response, the seat suspension dynamic travel and so on. For academic purposes and the practical engineering problem, it may be useful to introduce the complex problem in a simplified form.
Fig. 2. The vertical dynamic model of the seat system
The motion equations of the model can be written
as:
mzs = -Fs - Cs (Zs - q) - Kb1 (Zs - Zb1 ) - Ff