Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554 © 2018 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2017.4647 Original Scientific Paper Received for review: 2017-06-02 Received revised form: 2017-09-21 Accepted for publication: 2017-10-13 Numerical Predictions of Cavitating Flow Around a Marine Propeller and Kaplan Turbine Runner with Calibrated Cavitation Models Mitja Morgut1* - Dragica Jošt2 - Aljaž Škerlavaj2 - Enrico Nobile1 - Giorgio Contento1 1 University of Trieste, Department of Engineering and Architecture, Italy 2 Kolektor Turboinštitut, Slovenia Cavitating phenomena, which may occur in many industrial systems, can be modelled using several approaches. In this study a homogeneous multiphase model, used in combination with three previously calibrated mass transfer models, is evaluated for the numerical prediction of cavitating flow around a marine propeller and a Kaplan turbine runner. The simulations are performed using a commercial computational fluid dynamics (CFD) solver and the turbulence effects are modelled using, alternatively, the Reynolds averaged Navier Stokes (RANS) and scale adaptive simulation (SAS) approaches. The numerical results are compared with available experimental data. In the case of the propeller the thrust coefficient and the sketches of cavitation patterns are considered. In the case of the turbine the efficiency and draft tube losses, along with the cavitation pattern sketches, are compared. From the overall results it seems that, for the considered systems, the three different mass transfer models can guarantee similar levels of accuracy for the performance prediction. For a very detailed investigation of the fluid field, slight differences in the predicted shapes of the cavitation patterns can be observed. In addition, in the case of the propeller, the SAS simulation seems to guarantee a more accurate resolution of the cavitating tip vortex flow, while for the turbine, SAS simulations can significantly improve the predictions of the draft tube turbulent flow. Keywords: cavitation, marine propeller, Kaplan turbine, mass transfer models, RANS, SAS Highlights • CFD simulations of cavitating flow around a marine propeller and Kaplan turbine runner. • Homogeneous model used in combination with three previously calibrated mass transfer models. • Turbulence modelled using RANS and SAS approaches. • Calibrated mass transfer models guarantee similar levels of accuracy • SAS approach improves the local flow field resolution. 0 INTRODUCTION In modern market scenarios, the competitiveness of an enterprise is determined, not only by the quality of the product but also by its time to market. As a matter of fact, nowadays, computational fluid dynamics (CFD) technologies are routinely used for design purposes allowing, in general, more expensive and time consuming experimental tests to be performed only at the final stages of the project. Such an approach becomes particularly relevant for parametric and/or optimization studies, where several simulations can be performed in parallel. In the specific case of marine propellers and hydraulic turbines, CFD analysis can be effectively used to predict the overall machine performances as well as to investigate the effect of specific flow phenomena such as cavitation for instance [1] to [6]. Cavitation is the phenomenon that consists of the formation and activity of cavities (or bubbles) inside a liquid medium [7]. In flowing liquids it appears in low pressure regions where pressure, also owing to the system geometry, decreases below a certain threshold value. In the case of marine propellers and hydraulic turbines it is, usually, an undesirable phenomenon because in most cases it implies negative effects such as losses, efficiency reduction, noise, erosion and vibration [8] to [12]. In the last decades several CFD approaches have been developed to numerically investigate cavitating flow phenomena. A valuable review of different approaches is for instance provided by [13] and [14] and references therein. Among all the approaches, the most widely applied today is probably the so-called homogeneous transport-equation based model. In this approach the multiphase flow is treated as a homogeneous mixture of liquid and vapour, with variable density, and the relative motion between phases is neglected. The evaluation of the variable density field is based on an equation for void ratio with the source terms modelling the mass transfer rate due to cavitation, generally known as mass transfer model. In the literature there are available several mass transfer models relying on tunable parameters [14] even though interesting solutions for overcoming *Corr. Author's Address: University of Trieste, Department of Engineering and Architecture, via A. Valerio 10, 34127 Trieste, Italy, mmorgut@units.it 543 Strojniski vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554 empiricism have for instance been proposed by [15] and [16]. In this study the homogenous transport- equation based model is considered and three different mass transfer models are employed. More precisely, the mass transfer models originally proposed by Zwart et al. [17], Singhal et al. [18] and Kunz et al. [19] with empirical coefficients calibrated according to [20] are employed. The scope is to verify the applicability of the considered calibrated models to the numerical predictions of the cavitating flow around two different systems: marine propeller and Kaplan turbine. The investigation is performed considering the Potsdam propeller test case (PPTC) model propeller working in uniform inflow [21], and a model Kaplan turbine experimentally investigated by researchers at Kolektor-Turboinstitut, Slovenia. Even though the present study is carried out mainly to evaluate a possible more general character of the calibrated mass transfer models, related to the systems under consideration the influence of the turbulence modelling is also briefly evaluated. Thus, the simulations are performed using the standard Reynolds averaged Navier Stokes (RANS) approach and the more accurate and more time consuming Scale Adaptive Simulations (SAS). In the case of the steady state RANS simulations the workhorse Shear Stress Transport (SST) turbulence model [22] is used in combination with all the three different calibrated mass transfer models. For the evaluation of the possible improvement related to a more accurate turbulence modelling approach, time dependent SAS simulations are carried out using the SST-SAS turbulence model [23] in combination with only a certain mass transfer model for convenience. The simulations are carried out using ANSYS-CFX (CFX for brevity) commercial CFD solver which is based on the node-centered finite volume method (more precisely on the Control Volume-Based Finite Element Method (CVFEM)) [24] and [25]. The numerical results are compared with the available experimental data. For a quantitative comparison the thrust is evaluated for the marine propeller, while the draft tube losses and the efficiency are considered for Kaplan turbine. For a qualitative comparison the sketches of cavitation patterns predicted around the blades are considered for both cases. From this study it seems that for the prediction of the cavitating flow around a marine propeller and Kaplan turbine all the three different calibrated mass transfer models can be successfully employed. The machine performances can be predicted with a similar level of accuracy, even though small differences in the predicted cavitation patterns can be observed. As far as the turbulence modelling is concerned, the numerical results show that the SAS simulations could be used to improve the resolution of certain flow features such as the propeller cavitating tip vortex for example. Moreover, it seems that in the case of the Kaplan turbines, where the efficiency predictions are highly affected by the proper resolution of the unsteady draft tube turbulent structures, the SAS simulations could represent a good compromise between standard RANS simulations and the computationally more demanding and more accurate large eddy simulations (LES). The paper is structured as follows. First the mathematical model is presented. Then, the numerical predictions performed for marine propeller and Kaplan turbine are described. The descriptions follow the same scheme where the considered system is presented, the numerical and meshing strategies are described, and the results are discussed. Finally, the concluding remarks are given. 1 MATHEMATICAL MODEL Here, the homogeneous model is presented in the fixed frame of reference for convenience. 1.1 Governing Equations In the homogeneous multiphase transport equation-based model, the cavitating flow can be described by the following set of governing equations: V ■ U = m 1 Pv d(pU ) dt +V-(pUU) = -VP —V ■ t + SM (1) dt V ' p Cavitating flow is modelled as a mixture of two species i.e. vapour and liquid behaving as one. The phases are considered incompressible. They share the same velocity U and pressure fields P. The mixture density, p, and dynamic viscosity, p, are scaled, respectively, as: p = YPi + (-r)pv, V = YHI +(-r)i*iv- (2) 544 Morgut, M. - Jost, D. - Skerlavaj, A. - Nobile, E. - Contento, G. Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554 The interface mass transfer rate due to cavitation, m, can be modelled using three different calibrated mass transfer models. 1.2 Turbulence Modelling In order to model turbulence effects different approaches can mainly be applied, depending on the required accuracy and the available computational resources. In this study we adopted the standard RANS approach in combination with the workhorse SST turbulence model, and the more advanced SST-SAS model available in CFX. For a detailed description of the considered models we refer to [22], [23] and [26]. Here, we clarify that the SST-SAS model is an improved unsteady-RANS formulation, with the ability to adapt the length scale to resolved turbulent structures by including the von Karman length-scale into the turbulence scale equation. The information given by the von Karman length scale allows SST-SAS model to dynamically adjust to resolved structures mimicking a LES-like behaviour in unsteady regions of the flow field. At the same time, the model provides standard RANS capabilities in stable flow regions. 1.3 Mass Transfer Models The mass transfer models employed in this study were previously calibrated using an optimization strategy, where selected empirical coefficients of the considered models, were properly tuned for the prediction of the sheet cavity flow around a hydrofoil [20]. In the following the formulations of the considered mass transfer models are provided, and in Table 1 the calibrated empirical values namely Fe, Fc, Ce, C^ Cpr^ Ctfesb are collected. Zwart et al. model: -F„ ^ (1 -a) p y 12 Pv - P R„ 3 Pi 3apv 2 P - Pv rb V3 Pi if P < P, if P > P (3) Full cavitation model (FCM): -C K ppJ^i - f. ) if p < P K \ 3 pl _ 4k ¡2 P - Pv . ' C— P,pj---fv if P > P K \ 3 p, (4) Kunz et al. model: m = m + m : Cpmd PJ2 (1 -j) L cdeslPJ min [0, P - Pv ] " " (0.5pU^ ) (5) Table 1. Calibrated model coefficients Model Evaporation Condensation Zwart Fe = 300 Fc = 0.03 FCM Ce = 0.40 Cc = 2.3x10-4 Kunz Cdest = 4100 Cprod = 455 It is worth clarifying that the Zwart et. al model is the native CFX mass transfer model while the FCM and Kunz et al. models were additionally implemented using the cell expression language (CEL) available in CFX. In the case of the FCM, following [27], fv was replaced by a. In all simulations the mass transfer rate was considered positive if directed from vapour to liquid phase and the maximum density ratio pt /pv was clipped to 1000 for solver stability reasons. 2 MARINE MODEL SCALE PROPELLER The numerical predictions for cavitating PPTC propeller working in uniform inflow are presented. The considered propeller is a five-bladed, controllable pitch propeller having a diameter D=0.250 m. It was used as a blind test case at the 2011 Workshop on Cavitation and Propeller Performance. A significant amount of experimental data is currently available at [21]. 2.1 Numerical Strategy Due to the periodicity of the problem (uniform inflow and in this case neglected gravity) only one blade passage was modelled for computational convenience in all propeller simulations. Fig. 1 shows the shape of the computational domain. In Table 2 the values of the corresponding main dimensions are collected. Since the propeller rotation was simulated using multiple reference frame (MRF) approach the computational domain was subdivided into two regions namely rotating and fixed. In Fixed the governing equations were solved by considering a fixed frame of reference, while in rotating, the governing equations were solved using a rotating frame of reference. • + m = Numerical Predictions of Cavitating Flow Around a Marine Propeller and Kaplan Turbine Runner with Calibrated Cavitation Models 545 Strojniski vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554 Fig. 1. Shape of the computational domain; rotating region surrounded by front, aft and top interfaces The following boundary conditions were applied: on inlet boundary, the free-stream velocity components and a turbulence level of 1 % were set. The free-stream values (as well as the propeller rotational velocity) were set following the experimental setup [21]. The Reynolds number, ReP, was in range (1.7 to 1.8)x106. On outlet boundary, a fixed value of the static pressure equal to 202,650 Pa was imposed. On the periodic boundaries (sides of the domain), the rotational periodicity was ensured. On solid surfaces the no-slip boundary condition was applied, and on outer boundary, the slip condition was set. Steady state RANS and unsteady SAS simulations were performed. In the case of the RANS simulations the workhorse SST turbulence model was used, while for SAS simulations the SST-SAS model was employed. Both models were used in combination with the automatic wall treatment available in CFX. Table 2. Distances of the boundaries/surfaces from the propeller mid plane in axial direction for inlet, outlet, aft, and from the propeller rotation axis in radial direction for outer and top Inlet Outlet Outer Front Aft Top 2.30D 5.30D 5.00D 0.41D 0.31D 0.60D As far as the discretization of the advective terms is concerned, for the RANS simulations, the high resolution scheme was employed while a bounded second order central difference scheme was used in the SAS simulations. For time discretization a first order implicit time scheme was used. It is worth clarifying that in this study with SAS an almost stable cavitating-tip vortex flow was investigated (see Fig. 4). Thus, we assumed that, for this specific case, the more stable first order time scheme can be conveniently used and ensure a similar level of accuracy as the generally more unstable second order scheme. Table 3. PPTC propeller; thrust coefficient for RANS simulations with different mass transfer models J K kt,cfd kt,exp Zwart FCM Kunz 1.016 2.024 0.373 0.373 0.374 0.375 1.269 1.424 0.206 0.196 0.203 0.210 1.408 2.000 0.136 0.133 0.130 0.133 2.2 Meshing The computational grids for fixed and rotating were generated independently and then joined in CFX through the General Grid Interfaces (GGI) solver capabilities. Both meshes were hexa-structured and were created using ANSYS ICEM CFD (ICEM for brevity). The overall mesh had about 2.1 x 106 nodes with a proper refinement in the tip vortex region following [29]. The considered mesh arrangement proved to guarantee mesh independent results in former studies [30]. The average y+ value on the blade surface was about 32. Fig. 2 shows the blade surface mesh. Fig. 2. PPTC propeller, blade surface mesh 2.3 Results The simulations were carried out following the experimental setup suggested in [21]. The overall numerical predictions performed using the steady-state RANS approach compared well with the available experimental data. Regarding the thrust (thrust coefficient) only minor differences were observed among the results obtained varying the mass transfer model. From Table 544 Morgut, M. - Jost, D. - Skerlavaj, A. - Nobile, E. - Contento, G. Strojniski vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554 8. \ / \ \ . ,/ \ \ J X 0 5 / \ I /« LU Suction side Suction side Pressure side * ^