Comparison of mass transfer models for the numerical prediction of sheet cavitation around a hydrofoil Mitja Morgut a,⇑ , Enrico Nobile a , Ignacijo Biluš b a Dipartimento di Ingegneria Meccanica e Navale, University of Trieste, Trieste, Italy b Faculty of Mechanical Engineering, University of Maribor, Maribor, Slovenia article info Article history: Received 10 December 2010 Received in revised form 10 March 2011 Accepted 11 March 2011 Available online 17 March 2011 Keywords: Cavitation RANS Optimization Mass transfer model Hydrofoil abstract Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of methods. One strategy consists of using the RANS (Reynolds Averaged Navier Stokes) equations and an additional transport equation for the liquid volume fraction, where mass transfer rate due to cavitation is modelled by a mass transfer model. In this study, we compare three widespread mass transfer models available in literature for the prediction of sheet cavitation around a hydrofoil. These models share the common feature of employing empirical coefficients, to tune the models of condensation and evaporation processes, that can influence the accuracy and stability of the numerical predictions. In order to compare the different mass transfer models fairly and congruently, the empirical coefficients of the different mod- els are first well tuned using an optimization strategy. The resulting well tuned mass transfer models are then compared considering the flow around the NACA66(MOD) and NACA009 hydrofoils. The numerical predictions based on the three different tuned mass transfer models are very close to each other and in agreement with the experimental data. Moreover, the optimization strategy seems to be stable and accu- rate, and could be extended to additional mass transfer models and further flow problems. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Cavitation is the phenomenon that consists in the formation and activity of cavities (or bubbles) inside a liquid medium (Young, 1999). In flowing liquids it appears in low pressure regions where pressure, also owing to the system geometry, decreases below a certain threshold value. It can occur in hydraulic turbines and pumps, on marine propellers, rudders, and even in human body, for example in knee-joints. In the above examples, but also in other similar applications, cavitation is an undesirable phenomenon be- cause it usually imply negative design effects such as hydrody- namic losses, efficiency reduction, noise, erosion and vibration. In the last few decades, several CFD (Computational Fluid Dynamics) methods were developed to numerically investigate cavitating flow phenomena. Most of them were based on the homogeneous fluid approach. In this approach the multiphase flow is treated as a homogeneous mixture, with variable density, of li- quid and vapour, and the relative motion between phases is ne- glected. Different methods were proposed to evaluate the variable density field. Two common methods imply either a baro- tropic law (Coutier-Delgosha et al., 2003; Barre et al., 2009) or a transport equation model for void ratio with the source terms modelling the mass transfer due to cavitation (Kunz et al., 2000; Singhal et al., 2002; Senocak, 2002; Zwart et al., 2004) In the ANSYS-CFX 12 (which will be referred from now on CFX), a commercial CFD solver, the homogeneous fluid approach is based on the transport equation model. The continuity and momentum equations for the mixture and the transport equation for the liquid volume fraction are solved. In the continuity and volume fraction equations appropriate source terms are included in order to control the mass transfer between the two phases. These source terms can be modelled using different mass transfer models. The objective of this study was to verify the influence of the mass transfer model on the accuracy and stability of the numerical predictions of the two dimensional sheet cavitation around a hydrofoil. Thus we compared the Zwart model (Zwart et al., 2004) with the models inspired by the works of Kunz et al. (2000) and Singhal et al. (2002), respectively. The Zwart model is the native model of CFX, while the other two were added to CFX in the course of this study. Since the considered mass transfer models involve tunable parameters, to ensure a congruent compar- ison, all the three models were first equally well tuned for the pre- diction of sheet cavitation. More precisely, they were tuned by means of an optimization strategy considering the sheet cavity flow over the NACA66(MOD) hydrofoil at an incidence of 4°. The tuned models were then further compared investigating the lead- ing edge sheet cavitation over the same NACA66(MOD) hydrofoil at a different angle of attack of 6°, and on the NACA009 hydrofoil 0301-9322/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2011.03.005 ⇑ Corresponding author. Tel.: +39 040 558 3502; fax: +39 040 572033. E-mail address: mmorgut@units.it (M. Morgut). International Journal of Multiphase Flow 37 (2011) 620–626 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow