of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation. List of symbols c Hydrofoil chord h Maximum foil thickness W ∞ Inlet velocity p ∞ Inlet pressure x, y, z Cartesian coordinates u, v, w Spanwise, transverse and axial velocity x c , y c Vortex center coordinates r c Vortex core radius Re c Reynolds number (W ∞ c/ν) α Incidence angle τ Normalized tip clearance (gap/h) ω Vorticity Γ Circulation Γ * Normalized circulation (

In hydraulic turbines, the tip-leakage vortex is responsible for flow instabilities and for promoting erosion due to cavitation. To better understand the tip vortex flow, Reynoldsaveraged Navier-Stokes (RANS) and large eddy simulation (LES) computations are carried out to simulate the flow around a NACA0009 blade including the gap between the tip and the wall. The main focus of the study is to understand the influence of the gap width on the development of the tip vortex, as for instance its trajectory. The RANS computations are performed using the open source solver OpenFOAM 2.1.0, two incidences and five gaps are considered. The LESs are achieved using the YALES2 solver for one incidence and two gaps.The validation of the results is performed by comparisons with experimental data available downstream the trailing edge. The position of the vortex core, the mean velocity and the mean axial vorticity fields are compared at three different downstream locations. The results show that the mean behaviour of the tip vortex is well captured by the RANS and LES computations compared to the experiment. The LES results are also analysed to bring out the influence of the gap width on the development of the tip-leakage vortex. Finally, a law that matches the vortex trajectory from the leading edge to the mid-chord is proposed. Such a law can be helpful to determine, in case of cavitation, if the tip vortex will interact with the walls and cause erosion.

International audienceThis paper presents a numerical study of an aperiodic cavitation pocket developing in a Venturi flow. The mass transfer between phases is driven by a void ratio transport equation model. A new free-parameter closure relation is proposed and compared with other formulations. The re-entrant jet development, void ratio profiles and pressure fluctuations are analysed to discern results accuracy. Comparisons with available experimental data are done and good agreement is achieved

A compressible, multiphase, one-fluid RANS solver has been developed to study turbulent cavitating flows. The interplay between turbulence and cavitation regarding the unsteadiness and structure of the flow is complex and not well understood. This constitutes a determinant point to accurately simulate the dynamic behaviour of sheet cavities. In the present study, different formulations including compressibility effects on turbulence are investigated.Numerical results are given for two partial cavities on Venturi geometries and comparisons are made with experimental data. mean flow data. Moreover, the standard eddy-viscosity models based on the Boussinesq relation are known to over-produce eddy-viscosity, which reduces the development of the re-entrant jet and two-phase structure shedding [1].The link to compressibility effects on turbulence is not clear. DNS of the supersonic boundary layer demonstrated a reduction in k production as a consequence of compressibility [2,3,4]. In cavitating flows, the supersonic regime is reached in the mixture area because of the drastic diminution of the speed of sound. The detailed mechanisms of the interaction between turbulent flows and cavitation have not yet been clearly revealed, especially for phenomena occurring at small scales.Different strategies have been investigated to limit or to correct standard turbulence models. An arbitrary modification was proposed by Reboud to reduce the turbulent viscosity [1], and has been used successfully by different authors [5,6,7,8,9,10]. The Shear Stress Tensor (SST) correction proposed by Menter [11,12] to reduce the eddy-viscosity in case of positive pressure gradient and a variant based on realizability constraints [13] were tested for unsteady cavitating flows [14]. Other corrections are based on the modelling of compressibility effects of the vapour/liquid mixture in the turbulence model. Correction terms proposed by Wilcox [15] in the case of compressible flows were tested for unsteady periodic cavitating flows [6]. A sensitivity analysis of constants C ε1 and C ε2 , which directly influence the production and dissipation of turbulence kinetic energy, was conducted for a k − ε model and a cavitating hydrofoil case [16]. A k − ℓ model including a scale-adaptive term [17] was developped for cavitating flows [18]. This term allows the turbulence model to recognized the resolved scales in the flow andThe mass gain per unit volume due to phase change (evaporation or condensation) is noted Γ k = ρ k (u I − u k ).n k δ I where δ I is a Dirac distribution having the different interfaces as a support, u I the interface velocity and n k the vector normal to the interface directed outward from phase k. 7

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