Physical modelling of leading edge cavitation

Cavitation is usually the main physical phenomenon behind performance alterations in hydraulic machinery. For this reason, it is crucial to accurately predict its inception and development and to highlight a comprehensive relation between the cavitation development and the performances drop associated. The common cavitation models, based on numerical flow simulations, are intended to reproduce the general cavitation behavior, and their major focus is the cavitation onset and developed cavity shape prediction. In the present study, various methods in cavitation modelling are investigated. Specific computational methods are outlined for the two sensitive zones of cavity detachment and closure. Finally, an industrial case is investigated in order to highlight the mechanisms of head drop phenomenon in hydraulic machines. Current modelling techniques are reviewed together with physical arguments concerning the cavitation phenomenon, and a 2D hydrofoil test case is used to evaluate the models. A mono-fluid interface tracking model, a multiphase state-equation based model, and a multiphase transport-equation based model are discussed in terms of reproducing the cavitation flow characteristics as the cavitation inception, development, pressure distribution and velocity profiles in cavitation regimes. An innovative approach based on the local stress formulation is proposed. The non-viscous anisotropic stress is taken into account through the maximum tensile stress criterion for cavitation inception instead of the classical pressure threshold. The maximum tensile stress criterion, formulated using the shear strain rate formulation is used for CFD computations. The method is evaluated with the case of a parabolic nose leading edge flow with comparison to the boundary layer computations. The developed model is tested in the case of a 2D hydrofoil in both smooth and rough walls under different flow conditions. The ability of the model to take into account Reynolds and surface roughness effects, as observed in experimental investigations, is demonstrated. A comparative study of turbulence modelling for unsteady cavitation is presented which indicates a strong correlation between the cavitation unsteadiness predictions and the turbulence modelling. The adapted techniques in reproducing the unsteady cavitation flow are found to be either using an accurate filtering turbulence model to correctly capture the large eddies, or to modify the turbulent viscosity function, and thereby introducing an artificial compressibility effect. The simulated leading edge cavitation instability, in our case, occurs at a certain cavity length where the cavity closure corresponds to the high pressure gradient region and is governed mainly by the occurrence of the reentrant jet at the cavity closure. This phenomenon is found to be periodic and the shedding frequencies matches to the Strouhal law as observed in experiments. Finally, the multiphase mixture model is used in the case of an industrial inducer. The model provides satisfactory results for the prediction of the cavitation flow behavior and performance drop estimation for the operating points studied. An analysis based on global energy balance and local flow analysis demonstrates that the head drop is mainly caused by the lower torque generation and the hydraulic losses induced by the secondary flows. These phenomena occur when the cavity extends towards the throat region, leading to important changes in the flow structure.