Modélisation et simulation d’écoulements turbulents cavitants avec un modèle de transport de taux de vide
jury members
Mme Maria Vittoria SALVETTI Professeure, Université de Pise, Rapporteur
Mr Farid BAKIR, Professeur, ENSAM, Rapporteur
Mr Jean-Baptiste DEUFF Docteur, DGA Techniques Hydrodynamiques, Examinateur
Mme Claire SEGOUFFIN Ingénieur, Alstom Hydro France, Examinateur
Mme Henda DJERIDI Professeure, Grenoble-INP Président du Jury
Mr Eric GONCALVES DA SILVA Professeur, ENSMA, Directeur de Thèse.
Abstract
The computation of turbulent cavitating flows involves many difficulties both in modeling the physical phenomena and in the development of robust numerical methods. Indeed such flows are characterized by phase transitions and large density gradients, Mach number variation due to speed of sound decrease, two-phase turbulent areas and unsteadiness. This thesis follows experimental and numerical studies led at the Laboratoire des Ecoulements Géophysiques et Industriels which aim to improve the understanding and modeling of cavitating flows. Simulations are based on a compressible code coupled with a pre-conditionning technique which handles low-Mach number areas. The two-phase flows are reproduced using a one-fluid homogeneous model and temporal discretisation is performed using an implicit dual-time stepping method . The resolution is based on the RANS approach that couples conservation equations with firts-order closure models to compute eddy viscosity. In two-phase flows areas, the computation of thermodynamic quantities requires to close the system with equations of state (EOS). Thus, two formulations are investigated to determine the pressure in the mixture. The stiffened gas EOS is written with conservative quantities while a sinusoidal law deduces the pressure from the volume fraction of vapor (the void fraction). The present study improves the homogeneous equilibrium models by including a transport equation for the void ratio. The mass transfer between phases is assumed to be proportional to the divergence of the velocity. In addition to a better modeling of convection, expansion and collapse phenomenon, this added transport equation allows to relax the local thermodynamic equilibrium and to introduce a mestastable state to the vapor phase. 2D and 3D simulations are performed on Venturi type geometries characterized by the development of unstable partial cavitation pockets. The goal is to reproduce unsteadiness linked to each pro le such as the formation of a re-entrant jet or the quasi-periodic vapor clouds shedding. Numerical results highlight frequency variations of unsteadiness depending on the speed of sound computation. Moreover, the simulation conducted with a relaxed vapor density increase the pressure wave propagation magnitude generated by the collapse of cavitating structures. It contributes to the destabilization of the pocket. Finally, the role of the void ratio equation is analyzed by comparing the simulation results to those obtained subsequently from a model involving only three conservation equations.
Key words :Cavitation, URANS simulations, one-fluid homogeneous model, mass transfer, void ratio transport equation