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Stability of preconditioned Navier–Stokes equations associated with a cavitation model

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2005
auteur(s) Coutier Delgosha Olivier; Fortes-Patella Regiane; Reboud Jean-Luc; Hakimi N.; Hirsch C.
journal (abréviation) Computers and Fluids (Comput Fluid)
volume (numéro) 34 (3)
  
pages 319 – 349
résumé A 3D numerical model is proposed to simulate complex unsteady cavitating flows. The final objective is to predict instabilities due to cavitation in turbopump inducers. It was previously applied to simpler two-dimensional simulations such as a Venturi type section [Int. J. Numer. Meth. Fluids, in press] and foil sections [Int. J. JSME B 45(3) (2002)]. The model is based on the code FineTurbo significantly modified to take into account the cavitation process. The numerical scheme consists in a time-marching algorithm initially devoted to compressible flows. A low-speed preconditioner is applied to treat low Mach number flows. This numerical resolution is coupled to a single-fluid model of cavitation. The evolution of the density is governed by a barotropic state law proposed and validated previously by Delannoy and Kueny [Proc 1990 ASME Cavitation Multiphase Flow Forum 98 (1990) p. 153] and Coutier-Delgosha et al. [Int. J. Numer. Meth. Fluids 42 (2003) 527]. The present work focuses on the numerical stability of the Navier–Stokes equations associated to the barotropic state law. Fourier footprint representations are applied to several two-dimensional non-cavitating and cavitating flow field configurations, and the influence of the numerical and physical parameters on the stability is investigated. The influence of the preconditioner is also discussed: a modification is proposed in the two-phase areas, and its effect is tested in a two-dimensional Venturi type section flow configuration. A significant improvement is obtained concerning both the convergence level and speed.
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