Low-diffusion flux-splitting methods for real fluid flows with phase transitions

Methods for extending the AUSM+ low-diffusion flux-splitting scheme toward the calculation of real fluid flows Pt all speeds are presented, The single-phase behavior of the fluid is defined by the Sanchez-Lacombe equation of state (Sanchez, I. C,, and Lacombe, R. H., "An Elementary Molecular Theory of Classical Fluids: Pure Fluids," Journal of Physical Chemistry, Vol, 80, No. 21, 1976, pp, 2352-2362), a lattice-fluid description. Liquid-vapor phase transitions are modeled through a homogeneous equilibrium approach. Time-derivative preconditioning is utilized to allow effective integration of the equation system at all Row speeds and all states of compressibility, Modifications to the preconditioned variant of AUSM+ necessary to preserve solution accuracy under such renditions are presented in detail. One-dimensional results are presented for the faucet problem, a classic test case for multifluid algorithms, as well as for liquid octane flow through a converging-diverging nozzle, Two-dimensional calculations are presented for water flow over a hemisphere/cylinder geometry and liquid carbon dioxide how through a capillary nozzle, The results illustrate the effectiveness of the flux-splitting scheme in capturing such multiphase flow features as cavitation zones and vapor-liquid condensation shocks, as well as incompressible liquid and compressible vapor responses, within the framework of a single numerical algorithm.