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 at all speeds are presented. The single-phase behavior of the fluid is defined by the Sanchez-Lacombe equation of state, 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 flow speeds and all states of compressibility. Modifications to the preconditioned variant of AUSM+ necessary to preserve solution accuracy under such conditions 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 flow through a capillary nozzle

[1]  C. Brennen.  Cavitation and Bubble Dynamics , 1995 .

[2]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[3]  M. S. Liou,et al.  Progress Towards and Improved CFD Method : AUSM+ , 1995 .

[4]  Christopher J. Roy,et al.  Preconditioned multigrid methods for two-dimensional combustion calculations at all speeds , 1998 .

[5]  Stephen D. Heister,et al.  A Numerical Treatment for Attached Cavitation , 1994 .

[6]  Stojan Petelin,et al.  Modelling of Two-Phase Flow with Second-Order Accurate Scheme , 1997 .

[7]  I. Toumi.  A weak formulation of roe's approximate riemann solver , 1992 .

[8]  A. Kumbaro,et al.  An Approximate Linearized Riemann Solver for a Two-Fluid Model , 1996 .

[9]  J. Edwards,et al.  Low-Diffusion Flux-Splitting Methods for Flows at All Speeds , 1997 .

[10]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[11]  Charles L. Merkle,et al.  Computation of Flows with Arbitrary Equations of State , 1998 .

[12]  Feng Xiao,et al.  Strategy for unified solution of solid, liquid, gas and plasmas , 1999 .

[13]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[14]  J. Oefelein,et al.  Simulation and analysis of supercritical multiphase combustion processes , 1996 .

[15]  Hansong Tang,et al.  A Second-Order Accurate Capturing Scheme for 1D Inviscid Flows of Gas and Water with Vacuum Zones , 1996 .

[16]  Philip L. Roe,et al.  Characteristic time-stepping or local preconditioning of the Euler equations , 1991 .

[17]  Frédéric Coquel,et al.  A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows , 1997 .

[18]  Meng-Sing Liou,et al.  A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics) , 1994 .

[19]  Isaac C. Sanchez,et al.  An elementary molecular theory of classical fluids. Pure fluids , 1976 .

[20]  S. Heister,et al.  Modeling Hydrodynamic Nonequilibrium in Cavitating Flows , 1996 .

[21]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[22]  Meng-Sing Liou,et al.  Low-diffusion flux-splitting methods for real fluid flows at all speeds , 1999 .

[23]  Martin A. Reno,et al.  Coefficients for calculating thermodynamic and transport properties of individual species , 1993 .

[24]  V. Vatsa,et al.  Pressure updating methods for the steady-state fluid equations , 1995 .

[25]  Sengers,et al.  Crossover from singular to regular behavior of the transport properties of fluids in the critical region. , 1988, Physical review letters.

[26]  Jonathan Weiss,et al.  Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes , 1994 .

[27]  P. B. Butler,et al.  Numerical Study of Cavitation in the Wake of a Hypervelocity Underwater Projectile , 1999 .

[28]  W. David Kelton,et al.  Simulation analysis , 1983, WSC '83.

[29]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[30]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[31]  J. Edwards,et al.  Ausm schemes and extensions for low mach and multiphase flows , 1999 .

[32]  Dean W. Matson,et al.  Rapid expansion of supercritical fluid solutions: solute formation of powders, thin films, and fibers , 1987 .

[33]  W. Shyy,et al.  Dynamics of attached turbulent cavitating flows , 2001 .

[34]  J. Edwards.  A low-diffusion flux-splitting scheme for Navier-Stokes calculations , 1997 .

[35]  Meng-Sing Liou,et al.  Numerical speed of sound and its application to schemes for all speeds , 1999 .

[36]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .