A Preconditioned Flux-Differencing Scheme for Chemically Reacting Flows at all Mach Numbers

Abstract A new computation procedure is developed for solving time-accurate, chemically reacting flows over a wide range of Mach numbers. The algorithm is based on scaling the pressure terms in the momentum equations and preconditioning the conservation equations to circumvent numerical difficulties at low Mach numbers. The resulting equations are solved using the lower-upper (LU) factorization method in a fully-coupled manner, with incorporation of a flux-differencing upwind TVD scheme to achieve high-order spatial accuracy. The transient behavior of the modeled system is preserved through implementation of the dual time-stepping integration technique. The capabilities of the scheme are illustrated by applying it to selected problems, including one-dimensional nozzle flows, two-dimensional channel flows, rocket-motor internal flows, and acoustic waves in a porous chamber with surface transpiration.

[1]  Vigor Yang,et al.  A time-accurate implicit method for chemically reacting flows at all Mach numbers , 1991 .

[2]  S. Osher,et al.  A new class of high accuracy TVD schemes for hyperbolic conservation laws. [Total Variation Diminishing] , 1985 .

[3]  Bertil Gustafsson,et al.  A numerical method for incompressible and compressible flow problems with smooth solutions , 1986 .

[4]  K. Kuo,et al.  A comprehensive erosive-burning model for double-base propellants in strong turbulent shear flow , 1983 .

[5]  A. Jameson,et al.  Implicit schemes and LU decompositions , 1981 .

[6]  Charles L. Merkle,et al.  Computation of low-speed flow with heat addition , 1987 .

[7]  J. Shuen,et al.  Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations , 1992 .

[8]  Man Mohan Rai,et al.  Navier-Stokes Simulations of Blade-Vortex Interaction Using High-Order-Accurate Upwind Schemes , 1987 .

[9]  A. Godfrey.  Topics on spatially high-order accurate methods and pre-conditioning for the Navier-Stokes equations with finite-rate chemistry , 1992 .

[10]  V. Yang,et al.  Combustion of a double-base homogeneous propellant in a rocket motor , 1994 .

[11]  J. Shuen,et al.  A coupled implicit method for chemical non-equilibrium flows at all speeds , 1993 .

[12]  Charles Merkle,et al.  Time-accurate unsteady incompressible flow algorithms based on artificial compressibility , 1987 .

[13]  Jörn Sesterhenn,et al.  Flux-vector splitting for compressible low Mach number flow , 1993 .

[14]  D. Gottlieb,et al.  Splitting methods for low Mach number Euler and Navier-Stokes equations , 1989 .

[15]  S. Patankar,et al.  Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations , 1988 .

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

[17]  INTERACTIONS BETWEEN ACOUSTIC WAVES AND PREMIXED FLAMES IN POROUS CHAMBERS , 1994 .

[18]  F. C. Lockwood,et al.  On the prediction of two-dimensional supersonic viscous interactionsnear walls , 1977 .

[19]  A. A. Amsden,et al.  A numerical fluid dynamics calculation method for all flow speeds , 1971 .

[20]  C. Merkle,et al.  The relationship between pressure-based and density-based algorithms , 1992 .

[21]  Elaine S. Oran,et al.  Detailed modelling of combustion systems , 1981 .

[22]  H. Mcdonald,et al.  A low mach number Euler formulation and application to time-iterative LBI schemes , 1983 .