THE DERIVATION AND NUMERICAL SOLUTION OF THE EQUATIONS FOR ZERO MACH NUMBER COMBUSTION

Abstract We present a limiting system of equations to describe combustion processes at low Mach number in either confined or unbounded regions and numerically solve these equations for the case of a flame propagating in a closed vessel. This system allows for large heat release, substantial temperature and density variations, and substantial interaction with the hydrodynamic flow field, including the effects of turbulence. This limiting system is much simpler than the complete system of equations of compressible reacting gas flow since the detailed effects of acoustic waves have been removed. Using a combination of random vortex techniques and flame propagation algorithms specially designed for turbulent combustion, we describe a numerical method to solve these zero Mach number equations. We use this method to analyze the competing effects of viscosity, exothermicity, boundary conditions and pressure on the rate of combustion for a flame propagating in a swirling flow inside a square.

[1]  H. Baum,et al.  The Equations of Motion for Thermally Driven, Buoyant Flows. , 1978, Journal of research of the National Bureau of Standards.

[2]  A. Majda,et al.  Compressible and incompressible fluids , 1982 .

[3]  J. Sethian.  AN ANALYSIS OF FLAME PROPAGATION , 1982 .

[4]  A. K. Oppenheim,et al.  Numerical modelling of turbulent flow in a combustion tunnel , 1982, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  J. Sethian.  Turbulent combustion in open and closed vessels , 1984 .

[6]  P. Woodward,et al.  SLIC (Simple Line Interface Calculation) , 1976 .

[7]  Nonisobaric Flame Propagation , 1980 .

[8]  P. Embid,et al.  Well-posedness of the nonlinear equations for zero mach number combustion , 1987 .

[9]  B. Matkowsky,et al.  A New Model in Flame Theory , 1982 .

[10]  A. Chorin.  Flame advection and propagation algorithms , 1980 .

[11]  A. Chorin.  Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[13]  R. L. Alpert,et al.  The wrinkling of a flame due to viscosity , 1983 .

[14]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[15]  G. Sivashinsky,et al.  Hydrodynamic theory of flame propagation in an enclosed volume , 1979 .

[16]  James A. Sethian,et al.  NUMERICAL SIMULATION OF FLAME PROPAGATION IN A CLOSED VESSEL , 1983 .

[17]  Gregory I. Sivashinsky,et al.  An asymptotic derivation of two models in flame theory associated with the constant density approximation , 1979 .