TY - JOUR

T1 - The derivation and numerical solution of the equations for zero mach number combustion

AU - Majda, Andrew

AU - Sethian, James

N1 - Funding Information:
This work is supported in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Engineering, Mathematical and Geosciences Division of the U.S. Department of Energy under contract DE-AC03-76SF00098. The work of A. Majda is supported by A.R.O. Grant No. 483964-25530. The work of J. Sethian is supported by a National Science Foundation Mathematical Sciences Fellowship.

PY - 1985/1/1

Y1 - 1985/1/1

N2 - 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.

AB - 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.

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U2 - 10.1080/00102208508960376

DO - 10.1080/00102208508960376

M3 - Article

AN - SCOPUS:84948505075

VL - 42

SP - 185

EP - 205

JO - Combustion Science and Technology

JF - Combustion Science and Technology

SN - 0010-2202

IS - 3-4

ER -