Improved boundary conditions for viscous, reacting, compressible flows

Abstract

Previous studies on physical boundary conditions for flame–boundary interactions of an ideal, multicomponent, compressible gas have neglected reactive source terms in their boundary condition treatments. By combining analyses of incompletely parabolic systems with those based on the hyperbolic Euler equations, a rational set of boundary conditions is determined to address this shortcoming. Accompanying these conditions is a procedure for implementation into a multidimensional code. In the limits of zero reaction rate or one species, the boundary conditions reduce in a predictable way to cases found in the literature. Application is made to premixed and nonpremixed flames in one and two dimensions to establish efficacy. Inclusion of source terms in boundary conditions derived from characteristic analysis is essential to avoid unphysical generation of pressure and velocity gradients as well as flow reversals. Minor deficiencies in the boundary conditions are attributed primarily to the diffusive terms. Imposing vanishing diffusive boundary-normal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory.