A study of the low mach number flow model with time-dependent rapid chemistry

Abstract

A numerical study has been carried out on the validity of the low Mach number limit of the Navier-Stokes equations for unsteady chemically reacting flows. This limit is very useful since pressure waves are eliminated from the equations, and the analysis of many problems can be considerably simplified. The results from this research have shown that the model can lead to inconsistent results when rapid chemistry and density changes occur in a flow. The inconsistency is fundamental to the low Mach number model, and results in large dynamic pressure changes due to fluid particle acceleration. The high fluid particle acceleration follows directly from the assumption of constant thermodynamic pressure and rapid chemical reactions. In most applications the pressure changes quickly die out, and the assumptions of the model become valid. Besides the lack of physical validity the problem of large dynamic pressures leads to serious numerical problems due to lack of resolution and interaction with boundary conditions. The results of this study also apply to the Stephan model, and they give insight into many of the previous problems that occurred for low Mach number and incompressible flows. A method of correction for some of the numerical difficulties has been given in the paper, however the question of physical validity appears to be fundamental. Another topic contained in the paper is a comparison between the full Navier-Stokes equations and the low Mach number model for an one-dimensional, unsteady flame propagation problem. The results of this study show that the full Navier-Stokes equations can be competitive in terms of efficiency and accuracy for problems involving rapid chemistry.