Analysis of compressibility effects on Darrieus-Landau instability of deflagration wave

Department of Mechanical and Aerospace Engineering, Princeton University Princeton, NJ 08544, USA

Corresponding author: longting@phoenix.princeton.edu

Received: 7 December 1998
Accepted: 21 December 1999

Abstract

The Darrieus-Landau instability of propagating fronts, such as the flame front in combustion and ablation front in inertial confinement fusion, was analyzed with considering compressibility effects. It was shown that the assumption that the flame velocity is constant, relative to both the burned and unburned gas, cannot be applied to determine correctly the compressibility effect because it violates the conservation equations (Rankine-Hugoniot relation). Using the jump conditions from the Rankine-Hugoniot relation, we obtained a dispersion relation for the growth rate in terms of the wave number, the Mach number, and the density ratio of the burned to unburned gas. It was found that the growth rate first increases and then decreases with the Mach number and that the Chapman-Jouguet deflagration appears to be neutrally stable.