Bidimensional linear stability of a detonation wave: Kinetic approach and numerical results

Abstract

The bidimensional linear stability of a detonation wave is here addressed for a binary mixture of ideal gases which undergoes a reversible reaction of type A + A ⇌ B + B, using the classical ZND model to characterize the steady planar structure of the detonation wave. We start from the kinetic theory approach of the mixture and adopt the model used in [2] to describe the reactive collisional dynamics. Then the problem is studied at the hydrodynamic Euler limit of the kinetic model. This allows us to play with several parameters, such as the detonation wave velocity, the specific reaction heat, the activation energy of the chemical reaction and the ratio of the specific heats, and characterize the detonation wave solution in a wide parameter space. The linear stability of the steady detonation wave is analysed by introducing small transverse disturbances in their rear boundary and studying the response, over time, of the steady structure to the considered perturbations. We then present some numerical results to illustrate the detonation wave structure and its stability spectrum.