Steady dynamics of exothermic chemical wave fronts in van der Waals fluids

Abstract

We study the steady dynamics of an exothermic Fisher-Kolmogorov-Petrovsky-Piskunov chemical wave front traveling in a one-dimensional van der Waals fluid. The propagating wave is initiated by a nonuniformity in reactant concentration contrary to usual combustion ignition processes. The heat release and activation energy of the reaction play the role of control parameters. We recently proved that the propagation of an exothermic chemical wave front in a perfect gas displays a forbidden interval of stationary wave front speeds [G. Dumazer, M. Leda, B. Nowakowski, and A. Lemarchand, Phys. Rev. E 78, 016309 (2008)]. We examine how this result is modified for nonideal fluids and determine the effect of the van der Waals parameters and fluid density on the bifurcation between diffusion flames and Chapman-Jouguet detonation waves as heat release increases. Analytical predictions are confirmed by the numerical solution of the hydrodynamic equations including reaction kinetics.