Forbidden interval of propagation speed for exothermic chemical fronts

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

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.

Transition between an exothermic chemical wave front and a generic flame

We consider the two classes of exothermic chemical wave fronts, propagating toward a stable or an unstable steady state. The hydrodynamic equations for stream velocity, temperature, and concentrations are solved numerically for increasing values of the reaction heat. For a critical value of the heat release, we find a transition between a chemical front, whose speed depends on the chemical dynamics, and a generic flame, whose speed is entirely determined by heat release. We derive an analytical expression of the flame speed from the invariants of the hydrodynamic equations. This result substantiates macroscopic approaches widely used in combustion, in which the chemical models include only simplified reaction mechanisms.