The Propagation of a Chain Isothermal Flame in a Random Medium

Abstract

The dependences of the turbulent flame velocity in a random flow on the turbulence intensity have been studied in terms of the Kolmogorov–Petrovsky–Piskunov nonlinearity model in the one-dimensional case. We show that for a static random medium the turbulent velocity decreases and tends to zero with increasing turbulence intensity. This is explained by the fact that the random flow velocity is the random potential gradient, leading to traps and diffusion retardation. Apparently, this is a general fact: a random gradient velocity field in the two- and three-dimensional cases must give the same effect. This may be true not only for the Kolmogorov–Petrovsky–Piskunov nonlinearity. We have shown analytically that the introduction of a random nonzero mean velocity field accelerating the flame motion enables the flame to overcome the barriers more easily. For a dynamic medium an initial increase of the velocity with growing turbulence is possible in some ranges of scales in space and time. We consider an example of a two-dimensional random divergence-free field for which our numerical computation has shown an increase of the turbulent flame velocity.