Initiation and evolution of triple flames subject to thermal expansion and gravity

Abstract

We investigate the combined effects of thermal expansion and gravity on the initiation and evolution of triple flames. In particular, we provide a possible criterion for the thermal energy per unit depth required for triple flame ignition by a cylindrical ignition kernel. Further, we describe the transient evolution of triple flames after initiation. Steady, non-propagating, planar solutions representing “flame tubes” are determined. The flame tube solutions are unstable; in time-dependent simulations it is found that initial perturbations increasing the thermal energy of flame tubes lead to the propagation of a triple flame, while perturbations decreasing the thermal energy lead to extinction. Therefore it is concluded that the thermal energy of flame tubes may be used to define a possible ignition energy per unit depth for planar triple flames in the mixing layer, analogous to spherical flame balls for spherically expanding flames. This is the first paper to provide a detailed study of the ignition energy of planar triple flames. When gravity is not taken into account, flame tubes subject to thermal expansion are found not to induce a flow, so that the flame tube energy can be determined without having to solve the full Navier–Stokes equations.