Darrieus - Landau instability, growing cycloids and expanding flame acceleration

A premixed flame, propagating away from a point ignition source into an unlimited domain displays an increasing flame speed after the flame size has grown beyond a transition radius. Experiments by Gostintsev et al are described by the relation R = R1 + At3/2, where t is the time from ignition and, where SL is the flame burning velocity and is the thermal diffusivity. The non-dimensional function a() is determined from the experimental results to be equal to 0.0022, where is the density ratio across the flame. In the present work, two-dimensional Lagrangian simulations of flame propagation also display a radial growth with a 3/2 power-law behaviour. This is a potential flow model - no vorticity is included. Hence, the Darrieus - Landau hydrodynamic instability by itself can generate flame acceleration. The numerical results are summarized by the relation R = R1+(2/40)L(SLt/L)3/2, where L is a reference length and is the volume production ratio, = - 1. Equating the zone of velocity jump in the numerical sc...