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 + At^3/2, where t is the time from ignition and, where S_L 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 scheme with the temperature jump in hydrocarbon flames allows a definition of an effective thermal diffusivity in the numerical work as n = 0.0081SLL. With this relation, the radial growth is given as, in good agreement with the experimental result and the numerical results of Filyand et al.