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 = R-1 + At-3/2,, where,, t is the time from ignition and A = a(sigma)S-L(2)/root kappa:, where S-L is the flame burning velocity and kappa is the thermal diffusivity; The non-dimensional function a(sigma) is determined from the experimental results to be equal to 0.002 sigma(2), where sigma 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 Bow 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 = R-1 + (tau(2)/40)L(S(L)t/L)(3/2), where L is a reference length and tau is the volume production ratio, tau = sigma -: 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 kappa(N) = 0.0081S(L)L. With this relation, the radial growth is given as R = RI + 0.0023 tau(2)S(L)(2)t(3/2)/root kappa(N), in good agreement with the experimental result and the numerical results of Filyand et al.