Effect of gravity on hydrodynamically unstable flames

The hydrodynamic instability, due to the large deviation of density between fresh cold mixture and hot combusted products, was discovered by Darrieus and Landau. After seven or eight decades, many aspects of this intrinsic flame instability have been revealed, such as the effects of the flame front curvature and of flow strain rate, its influence on turbulent flames and the self-wrinkling and self-turbulization of expanding flames. In the present study we focus on the composite effects of thermal expansion, differential diffusion, and gravity on flame dynamics, based on a fully nonlinear, hydrodynamic model obtained by a multi-scale analysis that exploits the distinct length scales associated with such problems. The simulations verify the stabilization effect of gravity on planar flames propagating downwards, known from linear stability theory, and show that in the presence of gravity the nonlinear development beyond the stability threshold leads to cusp-like structures of smaller amplitude that propagate at a reduced speed. Finally, we observe that a judicious choice of the Markstein number, controlled by mixture composition and domain size, and of the Froude number creates richer morphological flame structures than in the absence of gravity.