UC Berkeley

Experiments have found substantial morphological differences between buoyancy-driven flames developing on the upper and lower surfaces of inclined burning plates. These differences cannot be explained on the basis of existing analytical solutions of steady semi-infinite flames, which provide identical descriptions for the top and bottom configurations. To investigate the potential role of flame instabilities in the experimentally observed flow differences, a temporal linear stability analysis is performed here. The problem is formulated in the limit of infinitely fast reaction, taking into account the non-unity Lewis number of the fuel vapor. The stability analysis incorporates non-parallel effects of the base flow and considers separately spanwise traveling waves and Görtler-like streamwise vortices. The solution to the stability eigenvalue problem determines the downstream location at which the flow becomes unstable, characterized by a critical value of the relevant Grashof number, whose value varies with the plate inclination angle. The results for the flame formed on the underside of the fuel surface indicate that instabilities emerge farther downstream than they do for a flame developing over the top of the fuel surface, in agreement with experimental observations. Increased buoyancy-induced vorticity production is reasoned to be responsible for the augmented instability tendency of topside flames.