Stability of inclined planar flames as a local approximation of weakly curved flames

Abstract

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.