Stability of Inclined Premixed Planar Flames

기울어진 예혼합 평면화염의 안정성

Stability of 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 becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational 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 flame wave depends on not only the flame angle but also the Lewis number. 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.