Hydrodynamic and diffusive instabilities in premixed flames

We now restrict our attention to premixed gaseous combustibles and address the question of the intrinsic stability of their deflagrative processes. The topic is a large one that has undergone extensive advancement in recent years. Here we shall only be able to touch on some of the highlights. The 

Here we shall be concerned with the stability of planar deflagrations to non-one-dimensional perturbations. We shall see that a richer variety 

At large values of the Zel dovich number, the chemical reaction is confined to a thin sheet in the flow. For all purposes except the analysis of the sheet structure, the sheet may be treated as a surface—for example, G(x, t) = 0—which in terms of the Cartesian coordinates (x, y, z) may be written locally as x = F y, z, t) if the x coordinate is not parallel to the sheet in its local orientation. When analyses are pursued in outer-scale variables, it is convenient to work in a coordinate system that moves with the sheet. For the undisturbed flow, let the x coordinate be normal to the planar flame, with the unburnt gas extending to x = — oo and the burnt gas to x = -1- oo. Employ the steady, adiabatic, laminar flame speed, measured in the burnt gas, = po Vq/p with Vq given by equation (5-78), and the thermal diffu- 

Under the assumption that the reaction sheet is smooth and nowhere parallel to the X axis, equation (1-1), through a transformation of variables, can be written as 

The coordinate transformation also enables a nondimensionai version of the equation for momentum conservation to be written from equations (1-2) and (1-5). For this purpose, Prandtl numbers based on the first and a modified second coefficient of viscosity, respectively, may be defined as Pr = and Prj = To allow for 

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