Zel’dovich number

The problem that has been defined here possesses the cold-boundary difficulty discussed in Section 5.3.2 and can be approached by the same variety of methods presented in Section 5.3. The asymptotic approach of Section 5.3.6 has been seen to be most attractive and will be adopted here. Thus we shall treat the Zel dovich number... 

The essential physical ideas apparently were first known to Zel dovich. The instability mechanisms can be explained by reference to Figure 9.9, where the arrows indicate directions of net fluxes of heat and species. A key element in the explanation is the fact that for large values of the Zel dovich number, the burning velocity depends mainly on the local flame temperature. This intuitively clear result is not entirely obvious from the formulation of Section 9.5.1 but may be motivated from it by employing RudY /d = as a rough approximation to equation (95) in the... 

Equation (77) and (dT/dx) =Q+ = 0 provide first approximations to the results obtained by a more formal derivation of jump conditions across the thin reaction zone. Equation (56) applies on each side of the reaction zone in this three-zone problem. To the lowest order in the Zel dovich number, T remains constant for x > 0. The problem for x < 0 becomes identical to that described by equations (56)-(58), with the replacements E, = i/(2R°),... 

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-... 

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