STRUCTURES OF FLOW AND MIXTURE-FRACTION FIELDS FOR COUNTERFLOW DIFFUSION FLAMES WITH SMALL STOICHIOMETRIC MIXTURE FRACTIONS

Asymptotic methods are used to evaluate a characteristic diffusion time (the reciprocal of the so-called ''scalar dissipation rate'') for counterflow diffusion flames. Attention is restricted to the practically important limit of small values of the stoichiometric mixture fraction, which results in large values of the stream function at the reaction sheet, a quantity that is employed here as a large expansion parameter. Three distinct layers are identified inside the viscous layer: (i) a convective-diffusive layer on the oxidizer side of the reaction sheet. (ii) a rotational inviscid layer on the fuel side of the reaction sheet, and (iii) a fuel-product mixing layer in the vicinity of the stagnation plane; all three of these layers are analyzed and matched. The matching produces analytic expressions for the stream function and mixture fraction at the reaction sheet and corrects formulas for the characteristic diffusion time previously derived on the basis of constant-density-flow or nonreactive-mixing-layer assumptions. Comparisons between analytical and numerical results demonstrate that the analytical results obtained in the present analysis provide accurate expressions for the characteristic diffusion times that are needed in analyses of flame structure and extinction.