A Investigation of Closure Models for Nonpremixed Turbulent Reacting Flow.

In this study direct numerical simulations (DNS) of statistically isotropic, decaying turbulence with a simple chemical reaction scheme are performed to investigate the stationary laminar flamelet (SLFM) and the conditional moment closure (CMC) models. A one-step, irreversible, isothermal second-order chemical reaction is considered. The accuracy of model predictions and the validity of fundamental assumptions made in the model derivations are examined. Trends in model behavior are obtained by varying the Reynolds number, stoichiometry, Damkohler number and the initial scalar blob size. DNS turbulence was found to be similar to grid turbulence of a lower Reynolds number. After sufficient mixing, the pdf of the conserved scalar (mixture fraction) dissipation rate was found to have a lognormal distribution. From early times the scalar dissipation pdf, conditioned on the conserved scalar, also followed a lognormal distribution. The assumption of the statistical independence of the conserved scalar and its dissipation rate was not justified in these simulations. The validity of the mapping closure (Kraichnan, 1989) and counterflow models of scalar mixing was also investigated. In general, the CMC model was found to be more accurate than SLFM. Insight into the behavior of SLFM was obtained by developing a condition under which the reaction is quasi-steady (as is assumed by SLFM). This condition was best met for the largest values of the scalar dissipation rate which are relatively rare. With increasing Damkohler number SLFM accuracy improved. SLFM was also found to be accurate (provided the Damkohler number is sufficiently large) in local mixing environments which approximate one-dimensional quasi-steady mixing. The validity of three closure assumptions used in the derivation of CMC was found to decrease as the Damkohler number, Reynolds number and the initial scalar blob size increased. Damkohler number effects were most influential. Significant error in the closure existed mostly for mixture fraction values at which the conditional mass fraction was small. This minimized the effect of closure error on mean quantities. Overall, the accuracy of CMC predictions of mean quantities was most dependent on the model used for the conditional scalar dissipation rate. With an accurate model for conditional scalar dissipation rate, CMC was in excellent agreement with the DNS data.