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Abstract
Experimental data of Bilger et al. (1991) pertaining to the compositional structure of a turbulent reactive scalar mixing layer are reproduced by a mathematical computational procedure utilizing the Pearson family (PF) of univariate and multivariate scalar probability density functions (pdfs). Aided by comparisons against these data and extensive additional data generated here by direct numerical simulations (DNS) of a spatially developing reacting mixing layer, an appraisal is made of the applicability and the extent of validity of the PF for statistical description of the reactant fluctuations. In accord with the experiment, a chemical reaction of the type A + B →Products is simulated in isothermal, incompressible flows. A wide range of the Damkohler number is considered including both frozen and equilibrium chemistry limits. The comparison of predicted results with laboratory data indicates that the PF generated pdfs are convenient for modeling the influence of turbulence on the mean reactant conversion rate. In particular, the Dirichlet frequency parameterized with the “scalar-energy” provides a reasonable means of portraying the multivariate scalar pdf. A more detailed comparative assessment of the model predictions against DNS data confirms the applicability of the Dirichlet pdf. However, the model portrays some drawbacks, the consequences of which are appraised by laboratory and DNS data.
With the use of PF generated pdf, the autospectral density function and the cross-spectral density function of the reacting scalars under equilibrium chemistry are related to the frequency spectrum of the mixture fraction. This relation is very convenient for predicting the spectral characteristics of reacting scalars in the central region of the laboratory mixing layer and in any other homogeneous flow configuration which yields an asymptotic Gaussian pdf for the mixture fraction. The correction to these spectral relations for asymptotic exponential pdfs is provided, and the infleucne of the Damköhler number on both the auto- and the cross-spectral density functions is assessed by the analysis of DNS data.
