A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

Abstract

A Direct Numerical Simulation (DNS) database was created representing mixing of species under high-pressure conditions. The configuration considered is that of a temporally evolving mixing layer. The database was examined and analyzed for the purpose of modeling some of the unclosed terms that appear in the Large Eddy Simulation (LES) equations. Several metrics are used to understand the LES modeling requirements. First, a statistical analysis of the DNS-database large-scale flow structures was performed to provide a metric for probing the accuracy of the proposed LES models as the flow fields obtained from accurate LESs should contain structures of morphology statistically similar to those observed in the filtered-and-coarsened DNS (FC-DNS) fields. To characterize the morphology of the large-scales structures, the Minkowski functionals of the iso-surfaces were evaluated for two different fields: the second-invariant of the rate of deformation tensor and the irreversible entropy production rate. To remove the presence of the small flow scales, both of these fields were computed using the FC-DNS solutions. It was found that the large-scale structures of the irreversible entropy production rate exhibit higher morphological complexity than those of the second invariant of the rate of deformation tensor, indicating that the burden of modeling will be on recovering the thermodynamic fields. Second, to evaluate the physical effects which must be modeled at the subfilter scale, an a priori analysis was conducted. This a priori analysis, conducted in the coarse-grid LES regime, revealed that standard closures for the filtered pressure, the filtered heat flux, and the filtered species mass fluxes, in which a filtered function of a variable is equal to the function of the filtered variable, may no longer be valid for the high-pressure flows considered in this study. The terms requiring modeling are the filtered pressure, the filtered heat flux, the filtered pressure work, and the filtered species mass fluxes. Improved models were developed based on a scale-similarity approach and were found to perform considerably better than the classical ones. These improved models were also assessed in an a posteriori study. Different combinations of the standard models and the improved ones were tested. At the relatively small Reynolds numbers achievable in DNS and at the relatively small filter widths used here, the standard models for the filtered pressure, the filtered heat flux, and the filtered species fluxes were found to yield accurate results for the morphology of the large-scale structures present in the flow. Analysis of the temporal evolution of several volume-averaged quantities representative of the mixing layer growth, and of the cross-stream variation of homogeneous-plane averages and second-order correlations, as well as of visualizations, indicated that the models performed equivalently for the conditions of the simulations. The expectation is that at the much larger Reynolds numbers and much larger filter widths used in practical applications, the improved models will have much more accurate performance than the standard one.

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