Least Squares Minimization Closure Models for LES of Turbulent Combustion

This work summarizes the development and testing of a new family of chemical closure models for large-eddy simulation (LES) of turbulent combustion using finite-rate chemistry. The goal of this research is to provide a simple, yet effective model that provides a correction to the ‘laminar chemistry’ prediction formed by evaluating chemical production terms using filtered-mean data. The general model takes the form \(\overline {\dot {{\omega }}_{s} (q)} =f(\overline {{q}},{\Delta } ,{\ldots } )\dot {{\omega }}_{s} (\overline {{q}})\), where the enhancement factor, f, accounts for the effects of the subgrid fluctuations on apparent reactivity as expressed at a given mesh level. A form for the enhancement factor is derived by least-squares minimization (LSM) of a ‘reactivity functional’ connecting information at different mesh levels. A modified a priori analysis, in which simultaneous large-eddy simulations are performed on fine and coarse mesh levels, is used to identify candidate modeled forms for the enhancement factor. In the modified a priori analysis, coarse-mesh realizations are constrained by the filtered fine-mesh velocity, allowing eddy structures to be highly correlated. Several LSM variants are described and tested through comparisons with experimental data. The test cases include three experiments conducted at the University of Virginia’s supersonic combustion facility involving non-premixed hydrogen and partially-premixed ethylene combustion as well as a premixed propane-air flame in the Volvo Validation Rig. The results demonstrate the capability of the models to provide a consistent (if modest in some cases) improvement in predictive capability, relative to ‘laminar chemistry’, in a cost-effective manner.