Subgrid modeling of the filtered equation of state with application to real-fluid turbulent mixing at supercritical pressures

Simulation of turbulent mixing and combustion at supercritical pressures requires the use of a real-fluid equation of state (EOS) to represent the nonideal, nonlinear thermodynamic behavior of fluids under these conditions. The simplified representation of the filtered EOS in the large eddy simulation methodology introduces inconsistencies in the computed filtered thermodynamic state. This study investigates these inconsistencies and novel subgrid modeling approaches to address these issues, using high-resolution direct numerical simulation of a transcritical mixing layer. Errors incurred by not accounting for subgrid effects in the EOS are quantified, and fundamental insights are drawn regarding the nature of these effects. Then, different modeling approaches are proposed and investigated to obtain a more accurate representation of the filtered EOS. The evaluation of the filtered EOS in terms of the Reynolds-filtered state variables is considered instead of the conventional Favre-filtered variables. A dynamic gradient model is formulated by building upon the ideas of dynamic modeling to render a functional form for the subgrid EOS expressed in terms of the resolved flow gradients. A scale-similarity model formulation for the subgrid EOS is also constructed and examined. Finally, a model for the filtered EOS is derived using a presumed filtered density function that accounts for the effect of subgrid-scale fluctuations. The performance of each model is evaluated using various metrics, and the relative accuracy of each modeling approach is compared and contrasted at different filter sizes.