A consistent, fully-coupled LES-FDF model for shock-turbulence-flame interactions with a filtered Rankine–Hugoniot energy closure

A hybrid Eulerian–Lagrangian Large Eddy Simulation (LES) - Filtered Density Function (FDF) approach leveraging the recently proposed filtered Rankine–Hugoniot (R–H) energy consistency closure is applied to a three-dimensional spatially evolving turbulent supersonic shear layer flame interacting with an impinging oblique shock. Major advancements include the incorporation of viscous dissipation and molecular micromixing effects in the evolution of Lagrangian particles. Additionally, a novel fractional step based backward density coupling algorithm is implemented to enable the feedback of compositional information from the Lagrangian FDF to the Eulerian LES solver. The hybrid framework is validated against a detailed high fidelity Direct Numerical Simulation (DNS) database of the same configuration, demonstrating its capability to accurately capture the coupled dynamics of shock–turbulence–chemistry interactions in high-speed reacting flows. Novelty and significance statement This research introduces a novel hybrid LES-FDF model, utilising a filtered Rankine–Hugoniot (R–H) energy-consistent closure, to model turbulent combustion in supersonic flows with discontinuities. The model and its numerical implementation are validated for a recent DNS of a 3D supersonic shear layer flame interacting with a wall-reflected oblique shock. It is significant because shear layer flames with impinging oblique shocks are common in modern high-speed aerospace combustors being used in rotating detonation engines and scramjets. The filtered R–H model demonstrates both consistency and accuracy and is a promising approach for high fidelity simulations of such engines at viable computational expense.