Modelling of Supersonic Combustion using a Filtered Rankine-Hugoniot LES-FDF Method

Abstract

A new energy consistency scheme using the filtered Rankine-Hugoniot (R-H) relation is tested and validated for a hybrid Eulerian/Lagrangian Large Eddy Simulation Filtered Density Function (LES-FDF) numerical method for modelling compressible high-speed combustion. This involves computing enthalpy redundantly on an Eulerian finite volume scheme, and an ensemble of Lagrangian particles which uses the filtered R-H relation to account for sub-grid effects. The method is tested against a three-dimensional, practical flame case: a turbulent non-premixed shear layer into an oblique shock. This was done including viscosity, and with a 35-step, 20-species chemistry model. Instantaneous and time-averaged measurements across the whole domain show numerically consistent temperature and enthalpy, validating energy consistency. Species were found to be better resolved in the FDF solver. Also, exclusion of Lagrangian sub-grid kinetic energy relaxation is shown to increase energy consistency error between solvers. Further, LES-FDF results were validated against DNS data showing low physical error. Overall, these results successfully validate the application of this novel method in practical, three-dimensional flame cases.