Effect of the Turbulent Schmidt Number on Supersonic Regime

From the analysis of the physics of supersonic combustion, a new subgrid scale model (ISCM) for Large Eddy Simulation has been derived. The ISCM model takes into account the effect of the Mach number (Ma) on mixing and combustion: in particular, by analyzing the dimensionless Navier-Stokes equations, it is based on the basic fact that, in the supersonic regime, the baroclinic and compressibility terms become important. Furthermore, at Ma>1 chemical kinetics and combustion are influenced by the dilatational term "∇·u". Large Eddy Numerical simulations of a supersonic combustion NASA-Langley test case1 have shown that the ISCM subgrid model is in a better agreement with experimental data than the Smagorinsky-Lilly model2: in fact, while the Smagorinsky-Lilly model predicts neither combustion nor vortex structures, the ISCM model predicts flame anchoring, streamwise vorticity and temperatures close to those observed in the experiments. However, while experiments show a more distributed combustion, numerical simulations show that combustion is confined near the air/H 2 interface. This could be due to the assumption of a constant turbulent Schmidt number. By looking ay the physics of the small scales and at their influence on the scalars turbulent transport, a novel SGS model for the turbulent diffusivity has been developed. In this new SGS model, the scalars transport is no longer supposed to be proportional only to the eddy viscosity, i.e. to the small scales turbulent velocity, but also to scalars fluctuations that must be accounted for. This advance in the ISCM model may therefore be the key to better reproduce experimental results. In order to evaluate the influence of the turbulent Schmidt number on the turbulent species transport, numerical simulations with different turbulent Schmidt numbers (Sct=0.4, 0.6, 0.7) have been performed