LES of a Supersonic Combustor with Variable Turbulent Prandtl and Schmidt Numbers

The analysis of the physics of supersonic combustion has pointed out that in supersonic flows the compressibility plays a key role on mixing and combustion. In fact, despite Papamoschou and Rosko stated that compressibility suppress the vertical motion at Mac>0.6, the dimensionless analysis reported below shows that increasing the streamwise vorticity, mixing is fast and efficient. In particular, by analyzing the dimensionless Navier-Stokes equations, it comes out that baroclinic and compressibility terms become important in the supersonic regime. Furthermore, at Ma>l also chemical kinetics and combustion are influenced by the dilatational term "∇-u". A new subgrid scale model (ISCM) for Large Eddy Simulation has been derived taking into account the effect of the Mach number (Ma) on mixing and combustion. 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 at 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. These LES simulations show that by decreasing Sc t from 0.7 to 0.6, the flame becomes stable and once ignited it does not quench. Furthermore, the flame is more intense and no longer confined to the H2/air interface. When decreasing Sct to 0.4, the flame stays steady but less intense. This means that the choice of the Sct is crucial to predict numerical results in a better agreement with experimental results. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.