Theoretical and Numerical analysis of the Turbulence scaling in Supersonic Flows

Supersonic mixing and combustion is critical to advanced airbreathing propulsion systems able to push vehicles well beyond M=4. Research in this field is of interest around the world. In fact, vehicles capable of such speed are being tested now in the US (HyTech, HyV), Russia and the UK-Australia (HyShot), in Japan, India, China and Korea. EU is funding the project LAPCAT to study the feasibility of a long range hypersonic commercial transport. In a SCRJ, the air stream flow captured by the inlet is decelerated but still maintaining supersonic conditions. Since the residence time is very short (~1ms), the study of a efficient mixing and combustion is a key issue in the ongoing research in compressible flows. Due to experimental difficulties in measuring complex high-speed unsteady flowfields, the most convenient way to understand unsteady features of supersonic mixing and combustion is the use of computational fluid dynamics. The complexity of physics involved makes the problem of considerable interest also from a numerical point of view. Therefore, resolution of a turbulent compressible reacting flow imply a threefold requirement: 1. a highly accurate non dissipative numerical scheme to properly simulate the strong gradients in the vicinity of the shock waves and the turbulent structures away from these discontinuities; 2. a proper modelling of the small subgrid scales for supersonic combustion, including the effect of compressibility on mixing and combustion; 3. a highly detailed kinetic scheme accounting for the radicals formation and recombination to properly predict the flame anchoring. A hybrid method capable of capturing shocks and, at the same time, of resolving with low dissipation turbulent structures away from discontinuities has been implemented in the present paper. A new subgrid scale model accounting for the nature of the turbulent in compressible regime is proposed. The introduction of detailed chemistry (the scheme of Warnatz, including 9 species and 38 reactions to account for radicals formation) results in more expensive computer run times and storage requirements. High velocity and density gradients, and high hydrogen diffusivity also poses some numerical critical issues. This work, based on this subgrid physical model and using LES shows that, in supersonic flows, the baroclinic and dilatational effects pump vorticity in the flow influencing the turbulent KE decay and the dissipative turbulence scale. © 2011 by Antonella Ingenito and Claudio Bruno. Published by the American Institute of Aeronautics and Astronautics, Inc.