A Favré averaged transition prediction model for hypersonic flows

Transition prediction is crucial for aerothermodynamic and thermal protection system design of hypersonic vehicles. The compressible form of laminar kinetic energy equation is derived based on Favré average formality in the present paper. A closure of the equation is deduced and simplified under certain hypotheses and scaling analysis. A laminar-to-turbulent transition prediction procedure is proposed for high Mach number flows based on the modeled Favré-averaged laminar kinetic energy equation, in conjunction with the Favré-averaged Navier-Stokes equations. The proposed model, with and without associated explicit compressibility terms, is then applied to simulate flows over flared-cones with a free-stream Mach number of 5.91, and the onset locations of the boundary layer transition under different wall conditions are estimated. The computed onset locations are compared with those obtained by the model based on a compressibility correction deduced from the reference-temperature concept, together with experimental data. It is revealed that the present model gives a more favorable transition prediction for hypersonic flows.

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