Local-Variable-Based Model for Hypersonic Boundary Layer Transition

Abstract

Based on the numerical study of the existing model, certain inconsistencies of the model were first allocated. It was found that the second-mode instability dominating the transition process in hypersonic boundary layers was not simulated properly by the model, and a single transport equation for total fluctuating kinetic energy would make the model fail to be self-consistent. To eliminate these discrepancies, a laminar kinetic energy transport equation was developed in terms of local variables. Then, a time scale correction function capable of reproducing the hypersonic transition process dominated by the second-mode instability was constructed. In addition, the transport equation for the intermittency factor, in which the self-consistent production and dissipation terms were constructed, was also revised. On this basis, the transport equations for the laminar kinetic energy and intermittency factor were coupled with the shear stress transport model through the concept of effective turbulent eddy viscosity to form a local-variable-based model for hypersonic boundary layer transition. Finally, hypersonic transition flows over a flat plate and a straight cone are employed to test and verify the model. Numerical results illustrate that both the transition onset and the length of the transition region predicted by the model agree well with the experimental data.