Local-Variable-Based Model for Hypersonic Boundary Layer Transition

摘要

Based on the numerical study of the existing K-omega-gamma 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 k-omega shear stress transport model through the concept of effective turbulent eddy viscosity to form a local-variable-based k-omega-kl-gamma 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 k-omega-kl-gamma model. Numerical results illustrate that both the transition onset and the length of the transition region predicted by the k-omega-kl-gamma model agree well with the experimental data.