Assessment of one- and two-equation turbulence models for hypersonic transitional flows

One- and two-equation turbulence models are examined for hypersonic perfect- and real-gas flows with laminar, transitional, and turbulent flow regions. These models were generally developed for incompressible flows, and the extension to the hypersonic flow regime is discussed. In particular, the compressible formulation of the turbulence diffusion term for one-equation models is examined. For the Spalart-Allmaras model, the standard method for forcing transition at a specified location is found to be inadequate for hypersonic flows. An alternative transition method is proposed and evaluated for a Mach 8 flat plate test case. This test case is also used to evaluate three different two-equation turbulence models: a low-Reynolds-number k-epsilon model, the Menter k-omega formulation, and the Wilcox k-omega model. These one- and two-equation models are then applied to the Mach 20 Reentry F flight vehicle. The Spalart-Allmaras model and both k-omega formulations are found to provide reasonable agreement with the flight data for heat flux, whereas the Baldwin-Barth and low-Reynolds-number k-epsilon models overpredict the turbulent heating rates by a factor of two. Careful attention is given to the numerical accuracy of the solutions in the areas of both iterative and grid convergence.