Turbulence modeling for hypersonic flows

Turbulence modeling for high-speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models, and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary-layer flows, shock-wave boundary-layer interactions, and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.