Abstract:

A set of compressible Reynolds stress model equations and the turbulent kinetic energy equation were derived with Reynolds average formality. A closure of the turbulent kinetic energy equation was then deduced and simplified under certain hypotheses, in conjunction with scaling analysis. A K-ε two-equation turbulence model was proposed based on the modeled turbulent kinetic energy equation and a conventional incompressible turbulent kinetic energy dissipation rate equation. The proposed model was then applied to simulate hypersonic turbulent flows over a flat-plate. The numerical results reveal that the present model would be favorable in comparison with some of the existing two-equation turbulence models, experimental data, and the estimations given by the semi-empirical formulations. Another test case on hypersonic flows over a ramp was then computed using the developed model, as well as some of the existing two-equation turbulence models. The comparative study shows that the compressibility corrections to the two-equation turbulence models are necessary for hypersonic ramp-type flows, and the numerical results by the present model are closest to the experiments simultaneously.

Key words: fluid , dynamic,  , turbulence , model,  , numerical , simulation,  , hypersonic,  , compressibility