NUMERICAL INVESTIGATION OF SEPARATED TRANSONIC TURBULENT FLOWS WITH A MULTIPLE-TIME-SCALE TURBULENCE MODEL

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Abstract
Numerical investigation of transonic flows separated by streamline curvature and shock wave-boundary layer interaction is presented. The free-stream Much numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus the equation is solved for incremental pressure rather than density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free-stream Mach numbers considered whereas various k-e turbulence models fail to predict such a reversed flow region at low free-Stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave-turbulent boundary layer interaction as the free-stream Mach number is increased. These numerical results show that the turbulence model can resolve the turbulence field subjected to extra strains caused by the streamline curvature and the shock wave-turbulent boundary layer interaction and that the numerical method yields a significantly accurate solution for the complex compressible turbulent flow.