WITHDRAWN: The Reynolds Stress Transport Budgets in a Hypersonic Shock-Separated Cylinder-Flare

Transport mechanisms of the Reynolds stresses and turbulent kinetic energy in a Mach 10 shock-separated cylinder-flare are investigated using solutions of wall-resolved large eddy simulations (LES). The transport processes of convection, production, diffusion, viscous dissipation, pressure strain and turbulent mass flux are analyzed. The turbulent stresses and turbulent kinetic energy show significant amplification through the shock-separated corner and post-shock region, particularly through the separation shear layer, reattachment region and shock line. Anisotropy of the stresses also increase in these regions, where the near-wall turbulence goes from one-component at the upstream equilibrium station to two-component in the separation bubble and post-shock nonequilibrium stations. RANS modeling of the transport budgets has typically been based on the budgets of canonical equilibrium flows, and to a lesser extent simple nonequilibrium flows. As a result much effort has been focused on modeling of the pressure strain and viscous dissipation terms, and to a lesser extent turbulent diffusion. Little attention has been given to modeling of the pressure diffusion, which is often ignored or lumped with turbulent diffusion via a single constant empirical coefficient. Turbulent mass flux is often simply ignored. In the configuration herein, the strong shock interaction amplifies all Reynolds stress transport budgets significantly in the separation zone and post-shock region, far exceeding that of supersonic and lower speed shock-boundary layer interaction flows. Pressure strain and pressure diffusion are prominent throughout the near-wall region, with inordinately large amplifications just following reattachment. Away from the wall these budgets are also important transport mechanisms. This indicates that accurate modeling of these terms are crucial to accurately capturing their effects on the Reynolds stresses, particularly in the post-shock region. The same conclusion is true for turbulent diffusion which plays a key role in many parts of the flowfield. The turbulent mass flux is generally small, but is particularly amplified just following reattachment and may also warrant modeling consideration.