Direct Numerical Simulation of High-Speed Boundary-Layer Separation due to Forward Facing Curvature

Abstract

Direct numerical simulations (DNS) of high-speed boundary-layer separation due to forward facing curvature for a nominal freestream Mach number of 5 are presented, with the goal of expanding an existing DNS database of turbulent boundary layers subject to pressure gradients due to wall curvature by parameterizing the wall shape. The existing and current database have been used to assess the limitations of currently available Reynolds-averaged Naiver-Stokes (RANS) turbulence models. The baseline wall geometry and flow conditions are representative of the experimental data of a Mach 4.9 turbulent boundary layer that was tested in the high-speed blow down wind tunnel at the National Aerothermochemistry Laboratory at Texas A&M University. The wall geometry is then modified by shortening the width of the hill by a factor of 5 while keep the hill height the same, which results in a larger curvature and flow separation at the foot of the curved wall. The DNS inflow is validated against the existing database and experimental results of Texas A&M University. An investigation of the flow field shows oscillations of the lambda shock due to the separation bubble growing and shrinking along the curved wall. An analysis of the Reynolds stresses show significant amplification of all the components of the Reynolds stress. A comparison of DNS with RANS results show that the Wilcox (2006) k−w and the k−w SST models predict an earlier onset of boundary-layer separation that leads to an significant overprediction of the separation bubble size. The Spalart-Allmaras model yields relatively better predictions in both the separation and reattachment points than the two-equation models.