Numerical Simulation Exploring Supersonic Flow Over a Forward-Facing Cylindrical Step

Abstract

This numerical study is a preliminary work exploring supersonic flow over an forwardfacing cylindrical step using unsteady Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulations (LES). The LES was obtained using a well-validated high-order NavierStokes flow solver employing a hybrid 6 th -order compact spatial discretization and 2 nd -order Roe scheme. An 8 th -order low-pass spatial filter was used to regularize the flow. The RANS simulations were performed using the same high-order hybrid scheme as the LES and a 2 nd -order k − turbulence model. Included in the results are comparisons of the unsteady RANS and LES solution techniques, and effects of Reynolds number and Mach number on the flow. Results from RANS simulations showed that as the Mach number increased, the length of the separation region upstream of the cylindrical step and the angle of the shock-wave emanating from the separation region both decreased. As the Reynolds number was lowered, the size of the separation region upstream of the step increased. When both the RANS and LES were performed at the same Reynolds number, the RANS predicted a much larger separation bubble than that observed in the LES. In general, the 2-D RANS solutions were found to adequately replicate the time-mean shock structure seen in the LES. The three-dimensional LES solutions provided insight into the degree of unsteadiness in the flow. The shock emanating from the upstream separation region globally displayed only minor motion at the foot of the separation shock due to interaction with the boundary layer. The reattachment shock off the cylindrical face had much larger displacement relative to the separation shock due to unsteadiness in the flow.