Numerical Investigation of Supersonic Flow Over a Wall-Mounted Cylinder

Abstract

This numerical investigation explores supersonic flow over a wall-mounted cylinder using Large Eddy Simulations (LES), unsteady Reynolds Averaged Navier-Stokes (RANS), Delayed Detached Eddy Simulation (DDES), and hybrid RANS/LES approaches. The LES was obtained using a well-validated high-order Navier-Stokes flow solver employing a hybrid 6-order compact spatial discretization and 2-order Roe scheme. An 8-order low-pass spatial filter was used to regularize the flow. The RANS and hybrid RANS/LES solutions were obtained with a 2-order k − turbulence model in conjunction with the high-order flow solver employed in the LES. Additional RANS and DDES results were obtained using a 5-order WENO scheme available in the OVERFLOW code. Results compare the characteristics of both time-mean and instantaneous solutions using the four turbulence modeling approaches. Overall, RANS solutions display favorable agreement with time-mean LES flow field structure and boundary layer characteristics. Unfortunately, both the DDES and hybrid RANS/LES approaches developed significantly longer separation regions upstream of the cylinder. In the hybrid RANS/LES approach, the length of the upstream separation shock was driven by the location chosen to transition from the RANS to hybrid RANS/LES model. For the DDES approach, the upstream separation shock shifted to a location very near the inflow boundary. Both the DDES and hybrid RANS/LES methodologies developed larger transitional/laminar separation regions because the upstream shock-wave/boundary-layer interaction was unable to force the development of small-scale turbulence structures necessary to overcome the reduction in eddy viscosity.