The Unsteady Shock–Boundary Layer Interaction in a Compressor Cascade—Part II: High-Fidelity Simulation

In the second part of this three-paper series, high-fidelity simulations of the transonic cascade TEAMAero at the aerodynamic design point with $Rein=1.35×106$ and $Main=1.21$ are presented. A high-order discontinuous Galerkin spectral element method with finite-volume subcell shock capturing is employed to simulate the flow based on an implicit large eddy simulation (LES) scheme and advanced over several buffeting cycles to reliably capture the shock unsteadiness. A study on the spanwise domain size shows that the shock oscillation amplitude decreases with increasing span, although its frequency and mean location remain fixed through the simulations. By comparing high- and low-resolution LES results, it is further presented that deviations from under-resolution are mostly limited to the separated region past the shock, where the high-fidelity results match experimental results more closely. In addition to the LES, low-fidelity unsteady Reynolds-averaged Navier–Stokes is shown to capture the shock unsteadiness correctly, but at a reduced amplitude and fails to match the force distributions on the blade surface. Through examination of instantaneous flow features, space–time relations and spectral proper orthogonal decomposition, a basic analysis of the shock–boundary layer interaction is presented and indicates that velocity perturbations travel upstream through the subsonic boundary layer and periodically cause oblique shock waves, transporting the information from the boundary layer into the passage.