A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part II: Shock Capturing and Transonic Flows

Abstract

Abstract In the second paper of this three-part series, we focus on the simulation of transonic test cases for turbomachinery applications using a high-order discontinuous Galerkin spectral element method (DGSEM). High-fidelity simulations of transonic compressors and turbines are particularly challenging, as they typically occur at high Reynolds numbers and require additional treatment to reliably capture the shock waves characterizing such flows. A recently developed finite-volume subcell shock capturing scheme tailored for the DGSEM is applied and evaluated with regard to the shock sensor. To this end, we conduct implicit large eddy simulations of a high-pressure turbine cascade from the public literature and a transonic compressor cascade measured at the German Aerospace Center, both at a high Reynolds number above 106. Based on the results, we examine modal-energy and flow-feature based shock indicator functions, compare the simulation data to experimental and numerical studies, and present an analysis of the unsteady features of the flows.