An Implementation of Improved Delayed Detached Eddy Simulation Discretized with Discontinuous Galerkin Method: Application to the Vortex System Simulation of a Highly-Loaded Turbine Cascade

Series of studies of substantial aerodynamic loss for highly-loaded turbine shows that due to the potential flow field induced by interaction of end-wall boundary layer, complex massive vortex system will be formed upstream of the blade leading edge; and the large-scale secondary flow is related to boundary layer separation of the incoming end wall. In this work, simulation for such secondary flow fields is performed by implicit time-integrated higher-order Discontinuous Galerkin method (DGM) for the numerical approximation of Shear-Stress-Transport background Improved Delayed Detached Eddy Simulation (SST-IDDES). The mean strain rate involved with mean rotation rate and shear rate is modified to preserve the anisotropic characteristics encountered in strong secondary flows. Control of stochastic oscillations in multi-scale vortex region is guaranteed by a local correction method based on streamline curvature which also extends model ability in predicting large adverse-pressure-gradient flows. To reduce the numerical oscillations caused by inviscid term in meshes with complex geometrical configuration, a modified entropy conserving flux-vector splitting is applied across cell edges, and state vector is corrected by penalization of gradient jumps. While focusing on the analysis of secondary-vortex-system structure, basic model validation is also provided: fully-developed turbulent flow on flat-plate is simulated to validate the basic accuracy of proposed methodology in computing the near-wall turbulence; the case of NACA4412 airfoil is performed to verify the model ability in predicting large scale flow separation. Reasonable results obtained by current model provide detailed microscale flow structure and sufficiently accurate calculation of turbulent characteristics.