Modification of DDES Based on SST kω Model for Tip Leakage Flow in Turbomachinery

Rotor tip leakage flow (TLF) is a typical flow in turbomachinery which has overall effects on its performance. The TLF is a complex three-dimensional high Reynolds number (Re) flowcan hardly be simulated by high-resolution calculation methods, such as large-eddy simulation (LES) or direct numerical simulation (DNS), due to high Reynolds number (Re) flow and complex geometries in real turbomachinery. Reynolds-averaged Navier-Stokes (RANS) based simulation is still the main method in engineering. Detached-eddy simulation (DES) is a kind of hybrid LES/RANS method which uses RANS to solve the flow near the wall and the turbulence model automatically converts to LES subgrid-scale away from the wall. DES has shown priority to RANS in simulation of the TLF, while the computation cost is much smaller compared to LES. One of the main issues influencing the accuracy of DES is the zoning function. Delayed DES (DDES) was proposed to protect the boundary layer from converting to LES too early, which improves the prediction of separation significantly. However, the TLF is close to the casing wall and blade, thus it could not be fully solved by LES because of the DDES shielding function.

In this study, both LES and DDES are conducted in a low-Reynolds number TLF model, which was proposed to reproduce the jet flow/main flow shear mechanism of the TLV rolling-up in turbomachinery. The flow model consists of a square duct with a longitudinal slit on the top of the side wall, with a main flow in the duct and a jet flow from the slit. In the LES simulation, the TLF region is well solved, showing that the grid density is enough to resolve the eddies for LES. The DDES uses the SST kω model and employs the same grid, but the turbulence field diverges from the LES result and the zoning function shows that the TLF region is not fully solved by LES method.

Based on the comparison between LES and DDES, a modification based on the turbulent Reynolds number is proposed to improve the zoning function of DDES based on the SST kω model. The modified DDES shows better performance in predicting the mean flow and turbulence field of the TLF in the flow model. Then the  modification is also examined using a real compressor rotor simulation, compared with measurement data, which shows its general performance. The results show that it could improve the DDES for predicting TLF in turbomachinery.