Comparison of DDES and URANS for unsteady tip leakage flow in an axial compressor rotor

Tip leakage flow (TLF) has a large impact on compressor performance and should be accurately predicted by CFD methods. New approaches to turbulence modelling, such as Delayed Detached Eddy Simulation (DDES) have been proposed which allow for greater accuracy of the numerical predictions while the mesh size as well as the central processing unit (CPU) time can be tremendously reduced. In this paper, the numerical simulation of the rotor in a low-speed large-scale axial compressor based on DDES and unsteady Reynolds-Averaged Navier-Stokes (URANS) turbulence models is performed subject to different working conditions of different tip gap sizes, to improve our understanding about the tip leakage vortex (TLV) dynamic mechanisms and discrepancy of these two methods. The rotor simulations are carried out on the same mesh based on the DDES requirements, and compared to experimental stereoscopic particle image velocimetry (SPIV) data before flow physics investigation. The simulation results capture the location of TLV and show qualitatively good agreement with experiments. DDES method brings improvements in time-averaged results over the Reynolds-Averaged Navier-Stokes (RANS) method. Firstly, the time-averaged and instantaneous results are compared to divide the TLV into three parts. Then the anisotropy of the Reynold stress of these two methods are analyzed in the tip leakage flow through Lumley triangle, to see the difference between the way to get the Reynold stress, using Boussinesq-type approximation in URANS and unsteady velocity fluctuation in DDES. The turbulent anisotropy can be derived from the nondimensional form of the anisotropy tensor. In the rotor simulation, the anisotropy varies along the TLV. The anisotropy of RANS method is weak because the eddy viscosity model is isotropic. Last, the velocity fluctuation data along the TLV core at different chord length are transformed to velocity spectra using fast Fourier transformation (FFT) method to discuss the TLV unsteadiness. The high frequency amplitude becomes obvious downstream the TLV because of losing stability. The result of URANS also has a conspicuous frequency but lower than DDES. The amplitude of URANS is much smaller. From this investigation it is determined that URANS can only predict the large-scale low-frequency dominant unsteady features. While the scale of dissipation and unsteadiness of TLV is small, the Reynolds averaging of URANS may neglect this unsteady phenomenon.