Time step criteria for rotor-stator unsteady simulations of turbomachinery

With the rapid improvement of computing power, unsteady Reynolds-Averaged Navier-Stokes (U-RANS) solvers are increasingly used to get a deeper comprehension of the rotor-stator unsteady flows inside turbomachinery. The dual-time stepping method is adopted in most U-RANS solvers and the determination of the optimal size of physical time step is a crucial procedure for rotor-stator U-RANS simulations, and it is the primary purpose of this paper. The criteria for determining the size of physical time step for rotor-stator interactions with and without filtering mixing plane were proposed through theoretical analysis. For conventional no-filtering U-RANS simulations, the number of physical time steps is determined by the number of circumferential grid points and the characteristic propagation velocity of flow. While for U-RANS simulations adopting the filtering mixing plane method, the number of retained harmonics through the filtering mixing plane plays an important role. Then, three numerical cases including subsonic rotor-stator interactions, IGV-rotor interactions and rotor-stator interactions coupled with inlet distortion, were carried out to verify the effectiveness of proposed criteria. The results showed that the requirement of time step independence can be satisfied when the number of physical time steps exceeds the number estimated by the criteria, thus the effectiveness of the proposed criteria has been verified.