Simulating unsteady flows in a compressor using immersed boundary method with turbulent wall model

Computations of unsteady turbulent flows in turbomachine are still challenging due to the complexity of geometry and relative motion between rotor and stator. A potential solution is using the immersed boundary method (IBM) for its advantages in simulating moving boundary problems, but it loses efficiency with increasing Reynolds number. In the present work, to accurately simulate unsteady flows in a compressor, the well-established turbulent wall model is adopted with the hierarchical Cartesian grid in IBM to alleviate the requirements of grid spacing for turbulent boundary layer simulation. First, verification of the flow solver on two-dimensional (2D) stationary cases of the non-inclined/inclined flat plate and zero attack NACA 0012 were conducted. Furthermore, the Tamaki et al. wall model which had been only validated in stationary problems was first extended to solve the moving boundary problem, i.e. plunging airfoil. Finally, the new immersed boundary solver employed Tamaki et al. wall model was used to simulate the classic rotor/stator interaction. The unsteady normal forces on stator blade of a low-speed compressor were examined with two different sizes of axial gap, i.e. 10% chord and 30% chord. With the large gap, the predicted phase and magnitude of the unsteady aerodynamic force agree with the measurements well. With the more challenging small gap, although the predicted phase of the peak force is lagged slightly with the measurements, the magnitude of the peak force is captured. The agreements between numerical results and measurements indicate the ability of the developed IBM solver based on Tamaki et al. wall model and hierarchical Cartesian grid in dealing with simulations of unsteady flows in turbomachine.