A hybrid viscous body force model for low-speed centrifugal compressors

The flow in centrifugal compressors is viscous and unsteady. Flow separation off the blades challenges the accuracy of simulations. A viscous body force model is expected to speed up numerical convergence and reduce the computational costs of unsteady simulations. In this paper, both stability and accuracy of the viscous body force model are investigated based on the case of a low-speed centrifugal compressor. First, two formulations of the viscous body forces are obtained from the expression of the viscous flux. Then, the numerical stability of two body force models is found to be related to drag coefficient and flow angle. For large negative drag coefficients, the viscous body forces would lead to divergences. Since unsteady Reynolds-averaged Navier-Stokes simulations show that two formulas have considerable accuracy, stability is considered as the main factor for modeling. With the findings, a hybrid viscous body force method is proposed. To assess the applicability of the hybrid model, two test cases are compared against the results obtained by unsteady Reynolds-averaged Navier-Stokes simulations. The first case is the capability evaluation of unsteady characteristics capture for low-speed centrifugal compressors. The simulation results show that the hybrid viscous body force model can capture main unsteady viscous characters, including wake vortexes and tip leakage flow. The other is the case in which the inlet total pressure is disturbed. It is found that fluctuations of pressure, temperature, and velocity predicted by the viscous body force method are close to unsteady Reynolds-averaged Navier-Stokes results. In addition, the time-accurate overall performance of the compressor with disturbance is also predicted satisfactorily. With the advantage in lowering computer resource requirement, the viscous body force model is a promising method for long length scale unsteady cases.