Unsteady numerical simulation in a centrifugal compressor using the time-inclined operator

A unique problem arising from the simulation of rotor-stator interactions is how to treat the unequal numbers of blades in rotor and stator. In the current paper, a numerical method for the calculation of unsteady stator/rotor interaction in turbomachinery stage of arbitrary pitch ratio using time-inclined operator is presented. It is developed on the basis of the program solving the three-dimensional, viscous, steady flow field in a centrifugal compressor. Dual time-stepping is adopted to realize the unsteady simulation; time-inclined operator is employed to transform the Navier-Stokes equations. It is realized without an approximation to a ratio of small integers or to scale geometry, the passages used for computation are minimum, and the computational time is also less than others. The viscous terms that neglected in other methods are classified in the source terms, thus, the effects of the viscous terms are never ignored in the case of transforming the Navier-Stokes equations using time-inclined operator. The results using time-inclined operator are also compared with the computation using NUMECA, it shows the program developed by the author can predict the flow field in the centrifugal compressor accurately.