Time Vector Marching Method for Analyzing Complex Periodic Unsteady Flows Within Turbomachinery

Abstract

The paper presents an efficient method for analyzing complex periodic unsteady flows within turbomachinery. The method transforms the original initial value problem of unsteady flows to a boundary value problem by taking advantage of temporal periodicity known a priori. This transform allows a pseudotime marching at all physical time instants to be performed simultaneously, for which the method is called the time vector marching (TVM) method. Time direction discretization can be achieved using finite difference schemes. A second-order backward scheme and a ninth-order mixed scheme are investigated. To demonstrate the stability, accuracy, and correctness of the TVM method, the one-dimensional (1-D) advection equation and a quasi-1-D Laval nozzle with time-varying inlet total pressures are used as the test cases. The unsteady flowfield within it was also analyzed using a time-domain dual time-stepping (DTS) method and the harmonic balance (HB) method to obtain the results as references. Further verification was carried out using a transonic compressor rotor with inlet absolute total pressure distortion. The phase-shift boundary condition was applied at geometric periodic boundaries to facilitate the use of a computational domain of one blade passage for a blade row. The time-averaged and instantaneous results of the DTS, HB, and TVM methods and associated time cost were compared and discussed.