Unsteady Simulation of a Two-Stage Cooled High Pressure Turbine Using an Efficient Non-Linear Harmonic Balance Method

The harmonic balance method is a mixed time domain and frequency domain approach for efficiently solving periodic unsteady flows. The implementation described in this paper is designed to efficiently handle the multiple frequencies that arise within a multistage turbomachine due to differing blade counts in each blade row. We present two alternative algorithms that can be used to determine which unique set of frequencies to consider in each blade row. The first, an all blade row algorithm, retains the complete set of frequencies produced by a given blade row’s interaction with all other blade rows. The second, a nearest neighbor algorithm, retains only the dominant frequencies in a given blade row that arise from direct interaction with the adjacent rows. A comparison of results from a multiple blade row simulation based on these two approaches is presented. We will demonstrate that unsteady blade row interactions are accurately captured with the reduced frequency set of the nearest neighbor algorithm, and at a lower computational cost compared to the all blade row algorithm. An unsteady simulation of a two-stage, cooled, high pressure turbine cascade is achieved using the present harmonic balance method and the nearest neighbor algorithm. The unsteady results obtained are compared to steady simulation results to demonstrate the value of performing an unsteady analysis. Considering an unsteady flow through a single blade row turbine blade passage, it is further shown that unsteady effects are important even if the objective is to obtain accurate time-averaged integrated values, such as efficiency.