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This paper presents a method for selecting harmonics and spinning modes for a rotor-stator interaction analysis using the time spectral method. Discrete Fourier transform of the circumferential distribution of conservative variables is performed to provide the necessary information for guiding selection of harmonics. The rules for the spinning mode selection are summarized from a lot of numerical analyses by changing the numbers of spinning modes. NASA stage 35 was used to demonstrate the effectiveness of the proposed selection method. INTRODUCTION Turbomachine is an integral part of an aeroengine or industrial gas turbine. To have a first-class aeroengine means to design an efficient turbomachine. The road to get a good turbomachine is bumpy because the flow inside turbomachines is always unsteady. It is much more difficult to comprehend the mechanism of unsteady flow than to know the existence of it. To better understand unsteady phenomenon, many numerical methods have been developed to analyse unsteady flows. The most direct method to analyse unsteady flow field is the time domain time marching method, which is relatively simple to implement. But the main downside is that it involves large memory and requires long computational time. In order to save computational time, we need a feasible path to analyse unsteady flow. The unsteady flow is sometimes periodic especially when it stems from a rotor-stator interaction. Therefore, the unsteady flow field can be approximated with truncated Fourier series. Besides, the blades in one row are identical to each other and evenly spaced along the circumferential direction. The unsteady flows in different passages have the same amplitude and a fixed phase difference. All these conditions are favourable for development of reduced order methods. There are several reduced order methods being proposed: the linear harmonic method [1~3], the nonlinear harmonic method [4~5], and the time spectral method [6~12]. In this investigation, we choose the time spectral method as the reduced order method to be investigated. The unsteady flow analysis based upon the time spectral method resolves unsteady flow at some selected time instants, which are quite often different for different blade rows. This is because in different blade rows, different number of time instants, due to different number of harmonics, are used. The selection of the number of harmonics is essential for the time spectral method. If the number of harmonics is too few, the flow field information cannot be obtained accurately. However, if the number of harmonics is too many, it will consume too much CPU time, leading to bad stiffness issue and even solution instability. Therefore, choosing a proper number of harmonics is very imperative in a time spectral analysis. Raymond C. Maple et al. [13] has proposed an adaptive harmonic balance method to determine the number of harmonics, which is difficult to implement unfortunately. Gomar et al. [14] has proposed a method of extracting tangential variations of the axial

Investigation of Numerical Analysis of Blade Row Interaction Unsteady Flows within Multi-row Turbomachines Using the Time Spectral Method