中文摘要：

基于叶片振荡诱导的非定常流具有时间周期性的特点,振荡叶栅非定常流可以用傅立叶级数来表达,继而,时域非定常欧拉方程则可以转化为频域定常傅立叶系数方程。定常傅立叶系数方程的求解采用了伪时间推进方法,同时采用本地时间步长和多重网格加速技术。文中傅立叶级数采用了一阶形式,求解系数方程所需的计算机时约为定常方程求解时的3-4倍,计算效率高。最后,文中对一个三维涡轮振荡叶栅进行了模拟,并与实验结果进行了对比。

英文摘要：

Aim. In turbomachine blade flutter analysis, the unsteady flows of interest are periodic in time. The key to prediction of blade flutter is to obtain accurately the corresponding unsteady flow response. We believe we are the first in China to do unsteady flow analysis in oscillating cascade using the Fouriertransform based method. In Section 1, we explain our method of analysis in some detail. Its three subsections are. Fourier transform （Subsection 1.1）, governing equations （Subsection 1.2）, and the numerical solution （Subsection 1.3）. In Subsection 1.2, the unsteady Euler equations are converted into steady Fourier coefficient equations. In Subsection 1.3, we employ the one-dimensional non-reflecting boundary conditions proposed in Ref. 7 by M. Giles. In Section 2, we give the results of a numerical example, whose cascade is the same as that in the first author＇s Ph. D. thesis .Reference 6 contains experimental results but its calculation method is different from that of this paper. As Fig. 1 in the full paper shows, the steady pressure coefficient distribution of the experimental data and the calculated results are in good agreement. The comparison of the two types of results, presented in Figs. 2 through 4 and Table 2, indicate preliminarily that the calculated unsteady pressure coefficient distribution and blade aerodamping distribution are consistent with the experimental results. At the same time, the computation load using the present unsteady flow analysis is only 3 - 4 times that to solve the baseline steady Euler equations.