Unsteady flow analysis in oscillating cascade using Fourier-transform based method

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 Fourier-transform 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 [6]. 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 aero-damping 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.