A Finite Element Solution of Cascade Flow in a Large-Distorted Periodic Flow

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A method for solving the analytical problem of a cascade in a distorted and oscillating periodic flow is developed here by using the finite element method. The vorticities in an unsteady inviscid rotational flow were calculated by a convective-difference scheme. The outlet flow angle was corrected by successive iteration taking into account the Kutta condition, whereas the strength of shedding vortices was determined from one-valued pressure condition. The fluid-dynamic forces acting on the blade are expressed in line integral forms in the upstream and downstream regions. The present method is applicable to the analysis of a cascade with arbitrary blade profile in a periodic waved flow with large disturbances. However it is limited to the case of wave-length equal to the pitch of cascade. An example of the flow through a cascade composed of segmented circles was solved for an upstream absolute flow with the same direction and varying in the sinusoidal travelling wave. The pertinent streamlines, equi-vorticity lines and the time-variation of the lift and drag are shown in the paper.
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