A Finite Element Analysis of Unsteady Diagonal Cascade Flows

抄録

The almost existing methods for analysing an unsteady two-dimensional cascade flow have treated the case of a plane flow. In this paper a method for the cascade flow on an arbitrary revolutional flow surface with an arbitrary varying passage height was proposed. In the method equations in terms of the vorticity component ζ normal to the flow surface and the stream function ψ are used. The equation for ζ is independent of the inclination of vorticity vectors and is calculated by a convective-difference scheme. The equation forψ is solved by using the Galerkin method. The treatments of trailing vortices were also developed. The method is applicable to the flows for arbitrary varying flow rates and rotor speeds and for non-uniform upstream velocity profiles due to the wakes. A numerical example of the flow with a sinusoidally oscillating flow rate is shown.