Inviscid analysis of transonic oscillating cascade flows using a dynamic mesh algorithm

Abstract

A locally implicit total-variation-diminishing scheme and a rigid-deformable dynamic mesh algorithm are formulated on the quadrilateral-triangular meshes. The unsteady Euler equations with moving domain effects are solved in a Cartesian coordinate system. For transonic flows around an oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies, and interblade phase angles, the calculated distributions of magnitude and phase angle of the first harmonic dynamic pressure difference coefficient agree better with experimental data than those from linearized theory and related numerical results on triangular meshes in most of the cases. Also, the numerical wiggles of instantaneous blade surface pressure coefficient distributions, which appeared on the triangular meshes, are eliminated. From the instantaneous pressure and Mach number contours, the unsteady flow phenomena, such as periodical characteristics, pressure wave and shock behaviors, and time-variations of zones with high Mach number gradient normal to the blade surfaces, are investigated. Furthermore, the lift coefficient distributions indicate that the oscillation .amplitude, reduced frequency, and interblade phase angle all have significant effects on the transonic oscillating cascade flows.