The 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 the transonic flows around 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 cancelled. 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 oscillating amplitude, reduced frequency and interblade phase angle all have significant effects on the transonic oscillating cascade flows.
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