For the two-dimensional steady and unsteady turbine cascade flows, the Euler/Navier–Stokes equations with Baldwin-Lomax turbulence model are solved in the Cartesian coordinate system. A locally implicit hybrid algorithm on mixed meshes is employed, where the convection-dominated part in the flow field is studied by a TVD scheme to obtain high-resolution results on the triangular elements, and the second- and fourth-order dissipative model is introduced on the O-type quadrilateral grid in the viscous-dominated region to minimize the numerical dissipation. When the steady subsonic and transonic turbulent flows are investigated, the distributions of isentropic Mach number on the blade surface, exit flow angle, and loss coefficient are obtained. Comparing the present results with the experimental data, the accuracy and reliability of the current approach are confirmed. By giving a moving wake-type total pressure profile at the inlet plane in the rotor-relative frame of reference, the unsteady transonic inviscid and turbulent flows calculations are performed to study the interaction of the upstream wake with a moving blade row. The Mach number contours, perturbation component of the unsteady velocity vectors, shear stress, and pressure distributions on the blade surface are presented. The physical phenomena, which include periodic flow separation on the suction side, bowing, chopping and distortion of incoming wake, negative jet, convection of the vortices and wake segments, and vortex shedding at the trailing edge, are observed. It is concluded that the unsteady aerodynamic behavior is strongly dependent on the wake/shock/boundary layer interactions.

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