A numerical solution procedure, which includes a locally implicit finite volume scheme and an adaptive mesh generation technique, has been developed to study airfoil and cascade flows. The Euler/Navier–Stokes, continuity, and energy equations, in conjunction with Baldwin-Lomax model for turbulent flow, are solved in the Cartesian coordinate system. To simulate physical phenomena efficiently and correctly, a mixed type of mesh, with unstructured triangular cells for the inviscid region and structured quadrilateral cells for the viscous, boundary layer, and wake regions, is introduced in this work. The inviscid flow passing through a channel with circular arc bump and the laminar flows over a flat plate with/without shock interaction are investigated to confirm the accuracy, convergence, and solution-adaptibility of the numerical approach. To prove the reliability and capability of the present solution procedure further, the inviscid/viscous results for flows over the NACA 0012 airfoil, NACA 65-(12)10 compressor, and one advanced transonic turbine cascade are compared to the numerical and experimental data given in related papers and reports.

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