SUMMARYAn e cient dual-time implicit approach combined with unstructured moving grids is presented to solve unsteady turbulent ows. Unstructured grids suitable for both inviscid and turbulent viscous ow regions are generated using a successive reÿnement method and the grid is moved adaptively based on the boundary movements. Special care is taken to maintain the quality of the grid near the surface. The unsteady two-dimensional compressible Navier-Stokes equations are discretized by an implicit approach in a real time basis. The resulting set of implicit non-linear equations is then solved iteratively in pseudotime using a Runge-Kutta scheme. The k-turbulence model equations are solved together with the main ow equations in a fully coupled manner. Results are presented for an unsteady transonic test case (AGARD CT5) about a NACA0012 oscillating airfoil and comparisons with experimental data showed good agreements.

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Unsteady compressible flows over a 60°swept delta wing with a sharp leading edge undergoing pitching maneuvers are computationally studied. Emphasis in this study is on possible supersonic flow structures and vortex breakdown during the pitching motion of a delta wing. Unstructured grid, k-x SST turbulence model and a dual-time implicit time integration were used. Accurate simulations were performed for various Mach numbers, initial and final angles of attack, and pitch rates to cover different flow structures and phenomena associated with them. The contours obtained by the numerical results which show the flow structures were compared with experimental visualization images. Variations of flow patterns, pressure coefficient on the wing surface, and the lift coefficient during a pitching maneuver are investigated. Vortex breakdown was observed for both subsonic and supersonic flows and its impact on the lift coefficient during the motion was shown.

Compressible flows over a 60° sweep delta wing with a sharp leading edge undergoing pitching oscillations are computationally studied. Emphasis in this study is on possible supersonic flow structures and their variations during the pitching motion of a delta wing. Unstructured grid, k-ωSST turbulence model and a dual-time implicit time integration are used. Accurate simulations are performed for various Mach number and angles of attack to cover different flow structures and phenomena associated with them. Variations of flow patterns in a crossflow plane, pressure coefficient on the wing surface, and hysteresis loops associated with vortex core location during a pitching cycle are investigated. The trends with Mach number, mean angle of attack, amplitude of pitching and pitching frequency are illustrated.

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