Computation of the Flows over Flapping Airfoils by the Euler Equations

To investigate the mechanism of thrust generation by flapping airfoils, the inviscid version of a three-dimensional unsteady compressible Euler/Navier Stokes flow solver is used to simulate the flow field around flapping airfoil NACA 0012 at low speeds. Sinusoidally plunging or/and pitching oscillations are studied. The compressible Euler code with a low free-stream Mach number of 0.1 or 0.05 can simulate the incompressible flows without leading-edge separation. The wake vortex structures are visualized by numerical methods: vorticity filled-contours, perturbation-velocity vector plots, and streamlines. The computed wake-vortex structures almost coincide with known low-speed test results. The time-averaged thrust coefficients, input-power coefficients, and the efficiency over a period of the oscillation versus the Strouhal number based on the total excursion of the trailing edge of the airfoil for a number of combined plunging and pitching cases agree well with the linear and non-linear incompressible potential-flow solutions in the literature. In comparison with known test data, the accuracy of the computed forces decreases when the leading-edge vortices appear and become strong enough to interfere with the trailing-edge vortices.

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