Computation of the flows over flapping airfoil by the euler equations

Abstract

To investigate the mechanism of thrust generation by Happing 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 in an uniform stream of 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-flow structures are visualized by the numerical methods: vorticity filled-contours, perturbation-velocity vector plots, and streamlines of the velocity field relative to the flapping airfoil. The computed wake-vortex structures and 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 plunging and pitching cases agree well with the test data and the non-linear incompressible potential-flow solutions in the literature. The agreement with the test data decreases when leading-edge vortices appear and become strong enough to interfere with the trailing-edge vortices.