Far-Field Analysis of the Aerodynamic Force by Lamb Vector Integrals

Abstract

A new far-field method is proposed for the analysis of the aerodynamic force acting on an airfoil in subsonic unsteady flow conditions given a numerical solution of the flowfield. For this purpose, a recent theory proposed by Wu et al. (Wu, J.-Z., Ma, H.-Y., and Zhou, M.-D., Vorticity and Vortex Dynamics, Springer, New York, 2006), relating the aerodynamic force acting on a body to the Lamb vector (the cross product ofthe vorticity by the velocity) in case of unsteady Navier-Stokes flow, has been extended to the analysis of high-Reynolds-number turbulent flows governed by the Reynolds-averaged Navier-Stokes equations. The applications showed here concern the analysis of numerical solutions around an airfoil in steady flow and in pitching oscillations including a dynamic-stall condition. Both lift and drag coefficients have been computed by means of Lamb vector integrals and have been compared with the reference near-field results (stress integration on the body). The method allows for the decomposition of the aerodynamic force in a contribution associated with the bound vorticity on the body and a contribution related to the free vorticity developing in the airfoil wake.