Viscous extension of vortex methods for unsteady aerodynamics

Abstract

The Kutta condition has been extensively used to determine aerodynamic loads of steady and unsteady flows over airfoils. Nevertheless, the application of this condition to unsteady flows has been controversial for decades. A viscous correction to the Kutta condition was recently developed by matching the potential flow solution with a special boundary layer theory that resolves the flow field in the immediate vicinity of the trailing edge: the triple-deck boundary layer theory. In this work, we utilize this viscous condition to extend two common numerical methods for unsteady aerodynamics to capture viscous effects on the dynamics of unsteady lift and pitching moment—we develop viscous versions of the traditional discrete vortex method and unsteady vortex lattice/panel method. The resulting aerodynamic loads obtained from the proposed numerical models are compared against higher-fidelity simulations of unsteady Reynolds-averaged Navier–Stokes equations for an airfoil undergoing step, harmonic, and complex maneuvers. The obtained results are consistently in better agreement with the unsteady Reynolds-averaged Navier–Stokes simulations in comparison to their potential flow counterpart. In conclusion, the developed numerical methods are capable of capturing (i) unsteady effects; (ii) viscous effects (e.g., viscosity-induced lag) on the dynamics of lift and moment at high frequencies and low Reynolds numbers; and (iii) wake deformation, for arbitrary time-varying motion.