On Satisfying the Kutta Condition in Unsteady Thin Aerofoil Theory
Abstract
Unsteady thinaerofoil theory is a loworder method for solving potentialflow aerodynamics on a camberline undergoing arbitrary motion. In this method, a Kutta condition must be applied at the trailing edge to uniquely specify the net circulation about the aerofoil. This article provides a critical discussion on applying the Kutta condition in unsteady flows, and introduces an improved method of doing so in unsteady thinaerofoil theory. Specifically, the shed wake at any discrete time step is represented by a continuous distribution of vorticity derived from the exact Wagner solution rather than by a point vortex or regularized vortex blob. Results in the article illustrate the effects of this improvement for cases of step change in angle of attack (Wagner problem), harmonic heaving motion (Theodorsen problem), and a pitchramphold manoeuvre. Exact analytical solutions and CFD simulations of the incompressible Euler equations are used for verification. The new approach is seen to satisfy the Kutta condition at all reduced frequencies, with velocities being finite and pressure difference going to zero at the trailing edge. It improves unsteady thinaerofoil theory in terms of theoretical rigour, computational cost and numerical accuracy.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08647
 Bibcode:
 2022arXiv220508647R
 Keywords:

 Physics  Fluid Dynamics