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Unsteady thin-aerofoil theory is a low-order method for solvingpotential-flow aerodynamics on a camber-line undergoing arbitrary motion. Inthis method, a Kutta condition must be applied at the trailing edge to uniquelyspecify the net circulation about the aerofoil. This article provides acritical discussion on applying the Kutta condition in unsteady flows, andintroduces an improved method of doing so in unsteady thin-aerofoil theory.Specifically, the shed wake at any discrete time step is represented by acontinuous distribution of vorticity derived from the exact Wagner solutionrather than by a point vortex or regularized vortex blob. Results in thearticle illustrate the effects of this improvement for cases of step change inangle of attack (Wagner problem), harmonic heaving motion (Theodorsen problem),and a pitch-ramp-hold manoeuvre. Exact analytical solutions and CFD simulationsof the incompressible Euler equations are used for verification. The newapproach is seen to satisfy the Kutta condition at all reduced frequencies,with velocities being finite and pressure difference going to zero at thetrailing edge. It improves unsteady thin-aerofoil theory in terms oftheoretical rigour, computational cost and numerical accuracy.

On Satisfying the Kutta Condition in Unsteady Thin Aerofoil Theory