On Satisfying the Kutta Condition in Unsteady Thin Aerofoil Theory

Kiran Ramesh

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arXiv · 2205.08647

On Satisfying the Kutta Condition in Unsteady Thin Aerofoil Theory

Kiran Ramesh

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Abstract

Unsteady thin-aerofoil theory is a low-order method for solving potential-flow aerodynamics on a camber-line 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 thin-aerofoil 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 pitch-ramp-hold 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 thin-aerofoil theory in terms of theoretical rigour, computational cost and numerical accuracy.

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Kiran Ramesh. 2022-05-17. On Satisfying the Kutta Condition in Unsteady Thin Aerofoil Theory. https://arxiv.org/abs/2205.08647

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