The seminal aerodynamics literature provides analytic predictions of the loads due to sinusoidal gusts (Sears and von Kármán), sharp-edged transverse gusts (Küssner), sinusoidal motions (Theodorsen), and step-change airfoil motions (Wagner). Although these workers determined the overall loads (circulation, lift, and moment), they did not explicitly derive the vortex sheet strength (which is used to compute these loads). Simply put, vortex sheet strength is the velocity difference above/below the airfoil, so it is related to the pressure distribution and therefore the loads. Knowledge of the vortex sheet strength is important because, to extend this seminal theory to include nonlinearities such as thickness–load coupling, viscous–load coupling, or boundary-layer separation, one needs to inform these calculations with the vortex sheet strength. The main contribution of this paper is a method to theoretically predict the vortex sheet strength in the seminal unsteady aerodynamics problems of Sears, Küssner, Theodorsen, and Wagner. These theoretical calculations are enabled by developing a numerical method for calculating the required Fourier coefficients. In addition, a unified presentation of linear unsteady aerodynamics theory is contributed, and examples are provided to illustrate the vortex sheet strength in each of the four seminal problems.
Vortex Sheet Strength in the Sears, Küssner, Theodorsen, and Wagner Aerodynamics Problems
AIAA Journal ; 56 , 3 ; 889-904
2018-01-29
16 pages
Article (Journal)
Electronic Resource
English
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