Improving vortex models via optimal control theory

Low-order inviscid point vortex models have demonstrated success in predicting the qualitative behavior of aerodynamic forces resulting from unsteady lifting surface maneuvers. However, the quantitative agreement is often lacking as a result of applying a Kutta condition at both edges in a fundamentally unsteady flow. The present work considers the low-order Eldredge-Wang impulse matching vortex model of a pitching plate. A constrained minimization problem is constructed within an optimal control framework and solved by means of variational principles. That is, we relax the Kutta condition imposed at the plate's edges and seek the time rate of change of the vortex strength that minimizes the discrepancy between the model-predicted and high-fodelity simulation force histories, while adhering to the dynamics of the low-order model. The framework developed provides a systematic means of determining the shortcomings of low-order point vortex models, thus providing a path to improvement and refinement. We find that the Kutta condition still holds quite well at the trailing edge, but that the leading edge model requires adjustment. These results will aid our understanding of appropriate leading and trailing edge boundary conditions, and lead to improvements of low-order vortex models of maneuvering aerodynamic flight.