Optimal surface morphing using adjoint optimization

We consider here aerodynamic flow control motivated by prescribed deformations on the surface of the aerodynamic body—an exciting actuation paradigm made possible by advances in materials science. Open loop control with this actuation strategy (and many others) are limited by intuition and challenges in designing appropriate amplitude and phase relationships with the flow dynamics to be controlled. In the current work, feedback control is used to achieve lift and drag improvements for flow over a NACA0012 airfoil at an angle of attack of U = 15◦ at a flow Reynolds number of '4 = 1,000. The control algorithm is solved as a constrained optimization problem where minimization of a cost functional is achieved by varying the normal actuation velocity on the surface of the airfoil. Cost functionals related to drag minimization and lift maximization are considered separately since the actuation configurations leading to these separate aims are expected to be distinct. Actuation is not restricted to have any predefined spatial or temporal properties and admits variation at every discretized point on the airfoil surface, at each time instance. The gradient based optimization procedure necessitates gradients of the cost functional with respect to each design parameter. The cost of this gradient computation is curtailed by the use of the adjoint of the constraint equation. The optimization procedure is executed over a time horizon of about 3 vortex shedding cycles. The resulting optimal actuation profiles for both drag and lift based cost functionals are analyzed and questions regarding sensitive spatial locations on the airfoil surface as well as temporal variation relative to the underlying shedding properties have been addressed. Where possible, comparisons have been made with the most efficient open loop control strategy from our previous work. Further, flow phenomena arising due to actuation have been discussed and actuation for lift maximization has been compared with that for drag minimization.