Lift tailoring on unsteady airfoils with leading-edge vortex shedding using an inverse aerodynamic approach

Abstract

In this paper, we present a physics-informed approach to tailor the lift profile of an unsteady airfoil through the execution of an appropriate maneuver. In previous research, a low-order aerodynamic model based on the unsteady thin airfoil theory was developed for predicting the flowfield and loads on airfoils undergoing arbitrary motions. The theory was phenomenologically augmented using the concept of leading edge suction parameter (LESP) to incorporate the capability to predict intermittent leading edge vortex (LEV) shedding. The criticality of LESP was used to predict the onset and termination of LEV shedding and thus model the effect of LEVs on the flowfield and loads for a prescribed motion. In the current work, an inverse aerodynamic formulation is developed based on this framework for tackling the inverse problem: to obtain the motion kinematics required for generating a prescribed lift profile for an airfoil operating in the dynamic-stall regime. The LEV-modeling capability of the aerodynamic model enables the motion-design algorithm to take into account the effect of complex phenomena, such as dynamic stall and LEV shedding, which are not taken into account in previous research approaches. Several case studies are presented to demonstrate various scenarios such as lift tracking using pitching and heaving motions, lift cancellation during unsteady motion, and the generation of a given lift profile using two equivalent motions. The kinematic profiles generated by the inverse formulation are also simulated using a high-fidelity unsteady computational fluid dynamics solver to validate the predictions.