Model Reduction in Discrete-Vortex Methods for Unsteady Airfoil Flows

Discrete-vortex methods are a class of low-order methods widely used to study unsteady aerodynamic phenomena. However, these methods demand high computational costs when subject to large number of vortices in the flowfield. This calls for model reduction in discrete-vortex methods. A model-reduction technique is applied to a recently developed discrete-vortex method in which the criticality of the leading-edge suction parameter (LESP) controls the initiation and termination of leading-edge vortices (LEVs). This method, called the LESP-modulated discrete-vortex method (LDVM), has been successfully used in recent work to study unsteady airfoil flows with LEV shedding. In this research, model reduction in the LDVM is achieved by amalgamating suitable pairs of discrete vortices identified through a condition that requires that the velocity at the airfoil leading edge is not affected by amalgamation. The amalgamated vortex is placed at an optimal location to ensure that the bound circulation and the leading-edge suction are conserved. The reduced-order model is able to predict the flow features and the force and moment coefficients in good agreement with the full model while having significantly lower runtimes. Use of physical quantities like leading-edge suction and bound circulation enables the easy implementation of this model-reduction strategy in other computational methods based on discrete-vortex elements.