Model Reduction in Discrete Vortex Methods for 2D Unsteady Aerodynamic Flows

Abstract

In this paper, we propose a method for model reduction in discrete-vortex methods. Discrete vortex methods have been successfully employed to model separated and unsteady airfoil flows. Earlier research revealed that a parameter called the Leading Edge Suction Parameter (LESP) can be used to model leading-edge vortex (LEV) shedding in unsteady flows. The LESP is a measure of suction developed at the leading edge, and whenever the LESP exceeds a critical value, a discrete vortex is released from the leading edge so as to keep the LESP at the critical value. Though the method was successful in predicting the forces on and the flow field around an airfoil in unsteady vortex-dominated flows,it was necessary to track a large number of discrete vortices in order to obtain the solution. The current study focuses on obtaining a model with a reduced number of leading-edge vortices, thus improving the computation time. Vortex shedding from the leading edge is modelled by a shear layer that comprises of a few discrete vortices, and a single concentrated vortex whose strength varies with time. The single vortex at the end of the shear layer accounts for the concentrated vortical structure that comprises several discrete vortex elements in conventional vortex methods. A merging algorithm is initiated when the edge of the shear layer starts rolling up. Suitable discrete vortices are identified using a kinematic criterion, and are merged to the growing vortex at every time step. The reduced order method is seen to bring down the number of discrete vortices shed from the leading edge significantly.