Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

Abstract

Unsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the A 0 term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.

Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

“…This flow feature signals the formation of the shear layer in which there is an eruption of surface flow into the mainstream. As in previous work [58,60], the instant when the spike in the negative C f region first reaches the zero value is taken as the time corresponding to initiation of LEV formation. In Fig.…”

“…They demonstrated that for flows around a given airfoil operating at a given Reynolds number, LEV shedding is always initiated at a critical value of the LESP [59] and is independent of motion kinematics, provided that LEV formation is not preceded by significant trailing-edge separation. Additionally, Ramesh et al [58] developed a novel low-order numerical solver, called LDVM, for 2D low Re unsteady flows, using the LESP to predict and modulate LEV shedding. In the LDVM, when the instantaneous value of LESP exceeds a predetermined critical value, LEV shedding is modeled by shedding a discrete vortex at each time step of the numerical method.…”

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

“…al 36 that the initiation and termination of leading-edge vorticity shedding is determined by a nondimensional measure of the suction at the leading edge. It has also been shown that this leading edge section parameter (LESP) is the same as leading coefficient A 0 in the Fourier series representing the bound vorticity.…”

“…Katz 18 has developed a discrete-vortex method for separated flow past an airfoil, where the location of separation on the airfoil has to be prescribed using information from experiments or other means. More recently, low-order methods based on discrete vortices have been developed by Ansari et al, 19 Wang & Eldredge, 20 Ramesh et al 21 to model leading edge vortices in unsteady flows, with applications toward insect flight and MAV aerodynamics. Though these methods are based on potential theory, they capture the essential physics in flows of interest by combining inviscid theory with discrete-vortex shedding.…”

“…A more general vortex shedding criterion is required to make discrete-vortex methods broadly applicable to a wide range of geometries (including airfoils with rounded leading edges) and arbitrary unsteady motions. Ramesh et al 21 have developed a discrete-vortex aerodynamic method to model unsteady flows with intermittent LEV shedding using a leading-edge suction parameter (LESP). The unique aspect of this method (LESP-modulated discrete vortex method, or, LDVM) is that vortex shedding is turned on or off at the leading edge using a criticality condition.…”