Impingement of a von Karman Vortex Street on a Delta Wing

Abstract

Introduction H IGH-PERFORMANCE military aircraft oftentimes employ delta-shaped wings. It is well documented that delta wings at a fixed angle of attack generate lift by separating a shear layer of fluid (air or water) at the leading edge, and this shear layer forms two strong counter-rotating vortices on either side of the wing.1−5 These leading-edge (LE) vortices are critical to the generation of lift, as they produce a large suction peak on the surface. Under certain conditions, the LE vortices are prone to undergo a change in their coherent structure. The vortex expands around the core, slows down axially, and forms either a bubble or a spiral, with the spiral form being more predominant at Reynolds numbers of interest to aircraft designers. This change, called vortex burst or breakdown, is dependent on the aspect ratio of the wing, angle of attack, pressure gradient, yaw angle, and swirl angle of the vortex, among others.6−8 Delta wings have evolved over the years and are now used primarily in the form of leading-edge extensions on many fighter aircraft. As these aircraft become more and more maneuverable, the understanding of the physics of time-dependent unsteady flows is becoming more important. The vortex burst has such a detrimental effect on the lift generation of delta wings that it is important to correctly model the flow, predict it with accuracy, and control the movement of the burst location. If accurate computational models of these maneuvers are to be developed, it is necessary to understand the mechanisms involved in vortex bursting and mixing on the lee side of the delta wing. This is true of so-called “hyperagile” maneuvers (like the Cobra maneuver), where research has been intense.9−13 The behavior of the burst location is sensitive to yaw. Aircraft performing the Cobra maneuver (or other high-angle-of-attack maneuvers) can be unstable in yaw.14−17 Sometimes, the wake of an aircraft’s forebody can have vortices at very high angles of attack.18 In other cases, close proximity of the delta wing to the wake of another aircraft would subject the delta to an external vortical flow. This inspired the authors to consider the effect of an impingement from another set of vortices upon the delta-wing’s leading-edge vortices. Because a von Karman vortex street has a well-known behavior,