Transonic Vortical Flow

Abstract

Transonic flow is generally associated with the inviscid fluid effects when a flow with a freestream Mach number M ∞ ≃ 1 accelerates to locally supersonic velocities, or decelerates to locally subsonic velocities, as it moves streamwise past a body. However, transonic flows can occur in many other circumstances such as on high lift devices at low M ∞, at the tips of helicopter blades, and around corners in ducts. In this paper, a class of transonic flows for slender, highly swept wings at high angle of attack (α ≥ 10°) will be considered. Under these conditions, leading edge vortices generally form as shown schematically in Figure 1. If M ∞ ~ 1, the streamwise flow can be transonic in the classical sense, leading to mixed subsonic-supersonic flow and shock waves on the wing. However, the leading edge vortices create additional transonic cross flow effects due to the high swirl velocities associated with them.