The Rolling Up of the Trailing Vortex Sheet and Its Effect on the Downwash Behind Wings

Abstract

The motion of the trailing vortices associated with a lifting wing is investigated by theoretical and visual-flow methods for the purpose of determining the proper vortex distribution to be used for downwash calculations. Both subsonic and supersonic speeds are considered in the analysis.It is found that the degree to which the vortices are rolled up depends upon the distance behind the wing and upon the lift coefficient, span loading, and aspect ratio of the wing. While the rolling up of the trailing vortices associated with high-aspectratio wings is of little practical importance, it is shown that, with low-aspect-ratio wings, the trailing vortex sheet may become essentially rolled up into two trailing vortex cores within a chord length of the trailing edge.The downwash fields associated with the two limiting cases of the flat vortex sheet and the fully rolled-up vortices are investigated in detail for both subsonic and supersonic speeds. The intermediate case in which the rolling-up process is only partially completed at the tail position is also discussed.

Aerodynamic Performance of Extended Formation Flight

“…The Rankine vortex is commonly used with the Prandtl method leading to a core size prediction a little over 8% of the wing span. 20 However, agreement with experimental results is rather poor. Experimental data show smaller core sizes, and that the assumption of all the vorticity being contained within the core is rather inaccurate.…”

“…This is often done by a method first proposed by Prandtl 18 and more fully developed separately by Milne-Thompson 19 and Spreiter & Sacks. 20 This method is based on conservation of mechanical energy applied over a large control volume containing the aircraft. It is assumed that the induced drag of the aircraft is approximately equal to the kinetic energy of the fluid in the Trefftz plane.…”

Wake Vortex Alleviation Using Rapidly Actuated Segmented Gurney Flaps

“…According to the estimates of Spreiter and Sacks (1951), the point at which the vortex is essentially fully rolled up occurs at X/c ≈ 2.75. We designate measurements performed upstream of this notional point as near wake measurements, and downstream of this point as intermediate wake measurements.…”

Aerodynamic Performance of Extended Formation Flight

“…This is often done by a method first proposed by Prandtl 18 and more fully developed separately by Milne-Thompson 19 and Spreiter & Sacks. 20 This method is based on conservation of mechanical energy applied over a large control volume containing the aircraft. It is assumed that the induced drag of the aircraft is approximately equal to the kinetic energy of the fluid in the Trefftz plane.…”