The Initial Roll-Up of a Thick, Two-Dimensional Wake Behind a Wing of Finite Span
TECHNION - ISRAEL INST OF TECH HAIFA DEPT OF AERONAUTICAL ENGINEERING
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Previous investigations of wing-wake roll-up have assumed the wake to be a vortex sheet of zero thickness. This immediately leads to the conclusion that, as soon as the process starts, a spiral of near axisymmetric form, with an infinite number of turns, forms at the edges, as predicted by the work at Kaden, which must apply to the early stages of roll-up for any sheet of zero thickness. In this report, the aforementioned unrealistic features are removed by assuming that the wake cross-section has a finite thickness and some plausible shape. A two-dimensional method, analogous to that of Westwater, is developed, assuming that the wake cross-section contains vorticity in an otherwise irrotational field. The wake is divided into triangular elements and the vorticity in these is determined by assuming a linear transverse velocity profile in the wake and that the intial, unrolled wake moves downwards as determined by the wing spanwise loading through ordinary wing-wake theory. Euler time-step integration is then used to calculate the wake development under its own induced velocity field, ignoring viscous dissipation. A finite spiral structure is observed to develop and, within the range covered, the thickness only seems to affect the number of turns in the spiral, other parameters seeming to be almost unaffected. Plans for continuation of the work are discussed.
- Fluid Mechanics