Flow Structure in a Model of Aircraft Trailing Vortices

Citation

Faddy, James Malcolm (2005) Flow Structure in a Model of Aircraft Trailing Vortices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RC42-JY40. https://resolver.caltech.edu/CaltechETD:etd-05272005-163801

Abstract

We consider a model of incompressible trailing vortices consisting of an array of counter-rotating structures in a doubly periodic domain, infinite in the vertical direction. The two-dimensional vortex array of Mallier and Maslowe is combined with an axial velocity profile chosen proportional to the initial axial vorticity to provide an initial condition for the vortex wake. This base flow is a weak solution of the three component steady Euler equations in two dimensions thus allowing its linear stability properties to be investigated. These are used to interpret several stages in the development of vortex structure observed in fully three-dimensional DNS at Reynolds numbers Gamma/(2 pi nu)=O(1000). For sufficiently high axial velocity, itseffect can be seen, in that each vortex in the linear array first develops helical structures before undergoing a period of relaminarization. At later times the more slowly growing co-operative elliptical instabilities become apparent; however, the helical structure persists and the observed vortical structures remain coherent for longer periods than in the absence of axial velocity. Using the stretched vortex subgrid model, large-eddy simulation runs are performed at higher Reynolds numbers and a mixing transition identified at about Re = 1-2 x 10⁴. Similar phenomena are observed in these simulations as are seen in the DNS. Next the spatial nature of the true aircraft wake is compared to the temporal approximation commonly employed to simplify the computational complexity of the problem. A model is formulated to acount for the average axial pressure gradients that develops in the spatial wake but is absent from the temporal simulation. The model enables jet- and wake-like axial flows to be distinguished and the subtle differences in the ensuing turbulent states investigated. Finally, the model is used to investigate co-rotating vortex merger, the new thrust term providing a mechanism to enhance the axial flow further destabilizing the base flow.

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