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Reynolds-stress measurements in a turbulent trailing vortex

Published online by Cambridge University Press:  20 April 2006

W. R. C. Phillips  and
J. A. H. Graham
W. R. C. Phillips
Affiliation:
Department of Mechanical Engineering, McGill University, Quebec, Canada Present address: University of Melbourne, Parkville, Victoria 3052, Australia.
J. A. H. Graham
Affiliation:
Department of Mechanical Engineering, McGill University, Quebec, Canada Present address: Canadian Pratt & Whitney Co., Longueuil, Quebec, Canada.
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Abstract

Measurements of a turbulent trailing vortex in zero pressure gradient are described. These include mean velocities and all the components of the Reynolds-stress tensor. The measurements were made using linearized hot wires at stations 45, 78 and 109 chordlengths downstream of the wing. Axisymmetric jets or wakes were added coaxially to the vortex while the total circulation was held constant, and their effect studied. It was found, as Poppleton and Mason & Marchman have reported, that increasing the flow force hastens the radial dispersion of vorticity; this is seen to be concurrent with higher turbulence intensities and Reynolds shear stresses. With the flux of excess axial momentum effectively zero, thereby approximating a turbulent line vortex, no discernible downstream change was observed in the velocity field and very little in the turbulence field.

A balance of terms in the mean-momentum equations is presented and discussed. It is seen that, in spite of the fact that the radial velocity is numerically much smaller than the axial velocity, terms that contain it, both in the axial- and tangential-momentum equations, cannot be ignored, unless the magnitude of the flow force (divided by the fluid density) is much less than the square of the total circulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 353 - 371
Copyright
© 1984 Cambridge University Press

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