Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T15:50:31.255Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, G. R., Barker, S. J., Bofah, K. K. & Saffman, P. G. 1974 J. Fluid Mech. 65, 325–336.
Barker, G. I. & Crow, S. 1977 J. Fluid Mech. 82, 659–671.
Batchelor, G. K. 1964 J. Fluid Mech. 20, 645–658.
Champagne, F. H. & Sleicher, C. A. 1967 J. Fluid Mech. 28, 177–182.
Corsiglia, V. R. & Dunham, E. R. 1976 NASA SP 409.
Govindaraju, S. P. & Saffman, P. G. 1971 Phys. Fluids 14, 2074–2080.
Graham, J. A. H., Newman, B. G. & Phillips, W. R. C. 1974 In Proc. 9th Congr. Intl Counc. Aero. Sci., no. 74–40.
Graham, J. A. H., Phillips, W. R. C. 1975 McGill Univ. MERL TN 75–1.
Guitton, D. E. 1968 McGill Univ. MERL TR 68–6.
Hoffmann, E. R. & Joubert, P. N. 1963 J. Fluid Mech. 16, 395–411.
Irwin, H. P. A. H. 1972 McGill Univ. MERL TN 72–1.
Long, R. R. 1961 J. Fluid Mech. 11, 611–626.
Leibovich, S. & Stewartson, K. 1983 J. Fluid Mech. 126, 335–356.
Mason, W. H. & Marchman, J. F. 1972 NASA CR 62078.
McCormick, B. W., Tangler, J. L. & Sherrieb, H. E. 1968 J. Aircraft 5, 260–267.
Moore, D. W. & Saffman, P. G. 1973 Proc. R. Soc. Lond. A 333, 491–508.
Morse, A. 1979 Ph.D. thesis, University of London.
Morton, B. R. 1969 J. Fluid Mech. 38, 315–333.
Perry, A. E., Lim, T. T. & Chong, M. S. 1980 J. Fluid Mech. 101, 243–256.
Phillips, W. R. C. 1981 J. Fluid Mech. 105, 451–467.
Phillips, W. R. C. 1984 J. Phys. E: Sci. Instrum. (submitted).
Poppleton, E. D. 1971a J. Aircraft 8, 672–673.
Poppleton, E. D. 1971b McGill Univ. MERL TN 71–1.
Pratte, B. D. & Keffer, J. F. 1972 Trans. ASME D: J. Basic Engng 94, 739–748.
Pullin, D. I. & Phillips, W. R. C. 1981 J. Fluid Mech. 104, 45–53.
Ribeiro, M. M. & Whitelaw, J. H. 1980 Proc. R. Soc. Lond. A 370, 281–301.
Singh, P. I. 1974 Doctoral dissertation, University of Colorado, Boulder.
Smith, H. C. 1980 J. Aircraft 17, 861–866.
Smith, P. A. 1973 Doctoral dissertation, McGill University.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Uberoi, M. S. 1977 Phys. Fluids 20, 1785.
Verstynen, H. A. & Dunham, R. E. 1973 NASA TN D-7172.
Vogel, W. M. 1968 McGill Univ. MERL TN 68–1.
Wygnanski, I. & Fiedler, H. E. 1969 J. Fluid Mech. 38, 577–612.