Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T04:17:09.473Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex pairs and rings interacting with shear-layer vortices

Published online by Cambridge University Press:  21 April 2006

M. Kiya ,
M. Ohyama  and
J. C. R. Hunt
M. Kiya
Affiliation:
Faculty of Engineering, Hokkaido University, Sapporo, 060, Japan
M. Ohyama
Affiliation:
Faculty of Engineering, Hokkaido University, Sapporo, 060, Japan
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

In order to understand how free-stream turbulence affects the vortex-pairing mechanism in free-mixing layers, water-flume experiments have been performed on the interaction between single vortex pairs (with circulation Γp) and also vortex rings propelled towards the rolling-up vortices (of circulation Γh) in a two-dimensional separated shear layer. The Reynolds number of an obstacle generating the shear layer is about 103 and of the vortex pairs and rings about 10–100. Our observations show that, if the ratio Γp/Γh exceeds about 1.4, the vortex pairs break away any shear-layer vortices in their path and if Γp/Γh is less than about 0.5 the shear-layer vortices destroy the vortex pair. But if Γp/Γh = 1.0 ± 0.4 the vortex pairs and shed vortices interact strongly, for example by a pairing between one vortex of the pair and the shed vortex, by the vortex pair eliminating coalescence of vortices in the shear layer, or by combining with the rolling-up vortices to generate large vortices. Qualitatively similar effects are observed with the vortex rings.

Numerical calculations of the interaction between an array of vortices on a line and a vortex pair are described. The results are similar to those of the physical experiments, in particular displaying the same sensitivity to Γp/Γh at Γp/Γh ≈ 1.0. It is suggested that these results demonstrate one important way in which free-stream turbulence interacts with shear layers and how shear layers interact with other vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 172 , November 1986 , pp. 1 - 15
Copyright
© 1991 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

Aref H.1983 Integrable, chaotic, and turbulent vortex motion in two-dimensional flows. Ann. Rev. Fluid Mech. 15, 345–389.Google Scholar
Batchelor G. K.1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bradshaw P.1974 Effects of free-stream turbulence on turbulent shear layers. Imperial College Aero Rep. 74–10.Google Scholar
Bradshaw, P. 1977 Interacting shear layers in turbomachines and diffusers. In Turbulence in Internal Flows: Turbomachinery and Other Engineering Applications (ed. S. N. B. Murthy), pp. 35–65. Hemisphere.
Brighton P. W. M.1977 Boundary layers and stratified flows past obstacles. Ph.D. thesis, University of Cambridge.
Castro I. P.1984 Effects of free-stream turbulence on low Reynolds number boundary layers. Trans. ASME I: J. Fluids Engng 106, 298–306.Google Scholar
Chandrsuda C., Mehta R. D., Weir, A. D. & Bradshaw P.1978 Effect of free-stream turbulence on large structure in turbulent mixing layers. J. Fluid Mech. 85, 693–704.Google Scholar
Crow S. C.1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Falco R. E.1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, S124–S132.Google Scholar
Gartshore I. S., Durbin, P. A. & Hunt J. C. R.1983 The production of turbulent stress in a shear flow by irrotational fluctuations. J. Fluid Mech. 137, 307–329.Google Scholar
Hancock, P. E. & Bradshaw P.1983 The effect of free-stream turbulence on turbulent boundary layers. Trans. ASME I: J. Fluids Engng 105, 284–289.Google Scholar
Head, M. R. & Bandyopadhyay P.1983 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.Google Scholar
Maxworthy T.1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32.Google Scholar
Maxworthy T.1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.Google Scholar
Odell, G. M. & Kovasznay L. S. G.1971 A new type of water channel with density stratification. J. Fluid Mech. 50, 535–543.Google Scholar
Oguchi, H. & Inoue O.1984 Mixing layer produced by a screen and its dependence on initial conditions. J. Fluid Mech. 142, 217–231.Google Scholar
Overman, E. A. & Zabusky N. J.1982 Evolution and merger of isolated vortex structures. Phys. Fluids 25, 1297–1305.Google Scholar
Perry, A. E. & Lim T. T.1978 Coherent structures in coflowing jets and wakes. J. Fluid Mech. 88, 451–463.Google Scholar
Pui, N. K. & Gartshore I. S.1979 Measurements of the growth rate and structure in plane turbulent mixing layers. J. Fluid Mech. 91, 111–130.Google Scholar
Saffman P. G.1970 The velocity of viscous vortex rings. Stud. Appl. Math. 49, 371–380.Google Scholar
Symes, C. R. & Fink L. E.1977 Effects of external turbulence upon the flow past cylinders. In Structure and Mechanism of Turbulence I (ed. H. Fiedler), pp. 86–102. Springer.
Tamura H., Kiya, M. & Arie M.1984 Vortex shedding from a two-dimensional blunt trailing edge with unequal external free-stream velocities. Bull. JSME 27, 1866–1872.Google Scholar
Tatsuno, M. & Honji H.1977 Two pairs of rectilinear vortices. J. Phys. Soc. Japan 42, 361–362.Google Scholar
Widnall, S. E. & Sullivan D. B.1973 On the stability of vortex rings Proc. R. Soc. Lond. A 332, 335–353.Google Scholar
Winant, C. D. & Browand F. K.1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar
Wygnanski I., Oster D., Fiedler, H. & Dziomba B.1979 On the preserverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer. J. Fluid Mech. 93, 325–335.Google Scholar
Yamada, H. & Matsui T.1979 Mutual slip-through of a pair of vortex rings. Phys. Fluids 22, 1245–1249.Google Scholar
Zabusky M. D., Hughes, M. H. & Roberts K. V.1979 Contour dynamics for the Euler equations in two dimensions. J. Comp. Phys. 30, 96–106.Google Scholar