Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T23:24:58.913Z Has data issue: false hasContentIssue false
  • English
  • Français

Organized large structure in the post-transition mixing layer. Part 1. Experimental evidence

Published online by Cambridge University Press:  26 November 2013

A. D’Ovidio  and
C. M. Coats
A. D’Ovidio
Affiliation:
Department of Engineering, University of Leicester, Leicester LE1 7RH, UK
C. M. Coats*
Affiliation:
Department of Engineering, University of Leicester, Leicester LE1 7RH, UK
*
†Email address for correspondence: cmc7@le.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

New flow-visualization experiments on mixing layers of various velocity and density ratios are reported. It is shown that, in mixing layers developing from laminar initial conditions, the familiar mechanism of growth by vortex amalgamation is replaced at the mixing transition by a previously unrecognized mechanism in which the spanwise-coherent large structures individually undergo continuous linear growth. In the organized post-transition flow it is this continuous linear growth of the individual structures that produces the self-similar growth of the mixing-layer thickness, with the occasional interactions between neighbouring structures occurring as a consequence of their growth, not its cause. It is also observed that periods during which the post-transition mixing layer comprises orderly processions of large structures alternate with periods during which no large-scale organization is apparent downstream of the transition location. These two fully turbulent flow states are characterized by different growth rates, entrainment ratios and orientations of the mixing layer relative to the free streams. The implications of these findings are discussed.

JFM classification

Boundary Layers: Free shear layers Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulent transition
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 466 - 498
Copyright
©2013 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

Abramovich, G. N. 1963 The Theory of Turbulent Jets, pp. 149–162.MIT.Google Scholar
Batt, R. G. 1975 Some measurements on the effect of tripping the two-dimensional shear layer. AIAA J. 13, 245–247.Google Scholar
Bell, J. H. & Mehta, R. D. 1990 Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28, 2034–2042.Google Scholar
Bell, J. H. & Mehta, R. D. 1992 Measurements of the streamwise vortical structures in a plane mixing layer. J. Fluid Mech. 239, 213–248.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structures in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26, 225–236.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.Google Scholar
Browand, F. K. & Latigo, B. O. 1979 Growth of the two-dimensional mixing layer from a turbulent and nonturbulent boundary layer. Phys. Fluids 22, 1011–1019.CrossRefGoogle Scholar
Browand, F. K. & Troutt, T. R. 1985 The turbulent mixing layer: geometry of large vortices. J. Fluid Mech. 158, 489–509.Google Scholar
Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127–144.Google Scholar
Brown, G. L. 1974 The entrainment and large structure in turbulent mixing layers. In Proceedings of Fifth Australasian Conference on Hydraulics and Fluid Dynamics, New Zealand, Christchurch, pp. 352–359.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.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
Clemens, N. T. & Mungal, M. G. 1995 Large-scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284, 171–216.CrossRefGoogle Scholar
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22, 427–509.Google Scholar
Coles, D. 1981 Prospects for useful research on coherent structure in turbulent shear flow. Proc. Indian Acad. Sci. (Eng. Sci.) 4, 111–127.Google Scholar
Damms, S. M. & Küchemann, D. 1974 On a vortex-sheet model for the mixing between two parallel streams. I. Description of the model and experimental evidence. Proc. R. Soc. (Lond.) A 339, 451–461.Google Scholar
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 1791–1796.Google Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Dimotakis, P. E. & Brown, G. L. 1976 The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J. Fluid Mech. 78, 535–560.Google Scholar
Dziomba, B. & Fiedler, H. E. 1985 Effect of initial conditions on two-dimensional free shear layers. J. Fluid Mech. 152, 419–442.CrossRefGoogle Scholar
Fiedler, H. E. & Mensing, P. 1985 The plane turbulent shear layer with periodic excitation. J. Fluid Mech. 150, 281–309.Google Scholar
George, W. K. 1989 The self-preservation of turbulent flows and its relation to initial conditions and coherent structure. In Advances in Turbulence (ed. Arndt, R. & George, W. K.), pp. 39–73. Hemisphere.Google Scholar
Hermanson, J. C. & Dimotakis, P. E. 1989 Effects of heat release in a turbulent, reacting shear layer. J. Fluid Mech. 199, 333–375.Google Scholar
Hernan, M. A. & Jimenez, J. 1982 Computer analysis of a high-speed film of a plane turbulent mixing layer. J. Fluid Mech. 119, 323–345.CrossRefGoogle Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.Google Scholar
Huang, L.-S. & Ho, C.-M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1985 An experimental study of organised motions in the turbulent plane mixing layer. J. Fluid Mech. 159, 85–104.Google Scholar
Jimenez, J. 1980 On the visual growth of a turbulent mixing layer. J. Fluid Mech. 96, 447–460.Google Scholar
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319–336.Google Scholar
Jimenez, J., Cogollos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125–143.Google Scholar
Karasso, P. S. & Mungal, M. G. 1996 Scalar mixing and reaction in plane liquid shear layers. J. Fluid Mech. 323, 23–63.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. (Dokl.) Acad. Sci. URSS 30, 301–305 Reprinted as Proc. R. Soc. (Lond.) A 434, 9–13, 1991.Google Scholar
Konrad, J. H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. PhD thesis, California Institute of Technology (Issued as Project SQUID Tech. Rep. CIT-8-PU).Google Scholar
Koochesfahani, M. M., Catherasoo, C. J., Dimotakis, P. E., Gharib, M. & LANG, D. B. 1979 Two-point LDV measurements in a plane mixing layer. AIAA J. 17, 1347–1351.Google Scholar
Koochesfahani, M. M. & Dimotakis, P. E. 1986 Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170, 83–112.Google Scholar
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.CrossRefGoogle Scholar
Lasheras, J. C., Cho, J. S. & Maxworthy, T. 1986 On the origin and evolution of streamwise vortical structures in a plane, free shear layer. J. Fluid Mech. 172, 231–258.Google Scholar
Liepman, H. W. & Laufer, J. 1947 Investigation of free turbulent mixing. NACA Tech. Note 1257.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.Google Scholar
Meyer, T. R., Dutton, J. C. & LUCHT, R. P. 2006 Coherent structures and turbulent molecular mixing in gaseous planar shear layers. J. Fluid Mech. 558, 179–205.CrossRefGoogle Scholar
Michalke, A. 1965 Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech. 22, 371–383.Google Scholar
Michalke, A. 1971 Der Einfluß variabler Dichte auf die Instabilität einer freien Scherschicht. Ing.-Arch. 40, 29–39.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 1137–1143.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of organised vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465–473.Google Scholar
Moser, R. D. & Rogers, M. M. 1991 Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3, 1128–1134.Google Scholar
Moser, R. D. & Rogers, M. M. 1993 The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247, 275–320.Google Scholar
Mungal, M. G. & Dimotakis, P. E. 1984 Mixing and combustion with low heat release in a turbulent mixing layer. J. Fluid Mech. 148, 349–382.Google Scholar
Mungal, M. G., Hermanson, J. C. & Dimotakis, P. E. 1985 Reynolds number effects on mixing and combustion in a reacting shear layer. AIAA J. 23, 1418–1423.Google Scholar
Nygaard, K. J. & Glezer, A. 1991 Evolution of streamwise vortices and generation of small-scale motion in a plane mixing layer. J. Fluid Mech. 231, 257–301.Google Scholar
Oster, D. & Wygnanski, I. 1982 The forced mixing layer between parallel streams. J. Fluid Mech. 123, 91–130.Google Scholar
Oster, D., Wygnanski, I. & Fiedler, H. E. 1977 Some preliminary observations on the effect of initial conditions on the structure of the two-dimensional turbulent mixing layer. In Turbulence in Internal Flows (ed. Murthy, S. N. B.), pp. 67–87. Hemisphere.Google Scholar
Pedley, T. J. 1990 An experimental investigation into coherent structures in free shear layer flows. PhD thesis, University of Leeds.Google Scholar
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholz rollup. J. Fluid Mech. 243, 183–226.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349–1357.Google Scholar
Slessor, M. D., Bond, C. L. & Dimotakis, P. E. 1998 Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions. J. Fluid Mech. 376, 115–138.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flows, 2nd edn. p. 196. Cambridge University Press.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517–519.CrossRefGoogle 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
Wood, D. H. & Bradshaw, P. 1982 A turbulent mixing layer constrained by a solid surface. Part 1. Measurements before reaching the surface. J. Fluid Mech. 122, 57–89.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327–361.CrossRefGoogle Scholar