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Vortical structure morphology in the initial region of a forced mixing layer: roll-up and pairing

Published online by Cambridge University Press:  26 April 2006

Richard L. Leboeuf  and
Rabindra D. Mehta
Richard L. Leboeuf
Affiliation:
Center for Turbulence Research, NASA Ames Research Center/Stanford University, Stanford, CA 94305, USA.
Rabindra D. Mehta
Affiliation:
Department of Aeronautics and Astronautics, JIAA, Stanford University, Stanford and Fluid Mechanics Laboratory, NASA Ames Research Center, Moffett Field, CA 94035-1000, USA
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Abstract

Detailed three-dimensional phase-averaged measurements of the spanwise and streamwise vorticity formation and evolution in a forced mixing layer have been obtained. A plane two-stream mixing layer with a velocity ratio (U2/U1) of 0.6, a maximum Reynolds number (Reδ) of about 3150 and laminar initial boundary layers was generated in a mixing layer wind tunnel. Acoustic forcing, consisting of a fundamental roll-up frequency and its subharmonic, was used to phase-lock the initial development and first pairing of the spanwise vortical structures. For the first time, phase-averaged measurements of all three velocity components have been obtained on a three-dimensional grid, yielding the spanwise and streamwise vorticity distributions without invoking Taylor's hypothesis. The phase-averaged results show that the streamwise vorticity first appears in the form of ‘ribs’ just upstream of the first spanwise vortex roll-up. At the same time, the first spanwise roller becomes kinked, thus also contributing to the streamwise vorticity. As a result, in cross-stream cuts through the spanwise rollers, the streamwise vorticity appears in a ‘three-tier’ arrangement with opposite-signed vorticity in the centre. In terms of phase-averaged quantities, the maximum streamwise vorticity in the initial ribs is equivalent to about 10–15% of the peak spanwise vorticity and the streamwise rib circulation is equivalent to about 5–10% of the spanwise circulation. Further downstream, the peak streamwise vorticity decreases with increasing distance, while the average circulation remains approximately constant. Downstream of the pairing, the streamwise vorticity levels in the spanwise rollers are reduced. However, the spanwise spacing of the streamwise vortices does not increase within the measurement domain. Phase-averaged Reynolds stress measurements show that relatively high stress levels (periodic and random) were generated in the cores of the spanwise vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 315 , 25 May 1996 , pp. 175 - 221
Copyright
© 1996 Cambridge University Press

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References

Ashurst, W. T. & Meiburg, E. 1988 Three-Dimensional shear layers via vortex dynamics. J. Fluid Mech. 189, 87–115.Google Scholar
Bell, J. H. & Mehta, R. D. 1989 Design and calibration of the mixing layer wind tunnel. JIAA Rep. TR-89. Dept. of Aeronautics and Astronautics, Stanford University.
Bell, J. H. & Mehta, R. D. 1990 Development of a two-stream mixing layer with 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
Bell, J. H., Plesniak, M. W. & Mehta, R. D. 1992 Spanwise averaging of plane mixing layer properties. AIAA J. 30, 835–837.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.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
Buell, J. C. 1991 A hybrid numerical method for three-dimensional spatially-developing free-shear flows. J. Comput. Phys. 95, 313–338.Google Scholar
Buell, J. C. & Mansour, N. N. 1989 Asymmetric effects in three-dimensional spatially-developing mixing layers. In Proc. Seventh Symp. Turbulent Shear Flows, Stanford University, August, pp. 9.2.1–9.2.6.
Hernan, M. A. & Jimenez, J. 1982 Computer analysis of a high-speed film of the plane mixing layer. J. Fluid Mech. 119, 323–345.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.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
Inoue, O. 1987 Three-dimensional vortex simulation of a plane mixing layer. In Proc. Sixth Symp. on Turbulent Shear Flows, Toulouse, France, September 7–9, pp. 22-1-1 to 22-1-6.
Inoue, O. 1992 Double-frequency forcing on spatially growing mixing layers. J. Fluid Mech. 234, 553–581.Google Scholar
Jimenez, J. 1983 A spanwise structure in the plane mixing layer. J. Fluid Mech. 132, 319–326.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
Konrad, J. H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Project SQUID Tech. Rep. CIT-8-PU; and PhD thesis, California Institute of Technology, 1977.
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
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.Google Scholar
Leboeuf, R. L. & Mehta, R. D. 1993 Streamwise vortex meander in a plane mixing layer. Phys. Fluids A 5, 1983–1991.Google Scholar
Leboeuf, R. L. & Mehta, R. D. 1995a Measurements of spanwise scale change in a forced mixing layer. J. Fluid Mech. 293, 305–319.Google Scholar
Leboeuf, R. L. & Mehta, R. D. 1995b On using Taylor's hypothesis for three-dimensional mixing layers. Phys. Fluids 7, 1516–1518.Google Scholar
Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S. & Riley, J. J. 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207–243.Google Scholar
Miyauchi, T., Kawano, K. & Shingou, M. 1991 The coherent structure in turbulent mixing layers (structure in the core and rib regions). Computers Fluids 19, 401–412.Google Scholar
Monkewitz, P. A. 1988 Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188, 223–252.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
Nygaard, K. J. & Glezer, A. 1990 Core instability of the spanwise vortices in a plane mixing layer. Phys. Fluids A 2, 461–463.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
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin-Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215–240.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59–82.Google Scholar
Riley, J. J. & Metcalfe, R. W. 1980 Direct numerical simulation of a perturbed turbulent mixing layer. AIAA Paper 80-0274.
Rogers, M. M. & Moser, R. D. 1991 The three-dimensional evolution of a plane mixing layer. Part 1. The Kelvin-Helmholtz rollup. NASA TM 103856.
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin-Helmholtz rollup. J. Fluid Mech. 243, 183–226.Google Scholar
Rogers, M. M. & Moser, R. D. 1993 Spanwise scale selection in plane mixing layers. J. Fluid Mech. 247, 321–337.Google Scholar
Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6, 903–923.Google Scholar
Townsend, A. A. 1976 Structure of Turbulent Shear Flow (2nd Edn). Cambridge University Press.
Tung, C. H. 1992 Initial streamwise vorticity formation in a two-stream mixing layer. PhD dissertation, Department of Mechanical Engineering, University of Houston.
Wallace, J. M. & Foss, J. F. 1995 The measurement of vorticity in turbulent flows. Ann. Rev. Fluid Mech. 27, 469–514.Google Scholar
Watmuff, J. H. 1995 High-speed real-time processing of cross-wire data. Expl Thermal Fluid Sci. J. 10, 74–85.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
Yang, Z. & Karlsonn, S. K. F. 1991 Evolution of coherent structures in a plane shear layer. Phys. Fluids A 3, 2207–2219.Google Scholar
Zhang, Y. Q., Ho, C. M. & Monkewitz, P. 1985 The mixing layer forced by fundamental and subharmonic. IUTAM Symp. on Laminar-Turbulent Transition, Novosibirsk (ed. V. Kozlov), pp. 385–395. Springer.