Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-14T00:39:04.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional structure of straight and curved plane wakes

Published online by Cambridge University Press:  26 April 2006

James H. Weygandt  and
Rabindra D. Mehta
James H. Weygandt
Affiliation:
Department of Aeronautics and Astronautics, JIAA, Stanford University, Stanford, CA 94305–4035, USA
Rabindra D. Mehta
Affiliation:
Department of Aeronautics and Astronautics, JIAA, Stanford University, Stanford, CA 94305–4035, USA Fluid Mechanics Laboratory, NASA Ames Research Center, Moffett Field, CA 94035-1000, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The formation and evolution of the three-dimensional structure of straight and mildly curved ($b/\bar{R} < 2\%$) flat plate wakes at relatively high Reynolds numbers (Reb = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 279 - 311
Copyright
© 1995 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

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. 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
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARDograph 169.
Breidenthal, R. 1980 Response of plane shear layers and wakes to strong three-dimensional disturbances. Phys. Fluids A 23, 1929–1934.Google Scholar
Buell, J. C. & Mansour, N. N. 1989 Near-field structures in three-dimensional spatially-developed wakes. In Proc. Tenth Australasian Fluid Mechanics Conf., Melbourne, Australia, pp. 3.21–3.24.
Chen, J. H., Cantwell, B. J. & Mansour, N. N. 1990 The effect of Mach number on the stability of a plane supersonic wake. Phys. Fluids A 2, 984–1003.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. R. Arndt & W. K. George), pp. 75–125. Hemisphere.
Gerrard, J. H. 1966 The three-dimensional structure of the wake of a circular cylinder. J. Fluid Mech. 25, 143–164.Google Scholar
Grant, H. L. 1958 The large eddies of turbulent motion. J. Fluid Mech. 4, 149–190.Google Scholar
Hayakawa, M. & Hussain, F. 1989 Three-dimensionality of organized structures in a plane turbulent wake. J. Fluid Mech. 206, 375–404.Google Scholar
Jovic, S. & Ramaprian, B. R. 1986 Large-scale structure of the turbulent wake behind a flat plate. IIHR Rep. 298. Inst. of Hydraulic Research, University of Iowa.
Koyama, H. 1983 Effects of streamline curvature on laminar and turbulent wakes. In Proc. Fourth Symp. on Turbulent Shear Flows, Karlsruhe, Germany, pp. 6.32–6.37.
Lasheras, J. C. & Meiburg, E. 1990 Three-dimensional vorticity modes in the wake of a flat plate. Phys. Fluids A 12, 371–380.Google Scholar
Maekawa, H., Moser, R. D. & Mansour, N. N. 1993 The three-dimensional evolution of a plane wake. In Proc. Ninth Symp. on Turbulent Shear Flows, Kyoto, Japan, August 16–18, pp. 3-2-1 to 3-2-6.
Meiburg, E. & Lasheras, J. C. 1988 Experimental and numerical investigation of the three-dimensional transition in plane wakes. J. Fluid Mech. 190, 1–37.Google Scholar
Morkovin, M. 1964 Flow around circular cylinders- a kaleidoscope of challenging fluid phenomena. ASME Symp. on Fully Separated Flows, pp. 102–118.
Moser, R. D. & Rogers, M. M. 1994 Direct simulation of a self-similar plane wake. AGARD Symp. on Application of Direct and Large Eddy Simulation, Crete, Greece, April 18–21, 1994.
Nakayama, A. 1987 Curvature and pressure-gradient effects on a small-defect wake. J. Fluid Mech. 175, 215–246.Google Scholar
Plesniak, M. W., Mehta, R. D. & Johnston, J. P. 1994 Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution. J. Fluid Mech. 270, 1–50.Google Scholar
Pot, P. J. 1979 Measurements in a 2-d wake and in a 2-d wake merging into a boundary layer. National Aerospace Laboratory Data Report, NLR TR-79063 U, The Netherlands.
Ramaprian, B. R., Patel, V. C. & Sastry, M. S. 1982 The symmetric turbulent wake of a flat plate. AIAA J. 20, 1228–1235.Google Scholar
Ramjee, V. & Neelakandan, D. 1989 Development of wake of a rectangular cylinder in a curved stream. Exps Fluids 7, 395–399.Google Scholar
Ramjee, V. & Neelakandan, D. 1990 Curvature effects on the wake of an airfoil and other bodies. Fluid Dyn. Res. 6, 1–13.Google Scholar
Ramjee, V., Tulapurkara, E. G. & Rajasekar, R. 1988 Development of airfoil wake in a longitudinally curved stream. AIAA J. 26, 948–953.Google Scholar
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. 1993a Spanwise scale selection in plane mixing layers. J. Fluid Mech. 247, 321–337.Google Scholar
Rogers, M. M. & Moser, R. D. 1993b The evolution of a self-similar turbulent plane wake. Bull. Am. Phys. Soc. 38, 2271.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
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.
Savill, A. M. 1983 The turbulence structure of a highly curved two-dimensional wake. In Structure of Complex Turbulent Shear Flow (ed. R. Dumas & L. Fulachier). Springer.
Taneda, S. 1959 Downstream development of the wakes behind cylinders. J. Phys. Soc. Japan 14, 843–848.Google Scholar
Towsend, A. A. 1956 Structure of Turbulent Shear Flow (1st Edn). Cambridge University Press.
Townsend, A. A. 1976 Structure of Turbulent Shear Flow (2nd Edn). Cambridge University Press.
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513–533.Google Scholar
Weygandt, J. H. & Mehta, R. D. 1993 Three-dimensional structure of straight and curved plane wakes. JIAA Rep. TR-110. Dept. of Aeronautics and Astronautics, Stanford University.
Williamson, C. H. K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.Google Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 31–71.Google Scholar