Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T08:57:39.146Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent structure in free-surface jet flows

Published online by Cambridge University Press:  26 April 2006

D. T. Walker ,
C.-Y. Chen  and
W. W. Willmarth
D. T. Walker
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109-2145, USA
C.-Y. Chen
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109-2145, USA
W. W. Willmarth
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Results of an experimental study of the interaction of a turbulent jet with a free surface when the jet issues parallel to the free surface are presented. Three different jets, with different exit velocities and jet-exit diameters, all located two jet-exit diameters below the free surface were studied. At this depth the jet flow, in each case, is fully turbulent before significant interaction with the free surface occurs. The effects of the Froude number (Fr) and the Reynolds number (Re) were investigated by varying the jet-exit velocity and jet-exit diameter. Froude-number effects were identified by increasing the Froude number from Fr = 1 to 8 at Re = 12700. Reynolds-number effects were identified by increasing the Reynolds number from Re = 12700 to 102000 at Fr = 1. Qualitative features of the subsurface flow and free-surface disturbances were examined using flow visualization. Measurements of all six Reynolds stresses and the three mean velocity components were obtained in two planes 16 and 32 jet diameters downstream using a three-component laser velocimeter. For all the jets, the interaction of vorticity tangential to the surface with its ‘image’ above the surface contributes to an outward flow near the free surface. This interaction is also shown to be directly related to the observed decrease in the surface-normal velocity fluctuations and the corresponding increase in the tangential velocity fluctuations near the free surface. At high Froude number, the larger surface disturbances diminish the interaction of the tangential vorticity with its image, resulting in a smaller outward flow and less energy transfer from the surface-normal to tangential velocity fluctuations near the surface. Energy is transferred instead to free-surface disturbances (waves) with the result that the turbulence kinetic energy is 20% lower and the Reynolds stresses are reduced. At high Reynolds number, the rate of evolution of the interaction of the jet with the free surface was reduced as shown by comparison of the rate of change with distance downstream of the local Reynolds and Froude numbers. In addition, the decay of tangential vorticity near the surface is slower than for low Reynolds number so that vortex filaments have time to undergo multiple reconnections to the free surface before they eventually decay.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 223 - 261
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

Anthony, D.G. 1990 The influence of a free surface on the development of turbulence in a submerged jet. PhD thesis, University of Michigan.
Anthony, D. G. & Willmarth, W. W. 1992 Turbulence measurements in a round jet near a free surface. J. Fluid Mech. 243, 699–720.Google Scholar
Brown, J. L. 1989 Geometric bias and time coincidence in 3-dimensional laser Doppler velocimeter systems. Exps Fluids 7, 25–32.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Davis, M. R. & Winarto, H. 1980 Jet diffusion from a circular nozzle above a solid wall. J. Fluid Mech. 101, 201–221.Google Scholar
Duncan, J. H. 1983 The breaking and non-breaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507–520.Google Scholar
Handler, R. A., Swean, T. F., Leighton, R. I. & Swearingen, J. D. 1993 Length scales and the energy balance for turbulence near a free surface. AIAA J. 31, 1998–2007.Google Scholar
Hecht, E. & Zajac, A. 1974 Optics. Addison-Wesley.
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Hirsa, A. & Willmarth, W. W. 1994 Measurements of vortex pair interaction with a clean or contaminated surface. J. Fluid Mech. 259, 25–45.Google Scholar
Hoekstra, M. 1991 Macro wake features of a range of ships. MARIN Rep. 410461–1-P. Maritime Research Institute Netherlands.
Hunt, J. & Graham, J. 1978 Free stream turbulence near plane boundaries. J. Fluid Mech. 84, 178–209.Google Scholar
Launder, B. E. & Rodi, W. 1983 The turbulent wall jet – measurements and modeling. Ann. Rev. Fluid Mech. 15, 429–459.Google Scholar
Liepmann, D. 1990 The near-field dynamics and entrainment field of submerged and near-surface jets. PhD thesis, University of California, San Diego.
Longuet-Higgins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.Google Scholar
Madnia, K. & Bernal, L. P. 1984 Interaction of a turbulent round jet with the free surface. J. Fluid Mech. 261, 305–332.Google Scholar
McLaughlin, D. K. & Tiederman, W. G. 1973 Biasing correction for individual realization laser anemometer measurements in turbulent flow. Phys. Fluids 16, 2082–2088.Google Scholar
Reed, A. M., Beck, R. F., Griffin, O. M. & Peltzer, R. D. 1990 Hydrodynamics of remotely sensed surface-ship wakes. Trans. Soc. Naval Archit. Mech. Engrs 98, 319–363.Google Scholar
Sterling, M. H., Gorman, M., Widmann, P. J., Coffman, S. C., Strozier, J. & Kiehn, R. M. 1987 Why are these disks dark? The optics of Rankine vortices. Phys. Fluids 30, 3624–3626.Google Scholar
Swean, T. F., Ramberg, S. E., Plesnia, M. W. & Stewart, M. B. 1989 Turbulent surface jet in a channel of limited depth. J. Hydraulic Engng 115, 1587–1606.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence MIT Press.
Walker, D. T. & Johnston, V. G. 1991 Observations of turbulence near the free surface in the wake of a model ship. In Dynamics of Bubbles and Vortices Near a Free Surface (ed. I. Sahin & G. Tryggvason). AMD-119. ASME.
Whiffen, M. C., Lau, J. C. & Smith, D. M. 1979 Design of LV experiments for turbulence measurements. In Laser Velocimetry and Particle Sizing (ed. H. D. Thompson & W. H. Stevenson), pp. 197–207. Hemisphere.
Willmarth, W. W. 1987 Design of a three-component fiber-optic laser-Doppler anemometer for wake measurements in a towing tank. Proc. Intl Towing Tank Conf. ITTC, Tokyo.
Wygananski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38, 577–612.Google Scholar