Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-20T01:45:31.975Z Has data issue: false hasContentIssue false
  • English
  • Français

The impact of a vortex ring on a wall

Published online by Cambridge University Press:  21 April 2006

J. D. A. Walker ,
C. R. Smith ,
A. W. Cerra  and
T. L. Doligalski
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA
C. R. Smith
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA
A. W. Cerra
Affiliation:
Steam Turbine Division, General Electric Corp., Boston, MA, USA
T. L. Doligalski
Affiliation:
US Army Research Office, Research Triangle Park, NC, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow induced by a vortex ring approaching a plane wall on a trajectory normal to the wall is investigated for an incompressible fluid which is otherwise stagnant. The detailed characteristics of the interaction of the ring with the flow near the surface have been observed experimentally for a wide variety of laminar rings, using dye in water to visualize the flow in the ring as well as near the plane surface. Numerical solutions are obtained for the trajectory of the ring as well as for the unsteady boundary-layer flow that develops on the wall. The experimental and theoretical results show that an unsteady separation develops in the boundary-layer flow, in the form of a secondary ring attached to the wall. A period of explosive boundary-layer growth then ensues and a strong viscous-inviscid interaction occurs in the form of the ejection of the secondary vortex ring from the boundary layer. The primary ring then interacts with the secondary ring and in some cases was observed to induce the formation of a third, tertiary, ring near the wall. The details of this process are investigated over a wide Reynolds number range. The results clearly show how one vortex ring can produce another, through an unsteady interaction with a viscous flow near the wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 99 - 140
Copyright
© 1987 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

Acarlar, M. S. & Smith, C. R. 1984 An experimental study of hairpin-type vortices as a potential flow structure of turbulent boundary layers. Report FM-5, Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pa.
Acarlar, M. S. & Smith, C. R. 1987a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protruberance. J. Fluid Mech. 175, 1–42.Google Scholar
Acarlar, M. S. & Smith, C. R. 1987b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.Google Scholar
Blasius, H. 1908 Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. angew. Math. Phys. 56, 1–37.Google Scholar
Bliss, D. B. 1970 The dynamics of curved rotational vortex lines. MS thesis. MIT.
Boldes, U. & Ferreri, J. C. 1973 Behavior of vortex rings in the vicinity of a wall. Phys. Fluids 16, 2005–2006.Google Scholar
Brasseur, J. G. & Chang, I.-D. 1981 Combination of kinematics with flow visualization to compute total circulation, AIAA J. 19, 878–884.Google Scholar
Cerra, A. W. & Smith, C. R. 1983 Experimental observations of vortex ring interaction with the fluid adjacent to a surface. Report FM-4. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA.
Dennis, S. C. R. & Walker, J. D. A. 1971 The initial flow past an impulsively started cylinder, J. Engng Maths 5, 263–278.Google Scholar
Didden, N. 1977 Untersuchung laminarer, instabiler Ringwirbel mittels Laser-Doppler-Anemometrie. Mitt Nr. 64, Göttingen: Max-Planck-Inst. Strömungsforschung.
Didden, N. & Ho, C.-M. 1985 Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235–256.Google Scholar
Doligalski, T. L. 1980 The influence of vortex motion on wall boundary layers. PhD thesis, Lehigh University.
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1980 A production mechanism for turbulent boundary layers. Prog. Astr. Aero. 72, 47–72.Google Scholar
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Ece, M. C., Walker, J. D. A. & Doligalski, T. L. 1984 The boundary layer on an impulsively started rotating and translating cylinder. Phys. Fluids 27, 1077–1089.Google Scholar
Ersoy, S. & Walker, J. D. A. 1985a Viscous flow induced by counter-rotating vortices. Phys. Fluids 28, 2687–2698.Google Scholar
Ersoy, S. & Walker, J. D. A. 1985b The viscous flow induced near a wall by counter-rotating vortex pairs and vortex loops. Report FM-8, Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA.
Fraenkel, L. E. 1972 Examples of steady vortex rings of small cross-section in an ideal fluid. J. Fluid Mech. 51, 119–135.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659–1660.Google Scholar
Helmholtz, H. 1867 On integrals of the hydrodynamic equations which express vortex motion. Phil. Mag. 33, 485–512.Google Scholar
Hicks, W. M. 1884 On the steady motion and the small vibrations of a hollow vortex. Phil. Trans. R. Soc. Lond. A 175, 161–195.Google Scholar
Jahnke, E. & Emde, F. 1945 Tables of Functions with Formulae and Curves. 4th edn. Dover.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Leonard, A. 1980 Vortex methods for flow stimulation. J. Comput. Phys. 37, 289–335.Google Scholar
Leonard, A. 1985 Three-dimensional vortex flows. Ann. Rev. Fluid Mech. 17, 523–559.Google Scholar
Magarvey, R. H. & MacLatchy, C. S. 1964 The formation and structure of vortex rings. Can. J. Phys. 42, 678–689.
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.Google Scholar
Milne-Thomson, L. M. 1963 Theoretical Hydrodynamics, 4th edn. Macmillan.
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 A visual study of turbulent shear flow. J. Fluid Mech. 61, 513–540.Google Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.Google Scholar
Riley, N. 1975 Unsteady laminar boundary layers. SIAM Rev. 17, 274–297.Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49, 371–380.Google Scholar
Saffman, P. G. 1975 On the formation of vortex rings. Stud. Appl. Maths 54, 261–268.Google Scholar
Saffman, P. G. & Baker, G. R. 1979 Vortex Interactions. Ann. Rev. Fluid Mech. 11, 95–122.Google Scholar
Sallet, D. W. & Widmayer, R. S. 1974 An experimental investigation of laminar and turbulent vortex rings in air. Z. Flugwiss 22, pp. 207–215.Google Scholar
Schneider, P. E. M. 1978a Morphologisch-phänomenologische Untersuchung der Umbildung von Ringwirbeln, die Körper anströmen, Göttingen: Max-Planck-Inst. Strömungsforchung.
Schneider, P. E. M. 1978b Werden, Bestehen, Instabilität, Regeneration. Vergehen eines Ringwirbels, Göttingen: Max-Planck-Inst. Strömungsforschung.
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215–235.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.Google Scholar
Sullivan, J. P., Widnall, S. E. & Ezekiel, S. 1973 Study of vortex rings using a laser doppler velocimeter. AIAA J. 11, 1384–1389.Google Scholar
Tung, C. & Ting, L. 1967 Motion and decay of a vortex ring. Phys. Fluids 10, 901–910.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating laminar boundary layer. J. Comp. Phys. 38, 125–140.Google Scholar
Walker, J. D. A. 1978 The boundary layer due to a rectilinear vortex. Proc. R. Soc. Lond. A 359, 167–188.Google Scholar
Walker, J. D. A., Scharhnorst, R. K. & Weigand, G. G. 1986 Wall layer models for the calculation of velocity and heat transfer in turbulent boundary layers. AIAA paper 86–0213.
Widnall, S. E., Bliss, D. B., Zalay, A. 1971 Theoretical and experimental study of the stability of a vortex pair. In Aircraft Wake Turbulence and its Detection (ed. G. Goldberg & R. Rogers), pp. 305–338. Oslo.
Widnall, S. E. & Sullivan, J. P. 1973 On the stability of vortex rings. Proc. R. Soc. Lond. A 332, 335–353.Google Scholar
Yamada, H. & Matsui, T. 1980 Visualization of vortex interaction using smoke-wire technique. International Symposium of Flow Visualization, Bochum, Germany, Ruhr-Universität Bochum, Inst. für Thermo und Fluiddynamik.