Journal of Engineering Mathematics

, Volume 26, Issue 2, pp 339–348 | Cite as

The swirling round laminar jet

  • Wei-Shien Hwang
  • Allen T. Chwang
Article
Received:
Accepted:
  • 129 Downloads

Abstract

The swirling round laminar jet in an unbounded viscous fluid is investigated in this paper. The axisymmetric laminar jet with a swirling velocity is simulated by a linear-momentum source and an angular-momentum source, both located at the origin. The first-order and the second-order solutions in the far field have been obtained by solving the complete Navier—Stokes equations. It is found that the first-order solution is the well-known round-laminar-jet solution without the swirling velocity obtained by Landau [2] and Squire [3]. The second-order solution represents a pure rotating flow. The swirling velocity predicted by the present solution is compared with that obtained by Loitsyanskii [15] and Görtler [16], who solved the corresponding boundary-layer equations. It is found that the swirling velocity predicted by the present theory is smaller than that obtained from the boundary-layer equations.

Keywords

Mathematical Modeling Industrial Mathematic Stokes Equation Viscous Fluid Present Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T.G. Hughes, R.B. Smith and D.H. Kiley, Stored chemical energy propulsion systems for underwater applications. AIAA J. Energy 7 (1983) 128–133.Google Scholar
  2. 2.
    L.D. Landau, A new exact solution of the Navier-Stokes equations. Dokl. Ak. Nauk. S.S.S.R. 43 (1944) 286–288.Google Scholar
  3. 3.
    H.B. Squire, The round laminar jet. Quart. J. Mech. Appl. Math. 4 (1951) 321–329.Google Scholar
  4. 4.
    H. Schlichting, Laminare strahlausbreitung. ZAMM 13 (1933) 260–263.Google Scholar
  5. 5.
    C. Sozou and W.M. Pickering, The round laminar jet: the development of the flow field. J. Fluid Mech. 80 (1977) 673–683.Google Scholar
  6. 6.
    C. Sozou, Development of the flow field of a point force in an infinite fluid. J. Fluid Mech. 91 (1979) 541–546.Google Scholar
  7. 7.
    G.I. Taylor, Flow induced by jets. J. Aero Sci. 25 (1958) 464–465.Google Scholar
  8. 8.
    K. Kraemer, Die Potentialstromung in der Umgebung von Freistrahlen. Z. Flugwiss. 19 (1971) 93–104.Google Scholar
  9. 9.
    H.B. Squire, Some viscous fluid flow problem. I: Jet emerging from a hole in a plane wall. Phil. Mag. 43 (1952) 942–945.Google Scholar
  10. 10.
    A.J.A. Morgan, On a class of laminar viscous flows within one or two bounding cones. Aero. Quart. 7 (1956) 225–239.Google Scholar
  11. 11.
    K. Potsch, Laminare Freistrahlen im Kegelraum. Z. Flugwiss. Weltraumforschung 5 (1981) 44–52.Google Scholar
  12. 12.
    W. Schneider, Flow induced by jets and plumes. J. Fluid Mech. 108 (1981) 55–65.Google Scholar
  13. 13.
    W. Schneider, Decay of momentum flux in submerged jets. J. Fluid Mech. 154 (1985) 91–110.Google Scholar
  14. 14.
    E. Zauner, Visualization of the viscous flow induced by a round jet. J. Fluid Mech. 154 (1985) 111–119.Google Scholar
  15. 15.
    L.G. Loitsyanskii, Motion of a swirling jet in an unbounded space filled with the same fluid. Prikl. Mat. Mekh. 17 (1953) 3–16.Google Scholar
  16. 16.
    H. Görtler, Theoretical investigation of the laminar boundary layer. Problem II — decay of swirl in an axially symmetrical jet, far from the orifice, Report for United States Air Force (Office of Scientific Research) Contract No. AF61 (514)-627-C (1954).Google Scholar
  17. 17.
    S.V. Fal'kovich, Spreading of a twisted stream in an infinite space flooded by the same fluid. Prikl. Mat. Mekh. 31 (1967) 304–310.Google Scholar
  18. 18.
    A.V. Zubtsov, A self-similar solution for a weakly swirling jet. Fluid Dyn. 19 (1984) 550–554.Google Scholar
  19. 19.
    I. Wygnanski, Swirling axisymmetrical laminar jet. The Physics of Fluids 13 (1970) 2455–2460.Google Scholar
  20. 20.
    R.R. Long, A vortex in an infinite viscous fluid. J. Fluid Mech. 11 (1961) 611–624.Google Scholar
  21. 21.
    M.R. Foster and P.W. Duck, Inviscid stability of Long's vortex. Phys. Fluids 25 (1982) 1715–1718.Google Scholar
  22. 22.
    M.R. Foster and F.T. Smith, Stability of Long's vortex at large flow force. J. Fluid Mech. 206 (1989) 405–432.Google Scholar
  23. 23.
    C.-S. Yih, F. Wu, A.K. Garg and S. Leibovich, Conical vortices: a class of exact solutions of the Navier-Stokes equations. Physics of Fluids 25 (1982) 2147–2158.Google Scholar
  24. 24.
    G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge: University Press (1967) pp. 205–211.Google Scholar
  25. 25.
    J.A. Geurst, Momentum-flux condition for Landau-Squire jet flow. J. Appl. Math. Phys. (ZAMP) 37 (1986) 666–672.Google Scholar
  26. 26.
    A.T. Chwang and T.Y. Wu, Hydrodynamics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67 (1975) 787–815.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Wei-Shien Hwang
    • 1
  • Allen T. Chwang
    • 1
  1. 1.Department of Mechanical Engineering, Institute of Hydraulic ResearchThe University of IowaIowa CityU.S.A.

Personalised recommendations