Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-21T10:25:20.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow induced by jets and plumes

Published online by Cambridge University Press:  20 April 2006

W. Schneider
W. Schneider
Affiliation:
Institut für Strömungslehre und Wärmeübertragung, Technische Universität Wien, Wiedner Hauptstraße 7, A-1040 Wien, Austria
Get access Rights & Permissions [Opens in a new window]

Abstract

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 55 - 65
Copyright
© 1981 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

Batchelor, G. K. 1970 An Introduction to Fluid Mechanics. Cambridge University Press.
Fujii, T. 1963 Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source. Int. J. Heat Mass Transfer 6, 597–606.Google Scholar
Kraemer, K. 1971 Die Potentialströmung in der Umgebung von Freistrahlen. Z. Flugwiss. 19, 93–104.Google Scholar
Mollendorf, J. C. & Gebhart, B. 1974 Axisymmetric natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Proc. 5th Int. Heat Transfer Conf., Tokyo, vol. v, pp. 10–14.
Morgan, A. J. A. 1956 On a class of laminar viscous flows within one or two bounding cones. Aero. Quart. 7, 225–239.Google Scholar
Potsch, K. 1981 Laminare Freistrahlen im Kegelraum. Z. Flugwiss. Weltraumforschung 5, 44–52.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Clarendon.
Rotta, J. C. 1972 Turbulente Strömungen. Teubner.
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.
Serrin, J. 1971 The swirling vortex. Phil. Trans. Roy. Soc. A 271, 325–360.Google Scholar
Squire, H. B. 1952 Some viscous fluid flow problems. I: Jet emerging from a hole in a plane wall. Phil. Mag. 43, 942–945.Google Scholar
Taylor, G. I. 1958 Flow induced by jets. J. Aero/Space Sci. 25, 464–465.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.