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Decay of momentum flux in submerged jets

Published online by Cambridge University Press:  20 April 2006

Wilhelm Schneider
Wilhelm Schneider
Affiliation:
Technische Universität Wien, Austria
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Abstract

Slender laminar and turbulent, plane and axisymmetric jets emerging from orifices in plane or conical walls are studied at large distances from the orifices. The entrainment of momentum coupled with the entrainment of volume into a jet is determined, and its effect on the flow field is analysed by combining inner and outer expansions with a multiple scaling approach.

In turbulent (plane or axisymmetric) jets, the axial velocity decreases more rapidly than predicted by classical boundary-layer solutions, and the momentum flux vanishes as the distance from the orifice tends to infinity. The analysis unveils a source of discrepancies in previous experimental data on turbulent jets.

In a laminar plane jet, the momentum flux changes but little. In a laminar axisymmetric jet, the momentum flux changes slowly, yet considerably. When a critical distance from the orifice is approached, the momentum flux in the jet becomes very small, the jet diameter very large, and a toroidal viscous eddy is predicted. The structure of the flow field is briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 91 - 110
Copyright
© 1985 Cambridge University Press

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References

Andrabe, E. N. Da C. 1939 The velocity distribution in a liquid-into-liquid jet. Part 2. The plane jet. Proc. Phys. Soc. 51, 784–793.Google Scholar
Bickley, W. 1937 The plane jet. Phil. Mag. 23, 727–731.Google Scholar
Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Blake, J. R. 1979 On the generation of viscous toroidal eddies in a cylinder. J. Fluid Mech. 95 209–222.Google Scholar
Bradbury, L. J. S. 1965 The structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23, 31–64.Google Scholar
Chanaud, R. C. & Powell, A. 1962 Experiments concerning the sound-sensitive jet. J. Acoust. Soc. Am. 34, 907–915.Google Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.Google Scholar
Goldschmidt, V. 1964 Two-phase flow in a two-dimensional turbulent jet. Ph.D. thesis. Syracuse University.
Goldschmidt, V. & Eskinazi, S. 1966 Two phase turbulent flow in a plane jet. Trans. ASME E: J. Appl. Mech. 33, 735–747Google Scholar
Goldschmidt, V. W., Moallemi, M. K. & Oler, J. W. 1983 Structures and flow reversal in turbulent plane jets. Phys. Fluids 26, 428–432.Google Scholar
Görtler, H. 1942 Berechnung von Aufgaben der freien Turbulenz auf Grund eines neuen Näherungsansatzes. Z. angew. Math. Mech. 22, 244–254.Google Scholar
Hanel, B. & Richter, E. 1979 Das Verhalten von Freistrahlen in verschiedenen Reynolds-Zahlbereichen. Luft- und Kältetechnik 1979, 12–17.Google Scholar
Heskestad, G. 1965 Hot wire measurements in a plane turbulent jet. Trans. ASME E: J. Appl. Mech. 32, 721–734 (Erratum 33, 710.)Google Scholar
Hussain, A. K. M. F. & Clark, A. R. 1977 Upstream influence on the near field of a plane turbulent jet. Phys. Fluids 20, 1416–1426.Google Scholar
Kotsovinos, N. E. 1975 A study of the entrainment and turbulence in a plane turbulent jet. W. M. Keck Lab. Hydraul. Water Resources, Calif. Inst. Tech. Rep. KH-R-32.Google Scholar
Kotsovinos, N. E. 1978 A note on the conservation of the axial momentum of a turbulent jet. J. Fluid Mech. 81, 55–63.Google Scholar
Kraemer, K. 1971 Die Potentialströmung in der Umgebung von Freistrahlen. Z. Flugwiss. 19, 93–104.Google Scholar
Liron, N. & Blake, J. R. 1981 Existence of viscous eddies near boundaries. J. Fluid Mech. 107, 109–129.Google Scholar
Miller, D. R. & Comings, E. W. 1957 Static pressure distribution in the free turbulent jet. J. Fluid Mech. 3, 1–16.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn p. 647. Macmillan.
Mitsotakis, K., Schneider, W. & Zauner, E. 1984 Second-order boundary-layer theory of laminar jet flows. Acta Mech. 53, 115–123.Google Scholar
Mollendorf, J. C. & Gebhart, B. 1973 An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without thermal buoyancy for symmetric and asymmetric disturbances. J. Fluid Mech. 61, 367–399.Google Scholar
Mörwald, K. 1984 Asymptotische Theorie 2. Ordnung für laminare, auftriebslose und auftriebserzeugte Freistrahlen. Diplomarbeit, Technische Universität Wien.
Plaschko, P. 1979 Helical instabilities of slowly divergent jets. J. Fluid Mech. 92, 209–215.Google Scholar
Potsch, K. 1981 Laminare Freistrahlen im Kegelraum. Z. Flugwiss. Weltraumforschung 5, 44–52.Google Scholar
Rankin, G. W., Sridhar, K., Arulraja, M. & Kumar, K. R. 1983 An experimental investigation of laminar axisymmetric submerged jets. J. Fluid Mech. 133, 217–231.Google Scholar
Reichardt, H. 1942 Gesetzmäßigkeiten der freien Turbulenz. VDI-Forschungsheft 414.
Reynolds, A. J. 1962 Observations of a liquid-into-liquid jet. J. Fluid Mech. 14, 552–556.Google Scholar
Ricou, F. P. & Spalding, D. B. 1961 Measurement of entrainment by axisymmetric turbulent jets. J. Fluid Mech. 11, 21–32.Google Scholar
Bosenhead, L. (ed.) 1963 Laminar Boundary Layers, pp. 150–155. Clarendon Press.
Rubin, S. G. & Falco, R. 1968 Plane laminar jet. AIAA J. 6, 186–187.Google Scholar
Sato, H. & Sakao, F. 1964 An experimental investigation of the instability of a two-dimensional jet at low Reynolds numbers. J. Fluid Mech. 20, 337–352.Google Scholar
Schlichting, H. 1933 Laminare Strahlausbreitung. Z. angew. Math. Mech. 13, 260–263.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory, 7th ed. McGraw-Hill.
Schneider, W. 1981 Flow induced by jets and plumes. J. Fluid Mech. 108, 55–65.Google Scholar
Schneider, W. 1983 Asymptotic analysis of jet flows. Invited lecture, XVIth Symposium on Advanced Problems and Methods in Fluid Mechanics, Spala, Poland; to be published in Fluid Dyn. Trans. vol. 12.
Sforza, P. M. & Mons, R. F. 1978 Mass, momentum, and energy transport in turbulent free jets. Intl J. Heat Mass Transfer 21, 371–384.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
Stewart, R. W. 1956 Irrotational motion associated with free turbulent flows. J. Fluid Mech. 1, 593–604.Google Scholar
Taylor, G. I. 1958 Flow induced by jets. J. Aero. Sci. 25, 464–465.Google Scholar
Tollmien, W. 1926 Berechnung turbulenter Ausbreitungsvorgänge. Z. angew. Math. Mech. 6, 468–478; [English transl. NACA TM 1085 (1945)].Google Scholar
Townsend, A. A. 1956, 1976 The Structure of Turbulent Shear Flow. 1st and 2nd ed. Cambridge University Press.
Wygnanski, I. 1964 The flow induced by two-dimensional and axisymmetric turbulent jets issuing normally from an infinite plane surface, Aeron. Q. 15, 373–380.Google Scholar
Zauner, E. 1984 Beiträge zum Einfluß von Auftrieb und Zuströmung auf Freistrahlen. Dissertation, Technische Universität, Wien.
Zauner, E. 1985 Visualization of the viscous flow induced by a round jet. J. Fluid Mech. 154, 111–119.Google Scholar