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Two-dimensional incompressible fluid jet penetration

Published online by Cambridge University Press:  28 March 2006

D. F. Hopkins
Affiliation:
Douglas Aircraft Company, Santa Monica, California
J. M. Robertson
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana

Abstract

The principal characteristics of jet penetration are the appearance of free stream-lines at the sides of the jet and of a dividing streamline, which separates the jet and penetrated fluid. Kinematic analysis of such flow via free-streamline theory and the notched hodograph is developed with one unspecified parameter, the ratio of jet to counterstream velocity in the steady flow case. The kinetics of the problem, appearing when the jet and penetrated (or counterstream) fluid differ in density, is simply related to the kinematic solution via the square root of the density ratio. Experiments, both steady state and transient with several liquids, are presented which generally verify the theory. The experiments also yield information on the magnitude of the parameter and indicate its variation with the density ratio.

Type
Research Article
Copyright
© 1967 Cambridge University Press

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References

Banks, R. B. & Bhavamai, A. 1965 Experimental study of the impingement of a liquid jet on the surface of a heavier liquid J. Fluid. Mech. 23, 229240.Google Scholar
Banks, R. B. & Chandrasekhara, D. V. 1963 Experimental investigation of the penetration of a high-velocity gas jet through a liquid surface J. Fluid Mech. 15, 1334.Google Scholar
Baron, J. R. & Alzner, E. 1963 An experimental investigation of a two-layer inviscid shock cap due to blunt-body nose injection J. Fluid Mech 15, 44245.Google Scholar
Birkhoff, G. 1948 Remarks on streamlines of discontinuity Rev. Cienc. Lima, Peru, 50, 105.Google Scholar
Birkhoff, G. & Caywood, T. 1949 Fluid flow patterns J. Appl. Phys. 20, 646.Google Scholar
Birkhoff, G., Macdougall, D. P., Pugh, E. M. & Taylor, G. I. 1948 Explosives with lined cavities J. Appl. Phys. 19, 563.Google Scholar
Charczenko, N. & Hennessey, K. W. 1961 Investigation of a retro-rocket exhausting from the nose of a blunt body into a supersonic free stream. NASA TN D-751.
Ehrich, F. F. 1953 Penetration and deflection of jets oblique to a general stream J. Aero. Sci. 20, 99104.Google Scholar
Eichelberger, R. J. 1956 Experimental test of the theory of penetration of metallic jets J. Appl. Phys. 27, 63.Google Scholar
Hopkins, D. F. 1962 A study of fluid jet penetration. Ph.D. thesis, Dept. of Mechanical Engineering, Univ. of Illinois, Urbana.
Lee, Dana 1932 Experiments on the distribution of fuel in fuel sprays. NACA Rept. no. 438.Google Scholar
Miller, H. E. & Beardsley, E. G. 1926 Spray penetration with a simple fuel injection nozzle. NACA Rept. no. 22.Google Scholar
Pack, D. C. & Evans, W. M. 1951 Penetration by high velocity jets. Phys. Soc. Proc. B 64, part 4.Google Scholar
Rao, T. R. K. 1958 Investigation of the penetration of a jet into a counterflow. M. S. thesis, Dept. of Mechanics and Hydraulics, University of Iowa, Iowa City.
Robertson, J. M. 1965 Hydrodynamics in Theory and Application. Englewood Cliffs, N.J.: Prentice-Hall.
Romeo, D. J. & Sterrett, J. R. 1963 Exploratory investigation of the effect of a forward-facing jet on the bow shock of a blunt body in a Mach number 6 free stream. NASA TN D-1605.
Roshko, A. 1954 A new hodograph for free-streamline theory. NACA TN 3168; also 1955 On the wake and drag of bluff bodies. J. Aero. Sci. 22, 124–32.
Singh, S. 1957 Penetration by high-speed metallic jets. Proc. Phys. Soc. 70, B, 867.Google Scholar
Stalder & Inouye, M. 1956 A method of reducing heat transfer to blunt bodies by air injection. NACA RM A 56 B 27 a.
Warren, C. H. E. 1960 An experimental investigation of the effects of ejecting a coolant gas at the nose of a bluff body J. Fluid Mech. 8, 40017.Google Scholar
Wuest, W. & Von Trotha, H. 1964 Reibungslose Strömung an Flügelnasen mit Ausblasen eines anderen Gases J. Mécanique, 3, 32343.Google Scholar