An exact partial solution to the compressible flow problems of jet formation and penetration in plane, steady flow
Author:
Robert R. Karpp
Journal:
Quart. Appl. Math. 42 (1984), 15-29
MSC:
Primary 76N10; Secondary 76G05
DOI:
https://doi.org/10.1090/qam/736502
MathSciNet review:
736502
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Abstract: A partial solution to the problem of the symmetric impact of two compressible fluid streams is derived. The plane, two-dimensional flow is assumed to be steady, and the inviscid, compressible fluid is of the Chaplygin (tangent gas) type. The equations governing this flow are transformed to the hodograph plane where an exact, closed-form solution for the stream function is obtained. The distribution of fluid properties along the plane of symmetry and the shape of free surface streamlines are determined by transformation back to the physical plane. The problem of a compressible fluid jet penetrating an infinite target of similar material is also solved by considering a limiting case of this solution. Differences between compressible and incompressible flows of the type considered are illustrated.
G. R. Cowan and A. H. Holtzman, Flow configurations in colliding plates: explosive bonding, J. Appl. Phys. 34, 928–939 (1963)
G. Birkhoff, D. P. MacDougall, E. M. Pugh, and G. I. Taylor, Explosives with lined cavities, J. Appl. Phys. 19, 563–582 (1948)
E. M. Pugh, R. J. Eichelberger, and N. Rostoker, Theory of jet formation by charges with lined conical cavities, J. Appl. Phys. 23, 532–536 (1952)
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948. MR 0029615
R. R. Karpp, An exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration, Los Alamos Scientific Laboratory report LA-8371, Los Alamos, New Mexico (October 1980)
- Garrett Birkhoff and E. H. Zarantonello, Jets, wakes, and cavities, Academic Press Inc., Publishers, New York, 1957. MR 0088230
- L. M. Milne-Thomson, Theoretical Hydrodynamics, The Macmillan Company, New York, N. Y., 1950. 2nd ed. MR 0033660
G. R. Cowan and A. H. Holtzman, Flow configurations in colliding plates: explosive bonding, J. Appl. Phys. 34, 928–939 (1963)
G. Birkhoff, D. P. MacDougall, E. M. Pugh, and G. I. Taylor, Explosives with lined cavities, J. Appl. Phys. 19, 563–582 (1948)
E. M. Pugh, R. J. Eichelberger, and N. Rostoker, Theory of jet formation by charges with lined conical cavities, J. Appl. Phys. 23, 532–536 (1952)
R. Courant and K. O. Friedrichs, Supersonic flow and shock waves (Interscience Publishers, Inc., New York, 1948), pp. 247–252
R. R. Karpp, An exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration, Los Alamos Scientific Laboratory report LA-8371, Los Alamos, New Mexico (October 1980)
G. Birkhoff and E. H. Zarantonello, Jets, wakes, and cavities (Academic Press, Inc., New York, 1957), pp. 185–189
L. M. Milne-Thomson, Theoretical hydrodynamics, 2nd Ed. (The Macmillan Co., New York, 1950), pp. 273–280
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Article copyright:
© Copyright 1984
American Mathematical Society