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On the response of a sphere to an acoustic pulse

Published online by Cambridge University Press:  29 March 2006

Samuel Temkin
Samuel Temkin
Affiliation:
Department of Mechanical Engineering, Rutgers University, New Brunswick
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Abstract

The motion of a rigid sphere responding to the passage of an acoustic pulse is considered by means of a simple approximate model which neglects the diffraction of the pulse front. The model is based on a solution of the equivalent inviscid problem and assumes that, initially, the flow field around the sphere corresponds to the steady incompressible flow of an inviscid fluid over a sphere at rest. For t > 0, the motion is studied by means of the unsteady Stokes equations. Results for the sphere's velocity, displacement and drag are obtained in closed form in terms of tabulated functions and compared with results obtained by using the Stokes drag. It is found that, when the ratio of gas density to sphere material density is finite, the initial response of the sphere differs considerably from that predicted by the use of the Stokes drag. However, when the ratio of gas density to sphere material density is infinitesimal, the differences disappear. These results may be of some importance in the study of shock-induced droplet collisions in aerosol clouds.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 2 , 25 July 1972 , pp. 339 - 349
Copyright
© 1972 Cambridge University Press

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References

Abramowitz, B. M. & Stegun, I. A. (eds.) 1964 Handbook of Mathematical Functions, Graphs, and Mathematical Tables. Washington: U.S. Government Printing Office.
Basset, A. B. 1888 Phil. Trans. 179, 43.
Crowe, C. T. & Willoughby, P. G. 1966 A.I.A.A. J. 4, 1677.
Fuchs, N. A. 1964 The Mechanics of Aerosols. Macmillan.
Goyer, G. G. 1965a Nature, 206, 1203.
Goyer, G. G. 1965b Nature, 206, 1302.
Hoenig, S. A. 1957 J. Appl. Phys. 28, 1218.
Marble, F. 1967 Astronautica Acta, 13, 159.
Milne-Thompson, L. M. 1950 Theoretical Hydrodynamics. Macmillan.
Ockendon, J. R. 1968 J. Fluid Mech. 34, 229.
Pearcey, T. & Hill, G. W. 1956 Austra. J. Phys. 9, 19.
Roberts, G. E. & Kaufman, H. 1966 Table of Laplace Transforms. Philadelphia: W. B. Saunders.
Rudinger, G. 1964 Phys. Fluids, 7, 658.
Temkin, S. 1969 J. Atmos. Sci. 26, 776.
Temkin, S. 1970 Phys. Fluids, 13, 1639.
Temkin, S. & Dobbins, R. A. 1966 J. Acoust. Soc. Am. 40, 317.
Yih, C.-S. 1969 Fluid Mechanics, p. 375. McGraw-Hill.
Yun, K. W. 1970 Ph.D. thesis, Oregon State University, Cornvallis.