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On the continuum theory for the large Reynolds number spherical expansion into a near vacuum

Published online by Cambridge University Press:  29 March 2006

N. C. Freeman ,
R. S. Johnson ,
S. Kumar  and
W. B. Bush
N. C. Freeman
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
R. S. Johnson
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
S. Kumar
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England Present address: Computer Centre, Hatfield Polytechnic, Hatfield, England.
W. B. Bush
Affiliation:
Department of Applied Mechanics and Engineering Science, University of California, San Diego
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Abstract

The steady, spherically symmetric flow of a compressible gas is considered. The gas is both viscous and heat-conducting. In the limit of very high Reynolds number (= α−1, α → 0) and correspondingly low pressure at infinity, the structure of the whole flow field is discussed. The five regions that arise by virtue of the limit α → 0 are briefly considered. Special care is given to the matching across the overlap domains and the first region (close to, but outside, the sonic point) and the fifth (where the pressure adjusts to its ambient value) are carefully examined. It is argued that the application of appropriate matching principles, together with judicious use of numerical solutions, allows an arbitrary pressure and temperature to be assigned to the background gas.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 4 , 29 April 1975 , pp. 625 - 638
Copyright
© 1975 Cambridge University Press

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References

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