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A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

Published online by Cambridge University Press:  29 March 2006

N. C. Freeman  and
S. Kumar
N. C. Freeman
Affiliation:
School of Mathematics, University of Newcastle-upon-Tyne
S. Kumar
Affiliation:
School of Mathematics, University of Newcastle-upon-Tyne
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Abstract

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 2 , 19 June 1973 , pp. 391 - 396
Copyright
© 1973 Cambridge University Press

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References

Brook, J. W. & Hamel, B. B. 1972 Phys. Fluids, 15, 1898–1912.
Bush, W. B. & Rosen, R. 1971 SIAM J. Appl. Math. 21, 393–406.
Freeman, N. C. & Kumar, S. 1972 J. Fluid Mech. 56, 523–532.
Ladyzhenskii, M. D. 1962 Prikl. Math. Mech. 26, 642–649.