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Transport processes in dilute gases over the whole range of Knudsen numbers. Part 2. Ultrasonic sound waves

Published online by Cambridge University Press:  19 April 2006

L. C. Woods  and
H. Troughton
L. C. Woods
Affiliation:
Mathematical Institute, Oxford University
H. Troughton
Affiliation:
Mathematical Institute, Oxford University
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Abstract

In part 1 (Woods 1979) generalized constitutive relations for the fluid stress p and the heat flux q were established by mean-free-path arguments. These relations are expected to hold over a wide range of Knudsen numbers K, but in the earlier paper, which presented the general theory, they were successfully tested only to O(K2), the order to which the Burnett constitutive equations are valid. It remains to verify the general theory at much higher K values, and to this end we have applied it to the propagation of forced sound waves in a rarefied monatomic gas.

Theories for such waves (based on the linearized Boltzmann equation) are available, and there are also experimental results for the speed and attenuation of waves up to K values of about 10. Our theory is in good agreement with experiment in the range 0 < K < 1. For K > 1 we obtain close agreement with experimental values of the wave speed, but as wave damping in this range is largely due to the unavoidable proximity of the wave transmitter – an effect not included in our calculations – we have found smaller values of the attenuation than obtaining in the experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 2 , 25 September 1980 , pp. 321 - 331
Copyright
© 1980 Cambridge University Press

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References

Buckner, J. K. & Ferziger, J. H. 1966 Phys. Fluids 9, 2309–2314, 2315–2322.
Cercignani, C. 1975 Theory and Application of the Boltzmann Equation. Scottish Academic.
Greenspan, M. 1956 J. Acoust. Soc. Am. 28, 644–648.
Hanson, F. B. & Morse, T. F. 1969 Phys. Fluids 12, 1564–1572.
Maidanik, G., Fox, H. L. & Heckl, M. 1965 Phys. Fluids 8, 259–265.
Maidanik, G. & Fox, H. L. 1965 J. Acoust. Soc. Am. 38, 477–478.
Meyer, E. & Sessler, G. 1957 Z. Phys. 149, 15–39.
Sirovich, L. & Thurber, J. K. 1965a J. Acoust. Soc. Am. 37, 329–339.
Sirovich, L. & Thurber, J. K. 1965b J. Acoust. Soc. Am. 38, 478–480.
Woods, L. C. 1965 J. Fluid Mech. 23, 315–323.
Woods, L. C. 1979 J. Fluid Mech. 93, 585–608.