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Testing continuum descriptions of low-Mach-number shock structures

Published online by Cambridge University Press:  26 April 2006

Gerald C. Pham-Van-Diep ,
Daniel A. Erwin  and
E. Phillip Muntz
Gerald C. Pham-Van-Diep
Affiliation:
University of Southern California, Department of Aerospace Engineering, Los Angeles, CA 90089–1191, USA
Daniel A. Erwin
Affiliation:
University of Southern California, Department of Aerospace Engineering, Los Angeles, CA 90089–1191, USA
E. Phillip Muntz
Affiliation:
University of Southern California, Department of Aerospace Engineering, Los Angeles, CA 90089–1191, USA
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Abstract

Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier—Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater than 1.2, the Burnett predictions are more accurate than the Navier—Stokes results. Temperature—density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 403 - 413
Copyright
© 1991 Cambridge University Press

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