Viscosity of argon at temperatures >2000 K from measured shock thickness

Macrossan, Michael N. and Lilley, Charles R. (2003) Viscosity of argon at temperatures >2000 K from measured shock thickness. Physics of Fluids, 15 11: 3452-3457. doi:10.1063/1.1616556

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Author Macrossan, Michael N.
Lilley, Charles R.
Title Viscosity of argon at temperatures >2000 K from measured shock thickness
Journal name Physics of Fluids   Check publisher's open access policy
ISSN 1070-6631
Publication date 2003-11
Sub-type Article (original research)
DOI 10.1063/1.1616556
Open Access Status File (Author Post-print)
Volume 15
Issue 11
Start page 3452
End page 3457
Total pages 6
Place of publication U.S.A.
Publisher American Institute of Physics
Collection year 2003
Language eng
Subject 240502 Fluid Physics
690302 Space transport
0203 Classical Physics
Abstract Mott-Smith's approximate theory of plane 1D shock structure (Phys. Rev., 82, 885-92, 1951; Phys. Rev., 5, 1325-36, 1962) suggests, for any intermolecular potential, the average number of collisions undergone by a molecule as it crosses the shock quickly approaches a limit as the Mach number increases. We check this with DSMC calculations and show that it can be used to estimate the gas viscosity at high temperatures from measurements of shock thickness. We consider a monatomic gas(gamma = 5/3) for five different collision models and hence five different viscosity laws mu = mu(T). The collision models are: the variable hard sphere, sigma ~ 1/g^upsilon, with three values of upsilon; the generalized hard sphere; and the Maitland-Smith potential. For shock Mach numbers M_1 greater than 4.48, all these collision models predict a shock thickness Delta = 11.0 lambda_s, where lambda_s is a suitably defined 'shock length scale', with a scatter approximately 2.5% (2 standard deviations). This shock length depends on the upstream flow speed, downstream density and a collision cross-section derived from the viscosity of the gas at a temperature T_g, characteristic of the collisions at relative speed g = u_1-u_2 between upstream and downstream molecules. Using Delta = 11 lambda_s and the experimental measurements of shock thickness in argon given by Alsmeyer (J. Fluid Mech. {74}, 498-513, 1976), we estimate the viscosity of argon at high values of T_g. These estimated values agree with the viscosity of argon recommended by the CRC Handbook of Chemistry and Physics (2001) at T approximately equal to 1,500 K. For T>2,000K, for which there appears to be no reliable direct measurements of viscosity, our estimated values lie between the extrapolated values recommended by the CRC Handbook and those predicted by the simple power law mu = mu__ref(T/T_ref ^0.72, with T_ref = 30 K and mu_ref = 2.283e-5 Pa s. Taking the error in the experimental measurements of Delta as the scatter in the results of Alsmeyer plus or minus 2%, we estimate the uncertainty in the viscosity deduced from the shock thickness measurements as less than plus or minus 5%. To this accuracy, our results agree with the power law predictions and disagree with the CRC Handbook values, for T > 3,000K.
Keyword Argon viscosity
High temperature viscosity
Shock thickness
Simple theory
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