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

Abstract

Mott-Smith’s kinetic theory of shock structure [Phys. Rev. 82, 885 (1951); C. Muckenfuss, Phys. Fluids 5, 1325 (1962)] suggests that, for any intermolecular potential, the average number of collisions undergone by a molecule as it crosses the shock approaches a limit as the Mach number increases. We check this with direct simulation Monte Carlo calculations and use it to estimate the gas viscosity at high temperatures from measurements of shock thickness. We consider a monatomic gas (γ=5/3) for five different collision models and hence five different viscosity laws μ=μ(T). The collision models are: the variable hard sphere, σ∝1/g2v, with three values of v; the generalized hard sphere; and the Maitland–Smith potential. For shock Mach numbers M1≳4.48, all these collision models predict a shock thickness Δ=11.0λs±2.5%, where λs is a suitably defined “shock length scale” which depends on a collision cross section derived from the viscosity of the gas at a temperature Tg, characteristic of the collisions between upstream and downstream molecules. Using Δ=11λs and the experimental measurements of shock thickness in argon given by Alsmeyer [J. Fluid Mech. 74, 498 (1976)], we estimate the viscosity of argon at high values of Tg. These estimates agree with the values recommended by the CRC Handbook of Chemistry and Physics, 82nd ed. (CRC Press, Boca Raton, FL, 2001) at T≈1500 K. For T≳2000 K, for which there appear to be no reliable direct measurements of viscosity, our estimated values lie between those recommended by the CRC Handbook and those predicted by the simple power law μ=μref(T/Tref)0.72, with Tref=300 K and μref=2.283×10−5 Pa s. Taking the error in the experimental measurements of Δ as the scatter in the results of Alsmeyer (±2%), we estimate the uncertainty in the viscosity predictions as less than ±5%. To this accuracy, our results agree with the power law predictions and disagree with the CRC Handbook values, for T≳3000 K.