Linear dependence of the bulk viscosity on shock wave thickness

Abstract

Currently, the bulk viscosity μb of a gas can only be obtained with an acoustic absorption experiment. A method is proposed that is primarily applicable to a dense polyatomic gas. In this circumstance, the density-based thickness Λρ is large, consisting of many thousands of mean-free paths. Moreover, the ratio μb/μ (μ is the shear viscosity) is linear with this thickness. Consequently, shock measurements of Λρ can be used to evaluate μb. The approach is illustrated using sulfur hexaflouride.

Effect of bulk viscosity in supersonic flow past spacecraft

“…However in the [7,9] it is shown that taking account of bulk viscosity in NS equations can substantially increase SW thickness and give density profiles close to experimental ones.…”

“…Some authors [8,9,12], using the relation μ b μ ≈ Z , take in some model hydrodynamic problems μ b ≈ 1000μ for carbon dioxide at room temperature. However, one should remember that the linear relations for the stress tensor (and also for a heat flow) hold only for small deviations from equilibrium (since the Chapman-Enskog method holds under the assumption of a weak deviations from equilibrium).…”

“…In papers [7,9] authors studied effect of bulk viscosity on one-dimensional shock wave structure. It has been shown, that taking into account BVC can strongly affect the solution and reduce discrepancies with the experimental profiles.…”

“…Emanuel et al [8][9][10] showed that taking account of the bulk viscosity can strongly affect the flow characteristics. They studied two problems.…”

A note on Stokes’ hypothesis

“…As a matter of fact, only in very particular conditions will the term κdivV be comparable to the thermodynamic pressure. This may happen, for instance, when the fluid is characterized by large values of κ (e.g., CO 2 ), and the motion is such that extremely large values of divV occur, as happens in hypersonic flows or in flows through shock waves (see [10,11]). …”