How Far Can 13 Moments Go in Modeling Microscale Gas Phenomena?

Abstract

The ability to capture nonequilibrium phenomena in rarefied gas flow using hydrodynamic models based on the Navier-Stokes-Fourier (NSF) equations and the regularized 13 moment equations (R13) are assessed. Results from the hydrodynamic models are compared against direct simulation Monte Carlo data obtained for planar Couette flow. The study shows that the R13 equations are able to capture the phenomenon of non-gradient heat flux up to a Knudsen number (Kn) of unity. In contrast, the NSF equations completely fail to predict this effect. For low Mach numbers, the R13 equations can reliably predict the temperature jump up to Kn = 1 and are also able to capture the correct trend at higher Mach numbers. However, the NSF equations can only provide an adequate description of the temperature jump for Kn < 0.25 and fail to exhibit the correct trend above this Knudsen number. For velocity slip, the R13 equations are in better agreement with the DSMC data but both hydrodynamic approaches fail to capture the nonlinearity of the velocity profile within the Knudsen layer. Overall, the R13 equations provide a much improved hydrodynamic description of the flow physics in the transition regime.

KEY WORDS:

• rarefied gas dynamics
• method of moments
• wall boundary conditions
• velocity slip
• temperature jump
• Couette flow

The authors gratefully acknowledge many helpful discussions with Stefan Stefanov (Institute of Mechanics, Bulgarian Academy of Sciences), Simon Mizzi (CCLRC Daresbury Laboratory/University of Strathclyde), and Yong-Hao Zhang (CCLRC Daresbury Laboratory). The authors also thank the Engineering and Physical Sciences Research Council (EPSRC) for their support of Collaborative Computational Project 12 (CCP12).