A phenomenological and extended continuum approach for modelling non-equilibrium flows

S. Mizzi*, R. W. Barber, D. R. Emerson, J. M. Reese, S. K. Stefanov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a new technique that combines Grad's 13-moment equations (G13) with a phenomenological approach to rarefied gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage of the present solution technique is that it does not require extra boundary conditions explicitly; Grad's equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method. This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium phenomena, which cannot be captured by the Navier-Stokes-Fourier constitutive equations or phenomenological modifications.

Original languageEnglish
Pages (from-to)273-283
Number of pages11
JournalContinuum Mechanics and Thermodynamics
Volume19
Issue number5
DOIs
Publication statusPublished - Oct 2007

Keywords

  • flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
  • micro- and nano- scale flow phenomena
  • rarefied gas dynamics
  • non-continuum effects
  • non-equilibrium gas dynamics
  • Knudsen layer
  • Gas flows
  • Extended hydrodynamics

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