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

Simon Mizzi, Robert W. Barber, David Emerson, Jason Reese, Stefan Stefanov

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.
LanguageEnglish
Pages273-283
Number of pages10
JournalContinuum Mechanics and Thermodynamics
Volume19
Issue number5
DOIs
Publication statusPublished - 2007

Fingerprint

nonequilibrium flow
Heat flux
continuums
Transition flow
Constitutive equations
moments
Flow of gases
heat flux
Conservation
Monte Carlo methods
Boundary conditions
transition flow
rarefied gases
Couette flow
conservation equations
constitutive equations
gas flow
Monte Carlo method
Costs
boundary conditions

Keywords

  • micro-electromechanical systems
  • nano-electromechanical systems nano-scale flow phenomena
  • gas dynamics
  • continuum effects

Cite this

Mizzi, Simon ; Barber, Robert W. ; Emerson, David ; Reese, Jason ; Stefanov, Stefan. / A phenomenological and extended continuum approach for modelling non-equilibrium flows. In: Continuum Mechanics and Thermodynamics. 2007 ; Vol. 19, No. 5. pp. 273-283.
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A phenomenological and extended continuum approach for modelling non-equilibrium flows. / Mizzi, Simon; Barber, Robert W.; Emerson, David; Reese, Jason; Stefanov, Stefan.

In: Continuum Mechanics and Thermodynamics, Vol. 19, No. 5, 2007, p. 273-283.

Research output: Contribution to journalArticle

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AU - Emerson, David

AU - Reese, Jason

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