A continuum model of gas flows with localized density variations

S.K. Dadzie, J.M. Reese, C.R. McInnes

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.
LanguageEnglish
Pages6079-6094
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number24
DOIs
Publication statusPublished - 15 Oct 2008

Fingerprint

Thermodynamic Properties
Continuum Model
Gas Flow
Kinetic Equation
kinetic equations
gas flow
thermodynamic properties
Rarefied Gas Flow
macroscopic equations
Gradient
continuums
compressible fluids
gradients
Thermodynamic Equilibrium
rarefied gases
Compressible Fluid
Kinetic Theory
Compressible Flow
Term
thermodynamic equilibrium

Keywords

  • gas kinetic theory
  • Boltzmann equation
  • compressible fluids
  • Navier-Stokes equations
  • rarefied gas dynamics
  • constitutive relations

Cite this

Dadzie, S.K. ; Reese, J.M. ; McInnes, C.R. / A continuum model of gas flows with localized density variations. In: Physica A: Statistical Mechanics and its Applications. 2008 ; Vol. 387, No. 24. pp. 6079-6094.
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A continuum model of gas flows with localized density variations. / Dadzie, S.K.; Reese, J.M.; McInnes, C.R.

In: Physica A: Statistical Mechanics and its Applications, Vol. 387, No. 24, 15.10.2008, p. 6079-6094.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Dadzie, S.K.

AU - Reese, J.M.

AU - McInnes, C.R.

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N2 - We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.

AB - We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.

KW - gas kinetic theory

KW - Boltzmann equation

KW - compressible fluids

KW - Navier-Stokes equations

KW - rarefied gas dynamics

KW - constitutive relations

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