Macroscopic description of rarefied gas flows in the transition regime

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dc.contributor.author Taheri Bonab, Peyman
dc.date.accessioned 2010-09-01T00:00:11Z
dc.date.available 2010-09-01T00:00:11Z
dc.date.copyright 2010 en
dc.date.issued 2010-09-01T00:00:11Z
dc.identifier.uri http://hdl.handle.net/1828/3018
dc.description.abstract The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation. en
dc.language English eng
dc.language.iso en en
dc.rights Available to the World Wide Web en
dc.subject kinetic theory of gases en
dc.subject rarefied gas flows en
dc.subject Grad's moment method en
dc.subject nonequilibrium gas dynamics en
dc.subject nonequilibrium flow en
dc.subject Knudsen boundary layers en
dc.subject Couette flow en
dc.subject Poiseuille flow en
dc.subject transpiration flow en
dc.subject kinetic boundary conditions en
dc.subject rarefaction effects en
dc.subject R13 equations en
dc.subject second order velocity slip condition en
dc.subject second order temperature jump condition en
dc.subject temperature dip in Poiseuille flow en
dc.subject Knudsen paradox en
dc.subject simultaneous Poiseuille and transpiration flows en
dc.subject thermomolecular pressure difference en
dc.subject Onsager's reciprocity relation en
dc.subject.lcsh UVic Subject Index::Sciences and Engineering::Engineering::Mechanical engineering en
dc.subject.lcsh UVic Subject Index::Sciences and Engineering::Physics::Fluid mechanics en
dc.subject.lcsh UVic Subject Index::Sciences and Engineering::Physics::Molecular en
dc.title Macroscopic description of rarefied gas flows in the transition regime en
dc.type Thesis en
dc.contributor.supervisor Struchtrup, Henning
dc.degree.department Dept. of Mechanical Engineering en
dc.degree.level Doctor of Philosophy Ph.D. en
dc.identifier.bibliographicCitation P. Taheri, A. S. Rana, H. Struchtrup, and M. Torrilhon. Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics. Cont. Mech. Thermodyn., 21:423, 2009 en
dc.identifier.bibliographicCitation P. Taheri and H. Struchtrup. Effects of rarefaction in microflows between coaxial cylinders. Phys. Rev. E, 80:066317, 2009 en
dc.identifier.bibliographicCitation P. Taheri and H. Struchtrup. Rarefaction effects in thermally-driven microflows. Physica A, 389:3069, 2010 en
dc.identifier.bibliographicCitation P. Taheri, M. Torrilhon and H. Struchtrup. Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations. Phys. Fluids, 21:017102, 2009. en

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