Mass flow rate for nearly-free molecular slit flow

Stewart, J. D.

doi:10.1017/s0022112069001315

Cited by 22 publications

(10 citation statements)

References 4 publications

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“…In addition, the slit flow offers, as it has pointed out in [4,2], the possibility of comparing theory and experiment, or different numerical approaches without having to assume a particular gas-wall interaction model or adjusting many flow parameters.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

2013

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Section: Introductionmentioning

confidence: 99%

“…Stewart [4] completed the previous study by the case of a finite pressure drop. Many authors performed the numerical simulations of the slit flow using the divers linearized kinetic equations, namely, the BGK kinetic equation [11] in [5,1], the S-model kinetic equation [12] in [9] and the McCormack model equation [14] in [7].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

2013

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“…[1,[4][5][6][7][8][9][10][11][12][13][14][15]. Liepmann [4] was the first to analyze both theoretically and experimentally the flow rate of rarefied gas through a slit into vacuum.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the Bhatnagar-Gross-Krook (BGK) model equation [16] is converted into an integral form, and the iterations are performed starting from the free molecular solution. Stewart [6] applied the same iterative procedure to a situation of gas flow driven by a finite pressure drop. Hasegawa and Sone [8] performed calculations of the slit flow driven by a small pressure difference using the linearized BGK kinetic model [16].…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

Graur

Polikarpov

Sharipov

2011

Z. Angew. Math. Phys.

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A rarefied gas flow through a thin slit at an arbitrary gas pressure ratio is calculated on the basis of the kinetic model equations (BGK and S-model) applying the discrete velocity method. The calculations are carried out for the whole range of the gas rarefaction from the free-molecular regime to the hydrodynamic one. Numerical data on the flow rate and distributions of density, bulk velocity and temperature are reported. Comparisons of the present results with those based on the direct simulation Monte Carlo method and on the linearized BGK kinetic equation are performed. The conditions of applicability of the linearized theory are discussed. (2010). 82B40 kinetic theory of gases. Mathematics Subject Classification

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“…Numerical works during the 60's investigate slit and orifice flows near the free molecular regime [143,144,145], with particular emphasis on flow into vacuum, but their range of applicability is small. In order to obtain the behaviour of the flow for any rarefaction regime, the most successful approaches rely on the Direct Simulation Monte Carlo (DSMC) method and the discrete velocity method (DVM).…”

Section: Flow Through Channelsmentioning

confidence: 99%

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

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The approval of the current dissertation by the Department of Mechanical Engineering of the University of Thessaly does not imply acceptance of the author's opinions (Law 5343/32 number 202 paragraph 2). Also, the views and opinions expressed herein do not necessarily reflect those of the European Commission. There are several other people who I feel that have contributed in the writing of this dissertation.The most important contributions, along with several helpful conversations, were made by Prof. F.Sharipov, who provided the basic concept of the channel end effect study, and Dr. Chr. Day along with the KIT personnel, who briefly introduced me in the world of experimental rarefied gas dynamics. It was also a priviledge to discuss and work for a brief period of time with Prof. A. Grecos, who tirelessly discussed with me on various subjects of statistical mechanics. Financial support for this Ph.D. has been provided by the Euratom Association -Hellenic Republic, to which I am deeply indepted. Also, partial support for conference mobility expenses has been received from the GASMEMS Marie Curie programme. In this work, non-equilibrium transport phenomena have been examined via the kinetic theory of gases. The behaviour of the gas in low pressure conditions or in low-dimensionality systems can not be captured by the usual Navier-Stokes formulation, in conjunction with the constitutive laws of Newton-Fourier-Fick. The limited number of intermolecular collisions results in departure from equilibrium and the particulate nature of the gas must be taken into account, greatly increasing the computational effort.The problem is described by the integro-differential Boltzmann equation, which is used to determine the distribution of particles in physical and molecular velocity space, as well as in time.There are difficulties associated with the seven-dimensional nature of the distribution function, as well as with the complexity of the collision term, which is usually substituted by an appropriate model.The most widely used and successful numerical methodologies, the Discrete Velocity Method (DVM) and the Direct Simulation Monte Carlo (DSMC), are applied here in the whole range of the Knudsen number. It is important to employ approaches based on kinetic theory, since these are the only ones which are valid for any rarefaction level.In this work, several problems including non-equilibrium phenomena are considered. The interaction of gases with solid surfaces is considered for several problems according to the CercignaniLampis boundary conditions. The non-linear form of this scattering kernel, which had not been pre- viously used in the literature, is applied on the problem of heat transfer between parallel plates and coaxial cylinders. Its linearized form has also been employed for both flow and heat transfer problems and a comparison with relevant experiments has lead to surface characterization with respect to argon and helium flows.Non-linear heat conduction phenomena are also studied for the parallel plates and coaxial c...

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Mass flow rate for nearly-free molecular slit flow

Cited by 22 publications

References 4 publications

Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

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