Numerical analysis of flows of rarefied gases in long channels with octagonal cross section shapes

Journal Article · Tue Dec 09 00:00:00 EST 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4902711· OSTI ID:22390542

Szalmas, L. ^[1]

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1. Center for Environmental Research and Sustainable Technology (UFT), University of Bremen, Leobener Str., Bremen 28359 (Germany)

Isothermal, pressure driven rarefied gas flows through long channels with octagonal cross section shapes are analyzed computationally. The capillary is between inlet and outlet reservoirs. The cross section is constant along the axial direction. The boundary condition at the solid-gas interface is assumed to be diffuse reflection. Since the channel is long, the gaseous velocity is small compared to the average molecular speed. Consequently, a linearized description can be used. The flow is described by the linearized Bhatnagar-Gross-Krook kinetic model. The solution of the problem is divided into two stages. First, the local flow field is determined by assuming the local pressure gradient. Secondly, the global flow behavior is deduced by the consideration of the conservation of the mass along the axis of the capillary. The kinetic equation is solved by the discrete velocity method on the cross section. Both spatial and velocity spaces are discretized. A body fitted rectangular grid is used for the spatial space. Near the boundary, first-order, while in the interior part of the flow domain, second-order finite-differences are applied to approximate the spatial derivatives. This combination results into an efficient and straightforward numerical treatment. The velocity space is represented by a Gauss-Legendre quadrature. The kinetic equation is solved in an iterative manner. The local dimensionless flow rate is calculated and tabulated for a wide range of the gaseous rarefaction for octagonal cross sections with various geometrical parameters. It exhibits the Knudsen minimum phenomenon. The flow rates in the octagonal channel are compared to those through capillaries with circular and square cross sections. Typical velocity profiles are also shown. The mass flow rate and the distribution of the pressure are determined and presented for global pressure driven flows.

• OSTI ID: 22390542
• Journal Information: AIP Conference Proceedings, Vol. 1628, Issue 1; Conference: 29. International Symposium on Rarefied Gas Dynamics, Xi'an (China), 13-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOUNDARY CONDITIONS
CAPILLARY FLOW
COMPARATIVE EVALUATIONS
FLOW RATE
GAS FLOW
GRIDS
INTERFACES
ITERATIVE METHODS
KINETIC EQUATIONS
MASS
MATHEMATICAL SOLUTIONS
NUMERICAL ANALYSIS
PRESSURE GRADIENTS
QUADRATURES
RAREFIED GASES
REFLECTION
SPACE
VELOCITY