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Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows

Published online by Cambridge University Press:  20 August 2015

Jaw-Yen Yang ,
Li-Hsin Hung  and
Yao-Tien Kuo
Jaw-Yen Yang*
Affiliation:
Center for Quantum Science and Engineering, National Taiwan University, Taipei 106, Taiwan Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Li-Hsin Hung*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Yao-Tien Kuo*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

Computations of microscopic circular pipe flow in a rarefied quantum gas are presented using a semiclassical axisymmetric lattice Boltzmann method. The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in two-dimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al. [Phys. Rev. E., 64 (2001), 011208] is adopted by adding forcing terms into the resulting microdynamic evolution equation. The determination of the forcing terms is dictated by yielding the emergent macroscopic equations toward a particular target form. The correct macroscopic equations of the incompressible axisymmetric viscous flows are recovered through the Chapman-Enskog expansion. The velocity profiles and the mass flow rates of pipe flows with several Knudsen numbers covering different flow regimes are presented. It is found the Knudsen minimum can be captured in all three statistics studied. The results also indicate distinct characteristics of the effects of quantum statistics.

Keywords

76P0582B4082D0582C4047.11.-j51.10.+y47.45.Ab67.10.JnSemiclassical lattice Boltzmann methodaxisymmetric flowsrarefied pipe flowKnudsen minimum
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 405 - 421
Copyright
Copyright © Global Science Press Limited 2011

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