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Unsteady motion of a slightly rarefied gas caused by a plate oscillating in its normal direction

Kazuo Aoki

Shingo Kosuge

Taiga Fujiwara

Thierry Goudon

  • Mathematics Division, National Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan and Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan

  • Center for Global Leadership Engineering Education, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan

  • Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan

  • Université Côte d'Azur, Inria, CNRS, LJAD, Parc Valrose, 06108 Nice, France

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Phys. Rev. Fluids 2, 013402 – Published 24 January, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.013402

Abstract

Unsteady motion of a rarefied gas between two parallel plates caused when one of the plates starts a harmonic oscillation in its normal direction is investigated under a slightly rarefied condition, i.e., for small Knudsen numbers. The compressible Navier-Stokes equations are employed and their appropriate temperature jump condition is derived systematically. The equations with the correct boundary conditions are solved numerically to give the unsteady flow field. In particular, the time-periodic solution established at later times is investigated in detail and it is shown that the one-period average of the oscillating part of the momentum and that of the energy transferred from the oscillating plate to the resting one take nonzero values in contrast to the linear theory. This confirms the numerical result based on the Bhatnagar-Gross-Krook model of the Boltzmann equation for intermediate Knudsen numbers [T. Tsuji and K. Aoki, Microfluid. Nanofluid. 16, 1033 (2014)]. It is also shown that the gas approaches the time-periodic motion exponentially fast in time.

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Phys. Rev. Fluids 2, 013402– Published 24 January, 2017
  • Received 29 September 2016

©2017 American Physical Society

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