Steady flows of a highly rarefied gas induced by nonuniform wall temperature

• Kosuge, Shingo

• Aoki, Kazuo

• Takata, Shigeru

• Hattori, Ryosuke

• Sakai, Daisuke

Abstract

Steady behavior of a rarefied gas between parallel plates with sinusoidal temperature distribution is investigated on the basis of the Boltzmann equation. The Cercignani–Lampis (CL) model or the Lord model for diffuse scattering with incomplete energy accommodation is adopted as the boundary condition on the plates. Most of the analysis is carried out numerically with special interest in the free-molecular limit. In the case of the CL model, the nonuniform temperature distribution of the plates may induce a steady free-molecular flow, which is in contrast with the earlier results for the Maxwell-type model [ Y. Sone, J. Méc. Théor. Appl. 3, 315 (1984) ; J. Méc. Théor. Appl. 4, 1 (1985) ]. This fact is confirmed through an accurate deterministic computation based on an integral equation. In addition, computations for a wide range of parameters by means of the direct simulation Monte Carlo method reveal that the flow field changes according to the accommodation coefficients and is classified into four types. The effect of intermolecular collisions on the flow is also examined. In the case of the Lord model, no steady flow of the free-molecular gas is induced as in the case of the Maxwell-type model. This result is extended to the case of a more general boundary condition that gives the cosine law (Lambert’s law) for the reflected molecular flux.

Journal

• Physics of Fluids

  Physics of Fluids 23 (3), 030603-, 2011-03

  American Institute of Physics

Keywords

• Boltzmann equation
• confined flow
• flow simulation
• integral equations
• molecular collisions
• Monte Carlo methods
• rarefied fluid dynamics
• temperature distribution

Details

• CRID: 1050282810714019200
• NII Article ID: 120004754327
• NII Book ID: AA10986202
• ISSN: 10706631
• ISSN: 10897666
• DOI: 10.1063/1.3558872
• HANDLE: 2433/159436
• Web Site: https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/1.3558872/15748608/030603_1_online.pdf
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN