Skip to main content
    • Aa
    • Aa

Oscillatory rarefied gas flow inside rectangular cavities

  • Lei Wu (a1), Jason M. Reese (a2) and Yonghao Zhang (a1)

Two-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

P. L. Bhatnagar , E. P. Gross  & M. Krook 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511525.

C. Cercignani 1990 Mathematical Methods in Kinetic Theory. Plenum.

L. Desvillettes  & S. Lorenzani 2012 Sound wave resonance in micro-electro-mechanical systems devices vibrating at high frequencies according to the kinetic theory of gases. Phys. Fluids 24, 092001.

T. Doi 2009 Numerical analysis of oscillatory Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation. Vacuum 84, 734737.

P. W. Duck 1982 Oscillatory flow inside a square cavity. J. Fluid Mech. 122, 215234.

D. R. Emerson , X. J. Gu , S. K. Stefanov , Y. H. Sun  & R. W. Barber 2007 Nonplanar oscillatory shear flow: from the continuum to the free-molecular regime. Phys. Fluids 19, 107105.

P. Gospodinov , V. Roussinov  & S. Stefan 2012 Nonisothermal oscillatory cylindrical Couette gas–surface flow in the slip regime: a computational study. Eur. J. Mech. (B/Fluids) 33, 1424.

X. J. Gu  & D. R. Emerson 2011 Modeling oscillatory flows in the transition regime using a high-order moment method. Microfluid Nanofluid 10, 389401.

N. G. Hadjiconstantinou 2002 Sound wave propagation in transition-regime micro- and nanochannels. Phys. Fluids 14, 802809.

L. H. Holway 1966 New statistical models for kinetic theory: methods of construction. Phys. Fluids 9, 16581673.

D. Kalempa  & F. Sharipov 2009 Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency. Phys. Fluids 21, 103601.

J. P. Meng  & Y. H. Zhang 2011 Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows. J. Comput. Phys. 230, 835849.

S. Naris  & D. Valougeorgis 2005 The driven cavity flow over the whole range of the Knudsen number. Phys. Fluids 17, 097106.

J. H. Park , P. Bahukudumbi  & A. Beskok 2004 Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime. Phys. Fluids 16, 317.

E. M. Shakhov 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 9596.

F. Sharipov  & D. Kalempa 2008a Numerical modelling of the sound propagation through a rarefied gas in a semi-infinite space on the basis of linearized kinetic equation. J. Acoust. Soc. Am. 124 (4), 19932001.

F. Sharipov  & D. Kalempa 2008b Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number. Microfluid Nanofluid 4, 363374.

P. Taheri , A. S. Rana , M. Torrilhon  & H. Struchtrup 2009 Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics. Contin. Mech. Thermodyn. 21, 423443.

S. Varoutis , D. Valougeorgis  & F. Sharipov 2008 Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities. J. Comput. Phys. 227, 62726287.

L. Wu , J. M. Reese  & Y. H. Zhang 2014 Solving the Boltzmann equation by the fast spectral method: application to microflows. J. Fluid Mech. 746, 5384.

Y. W. Yap  & J. E. Sader 2012 High accuracy numerical solutions of the Boltzmann Bhatnagar–Gross–Krook equation for steady and oscillatory Couette flows. Phys. Fluids 24, 032004.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 52 *
Loading metrics...

Abstract views

Total abstract views: 132 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th August 2017. This data will be updated every 24 hours.