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Oscillatory rarefied gas flow inside rectangular cavities

Published online by Cambridge University Press:  29 April 2014

Lei Wu ,
Jason M. Reese  and
Yonghao Zhang
Lei Wu
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
Jason M. Reese
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3JL, UK
Yonghao Zhang*
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
*
†Email address for correspondence: yonghao.zhang@strath.ac.uk
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Abstract

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.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Rarefied Gas Flow: Rarefied Gas Flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 350 - 367
Copyright
© 2014 Cambridge University Press 

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References

Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525.CrossRefGoogle Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flow. Oxford University Press.CrossRefGoogle Scholar
Cercignani, C. 1990 Mathematical Methods in Kinetic Theory. Plenum.Google Scholar
Desvillettes, L. & Lorenzani, S. 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.CrossRefGoogle Scholar
Doi, T. 2009 Numerical analysis of oscillatory Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation. Vacuum 84, 734–737.CrossRefGoogle Scholar
Duck, P. W. 1982 Oscillatory flow inside a square cavity. J. Fluid Mech. 122, 215–234.Google Scholar
Emerson, D. R., Gu, X. J., Stefanov, S. K., Sun, Y. H. & Barber, R. W. 2007 Nonplanar oscillatory shear flow: from the continuum to the free-molecular regime. Phys. Fluids 19, 107105.Google Scholar
Gospodinov, P., Roussinov, V. & Stefan, S. 2012 Nonisothermal oscillatory cylindrical Couette gas–surface flow in the slip regime: a computational study. Eur. J. Mech. (B/Fluids) 33, 14–24.Google Scholar
Gu, X. J. & Emerson, D. R. 2011 Modeling oscillatory flows in the transition regime using a high-order moment method. Microfluid Nanofluid 10, 389–401.CrossRefGoogle Scholar
Hadjiconstantinou, N. G. 2002 Sound wave propagation in transition-regime micro- and nanochannels. Phys. Fluids 14, 802–809.Google Scholar
Holway, L. H. 1966 New statistical models for kinetic theory: methods of construction. Phys. Fluids 9, 1658–1673.CrossRefGoogle Scholar
Kalempa, D. & Sharipov, F. 2009 Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency. Phys. Fluids 21, 103601.Google Scholar
Kalempa, D. & Sharipov, F. 2012 Sound propagation through a rarefied gas: influence of the gas–surface interaction. Intl J. Heat Fluid Flow 30, 190–199.Google Scholar
Karniadakis, G., Beskok, A. & Aluru, N. 2005 Microflows and Nanoflows: Fundamentals and Simulation. Springer.Google Scholar
Meng, J. P. & Zhang, Y. H. 2011 Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows. J. Comput. Phys. 230, 835–849.CrossRefGoogle Scholar
Naris, S. & Valougeorgis, D. 2005 The driven cavity flow over the whole range of the Knudsen number. Phys. Fluids 17, 097106.Google Scholar
Park, J. H., Bahukudumbi, P. & Beskok, A. 2004 Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime. Phys. Fluids 16, 317.CrossRefGoogle Scholar
Shakhov, E. M. 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 95–96.Google Scholar
Sharipov, F. & Kalempa, D. 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), 1993–2001.Google Scholar
Sharipov, F. & Kalempa, D. 2008b Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number. Microfluid Nanofluid 4, 363–374.Google Scholar
Shi, Y. & Sader, J. E. 2010 Lattice Boltzmann method for oscillatory Stokes flow with applications to micro- and nanodevices. Phys. Rev. 81, 036706.Google Scholar
Struchtrup, H. 2005 Macroscopic Transport Equations for Rarefied Gas Fows: Approximation Methods in Kinetic Theory. Springer.Google Scholar
Struchtrup, H. 2011 Resonance in rarefied gases. Contin. Mech. Thermodyn. 34, 361–376.Google Scholar
Taheri, P., Rana, A. S., Torrilhon, M. & Struchtrup, H. 2009 Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics. Contin. Mech. Thermodyn. 21, 423–443.CrossRefGoogle Scholar
Tang, G. H., Gu, X. J., Barber, R. W., Emerson, D. R. & Zhang, Y. H. 2008 Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow. Phys. Rev. 78, 026706.Google Scholar
Varoutis, S., Valougeorgis, D. & Sharipov, F. 2008 Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities. J. Comput. Phys. 227, 6272–6287.Google Scholar
Wu, L., Reese, J. M. & Zhang, Y. H. 2014 Solving the Boltzmann equation by the fast spectral method: application to microflows. J. Fluid Mech. 746, 53–84.Google Scholar
Yap, Y. W. & Sader, J. E. 2012 High accuracy numerical solutions of the Boltzmann Bhatnagar–Gross–Krook equation for steady and oscillatory Couette flows. Phys. Fluids 24, 032004.Google Scholar