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Modeling oscillatory flows in the transition regime using a high-order moment method

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Abstract

We present results using three different continuum-based models to study oscillatory flow in the transition regime. Data obtained from numerical solutions of the Boltzmann equation and the direct simulation Monte Carlo method, are used to assess the ability of the continuum models to capture important rarefaction effects. We further highlight the need to consider two Knudsen numbers: one based upon the length scale and the other upon the time scale. It is found that the regularized 26 moment model can follow kinetic theory in the early transition regime in terms of both Knudsen numbers but the regularized 13 moment equations can only be used up to the upper limit of the hydrodynamic regime. However, the subtle interplay of the length and time scales on oscillatory non-equilibrium flow causes the Navier–Stokes equations to fail even in the hydrodynamic regime. In addition, the effect of modifying the accommodation coefficient is also considered. It is found that reducing the accommodation coefficient on the stationary wall alone will increase the motion of the gas. However, gaseous movement will be reduced by changing both walls from diffusive to specular reflection.

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Acknowledgments

The authors would like to thank the Engineering and Physical Sciences Research Council (EPSRC) for their support of Collaborative Computational Project 12 (CCP12).

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Authors and Affiliations

  1. Computational Science and Engineering Department, STFC Daresbury Laboratory, Warrington, WA4 4AD, UK

    Xiao-Jun Gu & David R. Emerson

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  1. Xiao-Jun Gu
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  2. David R. Emerson
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Correspondence to Xiao-Jun Gu.

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Gu, XJ., Emerson, D.R. Modeling oscillatory flows in the transition regime using a high-order moment method. Microfluid Nanofluid 10, 389–401 (2011). https://doi.org/10.1007/s10404-010-0677-1

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