IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v463y2016icp25-36.html
   My bibliography  Save this article

Extended application of lattice Boltzmann method to rarefied gas flow in micro-channels

Author

Listed:
  • Yuan, Yudong
  • Rahman, Sheik

Abstract

Simulation of rarefied gas flow in micro-channels is of great interest owing to its diverse applications in many engineering fields. In this study, a multiple-relaxation-time lattice Boltzmann (MRT-LB) model with a general second-order slip boundary condition is presented to investigate the behaviour of gas flow with a wide range of Knudsen number in micro-channels. With the aid of a Bosanquet-type effective viscosity, the effective relaxation time is correlated with local Knudsen number (Kn) to account for the varying degree of rarefaction effect. Unlike previous studies, the derived accommodation coefficient r for the combined bounce-back/diffusive reflection (CBBDR) boundary condition is dependent on the local Kn, which allows more flexibility to simulate the slip velocity along the channel walls. When compared with results of other methods, such as linearised Boltzmann equation, experimental data, direct simulation Monte Carlo (DSMC) and Information Preservation DSMC (IP-DSMC), it is found that the LB model is capable of capturing the flow behaviour, including the velocity profile, flow rate, pressure distribution and Knudsen minimum of rarefied gas with Kn up to 10. The effect of Knudsen layer (KL) on the velocity of gas flow with a wide range of Kn is also discussed. It is found that KL effect is negligible in the continuum flow and y-independent in the free molecular flow, while in the intermediate range, especially in transition flow, KL effect is significant and particular efforts should be made to capture this effect.

Suggested Citation

  • Yuan, Yudong & Rahman, Sheik, 2016. "Extended application of lattice Boltzmann method to rarefied gas flow in micro-channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 25-36.
    • Handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:25-36
    DOI: 10.1016/j.physa.2016.06.123
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116303983
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.06.123?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhi-Wei Tian & Sheng Chen & Chu-Guang Zheng, 2010. "Lattice Boltzmann Simulation Of Gaseous Finite-Knudsen Microflows," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 769-783.
    2. Brenner, Howard, 2005. "Navier–Stokes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 60-132.
    3. G. H. Tang & W. Q. Tao & Y. L. He, 2004. "Lattice Boltzmann Method For Simulating Gas Flow In Microchannels," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 335-347.
    4. Tian, Zhi-Wei & Zou, Chun & Liu, Hong-Juan & Guo, Zhao-Li & Liu, Zhao-Hui & Zheng, Chu-Guang, 2007. "Lattice Boltzmann scheme for simulating thermal micro-flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 59-68.
    5. Brenner, Howard, 2006. "Fluid mechanics revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 190-224.
    6. Chen, Sheng & Tian, Zhiwei, 2009. "Simulation of microchannel flow using the lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4803-4810.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shi, Rui & Liu, Jishan & Wang, Xiaoming & Wei, Mingyao & Elsworth, Derek, 2021. "A critical analysis of shale laboratory permeability evolution data," Energy, Elsevier, vol. 236(C).
    2. Wang, Lingquan & Zeng, Zhong & Zhang, Liangqi & Qiao, Long & Zhang, Yi & Lu, Yiyu, 2018. "A new boundary scheme for simulation of gas flow in kerogen pores with considering surface diffusion effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 180-190.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tian, Zhiwei & Xing, Huilin & Tan, Yunliang & Gao, Jinfang, 2014. "A coupled lattice Boltzmann model for simulating reactive transport in CO2 injection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 155-164.
    2. Brenner, Howard, 2013. "Bivelocity hydrodynamics. Diffuse mass flux vs. diffuse volume flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 558-566.
    3. Karimipour, Arash & Hemmat Esfe, Mohammad & Safaei, Mohammad Reza & Toghraie Semiromi, Davood & Jafari, Saeed & Kazi, S.N., 2014. "Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 150-168.
    4. Abramov, Rafail V., 2017. "Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 532-557.
    5. Brenner, Howard, 2011. "Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier–Stokes–Fourier equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3216-3244.
    6. Janusz Badur & Michel Feidt & Paweł Ziółkowski, 2020. "Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics," Energies, MDPI, vol. 13(7), pages 1-34, April.
    7. Svärd, Magnus, 2018. "A new Eulerian model for viscous and heat conducting compressible flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 350-375.
    8. Bardow, André & Christian Öttinger, Hans, 2007. "Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 88-96.
    9. Brenner, Howard, 2012. "An example illustrating the incompleteness of the Navier–Stokes–Fourier equations for thermally compressible fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 966-978.
    10. Yang, Xu & Zhou, Wenning & Liu, Xunliang & Yan, Yuying, 2020. "A multiscale approach for simulation of shale gas transport in organic nanopores," Energy, Elsevier, vol. 210(C).
    11. Che Sidik, Nor Azwadi & Aisyah Razali, Siti, 2014. "Lattice Boltzmann method for convective heat transfer of nanofluids – A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 38(C), pages 864-875.
    12. Li, Chengwu & Zhao, Yuechao & Ai, Dihao & Wang, Qifei & Peng, Zhigao & Li, Yingjun, 2020. "Multi-component LBM-LES model of the air and methane flow in tunnels and its validation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    13. Tian, Zhi-Wei & Zou, Chun & Liu, Hong-Juan & Guo, Zhao-Li & Liu, Zhao-Hui & Zheng, Chu-Guang, 2007. "Lattice Boltzmann scheme for simulating thermal micro-flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 59-68.
    14. Li, Jiangtao & Zhou, Xiaofeng & Liu, Xibao & Gayubov, Abdumalik & Shamil, Sultanov, 2023. "Cross-scale diffusion characteristics in microscale fractures of tight and shale gas reservoirs considering real gas – mixture – body diffusion – water film coupling," Energy, Elsevier, vol. 283(C).
    15. Calgaro, Caterina & Creusé, Emmanuel & Goudon, Thierry & Krell, Stella, 2017. "Simulations of non homogeneous viscous flows with incompressibility constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 201-225.
    16. Chen, Sheng & Du, Rui, 2011. "Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity," Energy, Elsevier, vol. 36(3), pages 1721-1734.
    17. Chen, Sheng & Tian, Zhiwei, 2009. "Simulation of microchannel flow using the lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4803-4810.
    18. Goodarzi, Marjan & D’Orazio, Annunziata & Keshavarzi, Ahmad & Mousavi, Sayedali & Karimipour, Arash, 2018. "Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 210-233.
    19. Esfahani, Javad Abolfazli & Norouzi, Ali, 2014. "Two relaxation time lattice Boltzmann model for rarefied gas flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 51-61.
    20. Wang, Hui & Chen, Li & Qu, Zhiguo & Yin, Ying & Kang, Qinjun & Yu, Bo & Tao, Wen-Quan, 2020. "Modeling of multi-scale transport phenomena in shale gas production — A critical review," Applied Energy, Elsevier, vol. 262(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:25-36. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.