Numerical Analysis of Gas Flows in a Microchannel Using the Cascaded Lattice Boltzmann Method with Varying Bosanquet Parameter

Document Type : Full Length Research Article

Authors

1 Department of Mechanical Engineering, University of Kashan, Kashan, Iran

2 University of Kashan

Abstract

Abstract. In this paper, a Cascaded Lattice Boltzmann Method with second order slip boundary conditions is developed to study gas flows in a microchannel in the slip and transition flow regimes with a wide range of Knudsen numbers. For the first time the effect of wall confinement is considered on the effective mean free path of the gas molecules using a function with nonconstant Bosanquet parameter instead of the constant one. The constant-force driven and pressure-driven gas flows in a long microchannel are simulated under different conditions. The results of the velocity profile, pressure distribution, and mass flow rate are in good agreement with the benchmark solutions and experimental data reported in the literature. The Knudsen minimum phenomenon is also well captured by the present model. The proposed Cascaded Lattice Boltzmann Method shows a clear improvement in predicting the flow behaviors of microchannel gas flows for the previous classic and Cascaded Lattice Boltzmann Method

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Main Subjects

References

[1] AGRAWAL, A., DJENIDI, L. & AGRAWAL, A. 2009. Simulation of gas flow in microchannels with a single 90 bend. Computers & Fluids, 38, 1629-1637.
[2] AHMED, I. & BESKOK, A. 2002. Rarefaction, compressibility, and viscous heating in gas microfilters. Journal of Thermophysics and Heat Transfer, 16, 161-170.
[3] ARKILIC, E. B., SCHMIDT, M. A. & BREUER, K. S. 1997. Gaseous slip flow in long microchannels. Journal of Microelectromechanical systems, 6, 167- 178.
[4] ASADOLLAHI, A., RASHIDI, S. & ESFAHANI, J. A. 2017. Condensation process and phasechange in the presence of obstacles inside a minichannel. Meccanica, 52, 2265-2274.
[5] ASADOLLAHI, A., RASHIDI, S. & MOHAMAD, A. A. 2018. Removal of the liquid from a micro-object and controlling the surface wettability by using a rotating shellNumerical simulation by Lattice–Boltzmann method. Journal of Molecular Liquids, 272, 645-655.
[6] BECK, C. & ROEPSTORFF, G. 1990. From stochastic processes to the hydrodynamic equations. Physica A: Statistical Mechanics and its Applications, 165, 270-278.
[7] BESKOK, A. & KARNIADAKIS, G. E. 1999. Report: a model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophysical Engineering, 3, 43-77.
[8] 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. Physical review, 94, 511.
[9] CERCIGNANI, C. 1964. Higher order slip according to the linearized Boltzmann equation. CALIFORNIA UNIV BERKELEY INST OF ENGINEERING RESEARCH.
[10] CERCIGNANI, C. 1969. Mathematical methods in kinetic theory, Springer.
[11] CERCIGNANI, C. & DANERI, A. 1963. Flow of a rarefied gas between two parallel plates. Journal of Applied Physics, 34, 3509-3513.
[12] CERCIGNANI, C., LAMPIS, M. & LORENZANI, S. 2004. Variational approach to gas flows in microchannels. Physics of Fluids, 16, 3426- 3437.
[13] DUBOIS, F., FEVRIER, T. & GRAILLE, B. 2015a. Lattice Boltzmann schemes with relative velocities. Communications in Computational Physics, 17, 1088-1112.
[14] DUBOIS, F., FÉVRIER, T. & GRAILLE, B. 2015b. On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier–Stokes equations. Comptes Rendus Mécanique, 343, 599-610.
[15] FEI, L. & LUO, K. H. 2017. Consistent forcing scheme in the cascaded lattice Boltzmann method. Physical Review E, 96, 053307.
[16] GEIER, M., GREINER, A. & KORVINK, J. 2009. A factorized central moment lattice Boltzmann method. The European Physical Journal Special Topics, 171, 55-61.
[17] GEIER, M., GREINER, A. & KORVINK, J. G. 2006. Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Physical Review E, 73, 066705.
[18] GUO, Z., ZHAO, T. & SHI, Y. 2006. Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows. Journal of Applied physics, 99, 074903.
[19] GUO, Z. & ZHENG, C. 2008. Analysis of lattice Boltzmann equation for microscale gas flows: relaxation times, boundary conditions and the Knudsen layer. International Journal of Computational Fluid Dynamics, 22, 465- 473.
[20] GUO, Z., ZHENG, C. & SHI, B. 2008. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Physical Review E, 77, 036707.
[21] HADJICONSTANTINOU, N. G. 2003. Comment on Cercignani’s second-order slip coefficient. Physics of Fluids, 15, 2352-2354. [22] HOMAYOON, A., ISFAHANI, A. M., SHIRANI, E. & ASHRAFIZADEH, M. 2011. A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number. International Communications in Heat and Mass Transfer, 38, 827-832. [23] HOSSEINI, R., RASHIDI, S. & ESFAHANI, J. A. 2017. A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 3695-3706.
[24] KANDLIKAR, S., GARIMELLA, S., LI, D., COLIN, S. & KING, M. R. 2005. Heat transfer and fluid flow in minichannels and microchannels, elsevier.
[25] LECLAIRE, S., PELLERIN, N., REGGIO, M. & TRÉPANIER, J.-Y. 2014. Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications, 406, 307-319.
[26] LEE, T. & LIN, C.-L. 2005. Rarefaction and compressibility effects of the latticeBoltzmann-equation method in a gas microchannel. Physical Review E, 71, 046706. 38 M. Shomali / JHMTR 7 (2020) 25-38
[27] LI, Q., HE, Y., TANG, G. & TAO, W. 2011. Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluidics and nanofluidics, 10, 607-618.
[28] LIU, Q. & HE, Y.-L. 2016. Numerical modelling of microchannel gas flows in the transition flow regime using the cascaded lattice Boltzmann method. arXiv preprint arXiv:1603.01955.
[29] LIU, X. & GUO, Z. 2013. A lattice Boltzmann study of gas flows in a long micro-channel. Computers & Mathematics with Applications, 65, 186-193.
[30] LOCKERBY, D. A., REESE, J. M. & GALLIS, M. A. 2005. The usefulness of higher-order constitutive relations for describing the Knudsen layer. Physics of Fluids, 17, 100609.
[31] LOPEZ, P. 2014. Thermal Lattice Boltzmann Simulation for Rarefied Flow in Microchannels.
[32] LOYALKA, S., PETRELLIS, N. & STORVICK, T. 1975. Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface. The Physics of Fluids, 18, 1094- 1099.
[33] LYCETT-BROWN, D. & LUO, K. H. 2014. Multiphase cascaded lattice Boltzmann method. Computers & Mathematics with Applications, 67, 350-362.
[34] LYCETT-BROWN, D., LUO, K. H., LIU, R. & LV, P. 2014. Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method. Physics of Fluids, 26, 023303.
[35] MAXWELL, J. C. 1879. VII. On stresses in rarified gases arising from inequalities of temperature. Philosophical Transactions of the royal society of London, 231-256.
[36] MICHALIS, V. K., KALARAKIS, A. N., SKOURAS, E. D. & BURGANOS, V. N. 2010. Rarefaction effects on gas viscosity in the Knudsen transition regime. Microfluidics and nanofluidics, 9, 847-853.
[37] MOHAMAD, A. A. 2011. Lattice Boltzmann method: fundamentals and engineering applications with computer codes, Springer Science & Business Media.
[38] NING, Y., PREMNATH, K. N. & PATIL, D. V. 2016. Numerical study of the properties of the central moment lattice Boltzmann method. International Journal for Numerical Methods in Fluids, 82, 59-90.
[39] NIU, X., SHU, C. & CHEW, Y. 2004. A lattice Boltzmann BGK model for simulation of micro flows. EPL (Europhysics Letters), 67, 600.
[40] OHWADA, T., SONE, Y. & AOKI, K. 1989. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard‐sphere molecules. Physics of Fluids A: Fluid Dynamics, 1, 2042-2049.
[41] PREMNATH, K. N. & BANERJEE, S. 2009. Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments. Physical Review E, 80, 036702.
[42] RAHMATI, A. R. & NIAZI, S. 2015. Application and Comparison of Different Lattice Boltzmann Methods on Non-Uniform Meshes for Simulation of Micro Cavity and Micro Channel Flow. Journal of Computational Methods In Engineering, 34, 97-118.
[43] SHEN, C., TIAN, D.-B., XIE, C. & FAN, J. Examination of the LBM in simulation of microchannel flow in transitional regime. ASME 2003 1st International Conference on Microchannels and Minichannels, 2003. American Society of Mechanical Engineers, 405-410.
[44] SHOKOUHMAND, H. & ISFAHANI, A. M. 2011. An improved thermal lattice Boltzmann model for rarefied gas flows in wide range of Knudsen number. International communications in heat and mass transfer, 38, 1463-1469.
[45] STOPS, D. 1970. The mean free path of gas molecules in the transition regime. Journal of Physics D: Applied Physics, 3, 685. [46] TANG, G., ZHANG, Y., GU, X. & EMERSON, D. 2008. Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows. EPL (Europhysics Letters), 83, 40008.
[47] ZHANG, Y.-H., GU, X.-J., BARBER, R. W. & EMERSON, D. R. 2006. Capturing Knudsen layer phenomena using a lattice Boltzmann model. Physical Review E, 74, 046704. [48] ZHUO, C. & ZHONG, C. 2013. Filter-matrix lattice Boltzmann model for microchannel gas flows. Physical Review E, 88, 053311.

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History

  • Receive Date: 29 July 2019
  • Revise Date: 20 January 2020
  • Accept Date: 29 November 2019

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