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Two Dimensional Simulation of Fluid Flow and Heat Transfer in the Transition Flow Regime using a Lattice Boltzmann Approach

Authors: Mehdi Shamshiri, Mahmud Ashrafizaadeh


The significant effects of the interactions between the system boundaries and the near wall molecules in miniaturized gaseous devices lead to the formation of the Knudsen layer in which the Navier-Stokes-Fourier (NSF) equations fail to predict the correct associated phenomena. In this paper, the well-known lattice Boltzmann method (LBM) is employed to simulate the fluid flow and heat transfer processes in rarefied gaseous micro media. Persuaded by the problematic deficiency of the LBM in capturing the Knudsen layer phenomena, present study tends to concentrate on the effective molecular mean free path concept the main essence of which is to compensate the incapability of this mesoscopic method in dealing with the momentum and energy transport within the above mentioned kinetic boundary layer. The results show qualitative and quantitative accuracy comparable to the solutions of the linearized Boltzmann equation or the DSMC data for the Knudsen numbers of O (1) .

Keywords: Fluid Flow and Heat Transfer, Knudsen layer, Lattice Boltzmann method (LBM), Micro-scale numerical simulation, Transition regime

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[1] C. M. Ho and Y. C. Tai, "Micro-electro-mechanical systems (MEMS) and fluid flows," in Ann. Rev. Fluid Mech. 30, p. 579, 1998.
[2] S. Roy, S. Chakraborty, "Near-wall effects in micro scale Couette flow and heat transfer in the Maxwell-slip regimes," in Microfluid Nanofluid, 3, 437-449, 2007.
[3] J. Chun and D. L. Koch, "A direct simulation Monte Carlo method for rarefied gas flows in the limit of small Mach number," Phys. Fluids, 17, 107107, 2005.
[4] G. E. Karniadakis, A. Beskok, and N. Aluru, Micro flows and nano flows: Fundamentals and simulation, Springer, New York, 2005.
[5] C. Cercignani, Slow rarefied flows: Theory and application to Microelectro- mechanical systems, Birkhäuser Verlag, Basel, Switzerland, 2006.
[6] N. G. Hadjiconstantinou, A. Garcia, M. Bazant and G. He, "Statistical error in particle simulations of hydrodynamic phenomena," in J. Comput. Phys., 187, 274, 2003.
[7] F. Sharipov, L. M. G. Cumin, and D. Kalempa, "Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number," in Eur. J. Mech. B/Fluids, 23, 899, 2004.
[8] S. Chen and G. D. Doolen, "Lattice Boltzmann method for fluid flows," in Ann Rev Fluid Mech, 30:329-64, 1998.
[9] X. Nie, G. D. Doolen and S. Chen, "Lattice Boltzmann simulations of fluid flows in MEMS," in J Stat Phys, 107, (1/2), 279, 2002.
[10] Y. H. Zhang, R. S. Qin, Y. H. Sun, R. W. Barber, and D. R. Emerson, "Gas flow in microchannels - A lattice Boltzmann method approach," in J. Stat. Phys. 121, 257, 2005.
[11] W. S. Jiaung and J. R. Ho, "Lattice Boltzmann study on size effect with geometrical bending on phonon heat conduction in a nanoduct," in J Appli. Physics, V. 95, N. 3, 2004.
[12] D. Yua, R. Meia, L. S. Luo and W. Shyy, "Viscous flow computations with the method of lattice Boltzmann equation," in Progress in Aerospace Sciences, 39, 329-367, 2003.
[13] N. S. Martys and H. D. Chen, "Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method," in Phys. Rev. E, 53, 743, 1996.
[14] P. Zhou and C.W. Wu, "Numerical simulation of electrocapillary driven flows," in Micro and Nanosystems, 1, 57-62, 2009.
[15] Z. L. Guo and T. S. Zhao, "Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids," in Phys. Rev. E, 68, 035302(R), 2003.
[16] X. He, S. Chen and G. D. Doolen, "A novel thermal model for the lattice Boltzmann method in incompressible limit," in J. Comput. Phys., 146, 282, 1998.
[17] Y. Shi, T. S. Zhao and Z. L. Guo, "Thermal lattice Bhatnagar-Gross- Krook model for flows with viscous heat dissipation in the incompressible limit," in Phys. Rev. E, 70, 066310, 2004.
[18] G. H. Tang, X. J. Gu, R. W. Barber, and D. R. Emerson, "Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow," in Phys. Rev. E, 78, 026706, 2008.
[19] Ansumali S. and Karlin I. V., "Kinetic boundary conditions in the lattice Boltzmann method," in Phys. Rev. E, 66, 026311, 2002.
[20] Y. H. Zhang, X. J. Gu, R. W. Barber and D. R. Emerson, "A thermal lattice Boltzmann model for low speed rarefied gas flow," Daresbury Laboratory Technical Report, TR- 2006-002, 2006.
[21] X.D. Niu, C. Shu and Y.T. Chew, "A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows," in Computers & Fluids, 36, 273-281, 2007.
[22] L. Zheng, B. C. Shi and Z. H. Chai, "Lattice Boltzmann method for simulating the temperature jump and velocity slip in microchannels," in Commun. Comput. Phys., Vol. 2, No. 6, 1125-1138, 2007.
[23] T. Lee and C. L. Lin, "Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel," in Phys. Rev. E, 71, 046706, 2005.
[24] Y. H. Zhang, R. S. Qin and D. R. Emerson, "Lattice Boltzmann simulation of rarefied gas flows in microchannels," in Phys. Rev. E, 71, 047702, 2005.
[25] H. P. Kavehpour, M. Faghri and Y. Asako, "Effects of compressibility and rarefaction on gaseous flows in microchannels," in Numer Heat Transfer, Part A: Applications, 32, 677 - 696, 1997.
[26] G. H. Tang, Y. H. Zhang and D. R. Emerson, "Lattice Boltzmann models for nonequilibrium gas flows," in Phys. Rev. E, 77, 046701, 2008.
[27] Y. H. Zhang, X. J. Gu, R. W. Barber and D. R. Emerson, "Capturing Knudsen layer phenomena using a lattice Boltzmann model," in Phys. Rev. E, 74, 046704, 2006.
[28] M. Ashrafizaadeh, and M. Shamshiri, "Two dimensional simulation of fluid flow in the Knudsen layer using a lattice Boltzmann approach," in Proc. 13 Annual and 2nd international Fluid Dynamics Conference, University of Shiraz, Shiraz, 2010, submitted for publication.
[29] G. H. Tang, Y. H. Zhang, X. J. Gu, R. W. Barber, and D. R. Emerson, "Lattice Boltzmann model for thermal transpiration," in Phys. Rev. E, 79, 027701, 2009.
[30] Y. Sone, S. Takata and T. Ohwada, "Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules," in Eur. J. Mech. B-Fluids, 9, 273, 1990.
[31] M. A. Gallis, D. J. Rader and J. R. Torczynski, "Calculations of the nearwall thermophoretic force in rarefied gas flow," in Phys. Fluids, 14, 4290, 2002.