本研究目的在利用晶格波茲曼方法模擬雷諾數為1的顆粒流流經交錯排列之纖維的二維計算模型。顆粒運動軌跡由拉格朗日追踪法所描述, 結合了作用在顆粒上的阻力，重力，Saffman升力。我們探討了在顆粒尺寸為7奈米到500奈米，填充密度和纖維幾何形狀對顆粒捕捉效率之影響，此範圍包含了主要的顆粒捕捉機制:布朗擴散，攔截和慣性衝擊。填充密度的範圍為5.6%到19.63%。結果顯示纖維排列和顆粒收集有一定相關程度。本研究中採用的纖維幾何外形包含圓柱、菱形和正方形纖維。在幾何外形研究中，發現在攔截機制主導下菱形纖維有較佳的顆粒捕捉率。我們還利用晶格波茲曼細胞自動化方法在布朗擴散機制主導下模擬單一纖維與相連纖維之顆粒負載。其模擬結果顯示出了顆粒堆積圖像與位於表面的枝狀結構。

The aim of this paper is to present a 2-D computational model of particle-laden flows over staggered fibers at a Reynolds number of 1 by using a Lattice Boltzmann method. The trajectory of particle motion are described by Lagrangian tracking method with a combination of drag, gravity, Saffman lift force, Brownian forces acting on the particles. This study investigated the effect of packing density and fiber geometry in particle size from 7 nm to 500 nm, the range includes main particle collection mechanisms: Brownian diffusion, interception and inertial impaction. The packing density of fiber ranges from 5.6% to 19.63%. Present results show the correlation between fiber arrangements and particle collection. The fiber geometry adopted in the study includes cylinder, diamond and square. It is found out that among the geometries studied, fibers with diamond shape have higher particle capture efficiency in the interception mechanism dominated cases. We also simulate the particle loading on a single fiber and two attached fibers using a Lattice Boltzmann cellular automata method in Brownian diffusion dominated cases. The simulation results present the patterns of particle deposition and the dendrite structure on fiber surface.

論文審定書 i
致謝 ii
中文摘要 iii
ABSTRACT iv
CONTENTS v
LIST OF FIGURES vii
LIST OF TABLES xi
NOMENCLATURE xii
CHAPTER 1 1
INTRODUCTION 1
CHAPTER 2 4
PROPOSED METHODOLOGY 4
2.1 Fluid phase 4
2.1.1 Lattice Boltzmann method 4
2.1.2 D2Q9 8
2.1.3 Boundary conditions 8
2.2 Particle phase equation 11
2.3 The cell automation probabilistic model 14
CHAPTER 3 17
VALIDATION 17
3.1 Periodic flow 17
3.2 Particle transport 17
3.3 Particle transport for LBCA 20
CHAPTER 4 22
RESULTS 22
4.1 Effect of fiber packing density 25
4.2 Effect of fiber geometry 36
4.3 Effect of particle loading 42
CHAPTER 5 45
CONCLUSIONS 45
REFERENCE 46

[1] Kosinski, P., Kosinska, A., and Hoffmann, A. C., 2009, "Simulation of solid particles behaviour in a driven cavity flow," Powder Technology, 191(3), pp. 327-339.
[2] Yao, J., Zhao, Y., Hu, G., Fan, J., and Cen, K., 2009, "Numerical simulation of particle dispersion in the wake of a circular cylinder," Aerosol Sci Tech, 43(2), pp. 174-187.
[3] Yu, K., Lau, K., and Chan, C., 2004, "Numerical simulation of gas-particle flow in a single-side backward-facing step flow," J Comput Appl Math, 163(1), pp. 319-331.
[4] Dupuis, A., and Chopard, B., 2002, "Lattice gas modeling of scour formation under submarine pipelines," Journal of Computational Physics, 178(1), pp. 161-174.
[5] Mazzeo, M. D., and Coveney, P. V., 2008, "HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries," Computer Physics Communications, 178(12), pp. 894-914.
[6] Aidun, C. K., and Clausen, J. R., 2010, "Lattice-Boltzmann method for complex flows," Annual Review of Fluid Mechanics, 42, pp. 439-472.
[7] Ladd, A., and Verberg, R., 2001, "Lattice-Boltzmann simulations of particle-fluid suspensions," Journal of Statistical Physics, 104(5-6), pp. 1191-1251.
[8] Al‐Jahmany, Y. Y., Brenner, G., and Brunn, P. O., 2004, "Comparative study of lattice‐Boltzmann and finite volume methods for the simulation of laminar flow through a 4: 1 planar contraction," International journal for numerical methods in fluids, 46(9), pp. 903-920.
[9] Al-Zoubi, A., and Brenner, G., 2004, "Comparative study of thermal flows with different finite volume and lattice Boltzmann schemes," International Journal of Modern Physics C, 15(02), pp. 307-319.
[10] He, X., Doolen, G. D., and Clark, T., 2002, "Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier–Stokes equations," Journal of Computational Physics, 179(2), pp. 439-451.
[11] Martinez, D. O., Matthaeus, W. H., Chen, S., and Montgomery, D., 1994, "Comparison of spectral method and lattice Boltzmann simulations of two‐dimensional hydrodynamics," Physics of Fluids (1994-present), 6(3), pp. 1285-1298.
[12] Filippova, O., and Hänel, D., 1997, "Lattice-Boltzmann simulation of gas-particle flow in filters," Computers & Fluids, 26(7), pp. 697-712.
[13] Chen, S., Cheung, C., Chan, C., and Zhu, C., 2002, "Numerical simulation of aerosol collection in filters with staggered parallel rectangular fibres," Computational mechanics, 28(2), pp. 152-161.
[14] Li, X., Zhou, H., and Cen, K., 2008, "Influences of various vortex structures on the dispersion and deposition of small ash particles," Fuel, 87(7), pp. 1379-1382.
[15] Brandon, D. J., and Aggarwal, S., 2001, "A numerical investigation of particle deposition on a square cylinder placed in a channel flow," Aerosol Science & Technology, 34(4), pp. 340-352.
[16] Salmanzadeh, M., Rahnama, M., and Ahmadi, G., 2007, "Particle transport and deposition in a duct flow with a rectangular obstruction," Particulate Science and Technology, 25(5), pp. 401-412.
[17] Jafari, S., Salmanzadeh, M., Rahnama, M., and Ahmadi, G., 2010, "Investigation of particle dispersion and deposition in a channel with a square cylinder obstruction using the lattice Boltzmann method," Journal of Aerosol Science, 41(2), pp. 198-206.
[18] Masselot, A., and Chopard, B., 1998, "A lattice Boltzmann model for particle transport and deposition," EPL (Europhysics Letters), 42(3), p. 259.
[19] Chopard, B., and Masselot, A., 1999, "Cellular automata and lattice Boltzmann methods: a new approach to computational fluid dynamics and particle transport," Future Generation Computer Systems, 16(2), pp. 249-257.
[20] Chopard, B., Masselot, A., and Dupuis, A., 2000, "A lattice gas model for erosion and particles transport in a fluid," Computer physics communications, 129(1), pp. 167-176.
[21] Wang, H., Zhao, H., Wang, K., He, Y., and Zheng, C., 2013, "Simulation of filtration process for multi-fiber filter using the Lattice-Boltzmann two-phase flow model," Journal of Aerosol Science, 66, pp. 164-178.
[22] Wang, H., Zhao, H., Guo, Z., and Zheng, C., 2012, "Numerical simulation of particle capture process of fibrous filters using Lattice Boltzmann two-phase flow model," Powder Technology, 227, pp. 111-122.
[23] He, X., and Luo, L.-S., 1997, "Lattice Boltzmann model for the incompressible Navier–Stokes equation," Journal of Statistical Physics, 88(3-4), pp. 927-944.
[24] Tang, G., Tao, W., and He, Y., 2005, "Thermal boundary condition for the thermal lattice Boltzmann equation," Physical Review E, 72(1), p. 016703.
[25] Zou, Q., and He, X., 1997, "On pressure and velocity boundary conditions for the lattice Boltzmann BGK model," Physics of Fluids (1994-present), 9(6), pp. 1591-1598.
[26] Zou, Q., and He, X., 1996, "On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model," arXiv preprint comp-gas/9611001.
[27] Girimaji, S., 2012, "Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes," AIAA Journal, 51(1), pp. 278-279.
[28] Reist, P. C., 1993, "Aerosol science and technology. 2nd ed.," New York: McGraw-Hill.
[29] Saffman, P., 1965, "The lift on a small sphere in a slow shear flow," Journal of Fluid Mechanics, 22(02), pp. 385-400.
[30] Saffman, P., 1968, "Corrigendum to The lift on a small sphere in a slow shear flow," Journal of fluid mechanics, 31, p. 624.
[31] Li, A., and Ahmadi, G., 1992, "Dispersion and deposition of spherical particles from point sources in a turbulent channel flow," Aerosol science and technology, 16(4), pp. 209-226.
[32] Li, A., and Ahmadi, G., 1993, "Deposition of aerosols on surfaces in a turbulent channel flow," International Journal of Engineering Science, 31(3), pp. 435-451.
[33] Zare, A., Abouali, O., and Ahmadi, G., 2007, "Computational investigation of airflow, shock wave and nano-particle separation in supersonic and hypersonic impactors," Journal of Aerosol Science, 38(10), pp. 1015-1030.
[34] Akbar, M., Rahman, M., and Ghiaasiaan, S., 2009, "Particle transport in a small square enclosure in laminar natural convection," Journal of Aerosol Science, 40(9), pp. 747-761.
[35] Johnson, A. A., Tezduyar, T. E., and Liou, J., 1993, "Numerical simulation of flows past periodic arrays of cylinders," Computational mechanics, 11(5-6), pp. 371-383.
[36] Lee, K., and Liu, B., 1982, "Theoretical study of aerosol filtration by fibrous filters," Aerosol Science and Technology, 1(2), pp. 147-161.
[37] Stechkina, I., and Fuchs, N., 1966, "Studies on fibrous aerosol filters—I. Calculation of diffusional deposition of aerosols in fibrous filters," Annals of occupational Hygiene, 9(2), pp. 59-64.
[38] Yeh, H.-C., and Liu, B. Y., 1974, "Aerosol filtration by fibrous filters—I. Theoretical," Journal of Aerosol Science, 5(2), pp. 191-204.
[39] Brown, R. C., 1993, "Air Filtration: An Integrated Approach to the Theory and Applications of Fibrous Filters," Pergamon Press.