樹脂轉注成型為一種常見的複合材料製造方法，其製程大致可分為
關模、充模與開模等階段，充模階段為模具閉合後樹脂注入模具浸潤纖維並同時將空氣從排氣口排出的過程，而充模過程中樹脂浸潤纖維的流動行為為製作複材品質的重要因素。本文使用晶格波茲曼法搭配Shan-Chan提出的單組分偽勢模型與單向自由表面模型來模擬樹脂於模具內的流動情形，此方法相較於傳統計算流體力學方法的計算法則更為簡單與穩定。
考慮到實際纖維束形狀與排列形式的多樣性，本文採用圓形與橢圓
纖維束作為本文所探討的纖維束形狀，依纖維束排列型式與樹脂注入方
向，將其分為六種常見模型。透過改變樹脂與纖維的接觸角大小、充模速度、纖維束間距與纖維間隙等參數，探討樹脂注入六種模型時樹脂的流動行為與氣泡生成的差異。
依據各項參數的模擬比較結果，大致可提出以下結論，首先，本文所
使用的模擬方法，可成功匹配實際環氧樹脂的表面張力等材料性質與模
擬樹脂浸潤纖維時樹脂的流動行為，另外，透過改變單一參數，探討本文六種模型分別的氣泡生成情形。

Resin Transfer Molding (RTM) is a method for manufacturing polymer composite. The RTM process involves the resin injection into a mold cavity to infiltrate the fibers while the air is discharged from the outlet. Since the flow behavior of the resin infiltration in fibers is the key factor affecting the quality of the fabricated composite. In this thesis, we applied the Lattice Boltzmann method with single-component pseudo-potential model and single-phase free surface model to simulate the flow of resin infiltration in and between fiber bundles.
This method is simpler than the traditional computational fluid dynamics method in simulating the free surface flow with surface tension.
Because of the diversity of the fiber bundle shape and arrangement, we chose the circular and elliptical shapes to model fiber bundles in the simulations in order to reduce the amount of calculation. According to the fiber bundle arrangement and resin flow direction, it is divided into six models. The flow behavior of the resin injection and the possibility of bubble formation among those models were investigated by changing the factors as the resin and fiber contact angle, injection speed, fiber bundle spacing, fiber bundle arrangement, and the gaps between fibers.
This method used in this thesis successfully modeled the actual surface tension of epoxy resin, and simulated the flow behavior of the resin infiltration in fibers, which was also demonstrated to predict the possibility of air bubble formation in the fiber network during
the filling process.

[1] J. Williams, C. Morris, and B. Ennis, "Liquid flow through aligned fiber
beds," Polymer Engineering & Science, vol. 14, pp. 413-419, 1974.
[2] R. S. Parnas and F. Phelan, "The effect of heterogeneous porous media
on mold filling in resin transfer molding," Sampe Quarterly, vol. 22, pp.
53-60, 1991.
[3] J. Molnar, L. Trevino, and L. Lee, "Liquid flow in molds with prelocated
fiber mats," Polymer Composites, vol. 10, pp. 414-423, 1989.
[4] N. Patel, V. Rohatgi, and L. J. Lee, "Micro scale flow behavior and void
formation mechanism during impregnation through a unidirectional
stitched fiberglass mat," Polymer Engineering & Science, vol. 35, pp.
837-851, 1995.
[5] B. H. U. Frisch, and Y. Pomeau, "Lattice-gas cellular automata and
lattice Boltzmann models," Physical Review, vol. 56, pp. 1505-1508,
1986.
[6] S. Succi, The lattice Boltzmann equation: for fluid dynamics and beyond:
Oxford university press, 2001.
[7] G. R. McNamara and G. Zanetti, "Use of the Boltzmann equation to
simulate lattice gas automata," Phys Rev Lett, vol. 61, pp. 2332-2335,
Nov 14 1988.
[8] F. Higuera and J. Jimenez, "Boltzmann approach to lattice gas
simulations," EPL (Europhysics Letters), vol. 9, p. 663, 1989.
[9] F. Higuera, S. Succi, and R. Benzi, "Lattice gas dynamics with enhanced
collisions," EPL (Europhysics Letters), vol. 9, p. 345, 1989.
[10] H. Chen, S. Chen, and W. H. Matthaeus, "Recovery of the Navier-Stokes
equations using a lattice-gas Boltzmann method," Physical Review A, vol.
45, pp. R5339-R5342, 1992.
[11] Y. Qian, D. d'Humières, and P. Lallemand, "Lattice BGK models for
Navier-Stokes equation," EPL (Europhysics Letters), vol. 17, p. 479,
1992.
[12] P. L. Bhatnagar, E. P. Gross, and M. Krook, "A Model for Collision
Processes in Gases. I. Small Amplitude Processes in Charged and
95
Neutral One-Component Systems," Physical Review, vol. 94, pp. 511-
525, 1954.
[13] D. P. Ziegler, "boundary conditions for lattice Boltzmann simulation," j.
stat. phys, vol. 71, pp. 1171-1177, 1993.
[14] M. Y. Takaji Inamuro, and Fumimaru Ogino "a non-slip boundary
condition for lattice boltzmann simulations," physics of fluids, vol. 7, pp.
2928-2930, 1995.
[15] S. Chen, D. Martinez, and R. Mei, "On boundary conditions in lattice
Boltzmann methods," Physics of fluids, vol. 8, pp. 2527-2536, 1996.
[16] Q. Z. a. X. He, "On pressure and velocity boundary conditions for the
lattice Boltzmann BGK model," Phys. Fluids, vol. 9, pp. 1591-1598,
1997.
[17] A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, "Lattice
Boltzmann model of immiscible fluids," Physical Review A, vol. 43, pp.
4320-4327, 1991.
[18] D. H. R. a. J. M. Keller, "immiscible cellular automaton fluids," Journal
of Statistical Physics, vol. 52, pp. 1119-1127, 1988.
[19] X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows
with multiple phases and components," Physical Review E, vol. 47, pp.
1815-1819, 1993.
[20] M. R. Swift, W. R. Osborn, and J. M. Yeomans, "Lattice Boltzmann
simulation of nonideal fluids," Phys Rev Lett, vol. 75, pp. 830-833, Jul
31 1995.
[21] L.-S. Luo, "unified theory of lattice boltzmann models for nonideal
gases," Physical Review, vol. 81, pp. 1618-1621, 1998.
[22] X. S. X. He, G.D Doolen, "Discrete Boltzmann equation model for non
ideal gases," physical Review, vol. 57, pp. R13-R16, 1998.
[23] C. W. H. A. B. D. Nichols, "Volume of fluid (VOF) method for the
dynamics of free boundaries.pdf," Computational Physics, vol. 39, pp.
201-225, 1981.
[24] P. S. M. Sussman, S. Osher, "a level set approach for computing solutions
to incompressible two-phase flow," Computational physics, vol. 114, pp.
146-159, 1994.
[25] S. K. Ginzburg I, "Lattice Boltzmann model for Free-Surface flow and
its application to filling process in casting," Computational physics, pp.
61-99, 2003.
[26] C. Körner, M. Thies, T. Hofmann, N. Thürey, and U. Rüde, "Lattice
Boltzmann Model for Free Surface Flow for Modeling Foaming,"
Journal of Statistical Physics, vol. 121, pp. 179-196, 2005.
[27] N. Thürey, Rüde U, Körner C., "Interactive Free Surface Fluids with the
Lattice Boltzmann Method," University of Erlangen-Nuremberg,
Germany2005.
[28] Y.-S. H. Shing-Cheng Chang, amd Chieh-Li Chen "Lattice Boltzmann
simulation of fluid flows with fractal geometry: An unknown-index
algorithm," Chinese Society of Mechanical Engineers, vol. 32, pp. 523-
531, 2011.
[29] J. Hardy, Y. Pomeau, and O. de Pazzis, "Time Evolution of a Two-
Dimensional Classical Lattice System," Physical Review Letters, vol. 31,
pp. 276-279, 1973.
[30] U. Frisch, B. Hasslacher, and Y. Pomeau, "Lattice-gas automata for the
Navier-Stokes equation," Phys Rev Lett, vol. 56, pp. 1505-1508, Apr 07
1986.
[31] X. Shan and H. Chen, "Simulation of nonideal gases and liquid-gas phase
transitions by the lattice Boltzmann equation," Physical Review E, vol.
49, pp. 2941-2948, 1994.
[32] S. X. a. D. G, "Multi-component lattice-Boltzmann model with
interparticle interaction," Journal of Statistical Physics, vol. 81, pp. 379-
393, 1995.
[33] N. S. M. a. H. Chen, "Simulation of multicomponent fluids in complex
three-dimensional geometries by the lattice Boltzmann method,"
Physical Review, vol. 53, pp. 743-750, 1996.
[34] L. Chen, Q. Kang, Y. Mu, Y.-L. He, and W.-Q. Tao, "A critical review of
the pseudopotential multiphase lattice Boltzmann model: Methods and
applications," International Journal of Heat and Mass Transfer, vol. 76,
pp. 210-236, 2014.
[35] J. M.C. Sukop and D.T. Thorne, Lattice Boltzmann Modeling. Germany:
97
Springer-Verlag, 2005.
[36] X. Q. Xing, D. L. Butler, and C. Yang, "Lattice Boltzmann-based singlephase
method for free surface tracking of droplet motions," International
Journal for Numerical Methods in Fluids, vol. 53, pp. 333-351, 2006.
[37] R.-l. Zhang, Q.-f. Di, X.-l. Wang, and C.-y. Gu, "Numerical study of wall
wettabilities and topography on drag reduction effect in micro-channel
flow by Lattice Boltzmann Method," Journal of Hydrodynamics, Ser. B,
vol. 22, pp. 366-372, 2010.
[38] M. Saito, M. Takizawa, S. Sakuragi, and F. Tanei, "Infrared image guide
with bundled As–S glass fibers," Applied optics, vol. 24, pp. 2304-2308,
1985.
[39] 嚴培文, "真空輔助樹脂轉注成形法製造複合材料機翼結構肋之技
術與電腦模擬分析," 碩士, 紡織工程研究所, 逢甲大學, 台中市,
2007.
[40] T. Krüger, "Unit conversion in LBM," Germany.2011.
[41] W. B. Young, "Three ‐ dimensional nonisothermal mold filling
simulations in resin transfer molding," Polymer Composites, vol. 15, pp.
118-127, 1994.
[42] X. BAO, T. j. LU, R. WEI, Y. ZHANG, H. b. LI, H. CHEN, et al.,
"Application of Surface Contact Angle and Surface Tension
Measurements in the Identification of Gem Materials," Rock and
Mineral Analysis, vol. 33, pp. 681-689, 2014.
[43] N. Thürey and U. Rüde, "Stable free surface flows with the lattice
Boltzmann method on adaptively coarsened grids," Computing and
Visualization in Science, vol. 12, pp. 247-263, 2008.
[44] M. Schreiber, P. Neumann, S. Zimmer, and H.-J. Bungartz, "Free-
Surface Lattice-Boltzmann Simulation on Many-Core Architectures,"
Procedia Computer Science, vol. 4, pp. 984-993, 2011.
[45] 顏子翔, "應用晶格波茲曼法與場協同理論於不同阻礙物之背向階
梯管道熱流分析," 博士, 機械工程學系, 國立成功大學, 台南市,
2006.
[46] 李宜謙, "應用晶格波茲曼法模擬三維複雜幾何形狀管道之流動問
題," 碩士, 機械工程學系, 國立成功大學, 台南市, 2012.
[47] 林建城, "應用氣袋於可變形轉注成形法之研究," 碩士, 航空太空工
程學系, 國立成功大學, 台南市, 1996.
[48] 王成源, "RTM 製程模擬視窗程式設計," 碩士, 航空太空工程學系,
國立成功大學, 台南市, 2000.
[49] Shing-ChengChang, Lectures for the Lattice Boltzmann Method,
Department of Mechanical Engineering, NCKU, Taiwan, 2016.