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The gap flow field formed by two rotating cylinders and the fiber orientation in the gap flow field are studied numerically. The finite volume method on the collocated body fitted grid is used for solving the field. On the assumption that there is no relative motion between the fibers and the fluid, the motion of the fibers is determined. The velocities of fibers are calculated by bi-linear interpolation method. The orientation of fibers is obtained by solving the Jeffery equation. Periodic boundary conditions are used for the fiber motion to ensure that the fibers keep staying in the computational area. Two cases i. e., two cylinders rotate in the opposite directions with the same speed and only the mandrel cylinder rotates, are considered. Physical quantities, such as velocity and pressure, for each case are obtained. For the first case, the velocity and pressure are completely symmetric about the mid-line of the computational area and the absolute values of the maximum and minimum velocity are equal due to the fact that both the casing and mandrel cylinders rotate at the same speed. The absolute values of the maximum and minimum pressure are not equal because the radii of the two cylinders are different. For the second case that only the mandrel cylinder rotates, the symmetries of the velocity and pressure about the mid-line of the computational area can also be found although the absolute values of the maximum and minimum velocity are not equal because of the different velocities of the two cylinders. Fiber motions and orientations at different times for both cases are captured. The twisting of fibers (matrix) can be observed vividly. For the case that the casing and the mandrel cylinders rotate in the opposite directions, fibers move and orientate in a two-layer structure. While for the case that only the mandrel cylinder rotates, fibers move and orientation in a single-layered structure. For both cases, the fibers have a strong tendency to align along the stream lines of the field. The influence of the slenderness ratio of fibers on fiber orientation is also studied. A stronger tendency to align along the stream lines of the field can be found as the slenderness ratio of fibers increases.
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Keywords:
- concentric cylinders /
- body fitted coordinate /
- bi-linear interpolation /
- fiber orientation
[1] Yang B X, Ouyang J, Li X J 2012 Acta Phys. Sin. 61 044701 (in Chinese) [杨斌鑫, 欧阳洁, 栗雪娟 2012 61 044701]
[2] Zhang H P, Ouyang J, Ruan C L 2009 Acta Phys. Sin. 58 619 (in Chinese) [张红平, 欧阳洁, 阮春蕾 2009 58 619]
[3] Wan Z H, Sun Z L, You Z J 2007 J. Zhejiang Univ.-SC. 8 1435
[4] You Z J, Lin J Z, Yu Z S 2004 Fluid Dyn. Res. 34 251
[5] Pilipenko V N, Kalinichenko N M, Lemak A S 1981 Sov. Phys. Dokl. 26 646
[6] Wan Z H, Lin J Z, You Z J 2005 J. Zhejiang Univ.-SC. 6 1
[7] Wan Z H, Lin J Z, You Z J 2007 J. Zhejiang Univ. 23 41
[8] Parsheh M, Brown M L, Aidun C K 2006 J. Non-Newton. Fluid 136 38
[9] Khosla P K, Rubin S G 1974 Comput. Fluids 2 207
[10] Jasak H 1996 Ph. D. Dissertation (London:University of London)
[11] Pantaka S V 1980 Numerical heat transfer and fluid flow (London:CRC Press) p124
[12] Ouyang J, Li J H 1999 Chem. Eng. Sci. 54 2077
[13] Ouyang J, Li J H 1999 Chem. Eng. Sci. 54 5427
[14] Jeffery G B 1992 P. Roy. Soc. Lond. A 102 161
[15] Zhou K, Lin J Z 2008 Fiber Polym. 9 39
[16] Thompson J F, Thames F C, Martin C W 1974 J. Comput. Phys. 15 299
[17] Winslow A M 1967 J. Comput. Phys. 2 49
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[1] Yang B X, Ouyang J, Li X J 2012 Acta Phys. Sin. 61 044701 (in Chinese) [杨斌鑫, 欧阳洁, 栗雪娟 2012 61 044701]
[2] Zhang H P, Ouyang J, Ruan C L 2009 Acta Phys. Sin. 58 619 (in Chinese) [张红平, 欧阳洁, 阮春蕾 2009 58 619]
[3] Wan Z H, Sun Z L, You Z J 2007 J. Zhejiang Univ.-SC. 8 1435
[4] You Z J, Lin J Z, Yu Z S 2004 Fluid Dyn. Res. 34 251
[5] Pilipenko V N, Kalinichenko N M, Lemak A S 1981 Sov. Phys. Dokl. 26 646
[6] Wan Z H, Lin J Z, You Z J 2005 J. Zhejiang Univ.-SC. 6 1
[7] Wan Z H, Lin J Z, You Z J 2007 J. Zhejiang Univ. 23 41
[8] Parsheh M, Brown M L, Aidun C K 2006 J. Non-Newton. Fluid 136 38
[9] Khosla P K, Rubin S G 1974 Comput. Fluids 2 207
[10] Jasak H 1996 Ph. D. Dissertation (London:University of London)
[11] Pantaka S V 1980 Numerical heat transfer and fluid flow (London:CRC Press) p124
[12] Ouyang J, Li J H 1999 Chem. Eng. Sci. 54 2077
[13] Ouyang J, Li J H 1999 Chem. Eng. Sci. 54 5427
[14] Jeffery G B 1992 P. Roy. Soc. Lond. A 102 161
[15] Zhou K, Lin J Z 2008 Fiber Polym. 9 39
[16] Thompson J F, Thames F C, Martin C W 1974 J. Comput. Phys. 15 299
[17] Winslow A M 1967 J. Comput. Phys. 2 49
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