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本文对两同心旋转圆柱间隙形成的流场以及处于流场中的纤维运动和取向进行了数值研究. 在贴体坐标网格下求解了流场控制方程, 得到了流场中的速度、压力等物理量. 研究了两同心圆柱同速反向旋转以及仅内层圆柱旋转这两种情况下的纤维运动和取向状态. 得到了处于这两种情况下的纤维在流场中从静止到开始运动和取向直至最终达到稳定状态的动态详细过程. 结果表明, 当两个圆柱同速反向旋转时, 纤维运动与取向也相应的呈现两层结构; 而仅内圆柱旋转时, 纤维运动与取向呈单层结构. 在两种情况下, 纤维均沿流线方向运动和取向. 讨论了纤维长径比对纤维取向的影响, 结果表明随着纤维长径比的增加, 纤维沿流线取向的取向度逐渐增强.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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