On the solution of fiber orientation in two‐dimensional homogeneous flows
On the solution of fiber orientation in two‐dimensional homogeneous flows
复制标题
二维均匀流中纤维取向的求解
DOI：
10.1002/pen.760321208
复制
发表时间：
1992
影响因子：
3.2
通讯作者：
M. Altan
中科院分区：
文献类型：
--
作者：
S. Akbar;M. Altan
这项工作提出了一种分析技术来描述任意二维均匀流动中短纤维的取向行为。它示出的纤维取向，指定的单位矢量，可以分析计算在任何时刻使用任何初始取向和流动运动学。利用流体运动学计算得到的等效应变张量，用取向矢量分量来表示纤维随流体变形的旋转。然后，该技术用于评估大量纤维的取向行为，这些纤维从不同的初始取向开始，代表取向状态。通过考虑大量纤维的取向的频率分布曲线，统计地生成取向分布函数。结果表明，使用的解析解和统计方法的组合提供了一个方便的描述纤维取向行为。所产生的取向分布函数的精度被发现是依赖于在分析解决方案中使用的纤维的数量。统计方向分布函数进行了比较，某些均匀流的精确解，发现是在密切的协议。
This work presents an analytical technique to describe the orientation behavior of short fibers in arbitrary two-dimensional homogeneous flows. It is shown that the fiber orientation, specified by a unit vector, can be analytically calculated at any instant using any initial orientation and flow kinematics. The rotation of a fiber with the bulk fluid deformation is expressed in terms of orientation vector components by utilizing an equivalent strain tensor calculated from the fluid kinematics. This technique is then used to evaluate the orientation behavior of a large number of fibers starting from different initial orientations, representing an orientation state. The orientation distribution function is generated statistically by considering the frequency distribution curve of the orientation of the large number of fibers. It is shown that using a combination of analytical solutions and statistical methods provides a convenient description of fiber orientation behavior. The accuracy of the generated orientation distribution function is found to be dependent on the number of fibers used in the analytical solution. The statistical orientation distribution function is compared with the exact solutions for certain homogeneous flows and found to be in close agreement.