The present work analyzes numerical simulations of long flexible fibers in two-dimensional flows. The focus is on the frequency at which caustics occur and the characterization of the collisions among fibers. The continuous flexible fibers are modeled as a set of connected rigid cylinders, where forces are applied to the center of mass of each cylinder determining their motion and fiber deformation. A domestic numerical code, which implements a fourth-order Runge–Kutta method to solve the system of ordinary differential equations, was validated against experimental data in a previous study. The two-dimensional steady analytical velocity fields correspond to the Arnold–Beltrami–Childress flows. Simulations are performed for a wide range of Stokes numbers ranging from 0.05 to 10.87. In a previous study, the frequency of caustics formation was shown to correlate strongly with fiber clustering. Now, a dimensionless caustics frequency is related to the Stokes number. The number of collisions correlates negatively with the Stokes number and positively with the clustering and the frequency of caustics formation. At low Stokes numbers, collisions are preferentially perpendicular, decreasing the angle of collision as the Stokes number increases. Most of the collisions occur at low relative velocities between the two colliding fibers. The angle of collision is strongly determined by vorticity and inertia, while the relative velocities of the fibers colliding seem to be determined by the characteristic velocity field.

中文翻译：

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二维流场中长柔性纤维的碰撞和焦散频率

目前的工作分析了二维流动中长柔性纤维的数值模拟。重点是焦散发生的频率以及纤维之间碰撞的特征。连续柔性纤维被建模为一组连接的刚性圆柱体，其中力被施加到每个圆柱体的质心，确定它们的运动和纤维变形。在先前的研究中，使用四阶 Runge-Kutta 方法求解常微分方程组的国内数值代码已根据实验数据进行了验证。二维稳态解析速度场对应于 Arnold-Beltrami-Childress 流。对范围从 0.05 到 10.87 的斯托克斯数进行了模拟。在之前的一项研究中，焦散形成的频率被证明与纤维聚集密切相关。现在，无量纲焦散频率与斯托克斯数相关。碰撞次数与斯托克斯数呈负相关，与聚集和焦散形成频率呈正相关。在低斯托克斯数下，碰撞优先垂直，随着斯托克斯数增加，碰撞角度减小。大多数碰撞发生在两个碰撞纤维之间的低相对速度下。碰撞角度主要由涡度和惯性决定，而纤维碰撞的相对速度似乎由特征速度场决定。碰撞次数与斯托克斯数呈负相关，与聚集和焦散形成频率呈正相关。在低斯托克斯数下，碰撞优先垂直，随着斯托克斯数增加，碰撞角度减小。大多数碰撞发生在两个碰撞纤维之间的低相对速度下。碰撞角度主要由涡度和惯性决定，而纤维碰撞的相对速度似乎由特征速度场决定。碰撞次数与斯托克斯数呈负相关，与聚集和焦散形成频率呈正相关。在低斯托克斯数下，碰撞优先垂直，随着斯托克斯数增加，碰撞角度减小。大多数碰撞发生在两个碰撞纤维之间的低相对速度下。碰撞角度主要由涡度和惯性决定，而纤维碰撞的相对速度似乎由特征速度场决定。大多数碰撞发生在两个碰撞纤维之间的低相对速度下。碰撞角度主要由涡度和惯性决定，而纤维碰撞的相对速度似乎由特征速度场决定。大多数碰撞发生在两个碰撞纤维之间的低相对速度下。碰撞角度主要由涡度和惯性决定，而纤维碰撞的相对速度似乎由特征速度场决定。