【作者】 石兴；

【导师】 林建忠；

【作者基本信息】 浙江大学 ， 流体力学， 2002， 博士

【摘要】 纤维悬浮流是自然界和各种生产工程中都广泛存在的流动，该流动在复合材料、环境、纺织、制药等诸多方面起重要的作用。因此对纤维悬浮流进行研究有重要意义。本文采用理论、数值模拟和实验的手段，从两个角度来研究一些具有代表性的纤维悬浮流场。 一是研究大量纤维在大尺度拟序结构中的分布规律。主要用到的方法是谱方法和细长体理论。研究结果表明：在拟序结构占主导地位的流场中，大涡结构对纤维的分布有强烈的组织作用；表征纤维跟随性的Stokes数对纤维的空间分布起控制作用，小Stokes数的纤维均匀分布在流场中，当Stokes数增加到O(0.1)时，在大涡中心的纤维将离心到涡的边缘；纤维在大涡中的取向分布受Stokes数的影响不大，主要受流场控制，流场的拉伸方向及强度对纤维的影响更大；随着Stokes数的增大，混合层中，上下两层纤维的混合效果变差；连续介质模型在预测纤维的取向方面仍然适用，但不能全面反映拟序结构占主导地位的纤维悬浮流的全部特征。同时，计算结果与实验进行了对比，发现符合得较好。 二是采用格子Boltzmann方法对纤维运动进行了直接模拟。对纤维运动进行直接模拟的意义，除了对纤维本身的运动有了最直接的了解之外，还对建立两相流模型的封闭方程有重要意义。对于单根纤维的沉降，其稳定取向是轴线与重力方向垂直的方向；纤维的沉降速度随长径比的增加而增加，但趋势变缓；纤维的横向漂移随长径比增加而增加；长径比在3左右的纤维，旋转到稳定取向的速度最快。壁面对纤维的作用使纤维离开壁面，并且使纤维的沉降速度下降；平行于纤维轴线的平面的影响较垂直于纤维轴线的壁面大；本文成功模拟了两根纤维在不同初始相对位置的沉降过程，详细地描述了两根纤维相互作用；总的来说，只要纤维通过尾流耦合作用，尾流对纤维沉降是起促进作用；在剪切流中，Jeffery轨道周期随着Reynolds数的增加而增加；利用不连续Galerkin有限元和谱元方法成功地将格子Boltzmann方法应用到非结构网格上，使格子Boltzmann方法能更好地描述曲线边界。更多还原

【Abstract】 Fiber suspensions can be found in various natural phenomena and industrial processions and there still exist many unsolved problems. This thesis is divided into two parts to investigate fiber suspended flows.In the first part, the focus is put on the fiber distributions in large scale structures controlled flows. The mixing layer is selected as the example. The results reveal that the vortex has strong reorganizing effects on the fiber distributions. The Stokes number plays an important role in the distributions of fibers: fibers with small Stokes number have a homogenous distribution in the flow field, however, fibers with large Stokes numbers are centrifugated from the center of vortex and accumulated at the edge of the vortex. The fiber orientations are less affected by the Stokes number and depend more on the vortex structures. As the Stokes number increases, the fibers in the upper and lower layers are less mixed. The theory based on the continuum theory of fiber suspension is still successful in prediction on the fibers orientations, but can’t describe the whole characters in the large scale structures controlled fiber suspensions.In the second part, the motion of fibers is directly simulated via the lattice Boltzmann method. In the process of single fiber sedimentation, it is steady that the fiber axis orients horizontally. The terminal sedimentation rate and the lateral shifting rate increase with the particle aspect ratio. The fiber with the aspect ratio of about 2.8 rotates fastest to the stable location. The wall pushes the fibers away and hints the fibers sedimentation. The wall parallel to the fiber axis has stronger effect on the fiber than that vertical to the axis. In the shear flow, the period of the Jeffery orbit becomes longer while the Reynolds number increases. In this part, the sedimentation of two fibers with different initial distributions are successfully investigated. In conclusion, the wake accelerates the fibers sedimentation. At last, the discontinuous Galerkin method and spectral element method are successfully applied in the lattice Boltzmann method on the unstructured meshes, which makes it convenient in dealing with the curve boundary.更多还原