Hydrodynamic interaction of two neutrally-buoyant smooth spheres suspended in plane Poiseuille flow: the BEM simulations versus the MoR approximations
Hydrodynamic interaction of two neutrally-buoyant smooth spheres suspended in plane Poiseuille flow: the BEM simulations versus the MoR approximations
复制标题
悬浮在平面泊肃叶流中的两个中性浮力光滑球体的流体动力相互作用：BEM 模拟与 MoR 近似
DOI：
10.1007/s00466-005-0668-3
复制
发表时间：
2005-04
影响因子：
4.1
通讯作者：
J.W. Leggoe
中科院分区：
文献类型：
--
作者：
林文贤;A.L. Graham;M.S. Ingber;J.R. Abbott;J.W. Leggoe
剪切流中悬浮颗粒间的流体动力学相互作用是描述悬浮流宏观特性的基础。虽然在静态或线性剪切流中的这种相互作用已经很好地理解，但在非线性剪切场中的这种相互作用的研究却很少。在这项研究中，两个中性浮力光滑球之间的流体动力学相互作用的运动在可忽略的雷诺数在无界平面Poiffille流已被计算的三维边界元法（BEM）模拟。边界元法的结果进行了比较与反射法（莫尔）近似得到的分析结果。已经发现，如果球体上的元素的数量大于200，而莫尔近似法只有在球之间的最小间距相对较大时才能提供令人满意的预测，尽管这种莫尔方法的优点是可以通过求解以下方程来容易地计算在无限二次流中以可忽略的雷诺数自由运动的两个球之间的流体动力相互作用常微分方程此外，还发现在平面Poiffille流中，球对重心在剪切平面内有优先的跨流线迁移，这在简单剪切流中是不存在的。当具有较大平移速度的球体接近另一个球体时，这种迁移总是指向低剪切区域，并且当更快的球体在剪切平面中引导另一个球体时，这种迁移朝向高剪切区域反转。球对重心在涡度平面内也有跨流线的迁移，但这种迁移没有优先方向。这些迁移是对称的点，在那里的领域是在最小的分离，只有当流体动力学相互作用的领域是强的，是显着的。这些结果表明，球对重心的迁移可以归因于剪切场的非线性，这与莫尔近似是一致的。两个球体之间的流体动力学相互作用已被量化在各种条件下的边界元模拟相同和不同的球体。
The hydrodynamic interaction between two particles suspended in shear flows is fundamental to the macroscopic characterization of suspension flows. Although such interaction in quiescent or linear shear flow is well understood, studies on that in a nonlinear shear field are rare. In this study, the hydrodynamic interaction between two neutrally-buoyant smooth spheres moving at negligible Reynolds numbers in an unbounded plane Poiseuille flow has been calculated by three-dimensional boundary element method (BEM) simulations. The BEM results have been compared with the analytical results obtained with the method-of-reflection (MoR) approximations. The BEM simulations have been found to provide satisfactory predictions if the number of elements on the spheres are more than 200, whereas the MoR approximations provide satisfactory predictions only when the minimum separation between the spheres is relatively large although this MoR method has the advantage to easily calculate the hydrodynamic interaction between two spheres freely moving at negligible Reynolds numbers in unbounded quadratic flow by solving ordinary differential equations. Furthermore, it is found that there is a preferential cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of shear in plane Poiseuille flow which does not arise in simple shear flow. This migration is always directed towards low shear regions when the sphere having larger translational velocity approaches the other sphere, and reverses towards high shear regions when the faster sphere leads the other sphere in the plane of shear. There is also a cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. These migrations are symmetric about the point where the spheres are at the minimum separation, and are only significant when the hydrodynamic interaction of the spheres is strong. These results show that the migration of the center-of-gravity of the sphere-pair can be attributed to the nonlinearity of the shear field, which agrees with the MoR approximations. The hydrodynamic interaction between the two spheres has been quantified under various conditions by the BEM simulations for both identical and disparate spheres.