Summary of frictional drag coefficient relationships for spheres: Evolving solution strategies applied to an old problem
Summary of frictional drag coefficient relationships for spheres: Evolving solution strategies applied to an old problem
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DOI：
10.1016/j.ces.2017.04.037
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发表时间：
2017-08
影响因子：
4.7
通讯作者：
C. Ramírez
中科院分区：
文献类型：
--
作者：
C. Ramírez
1851年，斯托克斯报告了在缓慢或缓慢流动条件下，无界流体对稳定下落的球体施加的动能（形式阻力加摩擦阻力）的解析解。这个所谓的斯托克斯定律在20世纪早期被几位作者改进了，他们在描述牛顿绕球运动的纳维-斯托克斯方程中加入了斯托克斯忽略的惯性项的各种近似。Lapple和Shepherd（1940）在这一基础理论工作的基础上，绘制了一个具有里程碑意义的图，将实验摩擦阻力系数f（与动能大小成正比）与基于球体直径的雷诺数Re（0.1≤Re≤3.0E+06）联系起来。研究人员很快意识到Stokes定律（对Re< 0.1有效）不足以解释整个Re跨度的数据，从而产生了新的解决方法来预测（Re）。该交流给出了众所周知的（Re）关系的时间顺序列表，提供了对其开发中使用的基本原理和策略的见解。因此，现代化学工程师可以很容易地评估这个问题的发展，并认识到在淹没球体周围流体流动领域的剩余研究空白。
In 1851 Stokes reported his analytical solution for the kinetic force (form drag plus frictional drag) exerted by an unbounded fluid on a steadily falling sphere under very slow or creeping flow conditions. This so called Stokes’ law was improved in the early 20th Century by several authors, who included diverse approximations to the inertia term neglected by Stokes in the Navier-Stokes equation describing Newtonian fluid motion around the sphere. Lapple and Shepherd (1940) followed this fundamental theoretical work with a landmark plot relating the experimental frictional drag coefficientf(directly proportional to the magnitude of the kinetic force) to the sphere diameter-based Reynolds number (Re) for 0.1 ≤Re≤ 3.0E+06. Researchers quickly realized that Stokes’ law (valid forRe< 0.1) was insufficient to explain the data over the entire span ofRe, giving rise to new solution methodologies to predictf(Re). This communication gives a chronological listing of well-knownf(Re) relationships, providing insights on the rationale and strategies used in their development. The modern chemical engineer can therefore readily assess the evolution of this problem and realize the remaining research gaps in the field of fluid flow around submerged spheres.