发表机构
OXCBO Research（OXCBO研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究重新检验了Klyachko公式在有限雷诺数下球体阻力系数的准确性，发现其在Re<1000及分段扩展至3e5时表现合理，并通过示例展示了其在气溶胶动力学中的应用。
AI 中文摘要
评估在有限雷诺数Re下球体在流体中运动时的阻力系数Cd已成为流体动力学中的一个经典研究课题，由于缺乏闭合形式的数学解，多年来众多作者持续发表相关论文。迄今为止，计算Cd作为Re函数的数学公式只能通过将实验数据进行相关曲线拟合获得。其结果是各种具有不同数学拟合函数和越来越多拟合参数的公式并存。本研究聚焦于检验Klyachko 1934年提出的Cd公式的准确性，该公式使用两个常见分数作为拟合参数，能够对控制气溶胶球体直线运动的简化方程进行闭合形式积分。根据近期开发的公式计算得到的均方根相对误差值显示，Klyachko公式在Re小于1000时具有合理的准确性，其扩展到Re小于3e5时作为分段连续函数也表现良好，并且通过轻微修改有可能显著改进。因此，本文展示了几个示例，使用扩展的Klyachko公式研究直线加速度、计算气溶胶球体的终端速度等，为如何重新审视这一经典问题提供了新的视角。
英文摘要
Evaluating the drag coefficient Cd for a sphere moving in a fluid at finite Reynolds number Re has become a classical research subject in fluid dynamics, with publications appearing continuously by numerous authors over the years due to the unavailability of closed-form mathematical solutions. To date, mathematical formulas for calculating Cd as a function of Re can only be obtained by correlation curve fitting to experimental data. The consequence is the coexistence of various formulas with different mathematical fitting functions and an increasing number of fitting parameters. The present study focuses on examining the accuracy of Klyachko's 1934 formula for Cd with two common fractions as fitting parameters, which could enable closed form integration of a simplified equation governing rectilinear motion of aerosol spheres. The computed values of root-mean-square relative error from recently developed formulas show reasonable accuracy of the Klyachko formula for Re less than 1000 and its extension to Re less than 3e5 as a piecewise continuous function, with the possibility of significant improvement through a slight modification. Hence, a few demonstrative examples are presented using the extended Klyachko formula in the study of rectilinear acceleration, the calculation of the terminal velocity of aerosol spheres, and so forth, to shed fresh light on how this classical problem can be studied.
