论文标题
关于在高雷诺数处的拖曳系数和单个球的努塞尔数中的对数项的存在
On the Existence of Logarithmic Terms in the Drag Coefficient and Nusselt Number of a Single Sphere at High Reynolds Numbers
论文作者
论文摘要
在二十世纪下半叶开始时，Proudman和Pearson（J.Fluid。Mech。，2（3），1956年，1956年，第237-262页）表明，单个球的功能形式（$ c_d $）的功能形式（$ c_d $）的单一球体均匀流动均匀流动，这是一系列Logarithmic and Power the Weilter of power the Weilter and Power of Reyn of Reyn norks norks norks norks norks norks norks norks norks norks norks norks norks norks norks norks norks norks norks（通过使用符号回归机器学习方法，探索上述语句的有效性最高$ 10^{6} $。 $ \ log（re）$，加上stokes术语，部分符合上述语句。对数$ c_d $表达式可以推广（外推）以外的培训数据，并且是文献中第一个以可接受的准确性预测的$ re $ $ $ $ $的$ c_d $的快速减少（拖动危机）。围绕一个球体的对流，发现$ re $ $ $ $ $＆peclect $ pe $的对数术语在努塞尔特数字$ nu $的变化中起着至关重要的作用。
At the beginning of the second half of the twentieth century, Proudman and Pearson (J. Fluid. Mech.,2(3), 1956, pp.237-262) suggested that the functional form of the drag coefficient ($C_D$) of a single sphere subjected to uniform fluid flow consists of a series of logarithmic and power terms of the Reynolds number ($Re$).\ In this paper, we will explore the validity of the above statement for Reynolds numbers up to $10^{6}$ by using a symbolic regression machine learning method.\ The algorithm is trained by available experimental data and data from well-known correlations from the literature for $Re$ ranging from $0.1$ to $2\times 10^5$.\ Our results show that the functional form of the $C_D$ contains powers of $\log(Re)$, plus the Stokes term, fulfilling partially the statement made above. The logarithmic $C_D$ expressions can generalize (extrapolate) beyond the training data and are the first in the literature to predict with acceptable accuracy the rapid decrease (drag crisis) of the $C_D$ at high $Re$.\ We also find a connection between the root of the $Re$-dependent terms in the $C_D$ expression and the first point of laminar separation.\ We did the same analysis for the problem of heat transfer under forced convection around a sphere and found that the logarithmic terms of $Re$ and Peclect number $Pe$ play an essential role in the variation of the Nusselt number $Nu$.\ The machine learning algorithm independently found the asymptotic solution of Acrivos and Goddard (J. Fluid. Mech., 23(2),1965, pp.273-291).
