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arXiv 2007.10214physics.flu-dyn
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高Reynolds Numbers下单球阻力系数和努塞尔数中对数项的存在性

On the Existence of Logarithmic Terms in the Drag Coefficient and Nusselt Number of a Single Sphere at High Reynolds Numbers

Yousef El Hasadi, Johan Padding

摘要:

20世纪下半叶,Proudman和Pearson(J. Fluid.机械、2(3),1956,pp.237-262)提出,受到均匀流体流动的单个球体的阻力系数($C_D$)的函数形式由雷诺数($Re$)的一系列对数项和幂项组成。在本文中,我们将探讨上述声明的有效性雷诺数高达$10^{6}$通过使用符号回归机器学习方法。该算法是由现有的实验数据和数据从公知的相关性从$0.1$到$2\times 10^5$的$Re$的文献。我们的结果表明,$C_D$的功能形式包含权力的$\log(Re)$,加上斯托克斯项,部分履行上述声明。对数$C_D$表达式可以推广(外推)到训练数据之外,并且是文献中第一个以可接受的精度预测高$Re$时$C_D$的快速降低(阻力危机)的表达式。我们还发现了$C_D$表达式中$Re$依赖项的根与层流分离的第一个点之间的联系。我们对球周围的强制对流传热问题作了同样的分析,发现$Re$和Peclect数$Pe$的对数项对努塞尔数$Nu$的变化起着重要的作用。机器学习算法独立地找到了Acrivos和Goddard(J. Fluid.机械,23(2),1965,第273 -291页)。

英文摘要:

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).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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