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Pipe flow: a gateway to turbulence
Archive for History of Exact Sciences ( IF 0.5 ) Pub Date : 2020-10-02 , DOI: 10.1007/s00407-020-00263-y
Michael Eckert

Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers.

中文翻译:

管流:通往湍流的门户

管道流动一直是引起湍流研究的一个挑战——早在湍流本身被视为一个研究问题之前。从高架水库通过长管道排放水,例如凡尔赛的喷泉,建议调查与管道的不同直径和长度以及流速有关的阻力。尽管液压工程师进行了大量测量,但数据无法通过普遍接受的公式重现,更不用说理论推导了。供应高炉或矿井空气的长管道中的气流阻力似乎更难以合理阐述。19世纪,人们逐渐清楚,管流有层流和湍流两种模式。虽然前者可以在流体动力学理论的屋顶下被容纳,但后者被证明是难以捉摸的。当平滑管中的大量湍流管道流动数据显示为雷诺数的函数时,经验观察到的摩擦系数可作为搜索关于湍流皮肤摩擦的基本定律的指南。到 1930 年,对数“壁垒定律”似乎解决了这个问题。然而,管流作为一个研究课题并没有穷尽。它仍然在湍流研究的议程上名列前茅——无论是从层流到湍流的过渡,还是在非常大的雷诺数下完全发展的湍流。凭经验观察到的摩擦系数可作为寻找湍流皮肤摩擦基本定律的指南。到 1930 年,对数“壁垒定律”似乎解决了这个问题。然而,管流作为一个研究课题并没有穷尽。它仍然在湍流研究的议程上名列前茅——无论是从层流到湍流的过渡,还是在非常大的雷诺数下完全发展的湍流。凭经验观察到的摩擦系数可作为寻找湍流皮肤摩擦基本定律的指南。到 1930 年,对数“壁垒定律”似乎解决了这个问题。然而,管流作为一个研究课题并没有穷尽。它仍然在湍流研究的议程上名列前茅——无论是从层流到湍流的过渡,还是在非常大的雷诺数下完全发展的湍流。
更新日期:2020-10-02
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