小Reynolds数下粗糙圆管中黏性流场的理论解

徐志敏; 宋思远; 辛锋先; 杨肖虎; 卢天健

doi:10.21656/1000-0887.380223

小Reynolds数下粗糙圆管中黏性流场的理论解

doi: 10.21656/1000-0887.380223

徐志敏^1,2,
宋思远^1,2,
辛锋先^1,2,
杨肖虎^1,3,
卢天健^1,2

¹西安交通大学多功能材料与结构教育部重点实验室, 西安 710049;²机械结构强度与振动国家重点实验室(西安交通大学), 西安 710049;³西安交通大学人居环境与建筑工程学院, 西安 710049

基金项目: 国家自然科学基金（中德（NSFC-DFG）合作研究项目）（11761131003）;国家自然科学基金（51528501；11772248）;国家自然科学基金委员会-中国航天科技集团公司航天先进制造技术研究联合基金（U1737107）;陕西省留学人员科技活动择优资助项目（2017025）

详细信息

作者简介:
徐志敏（1995—），男，博士生(E-mail: 1239231863@qq.com)；辛锋先（1982—），男，副教授，博士生导师（通讯作者. E-mail: fxxin@mail.xjtu.edu.cn)；卢天建（1964—），男，教授，博士生导师(通讯作者. E-mail: tjlu@mail.xjtu.edu.cn).

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出版历程
- 收稿日期: 2017-08-04
- 修回日期: 2017-09-11
- 刊出日期: 2018-02-15

Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes

¹MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, P.R.China;²State Key Laboratory for Strength and Vibration of Mechanical Structures (Xi’an Jiaotong University), Xi’an 710049, P.R.China;³School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R.China

Funds: The National Natural Science Foundation of China（11761131003；51528501；11772248；U1737107）

摘要

摘要: 在小Reynolds数下，针对粗糙圆管和花瓣圆管中的流场问题，将管内的粗糙表面视为光滑表面受到小扰动的情况，采用修正的摄动方法，对流体参数做微小扰动下的摄动展开.同时将具有复杂形貌的边界条件进行Taylor展开，进而近似得到光滑边界处的边界条件.联立求解流体力学方程，在一阶摄动展开的前提下，得到压力梯度的近似解，从而求出管道的静流阻和曲折度.通过数值模拟得到的流体参数和采用修正摄动方法求出的结果吻合良好.
- 粗糙表面 /
- 小扰动 /
- 摄动方法 /
- 静流阻 /
- 曲折度
Abstract: In view of the viscous flow fields of small Reynolds numbers in rough circular tubes and petal circular tubes, the rough surface in the tube was considered as a smooth surface subjected to small disturbance. The perturbation method was used to expand the perturbation of fluid parameters under small disturbance. The boundary conditions with complex morphologies were expanded into the Taylor series, and the smooth boundary conditions were approximately obtained. Then the fluid mechanics equations were solved simultaneously to give the approximate solution of the pressure gradient under the premise of the 1storder perturbation expansion, and the static flow resistance and tortuosity of the pipeline were obtained. The results show that the fluid parameters determined with the modified perturbation method agree very well with those through numerical simulation, and the theoretical approximate solution of the flow field in the rough pipe is validated.
- rough surface /
- small disturbance /
- perturbation method /
- static flow resistance /
- tortuosity

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参考文献(15)

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[5]	COLEBROOK C F, WHITE C M. Experiments with fluid friction in roughened pipes[J]. Proceedings of the Royal Society of London (Series A): Mathematical and Physical Sciences,1937,161(906): 367-381.
[6]	COLEBROOK C F, BLENCH T, CHATLEY H, et al. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws[J]. Journal of the Institution of Civil Engineers,1939,12(8): 393-422.
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[10]	QU Weilin, MALA G M, LI Dongqing. Pressure-driven water flows in trapezoidal silicon microchannels[J]. International Journal of Heat & Mass Transfer,2000,43(3): 353-64.
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[13]	KANDLIKAR S G, SCHMITT D, CARRANO A L, et al. Characterization of surface roughness effects on pressure drop in single-phase flow in minichannels[J]. Physics of Fluids,2005,17(10): 100606. DOI: 10.1063/1.1896985.
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小Reynolds数下粗糙圆管中黏性流场的理论解

doi: 10.21656/1000-0887.380223

作者简介:
徐志敏（1995—），男，博士生(E-mail: 1239231863@qq.com)；辛锋先（1982—），男，副教授，博士生导师（通讯作者. E-mail: fxxin@mail.xjtu.edu.cn)；卢天建（1964—），男，教授，博士生导师(通讯作者. E-mail: tjlu@mail.xjtu.edu.cn).

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Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes

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留言板

小Reynolds数下粗糙圆管中黏性流场的理论解

doi: 10.21656/1000-0887.380223

作者简介: 徐志敏（1995—），男，博士生(E-mail: 1239231863@qq.com)；辛锋先（1982—），男，副教授，博士生导师（通讯作者. E-mail: fxxin@mail.xjtu.edu.cn)；卢天建（1964—），男，教授，博士生导师(通讯作者. E-mail: tjlu@mail.xjtu.edu.cn).

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出版历程

Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes

计量

出版历程

目录

作者简介:
徐志敏（1995—），男，博士生(E-mail: 1239231863@qq.com)；辛锋先（1982—），男，副教授，博士生导师（通讯作者. E-mail: fxxin@mail.xjtu.edu.cn)；卢天建（1964—），男，教授，博士生导师(通讯作者. E-mail: tjlu@mail.xjtu.edu.cn).