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小Reynolds数下粗糙圆管中黏性流场的理论解 预览 被引量:1

Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes
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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. 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 sub- jected 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 approxi- mate solution of the pressure gradient under the premise of the lst-order perturbation expan- sion, 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.
作者 徐志敏 宋思远 辛锋先 杨肖虎 卢天健 XU Zhimin, SONG Siyuan, XIN Fengxian, YANG Xiaohu, LU Tianjian,(1. MOE Key Laboratory for Multifunctional Materials and Structures, Xi' an Jiaotong University, Xi' an 710049, P.R. China; 2. State Key Laboratory for Strength and Vibration of Mechanical Structures ( Xi' an Jiaotong University), Xi' an 710049, P.R. China; 3. School of Human Settlements and Civil Engineering, Xi' an Jiaotong University Xi' an 710049, P.R.China)
出处 《应用数学和力学》 CSCD 北大核心 2018年第2期123-136,共14页 Applied Mathematics and Mechanics
基金 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一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)
关键词 粗糙表面 小扰动 摄动方法 静流阻 曲折度 rough surface small disturbance perturbation method static flow resistance tortuosity
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).
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