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.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 1storder 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.
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Key words:
- rough surface /
- small disturbance /
- perturbation method /
- static flow resistance /
- tortuosity
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