Low Reynolds number flows in a microscopic and tapered tube with a permeability
Low Reynolds number flows in a microscopic and tapered tube with a permeability
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DOI：
10.1088/1873-7005/aaed57
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发表时间：
2019-01
影响因子：
1.5
通讯作者：
R. Egashira;T. Fujikawa;H. Yaguchi;S. Fujikawa
中科院分区：
文献类型：
--
作者：
R. Egashira;T. Fujikawa;H. Yaguchi;S. Fujikawa
在定常条件下，对具有渗透率的微小锥形管内的低雷诺数流动进行了理论研究。从一组不可压缩的轴对称流动的Navier-Stokes方程出发，导出了管内主流的动量方程。利用四次多项式的速度分布，推导出压力的二阶非线性常微分方程组，其中含有Re_2和Re_2阶的非线性项。得到的解分为两类：一类是雷诺数远小于161的流动，另一类是雷诺数大于但小于248的流动。并与原非线性微分方程解的精确解进行了比较。阐明了管壁渗透率和主流雷诺数对压力损失、主流速度的轴向和径向分量以及阻力系数的影响。此外，作为可渗透锥形管内流动的特例，对可渗透直管中的流动进行了研究，结果表明，当主流流经可渗透壁面时，在较大的雷诺数下会出现逆压差。因此，对于渗透管和锥形管，所得到的结果包含了不渗透锥形管和不透直管中的流动，后者是Hagen-Poiseuille流的特例。
Low Reynolds number flows in a microscopic and tapered tube with a permeability are theoretically investigated in steady conditions. A momentum equation for the main flow in the tube is derived from a set of incompressible Navier-Stokes equations for an axisymmetric flow. The second-order nonlinear ordinary differential equation on a pressure is derived using a velocity profile of the fourth-order polynomials for the main flow, in which there are nonlinear terms of both orders of Re2 and Re. Solutions obtained are classified into two types; one is a flow with a Reynolds number far less than 161, whilst another is a flow with a Reynolds number larger than the former case but smaller than 248. They are compared with an exact solution of the original nonlinear differential equation. Effects of the permeability of the tube wall and the Reynolds number of the main flow upon the pressure loss, the axial and radial components of the main flow velocity, and the resistance coefficient are clarified. Furthermore, a flow in a permeable and straight tube is investigated as a special case of the permeable and tapered tube, and it is demonstrated that an adverse pressure gradient takes place at a relatively large Reynolds number when the main flow is withdrawn through the permeable wall. As a consequence, the results obtained for the permeable and tapered tube contain flows in both the impermeable tapered tube and the impermeable straight tube, the latter of which is Hagen-Poiseuille flow, as special cases.