AN INFINITE-SERIES SOLUTION FOR THE CREEPING MOTION THROUGH AN ORIFICE OF FINITE LENGTH
AN INFINITE-SERIES SOLUTION FOR THE CREEPING MOTION THROUGH AN ORIFICE OF FINITE LENGTH
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DOI：
10.1017/s0022112082000883
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发表时间：
1982-01-01
影响因子：
3.7
通讯作者：
PFEFFER, R
中科院分区：
文献类型：
--
作者：
DAGAN, Z;WEINBAUM, S;PFEFFER, R
本文给出了流体在低、中纵横比孔隙中蠕动黏性运动的无穷级数解。流场被分为两个简单有界的区域：一个由孔壁和进出面围成的圆柱形体积，以及孔外的无限半空间。首先在每个区域得到代表孔隙入口（出口）任意轴向和径向速度剖面的未知函数的解析解。这些未知的功能，然后确定匹配的法向和切向应力在孔隙开放。结果表明，在接近孔隙半径一半的入口距离后，速度剖面接近泊泽维尔剖面的1.5%以内。在远场，该解与Sampson（1891）得到的流过零厚度孔的流线模式完全匹配。通过孔隙的压降与纵横比呈线性关系，并通过简单的代数表达式近似（误差小于1%）。
This paper presents an infinite-series solution to the creeping viscous motion of a fluid through low- and moderate-aspect-ratio pores. The flow field is divided into two simply bounded regions: a cylindrical volume bounded by the walls of the pore and the entrance and exit planes, and an infinite half-space outside the pore. Analytic solutions are first obtained in each region for unknown functions representing arbitrary axial and radial velocity profiles at the pore entrance (exit). These unknown functions are then determined by matching the normal and tangential stress at the pore opening.The results indicate that the velocity profile approaches to within 1·5 per cent of a Poiseuille profile after a short entrance distance of half the pore radius. In the far field the solution matches exactly the streamline pattern for a flow through an orifice of zero thickness obtained by Sampson (1891). The pressure drop across the pore exhibits linear dependence on the aspect ratio and is closely approximated (less than one per cent error) by a simple algebraic expression.