半无穷平面到半无穷长圆管的低雷诺数流动
The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder
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摘要: 本文利用匹配法和配置法求出了粘性流体从半无穷平面到半无穷长圆管的Stokes流动的无穷级数形式的解.结果表明,经过圆柱半径的一半路程之后,速度剖面和Poiseuille剖面只差1%.初始段长度比Dagan的有限长圆管情形显著缩短,在孔口外的半无穷空间内,孔口右边的边界只对孔口附近一倍管径的区域有强烈影响.在此以外的区域内几乎没有影响.此外,本文还对压力和流量的关系进行了研究.Abstract: The infinite-series solutions for the creeping motion of a viscous imcomperssible fluid from half-space to semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of tube from the pore opening, the deviation of the velocity profile from the Poiseuille one becomes equal to or less than 1%.The inlet length in this case is considerably shorter than Dagan's finite circular cylinder one. In the half-space outside the cylinder pore the region, strongly affected by the tube wzll, is restricted within a narrow limit no more than one radius of the tube from the orifice. Beyond this region the solutions match almost exactly the Sampson's one for a flow through an orifice of Zero thickness, The relationship between the pressure drop and the volumetric flow rate is also considered in this paper.
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[1] Dagan,Z.,S.Weinbaum and R.Pfeffer.An infinite-series solution for the creeping motion through an orifice of finite length.J.Fluid Mech.,115(1982).502-523. [2] 吴望一,R. Skalak,应用数学和力学,4, 6(1983), 743-756. [3] Parmet,I.L.and E.Saibel,Axisymmetric creeping flow an orifice in a plane wall.Comm.Pure Appl.Math.18(1965),17. [4] Sampson, R.A Phil, Trans, Roy.Soc, Lond.,A182(1891), 449 [5] Erdelyi.A.,W.Magnus,F.Oberhettingen and F.G.Tricomi.Tables of Integral Transforms.Vol.11.McGraw-Hill.New York(1954). [6] Oberhettinger.F.,Table of Bessel Transforms,Springer Verlag.New York(1972). [7] Watson.G.M.,A Treatise on the Theory of Bessel Functions.2nd edition.Cambridge University Press.Cambridge,U.K.(1958). -
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