The creeping motion in the entry region of a semi-infinite circular cylindrical tube
18 Nov 1983-Applied Mathematics and Mechanics-english Edition (Kluwer Academic Publishers)-Vol. 4, Iss: 6, pp 833-848
About: This article is published in Applied Mathematics and Mechanics-english Edition.The article was published on 1983-11-18. It has received 4 citations till now. The article focuses on the topics: Stokes flow & Semi-infinite.
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TL;DR: In this paper, a new semianalytical method, Hamiltonian systematic method, for solving axisymmetric problems of Stokes flow is presented. But the method is not suitable for the case of nonzero-eigenvalue solutions.
Abstract: This paper presents a new semianalytical method, Hamiltonian systematic method, for solving axisymmetric problems of Stokes flow. In the system, nonzero-eigenvalue solutions can describe local effect near the boundary and therefore the influence of inlet radius on the flow can be investigated. A rule of minimal entrance length is discussed on the basis of the criteria which are defined by axial flow deviating from the full developed (Hagen–Poseuille) flow. Numerical results show that the entrance length is related to the inlet radius, and there is one minimal point on the relationship curve, namely, there is one minimal entrance length. Besides, pressures have the characteristic too and the minimal point is same. The method can also be generalized to other fields.
12 citations
TL;DR: In this article, infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into a semi-infinite circular cylinder are presented, and the results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%.
Abstract: The infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The inlet length in this case is comparable to that computed for a finite circular cylinder pore by Dagan et al.[1]. In the half-space outside the cylinder pore region, the flow is strongly affected by the wall. Beyond one radius of the tube from the orifice, the solutions match almost exactly the flow through an orifice of zero thickness given by Sampson[2]. The relationship between the pressure drop and the volumetric flow rate is also computed in the present paper for the semi-infinite tube.
6 citations
TL;DR: In this article, a new kind of series solution was derived for the Stokes entry flow into a semi-infinite circular cylindrical tube, where the present solutions don't involve infinite integral.
Abstract: The problem of Stokes entry flow into a semi-infinite circular cylindrical tube was studied in this paper. A new kind of series solutions was derived. Their evident difference from the solutions in References [1,2] is that the present solutions don't involve infinite integral. So they are favourable for calculation. We calculated an example by allocated method and obtained satisfied results.
3 citations
TL;DR: In this paper, a basic function method is developed to treat the incompressible viscous flow, and the flow in finite-length pipe is calculated, the velocity and pressure distribution of which solved by the method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit.
Abstract: Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two- and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.
2 citations