Helical Pipe Research Articles

Potential flow in helical pipes

In this paper we studied the potential flow in a helical pipe using an orthogonal system of coordinates fixed to the helical axis. The analysis was conducted both analitically by applying perturbative methods and numerically. Results show that the torsion of the helical axis has little effect on axial velocity in a torus provided with the same curvature of the helix. At the same time it induces a large secondary flow that is expected to have a relevant effect on the boundary layer on the walls of the helical pipe.

Finite element analysis of incompressible viscous flow in a helical pipe

This paper presents an accurate finite element procedure to deal with steady state, fully developed and incompressible viscous flow in helical pipes with arbitrary curvatures and torsions. The full Navier-Stokes equations and continuity equation have been explicitly derived using a non-orthogonal helical coordinate system. To obtain the final simultaneous non-linear algebraic equations, a pressure-velocity finite element formulation is formulated based on the Galerkin Method.

Spatial vibrations of eflical heal-exchange pipes excited by internal flow of a heat carrier

The principal result of the present work is that on the basis of the variational principle of Hamilton-Ostrogradskii we obtained a complete system of differential equations of the vibrations of helical heat exchange pipes excited by internal flow of the heat carrier, and the analytical formulation of the set of all permissible boundary conditions is provided. It was shown that from the presented system there follow as special cases many results obtained earlier in connection with curved and straight pipes and spatial rods. It was established that depending on the conditions of constraint of the ends of a heat exchange pipe, the system may be conservative or nonconservative. In the former case, loss of stability may be in flexural form when the critical flow rate is exceeded, in the latter case it is the flutter form. We examined actual examples of conservative and nonconservative systems, and we formulated boundary-value problems for them. The suggested equations and dependences may be the basis for further improvement of the theory of vibrations of spatial heat exchange pipes excited by a flow of heat carrier, by taking additionally into account the viscosity of the liquid, the nonsteady state of the flow, the initial stresses in the pipe, the rotary inertia of its sections, damping, and other factors in dependence on the problem under examination and the accuracy required for the actual applications. On the other hand, being very general, the equations and dependences may find applications of their own in practical engineering calculations.

On the effect of torsion on a helical pipe flow

An orthogonal coordinate system along a generic spatial curve has been introduced, and the Navier-Stokes equations for a steady incompressible viscous flow have been explicitly written in this frame of reference. As an application the flow in a helical pipe has been studied, and, formdii 5f curvature and torsion small compared with the radius of the pipe, the flow has been considered as a perturbed Poiseuille flow. The result is that for curvatures and torsions of the same order and for low Reynolds number the curvature induces on the flow a first-order effect on the parameter e =κa, where κ is the curvature and a the radius of the pipe, while the effect of the torsion on the flow is of the second order in E. This last result disagrees with those of Wang (1981), who, adopting a non-orthogonal coordinate system, found a first-order effect of torsion on the flow.

On the low-Reynolds-number flow in a helical pipe

A non-orthogonal helical co-ordinate system is introduced to study the effect of curvature and torsion on the flow in a helical pipe. It is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40. When the Reynolds number is of order unity, torsion induces a secondary flow consisting of one single recirculating cell while curvature causes an increased flow rate. These effects are quite different from the two recirculating cells and decreased flow rate at high Reynolds numbers.

Calendar

The problem of steady incompressible laminar flow in helically coiled pipes is addressed from an experimental and numerical point of view. At first a brief review of published works on the subject presents some of the main steps made toward the comprehension of the considered phenomenon. An experimental campaign performed in a facility simulating a helical tube of the Steam Generator of a Small-medium Modular Reactor (SMR) is presented and discussed. In particular, the measured values of the Darcy friction factor are analyzed and then compared with numerous empirical correlations for laminar flow in helical pipes available in literature, in order to compare their predictions of friction pressure losses. Moreover, different numerical codes are applied. In particular the hydraulic problem of laminar flow in helical ducts is solved making use of commercial software, namely FLUENT, OpenFOAM fluid dynamic codes and COMSOL Multiphysics. The numerical simulation allows to describe the effect of geometry on the flow through the onset of a secondary motion and the deformation of the axial velocity profile, which affects in turn the friction factor. The prediction capabilities of the adopted codes are assessed comparing numerical friction factor values with experimental data and literature correlations. Maximum deviations result of the order of few percent.

フィラメント・ワインディング・パイプの静的および疲れ曲げ強度

This paper presents the results of analysis and tests conducted on the static bending strength of carbon fiber filament-wound (F.W.) cylindrical pipes and also the results of tests on fatigue flexural strength of the same F.W. pipes. The relation between the winding angles of F.W. pipes and their fracture strengths under pure bending is investigated. The analytical method of the fracture strength of F.W. pipe is as follows; the threedimensional stress components referring to the plane including fibers are analysed, taking account of the elastic failure prior to the overall fracture and then are compared with the fundamental strengths corresponding to the four kinds of fracture mechanisms of unidirectional fiber reinforced composites. As the results of the analysis, the fracture modes under pure bending of the helical winding pipe are determined in relation to its winding angle; 1) Winding angle α=0°∼10°, Fracture caused by compression stress in the fiber direction. 2) Winding angle α=15°∼30°, Fracture caused by tensile stress normal to fibers. 3) Winding angle α=35°∼50°, Fracture caused by shear stress. 4) Winding angle α=55°∼90°, Fracture caused by tensile stress normal to fibers. The static and fatigue flexural tests are done on carbon fiber F.W. pipes in which helical winding angles are α=15°, 25°, 35°, 45°. By using a newly-devised chuck, the fatigue test of the F.W. cylindrical pipe was carried out successfully. The bending fracture test results on the fracture strength and fracture modes coincide with the analytical ones. The flexural fatigue test results which showed that the ratio of the flexural fatigue strength at 107 cycles to the static bending strength are about 0.3 for the helical winding angle α=15°, 25°, and about 0.2 for α=35°, 45°.

Flow through a helical pipe with rectangular cross-section

The effects of torsion, aspect ratio and curvature on the flow in a helical pipe of rectangular cross- section are studied by introducing a non-orthogonal helical coordinate system. Spectral method is applied as main tool for numerical approach where Chebyshev polynomial is used. The numerical calculations are obtained by the iterative method. The calculations are carried out for 0≤ δ ≤0.02, 1≤ λ ≤ 2.85, 1≤ γ ≤2.4, at Dn = 50 & 100 respectively, where d is the non-dimensional curvature, l the torsion parameter, g the aspect ratio and Dn the pressure driven parameter (Dean number).DOI: http://dx.doi.org/10.3329/jname.v4i2.991 Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.99-110