PERTURBATION SOLUTION OF SECONDARY FLOW OF POWER-LAW FLUID IN HELICAL PIPES WITH CIRCULAR CROSS-SECTION

In terms of tensor analysis technique, the Navier-Stokes equations in helical coordinate system were derived. A steady incompressible flow of power-law fluid in helical pipes at low Reynolds number was investigated by the perturbation method. A second order solution of secondary flow was worked out. The secondary flow characteristics in helical pipes are analyzed. The effects of the number Dn, curvature and torsion on the secondary flow at different flow parameters were discussed. The results show that the secondary flow pattern changes from a single vortex to two vortices as the number Dn increases at a given curvature and a given torsion. Because of the effect of torsion, the secondary flow pattern changes from two almost symmetrical vortices to a single vortex as the torsion of the helical pipe increases while the Reynolds number and curvature hold constant. The secondary flow pattern cannot be affected by the curvature of the helical pipe at a given Dn number.

Hot-rolled strips of up to 19 mm in thickness and their processing to helically welded large diameter pipes of grade X80

Hot-rolled wide strip for production of large diameter,heavy gauged(up to 19 mm) helical line pipe grade X80 was a priority development over the last three years.Microstructure,texture and mechanical properties of strips have been characterised.Also the welding conditions have been simulated.The favourable microstructure is achieved by the proper selection of an appropriate chemical composition of low carbon content and increased niobium micro alloying in combination with suitable strictly controlled hot-rolling parameters.The addition of niobium in combination with the adjustment of other alloying elements increases the recrystallisation stop temperature and thus makes it possible to apply a high temperature processing(HTP) concept.The homogeneous bainitic microstructure across the strip gauge is then formed during accelerated cooling on the run-out table of the hot-rolling mill.All results indicated excellent properties of these hot strips which make it suitable for spiral pipes of grade X80 for example 18.9mm×Φ1 220 mm at dimension.

A Contraction-expansion Helical Mixer in the Laminar Regime

A contraction-expansion helical mixer which combines several features, viz. helical pipes for induction of secondary flows and sudden expansion and contraction array tor expansion vortices, has been designed to en- hance flow mixing. A fast competitive-consecutive diazo coupling reaction is used to test the mixing efficiency of contraction-expansion helical mixer. Furthermore, an image processing technique is applied for data visualization and monitoring the extent of mixing. The mixing performance is found to be superior in comparison to the regular helical mixer in the range of Reynolds number from 170 to 1540. Moreover, the mixing time of contraction-expansion helical mixer was found to be reduced by more than 25% compared to the regular helical pipe. Finally, a simple correlation is proposed for predicting the mixing time.

FLUID FLOW IN A HELICAL PIPE

Without simplifying the N-S equations of Germano's[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.

On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe＇s geometry on the effective flow.

A STUDY ON THE UNSTEADY FLOW IN A HELICAL PIPE

A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels, using the method of bi-parameter perturbation. The second order perturbation results were obtained and the characteristics were analyzed at different time of the axial velocity, of the secondary flow, and of the wall shearing stress. Also done the analysis of above-mentioned variables that varied along with time and Womersley number. The results indicate that for a helical pipe, the torsion exerts the main influence on the distribution of secondary flow velocity, especially when the absolute value of axial press gradient is rather small. The severe variation of stream function takes place within a very short period, during which time the stream function develops from positive value to negative value and vice versa, while in most cases in a cycle, the variation is smooth. The wall shearing stress changes severely with theta too.

Experimental Study of the Flow in Helical Circular Pipes:Torsion Effect on the Flow Velocity and Turbulence

An objective of the present paper is to experimentally clarify the torsion effect on the flow in helical circular pipes. We have made six helical circular pipes having different pitches and common non-dimensional curvature δ of about 0.1. The torsion parameter β0, which is defined by β0 = τ/（2δ）1/2 with non-dimensional torsion r, are taken to be 0.02, 0.45, 0.69, 1.01, 1.38 and 1.89 covering from small to very large pitch. The velocity distributions and the turbulence of the flow are measured using an X-type hot-wire anemometer in the range of the Reynolds number from 200 to 20000. The results obtained are summarized as follows： The mean secondary flow pattern in a cross section of the pipe changes from an ordinary twin-vortex type as is seen in a curved pipe without torsion （toroidal pipe） to a single vortex type after one of the twin-vortex gradually disappears as β0 increases. The circulation direction of the single vortex is the same as the direction of torsion of the pipe. The mean velocity distribution of the axial flow is similar to that of the toroidal pipe at small β0, but changes its shape as β0 increases, and attains the shape similar to that in a straight circular pipe when ,β0 = 1.89. It is also found that the critical Reynolds number, at which the flow shows a marginal behavior to turbulence, decreases as ,β0 increases for small ,β0, and then increases after taking a minimum at ,β0 ≈ 1.4 as ,β0 increases. The minimum of the critical Reynolds number experimentally obtained is about 400 at ,β0 ≈ 1.4.

A STUDY ON THE FLOW IN HELICAL ELLIPTICAL PIPES WITH GALERKIN METHOD

The fully developed laminar flow in helical elliptical pipes is influenced by curvature, torsion and aspect ratio of cross-section. With the aid of the symbolic manipulation technique, the governing equations were solved by the Galerkin method, The procedures of implementing the Galerkin method for flows in curvilinear pipes were discussed. The effects of the aspect ratio and torsion on the flow structure, wall shear stress and flow ratio were examined in detail. The results show that the flow characteristic for aspect ratio larger than unit is quite different from those for the aspect ratio smaller than unit.

Numerical investigation of flow and heat transfer performances of horizontal spiral-coil pipes

The flow and heat transfer performances of horizontal spiral-coil pipes of circular and elliptical cross-sections are studied.The numerical results are compared with the experimental data,to verify the numerical method.The effects of the inlet water mass flow rate,the structural parameters,the helical pitch and the radius ratio on the heat transfer performances are investigated.Performances of the secondary fluid flow with different radius ratios are also investigated.Numerical results demonstrate that the heat transfer coefficient and the Nusselt number increase with the increase of the water mass flow rate or the helical pitch.The maximum heat transfer coefficient and the maximum Nusselt number are obtained when the radius ratio is equal to 1.00.In addition,the fluid particle moves spirally along the pipe and the velocity changes periodically.The particle flow intensity and the spiral movement frequency decrease significantly with the increase of the radius ratio.Besides,the secondary flow profile in the horizontal spiral-coil pipe contains two oppositely rotating eddies,and the eddy intensity decreases significantly along the pipe owing to the change of curvature.The decreasing tendency of the eddy intensity along the pipe increases with the increase of the radius ratio.