scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Unsteady viscous flow in a curved pipe

1971 ◽  
Vol 45 (1) ◽  
pp. 13-31 ◽  
Author(s):  
W. H. Lyne
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Asymptotic Theory ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Curved Pipe ◽  
Unsteady Viscous Flow

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency ω. The radius of the pipeais assumed small in relation to the radius of curvature of its axisR. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number$R_s = \overline{W}^2a/R \omega\nu$, where$\overline{W}$is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of β it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.

Viscous laminar flow in a curved pipe of elliptical cross-section

1987 ◽  
Vol 184 ◽  
pp. 571-580 ◽  
Author(s):  
H. C. Topakoglu ◽  
M. A. Ebadian
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Finite Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Expansion Method ◽  
Elliptic Cross Section ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Elliptic Cross

In this paper, the analysis on secondary flow in curved elliptic pipes of Topakoglu & Ebadian (1985) has been extended up to a point where the rate-of-flow expression is obtained for any value of flatness ratio of the elliptic cross-section. The analysis is based on the double expansion method of Topakoglu (1967). Therefore, no approximation is involved in any step other than the natural limitation of the finite number of calculated terms of the expansions. The obtained results are systematically plotted against the curvature of centreline of the curved pipe for different values of Reynolds number.

scholarly journals Numerical Study of Turbulent Secondary Flows in Curved Ducts

1990 ◽  
Vol 112 (2) ◽  
pp. 205-211 ◽  
Author(s):  
N. Hur ◽  
S. Thangam ◽  
C. G. Speziale
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Secondary Flows ◽  
Fully Developed Turbulent Flow ◽  
Volume Method ◽  
Curved Ducts ◽  
Good Agreement

The pressure driven, fully developed turbulent flow of an incompressible viscous fluid in curved ducts of square cross-section is studied numerically by making use of a finite volume method. A nonlinear K -1 model is used to represent the turbulence. The results for both straight and curved ducts are presented. For the case of fully developed turbulent flow in straight ducts, the secondary flow is characterized by an eight-vortex structure for which the computed flowfield is shown to be in good agreement with available experimental data. The introduction of moderate curvature is shown to cause a substantial increase in the strength of the secondary flow and to change the secondary flow pattern to either a double-vortex or a four-vortex configuration.

Pulsating flow in a curved tube

1973 ◽  
Vol 59 (4) ◽  
pp. 693-705 ◽  
Author(s):  
R. G. Zalosh ◽  
W. G. Nelson
Keyword(s):  
Flow Field ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Analytic Solutions ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Tube Cross Section ◽  
Curved Tube

An analysis is presented of laminar fully developed flow in a curved tube of circular cross-section under the influence of a pressure gradient oscillating sinusoidally in time. The governing equations are linearized by an expansion valid for small values of the parameter (a/R) [Ka/ων]2, where a is the radius of the tube cross-section, R is the radius of curvature, ν is the kinematic viscosity of the fluid and K and ω are the amplitude and frequency, respectively, of the pressure gradient. A solution involving numerical evaluation of finite Hankel transforms is obtained for arbitrary values of the parameter α = a(ω/ν)½. In addition, closed-form analytic solutions are derived for both small and large values of α. The secondary flow is found to consist of a steady component and a component oscillatory at a frequency 2ω, while the axial velocity perturbation oscillates at ω and 3ω. The small-α flow field is similar to the low Dean number steady flow configuration, whereas the large-α flow field is altered and includes secondary flow directed towards the centre of curvature.

Steady motion within a curved pipe

1976 ◽  
Vol 347 (1650) ◽  
pp. 345-370 ◽  
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Steady Motion ◽  
Careful Consideration ◽  
Dean Number ◽  
Curved Pipe ◽  
Boundary Layer Problem ◽  
Flow Models ◽  
Passive Flow ◽  
Secondary Motion

The forcing of fluid through a tube, of uniform cross section (~ a ) and coiled to form an arc of a circle of radius R (≫ a ), by the application of a steady constant pressure gradient along the tube is discussed for large values of the Dean number D . An asymptotic description is presented for the fully-developed laminar flow within a general symmetric section, in which there is outward centrifuging of the secondary motion in the inviscid core, supplemented by a faster viscous return motion near the pipewalls, while the downpipe velocity increases steadily across the core. A similarity solution of the viscous flow, with the associated core flow thereby being determined, is calculated for a triangular cross section, but for a rectangular tube analytical and numerical arguments are put forward that point fairly conclusively to the non-existence of an attached laminar motion, near the inside bend at least, at high Dean numbers. For if the pressure-gradient is imagined to vary like the m th power of distance across the section, then computed results indicate that local solutions of the boundary layer problem can be found only for ( m -1/2). The assertion is backed up by an analytical study for small positive values of ( m -1/2). The dynamical properties in the neighbourhood of a flat outside bend, or of a ‘pinched' inside bend, of a tube also need careful consideration, although these may be essentially passive flow regions and some account of the local features there can be given. Near a flat outside bend two possible flow models arise, depending on the local nature of the coreflow.

Peristaltic motion

1967 ◽  
Vol 29 (4) ◽  
pp. 731-743 ◽  
Author(s):  
J. C. Burns ◽  
T. Parkes
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Cross Section ◽  
Stokes Flow ◽  
Peristaltic Motion ◽  
Axially Symmetric ◽  
First Case ◽  
Pipe Radius ◽  
The Mean ◽  
Perturbation Solutions

The flow of a viscous fluid through axially symmetric pipes and symmetrical channels is investigated under the assumption that the Reynolds number is small enough for the Stokes flow approximations to be made. It is assumed that the cross-section of the pipe or channel varies sinusoidally along the length. The flow is produced by a prescribed pressure gradient and by the variation in cross-section that occurs during the passage of a prescribed sinusoidal peristaltic wave along the walls. The theory is applied in particular to two extreme cases, peristaltic motion with no pressure gradient and flow under pressure along a pipe or channel with fixed walls and sinusoidally varying cross-section. Perturbation solutions are found for the stream function in powers of the ratio of the amplitude of the variation in the pipe radius or channel breadth to the mean radius or breadth respectively. These solutions are used to calculate, in particular, the flux through the pipe or channel for a given wave velocity in the first case and for a given pressure gradient in the second case. With a suitable notation it is possible to combine the analysis required for the two cases of pipe and channel flow.

Pulsating Flow for Mixing Intensification in a Twisted Curved Pipe

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
B. Timité ◽  
M. Jarrahi ◽  
C. Castelain ◽  
H. Peerhossaini
Keyword(s):  
Secondary Flow ◽  
Pipe Flow ◽  
Numerical Study ◽  
Pulsating Flow ◽  
Experimental Results ◽  
Chaotic Advection ◽  
Mean Deviation ◽  
Mixing Enhancement ◽  
Curved Pipe ◽  
Deceleration Phase

This work concerns the manipulation of a twisted curved-pipe flow for mixing enhancement. Previous works have shown that geometrical perturbations to a curved-pipe flow can increase mixing and heat transfer by chaotic advection. In this work the flow entering the twisted pipe undergoes a pulsatile motion. The flow is studied experimentally and numerically. The numerical study is carried out by a computational fluid dynamics (CFD) code (FLUENT 6) in which a pulsatile velocity field is imposed as an inlet condition. The experimental setup involves principally a “Scotch-yoke” pulsatile generator and a twisted curved pipe. Laser Doppler velocimetry measurements have shown that the Scotch-yoke generator produces pure sinusoidal instantaneous mean velocities with a mean deviation of 3%. Visualizations by laser-induced fluorescence and velocity measurements, coupled with the numerical results, have permitted analysis of the evolution of the swirling secondary flow structures that develop along the bends during the pulsation phase. These measurements were made for a range of steady Reynolds number (300≤Rest≤1200), frequency parameter (1≤α=r0⋅(ω/υ)1/2<20), and two velocity component ratios (β=Umax,osc/Ust). We observe satisfactory agreement between the numerical and experimental results. For high β, the secondary flow structure is modified by a Lyne instability and a siphon effect during the deceleration phase. The intensity of the secondary flow decreases as the parameter α increases during the acceleration phase. During the deceleration phase, under the effect of reverse flow, the secondary flow intensity increases with the appearance of Lyne flow. Experimental results also show that pulsating flow through a twisted curved pipe increases mixing over the steady twisted curved pipe. This mixing enhancement increases with β.

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