Experimental study of wall shear rates in the entry region of a curved tube

Local wall shear rates in steady flow in the entry region of a curved tube have been measured by the electrochemical limiting current method. A semi-circular rigid tube of circular cross-section with radius ratio 1/7 has been employed for a range of Dean number between 139 and 2868. The circumferential and axial distributions of the wall shear rates have been measured at 20° circumferential increments at five different sections of the entry region.

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Pulsating flow in a curved tube

Journal of Fluid Mechanics ◽

10.1017/s0022112073001795 ◽

1973 ◽

Vol 59 (4) ◽

pp. 693-705 ◽

Cited By ~ 57

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.

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An experimental study of pressure drop in helical pipes

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0020 ◽

1994 ◽

Vol 444 (1921) ◽

pp. 307-316 ◽

Cited By ~ 13

Keyword(s):

Experimental Study ◽

Reynolds Number ◽

Cross Section ◽

Circular Cross Section ◽

Square Root ◽

Dean Number ◽

Curvature Ratio ◽

Pressure Drops ◽

Newtonian Flows ◽

Fanning Friction Factor

Pressure drops of fully-developed incompressible laminar newtonian flows in helical pipes of constant circular cross-section having a finite pitch are experimentally investigated. For the case of loosely coiled pipes of 0 < η/λ < 41.22, f Re ( f is the Fanning friction factor and Re is the Reynolds number) is found to be proportional to the square root of the flow Dean number, Dn = Re λ ½ . Here λ and η are the normalized curvature ratio and torsion which incorporate both the coil radius and its pitch. In all cases studied, the experimental results for f Re are in excellent agreement with the theoretical prediction of Liu & Masliyah.

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Secondary flow in a curved tube

Journal of Fluid Mechanics ◽

10.1017/s0022112073001096 ◽

1973 ◽

Vol 57 (1) ◽

pp. 167-176 ◽

Cited By ~ 49

Author(s):

D. Greenspan

Keyword(s):

Nonlinear System ◽

Incompressible Fluid ◽

Cross Section ◽

Finite Differences ◽

Entire Range ◽

Steady Motion ◽

Circular Cross Section ◽

Reynolds Numbers ◽

Curved Tube ◽

Computer Calculations

The work of Dean and that of McConalogue & Srivastava on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended through the entire range of Reynolds numbers for which the flow is laminar. The coupled nonlinear system of partial differential equations which defines the motion is solved numerically by finite differences. Computer calculations are described and physical implications are discussed.

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Equilibrium radial positions of neutrally buoyant spherical particles over the circular cross-section in Poiseuille flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.881 ◽

2017 ◽

Vol 813 ◽

pp. 750-767 ◽

Cited By ~ 12

Author(s):

Yusuke Morita ◽

Tomoaki Itano ◽

Masako Sugihara-Seki

Keyword(s):

Experimental Study ◽

Cross Section ◽

Poiseuille Flow ◽

Equilibrium Position ◽

Probability Function ◽

Circular Cross Section ◽

Spherical Particles ◽

Inertial Migration ◽

Entry Length ◽

Neutrally Buoyant

An experimental study of the inertial migration of neutrally buoyant spherical particles suspended in the Poiseuille flow through circular tubes has been conducted at Reynolds numbers $(Re)$ from 100 to 1100 for particle-to-tube diameter ratios of ${\sim}$0.1. The distributions of particles in the tube cross-section were measured at various distances from the tube inlet and the radial probability function of particles was calculated. At relatively high $Re$, the radial probability function was found to have two peaks, corresponding to the so-called Segre–Silberberg annulus and the inner annulus, the latter of which was first reported experimentally by Matas et al. (J. Fluid Mech. vol. 515, 2004, pp. 171–195) to represent accumulation of particles at smaller radial positions than the Segre–Silberberg annulus. They assumed that the inner annulus would be an equilibrium position of particles, where the resultant lateral force on the particles disappears, similar to the Segre–Silberberg annulus. The present experimental study showed that the fraction of particles observed on the Segre–Silberberg annulus increased and the fraction on the inner annulus decreased further downstream, accompanying an outward shift of the inner annulus towards the Segre–Silberberg annulus and a decrease in its width. These results suggested that if the tubes were long enough, the inner annulus would disappear such that all particles would be focused on the Segre–Silberberg annulus for $Re<1000$. At the cross-section nearest to the tube inlet, particles were absent in the peripheral region close to the tube wall including the expected Segre–Silberberg annulus position for $Re>700$. In addition, the entry length after which radial migration has fully developed was found to increase with increasing $Re$, in contrast to the conventional estimate. These results may be related to the developing flow in the tube entrance region where the radial force profile would be different from that of the fully developed Poiseuille flow and there may not be an equilibrium position corresponding to the Segre–Silberberg annulus.

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Experimental Study of Nonlinear Effects under Torsion of the Uniform Cylinder with Initially Circular Cross Section

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.243.29 ◽

2015 ◽

Vol 243 ◽

pp. 29-34

Author(s):

V.P. Bachurikhin ◽

I.E. Keller ◽

A.F. Merzlyakov ◽

M.A. Yurlov

Keyword(s):

Experimental Study ◽

Cross Section ◽

Nonlinear Effect ◽

Cylindrical Specimen ◽

Axial Stress ◽

Circular Cross Section ◽

Nonlinear Effects ◽

Fixed Length ◽

Oscillatory Component

The results of experiments related to torsion of uniform cylindrical specimen at the fixed length between the specimens ends are presented in this paper. Axial stress has been found, initially stretching and then compressing the sample which has an oscillatory component with the period of one turn. Reasons of this nonlinear effect that are not described in the references are discussed here.

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Foam-Filled Grooved Tubes with Circular Cross Section Under Axial Compression: An Experimental Study

Iranian Journal of Science and Technology Transactions of Mechanical Engineering ◽

10.1007/s40997-017-0106-0 ◽

2017 ◽

Vol 42 (4) ◽

pp. 401-413 ◽

Cited By ~ 5

Author(s):

Mohammad Mahdi Abedi ◽

Abbas Niknejad ◽

Gholam Hossein Liaghat ◽

Mohammad Zamani Nejad

Keyword(s):

Experimental Study ◽

Axial Compression ◽

Cross Section ◽

Circular Cross Section ◽

Foam Filled

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Large Curvature Effect on Pulsatile Entrance Flow in a Curved Tube: Model Experiment Simulating Blood Flow in an Aortic Arch

Journal of Biomechanical Engineering ◽

10.1115/1.2795957 ◽

1996 ◽

Vol 118 (2) ◽

pp. 180-186 ◽

Cited By ~ 37

Author(s):

T. Naruse ◽

K. Tanishita

Keyword(s):

Blood Flow ◽

Aortic Arch ◽

Maximum Velocity ◽

Curvature Radius ◽

Wall Region ◽

Dean Number ◽

Large Curvature ◽

Curved Tube ◽

Wall Shear ◽

Entrance Flow

We measured the velocity profiles of pulsatile entrance flow in a strongly curved tube using a laser-Doppler anemometer in order to simulate blood flow in the aortic arch under various conditions, i.e., a ratio of tube to curvature radius of 1/3, Womersley parameters of 12 and 18, and peak Dean number up to 1200. Axial isovelocity contours of the cross-section showed the potential vortex to be near the entrance, and with the maximum velocity there being skewed towards the inner wall; thereafter shifting towards the outer wall. During the deceleration phase, reverse axial flow occurred near the inner wall, and a region of this flow extended downstream. The large curvature contributes to the enhancement of the secondary flow and flow reversal, which elevates the wall-shear stress oscillations. The location of elevated wall-shear oscillations corresponds to the vessel wall region where atherosclerotic formation frequently occurs; thereby indicating that both the large curvature and pulsatility play key roles in formation of localized atherosclerotic lesions.

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Calculation of the steady flow through a curved tube using a new finite-difference method

Journal of Fluid Mechanics ◽

10.1017/s0022112080000705 ◽

1980 ◽

Vol 99 (3) ◽

pp. 449-467 ◽

Cited By ~ 40

Author(s):

S. C. R. Dennis

Keyword(s):

Finite Difference ◽

Steady Flow ◽

Stokes Equations ◽

Steady Motion ◽

Circular Cross Section ◽

Navier Stokes ◽

Dean Number ◽

Numerical Work ◽

Curved Tube ◽

Flow Through

A numerical method is described which is suitable for solving the equations governing the steady motion of a viscous fluid through a slightly curved tube of circular cross-section but which is also applicable to the solution of any problem governed by the steady two-dimensional Navier–Stokes equations in the plane polar co-ordinate system. The governing equations are approximated by a scheme which yields finite-difference equations which are of second-order accuracy with respect to the grid sizes but which have associated matrices which are diagonally dominant. This makes them generally more amenable to solution by iterative techniques than the approximations obtained using standard central differences, while preserving the same order of accuracy.The main object of the investigation is to obtain numerical results for the problem of steady flow through a curved tube which corroborate previous numerical work on this problem in view of a recent paper (Van Dyke 1978) which tends to cast doubt on the accuracy of previous calculations at moderately high values of the Dean number; this is the appropriate Reynolds-number parameter in this problem. The present calculations tend to verify the accuracy of previous results for Dean numbers up to 5000, beyond which it is difficult to obtain accurate results. Calculated properties of the flow are compared with those obtained in previous numerical work, with the predictions of boundary-layer theory for large Dean numbers and with the predictions of Van Dyke (1978).

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