scholarly journals Secondary flow in a curved tube

1973 ◽  
Vol 57 (1) ◽  
pp. 167-176 ◽  
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.

Motion of a fluid in a curved tube

1968 ◽  
Vol 307 (1488) ◽  
pp. 37-53 ◽  
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Outer Boundary ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Polar Angle ◽  
Straight Tube ◽  
Curved Tube ◽  
Series Development

Dean’s work on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended. A method using a Fourier-series development with respect to the polar angle in the plane of cross-section is formulated and the resulting coupled non­linear equations solved numerically. The results are presented in terms of a single variable D = 4 R √(2 a/L ), where R is the Reynolds number, a the radius of cross-section of the tube, and L the radius of the curve. The results cover the range of D from 96 (the upper limit of Dean’s work) to over 600. From these it is found that the secondary flow becomes very appreciable for D = 600, moving the position of maximum axial velocity to a distance less than 0.38 a from the outer boundary, and decreasing the flux by 28% of its value for the straight tube. These calculations fill a large part of the gap in existing knowledge of secondary flow patterns, which lies in the upper range of Reynolds number for which flow is laminar. This range is of particular interest in the investigation of the cardiovascular system

scholarly journals Analogue tuning of particle focusing in elasto-inertial flow

Meccanica ◽  
2021 ◽  
Author(s):  
I. Banerjee ◽  
M. E. Rosti ◽  
T. Kumar ◽  
L. Brandt ◽  
A. Russom
Keyword(s):  
Numerical Simulations ◽  
Cross Section ◽  
Immersed Boundary Method ◽  
Circular Cross Section ◽  
Finite Size ◽  
Reynolds Numbers ◽  
Immersed Boundary ◽  
Particle Focusing ◽  
Inertial Flow ◽  
Particle Behaviour

AbstractWe report a unique tuneable analogue trend in particle focusing in the laminar and weak viscoelastic regime of elasto-inertial flows. We observe experimentally that particles in circular cross-section microchannels can be tuned to any focusing bandwidths that lie between the “Segre-Silberberg annulus” and the centre of a circular microcapillary. We use direct numerical simulations to investigate this phenomenon and to understand how minute amounts of elasticity affect the focussing of particles at increasing flow rates. An Immersed Boundary Method is used to account for the presence of the particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyse the particle behaviour at Reynolds numbers higher than what is allowed by the experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final focussing positions and extend our predictions to other geometries such as the square cross section. We believe complex effects originate due to a combination of inertia and elasticity in the weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other’s effect completely, leading to a number of intermediate focusing positions. The present study provides a fundamental new understanding of particle focusing in weakly elastic and strongly inertial flows, whose findings can be exploited for potentially multiple microfluidics-based biological sorting applications.

Friction Factor Determination for Flow Through Finite Wire-Mesh Woven-Screen Matrices

1997 ◽  
Vol 119 (4) ◽  
pp. 847-851 ◽  
Author(s):  
J. R. Sodre´ ◽  
J. A. R. Parise
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Mesh Size ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Wire Mesh ◽  
Hydraulic Radius ◽  
Fully Developed Flow ◽  
Flow Through ◽  
Screen Mesh

Experiments were carried out to determine the pressure drop through an annular conduit filled with a plain square wire-mesh woven-screen matrix. The tests involved turbulent fully developed flow of air at steady-state conditions, with the modified Reynolds number (M(1−ε)/Re), based on the hydraulic radius of the packed bed, ranging from 5 × 10−4 to 5 × 10−3. The test section was built according to the geometry of a Stirling engine, simulating an annular regenerator with a radius ratio of 1.369 and a screen of mesh size 10. A corrected Ergun equation was used to correlate the experimental data, considering the wall effects. Comparisons with results obtained by other authors extended the validation of the correlation obtained to a wider range of modified Reynolds numbers (1 × 10−4 ≤ M(1 − ε)/Re ≤ 1) and to different screen mesh sizes. The correlation has been found to work for annular and circular cross-section beds.

Influence of Surface Roughness on Shear Flow

2004 ◽  
Vol 71 (4) ◽  
pp. 459-464 ◽  
Author(s):  
S. Bhattacharyya ◽  
S. Mahapatra ◽  
F. T. Smith
Keyword(s):  
Cross Section ◽  
Numerical Solutions ◽  
Flat Surface ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Uniform Shear

The local planar flow of incompressible fluid past an obstacle of semi-circular cross section is considered, the obstacle being mounted on a long flat surface. The far-field motion is one of uniform shear. Direct numerical solutions of the Navier-Stokes equations are described over a range of Reynolds numbers. The downstream eddy length and upstream position of maximum pressure gradient are found to agree with increased Reynolds number theory; in particular the agreement for the former quantity is close for Reynolds numbers above about 50.

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

1980 ◽  
Vol 99 (3) ◽  
pp. 449-467 ◽  
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).

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

1979 ◽  
Vol 93 (3) ◽  
pp. 465-489 ◽  
Author(s):  
U. S. Choi ◽  
L. Talbot ◽  
I. Cornet
Keyword(s):  
Experimental Study ◽  
Cross Section ◽  
Circular Cross Section ◽  
Current Method ◽  
Limiting Current ◽  
Dean Number ◽  
Shear Rates ◽  
Rigid Tube ◽  
Curved Tube ◽  
Wall Shear

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.

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.

Numerical investigation of the effect of water/Al2O3 nanofluid on heat transfer in trapezoidal, sinusoidal and stepped microchannels

2019 ◽  
Vol 30 (5) ◽  
pp. 2439-2465 ◽  
Author(s):  
Vahid Jaferian ◽  
Davood Toghraie ◽  
Farzad Pourfattah ◽  
Omid Ali Akbari ◽  
Pouyan Talebizadehsardari
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Volume Fraction ◽  
Pure Water ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Two Phase ◽  
Content Type

Purpose The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode. Design/methodology/approach The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers. Findings Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels. Originality/value Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.

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