Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

Experimental velocity profiles in laminar flow around spheres at intermediate Reynolds numbers

1975 ◽  
Vol 68 (3) ◽  
pp. 591-608 ◽  
Author(s):  
L. E. Seeley ◽  
R. L. Hummel ◽  
J. W. Smith
Keyword(s):  
Laminar Flow ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Separation Point ◽  
Navier Stokes ◽  
Similar Data ◽  
Navier Stokes Equation ◽  
Stream Functions ◽  
The Difference ◽  
Grid Points

Normal and tangential velocities in the boundary layer and out into the free stream have been obtained using a non-disturbing flow visualization technique for uniform laminar flow around a sphere. The non-similar data are available in tables at 2.5° intervals from 20° from the front to about 15° past the separation point a t Reynolds numbers of 290, 750, 1300 and 3000. Stream functions calculated by LeClair using a numerical solution of the Navier-Stokes equation at Re 21 300 are not in good agreement with measured values from 30° to 60°, but are in much better agreement around the separation point. Too few grid points near the sphere where the tangential velocities rise to a maximum above free-stream values may account for the difference.

Symbolic Calculation of Laminar Convection in Uniformly Heated Horizontal Pipe at High Prandtl Number

2010 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Laminar Flow ◽  
Prandtl Number ◽  
Reynolds Numbers ◽  
Similarity Parameter ◽  
Horizontal Pipe ◽  
Symbolic Calculation ◽  
High Prandtl Number ◽  
Flow Through ◽  
Laminar Convection ◽  
Steady Laminar

We consider fully developed steady laminar flow through a uniformly heated horizontal pipe is simplified by assuming infinite Prandtl number. The solution is expanded in powers of a single combined similarity parameter which is the product of the Prandtl, Rayleigh, and Reynolds numbers and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of exactness is almost the same order of the radius of convergence but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

scholarly journals Unstructured Grid Solutions for Incompressible Laminar Flow over a Circular Cylinder Using a Particular Finite Volume-Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mahdi Yousefifard ◽  
Parviz Ghadimi ◽  
Rahim Zamanian
Keyword(s):  
Laminar Flow ◽  
Circular Cylinder ◽  
High Performance ◽  
Unstructured Grid ◽  
Unstructured Grids ◽  
Control Volume ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equation

A numerical modeling of a 2D Navier-Stokes equation by a particular vertex centered control volume framework on an unstructured grid is presented in this paper. Triangular elements are applied with an effective high performance fully coupled algorithm, to simulate incompressible laminar flow over a circular cylinder. The cell face velocities in the discretization of the continuity and momentum equations are calculated by a combined linear and momentum interpolation scheme, respectively, and their performances are compared. Flow analyses have been conducted based on various Reynolds numbers up to 200 for the steady and unsteady flows using structured and unstructured grids. The robustness and accuracy of the scheme in the unstructured mesh are proved using the benchmark problems of incompressible laminar flow over a circular cylinder at low and medium Reynolds numbers. Results have been compared with the structured grid results, both cases with equal cell numbers and same strategy for the mesh refinement. Current results display good agreement with the experimental values. Overall, it is shown that, using the suggested method for the current problem, unstructured grids are highly competitive with the structured grids.

scholarly journals Application of Navier – Stokes Equation to Solve Fluid Flow Problems

2020 ◽  
pp. 101-114
Author(s):  
Ebiendele Ebosole Peter ◽  
Adamu Bala
Keyword(s):  
Fluid Flow ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Flow Through

The Navier – Stokes equations were used to obtain the velocity profile for two different fluid flow problems, firstly to a laminar flow through a pipe and secondly to flow of incompressible fluid between two boundaries, one boundary is the air and the other boundary moving with a velocity, inclined at an angle . The velocity profiles were obtained and presented in a diagram of showing how the fluid flow through the channels.

Laminar flow through a slowly rotating straight pipe

1985 ◽  
Vol 150 ◽  
pp. 1-21 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
Similarity Parameter ◽  
Low Reynolds Numbers ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Square Root Singularity ◽  
Flow Through ◽  
Steady Laminar

We consider fully developed steady laminar flow through a pipe that is rotating slowly about a line perpendicular to its own axis. The solution is expanded for low Reynolds numbers in powers of a single combined similarity parameter and the series extended to 34 terms by computer. Analysis shows that convergence is limited by a square-root singularity on the negative real axis of the similarity parameter. An Euler transformation and extraction of the leading, secondary and tertiary singularities at infinity render the series accurate for all values of the similarity parameter. The major conclusion of this investigation is that the friction ratio in a slowly rotating pipe grows asymptotically as the ⅛ power of the similarity parameter and not as the ¼ power as previously deduced from boundary-layer analysis. This discrepancy between the present computer-extended method and boundary-layer analysis has also occurred in the similar problem of flow through a loosely coiled pipe (Van Dyke 1978).

Suppression of vortex shedding behind a circular cylinder by another control cylinder at low Reynolds numbers

2007 ◽  
Vol 573 ◽  
pp. 171-190 ◽  
Author(s):  
A. DIPANKAR ◽  
T. K. SENGUPTA ◽  
S. B. TALLA
Keyword(s):  
Vortex Shedding ◽  
Physical Mechanism ◽  
Grid Method ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Control Cylinder

Vortex shedding behind a cylinder can be controlled by placing another small cylinder behind it, at low Reynolds numbers. This has been demonstrated experimentally by Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 74). These authors also provided preliminary numerical results, modelling the control cylinder by the innovative application of boundary conditions on some selective nodes. There are no other computational and theoretical studies that have explored the physical mechanism. In the present work, using an over-set grid method, we report and verify numerically the experimental results for flow past a pair of cylinders. Apart from providing an accurate solution of the Navier–Stokes equation, we also employ an energy-based receptivity analysis method to discuss some aspects of the physical mechanism behind vortex shedding and its control. These results are compared with the flow picture developed using a dynamical system approach based on the proper orthogonal decomposition (POD) technique.

scholarly journals Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid Substrate

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Hyun Jun Jeong ◽  
Wook Ryol Hwang ◽  
Chongyoup Kim
Keyword(s):  
Numerical Simulations ◽  
Solid Surface ◽  
Reynolds Numbers ◽  
Suspended Particles ◽  
Solid Substrate ◽  
Oscillatory Behavior ◽  
Navier Stokes ◽  
Droplet Spreading ◽  
Navier Stokes Equation ◽  
The Impact

We present two-dimensional numerical simulations of the impact and spreading of a droplet containing a number of small particles on a flat solid surface, just after hitting the solid surface, to understand particle effects on spreading dynamics of a particle-laden droplet for the application to the industrial inkjet printing process. The Navier-Stokes equation is solved by a finite-element-based computational scheme that employs the level-set method for the accurate interface description between the drop fluid and air and a fictitious domain method for suspended particles to account for full hydrodynamic interaction. Focusing on the particle effect on droplet spreading and recoil behaviors, we report that suspended particles suppress the droplet oscillation and deformation, by investigating the drop deformations for various Reynolds numbers. This suppressed oscillatory behavior of the particulate droplet has been interpreted with the enhanced energy dissipation due to the presence of particles.

The Onset of Turbulence: Insights Into the Navier-Stokes Equations

2017 ◽  
Author(s):  
Carl E. Rathmann
Keyword(s):  
Stokes Equations ◽  
Direct Consequence ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Fluid Behavior ◽  
Onset Of Turbulence ◽  
And Mathematics ◽  
High Reynolds

For well over 150 years now, theoreticians and practitioners have been developing and teaching students easily visualized models of fluid behavior that distinguish between the laminar and turbulent fluid regimes. Because of an emphasis on applications, perhaps insufficient attention has been paid to actually understanding the mechanisms by which fluids transition between these regimes. Summarized in this paper is the product of four decades of research into the sources of these mechanisms, at least one of which is a direct consequence of the non-linear terms of the Navier-Stokes equation. A scheme utilizing chaotic dynamic effects that become dominant only for sufficiently high Reynolds numbers is explored. This paper is designed to be of interest to faculty in the engineering, chemistry, physics, biology and mathematics disciplines as well as to practitioners in these and related applications.

Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
Author(s):  
Alain Merlen ◽  
Christophe Frankiewicz
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Around A Cylinder ◽  
Low Reynolds Numbers ◽  
Initial Location ◽  
Upstream Pressure ◽  
Small Reynolds Numbers ◽  
Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

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