Numerical Analysis of Fully Developed Flow in Curved Square Ducts With Internal Fins

2004 ◽  
Vol 126 (5) ◽  
pp. 752-757 ◽  
Author(s):  
P. K. Papadopoulos ◽  
P. M. Hatzikonstantinou
Keyword(s):  
Friction Factor ◽  
Functional Relation ◽  
Transverse Plane ◽  
Complex Flow ◽  
Dean Number ◽  
Simple Method ◽  
Fully Developed Flow ◽  
Square Duct ◽  
Internal Fins ◽  
Square Ducts

The laminar incompressible flow in a curved square duct with two or four internal longitudinal fins is studied numerically with the SIMPLE method. The results show an increase of the friction factor depending on the fin height and the Dean number. The visualization of the flow reveals the existence of complex flow patterns in the transverse plane of the channel, where up to ten vortices are found to form. The effect of the curvature on the friction factor is examined and a functional relation for the latter is developed in terms of the Dean number and the fin height.

Fully Developed Flow in Curved Channels of Square Cross Sections Inclined

1989 ◽  
Vol 111 (2) ◽  
pp. 172-177 ◽  
Author(s):  
Tay-Yueh Duh ◽  
Yaw-Dong Shih
Keyword(s):  
Friction Factor ◽  
Cross Sections ◽  
Outer Wall ◽  
Dean Number ◽  
Fully Developed Flow ◽  
Minimum Value ◽  
Curved Channels ◽  
Factor Ratio ◽  
Inclination Angles ◽  
Factor Ratios

The fully developed viscous flow in curved channels of obliquely oriented square cross section with angle of inclination is analyzed for an incompressible fluid. A nonorthogonal helical coordinate system is introduced to study the flow field for various angles of inclination. To obtain a stationary numerical solution, a primitive-variable formulation of the pressure-velocity finite-difference scheme is formulated based on an ADI method. The results for the channel at zero angle are compared with data available in the literature. Detailed predictions of secondary-flow streamlines, axial velocities and friction factor ratios show that there are significant changes at inclination angles 0, 15, 30, 45, 60, and 75 deg. At a certain Dean number, it is found that no additional pair of vortices appears near the outer wall, except for angle of inclination 0 deg. If the Dean number is less than 125 the friction factor ratio has a minimum value at zero angle. If the Dean number is greater than 125, the minimum value of the friction factor ratio occurs at the angles of rotation 15 and 75 deg.

Numerical Procedure for the Laminar Developed Flow in a Helical Square Duct

2005 ◽  
Vol 127 (1) ◽  
pp. 136-148 ◽  
Author(s):  
V. D. Sakalis ◽  
P. M. Hatzikonstantinou ◽  
P. K. Papadopoulos
Keyword(s):  
Laminar Flow ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Procedure ◽  
Governing Equations ◽  
Axial Pressure ◽  
Dean Number ◽  
Square Duct ◽  
Orthogonal Coordinate System ◽  
Axial Pressure Gradient

The incompressible fully developed laminar flow in a helically duct of square cross section is studied expressing the governing equations in terms of an orthogonal coordinate system. Numerical results are obtained with the described continuity, vorticity, and pressure (CVP) numerical method using a colocation grid for all variables. Since there are not approximations, the interaction effects of curvature, torsion and axial pressure gradient on the velocity components and the friction factor are presented. The results show that the torsion deforms substantially the symmetry of the two centrifugal vortices of the secondary flow, which for large values of torsion combined with small curvature tend to one vortex covering the whole cross section. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behavior which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers.

The Effect of Torsion on the Bifurcation Structure of Laminar Flow in a Helical Square Duct

1995 ◽  
Vol 117 (2) ◽  
pp. 242-248 ◽  
Author(s):  
C. J. Bolinder
Keyword(s):  
Friction Factor ◽  
Flow Problem ◽  
Stable Solution ◽  
Flow Properties ◽  
Fully Developed Flow ◽  
Square Duct ◽  
New Correlation ◽  
Small Pitch ◽  
Simplec Algorithm ◽  
Volume Method

The laminar fully developed flow problem in a helical square duct with a finite pitch is solved numerically using the finite-volume method with the SIMPLEC algorithm. h2-extrapolation is used to locate the limit points of the stable solution branches. Results for the friction factor are presented. For helical ducts of small pitch, or torsion, it is verified that all investigated flow properties are very similar to those for a toroidal duct with the same dimensionless curvature. A new correlation is proposed for the friction factor ratio.

A Numerical Investigation of Developing Flow in Concentric and Eccentric Curved Square Annuli

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
M. R. H. Nobari ◽  
D. Rajaei
Keyword(s):  
Aspect Ratio ◽  
Friction Factor ◽  
Second Order ◽  
Projection Algorithm ◽  
Staggered Grid ◽  
Square Root ◽  
Governing Equations ◽  
Dean Number ◽  
Square Duct ◽  
Continuity Equations

In this article developing incompressible viscous fluid flow in concentric and eccentric curved square annuli are numerically studied. A second order finite difference method based on the projection algorithm is implemented to solve the governing equations, including the full Navier–Stokes and continuity equations in a cylindrical coordinate system. To discretize the governing equations in the square annulus, a uniform staggered grid is used to enforce an exact second order numerical scheme. The effects of the governing nondimensional parameters involving the aspect ratio, curvature, Reynolds number, Dean number, and eccentricity on the flow field, both in developing and fully developed regions of the curved annular square duct, are studied in detail. The numerical results obtained indicate that the friction factor in the eccentric curved square annulus increases with the square root of the Dean number (κ1/2) and the aspect ratio and decreases with the eccentricity. Furthermore, when the square root of the Dean number becomes larger than about 17.3, the friction factor increases linearly with the square root of the Dean number in the range of the current study.

Heat Transfer in Internally Finned Tubes

1976 ◽  
Vol 98 (2) ◽  
pp. 257-261 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Uniform Heat Flux ◽  
Heat Transfer Characteristics ◽  
Fully Developed Flow ◽  
Maximum Heat ◽  
Finned Tubes ◽  
Maximum Heat Transfer ◽  
Internal Fins ◽  
Laminar Forced Convection

Heat transfer characteristics for a laminar forced convection fully developed flow in an internally finned circular tube with axially uniform heat flux with peripherally uniform temperature are obtained using a finite element method. For a given fin geometry, the Nusselt number based on inside tube diameter was higher than that for a smooth tube. Also, it was found that for maximum heat transfer there exists an optimum fin number for a given fin configuration. The internal fins are of triangular shape.

Flowfield and Pressure Measurements in a Rotating Two-Pass Duct With Staggered Rounded Ribs Skewed 45Degrees to the Flow

2004 ◽  
Vol 128 (2) ◽  
pp. 340-348 ◽  
Author(s):  
Tong-Miin Liou ◽  
Y. Sian Hwang ◽  
Yi-Chen Li
Keyword(s):  
Friction Factor ◽  
Pressure Coefficient ◽  
Operating Conditions ◽  
Friction Loss ◽  
Main Stream ◽  
Pressure Measurements ◽  
Height Ratio ◽  
Mean Velocity ◽  
Square Duct ◽  
Pressure Distributions

Laser-Doppler velocimetry and pressure measurements are presented of the local velocity and wall pressure distributions in a rotating two-pass square duct with staggered ribs placed on the leading and trailing walls at an angle of 45deg to the main stream. The ribs were square in cross section with the radii of rounds and fillets to rib height ratios of 0.33. The rib-height/duct-height ratio and the pitch/rib-height ratio were 0.136 and 10, respectively. The duct Reynolds number was 1×104 and rotation number Ro ranged from 0 to 0.2. Results are documented in terms of the evolutions of both main flow and cross-stream secondary flow, the distributions of the pressure coefficient, and the variation of friction factor with Ro. For CFD reference, the periodic fully developed flow condition is absent for the present length of the rotating passage roughened with staggered 45deg ribs. In addition, the relationships between the regional averaged Nusselt number, transverse and convective mean velocity component, and turbulent kinetic energy are addressed. Using these relationships the general superiority of heat transfer enhancement of the staggered 45deg ribs arrangement over the in-line one can be reasonably illustrated. Simple expressions are obtained to correlate the friction factor with Ro, which are lacking in the published literature for passages ribbed with staggered 45deg ribs. The staggered 45deg ribs are found to reduce the friction loss to about 88%±1% of the in-line 45deg ribs for the rotating passage under the same operating conditions. The respective contributions of the angled ribs and passage rotation on the passage friction loss are identified.

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

Measurement of Laminar Flow Development in a Square Duct Using a Laser-Doppler Flowmeter

1967 ◽  
Vol 34 (4) ◽  
pp. 813-818 ◽  
Author(s):  
R. J. Goldstein ◽  
D. K. Kreid
Keyword(s):  
Laminar Flow ◽  
Precision Measurement ◽  
Fluid Velocity ◽  
Flow Distribution ◽  
Flow Region ◽  
Optical Technique ◽  
Fully Developed Flow ◽  
Square Duct ◽  
Flow Development ◽  
Doppler Flowmeter

A system for precision measurement of fluid velocity is developed and applied to determine the laminar flow distribution in a square duct. The experimental technique consists of measuring the Doppler shift of laser radiation scattered by particles moving with the fluid. From this frequency shift, the fluid velocity is inferred. Measurements in the entrance region and fully developed flow region of a square duct indicate that the velocity profile development takes place in a somewhat longer section of the duct than had been predicted. Measurements of the fully developed flow indicate that the optical technique used is capable of measuring velocity within an accuracy of at least 0.1 percent.

Flow in Rotating Straight Pipes of Circular Cross Section

1971 ◽  
Vol 93 (3) ◽  
pp. 383-394 ◽  
Author(s):  
H. Ito¯ ◽  
K. Nanbu
Keyword(s):  
Friction Factor ◽  
Cross Section ◽  
Circular Cross Section ◽  
Constant Angular Velocity ◽  
Smooth Wall ◽  
Good Qualitative Agreement ◽  
Fully Developed Flow ◽  
Number Range ◽  
Friction Factors ◽  
Laminar And Turbulent Flow

The friction factor for fully developed flow in smooth wall straight pipes of circular cross section rotating at a constant angular velocity about an axis perpendicular to its own has been measured in the Reynolds number range from 20 to 60,000. Empirical equations for friction factors for small values of RΩ/R were presented for both laminar and turbulent flow. In the case of laminar flow, an approximate analysis based on the assumption that the flow consists of a frictionless central core surrounded by a boundary layer was presented. The results were in good qualitative agreement with experimental results in regard to the friction factor, velocity distribution in the plane of symmetry and pressure distribution along the circumferential wall of the pipe.

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