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.

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 for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

The Torsion Effect on Fully Developed Laminar Flow in Helical Square Ducts

1993 ◽  
Vol 115 (2) ◽  
pp. 292-301 ◽  
Author(s):  
Wen-Hwa Chen ◽  
Ray Jan
Keyword(s):  
Laminar Flow ◽  
Secondary Flow ◽  
Friction Factor ◽  
Stokes Equations ◽  
Axial Flow ◽  
Outer Wall ◽  
Square Duct ◽  
Torsion Effect ◽  
Inclined Angle ◽  
Curvature And Torsion

The continuity equation and Navier-Stokes equations derived from a non-orthogonal helical coordinate system are solved by the Galerkin finite-element method in an attempt to study the torsion effect on the fully developed laminar flow in the helical square duct. Since high-order terms of curvature and torsion are considered, the approach is also applicable to the problems with finite curvature and torsion. The interaction effects of curvature, torsion, and the inclined angle of the cross section on the secondary flow, axial velocity, and friction factor in the helical square duct are presented. The results show that the torsion has more pronounced effect on the secondary flow rather than the axial flow. In addition, unlike the flow in the toroidal square duct, Dean’s instability of the secondary flow, which occurs near the outer wall in the helical square duct, can be avoided due to the effects of torsion and/or inclined angle. In such cases, a decrease of the friction factor is observed. However, as the pressure gradient decreases to a small value, the friction factor for the toroidal square duct is also applicable to the helical square duct.

Heat Transfer and Pressure Drop Correlation for Helicoidal Pipes of Rectangular Cross Section

2009 ◽  
Author(s):  
Christopher Katinas ◽  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Dean Number ◽  
Curvature Effects ◽  
The Impact

In this study, flow and heat transfer for laminar flow in curved channels of rectangular cross section is examined. The focus of the numerical solutions is on rectangular cross sections with an aspect ratio less than one, since little information is available for heat transfer in curved rectangular pipes whose width is greater than height. The study examines the impact of the aspect ratio and Dean number on both friction factor and Nusselt number. The results show that although both friction factor and Nusselt number increase as a result of curvature effects, the heat transfer enhancements significantly outweigh the friction factor penalty. Numerical solutions in this study consider the more realistic case of hydrodynamically developed and thermally developing flow.

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.

3D Simulation of Dean Vortices at 30° Position of 180° Curved Duct of Square Cross-Section under Opposing Buoyancy

2018 ◽  
Vol 389 ◽  
pp. 153-163 ◽  
Author(s):  
Mourad Mokeddem ◽  
Houssem Laidoudi ◽  
Mohamed Bouzit
Keyword(s):  
Cross Section ◽  
Richardson Number ◽  
Three Dimensions ◽  
Governing Equations ◽  
Dean Number ◽  
Thermal Buoyancy ◽  
Dean Vortices ◽  
Flow And Heat Transfer ◽  
Curved Duct ◽  
Physical Phenomena

3D numerical simulations are performed to analyze correctly the effect of opposing thermal buoyancy and Dean number on Dean vortices, fluid flow and heat transfer through 180° curved duct of square cross-section. Due to tremendous found results, this works emphasizes only at the position 30° of the bend portion. The governing equations involving momentum, continuity and energy are solved in three dimensions under these assumptions: the flow is laminar, steady-state and incompressible. The present study is investigated in the range of these conditions: Dean number of De = 125 to 150, Richardson number of Ri = 0 to 2 at Pr = 1. The principal obtained results are represented in forms of streamlines and isotherms to analyze and to discuss the found physical phenomena. The local Nusselt number along the wall of square cross-section is also computed and presented. The main found point is that the opposing thermal buoyancy has a tendency to eliminate the effect of centrifugal force at the position 30° of bend portion of 180° curved duct.

Theoretical Study of the Laminar Flow in a Channel With Moving Bars

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Hai-Ping Hu ◽  
Rong-Hua Yeh
Keyword(s):  
Laminar Flow ◽  
Cross Section ◽  
Eigenfunction Expansion ◽  
Theoretical Study ◽  
Reverse Flow ◽  
Governing Equations ◽  
Match Method ◽  
Poisson Equations ◽  
Aspect Ratios ◽  
The Mean

This paper presents a study of the laminar flow in a channel with longitudinal moving bars arrayed along the channel width. The governing equations describing the fluid, which flows along the direction of the bar’s length, are expressed with double Poisson equations and are solved by eigenfunction-expansion and point-match method. The result shows that when the solid bars move forward, the fluid flow will move in the same direction, and the f Re decreases as the positive velocity of bars increases. However, when the bars move backward, a reverse flow will occur in the channel, and the f Re is higher at larger negative velocity of bars. For a channel flow with moving bars, the f Re value is not a constant, such as a classical one without moving bars, in which the f Re value is a constant. Furthermore, when the area of the cross section of the bar is fixed, both the mean velocities and the f Re values of the fluid can be obtained under different velocities and aspect ratios of the bars.

Laminar flow in rotating curved pipes

1996 ◽  
Vol 329 ◽  
pp. 373-388 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Experimental Data ◽  
Laminar Flow ◽  
Friction Factor ◽  
Flow Structure ◽  
Flow Characteristics ◽  
Laminar Flows ◽  
Dean Number ◽  
Governing Parameter ◽  
Curved Pipes ◽  
Wide Range

When a curved pipe rotates about the centre of curvature, the fluid flowing in it is subjected to both Coriolis and centrifugal forces. Based on the analogy between laminar flows in stationary curved pipes and in orthogonally rotating pipes, the flow characteristics of fully developed laminar flow in rotating curved pipes are made clear and definite by similarity arguments, computational studies and using experimental data. Similarity arguments clarify that the flow characteristics in loosely coiled rotating pipes are governed by three parameters: the Dean number KLC, a body force ratio F and the Rossby number Ro. As the effect of Ro is negligible when Ro is large, computational results are presented for this case first, and then the effect of Ro is studied. Flow structure and friction factor are studied in detail. Variations of flow structure show secondary flow reversal at F ≈ −1, where the two body forces are of the same order but in opposite directions. It is also shown how the Taylor–Proudman effect dominates the flow structure when Ro is small. Computed curves of the friction factor for constant Dean number have their minimum at F ≈ −1. A composite parameter KL is introduced as a convenient governing parameter and used to correlate the characteristics. By applying KL to the analogy formula previously derived for two limiting flows, a semi-empirical formula for the friction factor is presented, which shows good agreement with the experimental data for a wide range of the parameters.

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