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.

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.

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.

Experiments on laminar flow in curved channels of square section

1971 ◽  
Vol 48 (3) ◽  
pp. 417-422 ◽  
Author(s):  
J. A. Baylis
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Laminar Flow ◽  
Friction Factor ◽  
Experimental Results ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Rectangular Section ◽  
Curved Channels ◽  
Channel Dimension

Recently Cheng & Akiyama (1970) published a numerical analysis of laminar flow in curved channels of square and rectangular section. Experimental results are presented here for flow in curved channels of square section. The channels were toroidal in shape, and the flow was driven electromagnetically. Various ratios of the channel dimension d to the channel radius of curvature, R, were used to investigate the dependence of friction factor, f, on the Dean number K, and the Reynolds number, Re. For 5 × 102 < K < 7 × 104 the formula (fRe) = 1·51 K½ was found to fit all the results, although R/d was varied from 17·5 down to the low value of 1·75. At lower values of K the analysis of Cheng & Akiyama was approximately validated.

scholarly journals Fluid boundaries shaping using the method of kinetic balance

2006 ◽  
Vol 10 (4) ◽  
pp. 153-162
Author(s):  
Miroslav Benisek ◽  
Svetislav Cantrak ◽  
Milos Nedeljkovic ◽  
Djordje Cantrak ◽  
Dejan Ilic ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Fluid Mechanics ◽  
Cross Sections ◽  
Hydraulic Engineering ◽  
Optimum Shape ◽  
Curved Channels ◽  
Unsteady Fluid Flow ◽  
Unsteady Fluid ◽  
Flow Boundaries ◽  
Dead Water

Fluid flow in curved channels with various cross-sections, as a common problem in theoretical and applied fluid mechanics, is a very complex and quite undiscovered phenomenon. Defining the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering?s task. Method of kinetic balance is described and used for this purpose, what is illustrated with few examples. .

Particle Dispersion and Deposition in a Curved Duct

2009 ◽  
Author(s):  
C. M. Winkler ◽  
S. P. Vanka
Keyword(s):  
Particle Deposition ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Outer Wall ◽  
Particle Dispersion ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Particle Volume ◽  
Particle Tracking Method ◽  
Dean Vortex

Particle transport in ducts of square cross-section with constant streamwise curvature is studied using numerical simulations. The flow is laminar, with Reynolds numbers of Reτ = 40 and 67, based on the friction velocity and duct width. The corresponding Dean numbers for these cases are 82.45 and 184.5, respectively, where De = Rea/R, a is the duct width and R is the radius of curvature. A Lagrangian particle tracking method is used to account for the particle trajectories, with the particle volume fraction assumed to be low such that inter-particle collisions and two-way coupling effects are negligible. Four particle sizes are studied, τp+ = 0.01, 0.05, 0.1, and 1. Particle dispersion patterns are shown for each Dean number, and the steady-state particle locations are found to be reflective of the Dean vortex structure. Particle deposition on the walls is shown to be dependent upon both the Dean number and particle response time, with the four-cell Dean vortex pattern able to prevent particle deposition along the center of the outer wall.

A Study of Convective Heat Transfer and Pressure Drop Phenomena in Curved Microchannels

2010 ◽  
Author(s):  
Heng-Chih Tang ◽  
Tien-Chien Jen ◽  
Yi-Hsin Yen ◽  
Jyh-Tong Teng
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Cooling System ◽  
Outer Wall ◽  
Flow Patterns ◽  
Hydraulic Diameter ◽  
Main Stream ◽  
Dean Number

The research conducted in this paper was based on numerical simulation analysis that investigated the relationships between convective heat transfer and pressure drops and the flow patterns between conventional straight channels and curved microchannels. The main goal is to thoroughly investigate thermo-fluidic phenomena in curved microchannels and to determine the optimal design for the curved microchannel cooling system. Commercial numerical software (ESI-CFD) was used to simulate all cases studied in this paper. The computer simulated results were compared with actual experimental results to evaluate its accuracy. Six cases of different dimensions were studied. Results obtained from this study showed that when the dimensions of curved microchannels are smaller than 40 μm in height, conventional macro fluidic theory can still be used, since the numerically simulated results are in good agreement (<6% difference) with those obtained experimentally. Hydraulic diameter is the factor affects the pressure drop. Larger hydraulic diameter causes smaller pressure drop while smaller hydraulic diameter results in higher pressure drop. Secondary flow patterns and Nusselt numbers are also illustrated in this paper. When the Dean number is lower than 400, the pressure drop of fluid in 40 μm height models is similar to that found in straight microchannels. For the velocity profiles in the curved microchannels, the main stream is at the center of the curved microchannel first. But it is gradually offsets to the outer wall when the mass flow rates increases. The centrifugal force due to the curve geometry is the main reason that results in the shifting of the main flow toward the outer wall of the microchannel.

A Numerical Study of Dean Instability in Non-Newtonian Fluids

2005 ◽  
Vol 128 (1) ◽  
pp. 34-41 ◽  
Author(s):  
H. Fellouah ◽  
C. Castelain ◽  
A. Ould El Moctar ◽  
H. Peerhossaini
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Power Law ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Newtonian Fluids ◽  
Dean Number ◽  
Bingham Number ◽  
Curved Channels ◽  
Power Law Index

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document