Numerical Analysis of Laminar Flow in Curved Elliptic Ducts

1991 ◽  
Vol 113 (4) ◽  
pp. 555-562 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Cross Section ◽  
Stokes Equations ◽  
Control Volume ◽  
Major Axis ◽  
Minor Axis ◽  
Dean Number ◽  
Axis Ratio ◽  
Symmetry Line ◽  
Curved Duct

The complete form of the Navier-Stokes equations is solved in this paper for a steady, incompressible, fully developed laminar flow in a curved duct of elliptic cross section. This is achieved by the use of the control volume-based finite difference method via the numerically generated boundary fitted coordinate system. The curvature ratio is included in the primitive variable governing equations, which are solved based on the SIMPLE algorithm. Solutions are obtained for the minor-axis to major-axis ratios of the elliptic duct, 0.2, 0.5, and 0.8, and for Dean numbers ranging from 11.41 to 635.7. It is found that only one pair of vortices appears on the cross-section, even at a Dean number of 635.7. The friction factor and the ratios of the curved duct to straight duct are tabulated and the correlation equation is developed. Furthermore, the distribution of the axial velocity is displayed graphically to illustrate its variations with the Dean number and the minor-axis to major-axis ratio of the elliptic duct on the horizontal symmetry line and on the half-vertical symmetry line. The present method is also applied to solve for a fully developed laminar flow in a curved square flow. The results are compared with the data available in the literature and very close agreement is observed.

Quantitative diagenetic analyses of Edmontosaurus regalis (Dinosauria: Hadrosauridae) postcranial elements from the Danek Bonebed, Upper Cretaceous Horseshoe Canyon Formation, Edmonton, Alberta, Canada: implications for allometric studies of fossil organisms

2014 ◽  
Vol 51 (11) ◽  
pp. 1007-1016 ◽  
Author(s):  
Mackenzie Baert ◽  
Michael E. Burns ◽  
Philip J. Currie
Keyword(s):  
Cross Section ◽  
Upper Cretaceous ◽  
Strong Relationship ◽  
Major Axis ◽  
Minor Axis ◽  
Morphological Features ◽  
Fossil Assemblages ◽  
Fossil Vertebrate ◽  
Horseshoe Canyon Formation ◽  
Upper Campanian

For fossil assemblages, quantitative size and shape studies are often complicated by diagenetic distortion. Different vertebrate elements, although subjected to similar burial stresses, exhibit deformations based upon their original shapes; this hypothesis is tested here by quantitatively comparing deformed humeri and femora from the Danek Bonebed (a monodominant Edmontosaurus regalis bonebed from the upper Campanian Horseshoe Canyon Formation in Edmonton, Alberta, Canada) with samples of undeformed humeri and femora from modern and fossil assemblages. Analyses suggest that at the Danek Bonebed a strong relationship exists between element length and circumference despite being distorted by crushing deformation. Major and minor axes of the midshaft cross section, however, were not uniformly distorted. Although their anatomical position did not change, the major axis became longer relative to the minor axis in distorted specimens. A regression based on the undeformed humeri was not able to accurately predict circumference in the Danek humeri. Further study might quantify the deformation of other bones in the Danek Bonebed and could be extended to other assemblages and genera. Caution should be taken when conducting studies in which diagenetic crushing may have altered morphological features of fossil vertebrate remains.

Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

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.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

On Viscous Flow in Semi-Elliptic Ducts

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Laminar Flow ◽  
Viscous Flow ◽  
Major Axis ◽  
Minor Axis ◽  
Series Solutions ◽  
Straight Wall

The exact series solutions for the laminar flow in a semi-elliptic duct are presented. The present work studies the semi-elliptic duct with the minor axis as the straight wall, which complements that of Alassar and Abushoshah who used the major axis. Properties of the two types of semi-elliptic ducts are given, including the asymptotic Poiseuille numbers.

Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

1993 ◽  
Vol 115 (4A) ◽  
pp. 432-440 ◽  
Author(s):  
C. Ribreau ◽  
S. Naili ◽  
M. Bonis ◽  
A. Langlet
Keyword(s):  
Contact Pressure ◽  
Cross Section ◽  
External Pressure ◽  
Straight Line Segment ◽  
Minor Axis ◽  
Cross Sectional ◽  
Axis Ratio ◽  
Straight Line ◽  
Thin Walled ◽  
The Cross

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko, defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1. For p<p1, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

A new calculation formula to describe the dynamic pressure of water jet peening with elliptical nozzle for high-efficiency treatment

2021 ◽  
pp. 095440622110586
Author(s):  
Hong-Xiang Zheng ◽  
Yun Luo ◽  
Bao-Zhu Zhang ◽  
Wen-Chun Jiang ◽  
Shan-Tung Tu
Keyword(s):  
High Efficiency ◽  
Dynamic Pressure ◽  
Major Axis ◽  
Water Jet ◽  
Minor Axis ◽  
Welding Residual Stress ◽  
Axial Distance ◽  
Treatment Area ◽  
Axis Ratio ◽  
Core Length

Water jet peening is a good potential method to control welding residual stresses. The water jet with elliptical nozzle can improve the treatment efficiency due to its large treatment area. In this article, the water jet velocity and dynamic pressure for different elliptical nozzle dimensions and standoff distances are discussed by numerical simulation. The results show that when the axial distance is 10 mm, the effective impact diameter of the elliptical nozzle a/b=8–12 is about 2 times or more than that of the circular nozzle. The length of the jet core of the elliptical nozzle is only related to the outlet structure and is independent of the inlet pressure. The correlation between the dimensionless core length of the elliptical water jet and its long and short axes is derived. When the ratio of the major axis to the minor axis is between 7 and 13, the core length of the elliptical water jet is 7–7.5 times that of its minor axis. Combining the suitable treatment area and dynamic pressure, the elliptical nozzle with an axis ratio of 8 is recommended to control the welding residual stress. Finally, a new formula for calculating dynamic pressure distribution is proposed for the elliptical nozzle water jet at different stages.

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.

Flow Instability in a Curved Duct of Rectangular Cross Section

1992 ◽  
Vol 114 (4) ◽  
pp. 585-592 ◽  
Author(s):  
A. Belaidi ◽  
M. W. Johnson ◽  
J. A. C. Humphrey
Keyword(s):  
Cross Section ◽  
Flow Instability ◽  
Rectangular Cross Section ◽  
Symmetry Plane ◽  
Side Wall ◽  
Secondary Flows ◽  
Bend Angle ◽  
Dean Number ◽  
Curved Duct ◽  
Time Histories

An experimental investigation has been carried out in a curved duct of rectangular cross section in order to study the development of flow instability in such geometries. Hot wire anemometry was used to obtain detailed measurements of velocity on the symmetry plane of the duct for different curvature ratios. As the duct Dean number is increased, a centrifugal instability develops and the Dean vortices are seen to oscillate along the inner wall. To understand the contribution of these vortices to the laminar-turbulent transition, time histories and spectra of the flow were taken on the symmetry plane of the duct for different Reynolds numbers. These data reveal a time-periodic motion along the inner wall where the secondary flows originating from the side wall boundary layers collide. The bend angle where this instability develops depends on the Reynolds number while the frequency of the instability depends on the curvature ratio of the bend.

Experiment on Laminar Flow in a Rotating, Curved Duct of Rectangular Cross Section

1984 ◽  
Vol 106 (1) ◽  
pp. 38-44 ◽  
Author(s):  
Mark D. Hoover ◽  
Werner Sto¨ber ◽  
Gerd Morawietz
Keyword(s):  
Laminar Flow ◽  
Cross Section ◽  
Laser Doppler Anemometry ◽  
Rectangular Cross Section ◽  
Boundary Layer Theory ◽  
Rossby Number ◽  
Curved Duct ◽  
Duct Geometry ◽  
Primary Velocity ◽  
Direction Opposite

Experimental results are presented here for laminar flow in a rotating, curved duct of rectangular cross section. The duct geometry is that of the spiral duct aerosol centrifuge designed by Sto¨ber and Flachsbart (1969). Primary velocity was measured by laser Doppler anemometry. Secondary flow velocity was characterized by dye injection. The experiment was done in a dynamically similar Plexiglas mock-up of the centrifuge. Water flow in the mock-up simulated air flow in the aerosol centrifuge. The Reynolds number based on hydraulic diameter was 500. The Rossby number was 0.16. The duct aspect ratio was 3.3. Results are compared for flow in a straight stationary duct, the curved duct with no rotation, the curved duct with rotation in the direction of flow and the curved duct with rotation in the direction opposite of flow. There is agreement between the observed flow and the boundary layer theory of Ludwieg (1951).

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