The Case for the Elliptical Spine

2003 ◽  
Vol 125 (2) ◽  
pp. 217-220
Author(s):  
Gerald L. McIntyre ◽  
Allan D. Kraus
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Input Admittance ◽  
Elliptical Cross ◽  
Fin Efficiency ◽  
Temperature Excess

The spine (fin) efficiency is abandoned and the input admittance, defined as the ratio of the heat dissipated by the spine to the temperature excess at the spine base, is established as the parameter for comparison of the performance of the spines of circular, square and elliptical cross section. It is shown that the square cross section outperforms the circular cross section and by adjusting the aspect ratio of the elliptical spine, the spine can meet and eventually surpass the performance of the square spine.

Two-Phase Flow (Oil and Water) in Ducts with the Elliptical Cross-Section: Modeling and Simulation

2019 ◽  
Vol 24 ◽  
pp. 61-75
Author(s):  
J.L. de Oliveira ◽  
A.G. Barbosa de Lima ◽  
R. Pereira Ramos ◽  
H. Luma Fernandes Magalhães ◽  
W.R. Gomes dos Santos ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Aspect Ratio ◽  
Cross Section ◽  
Operating Cost ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Two Phase ◽  
Elliptical Cross ◽  
Ansys Cfx ◽  
Velocity Pressure

In the oil industry, pipelines (circular ducts) are widely used for the transportation of oil and yours derived. Because of their advantages, such as low operating cost and increased safety during transportation, pipelines have become indispensable for transporting oil in large quantities and for long distances. As an alternative to this problem, the transport of oil and water can be accomplished using ducts with an elliptical cross-section. Thus, this work has the objective of studying the flow of oil and water in cylindrical ducts with an elliptical cross-section by using the Ansys CFX software. Results of the velocity, pressure and volumetric fraction distributions of the oil and water phases are presented and analyzed. By applying the same inlet velocity to oil and water, revealed that the elliptical duct, with aspect ratio equal to 5.0, has a pressure drop less (84.2%) than the pressure drop obtained for one duct of circular cross-section (aspect ratio equal to 1.0).

scholarly journals Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Mechanika ◽  
2021 ◽  
Vol 27 (4) ◽  
pp. 327-334
Author(s):  
Yuan WANG ◽  
Qingchun WANG ◽  
Zehao SU
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Helical Spring ◽  
Element Analysis ◽  
Elliptical Cross ◽  
Stiffness Property ◽  
Regression Formula

 Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion. 

scholarly journals Interaction of a shear wall with the soil for incident plane SH waves: Elliptical rigid foundation

1974 ◽  
Vol 64 (6) ◽  
pp. 1825-1842
Author(s):  
H. L. Wong ◽  
M. D. Trifunac
Keyword(s):  
Cross Section ◽  
Incidence Angle ◽  
Circular Cross Section ◽  
Closed Form Solution ◽  
Shear Wall ◽  
Elliptical Cross Section ◽  
Rigid Foundation ◽  
Sh Waves ◽  
Elliptical Cross ◽  
Plane Sh Waves

abstract The closed-form solution of the dynamic interaction of an elastic shear wall and the elastic homogeneous half-space, previously known only for the rigid foundation with circular cross section, has been generalized to apply for the foundation with elliptical cross section. It is shown that the interaction equation depends on the incidence angle of plane SH waves and that this dependence gradually disappears as the elliptical cross section approaches the circular one. The effectiveness with which the rigid foundation can scatter the incident energy has been found to increase with the depth of the foundation.

Equilibrium tilt of slippery elliptical rods in creeping simple shear

2021 ◽  
Vol 931 ◽  
Author(s):  
Darren G. Crowdy
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Simple Shear ◽  
Slip Length ◽  
Continuation Method ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Simple Shear Flow ◽  
Elliptical Cross ◽  
Navier Slip

It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter $\lambda$ is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle $(1/2)\cos ^{-1}((1-k)/(1+k))$ to the flow direction where $0 \le k \le 1$ is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of $1/\lambda$ and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle $k < 1$ provided $\lambda \ge \lambda _{crit}(k)$ where $\lambda _{crit}(k)$ is a critical Navier-slip length parameter determined here. As the case $k \to 1$ of a circular cross-section is approached, it is found that $\lambda _{crit}(k) \to \infty$ , so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.

Interface Parameters of Composite Materials with an Elliptical Cross-Section Fiber Bundle

2013 ◽  
Vol 275-277 ◽  
pp. 1688-1692
Author(s):  
Zhi Min Xie ◽  
Dong Liang Chai ◽  
Hai Wen Du ◽  
Chang Qing Miao
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Fiber Bundle ◽  
Biaxial Tension ◽  
Pure Shear ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Plane Shear ◽  
Elliptical Cross ◽  
Interface Parameters

How to design the interfacial properties is a significant fundamental issue in the field of the composite materials, while little work was concerned with the mechanical design of the interface for the fiber reinforced polymer. In the present work, a fiber bundle embedded in the matrix was described as a transversely isotropic material. Based on the imperfect interface conditions, the interface parameters were derived to satisfy the neutral conditions for the composite materials reinforced by the elliptical cross-section fiber bundle. It is found that the interface parameter is not always associated with the applied loading in the case of the anti-plane shear. In the state of equal-biaxial tension, the normal interface parameter is merely related to the mechanical properties of components except for the shape of the fiber bundle, but independent of the loading magnitude. In the other cases of pure shear and uniaxial tension, the neutral interface does not exist except that the fiber bundle has a circular cross-section. It is also found that the interface parameters can be expressed in the forms similar to that for an isotropic inclusion by using Kolosov constant in the in-plane deformations.

Design Formulae for Elliptical Cross-Section Helical Springs

1992 ◽  
Vol 114 (4) ◽  
pp. 667-669 ◽  
Author(s):  
Kosuke Nagaya ◽  
Yasuo Hirata ◽  
Toyoaki Tsurumi ◽  
Sadahiko Takeda ◽  
Ken-ichi Nagai ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Aspect Ratio ◽  
Cross Section ◽  
Maximum Stress ◽  
The Other ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Design Formula ◽  
Helical Springs ◽  
Present Design

The maximum stress in elliptical cross-section coil springs with a certain aspect ratio becomes small as compared to the other springs used in practical machines. This article presents a simplified stress expression for designing elliptical cross-section coil springs. The stresses obtained by the present design formula are compared with those by calculated using numerical methods. It is ascertained that the present formula is applicable to design the elliptical cross-section coil springs.

Viscosity estimates of salt in the Hormuz and Namakdan salt diapirs, Persian Gulf

2010 ◽  
Vol 147 (4) ◽  
pp. 497-507 ◽  
Author(s):  
SOUMYAJIT MUKHERJEE ◽  
CHRISTOPHER J. TALBOT ◽  
HEMIN A. KOYI
Keyword(s):  
Grain Size ◽  
Cross Section ◽  
Dynamic Viscosity ◽  
Persian Gulf ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Surface Profiles ◽  
The Persian Gulf ◽  
Existing Data

AbstractThe parabolic surface profiles of the Hormuz and Namakdan salt diapirs in the Persian Gulf suggest that they have been extruding with Newtonian viscous rheologies for the last 104 years. We derive velocity profiles for these diapirs, neglecting gravitational spreading and erosion/dissolution while assuming incompressible Newtonian rheology of the salt. Fitting known rates of extrusion at specific points in its elliptical cross-section, the dynamic viscosity of the salt of the Hormuz diapir is found to range between 1018 and 1021 Pa s. Approximating its sub-circular cross-section to a perfect circle, the range of viscosity of the salt of the Namakdan diapir is obtained as 1017–1021 Pa s. These calculated viscosities fall within the range for naturally flowing salts elsewhere and for other salt diapirs but are broader than those for salts with Newtonian rheology deforming at room temperatures. The salts of the Hormuz and Namakdan diapirs are expected to exhibit a broader range of grain size, which matches the limited existing data.

Measurements of a Wall Jet Impinging Onto a Forward Facing Step

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
D. C. Langer ◽  
B. A. Fleck ◽  
D. J. Wilson
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Cfd Simulation ◽  
Velocity Ratio ◽  
Water Channel ◽  
Cross Flow ◽  
Elliptical Cross Section ◽  
Navier Stokes ◽  
Wall Jet ◽  
Elliptical Cross

This study examines a horizontal wall jet impinging onto a forward facing vertical step in a cross-flow. Planar laser induced fluorescence (PLIF) experiments in a 68×40 mm2 water channel indicate how the wall-jet flow after impinging onto the step becomes a vertical jet with an elliptical cross section. This study proposes predictive empirical correlations for the aspect ratio and perimeter of the jet’s elliptical cross section based on the step geometry and the inlet flow conditions. A numerical model is also presented, which was produced from a commercial Reynolds averaged Navier–Stokes computational fluid dynamics (CFD) code with the k-ϵ closure model. The experimental results were well represented by correlations for the perimeter P and aspect ratio S using the parameters H (the step height), L∘ (the distance from the jet represented as a point source to the step), and R (the velocity ratio). The CFD simulation was able to predict the trends in the perimeter (under different conditions), aspect ratio, and the shape of the concentration profile, but overpredicted the jet’s perimeter by approximately 50%. The results of these tests are required as input parameters when modeling jet trajectories.

Magnetization and AC loss in a superconductor with an elliptical cross-section and arbitrary aspect ratio

2002 ◽  
Vol 377 (1-2) ◽  
pp. 156-164 ◽  
Author(s):  
Bennie ten Haken ◽  
Jan-Jaap Rabbers ◽  
Herman H.J. ten Kate
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Ac Loss ◽  
Elliptical Cross Section ◽  
Elliptical Cross

On the steady laminar flow of an incompressible viscous fluid in a curved pipe of elliptical cross-section

1985 ◽  
Vol 158 ◽  
pp. 329-340 ◽  
Author(s):  
H. C. Topakoglu ◽  
M. A. Ebadian
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Radius Of Curvature ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Ellipticity Ratio ◽  
Explicit Expressions

A literature survey (Berger, Talbot & Yao 1983) indicates that laminar viscous flow in curved pipes has been extensively investigated. Most of the existing analytical results deal with the case of circular cross-section. The important studies dealing with elliptical cross-sections are mainly due to Thomas & Walters (1965) and Srivastava (1980). The analysis of Thomas & Walters is based on Dean's (1927, 1928) approach in which the simplified forms of the momentum and continuity equations have been used. The analysis of Srivastava is essentially a seminumerical approach, in which no explicit expressions have been presented.In this paper, using elliptic coordinates and following the unsimplified formulation of Topakoglu (1967), the flow in a curved pipe of elliptical cross-section is analysed. Two different geometries have been considered: (i) with the major axis of the ellipse placed in the direction of the radius of curvature; and (ii) with the minor axis of the ellipse placed in the direction of the radius of curvature. For both cases explicit expressions for the first term of the expansion of the secondary-flow stream function as a function of the ellipticity ratio of the elliptic section have been obtained. After selecting a typical numerical value for the ellipticity ratio, the secondary-flow streamlines are plotted. The results are compared with that of Thomas & Walters. The remaining terms of the expansion of the flow field are not included, but they will be analysed in a future paper.

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