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

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).

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The Case for the Elliptical Spine

Journal of Electronic Packaging ◽

10.1115/1.1569261 ◽

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.

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

Mechanika ◽

10.5755/j02.mech.24907 ◽

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.

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Equilibrium tilt of slippery elliptical rods in creeping simple shear

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.936 ◽

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.275-277.1688 ◽

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.

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

Bulletin of the Seismological Society of America ◽

10.1785/bssa0640061825 ◽

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.

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Design Formulae for Elliptical Cross-Section Helical Springs

Journal of Mechanical Design ◽

10.1115/1.2917058 ◽

1992 ◽

Vol 114 (4) ◽

pp. 667-669 ◽

Cited By ~ 2

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.

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Numerical investigation of the effect of water/Al2O3 nanofluid on heat transfer in trapezoidal, sinusoidal and stepped microchannels

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-05-2019-0377 ◽

2019 ◽

Vol 30 (5) ◽

pp. 2439-2465 ◽

Cited By ~ 6

Author(s):

Vahid Jaferian ◽

Davood Toghraie ◽

Farzad Pourfattah ◽

Omid Ali Akbari ◽

Pouyan Talebizadehsardari

Keyword(s):

Heat Transfer ◽

Pressure Drop ◽

Cross Section ◽

Cross Sections ◽

Volume Fraction ◽

Pure Water ◽

Circular Cross Section ◽

Reynolds Numbers ◽

Two Phase ◽

Content Type

Purpose The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode. Design/methodology/approach The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers. Findings Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels. Originality/value Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.

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

Geological Magazine ◽

10.1017/s001675680999077x ◽

2010 ◽

Vol 147 (4) ◽

pp. 497-507 ◽

Cited By ~ 62

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.

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Measurements of a Wall Jet Impinging Onto a Forward Facing Step

Journal of Fluids Engineering ◽

10.1115/1.3203201 ◽

2009 ◽

Vol 131 (9) ◽

Cited By ~ 1

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.

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