Elliptical Cross Section Research Articles

Temperature distribution in an elliptical body without internal heat sources under boundary conditions of the third kind with partial adiabatic isolation

The article deals with the distribution of the temperature field in an elliptical body without internal heat sources. In this case, the boundary conditions are boundary conditions of the third kind. The solution is found when moving to an elliptic coordinate system. The author has obtained an analytical solution for the distribution of the temperature field in a body with an elliptical cross section of infinite length at a given ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.

Determination of the optimal size of the fuel element of the elliptical cross-section of a nuclear reactor

The work is devoted to the process of heat exchange of a nuclear reactor. Attention was paid to improving the reliability of the fuel rods of the nuclear reactor. At the same time, two cases of the cross section of the rod shell were considered: cylindrical and elliptical. Based on the application of the differentiation method, it was shown that the level of thermal stresses arising during the transition from a circular cross-section to an elliptical one decreases. Which confirms the choice of the section of the reduced elements in the form of an ellipse. The optimal size of the section itself was also obtained. The obtained result is useful because by varying the geometric shape of the cross-section, it is possible to reduce the level of thermal stresses that occur, and, consequently, to increase the reliability and durability of nuclear rocket engine designs.

NUMERICAL SIMULATION ON FLOW AND HEAT TRANSFER CHARACTERISTICS IN A RECTANGULAR CHANNEL WITH KAGOME TRUSS CORES: THE INFLUENCE OF STRUT CROSS-SECTION ELLIPTICITY

The traditional Kagome trusses have circular cross-section ligaments. In this study, a Kagome truss with elliptical cross-sectional ligaments instead of circular cross-sectional ligaments is proposed. Additionally, a scheme for transforming the circular cross-sectional ligament into an elliptical ligament, which maintains the same cross-sectional area as the circular cross-sectional ligament, is proposed. Four Kagome truss structures with different cross-sectional ligaments are designed. Model-4 is a Kagome truss with traditional circular cross-sectional ligaments, whereas model-1, model-2, and model-3 are Kagome trusses of elliptical cross-sectional ligaments, with the major-to-minor axes ratio gradually decreasing from model-1 to model-3. Furthermore, the pressure drop and heat transfer performance of different models at different flow velocities are analyzed. A dimensionless number eta; characterizing the overall heat transfer performance is introduced to evaluate the overall performance. The results reveal that model-1, with a major-to-minor axes ratio of 4, achieved the most minor pressure drop at all velocities, and model-2 has the best heat transfer performance at high velocities. The average overall heat transfer performances of model-1, model-2, and model-3 are 5.9%, 16.3%, and 13.3% higher than that of model-4, respectively, thereby demonstrating the significance of elliptical optimization. The best overall heat transfer performance is exhibited when the major-to-minor axes ratio of the ellipse is 2.04.

The Influence of Cross-Section Shape on Failure of Rock Surrounding the Main Tunnel in a Water-Sealed Cavern

The influence of cross-section shape on rock stability was investigated by designing a similar model test and numerical simulation using particle flow code (PFC). The test results showed that the left- and right-hand sides of the entrance are subjected to tension, mainly forming vertical cracks or oblique cracks with a large dip angle. The vicinity of the entrance is subjected to the shear effect and the overall failure of the model is brittle in the similar test. Mesoscopic fractures mainly appear as tensile fractures, and a small number of shear fractures are found in the vicinity of the entrance. A long narrow coalescent-fracture zone is separately formed at the left- and right-hand sides of the entrance when approaching peak load in PFC test. Stress concentration occurs at the end of the long axis of the elliptic cross-section. The stress is high at the arch foot and spandrel of a horseshoe-shaped cross-section and a coalescent fracture zone formed at the arch foot on the right-hand side caused the tunnel to fail. The ovoid-shaped and vertical-wall-arched cross-sections are under significant tension, owing to the force chains distributed along the tunnel wall, show a large included angle with the tunnel wall. From the perspective of bearing capacity, a circle is the best section. From the perspective of failure mode, the horseshoe-shaped section is more suitable for use in corresponding practical engineering.

Full-field geometric imperfection and effect on cross-section capacity of circular steel tubes

Measurements on the geometric imperfection of circular steel tubes used in building structures were limited to specific longitudinal lines of the outer surface in existing studies. This study is aimed at detecting full-field geometric imperfection of circular steel tubes and evaluating its influence on cross-section capacity. First, geometric imperfections of 71 specimens consisting of four common types (i.e., hot-rolled and cold-rolled carbon steel circular tubes, cold-drawn and cold-rolled stainless steel circular tubes) were measured using laser scanning techniques. Observations from 3D scanning models demonstrate that the dominant imperfections for seamless tubes (hot-rolled carbon and cold-drawn stainless steel circular tubes) are cross-section ellipticity and uneven thickness, while welded tubes (cold-rolled carbon and stainless steel circular tubes) are mostly influenced by cross-section ellipticity. Based on the measured geometric profile data, imperfection distribution modes of outer-surface and thickness were proposed separately, and then imported to finite element (FE) simulation. Parametric analysis was conducted to evaluate the influence of geometric imperfections on cross-section compression and bending capacity values. Totally, seven types of outer-surface and three types of thickness imperfection distribution modes were used. Simulation results indicate that considering geometric imperfections generates negligible influence on cross-section capacity for the circular steel tubes studied. Finally, the influence of mesh density on capacity prediction of circular steel tubes was discussed. This study illustrates the actual full-field geometric imperfection distribution of circular steel tubes and discusses its effect on cross-section capacity, which provides useful information for improving the efficiency and accuracy of FE analysis on circular steel tubes.

Free-shape modeling and optimization for cold plates with tree-like channels

The use of cold plates is often considered a preferred cooling strategy to quickly remove detained heat from inside the system, which is widely used in engineering applications such as battery thermal management systems (BTMSs). Structural designs are essential to cold plate designs and serve as the foundation for other subsequent designs. This study introduces a free-shape modeling method for the structural design of cold plates with tree-like channels. The geometric characteristics include tree-like features (branching angles, lengths, numbers, and levels), passage patterns, elliptical cross-section sizes and shapes, and channel twists. They can all be freely revised by adjusting the related control parameters. A case of Cold Plates with Tree-like and Straight Channels (CPTSC), which is frequently found in BTMSs, is designed to verify the universality and effectiveness of the proposed free-shape modeling method. After that, the optimization technology based on the NSGA-II evolutionary algorithm is used to minimize the average temperature (overall thermal performance) and root mean square temperature (temperature uniformity) of top and bottom surfaces. The generalized minimum residual (GMRES) method is utilized for the numerical analyzes, and the numerical results indicate that the resulting designs can reduce the average temperature and root mean square temperature by up to 5.91 K (1.75%) and 2.06 K (23.54%), respectively, for Re=1000 and a total power of 600 W. The numerical and experimental results show that the structure of the best compromised solution reduces both thermal indicators by 5.79 K (1.72%) and 1.88 K (21.49%), respectively. This work provides a guideline for the design of tree-like structures that can be used not only in flat-panel cold plates but also in disk-shaped cold plates, heat sink with fins, and heat sink filled with phase change materials.

Physiological peristaltic flow of Jeffrey fluid inside an elliptic cross section with heat and mass transfer: Exact solutions through Polynomial solution technique

AbstractAn interpretation of heat and mass transfer for the peristaltic flow of a non‐Newtonian Jeffrey fluid inside a duct having an elliptic cross‐section is mathematically investigated. We have considered constant heat absorption for the present study and a descriptive heat as well as mass transfer analysis is carried out. Exact solutions are computed by utilizing a polynomial solution technique to solve the dimensionless partial differential equations appearing in the problem. A purposeful and detailed graphical assessment is provided for the final mathematical results. Velocity as well as temperature profiles attain highest value at the core region of duct while these profiles gradually decline toward duct boundaries. The incrementing value of λ1 is resulting in an increase of flow and since λ1 is the dimensionless ratio of relaxation to retardation time, it means that the increasing value of λ1 results in an increase of relaxation time but it also results in decline of retardation time.

Non-Newtonian characteristics of blood flow in a multi-stenosed elliptical artery: A case of sensitivity analysis

The occurrence and growth of stenosis effectively interrupt the blood flow in the artery, which may result in vascular disease. It makes the study of blood flow in the artery narrowed with crucial stenosis. This work studies the non-Newtonian nature of blood flow in a diseased artery with an elliptic cross-section. The artery is harmed due to several stenosis, which diminishes its lumen. The Phan-Thein–Tanner fluid is considered to analyze the non-Newtonian characteristics of blood. The Phan-Thein–Tanner fluid model is much suitable for blood flow analysis because of its viscoelastic and shear thinning properties. The governing equations are processed to dimensionless form by employing dimensionless variables and assumptions for a mild stenosis case. The solutions of the nondimensional equations are acquired analytically. The visual examination of the exact solutions is discussed in detail. The fluid velocity is strongly affected by stenosis height, and a more significant disorder is generated in the constricted region with the growing size of stenosis. The flow velocity is found as a decreasing function of the Weissenberg number. The velocity profile is parabolic and axisymmetric as well. The most significant and least influential physical constraints are identified by completing the local sensitivity analysis.

Development of micromixer for efficient mixing of blood and insulin in human arteries

In the present work, the computational analysis of passive micromixer with embedded obstacles is studied in detail. It also focuses on Y shaped microchannel with internal embedded obstacles. Different types of Y shaped microchannels are designed by altering the cross section, mixing length and number of obstacles. For simplicity, same velocities at both blood and insulin inlets are assumed. Microchannels are designed in CATIA V5 software and simulations were performed using ANSYS CFX 19.0 solver for steady state condition. Identification of geometric variables correlation with flow field variables is considered for better mixing design. Simulation results are compared with the help of calculating volume fraction at each section and average volume fraction at outlet with each other. It is found that, microchannel having rectangular cross section with circular and rectangular obstacles with reduced length for insulin inlet is giving highest average volume fraction at outlet. Also, one with elliptical cross section is able to give uniform average volume fraction at outlet. By observing mixing profile, it is seen that there is significant increase in mixing behaviour by introducing embedded obstacles as compared to without using it.

THE STRENGTH OF UNDERGROUND HORIZONTAL WORKINGS OF ELLIPTICAL CROSS-SECTION SHAPE SUBJECTED TO ALL-ROUND UNIFORM PRESSURE

The paper presents the results of a study to determine the stress state on the contours of underground workings, the cross-section of which has the form of an ellipse with a fixed value of the large semi-axis. For workings of this type, at different values of the ellipse parameter, the permissible depths of laying and the values of uniform pressure at the points of their contours are determined, at which normal tangential stresses do not exceed the tensile and compressive strength limits of the host rock. Based on the strength condition used in the work, the values of the permissible depths of the workings are calculated for varying values of uniform pressure applied at the points of the workings contours and the specified values of the lateral expansion coefficient of the rock. The permissible values of the stretching uniform pressure at the points of the contours of the elliptical shape of the cross-section with a change in the depth of laying, the specified values of the lateral expansion coefficient of the rock and the ellipse parameter are given. In addition, the paper presents formulas on the basis of which the problem of stress distribution at the points of contours whose cross-section has the shape of an ellipse with a fixed value of the large semi-axis is considered. It is established that when the intensity of the stretching uniform pressure applied at the points of the contours of the workings of an elliptical cross-section shape changes, and the specified values of the ellipse parameter, the depth of the workings and the magnitude of the lateral expansion coefficient of the host rock, sections of the contours on which tensile and compressive stresses act are highlighted. When changing the depths of the workings of the elliptical cross-section shape, sections of contours are identified on which tensile and compressive stresses act at given values of the ellipse parameter, the intensity of the stretching uniform pressure applied to the points of the contours, and the values of the lateral expansion coefficient of the rock.

All-optical quantum vacuum signals in two-beam collisions

We study the collision of two optical laser pulses in a pump-probe setup using beams with circular and elliptic cross section and estimate the number of discernible signal photons induced by quantum vacuum nonlinearities. In this analysis we study strategies to optimize the quantum vacuum signal discernible from the background of the driving lasers. One of the main results is that the collision of two maximally focused lasers does not lead to the best discernible signal. Instead, widening the focus typically improves the signal to background separation in the far field. For petawatt class lasers, an optimal choice of the focus waist yields several discernible photons per shot in contrast to no discernible signal for tight focusing. Further enhancement is possible by using an elliptical waist.

Electrohydrodynamic (EHD) effects on condensation heat transfer of R-11 on circular and elliptical cylinders: An experimental study

In the current experimental research, electrohydrodynamic (EHD) assisted condensation heat transfer of R-11 on a horizontal cylinder is studied for two different cases of circular and elliptical cross sections. Experiments are carried out for different various tilting angles of the elliptical cylinder. Furthermore, effects the involving parameters such as electric voltage, electrode-cylinder distance, and imposed evaporative heat flux are investigated. A separate set of complementary experiments is also conducted to visualize the EHD influence on instability of the condensate liquid surface. The electric field effects are shown to start at a specific voltage depending on the electrode-cylinder distance. Passing the onset of EHD initiation point, slight increase of the condensation heat transfer at low voltages is followed by a significant rise at elevated voltages until the electric discharge takes place. It is shown that increasing the electrode-cylinder distance causes the reduction of the heat transfer rate due to the weakened electric field. However, it delays the electric discharge and thus extends the maximum possible heat transfer enhancement. Results also indicate that the condensation heat transfer on the elliptical cylinder inversely depends on the angle between the minor diameter and horizontal direction. The elliptical cylinder generally facilitates the separation and falling of the condensate film thus leads to a maximum of 24% higher heat transfer enhancement compared to the circular cylinder. Moreover, visual observations of the condensation process reveal that thinning and disturbance of the liquid condensate film change of the film to pseudo-dropwise condensation are the two main possible mechanisms responsible for the heat transfer enhancement under the applied electric field. The maximum heat transfer enhancement values of 3.17 and 3.36 are obtained at electrode voltage of V = 24 kV, for circular and elliptical cylinders respectively.

Axisymmetric buckling analysis of submerged hemi-elliptic toroidal shells

Toroidal shells have been widely used in various industrial applications for over a decade. Most studies on buckling behavior have focused on circular toroidal shells with uniform loads. In contrast, the existing literature on the shell buckling of a toroid with elliptical cross-sections has received limited attention. This study aims to present numerical solutions for axisymmetric buckling of hemi-elliptic toroidal shells under linearly hydrostatic pressure to append available data and results in this field. The thickness of the hemi-elliptic toroidal shells is assumed to be constant before and after the buckling state. Solution procedures for solving critical buckling loads dealt with eigenvalue problems and were formulated by an energy approach. All relevant parameters such as membrane and bending strain components and in-plane stress resultants were derived based on differential geometry. An in-house FEM program solved the weak formulation derived from a variational method. The buckling results for elliptic toroidal shells with various b/a ratios were established as the critical seawater depth and compared to the previously published results. Additionally, parametric studies on the effect of the variable b/a ratios and the major radius R of elliptic toroidal shells on the axisymmetric buckling loads and mode shapes were examined thoroughly and addressed in more detail herein.

An Approximate Method for Predicting the Friction Factor of Viscoplastic Shear-Thinning Fluids in Non-Circular Channels of Regular Cross-Sections.

The objective of this study is to provide a straightforward generalized simple and quick method for the prediction of the friction factor for fully developed laminar flow of viscoplastic shear-thinning fluids in non-circular channels of regular cross-sections. The most frequently represented substances processed under these conditions are polymers in the processing and plastics industry. A generalized approximate method was proposed to express the relationship between the friction factor and the Reynolds number for the Herschel-Bulkley rheological model. This method uses the generalized Reynolds number for power-law fluids. Moreover, an additional simplified method for rapid engineering calculations was obtained as well. The suggested method was verified by comparing experimental data for concentric annulus found in the literature and results from simulations for concentric annulus, rectangular, square duct with a central cylindrical core and elliptical cross-sections. The results showed that the suggested methods enable us to estimate the friction factor with high accuracy for the investigated geometries.

Sensitivity of puff dynamics and airborne droplet nuclei distribution to variations in violent expiration events

We use large eddy simulations to investigate the puff and droplet dynamics from violent expiratory events such as coughs and sneezes in the first few seconds following an ejection. For each of the eleven simulations considered, over 60,000 droplets are ejected and individually tracked using the point-particle Euler–Lagrange approach. We test the sensitivity of the puff and droplet dynamics to various parameters including the ejection volume, momentum, and orientation. We also explore the effect of the mouth shape on the aforementioned dynamics by considering elliptical and circular inlet cross-sections. The results from the simulations compare favorably with a recent theoretical framework put forth by Balachandar et al. (2020) in terms of the puff size and propagation velocity. More importantly however, the theory is able to accurately predict the number and size spectra of the potentially virus-laden droplet nuclei that remain airborne within the puff. We observe that the ejection angle and mouth shape do not significantly affect the puff and droplet dynamics. Additionally, we quantify the carrying capacity of the detached puff portions in terms of the number and size spectra of droplets/droplet nuclei suspended within.

Axial Compression Test and Numerical Investigation of Concrete-Filled Double-Skin Elliptical Tubular Short Columns

To probe into the performance of concrete-filled double-skin elliptical steel tubular (CFDEST) members, this paper designs and conducts an experiment on CFDEST short columns imposed with axial pressure, and finite element (FE) models of the axially compressed CFDEST stub columns are established and verified by the test outcomes, taking the influences of elliptical cross-section and hollow ratio into account. The impressions of various parameters, such as hollow ratio, diameter-to-thickness ratio, aspect ratio and so on, on the load-bearing capacity, initial rigidity and ductility property were investigated systematically. Moreover, the typical failure modes, contact pressure and concrete longitudinal stress of the axially compressed CFDEST short column are revealed. In light of the findings acquired by the laboratory tests and numerical analyses, the calculation formulae for evaluating the axial compress capacity of the CFDEST short column are proposed by taking the impact of the sectional aspect ratio and hollow ratio into account. The results indicate that the failure morphologies of axially compressed CFDEST short columns mainly include outward local bulges of the outside EST, the inward bulges of the inside EST and the crushing of core concrete. The axial compress capacity of the CFDEST short column would increase with the decrease in the sectional hollow ratio and aspect ratio. The calculation method is proved to be an accurate and reliable approach to evaluate the axial compress capacity of the CFDEST short column.

Experimental Measurements of Drag and Lift Coefficient on Building with an Elliptical Cross-section

Abstract The characteristics of aerodynamic forces acting on an elliptic cylinder with an aspect ratio of 0.5 with a wind attack angle from 0 to 90° and subjected to the boundary layer wind tunnel were investigated. The model was initially calibrated and compared with the existing work. The aspect ratio of the investigated model was 0.5, and the model was emerging in a turbulent flow. The mean and fluctuating drag and lift coefficients were investigated. The minimum drag coefficient occurred in the wind direction of 0° and the maximum at 90°. The lift coefficient was the largest in the 30° wind direction and the smallest at 0°. Fluctuating coefficients were similar profiles as the mean coefficients. Around the 30° wind direction, an inappropriate phenomenon occurred, caused by the generation of asymmetrical vortices structures and wake instabilities.

Exploring AZ31B magnesium alloy for innovative micro products by reverse-μEDM

• Fabrication feasibility test for arrayed microprotrusions of AZ31B Mg alloy. • The arrayed microprotrusions are in elliptical and aerofoil cross-sections. • Exploring Reverse-µEDM integrated with Laser beam µ-machining for this purpose. • Analysing surface finish, migration of tool materials to workpiece and MRR. Fabrication of complex and filigree magnesium alloy 3D-medical implants is very difficult by conventional processes. The present work examines the feasibility of fabricating arrayed microstructures (protrusions) of magnesium AZ31B Mg alloy in unconventional profiles. For this, Reverse-µEDM integrated with laser beam micromachining (LBµM), as a new hybrid technology, is employed. A capacitance of 10 nF, a voltage of 110 V and a feed rate of 10 µm/min for Reverse-µEDM led to better machining responses in terms of materials removal rate, tool wear, and avg. surface roughness compared to other parametric settings. Considering the importance of the biocompatibility of materials, the surface integrity of the fabricated microstructures is also analyzed.

Nanofluids in Zigzag Elliptical Tube Heat Exchanger: A Design Perspective

Abstract Nanofluids contain nanometer-sized particles in suspension to enhance heat transfer by increasing the thermal conductivity. This paper provides an overview of particle size and volume fraction of nanofluids, and their roles in enhancing the heat transfer. Often, the transfer of heat is enhanced by dispersed particles with small diameter and high concentration despite some debate about the governing effects. The design of elliptical cross-section and zigzag tube also sheds insight into augmenting heat transfer for future research directions and applications.

Two-axis flexure hinges with variable elliptical transverse cross-sections

Flexure hinges are fundamental elements of compliant mechanisms. Therefore, the development of novel primitive flexure hinges is of great value. In this study, the basic structures of notch-type flexure hinges were extended by focusing on their transverse cross-sections, that is, the cross-sections perpendicular to the central axis. A group of primitive flexure hinges with variable elliptical transverse cross-sections (ETC) was developed and investigated. Analytical models for ETC flexure hinges were developed and verified through finite element analyses and experiments. The anisotropic two-axis compliances of the ETC flexure hinges were evaluated using computational analyses. The differences and relations in compliances, rotational precisions, and stresses between the ETC and existing primitive flexure hinges are discussed. An application case of the ETC flexure hinges is presented, which improves the ETC-based compliant mechanisms that can achieve much higher actuation efficiency owing to the simultaneous increase in compliances and decrease in stress concentration. The ETC flexure hinges enhance the design space of the primitive flexure hinges, addressing the knowledge gap between flexure hinges with rectangular and circular transverse cross-sections.