Elliptical Configurations Research Articles

Experimental and numerical study on the effects of shaped multi-holes on the effectiveness of film cooling

In the present work, experimental and numerical study has been performed to investigate the effects of a novel film-cooling design with shaped multi-holes on the film-cooling effectiveness over a flat plate. A single cylindrical hole with 11.1 mm diameter has been replaced by multi-holes (14 holes with 2.97 mm diameter) with elliptical and fan-shaped configurations. The exit area, length to diameter ratio (L/D = 4.0) and injection angle (35°) of multi-holes are selected identical to the single cylindrical hole. The multi-holes were machined with a fixed spacing pitch (33.3 mm) between the centers of two adjacent holes. The surface temperature of the test plate was measured by an infrared camera. The experimental studies were performed at blowing ratios of 0.5 and 2. The numerical results based on the steady RANS with realizable k–e turbulence model and enhanced wall treatment were capable to predict the influence of the shape of multi-hole configurations on overall adiabatic film-cooling effectiveness. The experimental and numerical results showed that replacing a single hole with a shaped multi-hole leads to a considerable increase in film-cooling effectiveness in both axial and lateral directions. According to the results at blowing ratio of 2.0, the elliptical and fan-shaped configurations provide a higher area-averaged film-cooling effectiveness by 75% and 248.2% in comparison with the single hole, respectively.

A novel three axis Semi Elliptic Manipulator Configuration for simultaneous Multi Point Operations

A new three axes robotic configuration named as “Semi Elliptic Configuration” has been explored here. The configuration’s topology, working principle, forward kinematics, inverse kinematics and application have been described in this article. The inverse and forward kinematic equations have been derived using more fundamental mathematical tools like plane coordinate geometry, trigonometry and properties of triangles instead of using DH parameters, Transformation and Jacobian matrices. The configuration’s name has been derived from the unconventional geometry of the work volume within which it operates. Unlike the cubically shaped work volume of a typical XYZ Cartesian robotic configuration, its shape has been warped towards the edge containing the vertical Z-axis. It was found that the edges enclosing the face opposite to the Z-axis is part of an Ellipse. Two mutually perpendicular co-planar arms originating from the Z-axis enclose the semi elliptic boundary. Two manipulators of such configuration could be accommodated and be made to work independently within the cubical volume occupied by the perpendicular arms. It was found that the configuration’s work volume leaves a void region within the volume of occupancy of the configuration’s structure, which proved to be a disadvantage in certain applications and an advantage in others. An enhancement has been proposed to work around this restriction. The modification allows the configuration to expand its work volume into the void regions. The superior version of the Semi elliptic configuration was named “Enhanced Semi Elliptic Configuration”.

Assessment of thermal characteristics of square wavy plates

AbstractIn this paper, the thermal characteristics and air flow behavior over heated square plate of wavy configurations are assessed. Two cases of heated wavy configurations were considered, one having an elliptical and other with the sinusoidal cross‐sectional shape to augment heat transfer rate over the plate. To explore the impact of wavy configurations of plate on convective heat transfer, the Rayleigh numbers in the range of 104 to 1013 were considered. The steady‐state two‐dimensional momentum and energy equations were solved using a validated numerical model. The numerical results in terms of Nusselt numbers, Rayleigh numbers, aspect ratio (AR), and flow/temperature distribution over the plate are presented. The variations in the heat transfer coefficient and temperature contours with Rayleigh number and AR of waves were concentrated for both the elliptical and sinusoidal configurations of the plate. The results obtained indicate that the enhancement in heat transfer rate from the heated plate depends on the Rayleigh number, the AR of waves, plate configuration, and the Prandtl number.

Differential Sorting of Microparticles Using Spiral Microchannels with Elliptic Configurations.

Label-free, size-dependent cell-sorting applications based on inertial focusing phenomena have attracted much interest during the last decade. The separation capability heavily depends on the precision of microparticle focusing. In this study, five-loop spiral microchannels with a height of 90 µm and a width of 500 µm are introduced. Unlike their original spiral counterparts, these channels have elliptic configurations of varying initial aspect ratios, namely major axis to minor axis ratios of 3:2, 11:9, 9:11, and 2:3. Accordingly, the curvature of these configurations increases in a curvilinear manner through the channel. The effects of the alternating curvature and channel Reynolds number on the focusing of fluorescent microparticles with sizes of 10 and 20 µm in the prepared suspensions were investigated. At volumetric flow rates between 0.5 and 3.5 mL/min (allowing separation), each channel was tested to collect samples at the designated outlets. Then, these samples were analyzed by counting the particles. These curved channels were capable of separating 20 and 10 µm particles with total yields up to approximately 95% and 90%, respectively. The results exhibited that the level of enrichment and the focusing behavior of the proposed configurations are promising compared to the existing microfluidic channel configurations.

Kinematic signatures of reverberation mapping of close binaries of supermassive black holes in active galactic nuclei

Context. An unresolved region in the relative vicinity of the event horizon of a supermassive black holes (SMBH) in active galactic nuclei (AGN) radiates strongly variable optical continuum and broad-line emission flux. These fluxes can be processed into two-dimensional transfer functions (2DTF) of material flows that encrypt various information about these unresolved structures. An intense search for kinematic signatures of reverberation mapping of close binary SMBH (SMBBH) is currently ongoing. Aims. Elliptical SMBBH systems (i.e. both orbits and disc-like broad-line regions (BLR) are elliptic) have not been assessed in 2DTF studies. We aim to numerically infer such a 2DTF because the geometry of the unresolved region is imprinted on their optical emission. Through this, we determine their specific kinematical signatures. Methods. We simulated the geometry and kinematics of SMBBH whose components are on elliptical orbits. Each SMBH had a disc-like elliptical BLR. The SMBHs were active and orbited each other tightly at a subparsec distance. Results. Here we calculate for the first time 2DTF, as defined in the velocity-time delay plane, for several elliptical configurations of SMBBH orbits and their BLRs. We find that these very complex configurations are clearly resolved in maps. These results are distinct from those obtained from circular and disc-wind geometry. We calculate the expected line variability for all SMBBH configurations. We show that the line shapes are influenced by the orbital phase of the SMBBH. Some line profiles resemble observed profiles, but they can also be much deformed to look like those from the disc-wind model. Conclusions. First, our results imply that using our 2DTF, we can detect and quantify kinematic signatures of elliptical SMBBH. Second, the calculated expected line profiles share some intriguing similarities with observed profiles, but also with some profiles that are synthesised in disc-wind models. To overcome the non-uniqueness of the spectral line shapes as markers of SMBBH, they must be accompanied with 2DTF.

Hypersonic Flow Past Over an Elliptic Nose Cone Configurations: International Conference on Recent Trends in Artificial Intelligence, IOT, Smart Cities & Applications (ICAISC-2020)

The present work provides a detailed study of the hypersonic flow over elliptical nose cones at a Mach number of 5.8, numerically. The main focus of the paper is to determine parameters of the nose cones which provide minimum aerodynamic drag and heating. The conjugate heat transfer method is used to examine aerodynamic heat transfer between gas and surface accommodations for different fineness ratios at zero angle of attack. It is observed that for higher fineness ratio provide minimum drag. It also shows the detailed comparison of the flow/shock features in the vicinity of the elliptical nose cones for different fineness ratios in order to determine its influence on aerodynamic drag and heating. It is also noticed that the aerodynamic heating is almost same for all fineness ratios. In general, the present study reveals that at higher fineness ratios are preferred for achieving aerodynamic characteristics in hypervelocity vehicles.

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n > 1) than the other fluids (n ⩽ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.

Electrowetting induced droplet jumping over a bump

We study electrowetting induced droplet jumping over a system consisting of a flat surface and a topographical bump mounted on the surface. Different bump shapes including triangular and elliptical configurations are considered and the results are compared with the results of the flat surface. The results indicate that droplet jumping is enhanced over the bumps and the droplet jumps to larger heights compared with the flat surface because of the lower viscous dissipation. The shape of the bump can considerably affect the droplet dynamics. Between the considered shapes the triangular bump provides a larger dynamic and the droplet on the surface with this bump can jump with larger velocity. The electrowetting number, intrinsic contact angle, droplet–ambient liquid viscosity ratio, and the Ohnesorge number have also significant effects on the jumping process. By increasing the electrowetting number, intrinsic contact angle and droplet–ambient liquid viscosity ratio, the droplet height increases. However, increasing Ohnesorge number reduces the droplet height.

Fluid flow, heat transfer and entropy generation analyses of turbulent forced convection through isotropic porous media using RANS models

Abstract Turbulent fluid flow, heat transfer and entropy generation through isotropic porous media were investigated utilizing two RANS models, i.e., RNG k - e and SST k - ω . Circular, longitudinal elliptical and transverse elliptical cross-sectional configurations were analyzed with symmetrical boundary conditions for the upper and lower lines and periodic boundary conditions for the back and front lines. Evaluation of the temperature contours indicated two low-temperature regions behind the solid rods of the transverse elliptical cross-sectional configuration exist. For a given specific normalized pressure gradient, dimensionless turbulence kinetic energy, Nusselt number, and heat transfer efficiency, the RNG k - e model resulted in more reliable results for the dimensionless turbulence kinetic energy at low Reynolds numbers when compared with the SST k - ω model. Using the thermal analysis of the three cross-sectional configurations investigated, the longitudinal elliptical resulted in higher heat transfer efficiencies when compared with the circular and transverse elliptical cross-sectional configurations. When the influence of the turbulence effects were included in the entropy generation rate, a second law of thermodynamics analysis indicated that the longitudinal elliptical cross-sectional configuration resulted in a lower entropy generation rate when compared with the circular and transverse elliptical cross-sectional configurations. Combining the results of the first and second law analyses for the three cross-sectional configurations, it is apparent that isotropic porous media consisting of the longitudinal elliptical cross-sectional configuration can simultaneously result in a high heat transfer efficiency and low entropy generation rate.

Impact of Clinically Relevant Elliptical Deformations on the Damage Patterns of Sagging and Stretched Leaflets in a Bioprosthetic Heart Valve.

After implantation of a transcatheter bioprosthetic heart valve its original circular circumference may become distorted, which can lead to changes in leaflet coaptation and leaflets that are stretched or sagging. This may lead to early structural deterioration of the valve as seen in some explanted transcatheter heart valves. Our in vitro study evaluates the effect of leaflet deformations seen in elliptical configurations on the damage patterns of the leaflets, with circular valve deformation as the control. Bovine pericardial tissue heart valves were subjected to accelerated wear testing under both circular (N = 2) and elliptical (N = 4) configurations. The elliptical configurations were created by placing the valve inside custom-made elliptical holders, which caused the leaflets to sag or stretch. The hydrodynamic performance of the valves was monitored and high resolution images were acquired to evaluate leaflet damage patterns over time. In the elliptically deformed valves, sagging leaflets experienced more damage from wear compared to stretched leaflets; the undistorted leaflets of the circular valves experienced the least leaflet damage. Free-edge thinning and tearing were the primary modes of damage in the sagging leaflets. Belly region thinning was seen in the undistorted and stretched leaflets. Leaflet and fabric tears at the commissures were seen in all valve configurations. Free-edge tearing and commissure tears were the leading cause of valve hydrodynamic incompetence. Our study shows that mechanical wear affects heart valve pericardial leaflets differently based on whether they are undistorted, stretched, or sagging in a valve configuration. Sagging leaflets are more likely to be subjected to free-edge tear than stretched or undistorted leaflets. Reducing leaflet stress at the free edge of non-circular valve configurations should be an important factor to consider in the design and/or deployment of transcatheter bioprosthetic heart valves to improve their long-term performance.

On the Existence of Poncelet-Morley Points in Euclidean Geometry

In this paper, we prove the existence of the Poncelet-Morley point for a given elliptic configuration. The paper ends with an application of such a point in angle trisection problem.

Manipulation of photonic nanojet using liquid crystals for elliptical and circular core-shell variations

We present theoretical studies on a tunable photonic nanojet (PNJ) created by adapting a shell and liquid crystal (LC) core architecture. The shell is made of indium tin oxide and the core is infiltrated with nematic LCs. The application of an external static electric field to the LCs modifies their refractive index, and this allows tuning the PNJ effect in the proposed system. In addition to nonresonant excitation, resonant PNJ excitation is also obtained from a hybrid structure. Both nonresonant and resonant internal field excitations of circular and elliptical PNJ configurations are examined by using a high-resolution finite-difference time-domain method. The calculated results indicate that the proposed PNJ configurations with tunable refractive indices lead to significant changes in some parameters such as decay length, focal distance, full width at half maximum and electric field intensity. Such PNJ designs can be employed in high-resolution optical sensors, optical trapping, and high-density data storage.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604–614 (2004)] is presented for relevant scenarios.

A 5th order video band elliptic filter topology using OTRA based Fleischer Tow Biquad with MOS-C Realization

A new 5th order video band elliptic filter topology is presented. In video applications high order elliptic filters were used. The proposed 5th-order lowpass filter was simulated with PSPICE simulation program. The elliptic filter configuration consists of two cascade connected lowpass notch filters and a lowpass filter which is obtained using OTRA based Fleischer Tow biquad. After designing the 5th order video band elliptic filter topology, the MOS-C realization is obtained and used in PSPICE simulation.

Evaluation of stress intensity factors from stress concentration factors for a crack embedded in dissimilar elliptic inclusion

This paper provides a solution for stress intensity factors for a crack embedded in an elliptic inclusion. The inclusion is bonded to an infinite matrix. The inclusion and the infinite matrix have different elastic properties. The crack is replaced by a very slender elliptic configuration. After this replacement, the stress concentration factor can be evaluated. The stress intensity factor at the crack tip can be evaluated from the stress concentration factor by using an available equation. In the solution, the complex variable function method, conformal mapping and the matrix transfer method are used.

Physical Insight into Fuel-Air Mixing for Upstream-Fuel-Injected Scramjets via Multi-Objective Design Optimization

Fuel injection and mixing into air play a crucial role in the operation of hypersonic airbreathing propulsion systems, particularly scramjet engines featuring upstream fuel injection. This study applies an advanced design methodology combining computational fluid dynamics and evolutionary algorithms assisted by surrogate modeling to a multi-objective optimization for fuel injection in a Mach 5.7 crossflow after the initial compression in a scramjet intake operating at Mach 7.6. Optimization is performed for elliptical injector configurations defined by four design parameters (i.e., the injection angle, spanwise spacing, aspect ratio, and radius of the injector), simultaneously aiming to maximize three objectives, that is, fuel/air mixing, total pressure saving, and fuel penetration into the crossflow. Statistical methods based on global sensitivity analysis are employed to assess the optimization results in conjunction with surrogate models to identify key design factors with respect to the three design objectives and additional performance measures. Major effects of the injection angle and aspect ratio have been observed on all considered design criteria. The spanwise spacing has been found to have considerable influence on the total pressure recovery, fuel penetration, and lateral spread when the injection pressure is adjusted to maintain a constant fuel/air equivalence ratio. Low-angle fuel injection through a highly elliptic orifice with wide spanwise spacing demonstrated the most comprehensive advantages in overall aspects.

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

A novel domain integral approach is introduced for the accurate computation of pointwise J-integral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular and line elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2–3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

Shifting and breakup instabilities of squeezed elliptic jets

Liquid jets are inherently unstable and breakup into drops due to capillary instability driven by surface tension. Elliptic jets have been studied and reported to be more unstable than circular jets. The reason for their increased instability has been often ascribed to the axis-switching of elliptic jets. We theoretically elucidate, for the first time, that even in the absence of axis-switching, an elliptic jet exhibits greater instability compared to circular jets solely due to interfacial curvature effects. For this purpose, we analyse the stability of a jet with elliptic cross-section subject to a non-uniform ambient pressure. This azimuthally dependent pressure distribution in the ambient fluid helps to prescribe a static base state for the elliptic jet and maintain the azimuthally varying curvature of the interface. Physically, this mathematical treatment implies that the jet is squeezed into an elliptic configuration by a non-uniform pressure distribution in the passive ambient fluid and therefore cannot exhibit axis-switching. The jet is assumed to be incompressible and inviscid. The stability of such a jet is analyzed using Rayleigh’s Work Principle (RWP) and linear stability theory. It is also shown that in addition to capillary breakup, analogous to that of classical circular jets, squeezed elliptic jets are found to exhibit a shifting mode instability, in which the entire jet translates parallel to its major axis. Both capillary breakup and shifting modes are rendered more unstable by an increase in ellipticity. For low ellipticity, the breakup mode exhibits higher growth rates as compared to the shifting mode. We show that there exists a critical ellipticity beyond which the shifting mode starts to dominate the capillary breakup mode. Predictions from both RWP and linear stability theory converge to Rayleigh’s classic results for a circular cylindrical jet.

Planar Structure Optimization of Extraordinary Magnetoresistance in Semiconductor–Metal Hybrids

The performance of extraordinary magnetoresistance (EMR) depends on the material parameters, hybrid structure design, contacts configuration, and manufacturing technology. In this paper, we pay close attention to the hybrid structure of the EMR device. A semiconductor–metal hybrid model based on the finite element method (FEM) is constructed to study the EMR effect, and the results show good agreement with the experimental data. The analysis of the van der Pauw plate structure indicates that the relationship between the two voltage probe contacts and the different EMR structures is the key factor to the design optimization. Accordingly, we find that the elliptic inclusion configurations improve the performance of the van der Pauw structure of EMR devices within a wide range of applied magnetic field (0–5 T). The bar-type and multibranched inclusion structures are subsequently optimized based on this principle. The new structures show excellent performance; more specifically, the modified multibranched inclusion structure displays a 2-fold increase in the magnetoresistance at 0.1 T and more than 2-order-of-magnitude increase at 5 T when compared with the original structure.

On the co-orbital motion of two planets in quasi-circular orbits

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the Anti-Lagrange (Giuppone et al., 2010) orbits and some second sort orbits discovered by Poincar\'e. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the Anti-Lagrange orbits bifurcate from the same fixed point L4.