Hyperboloid Shape Research Articles

Numerical investigation of the hydrothermal performance of novel pin-fin heat sinks with hyperbolic, wavy, and crinkle geometries and various perforations

In the current work, pin-finned heat sink applications comprising crucial thermal engineering problems are taken into account. Nonetheless, design optimization is still required. The goal of the study was to fill a gap in the literature by using staggered pin fins using a variety of new combinations of perforation and fin shapes. For the pin-fin arrays under consideration, three-dimensional incompressible flow and heat transport are modeled using the ANSYS Fluent software. With the proper boundary conditions included, all of the governing equations of fluid flow are numerically solved. The turbulence is modeled by a realizable κ-ε model. The Nusselt number (Nu) improved by 47.85% and 50.93% for the elliptical perforated wavy pin fin and wavy perforated crinkle pin fin, respectively, at a Reynolds number of 44502. Approximately 13% pressure drop reduction was seen for an elliptical perforated hyperboloid shape that yields hydrothermal performance factor (HTPF) of roughly 45% compared to the cylindrical case. Also, at Re = 44502, the promising Copper-Diamond composite on a hyperboloid shaped pin fin with elliptical perforation case increased the HTPF by 95%. For a variety of industrial applications, this design can be incorporated.

Calculation of tunneling current across trapezoidal potential barrier in a scanning tunneling microscope

Accurate calculation of the tunneling currents in a scanning tunneling microscope (STM) is needed for developing image processing algorithms that convert raw data of the STM into surface topographic images. In this paper, an accurate calculation of the tunneling current for several tip–sample distances, bias voltages, and tips of a hyperboloidal shape with several radii of curvature is carried out. The main features of this calculation are the following. Non-WKB exact solutions to the trapezoidal (linear) potential in the barrier region are used to calculate the tunneling probabilities. Pauli blocking effects on both forward and reverse current densities are introduced. Finite temperature (viz. 300K) calculation in which electrons belonging to a narrow band of energy about the Fermi level contribute to tunneling is carried out. Integration over a field line method is used to obtain tunneling currents for the nonplanar hyperboloidal shaped tips, using the expressions obtained in the paper, for planar model current densities. An estimate of the lateral resolution is introduced. Earlier works do not consider all these aspects together in a single calculation. Tunneling currents are found to increase rapidly with increasing bias voltage and decrease exponentially with increasing tip–sample distances. Airy function determined currents are a more accurate function of a tip–sample distance than the WKB determined currents. Pauli effects are found to not always reduce currents from their non-Pauli values. The lateral resolution is found to be degraded for blunter tips, larger bias voltages, and larger tip–sample distances.

Ordinary Hall anomaly due to the Fermi surface shape in MnAs

We analyze the influence of the Fermi surface (FS) shape on magnetotransport properties, particularly on the Hall effect in the MnAs compound. Evidence of opposite conduction polarities for different crystal directions (goniopolarity) and a strong dependence of carrier type has been observed in MnAs films with an applied magnetic field. To understand this behavior, we developed a semiclassical model together with the Boltzmann transport theory that takes into account both the applied magnetic field and the FS shape. The MnAs FS is obtained by means of density functional theory, showing a clear dominance of the hyperboloid shape. Our study corroborates that the specific topology of the Fermi surface gives rise to a goniopolar behavior in the Hall transport. These theoretical results are supported by magnetotransport measurements on MnAs thin layers epitaxially grown on GaAs(001) and on GaAs(111), allowing us to explore the transport characteristics for two different crystal directions of the system.

Monte Carlo Ray-Tracing Simulation of a Cassegrain Solar Concentrator Module for CPV

The concentration ratio is one of the most important characteristics in designing a Cassegrain solar concentrator since it directly affects the performance of high-density solar energy applications such as concentrated photovoltaics (CPVs). In this study, solar concentrator modules that have different configurations were proposed and their performances were compared by means of a Monte Carlo ray-tracing algorithm to identify the optimal configurations. The first solar concentrator design includes a primary parabolic concentrator, a parabolic secondary reflector, and a homogenizer. The second design, on the other hand, includes a parabolic primary concentrator, a secondary hyperbolic concentrator, and a homogenizer. Two different reflectance were applied to find the ideal concentration ratio and the actual concentration ratio. In addition, uniform rays and solar rays also were compared to estimate their efficiency. Results revealed that both modules show identical concentration ratios of 610 when the tracking error is not considered. However, the concentration ratio of the first design rapidly drops when the sun tracking error overshoots even 0.1°, whereas the concentration ratio of the second design remained constant within the range of the 0.8° tracking error. It was concluded that a paraboloidal reflector is not appropriate for the second mirror in a Cassegrain concentrator due to its low acceptance angle. The maximum collection efficiency was achieved when the f-number is smaller and the rim angle is bigger and when the secondary reflector is in a hyperboloid shape. The target area has to be rather bigger with a shorter focal length for the secondary reflector to obtain a wider acceptance angle.

Analysis of hyperboloid cooling tower projection on 2D shape

This paper undertakes the problem of mapping a hyperboloid cooling tower on a single plane. Measurements performed by ground-based laser scanning technology quickly deliver substantial amounts of geometric data of the tower’s outer wall. The essence of the article is projection of the rotational hyperboloid on a plane. The shape of the hyperboloid cooling tower is not directly expandable to a single plane. Mapping a hyperboloid shape on a plane is, therefore, associated with distortions. This paper presents a comparison between cylindrical and conic projection of a hyperboloid cooling tower. The most popular method of mapping hyperboloid is cylindrical projection. The cylinder’s side surface is easily developed on the drawing sheet. For the hyperboloid cooling tower, the biggest distortions occur in the latitudinal direction and reach the highest values at the top and bottom edges. The equation (13) describe distortion for the cylindrical projection. The equation (18) describe distortion for the conical projection. This paper presents results obtained from the performed measurement. The analysis found that cone mapping produces less distortion than cylindrical projection for the hyperboloid cooling tower. We think, that in conical projection, the shape of a hyperboloid cooling tower and theoretical conic shape have better corresponding together than in cylindrical projection.

Technical and safety aspects at the demolition by blasting works of a cooling tower with a high of 72.00 m

From the point of view of demolition, one of the most interesting construction categories is the hyperboloid shape cooling towers. These seemingly fragile structures support at the base on a reinforced concrete belt and pillars. An important element to be taken into account when choosing the demolition solution is the slope of the tower. As this ratio between tower height and base diameter is greater (4-5), the easier is the demolition of the tower by overturning, respectively by moving the centre of gravity of the construction away from its base. In the case of the cooling tower described in this article, its height was 72.00 m and the base diameter of 52.00 m - the slope ratio index being less than 2, which was why the chosen solution of demolition was that of partial lateral collapse followed by a total crash of the tower on its position. The article describes how to perform the demolition of the cooling tower, the technical and safety solutions adopted for its successful collapse in the intended direction, in very sensitive location conditions regarding the constructions and installations in its immediate vicinity.

Geometric modelling and materially nonlinear numerical analysis of shells in the shape of one-sheet hyperboloid of revolution

Aims of research. A surface of revolution is generated by rotation of a plane curve z = f(x) about an axis Oz called the axis of rotation. This paper provides information on hyperboloids of revolution surfaces and their classification. Their geometric modeling, linear and materially nonlinear analysis are worked out. Methods. Hyperboloids of revolution middle surface is plotted using the software MathCAD. The linear and materially nonlinear numerical analyses of thin shells of the shape of an hyperboloid of revolution surfaces on stress-strain state is given in this paper, using the finite elements method in a computer software R-FEM, the material which we use in our model is concrete with isotopic nonlinear 2D/3D stress-strain curve for materially nonlinear analysis and linear stress-strain curve for linear analyses. Comparison is done with the result of the finite elements linear analysis of their strain-stress results. Results. That displacements in the investigated shells subject to self-weight, wind load with materially nonlinear analysis are bigger than which done by linear analysis, in the other side the displacements is similarity subjected to free vibration load case. Based on these results, conclusions are made for the whole paper.

Proposed percutaneous aortic valve prosthesis made of cryogel.

Transcatheter heart valves are promising for high-risk patients. Generally, their leaflets are made of pericardium stented in a Nitinol basket. Despite their relative success, they are associated with significant complications such as valve migration, implantation risks, stroke, coronary obstruction, myocardial infraction, acute kidney injury (which all are due to the release of detached solid calcific pieces in to the blood stream) and expected issues existing with tissue valves such as leaflet calcification. This study is an attempt to fabricate the first ever polymeric percutaneous valves made of cryogel following the geometry and mechanical properties of porcine aortic valve to address some of the above-mentioned shortcomings. A novel, one-piece, tricuspid percutaneous valve, consisting of leaflets made entirely from the hydrogel, polyvinyl alcohol cryogel reinforced by bacterial cellulose natural nanocomposite, attached to a Nitinol basket was developed and demonstrated. Following the natural geometry of the valve, a novel approach was applied based on the revolution about an axis of a hyperboloid shape. The geometry was modified based on avoiding sharp warpage of leaflets and removal of the central opening orifice area of the valve when valve is fully closed using the finite element analysis. The modified geometry was replaced by a cloud of (control) points and was essentially converted to Bezier surfaces for further adjustment. A cavity mold was then designed and fabricated to form the valve. The fabricated valve was sewn into the Nitinol basket which is covered by Dacron cloth. The models presented in this study merit further development and revisions for both aortic and mitral positions.

Comparison of buckling loads of hyperboloidal and cylindrical lattice structures

Cylindrical lattice structures are types of lightweight structures and can utilize the orthotropy of fiber-reinforced composite materials. Maximization of the buckling loads is important because they dominate the strength of the structures. On the basis of the fact that a hyperboloidal shape deviation increases the buckling loads of cylindrical homogeneous shells, the changes in the buckling loads of cylindrical lattice structures with a hyperboloidal shape deviation are discussed. Further, the buckling loads of both conventional cylindrical lattice structures and shape-deviated hyperboloidal lattice structures with respect to the compressive, bending, and torsional loads are calculated using a finite element method. The results show that the shape deviation decreases the buckling loads, while the change in mass is negligible. The effects of the shape deviation on the buckling loads differ between homogeneous shell structures and lattice structures.

Experimental Investigation of Vortex Structures in Wake of Hyperboloid-Shaped Model by Means of 2D Particle Image Velocimetry Measurement

This paper deals with flow around a bluff body of hyperboloid shape. It consists of results gathered in the course of research by means of Particle Image Velocimetry (PIV). The experiments were carried out by means of low-frequency 2D PIV in a range of Reynolds numbers from 40000 to 50000. A hyperboloid-shaped model was measured in a wind tunnel with a modelled atmospheric boundary layer (and additionally, in a low-speed wind tunnel with low turbulence). The model was tested in a subcritical range of Reynolds numbers and various planes in a wake of the model were captured with the intention of getting an estimation of 3D flow structures. The tunnel with the modelled atmospheric boundary layer has a high rate of turbulence, so the influence of the turbulence of incoming flow on the wake could be outlined. The ratio of the height of the model to a thickness of the modelled boundary layer in the tunnel was 1/3, meaning the turbulence in the boundary layer strongly influenced the flow around the model; it suppresses the wake which leads to a lot shorter area of recirculation than low turbulence incoming flow would cause.

Study of flow around model of cooling tower by means of 2D Particle Image Velocimetry measurement

This paper deals with flow around a bluff body of hyperboloid shape. It combines results gathered in the course of research by means of Particle Image Velocimetry (PIV). The experiments were carried out by means of low-frequency 2D PIV and the Reynolds number was 43 000.

A hyperboloid structure as a mechanical model of the carbon bond

We present a new mechanical model of interatomic bonds, which can be used to describe the elastic properties of the carbon allotropes, such as graphite, diamond, fullerene, and carbon nanotubes. The interatomic bond is modeled by a hyperboloid–shape truss structure. The elastic characteristics of this bond are determined. Previous known structural models also used elastic elements (beams, trusses) to simulate a carbon bond. However unlike them our model satisfies to the correct ratio of the longitudinal and lateral stiffness, observed from the previous experimental and theoretical results. Parameters of the bond in application for graphene and diamond were determined.

Measurement of cosmic rays with LOFAR

The LOw Frequency ARay (LOFAR) is a multipurpose radio-antenna array aimed to detect radio signals in the 10 – 240 MHz frequency range, covering a large surface in Northern Europe with a higher density in the Northern Netherlands. Radio emission in the atmosphere is produced by cosmic-ray induced air showers through the interaction of charged particles with the Earth magnetic field. The detection of radio signals allows to reconstruct several properties of the observed cascade. We review here all important results achieved in the last years. We proved that the radio-signal distribution at ground level is described by a two-dimensional pattern, which is well fitted by a double Gaussian function. The radio-signal arrival time and polarization have been measured, thus providing additional information on the extensive air shower geometry, and on the radio emission processes. We also showed that the radio signal reaches ground in a thin, curved wavefront which is best parametrized by a hyperboloid shape centred around the shower axis. Radio emission has also been studied under thunderstorm conditions and compared to fair weather conditions. Moreover, by using a hybrid reconstruction technique, we performed mass composition measurements in the energy range 1017 – 1018 eV.

Experimental Study on Branch and Diffuse Type of Streamers in Leader Restrike of Long Air Gap Discharge**supported by the Fund of the National Priority Basic Research of China (2011CB209403) and National Natural Science Foundation of China (Nos. 51325703, 51377094, 51577098)

One of the main problems in the Ultra High Voltage (UHV) transmission project is to choose the external insulation distance, which requires a deep understanding of the long air gap discharge mechanism. The leader-streamer propagation is one of most important stages in long air gap discharge. In the conductor-tower lattice configuration, we have measured the voltage, the current on the high voltage side and the electric field in the gap. While the streamer in the leader-streamer system presented a conical or hyperboloid diffuse shape, the clear branch structure streamer in front of the leader was firstly observed by a high speed camera in the experiment. Besides, it is found that the leader velocity, width and injected charge for the branch type streamer are greater than those of a diffuse type. We propose that the phenomenon results from the high humidity, which was 15.5-16.5 g/m3 in our experiment.

The shape of the radio wavefront of extensive air showers as measured with LOFAR

Extensive air showers, induced by high energy cosmic rays impinging on the Earth’s atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the incident wavefront is non-planar. A spherical, conical or hyperbolic shape of the wavefront has been proposed, but measurements of individual air showers have been inconclusive so far. For a selected high-quality sample of 161 measured extensive air showers, we have reconstructed the wavefront by measuring pulse arrival times to sub-nanosecond precision in 200 to 350 individual antennas. For each measured air shower, we have fitted a conical, spherical, and hyperboloid shape to the arrival times. The fit quality and a likelihood analysis show that a hyperboloid is the best parameterization. Using a non-planar wavefront shape gives an improved angular resolution, when reconstructing the shower arrival direction. Furthermore, a dependence of the wavefront shape on the shower geometry can be seen. This suggests that it will be possible to use a wavefront shape analysis to get an additional handle on the atmospheric depth of the shower maximum, which is sensitive to the mass of the primary particle.

Analysis of nonuniform field emission from a sharp tip emitter of Lorentzian or hyperboloid shape

For a sharp tip emitter, due to the non-uniform emission feature and the electron beam expansion in the vacuum, it is difficult to precisely determine the average field enhancement factor βc as well as the effective emission area Seff for a single field emitter. In this paper, we conduct a numerical experiment to simulate the electron field emission from a sharp tip emitter (Lorentzian or hyperboloid shape). By collecting the emission current Itot at the finite anode area Stot, we establish the criteria in using Fowler-Nordheim plot to estimate both βc and Seff, which agree well with our initial emission condition. It is found that the values of βc and Seff depend on the emitter's properties as well as the size of the anode area Stot. In order to determine the precise value of βc, Stot must be large enough to collect all the emitted electrons from the sharp tip (e.g., Itot reaches maximum). As an example, a Lorentzian type emitter with an aspect ratio of 10 (height over width), the effective enhancement factor is about βc=33 as compared to the maximal enhancement of 35 at the apex. At similar maximal enhancement factor at the apex (=360), both types of emitters will give different average field enhancement dependent on the collecting area. The extension of this simple model to a statistical more complicated model to simulate field emission from a cathode consisting of many field emitters is also briefly discussed. This paper should be useful to analyze and characterize field emission data together with experimental measurement.

Onset of space charge limited current for field emission from a single sharp tip

A protrusive model of the Child-Langmuir (CL) law is proposed for non-uniform electron field emission from a sharp tip of either Lorentzian or hyperboloid shape. The model is expressed as Jc = μ×J1D at large electric field higher than a critical value Ec, and J1D is the classical one-dimensional CL law. It is found that the enhancement μ over the 1D CL law depends only on the calculated field enhancement factor (β) of the emitter and is independent of the work function and gap spacing. In particular, μ increases with β and it converges to a constant at β≫ 1 for a very sharp tip with small emission area.

Formation of a Hot Electron Ring in an ECR Mirror Trap Through a Particle-in-Cell Simulation Study

Plasma structure and electron ring formation in a magnetic mirror trap under electron cyclotron resonance (ECR) conditions is studied numerically through a simulation of the Newton–Lorentz equation by a particle-in-cell method. The plasma self-generated electric field is calculated through a numerical solution of the Poisson equation with the help of the fast Fourier transform technique. The zone where the ECR conditions are fulfilled is almost of a one-sheet hyperboloid shape. It is shown that in the middle transversal plane of the trap, a stable gyrating electron ring is formed. Some trajectories of the hot and superhot electrons comprising the ring are visualized.

Classical and quantum transport through entropic barriers modeled by hardwall hyperboloidal constrictions

We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrödinger equation and the classical equations of motion for these geometries, we study in detail the quantum transmission probabilities and the associated quantum resonances, and relate them to the classical phase structures which govern the transport through the constrictions. These classical phase structures are compared to the analogous structures which, as has been shown only recently, govern reaction type dynamics in smooth systems. Although the systems studied in this paper are special due their separability they can be taken as a guide to study entropic barriers resulting from constriction geometries that lead to non-separable dynamics.

PRECLINICAL ASSESSMENT OF ANATOMICAL SHOULDER REPLACEMENT: THE TRUTH ABOUT THE HUMERAL HEAD

Objective. Our aim was to develop a mathematical model to calculate forces, tension and stretching in the hip joint capsule, under conditions caused by the joint effusion usually accompanying hip disease.Design. A mathematical model was developed, based on experimental data from cadaver studies.Background. Intracapsular pressure is important with respect to the degree of painless movement in the hip. Previously, we established the relations between the rotation around the axis of the neck of the femur, joint effusion, intracapsular pressure and joint stability.Methods. In six cadaver adult hips the joint distraction, the traction force along and the rotation around the axis of the neck of the femur and the intracapsular pressure, were simultaneously monitored as the volume of intracapsularly infused saline was increased. The elasticity-constants included in the extracted formula for the fluid pressure were calculated in a designed computer software based on these experimental data.Results. Presented in Figures 3–12.Conclusions. In the normal joint there is no increase in intracapsular pressure, nor any tension in the hyperboloid shape capsule within the normal range of rotation around the axis of the neck of the femur. This shape is distorted in a hip with effusion, rotation then resulting in an increased intracapsular pressure and tension in the capsule, with potential risk of ruptures.