scholarly journals A Refined Mathematical Model of Physical Processes in a Conductor at a High-Current Pulse Discharge

2021 ◽  
Vol 60 (3) ◽  
pp. 124-132
Author(s):  
Yevgen Bajda ◽  
Michael Pantelyat
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Current Density ◽  
Thermal Stresses ◽  
Pulse Discharge ◽  
Circular Cross Section ◽  
Nonuniform Heating ◽  
Physical Processes ◽  
Short Term ◽  
The Cross

A novel mathematical model describing physical processes during the flow of an aperiodic pulse current with amplitude of 100 kA along a conductor with a circular cross-section is proposed and investigated. It is shown how a short-term electric discharge of an aperiodic shape affects the distribution of the current density in the cross-section of the conductor, causing its nonuniform heating and the appearance of significant thermal forces as well as mechanical stresses and strains. Based on the developed mathematical model, the relation-ship between electromagnetic, thermal and mechanical phenomena is shown, allowing a deeper understanding of the multiphysics processes taking place. The maximum values of the current density are calculated, which on the surface of the conductor reach values of 47 kA/mm2, while the temperature rise of a copper conductor with a diameter of 2.44 mm is no more than 80ºC at high temperature gradients, which causes the appearance of thermal stresses that have value (40–50)% of the value of the short-term strength limit of electrical copper. Utilization of this model allows to more accurately determine the required conductor cross-section based on the characteristics of electromagnetic, thermal and mechanical pro-cesses. It is shown that the simplified model (the condition for the uniform distribution of the current over the cross-section) gives significantly underestimated values of temperatures and does not take into account temperature deformations.

scholarly journals Transient Current Density in a Pair of Long Parallel Conductors

2021 ◽  
Vol 11 (15) ◽  
pp. 6920
Author(s):  
Oldřich Coufal
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Current Density ◽  
Circular Cross Section ◽  
Transient Current ◽  
Constant Current ◽  
Voltage Source ◽  
Sinusoidal Voltage ◽  
Steady State Current ◽  
Maximum Current

Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

scholarly journals Validation of Welding Simulations Using Thermal Strains Measured with DIC

2011 ◽  
Vol 70 ◽  
pp. 129-134 ◽  
Author(s):  
Maarten De Strycker ◽  
Pascal Lava ◽  
Wim Van Paepegem ◽  
Luc Schueremans ◽  
Dimitri Debruyne
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Circular Cross Section ◽  
Welding Process ◽  
Weld Bead ◽  
Image Correlation ◽  
Steel Tubes ◽  
Element Analysis ◽  
Strain Evolution ◽  
The Cross

Residual stresses can affect the performance of steel tubes in many ways and as a result their magnitude and distribution is of particular interest to many applications. Residual stresses in cold-rolled steel tubes mainly originate from the rolling of a flat plate into a circular cross section (involving plastic deformations) and the weld bead that closes the cross section (involving non-uniform heating and cooling). Focus in this contribution is on the longitudinal weld bead that closes the cross section. To reveal the residual stresses in the tubes under consideration, a finite element analysis (FEA) of the welding step in the production process is made. The FEA of the welding process is validated with the temperature evolution of the thermal simulation and the strain evolution for the mechanical part of the analysis. Several methods for measuring the strain evolution are available and in this contribution it is investigated if the Digital Image Correlation (DIC) technique can record the strain evolution during welding. It is shown that the strain evolution obtained with DIC is in agreement with that found by electrical resistance strain gauges. The results of these experimental measuring methods are compared with numerical results from a FEA of the welding process.

scholarly journals The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

The pancaking of coronal mass ejections: an in situ attestation

2020 ◽  
Vol 493 (1) ◽  
pp. L16-L21 ◽  
Author(s):  
Anil N Raghav ◽  
Zubair I Shaikh
Keyword(s):  
Cross Section ◽  
Space Weather ◽  
Coronal Mass Ejections ◽  
Arrival Time ◽  
Interplanetary Space ◽  
Morphological Evolution ◽  
Circular Cross Section ◽  
Primary Concern ◽  
The Cross

ABSTRACT The interplanetary counterparts of coronal mass ejections (ICMEs) are the leading driver of severe space weather. Their morphological evolution in interplanetary space and the prediction of their arrival time at Earth are the ultimate focus of space weather studies, because of their scientific and technological effects. Several investigations in the last couple of decades have assumed that ICMEs have a circular cross-section. Moreover, various models have also been developed to understand the morphology of ICMEs based on their deformed cross-section. In fact, simulation studies have suggested that the initial circular cross-section flattens significantly during their propagation in the solar wind and this is referred to as ‘pancaking’. However, an observational verification of this phenmenon is still pending and it will eventually be the primary concern of several morphological models. Here, we report the first unambiguous observational evidence of extreme flattening of the cross-section of ICMEs, similar to pancaking, based on in situ measurements of 30 ICME events. In fact, we conclude that the cross-section of ICME flux ropes transformed into a two-dimensional planar magnetic structure. Such a deformed morphological feature not only alters the prediction of their arrival time but also has significant implications in solar-terrestrial physics, the energy budget of the heliosphere, charged particle energization, turbulence dissipation and enhanced geo-effectiveness, etc.

Modeling the Phonon Transport in Nanowire with Different Cross-Section

2013 ◽  
Vol 401-403 ◽  
pp. 852-855
Author(s):  
Gao Hui Su ◽  
Zi Chun Yang ◽  
Feng Rui Sun
Keyword(s):  
Thermal Conductivity ◽  
Cross Section ◽  
Diffuse Reflection ◽  
Silicon Nanowire ◽  
Circular Cross Section ◽  
Phonon Transport ◽  
Reflection Mode ◽  
Section Shape ◽  
Section Size ◽  
The Cross

The phonon transport in silicon nanowire was simulated by Monte Carlo Method (MCM). The effect on the phonon transport of the boundary reflection mode, cross-section size and cross-section shape was studied. Analysis shows that diffuse reflection can result in phonon accumulation at the circumferential boundary. As the cross-section size decrease, the nonuniformity of the temperature distribution within the cross-section becomes more severe. When the area of the square cross-section silicon nanowire (SCSN) is equal to that of the circular cross-section silicon nanowire (CCSN), the thermal conductivity of them is more close to each other.

Mathematical Modeling of the Circulation in the Liver Lobule

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Andrea Bonfiglio ◽  
Kritsada Leungchavaphongse ◽  
Rodolfo Repetto ◽  
Jennifer H. Siggers
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Cross Section ◽  
Cross Sections ◽  
Total Blood ◽  
Liver Lobule ◽  
Tissue Compliance ◽  
Two Dimensional Flow ◽  
Qualitative Effect ◽  
The Cross

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.

scholarly journals Amplified cross-linking efficiency of self-assembled monolayers through targeted dissociative electron attachment for the production of carbon nanomembranes

2017 ◽  
Vol 8 ◽  
pp. 2562-2571 ◽  
Author(s):  
Sascha Koch ◽  
Christopher D Kaiser ◽  
Paul Penner ◽  
Michael Barclay ◽  
Lena Frommeyer ◽  
...  
Keyword(s):  
Cross Section ◽  
Current Density ◽  
Electron Attachment ◽  
The Other ◽  
Self Assembled Monolayers ◽  
Cross Linking ◽  
Dissociative Electron Attachment ◽  
Electron Dose ◽  
Assembled Monolayers ◽  
The Cross

The determination of the negative ion yield of 2′-chloro-1,1′-biphenyl (2-Cl-BP), 2′-bromo-1,1′-biphenyl (2-Br-BP) and 2′-iodo-1,1′-biphenyl (2-I-BP) upon dissociative electron attachment (DEA) at an electron energy of 0 eV revealed cross section values that were more than ten times higher for iodide loss from 2-I-BP than for the other halogenides from the respective biphenyls (BPs). Comparison with dissociative ionization mass spectra shows that the ratio of the efficiency of electron impact ionization induced fragmentation of 2-I-BP, 2-Br-BP, and 2-Cl-BP amounts to approximately 1:0.7:0.6. Inspired by these results, self-assembled monolayers (SAMs) of the respective biphenyl-4-thiols, 2-Cl-BPT, 2-Br-BPT, 2-I-BPT as well as BPT, were grown on a Au(111) substrate and exposed to 50 eV electrons. The effect of electron irradiation was investigated by X-ray photoelectron spectroscopy (XPS), to determine whether the high relative DEA cross section for iodide loss from 2-I-BPT as compared to 2-Br-BP and 2-Cl-BP is reflected in the cross-linking efficiency of SAMs made from these materials. Such sensitization could reduce the electron dose needed for the cross-linking process and may thus lead to a significantly faster conversion of the respective SAMs into carbon nanomembranes (CNMs) without the need for an increased current density. XPS data support the notation that DEA sensitization may be used to achieve more efficient electron-induced cross-linking of SAMs, revealing more than ten times faster cross-linking of 2-I-BPT SAMs compared to those made from the other halogenated biphenyls or from native BPT at the same current density. Furthermore, the transfer of a freestanding membrane onto a TEM grid and the subsequent investigation by helium ion microscopy (HIM) verified the existence of a mechanically stable CNM created from 2-I-BPT after exposure to an electron dose as low as 1.8 mC/cm2. In contrast, SAMs made from BPT, 2-Cl-BPT and 2-Br-BPT did not form stable CNMs after a significantly higher electron dose of 9 mC/cm2.

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