Thin Circular Disk Research Articles

Fission gas release behaviour of a 103 GWd/tHM fuel disc during a 1200 °C annealing test

Within the Nuclear Fuel Industry Research (NFIR) program, several fuel variants, in the form of thin circular discs, were irradiated in the Halden Boiling Water Reactor (HBWR) to a range of burn-ups ∼100GWd/tHM. The design of the assembly was similar to that used in other HBWR programs: the assembly contained several rods with fuel discs sandwiched between Mo discs, which limited temperature gradients within the fuel discs. One such rod contained standard grain UO2 discs (3D grain size=18μm) reaching a burn-up of 103GWd/tHM. After the irradiation, the gas release upon rod puncturing was measured to be 2.9%.Detailed characterizations of one of these irradiated UO2 discs, using electron probe microanalysis (EPMA), scanning electron microscopy (SEM) and secondary ion mass spectrometry (SIMS), were performed in a CEA Cadarache hot laboratory. Examination revealed the high burn-up structure (HBS) formation throughout the whole of the disc, also the fission gas distribution within this HBS, with a very high proportion of the gas in the HBS bubbles. A sibling disc was submitted to a temperature transient up to 1200°C in the out-of-pile (OOP) annealing test device “Merarg” at a relatively low temperature ramp rate (0.2°C/s). In addition to the total gas release during this annealing test, the release peaks throughout the temperature range were monitored. The fuel was then characterized with the same microanalysis techniques as before the annealing test to investigate the effects of this test on the microstructure of the fuel and on the fission gases.It provided valuable insights into fission gas localization and the release behaviour in UO2 fuel with high burn-up structure (HBS).

Multiphysics of Multilayered and Functionally Graded Cylinders Under Prescribed Hygrothermomagnetoelectromechanical Loading

This paper examines the multiphysics of multilayered and functionally graded cylinders subjected to steady-state hygrothermomagnetoelectromechanical loading. The cylinder is assumed to be axisymmetric, infinitely long, and with either hollow or solid cross section that is, both polarized and magnetized radially. The multiphysics model is used to investigate the effect of moisture, temperature, magnetic, electric, and mechanical loadings. The influence of imperfectly bonded interfaces is also accounted for in the governing equations. Exact solutions of differential equations are obtained for each homogenous layer of the multilayered cylinder. The results are verified with those available in literature for a homogenous infinitely long cylinder and can also be applied to study the multiphysics of thin circular disks. Maps are presented for solid and hollow cylinders to visualize the effect of hygrothermomagnetoelectromechanical loading, heterogeneity of bonded layers, and imperfectly bonded interfaces. The plots offer insight into the behavior of heterogeneous magnetoelectroelastic media in a steady state hygrothermal field.

Construction of Tensorial Green's Functions for the Linearized Gilbert Equation for Magnetization Dynamics

It is shown that the equations for the components of the tensorial Green's function for the linearized Gilbert equation are in general very complicated coupled integro-differential equations, mainly because of the effect of dipolar couplings. As an example the theory is worked out for very thin circular discs with circular magnetization at zero external field. Analytical solutions for the components of the tensorial Green's function are obtained for those discs by neglecting dipolar couplings.

Shielding of a low-frequency electric field by a multilayer circular disk

We have solved the boundary-value problem with nonclassical boundary conditions, which describes the penetration of a low-frequency field through a multilayer thin circular disk. The solution of the problem is reduced to solving the Fredholm integral equation of the second kind. The influence of some parameters of the problem on the shielding factor is investigated numerically.

Three coins in a fountain

AbstractIf, in a large expanse of fluid such as air or water, an object that is heavier than the fluid displaced is released from rest, it descends in a manner that can depend in a complex way on its geometry and density (relative to that of the fluid), and on the fluid viscosity, which, as in other fluid contexts, remains important no matter how small this viscosity may be. A major numerical attack on this problem for the case in which the object is a thin circular disc is presented by Auguste, Magnaudet & Fabre (J. Fluid Mech., vol. 719, 2013, pp. 388–405).

Analysis of Thermoelastic Deformation of a Thin Hollow Circular Disk Due to Partially Distributed Heat Supply

We consider a thin hollow circular disk occupying the space D: a ≤ r ≤ b, −h/2 ≤ z ≤ h/2 and discuss the thermoelastic problem. The initial temperature of the disk is the same as the temperature of the surrounding medium, which is kept constant. The fixed circular edges are thermally insulated. The disk is subjected to a partially distributed and axisymmetric heat supply on the upper surface, while the lower surface is thermally insulated. To develop the analysis for the temperature field, we introduce the method of integral transforms. The results, obtained in a series form in terms of Bessel functions, are illustrated numerically.

Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion

AbstractThis paper describes an experimental investigation of the dynamics of a freely falling thin circular disk in still water. The flow patterns of the disk zigzag motion are studied using dye visualization and particle image velocimetry. Time-resolved disk motions with six degrees of freedom are obtained with a stereoscopic vision method. The flow separation and vortex shedding are found to change with the Reynolds number, $\mathit{Re}$. At high Reynolds numbers a new dipole vortex is shed that is significantly different from Kármán-type vortices. The vortical structures are mainly composed of leading-edge vortices, a counter-rotating vortex pair and secondary trailing-edge vortices. The amplitude of the horizontal oscillation is also dependent on the Reynolds number with a critical Reynolds number ${\mathit{Re}}_{cr} \approx 2000$, where the oscillatory amplitude is proportional to $\mathit{Re}$ for $\mathit{Re}\lt {\mathit{Re}}_{cr} $, but becomes invariant for $\mathit{Re}\gt {\mathit{Re}}_{cr} $. Three-dimensional dipolar vortices were also observed experimentally.

Effects of Geometric Factors and Material Properties on Stress Behavior in Rotating Disk

In this study, effects of geometric factors and material properties are investigated on stress behavior of circular rotating disk with constant rotation in various industrial mechanisms using equilibrium equations, geometric relations and stress functions. In this way, research on a thin uniform and homogeneous circular disk under constant rotation is considered. The rotating motion produces centrifugal acceleration on each element of the rotating disk, and this rotating motion becomes the source of external loading for the mentioned problem. Additional exterior loadings are not assumed in this problem. It is comfortable to handle the centrifugal force loading by relating it to a body force density via the disk in order to increase strength (maximum stress) of circular rotating disk. Eventually, stress behavior of rotating disk is analyzed with considering geometric factors and material properties analytically. Finally, it is concluded that the mentioned factors affect on increasing and decreasing stress values of circular rotating disk under constant rotation.

Formation process of the vortex ring generated by an impulsively started circular disc

AbstractWe present an experimental study on the axisymmetric vortex ring generated by a thin circular disc. The velocity and vorticity fields are measured by digital particle image velocimetry (DPIV). The finite-time Lyapunov exponent fields and the Lagrangian coherent structures (LCSs) of the vortex flow are computed in order to analyse the transport of the fluid during its formation and identify the boundary of the vortex ring. The volume, circulation and energy of the vortex ring are calculated. It is found that the formation of the vortex ring basically includes three phases: a rapid growth phase, a stable growth phase and a non-axisymmetric phase. In the rapid growth phase (dimensionless time $0\lt {T}_{n} \lt 0. 2$) during which Taylor’s inviscid estimation is valid, the circulation of the vortex ring grows and the translational velocity of the vortex ring decreases. In the stable growth phase ($0. 2\lt {T}_{n} \lt 4$), the growth rate of the circulation decreases gradually. In the non-axisymmetric phase (${T}_{n} \gt 4$), the ring loses axisymmetry due to instability. Compared with the vortex ring generated by the laminar flow from an orifice, the one generated by a circular disc always moves with the disc, and the entrained fluid decreases and the saturated circulation increases. The temporal impulse exerted by the moving disc on the fluid is estimated by DPIV measurements and is calculated using the direct momentum conservation method. The momentum of the control volume enclosing the LCS is found to occupy 64–68 % of the entire impulse exerted by the disc on the fluid.

Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft3, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f 1(z, t) and f 2(z, t), f 3(r, t) and f 4(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.

Viscous Marangoni propulsion

AbstractMarangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low capillary, Péclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50 %.

Pulsed Multichannel Discharge Array in Water With Stacked Circular Disk Electrodes

A simple yet effective system using stacked circular disk electrodes is developed to generate pulsed multichannel discharge array in water. Images of the pulsed multichannel discharge generated in water were obtained by applying pulsed high voltage over thin circular metal disks sandwiched between a pair of dielectric disks. By stacking multiple circular disks, the present discharge array system can produce large-volume plasma desired for the treatment of a large volume of water.

Note: An underwater multi-channel plasma array for water sterilization

A simple yet effective method to generate multi-channel plasma array in water is presented in this paper. Thin circular metal disks sandwiched between dielectric layers were used, allowing the production of large-volume underwater plasma array with higher stability. The system can be further scaled up by stacking multiple metal disks, making it suitable for large-scale industrial water treatment. Generation of UV and reactive species was identified by optical emission spectroscopy. Sterilization experiments were performed. Results show that the device was effective in deactivating E. coli in water over a wide range of initial concentrations ranging from 10(4) to 10(8) CFU/ml.

Foliage Attenuation Over Mixed Terrains in Rural Areas for Broadband Wireless Access at 3.5 GHz

This paper reports the modeling of foliage attenuation for a broadband wireless access system deployed over mixed terrains in rural areas at 3.5 GHz. The foliage is composed of leaves and leafstalks, and are the dominant scatterers along the transmission paths. The foliage attenuation is determined using the Torrico-Lang model combined with digital topography information. In this model, leaves are modeled as thin lossy circular dielectric discs whereas leafstalks (petioles) are modeled as thin lossy dielectric cylinders. Three measurement campaigns were performed using the mobile WiMAX system (IEEE 802.16 e) deployed in Hetzwege/Abbendorf during winter, spring and mid-summer. Using the winter data as a baseline, the foliage loss due to different degrees of foliation in spring and in winter is studied. The derived foliage loss is then verified and compared with an empirical exponential decay model.

Rotational microfluidic motor for on-chip microcentrifugation

We report on the design of a surface acoustic wave (SAW) driven fluid-coupled micromotor which runs at high rotational velocities. A pair of opposing SAWs generated on a lithium niobate substrate are each obliquely passed into either side of a fluid drop to drive rotation of the fluid, and the thin circular disk set on the drop. Using water for the drop, a 5 mm diameter disk was driven with rotation speeds and start-up torques up to 2250 rpm and 60 nN m, respectively. Most importantly for lab-on-a-chip applications, radial accelerations of 172 m/s2 was obtained, presenting possibilities for microcentrifugation, flow sequencing, assays, and cell culturing in truly microscale lab-on-a-chip devices.

О финальном движении скользящих и вращающихся дисков с однородным кулоновым трением

Abstract We review previous investigations concerning the terminal motion of disks sliding and spinning with uniform dry friction across a horizontal plane. Previous analyses show that a thin circular ring or uniform circular disk of radius R always stops sliding and spinning at the same instant. Moreover, under arbitrary nonzero initial values of translational speed v and angular rotation rate ω , the terminal value of the speed ratio ϵ 0 = v / R ω is always 1.0 for the ring and 0.653 for the uniform disk. In the current study we show that an annular disk of radius ratio η = R 1 / R 2 stops sliding and spinning at the same time, but with a terminal speed ratio dependent on η . For a two-tier disk with lower tier of thickness H 1 and radius R 1 and upper tier of thickness H 2 and radius R 2 , the motion depends on both η and the thickness ratio λ = H 1 / H 2 . While translation and rotation stop simultaneously, their terminal ratio ϵ 0 either vanishes when k > 2 / 3 , is a nonzero constant when 1 / 2 k 2 / 3 , or diverges when k 1 / 2 , where k is the normalized radius of gyration. These three regimes are in agreement with those found by Goyal et al. [S. Goyal, A. Ruina, J. Papadopoulos, Wear 143 (1991) 331] for generic axisymmetric bodies with varying radii of gyration using geometric methods. New experiments with PVC disks sliding on a nylon fabric stretched over a plexiglass plate only partially corroborate the three different types of terminal motions, suggesting more complexity in the description of friction.

Quasi-static Thermal Deflection of a Thin Clamped Hollow Circular Disk Due to Heat Generation

This paper deals with the determination of the thermal deflection in a thin clamped hollow circular disk defined as a ≤ r ≤ b; 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. A thin hollow circular disk is considered having an arbitrary initial temperature and subjected to heat flux at the outer circular boundary (r = b) where an inner circular boundary (r = a) is at zero heat flux. Also, the upper surface (z = h) and the lower surface (z = 0) of the disk are at zero temperature. The governing heat conduction equation has been solved by using an integral transform technique. The inner and outer edges of the disk are clamped \({\frac{\partial \omega }{\partial r}=0}\) at r = a, r = b. The results are obtained in a series form in terms of Bessel’s functions and are illustrated graphically.

Experimental Study of a Starting Vortex Ring Generated by a Thin Circular Disk

The formation process of vortex ring generated by a thin circular disk was studied experimentally in this paper. A thin circular disk installed a linear motion stage was used to generate the vortex rings. Digital Particle Image Velocimetry (DPIV) was used to measure the velocity and vorticity fields. The finite-time Lyapunov exponent field corresponding to the vortex flow was computed to identify Lagrangian coherent structures of the starting vortex. The results reveal the existence of a flux window between repelling Lagrangian Coherent Structures (rLCS) and attracting Lagrangian Coherent Structures (aLCS), through which the shear flow is entrained into the vortex. The flux window is closed gradually during the starting process. Once the flux window shut down, the formation process of the vortex ring finishes, as the shear flow with vorticity cannot be entrained in the vortex ring.

Analytic expressions for critical-state ac susceptibility of rectangular superconducting films in perpendicular magnetic field

A set of analytic expressions for the critical-state magnetization and ac susceptibility χ ′ - j χ ″ curves of rectangular superconducting films of arbitrary aspect ratio in perpendicular field is obtained. They are formulated based on the exact/accurate high/low-field limits for rectangular films together with the exact analytic formulas for thin circular disks. Thus, the accuracy of the expressions is very high in high and low fields. At a characteristic intermediate field amplitude, where χ ″ takes its maximum, the error is checked by direct numerical calculations to be well below 1%. Thus, the provided expressions can be conveniently and satisfactorily used for practical and theoretical researches of superconducting materials, such as coated conductors.

A DISK OF YOUNG STARS AT THE GALACTIC CENTER AS DETERMINED BY INDIVIDUAL STELLAR ORBITS

We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive, young stars located within 3.5" (0.14 pc) of the supermassive black hole at the Galactic Center. Our proper motion measurements have uncertainties of only 0.07 mas/yr (3 km/s), which is ~7 times better than previous proper motion measurements for these stars, and enables us to measure accelerations as low as 0.2 mas/yr^2 (7 km/s/yr). Using these measurements, line-of-sight velocities from the literature, and 3D velocities for additional young stars in the central parsec, we constrain the true orbit of each individual star and directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed. Analysis of the stellar orbits reveals only one of the previously proposed disks of young stars using a method that is capable of detecting disks containing at least 7 stars. The detected disk contains 50% of the young stars, is inclined by ~115 deg from the plane of the sky, and is oriented at a position angle of ~100 deg East of North. Additionally, the on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger projected radii as \propto r^-2. The disk has an out-of-the-disk velocity dispersion of 28 +/- 6 km/s, which corresponds to a half-opening angle of 7 +/- 2 deg, and several candidate disk members have eccentricities greater than 0.2. Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple, thin circular disk.