Spherical Container Research Articles

Research on Accurate Ultrasonic Positioning Error under the Special Environment

This paper studies how to achieve the accurate position by an ultrasonic positioning system, which is for locating the autonomous vehicle in a special giant spherical container. A localization method using the least squares with a plane array which consists of four elements is proposed, the reason that causes the location error is analysed, and the relationship among the target distance and the array shape and the error of the ultrasonic positioning system is studied by Monte Carlo simulations. Finnally, in order to verify the positioning effect, the positioning experiment is done in an anechoic tank, the experimental results shown that when the ranging error is less than 20 mm, the positioning accuracy of x-y plane is less than about 30 mm.

The effect of glycerin solution density and viscosity on vibration amplitude of oblique different piezoelectric MC near the surface in 3D modeling

The surface topography in nanoscale is one of the most important applications of AFM. The analysis of piezoelectric microcantilevers vibration behavior is essential to improve the AFM performance. To this end, one of the appropriate methods to simulate the dynamic behavior of microcantilever (MC) is a numerical solution with FEM in the 3D modeling using COMSOL software. The present study aims to simulate different geometries of the four-layered AFM piezoelectric MCs in 2D and 3D modeling in a liquid medium using COMSOL software. The 3D simulation was done in a spherical container using FSI domain in COMSOL. In 2D modeling by applying Hamilton’s Principle based on Euler–Bernoulli Beam theory, the governing motion equation was derived and discretized with FEM. In this mode, the hydrodynamic force was assumed with a string of spheres. The effect of this force along with the squeezed-film force was considered on MC equations. The effect of fluid density and viscosity on the MC vibrations that immersed in different glycerin solutions was investigated in 2D and 3D modes and the results were compared with the experimental results. The frequencies and time responses of MC close to the surface were obtained considering tip-sample forces. The surface topography of MCs different geometries were compared in the liquid medium and the comparison was done in both tapping and non-contact mode. Various types of surface roughness were considered in the topography for MC different geometries. Also, the effect of geometric dimensions on the surface topography was investigated. In liquid medium, MC is installed at an oblique position to avoid damaging the MC due to the squeezed-film force in the vicinity of MC surface. Finally, the effect of MC’s angle on surface topography and time response of the system was investigated.

A hybrid algorithm for packing identical spheres into a container

Packing identical spheres occur in several commercial and industrial contexts, like automated radio-surgical treatment planning and in materials science for studying the dynamic behavior of granular material systems. In this paper, a hybrid algorithm is proposed for approximately solving the identical sphere packing problem. Given a set of identical spheres and a large container (open or spherical container), the goal of the problem is to find a smallest container that contains all spheres without overlapping between spheres and between spheres and the container. The proposed algorithm combines both particle swarm optimization and an efficient continuous local optimization procedure. The swarm optimization generates a series of diversified populations of particles whereas the continuous optimization serves either to repair the infeasibility of solutions or improve their qualities. The performance of the proposed algorithm is evaluated on a set of standard benchmark instances and its obtained results are compared to those reached by the more recent methods available in the literature. The experimental part shows that the proposed approach remains competitive, where it is able to reach 47 new upper bounds out of the 93 tested instances.

Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

Studies on the inward spherical solidification of a phase change material dispersed with macro particles

This paper investigates numerically the solidification of a phase change material (PCM) dispersed with high conductivity macro particles inside a spherical container. The formulation takes into account the addition of particles invoking an effective thermal conductivity model. A case study has been made comparing the experimental results available in the open literature for the solidification of a pure PCM case (without particles) to investigate the influence of particles. The results show that the addition of particles between 10 and 50% by volume, enhances the heat transfer rate by about 13.5 and 59% respectively. Parametric studies have been carried out to investigate the influence of relevant dimensionless numbers such as Biot number (Bi) and Stefan number (Ste) on the solidification characteristics of the PCM for different particle fractions. The role of particles was found to be significant at lower Ste compared to Bi. It has been concluded that the effect of particle fraction on the solidification is more compared to that of particle-PCM thermal conductivity ratio. It was found that there is no restriction on the choice of particle material for a given PCM, as long as the particle-PCM thermal conductivity ratio considered remain larger than 5.

Influential factors of vented explosion position on maximum explosion overpressure of methane‐air mixture explosion in single spherical container and linked vessels

An explosion venting system is established to examine the influencing factors of the vented explosion position for a single vessel, a single vessel connected by pipes and two vessels connected by pipes during the explosion venting process of a methane‐air mixture. Relative to a single vessel, it is shown that the maximum explosion venting pressure of the lateral vented explosion does not appear to vary greatly from that of a top vented explosion. It appears that as the volume of the spherical vessel increases, the maximum pressure increases. The maximum overpressure for an explosion venting on the top and side does not vary for either a large or small vessel connected by pipes. However, as the maximum explosion overpressure in the pipe increases, the maximum explosion overpressure peak occurs at the end of the pipe, and the explosion flame that propagates in the pipe accelerates and enlarges. Compared with an airtight explosion, an explosion venting on the top and side of a single vessel is more effective for both a large and small vessel connected by pipes. The pressure in the vessel and pipe appears to fluctuate and produces multiple peaks in the explosion venting process. Ignition in a large vessel is more dangerous than ignition in a small vessel under an airtight condition for two vessels connected by pipes. Regardless of the ignition position in the large or small vessel, the explosion venting effect in the small vessel is better than that in the large vessel. © 2017 American Institute of Chemical Engineers Process Saf Prog 37: 248–255, 2018

Oscillatory and streaming flow between two spheres due to combined oscillations

The flow induced by the combined torsional and transverse oscillations of a sphere with amplitude ratio $\unicode[STIX]{x1D6FC}$ and phase difference $\unicode[STIX]{x1D6FD}$ in a concentric spherical container is examined. Analytical solutions of the leading-order flow field and shear stress profiles have been obtained. Steady streaming flows are also analysed not only for the case of unrestricted Womersley number $|M|$, but also in the low-frequency $(|M|\ll 1)$ and high-frequency ($|M|\gg 1$) limits. At high frequency, the flow field has been divided into three regions: two boundary layers and the outer region. The streaming flow field is determined for the limiting case of the streaming Reynolds number $R_{s}\ll 1$. The results are compared with those of single torsional or transverse oscillation, and found to match very well. The amplitude ratio $\unicode[STIX]{x1D6FC}$ and phase difference $\unicode[STIX]{x1D6FD}$, in determining the streaming, are also discussed. The number and direction of steady streaming recirculation on the $r$–$\unicode[STIX]{x1D703}$ plane depend on value of the amplitude ratio $\unicode[STIX]{x1D6FC}$. The phase difference $\unicode[STIX]{x1D6FD}$ plays a dominant role in the azimuthal velocity $u_{1\unicode[STIX]{x1D719}}^{(s)}$ of steady streaming. When $\unicode[STIX]{x1D6FD}$ is approximately $(2n+1)\unicode[STIX]{x03C0}/2$, $u_{1\unicode[STIX]{x1D719}}^{(s)}$ vanishes under low-frequency oscillation, while steady streaming has a recirculation on the $r$–$\unicode[STIX]{x1D719}$ plane under higher-frequency oscillation.

Characterization of columnar inertial modes in rapidly rotating spheres and spheroids.

We consider fluid-filled spheres and spheroidal containers of eccentricity ϵ in rapid rotation, as a proxy for the interior dynamics of stars and planets. The fluid motion is assumed to be quasi-geostrophic (QG): horizontal motions are invariant parallel to the rotation axis z, a characteristic which is handled by use of a stream function formulation which additionally enforces mass conservation and non-penetration at the boundary. By linearizing about a quiescent background state, we investigate a variety of methods to study the QG inviscid inertial wave modes which are compared with fully three-dimensional (3D) calculations. We consider the recently proposed weak formulation of the inviscid system valid in spheroids of arbitrary eccentricity, to which we present novel closed-form polynomial solutions. Our modal solutions accurately represent, in both spatial structure and frequency, the most z-invariant of the inertial wave modes in a spheroid, and constitute a simple basis set for the analysis of rotationally dominated fluids. We further show that these new solutions are more accurate than those of the classical axial-vorticity equation, which is independent of ϵ and thus fails to properly encode the container geometry. We also consider the effects of viscosity for the cases of both no-slip and stress-free boundary conditions for a spherical container. Calculations performed under the columnar approximation are compared with 3D solutions and excellent agreement has been found despite fundamental differences in the two formulations.

Investigation on Phase Change Behavior of Paraffin Phase Change Material in a Spherical Capsule for Solar Thermal Storage Units

ABSTRACTIn this work, the melting and solidification behaviour of paraffin phase change material encapsulated in a stainless steel spherical container has been studied experimentally. A computational fluid dynamics analysis has also been performed for the encapsulated phase change material (PCM) during phase change process. In the melting process, the hot air, used as the heat transfer fluid enters the test section and flows over the spherical capsule resulting in the melting of phase change material. In the solidification process, the ambient air flows over the capsule and received heat from phase change material resulting in the solidification of phase change material. In the computational fluid dynamics, the constant wall boundary condition is employed for both melting (75°C) and solidification (36°C) processes since the internal conductive resistance offered by the PCM is much higher compared to the outer surface convective resistance. The time required for complete solidification and melting of the phase change material obtained from the computational fluid dynamics analysis are validated with the experimental results and a reasonable agreement is achieved. The reason for the deviation between the results are analyzed and reported.

Impact Analyses of a Tennis Ball onto Water-Filled Containers

Water-filled containers have long known for its structural characteristic of impact load absorption. This paper presents design of structures resisting to impact load resulting from a high-velocity tennis ball. One cubic meter water containers consisting of rectangular, cylindrical, and spherical water containers and water levels were studied for their stress distribution and deformation during maximum deformation period using finite element analysis in the ANSYS 15.0 software. The containers were modeled by using shell elements and made of elasto-plastic material of HDPE plastic. The filled water was model by using fluid elements. We found that as ball velocity increased, maximum von Mises stress increased. However, for post-yielding behavior, maximum von Mises stress approached a constant near yield stress of HDPE material. As ball velocity increases, deformation increases. When water level increased, maximum deformation decreased. For the rectangular container, when the water level increases, the maximum von Mises stress increases while maximum deformation decreases. For the cylindrical and spherical containers, when water level increases, both maximum von Mises stress and maximum deformation decreases. The fully-filled spherical water container had illustrated the superb capabilities to absorb and to dissipate impact load to the rest of the container structure.

Competition between finite-size effects and dipole–dipole interactions in few-atom systems

In this paper, we study the competition between finite-size effects (i.e. discernibility of particles) and dipole–dipole interactions in few-atom systems coupled to the electromagnetic field in vacuum. We consider two hallmarks of cooperative effects, superradiance and subradiance, and compute for each the rate of energy radiated by the atoms and the coherence of the atomic state during the time evolution. We adopt a statistical approach in order to extract the typical behaviour of the atomic dynamics and average over random atomic distributions in spherical containers with prescribed with k0 the radiation wavenumber and R the average interatomic distance. Our approach allows us to highlight the tradeoff between finite-size effects and dipole–dipole interactions in superradiance/subradiance. In particular, we show the existence of an optimal value of for which the superradiant intensity and coherence pulses are the less affected by dephasing effects induced by dipole–dipole interactions and finite-size effects.

CFD simulation of melting process of phase change materials (PCMs) in a spherical capsule

The present study is focused on CFD simulation of constrained melting of Phase Change Materials (PCMs) in a spherical container. To investigate the melting process of the PCM, its melting fraction was analyzed at different times. The results indicated the existence of thermally stable layers on the top of the sphere. Moreover, inspection of the calculated temperatures at different points along the vertical axis indicates the existence of some disturbances at the bottom of the sphere due to the natural convection. After the validation of the results, the effects of different parameters such as the surface temperature of the capsule, the initial temperature and the size of the spherical capsules, on the melting process were investigated. The initial temperature did not affect the melting rate, whereas melting rate increased by increasing the surface temperature of the capsule and also decreasing the diameter of the sphere. The results showed that the surface temperature of capsule compared to geometrical parameters and other operational conditions can have a greater influence on the melting rate and the heat flux.

Measurement of the torque on diluted ferrofluid samples in rotating magnetic fields

We study magnetic suspensions with different concentrations of ferromagnetic nanoparticles in a spherical container under the action of a rotating magnetic field. Experimental data on the concentration dependence of the rotational effect, viz. the torque exerted by the magnetic field, are presented. We explain the observed torque characteristics using a model that takes into account field-driven aggregation of the magnetic nanoparticles in stationary or slowly rotating fields. At sufficiently high rotation rates, the rotating magnetic field obviously destroys these aggregates, which results in a decreasing torque with increasing rotation frequency of the field.

Slow viscous stream over a non-Newtonian fluid sphere in an axisymmetric deformed spherical vessel

The creeping motion of a non-Newtonian (Reiner-Rivlin) liquid sphere at the instant it passes the center of an approximate spherical container is discussed. The flow in the spheroidal container is governed by the Stokes equation, while for the flow inside the Reiner-Rivlin liquid sphere, the expression for the stream function is obtained by expressing it in the power series of a parameter S , characterizing the cross-viscosity. Both the flow fields are then determined explicitly by matching the boundary conditions at the interface of Newtonian fluid and non-Newtonian fluid, and also the condition of imperviousness and no-slip on the outer surface. As an application, we have considered an oblate spheroidal container. The drag and wall effects on the liquid spherical body are evaluated. Their variations with regard to the separation parameter l , viscosity ratio \( \lambda\), cross-viscosity S, and deformation parameter \( \varepsilon\) are studied and demonstrated graphically. Several renowned cases are derived from the present analysis. It is observed that the drag not only varies with \( \varepsilon\), but as l increases, the rate of change in behavior of drag force also increases. The influences of these parameters on the wall effects has also been studied and presented in a table.

Hot pressure welding of hemispherical shells

The process and methods of calculating the conditions of pressure welding of hemispherical shells in local deformation are proposed. It is assumed that the material is viscoplastic. An energy method for calculating the parameters of the process is proposed. The results are presented and components and spherical containers made of a titanium alloy are described.

Two phase microfluidics with inviscid drops: Effects of total flow rate and delayed surfactant addition

ABSTRACTThe microfluidic production of droplets is a well controllable process, which allows templating small spherical containers that can subsequently be transferred into uniformly sized polymer microgel particles by a crosslinking reaction. Recently, the per-channel production rate of N-isopropylacrylamide (NIPAAm) droplets (w-phase) dispersed in a low-viscosity fluorocarbon oil (o-phase) could be increased by a delayed surfactant addition, while maintaining the advantageous dripping regime. Here it should be evaluated, if delayed surfactant addition can be applied to enhance droplet production also for high viscosity continuous phases, which is associated with a change to an inviscid drop scenario compared to the previously used setting of viscous drops. It could be illustrated that the concept of delayed surfactant addition holds true also for viscous continuous phases and allows ∼8 fold increased flow rates in the dripping regime. Surprisingly, the droplet size increased at higher total flow rate with constant flow rate ratios of w- and o-phases, which is discussed in the light of viscous dissipation, microchannel bulging and viscosity of the continuous phase. More rigid microchannels such as from glass may allow further exploring this phenomenon in the future.

Segregation of granular mixtures in a spherical tumbler.

Segregation of polydisperse granular materials in rotating containers is a ubiquitous but still not satisfactorily understood phenomenon. This study describes axial segregation of bidisperse granular mixtures of glass beads in a spherical container, rotating about its horizontal axis. Depending on the filling fraction of the mixer and on the composition of the mixture, qualitatively different spontaneously formed patterns are observed. For technical applications, the well-localized segregated bands allow a convenient separation of individual components of the mixtures. It is particularly surprising that the initial compositions of the granular mixtures have a fundamental influence on the location of the segregated bands. This evidences a collective pattern forming mechanism. The spontaneous formation of these bands cannot simply be traced back to individual particle dynamics. Existing models for segregation in spherical mixers are critically examined and extensions are suggested.

Slow Steady Rotation of an Approximate Sphere in an Approximate Spherical Container with Slip Surfaces

The slow steady rotation of an approximate sphere (whose shape deviates slightly from that of a sphere) in a concentric approximate spherical container is studied analytically. The slip boundary condition is applied at the particle and container surfaces. An exact solution is obtained to the first order in the small parameter characterizing the deformation. The hydrodynamic couple and coupling coefficient exerted on the particle in presence of the cavity is calculated. As an application, the case of flow past spheroid in a spheroidal container is considered and the couple experienced by spheroid is evaluated. In the limiting cases, the hydrodynamic couple acting on the sphere in an unbounded medium is obtained in case of no slip condition. It is noticed that under the Stokesian assumption, the deformation in the body has significant influence on the couple experienced.

Optimization of packing polyhedra in spherical and cylindrical containers

The study focuses on the problem of packing a given set of arbitrary polyhedra allowing continuous rotation in a container of a minimum size (a sphere with a minimum radius or a cylinder with a minimum coefficient of homothety). Non-overlapping and containment constraints are described by means of radical-free quasi-phi-functions. This allows building a mathematical model as a nonlinear programming problem with a domain of feasible solutions that is described as a system of inequalities with smooth functions. The proposed solution strategy includes a fast algorithm for generating valid starting points and the COMPOLY-S optimization procedure that reduces the nonlinear programming problem with a large number of variables and a large number of inequalities to a sequence of smaller tasks and fewer non-linear inequalities. The COMPOLY-S procedure significantly reduces the computational cost (time and memory) and allows an efficient use of modern local and global NLP-solvers, such as IPOPT, Baron, LindoGlobal and GloMIQO, for solving nonlinear programming problems.

Solidification characteristics of water based graphene nanofluid PCM in a spherical capsule for cool thermal energy storage applications

This study aimed to investigate the solidification behavior of water dispersed with graphene nanoplatelets (GNPs) in a spherical container during solidification. The nanofluid phase change materials (NFPCMs) with GNP mass concentrations of 0.3%, 0.6%, 0.9% and 1.2% were prepared and their corresponding thermal conductivity was measured both in liquid and solid states. The thermal conductivity data showed the linear and nonlinear enhancement in liquid and solid state, respectively. The addition of GNPs resulted to an appreciable reduction in the subcooling of water from −7 °C to −2.5 °C along with reduction of 25% in solidification time owing to its high thermal conductivity and larger specific surface area. The onset of solidification got advanced in the case of NFPCM due to higher cooling rate in the subcooling region for any given driving potential. The accelerated mode of energy charging occurred during 78% of total solidification time.