Spherical Container Research Articles

Phase behavior and dynamics in a colloid-polymer mixture under spherical confinement.

From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.

Flame behaviors and explosion characteristics of two‐phase propylene oxide/air mixture under different ambient pressures

AbstractPropylene oxide (PO) is widely used in fuel‐air explosives and pulse detonation engines. Based on computational fluid dynamics, the effects of ignition position, initial pressure, and mass concentration on the explosion characteristics of the PO/air mixture were studied by using a 20 L spherical container. The results showed that the ignition position had a significant effect on the flame structure. When the fuel cloud was ignited at the center, the flame structure experienced spherical, elliptical, and tulip shapes. The explosion time first decreased and then increased with the increase of ignition position, while the maximum explosion pressure decreased correspondingly. The maximum explosion pressure and the temperature had an inverted “U” correlation with concentration at normal pressure. However, the overpressure was insensitive to concentration in the negative pressure condition. The maximum flame temperature showed different flame behaviors under different initial negative pressures and cloud concentrations. This study provides a theoretical basis for understanding the explosion behaviors of PO/air mixture with different ignition positions and initial vacuum pressures, which is of great significance in preventing explosion accidents.

Effect of Pressure on the Distribution of Electrons in a Cluster of H2S.

We carry out a theoretical study of the effect of pressure on the atomic and electronic distribution of a cluster made of 155 H2S molecules. The pressure was modeled by bringing the cluster into a spherical container made of 500 helium atoms and reducing the diameter of the container. We did ab initio molecular calculations using DFT. At the lowest pressure, the S-H-S angle between two neighboring H2S molecules has a distribution with a mean value of 167.1°. This angle will be shorter as pressure increases, reaching a distribution with a mean value of 125.5° at the highest pressure. Changes in this angle result from a strong S-S interaction, displacing the H atoms from the line joining the sulfur atoms. This rearrangement of the atomic distribution generates hydrogen-rich spatial regions. We analyzed the evolution of Mulliken charges on S and H atoms in the cluster with pressure, finding that electrons move from S to H atoms, suggesting that these hydrogen-rich regions should be responsible for the electrical conductivity and, consequently, also for the superconductivity in solid H2S under pressure.

Explosion behaviors of vapor–liquid propylene oxide/air mixture under high-temperature source ignition

Propylene oxide (PO) is widely used in fuel–air explosive (FAE) and pulse detonation engines (PDE). The explosion process of PO/air mixture in a 20 L spherical container under high-temperature source ignition was studied through experiment and numerical simulation. A good agreement was observed between the experimental and simulation results. The ignition temperature (1100–2500 K) and initial droplet size (10–200 μm) had no obvious effect on the maximum explosion pressure (Pmax) at a nominal concentration of 130 g/m3. Explosion time (te) and reaction time (tr) of PO aerosol explosion increased with the increase in initial droplet size. The flame propagation process in the direction of 90° was not the same as that of 45°. Explosion flame propagated from the center to the surrounding area, then sagged along wall facing the center and presented a U-shape. Explosion time at ignition temperature of 1600 K was 29.63 ms, which was the shortest compared with the temperature of 2000 K, 2500 K, and 1100 K. The influence of ignition temperature on te was more obvious than that of initial droplet size. The flame propagation mechanism of droplet sizes of 10 μm and 50 μm was different from that of 100 μm and 200 μm. The time to reach the maximum flame temperature(tf) increased with the increase in droplet size; the flame propagation speed decreased with the increasing droplet size, and the maximum flame velocity can reach 6.07 m/s.

Theory of sphere motions in viscous fluids including elasticity and compressibility

We study the motions of an elastic sphere and a compressible fluid sphere suspended in a compressible fluid. To this end, we use a scheme of a vector representation for the velocity in hydrodynamics and for the displacement in elasticity. First, we calculate the steady-state elastic displacement of a solid sphere under a gravity and a surface-tension gradient. Second, we examine the finite-size effects in a spherical container and find bulk acoustic resonance induced by an oscillating solid sphere. Third, applying periodic forces, we calculate the displacement, the velocity field, and the frequency-dependent friction constant for an elastic sphere and a compressible fluid sphere. We find complex acoustic effects sensitively depending on the frequency.

Improved theory of the elastic-plastic response of spherical containment vessels subjected to internal blast loading and its application

Baker built the displacement equations of motion for a thin spherical shell to spherically symmetric internal blast loading, and further provided the analytical solution of the elastic-plastic response under a triangular decaying pressure, neglecting shell thinning and radius variation [1], which was widely used in the fields of analysis and design of explosion containment vessels. However, it appears that some improvements and corrections are needed when we revisit this classic problem. In this paper, the elastic-plastic response of thin spherical shells is investigated mathematically. The complete equations of motion for three models are developed. Then the main ideas of the analytical and numerical methods are presented, as well as some important procedures and results by using Laplace transform techniques, which are convenient to use and generalize. Three typical examples are solved to exhibit differences between our improved theory and Baker’s [1]. Furthermore, our models are employed to gain some insights into response regularities, including the effect of various degrees of strain-hardening on maximum displacements under impulsive loading, and the effect of loading duration on the shell displacement for a perfectly plastic material.

Experimental performance of a finned spherical container in cold thermal storage for tropical buildings.

The heating and cooling of buildings consume almost 40% of global energy consumption. Cooling building spaces require more input energy compared to heating in tropical buildings. The power tariff varies according to the base and peak demands. This research mainly minimizes peak electricity demand by operating cold thermal storage using deionized water as a phase change material (PCM). The experimental work investigates the partial charging of deionized water in an internally finned stainless steel spherical container immersed in a constant temperature bath. Encapsulated PCM is tested with constant bath temperatures of - 6 ℃, - 9 ℃, and - 12 ℃. Radial copper fins with a diameter of 3mm are attached inside the container. The selected fin lengths are 7.5mm, 13.5mm, and 19.5mm. The fin length of 13.5mm is significantly reducing the freezing period. An effective reduction in the charging duration of 52% is observed at - 6 ℃ bath temperature. Partial charging is recommended by incorporating twice the amount of PCM in the design stage and utilizing 50% freezing during operation to achieve up to 52% energy savings. Therefore, the current findings help design effective cold storage for large-scale air-conditioning in buildings.

Математичні моделі та алгоритми оптимальної упаковки куль та кубів у сферичний та кубічний контейнери

Розглянуто математичні моделі та алгоритми оптимальної збалансованоїрозрідженої упаковки куль та кубів у сферичний та кубічний контейнери.Збалансованою розрідженою (задаються допустимі відстані між обʼєктами)упаковкою об’єктів у зовнішній контейнер є така їх упаковка, коли центрваги сімейства об’єктів збігається з центром зовнішнього контейнера, авідстані між об’єктами та відстані від них до зовнішнього контейнера булине менші за наперед задані величини. Наведено математичні моделі, послідовні та паралельні алгоритми розв’язання задач знаходження збалансованої розрідженої упаковки куль різних радіусів у сферичний та кубічнийконтейнери. Наведено математичну модель задачі знаходження збалансованої розрідженої упаковки кубів у куб мінімального обʼєму за умови, щосторони всіх кубів паралельні осям координат, та опис негладкої штрафноїфункції для пошуку локальних мінімумів задачі. Досліджувані задачівідносяться до класу NP-важких задач. Математичні моделі представленібагатоекстремальними задачами нелінійного програмування. Для пошукунайкращого допустимого розвʼязку застосовується метод мультистарту усполученні з r-алгоритмом Шора. Для цього задача зводиться до задачібезумовної оптимізації за допомогою штрафних функцій у вигляді функціймаксимуму, а для пошуку локальних мінімумів із набору стартових точокзастосовуються методи мінімізації негладких функцій, що базуються навикористанні програмних реалізацій r-алгоритму. Математичні моделі тапослідовні і паралельні алгоритми, що розглядаються, можна використатидля розробки програмних засобів розв’язування задач знаходження збалансованої розрідженої упаковки сферичних та кубічних обʼєктів у сферичніта кубічні контейнери. Матеріал представлено в трьох розділах. У розд. 1 наведено математичну модель та алгоритми розв’язання задачі знаходження збалансованої розрідженої упаковки куль різних радіусів у сферичнийконтейнер. Описано послідовний та паралельний алгоритми знаходженнянайкращого допустимого розв’язку задач. У розд. 2 наведено математичну модель та алгоритми розв’язання задачі знаходження збалансованої розрідженоїупаковки куль різних радіусів у кубічний контейнер. Описано послідовний тапаралельний алгоритми знаходження найкращого допустимого розв’язкузадач. У розд. 3 наведено математичну модель задачі знаходження збалансованої розрідженої упаковки кубів у кубічний контейнер. Наведено описнегладкої штрафної функції для пошуку локальних мінімумів задачі.

Investigating the Use of C/SiC Ceramic Composites in an Innovative Light-Water Reactor Core Grouping Catcher

China Nuclear Power Engineering, Northwestern Polytechnical University, and Beijing Institute of Technology have undertaken a joint research work with the goal of developing corium retention containers for use in an innovative light-water reactor core grouping catcher (CGC). In Serious Accidents (SAs), the corium will be retained in the C/SiC ceramic composite spherical shell container and thrown into the pool for passive cooling. In order to investigate the capability of the C/SiC ceramic composites to withstand the high temperature of 1800°C and the huge thermal shock at the initial stage of cooling, in this work, the high-temperature performance of these composites is studied. Furthermore, the compatibility of these composites with corium is investigated, and a retention container design prototype is proposed. The thermal conductivity, thermal expansion coefficient, high-temperature tensile strength, and thermal shock resistance of the candidate C/SiC specimens to be used in the manufacturing of the detention container are measured. The FactSage software package is used for the chemical compatibility study and product composition analysis of the composite SiC deposition layer and corium. The corrosion process of the SiC deposition layer of the composite material caused by corium is investigated through high-temperature corrosion tests and the electron microscopy analysis of the SiC specimen with the incorporation of CeO2. The results show that the C/SiC ceramic composite can meet the design criteria of the CGC corium retention container, and it is impossible to cause a carbon reaction disaster through the failure of the composite SiC deposition layer.

DEVELOPMENT OF MODELS OF POLYHEDRON CONTAINERS FOR DELIVERY OF FIRE-EXTINGUISHING SUBSTANCES

Geometric models of containers for the delivery of extinguishing agents to a fire zone located at a considerable distance are proposed. The transportation technology is based on a mechanical throwing operation. For this, a substance (for example, a fire extinguishing powder) is placed in a hard shell - a special container. After delivery to the fire site, the container must collapse and release a substance that will assist in extinguishing the fire. The existing method of remote delivery uses a container that is in the shape of a cylinder. In this case, a pneumatic gun is used as a launch pad. The difficulty lies in the fact that in order to ensure stability of motion during the flight, the cylinder must rotate around its axis. The starting impulse to such rotation when the barrel passes through the muzzle of the air gun is provided by compressed air flows that are difficult to commute.
 Therefore, it becomes necessary to develop new methods for the remote delivery of fire extinguishing agents to the fire zone by applying other principles of throwing. Among such methods, attention is drawn to the use of trebuchet mechanisms and impulse installations. In the case of using trebuchet mechanisms for containers, shapes close to spherical are chosen. For impulse installations (with squibs), it is advisable to use containers consisting of two spherical containers connected by a rod (like a sports dumbbell). In this case, the initiation of the rotational-translational movement of the dumbbell in the vertical plane is carried out due to the action of explosive impulses directed at each of its loads in a pre-calculated manner.
 For practical application of trebuchet mechanisms or impulse installations, it is necessary to develop container shell designs. To do this, you need to combine solutions to several problems with conflicting requirements. First, the construction of the dumbbell must be strong and withstand the starting forces and stresses of the flight phase. Secondly, the structure must ensure its instant destruction after delivery to the fire zone. And, thirdly, the design of the dumbbell should provide a convenient technology for filling containers with fire extinguishing agents. It is proposed to solve this problem using polyhedral bodies.

Influence of functionalized graphene nanoplatelets on the phase transition performance of DI water-based NEPCMs for cool thermal storage systems

ABSTRACT This research paper describes the experimental investigation of the phase change characteristics of deionized (DI) water with the addition of functionalized graphene nanoplatelets (FGNP) in a spherical container used in cool thermal energy storage (CTES) systems. The nano-enhanced phase change materials (NEPCMs) are developed by the dissolution of FGNP in the mass concentrations of 0.25%, 0.50%, and 0.75% with DI water. The thermal conductivity (TC) and phase change enthalpy (H) of the NEPCMs were measured experimentally using the transient hot-wire method and DSC 214 polymer, respectively. At heat transfer fluid (HTF) temperatures of −10°C and 15°C, the mass fraction of 0.75 improves thermal conductivity by 48.2% and 33.2% in the solid and liquid phases, respectively. At a heating rate of 1K min-1, the addition of FGNP significantly reduces the H of the base PCM in both crystallization and melting processes. The maximum reduction in crystallization and melting time was recorded to be 32.4% and 52.4% in a spherical container with the addition of maximum concentration of FGNP at the HTF temperatures of −8°C and 25°C, respectively.

Comparative study of heat transfer enhancement in a latent heat thermal energy storage system using mild steel and stainless steel spherical PCM containers

Thermal energy storage (TES) systems that employ latent heat storage materials have recently received more consideration because of their large heat storage volume and isothermal characteristics during heat storage and heat discharge. The phase change material (PCM) in the LHTES system accumulates large amounts of energy to a slight temperature extent by altering its phase. However, the low thermal conductivity of PCM is a major issue while using it in the LHTES system. Solid metal fins are used in PCM containers to surge the heat transfer rate and decrease the melting time. In this study, the experiments were performed under experimental conditions controlled using different mass flow rates of 2 L/min, 4 L/min, 6 L/min, and the heat transfer fluid (HTF) inlet temperature for the storage process is 70 ℃. The characteristics of the LHTES system are analyzed to accumulate the thermal energy in the spherical PCM container with and without solid internal fins. In this study, the granulated paraffin wax with a melting temperature of 61 ℃ was used as PCM. The water is used as the HTF to transfer the thermal energy from the source to the TES tank. The changes in temperature differences have been experimented with different HTF flow rates with all configurations of PCM containers to examine the temperature distribution. While increasing the flow rate between 2 and 6 L/min, we note that loading time is decreased by 38.46 % and 37.50 % for the case of stainless steel with fins and without fins spherical containers. The charging time is fallen by 36.36 % and 35.71 % while increasing the flow rate between 2 and 6 L/min for the case of mild steel with fins and without fins spherical containers. The cumulative heat stored is higher for fin configuration than no fin configuration spherical PCM containers.

Simple bladeless mixer with liquid–gas interface

A constantly rotating spherical container sustains turbulence of a fluid partially filling it. This simple turbulence generator has the potential for wide engineering applications as a bladeless mixer. Using the coupled level-set and volume of fluid method and the boundary data immersion method, we conduct direct numerical simulations of liquid–gas flow in a spherical container rotating about a horizontal axis to investigate the driving mechanism of turbulence, flow dependence on the filling rate $\varPsi$ and the mixing ability of the sustained turbulence. Even if the Froude number $Fr$ is small enough ( $Fr\lesssim 10^{-3}$ ) for the liquid–gas interface to be undeformed, if the Reynolds number $Re$ is large enough ( $Re\gtrsim 10^3$ ), small-scale turbulent eddies are sustained by being stretched in shear flow around a counter-rotating pair of container-size vortices, whose swirling directions depend on $\varPsi$ . We clarify that the angle of flow near the solid wall colliding with the interface controls the swirling direction of these container-size vortices. Furthermore, we track fluid particles in the liquid phase to quantify mixing properties to show that almost perfect mixing occurs after approximately 10 spins of the container for lower $\varPsi$ ( $\lesssim 0.5$ ), whereas the mixing requires less energy consumption for higher $\varPsi$ ( $\gtrsim 0.7$ ) at the examined $Re=O(10^3)$ .

Biomolecular Binding under Confinement: Statistical Predictions of Steric Influence in Absence of Long-Distance Interactions.

We propose a theoretical model for the influence of confinement on biomolecular binding at the single-molecule scale at equilibrium, based on the change of the number of microstates (localization and orientation) upon reaction. Three cases are discussed: DNA sequences shorter and longer than the single strain DNA Kuhn length and spherical proteins, confined into a spherical container (liposome, droplet, etc.). The influence of confinement is found to be highly dependent on the molecular structure and significant for large molecules (relative to container size).

The effect of surfactant on the drag and wall correction factor of a drop in a bounded medium

Abstract In the present article, the analytical solution for creeping motion of a drop/bubble characterized by insoluble surfactant is examined at the instant it passes the center of a spherical container filled with Newtonian fluid at low Reynolds number. The presence of surfactant characterizes the interfacial region by an axisymmetric interfacial tension gradient and coefficient of surface dilatational viscosity. Under the assumption of the small capillary number, the deformation of spherical phase interface is not taken into account. The computations not only yield information on drag force and wall correction factor, but also on interfacial velocity and flow field for different values of surface tension gradient and surface dilatational viscosity. In the limiting cases, the analytical solutions describing the drag force and wall correction factor for a drop in a bounded medium reduces to expressions previously stated by other authors in literature. The results reveal the strong influence of the surface dilatational viscosity and surface tension gradient on the motion of drop/bubble. Increasing the surface tension gradient and surface dilatational viscosity, results in linear variation of drag force. When the surface tension gradient increases, the drag force for unbounded medium increases more as compared to the bounded medium hence wall correction factor decreases with increase in surface tension gradient whereas it increases with increase in surface dilatational viscosity.

Effect of electrostatic interactions on particle dispersion in a rotating spherical container

Triboelectric charging and electrostatic interactions are commonly encountered in many powder handling processes. In this paper, the electrostatic behaviours of particles in a rotating spherical container were examined, in particular, the electrostatic dispersion of particles was recorded with a camera and then quantitatively analysed. The effects of the Coulomb's repulsive force and the attractive image force on the degree of particle dispersion, the motion of individual particles, formation and geometrical shape of particle clusters were analysed. The results show that the degree of particle dispersion increases with the charging time until it achieves a saturation value. The particle cluster formation undergoes five distinctive regimes and is governed by the external forces from the container wall, while the collective effect of both the extra-particle force and the Coulomb's repulsive force determines the evolution of the cluster shape.

Applying Bayesian Markov chain Monte Carlo (MCMC) modeling to predict the melting behavior of phase change materials

A key practical application of PCM-based spherical containers is in packed bed thermal energy storage (TES) devices utilized for air conditioning in large buildings. Proposing high-precision models for the melting characteristics in spherical containers can provide deep insights into the design of TES systems. Herein, a methodology based on Bayesian inference was adopted to provide reliable models that predict the melting rate (f) and surface-averaged Nusselt number (Nu) as two significant factors in PCM melting process in spherical heat storage units. Five proposed models for f and Nu prediction were applied to available datasets. The input of Bayesian-based predictive models included three important dimensionless parameters of the melting problem, namely Ste, Gr, and Fo. Ste (Stefan number) describes the driving force of melting, Gr (Grashof number) reflects the natural convection intensity, and Fo (Fourier number) represents the dimensionless time. For accurate inference of model parameters using the Bayesian Markov chain Monte Carlo (MCMC) technique, an analysis was performed by coding in the WinBUGS language. Several statistical performance criteria (R2, RMSE, and MSE) were utilized to evaluate the efficiency of Bayesian-based predictive models. The results showed that model #4 recorded R2 = 0.980 in the prediction of melting rate. Furthermore, model #5 with R2 = 0.966, had the best performance in predicting the values of surface-averaged Nusselt number. The models recommended in this research yield superior results compared to the previous study, which suggested R2 = 0.975 and R2 = 0. 925 for f and Nu, respectively.

Solidification characteristics in a spherical capsule integrated with pin fins and rectangular fins - a comparative study

This study aims at investigating the solidification characteristics in a spherical capsule with pin fins and rectangular fins of same length and volume immersed in a constant temperature bath (-6°C, -9°C, -12°C). The fins are made of copper and are attached to the inner surface of the spherical capsule. The fin lengths correspond to the annulus fill volume margin of 75% taken on the inside wall of the spherical container. The findings showed that the overall solidification period of the capsules with rectangular fins was reduced. Also, the subcooling phenomena is completely eliminated at bath temperature of -6°C. Results also indicated that 50% PCM mass is reduced effectively with the provision of fins. Thus, with the employment of rectangular fins better potential energy savings can be attained when operated at partial charging mode at higher bath temperature.

Nonadiabatic localization of H2 in the field of two external positive tip charges

For two external spherical tips with equal positive charges, the ground state of a hydrogen molecule is variationally determined within the quantum Monte Carlo scheme. For finiteness, the system is enclosed in a spherical container with randomly reflecting unstructured walls. The 12-dimensional system of two protons and two electrons is investigated ab initio without any adiabatic restrictions. We focus on the hydrogen center of mass (COM) distribution in continuation of previous work on ground state and vibration modes at a COM that was fixed in space. Our general purpose is to control the molecule’s position and orientation by external means, such as by two charged tips. To this end, knowledge is needed in order to find specific COM regions with a desired molecular orientation in the container at significant probability density of the molecule.

Effect of insoluble surfactants on the motion of Reiner–Rivlin fluid sphere in a spherical container with Newtonian fluid

Effect of insoluble surfactants on the motion of Reiner–Rivlin fluid sphere in a spherical container with Newtonian fluid