Three-dimensional Simulation of Gas/Solid Flow in Spout-fluid Beds with Kinetic Theory of Granular Flow

A three-dimensional Eulerian multiphase model, with closure law according to the kinetic theory of granular flow, was used to study the gas/solid flow behaviors in spout-fluid beds. The influences of the coefficient of restitution due to non-ideal particle collisions on the simulated results were tested. It is demonstrated that the simulated result is strongly affected by the coefficient of restitution. Comparison of simulations with experiments in a small spout-fluid bed showed that an appropriate coefficient of restitution of 0.93 was necessary to simulate the flow characteristics in an underdesigned large size of spout-fluid bed coal gasifier with diameter of lm and height of 6m. The internal jet and gas/solid flow patterns at different operating conditions were obtained. The simulations show that an optimal gas/solid flow pattern for coal gasification is found when the spouting gas flow rate is equal to the fluidizing gas flow rate and the total of them is two and a half times the minimum fluidizing gas flow rate. Besides, the radial distributions of particle velocity and gas velocity show similar tendencies; the radial distributions of particle phase pressure due to particle collisions and the particle pseudo-temperature corresponding to the macroscopic kinetic energy of the random particle motion also show similar tendencies. These indicate that both gas drag force and particle collisions dominate the movement of particles.

Flow Behaviors of Gas-Solid Injector by 3D Simulation with Kinetic Theory of Granular Flow

A computational study on the flow behavior of a gas-solid injector by Eulerian approach was carried out. The gas phase was modeled with k-ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The simulations by Eulerian two-fluid model （TFM） were compared with the corresponding results by discrete element method （DEM） and experiments. It was showed that TFM simulated results were in reasonable agreement with the experimental and DEM simulated results. Based on TFM simulations, gas-solid flow pattern, gas velocity, particle velocity and the static pressure under different driving jet velocity, backpressure and convergent section angle were obtained. The results showed that the time average axial gas velocity sharply decreased and then slightly increased to a constant value in the horizontal conveying pipe. The time average axial particle velocity increased initially and then decreased, but in the outlet region of the convergent section the particle velocity remarkably increased once more to the maximal value. As a whole, the static pressure distribution change trends were found to be independent on driving gas velocity, backpressure and convergent section angle. However, the static pressure increased with increase of convergent section angle and gas jet velocities. The difference of static pressure to backpressure increased with increasing backpressure.

Kinetic theory of geodesic acoustic modes in toroidal plasmas:a brief review

Geodesic acoustic modes（GAM） are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave-particle interactions are discussed,with the application to resonant excitation by energetic particles（EPs）.The theory of EP-induced GAM（EGAM） is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.

Neoclassical Kinetic Theory for the Shaped Tokamaks

Neoclassical transport for the shaped tokamak with X point is investigated using Hamiltonian formalism. For a set of Soloveev's configurations, the neoclassical diffusion coefficient is rigorously derived for the plateau regime which is inversely proportional to the connection length. When an X point appears on plasma boundary, the diffusion coefficient is greatly reduced by a much longer connection length compared with a circular cross-section plasma. Since the formalism is not limited for aspect ratio, for A = 1.3, it may be valid in a very narrow range of collisionality, 0.8 < V*i < 1.0, at / o = 0.95. In the range of collisionality, the detrapping rate is very high.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.

SYNTHESIZING KINETICS AND MICRO-CHARACTERIZATION OF SPINEL LiMn_(2)O_(4) FOR LITHIUM-ION BATTERY CATHODE MATERIAL

The reaction process during synthesis of LiMn2O4 with LiOH&middotH2O and MnO2 was studied by means of DTA in dynamical air atmosphere, and it could be applied as an important theoretical principle for preparing LiMn2O4. The active energies of four reaction processes were obtained with Doyle-Ozawa method and Kissinger method as follows: 66.299, 72.640, 128.11 and 113.876 kJ&middotmol-1, respectively. Reaction orders, frequency factors and kinetic equations of each reaction were determined by Kissinger method. XRD, SEM and TEM show that the synthesized LiMn2O4 is a pure phase, with regular appearance and higher ratio-surface.

The Predictive Potential of the Kinetic Model of Aging of Living Systems in Demography

An original mathematical model,previously tested by the authors on other non-demographic objects,is proposed for describing and forecasting demographic systems—the population of the countries of the World using the examples of the USA,China and Russia,as well as the number of mice in the“mouse paradise”experiment of the American scientist John Calhoun.The proposed approach allows us to describe the stages and features of this dynamics:population growth in the USA,growth and possible decrease in the population in China,loss of a part of the population of the Russian Empire and the USSR due to two world wars and the collapse of the USSR,biological degradation of the“mouse paradise”up to its complete extinction.The use of the kinetic model of aging of various types of living systems to predict the development of the number of demographic systems is based on the assumptions that the aging and development processes are related to each other and have the same statistical regularity,reflecting the fractal principle of Nature-the unity of structure and function.The results obtained suggest that a person,a population of the World,humanity and other biological species develop and simultaneously age like each other under the conditions of the always existing syndrome of general adaptation(stress)and according to the same pattern corresponding to the mathematical model proposed here.

A kinetic description of the impact of agent competence and psychological factors on investment decision-making

The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agents set their own investment strategies.The herding behavior is considered when analyzing the impact of an agent's psychological factors on investment decision-making.A nonlinear Boltzmann model containing herding behavior,agent competence and irrational behavior is employed to investigate investment decision-making.To characterize the agent's irrational behavior,we utilize a value function which includes current and ideal-investment decisions to describe the agent's irrational behavior.Employing the asymptotic procedure,we obtain the Fokker-Planck equation from the Boltzmann equation.Numerical results and the stationary solution of the obtained Fokker-Planck equation illustrate how herding behavior,agent competence,psychological factors,and irrational behavior affect investment decision-making,i.e.,herding behavior has both advantages and disadvantages for investment decision-making,and the agent's competence to invest helps the agent to increase income and to reduce loss.

Physical Macrohardness of the Kinetic Indentation of the Material: Function and Universal Unit of Measure (Part 1)

Three directions of development of kinetic indentation methods.Physical-energetic analysis of the indentation force diagram according to ISO 14577.Physical theory and universal criterion for the macrohardness of a material.Model of the physical process,thermomechanical potential,function of the state of the kinetic macroindentation process.Method for determining the physical function and unit of measurement of the kinetic macrohardness of a material.The ratio of the values of the empirical(standard)and physical macrohardness of the material.Physical reason for the appearance of the size effect in empirical indentation methods.The principle of determining the standard value of physical macrohardness.

Structural build-up model for three-dimensional concrete printing based on kinetics theory

The thixotropic structural build-up is crucial in extrusion-based three-dimensional(3D)concrete printing.This paper uses a theoretical model to predict the evolution of static and dynamic yield stress for printed concrete.The model employs a structural kinetics framework to create a time-independent constitutive link between shear stress and shear rate.The model considers flocculation,deflocculation,and chemical hydration to anticipate structural buildability.The reversible and irreversible contributions that occur throughout the build-up,breakdown,and hydration are defined based on the proposed structural parameters.Additionally,detailed parametric studies are conducted to evaluate the impact of model parameters.It is revealed that the proposed model is in good agreement with the experimental results,and it effectively characterizes the structural build-up of 3D printable concrete.

Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters.

A wealth distribution model with a non-Maxwellian collision kernel

A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

Simulation of the Clustering Phenomenon in a Fast Fluidized Bed: The Importance of Drag Correlation

Drag force is a key parameter in the numerical modeling of gas-particle flow in circulating fluidized beds. The reliability of current drag force correlations over the regime of fast fluidization has, however, not been thoroughly investigated. In this article, a drag force correlation accounting for the clustering effects for Geldart A particles is used to simulate the behaviors typical of fast fluidization, including dynamic evolution of clusters as well as time- averaged axial and lateral voidage profiles. Diverse images of clusters are captured and the time-averaged profiles of voidage are shown to be in quantitative agreement with the present empirical correlation. The results based on different constitutive correlations of drag force show the importance of the choice of drag force in modeling fast-fluidized beds. This drag force correlation, based on a simple averaging assumption, could give some basic insights about the magnitude of the drag reduction.

Wave Breaking Phenomena of Irregular Waves Combined with Opposing Current

Experimental study and theoretical analysis show that the critical value of relative wave height (H / d)b given by Goda and the critical wave steepness (H / L)b given by Michell and Miche can be adopted as the spilling breaking indices of regular waves. According to the same principle, a systematic theoretical analysis and experiment of irregular wave have been done by the authors in order to solve the breaking problem of irregular waves. It is indicated that the authors' method for determining wave breaking of regular waves can also be used for irregular waves.

Moving contact line problem: Advances and perspectives

The solid-liquid interface, which is ubiquitous in nature and our daily life, plays fundamental roles in a variety of physical-chemical-biological- mechanical phenomena, for example in lubrication, crystal growth, and many biological reactions that govern the building of human body and the functioning of brain. A surge of interests in the moving contact line （MCL） problem, which is still going on today, can be traced back to 1970s primarily because of the exis- tence of the ＂Huh-Scriven paradox＂. This paper, mainly from a solid mechanics perspective, describes very briefly the multidisciplinary nature of the MCL problem, then summarizes some major advances in this exciting research area, and some future directions are presented.

Recent developments in chiral and spin polarization effects in heavy-ion collisions

We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions.We present updated experimental results for the chiral magnetic effect and related phenomena.The time evolution of the magnetic fields in different models is discussed.The newly developed quantum kinetic theory for massive fermions is reviewed.We present theoretical and experimental results for the polarization of K hyperons and the q00 value of vector mesons.

Pseudo-Fluid Simulation of Transient Behaviors in a CFB Riser

The kinetic theory of granular flow (KTGF) is modified to fit the Einstein′s equation for effective viscosity of dilute flow. A pseudo-fluid approach based on this modified KTGF is used to simulate the dynamic formation and dissipation of clusters in a circulating fluidized bed riser. The agglomeration of particles reduces slip velocity within particle clusters, and hence results in two reverse trends: discrete particles are lifted by air while particle clusters fall down along the wall. The dynamic equilibrium of these two types of motion leads to the characteristic sigmoid profile of solid concentration along the longitudinal direction. The predicted solid velocity, lateral and longitudinal profiles of solid volume fraction and annulus thickness are in reasonable agreement with experimental results.

Study on the solid-liquid suspension behavior in a tank stirred by the long-short blades impeller

We investigated the solid–liquid suspension characteristics in the tank with a liquid height/tank diameter ratio of 1.5 stirred by a novel long-short blades(LSB) impeller by the Euler granular flow model coupled with the standard k–ε turbulence model. After validation of the local solid holdup by experiments,numerical predictions have been successfully used to explain the influences of impeller rotating speed,particle density, particle size, liquid viscosity and initial solid loading on the solid suspension behavior,i.e. smaller particles with lower density are more likely to be suspended evenly in the liquid with higher liquid viscosity. At a low impeller rotating speed(N), increase in N leads to an obvious improvement in the solid distribution homogeneity. Moreover, the proposed LSB impeller has obvious advantages in the uniform distribution of the solid particles compared with single Rushton turbine(RT), dual RT impellers or CBY hydrofoil impeller under the same power consumption.

Calculation of Transport Properties of CF4＋Noble Gas Mixtures

The present work is concerned with determining the viscosity,diffusion,thermal diffusion factor and thermal conductivity of five equimolar binary gas mixtures including:CF4-He,CF4-Ne,CF4-Ar,CF4-Kr,CF4-Xe from the principle of corresponding states of viscosity by the inversion technique.The Lennard-Jones (12-6) model potential is used as the initial model potential.The calculated interaction potential energies obtained from the inversion procedure is employed to reproduce the viscosities,diffusions,thermal diffusion factors,and thermal conductivities.The accuracies of the calculated viscosity and diffusion coefficients were 1% and 4%,respectively.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.