Propagation of nonlinear waves in a fluidized bed in the presence of interaction between the particles of the dispersed phase

A model of a fluidized bed as a medium consisting of two interacting interpenetrating ideal fluids is used to investigate the propagation of one-dimensional linear and nonlinear perturbations of the particle concentration in a gas-fluidized bed. The interaction of the particles with each other is taken into account by introducing into the momentum conservation equation for the dispersed phase an effective pressure that depends on the local porosity of the bed and the relative velocity of the dispersed and dispersion phases. The conditions of hyperbolicity of the system of equations describing wave propagation are determined. The stability of the uniform state is investigated. Dispersion effects in the fluidized bed are considered. The propagation of a steady dispersed-phase concentration wave is investigated. The conditions of formation of concentration discontinuities at the steady wave front are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–89, March–April, 1987.     

The propagation of nonlinear waves in a bidisperse fluidized bed

A study is made of the propagation of nonlinear kinematic waves of concentrations of solid particles in a fluidized bed of particles of two different sizes. A hyperbolic system of quasilinear equations is obtained which describes the propagation of the waves. A dependence of the characteristic velocities on the concentrations of the phases and the ratio of the sizes of the particles is found. The influence of an admixture of fine particles on the propagation of porosity waves in the fluidized bed is analyzed. The nature of the formation of jumps in the porosity depending on the concentration of the admixture is studied, as is the process of the transfer of the admixture of fine particles in the bed. The nature of the propagation of nonlinear waves in a fluidized bed of identical particles is clarified. A characteristic velocity is found and conditions are determined for the formation of discontinuities of concentration of the dispserse phase in rarefaction compression waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–58, January–February, 1985.     

Motion of inhomogeneities of a developed fluidized bed at small reynolds numbers

The instability of a fluidized system in which the particles are uniformly distributed in space [1–3] leads to the development of local inhomogeneities in the internal structure, these taking the form of more or less stable formations of packets of particles [4]. In accordance with the existing ideas based on experimental data [5–8, 13], the particle concentration within a packet may vary in a wide range from very small values (10^–2–10^–3 [8]) for bubbles to the concentration of the unfluidized bed for bunches of particles in a nearly closely packed state. The paper considers the steady disturbed motion of the fluid and solid phases near an ascending or descending packet of particles in a developed fluidized bed. It is assumed that the motion of the solid phase corresponds to a creeping flow of viscous fluid, and the viscosity of the fluidizing agent is taken into account only in the terms that describe the interphase interaction. The velocity fields and pressure distributions of the phases inside and outside a packet are determined. If the particle concentration within a packet tends to zero, the solution describes the slow motion of a bubble in a fluidized bed. The results of the paper are compared with results obtained earlier for the model of ideal fluids [9] and Batchelor's model [10], in which the fluidized bed is treated in a simplified form as a viscous quasihomogeneous continuum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–65, July–August, 1984.     

Propagation of disturbances in a two-phase magnetic particle dispersion

The propagation of one-dimensional vertical perturbations of the magnetic particle concentration in a liquid-particle or gas-particle disperse medium in an external uniform magnetic field, oriented parallel or antiparallel to the force of gravity, is considered. The propagation of linear disturbances is analyzed. Linear stability criteria for layers of magnetized particles fluidized with a gas or liquid are found. The propagation of nonlinear long (kinematic) concentration waves in a medium containing dispersed magnetized particles is investigated. It is shown that in the kinematic wave approximation the propagation of the nonlinear concentration perturbations can be described by the Burgers equation. The formation of regions with a sharp change in concentration (shock fronts) is analyzed. The structure of the shock front, in particular its width, is found. It is shown that a magnetic field leads to broadening of the shock front, thus preventing the formation of concentration discontinuities and hence leading to the smearing of the boundaries of the inhomogeneities formed in the fluidized bed. This provides a basis for a qualitative explanation of the stabilization of developed nonuniform fluidized beds of magnetic particles in a magnetic field.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 76–83, July–August, 1992.     

Steady concentration waves and dispersion effects in a gas-particle two-phase medium with weak particle interaction

The model of a concentrated two-phase medium constructed in [1–3] with allowance for the random small-scale motion of the dispersed phase due to particle interaction is used for analyzing steady particle concentration waves and dispersion effects in the case of negligibly small rates of generation and dissipation of the energy of small-scale motion. The propagation of one-dimensional disturbances in a direction parallel or antiparallel to the force of gravity is investigated. The structure of the steady wave front is found and the conditions of formation of internal concentration discontinuities at the front are determined. Dispersion effects are investigated for weakly nonlinear waves. The results can be used for analyzing wave phenomena in a gas-fluidized bed, a falling bed, pneumatic transport and fast fluidization systems, etc. The model proposed in [1–3] was developed in [4] in order to investigate steady waves and dispersion effects at high rates of generation and dissipation of the energy of small-scale motion of the dispersed phase and in [5] in order to analyze the propagation of particle concentration discontinuities for finite rates of generation and dissipation of the energy of random motion and linear stability in the presence of weak particle interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–48, January–February, 1990.     

A solids mixing rate correlation for small scale fluidized beds

A new first degree solids mixing rate is proposed to evaluate the mixing of solids in small scale fluidized beds. Particle mixing experiments were carried out in a 2D fluidized bed with a cross-section of 0.02 m × 0.2 m and a height of 1 m. White and black particles with average diameters of 850 and 450 μm were used in our experiments. Image processing was used to measure the concentration of the tracers at different times. The effects of four representative operating parameters (superficial gas velocity, ratio of tracer particles to bed particles, tracer particle position, and particle size) on mixing are discussed with reference to the mixing index. We found that the Lacey index depends on the concentration of the tracers. The position of the tracers affects the initial mixing rate but not the final degree of mixing. However, the new mixing rate equation does not depend on the initial configuration of the particles because this situation is considered to be the initial condition. Using the data obtained in this work and that found in literature, an empirical correlation is proposed to evaluate the mixing rate constant as a function of dimensionless numbers (Archimedes, Reynolds, and Froude) in small scale fluidized beds. This correlation allows for an estimation of the mixing rate under different operating conditions and for the detection of the end point and/or the time of mixing.     

Experimental and computational studies on flow behavior of gas–solid fluidized bed with disparately sized binary particles

This paper presents experimental and computational studies on the flow behavior of a gas-solid fluidized bed with disparately sized binary particle mixtures. The mixing/segregation behavior and segregation efficiency of the small and large particles are investigated experimentally. Particle composition and operating conditions that influence the fluidization behavior of mixing/segregation are examined. Based on the granular kinetics theory, a multi-fluid CFD model has been developed and verified against the experimental results. The simulation results are in reasonable agreement with experimental data. The results showed that the smaller particles are found near the bed surface while the larger particles tend to settle down to the bed bottom in turbulent fluidized bed. However, complete segregation of the binary particles does not occur in the gas velocity range of 0.695-0.904 m/s. Segregation efficiency increases with increasing gas velocity and mean residence time of the binary particles, but decreases with increasing the small particle concentration. The calculated results also show that the small particles move downward in the wall region and upward in the core. Due to the effect of large particles on the movement of small particles, the small particles present a more turbulent velocity profile in the dense phase than that in the dilute phase.     

An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles. Typical particles are selected representing three kinds of particle motion： a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom de-fluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.     

Heat transfer and hydrodynamic studies on two- and three-phase fluidized beds of floating bubble breakers

Heat transfer characteristics in three-phase fluidized beds of floating bubble breakers have been studied in a 0.142 m I.D. x 2.0 m high Plexiglas column fitted with an axially mounted cylindrical heater.Effects of the liquid and gas velocities, the particle size, the volume ratio of floating bubble breaker to particles on phase holdup, the vertical bubble length, and the heat transfer coefficient have been determined.In the bubble-coalescing regime, the heat transfer coefficient in three-phase fluidized beds having the volume ratio V_f/V_s of 10–15% produced a maximum increase in heat transfer coefficient of about 20% in comparison to that in the bed without floating bubble breakers. Also, bubble length and gas-phase holdups exhibited their maximum and minimum values at a volume ratio of 10–15%. The heat transfer coefficient in three-phase fluidized beds of floating bubble breakers can be estimated from the surface renewal model with isotropic turbulence theory.Heat transfer coefficients expressed in terms of the Nusselt number have been correlated with the particle Reynolds number and the volume ratio of floating bubble breakers to particles.     

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system b...     

Interaction of local inhomogeneities of a fluidized bed

In connection with an analysis of transport processes in fluidized beds a study is made of the steady motion of a system of local inhomogeneities of the bed porosity, which are modeled by packets of particles. The interaction of the inhomogeneities is taken into account on the basis of a cell model. The velocity fields and the pressure distributions of the solid and gas phases together with the rising and sinking velocities of the system of packets are determined in the approximation of a double continuum. The flow regimes of the fluidizing agent are investigated. It is shown that with increasing concentration of packets in the bed the velocity of their motion decreases, and the circulation region of the dispersion medium surrounding a packet or trapped within it contracts. The dependence of the rate of flow of the fluidizing agent through the transverse section of the reactor on the concentration of packets in the bed is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–49, January–February, 1991.     

Parallelization of pseudo-particle modeling and its application in simulating gas–solid fluidization

Pseudo-Particle Modeling (PPM) is a particle method proposed by Ge and Li in 1996 [Ge, W., & Li, J. (1996). Pseudo-particle approach to hydrodynamics of particle–fluid systems. In M. Kwauk & J. Li (Eds.), Proceedings of the 5th international conference on circulating fluidized bed (pp. 260–265). Beijing: Science Press] and has been used to explore the microscopic mechanism in complex particle–fluid systems. But as a particle method, high computational cost remains a main obstacle for its large-scale application; therefore, parallel implementation of this method is highly desirable. Parallelization of two-dimensional PPM was carried out by spatial decomposition in this paper. The time costs of the major functions in the program were analyzed and the program was then optimized for higher efficiency by dynamic load balancing and resetting of particle arrays. Finally, simulation on a gas–solid fluidized bed with 102,400 solid particles and 1.8 × 10⁷ pseudo-particles was performed successfully with this code, indicating its scalability in future applications.     

图像技术在非均匀布风流化床颗粒运动分析中的应用

通过实验得到了非均匀布风流化床内示踪颗粒在床层内的运动历程,以及床层内颗粒的浓度分布随时间的变化,并发纳得到颗料在非均匀布风的内旋流流化床中不同区域的扩散系数,内旋流流化床颗粒的纵向扩散系数和横向扩散系数大小相近,横向扩散系数明显大于均匀布风的鼓泡床的横向扩散系数,具有较好的横向扩散特性,有利于使流化床内横向不均匀的状况得到改善。     

Thermomechanical oscillations of a fluidized bed

Within the framework of the simplest one-dimensional model of a fluidized bed as a medium consisting of two interpenetrating interacting fluids, it is shown in the paper that linear thermomechanical oscillations can occur if the gas viscosity depends on the temperature and a nonisothermic chemical reaction takes place in the fluidized bed. The conditions under which oscillations occur and their frequencies are determined and their dependence on the fluidization parameters, the heat loss (or supply) rate, the rate and heat of the reaction, and quantities characterizing the dependence of the gas viscosity on the temperature and the force of the interphase interaction on the concentration of the solid particles is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 75–80, September–October, 1984.     

Experimental analysis of volatile liquid injection into a fluidized bed

Experiments were conducted on a lab-scale fluidized bed to study the distribution of liquid ethanol injected into fluidized catalyst particles. Electrical capacitance measurements were used to study the liquid distribution inside the bed, and a new method was developed to determine the liquid content inside fluidized beds of fluid catalytic cracking particles. The results shed light on the complex liquid injection region and reveal the strong effect of superficial gas velocity on liquid distribution inside the fluidized bed, which is also affected by the imbibition of liquid inside particle pores. Particle internal porosity was found to play a major role when the changing mass of liquid in the bed was monitored. The results also showed that the duration of liquid injection affected liquid–solid contact inside the bed and that liquid–solid mixing was not homogeneous during the limited liquid injection time.     

Euler–Lagrange/DEM simulation of wood gasification in a bubbling fluidized bed reactor

We present an Euler–Lagrange method for the simulation of wood gasification in a bubbling fluidized bed. The gas phase is modeled as a continuum using the 2D Navier–Stokes equations and the solid phase is modeled by a Discrete Element Method (DEM) using a soft-sphere approach for the particle collision dynamic. Turbulence is included via a Large-Eddy approach using the Smagorinsky sub-grid model. The model takes into account detailed gas phase chemistry, zero-dimensional modeling of the pyrolysis and gasification of each individual particle, particle shrinkage, and heat and mass transfer between the gas phase and the particulate phase. We investigate the influence of wood feeding rate and compare exhaust gas compositions and temperature results obtained with the model against experimental data of a laboratory scale bubbling fluidized bed reactor.     

Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles

This paper examines the suitability of various drag models for predicting the hydrodynamics of the turbulent fluidization of FCC particles on the Fluent V6.2 platform. The drag models included those of Syamlal–O’Brien, Gidaspow, modified Syamlal–O’Brien, and McKeen. Comparison between experimental data and simulated results showed that the Syamlal–O’Brien, Gidaspow, and modified Syamlal–O’Brien drag models highly overestimated gas–solid momentum exchange and could not predict the formation of dense phase in the fluidized bed, while the McKeen drag model could not capture the dilute characteristics due to underestimation of drag force. The standard Gidaspow drag model was then modified by adopting the effective particle cluster diameter to account for particle clusters, which was, however, proved inapplicable for FCC particle turbulent fluidization. A four-zone drag model (dense phase, sub-dense phase, sub-dilute phase and dilute phase) was finally proposed to calculate the gas–solid exchange coefficient in the turbulent fluidization of FCC particles, and was validated by satisfactory agreement between prediction and experiment.     

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.     

Experiments on the local heat transfer characteristics of a circulating fluidized bed

The role of particle diameter in the heat transfer of a gas–solid suspension to the walls of a circulating fluidized bed was studied for particles of uniform size. This work reports and analyzes new experimental results for the local bed to wall heat transfer coefficient, not including the radiation component, in a long active heat transfer surface length laboratory bed, which extend previous findings and clear up some divergences. The research included determining the effects of extension and location of the heat transfer surface, circulating solids mass flux and average suspension density. An experimental set-up was built, with a 72.5 mm internal diameter riser, 6.0 m high, composed of six double pipe heat exchangers, 0.93 m high, located one above the other. Five narrow sized diameter quartz sand particles − 179, 230, 385, 460 and 545 μm − were tested. Temperature was kept approximately constant at 423 K and the superficial gas velocity at 10.5 m/s. The major influence of suspension density on the wall heat transfer was confirmed, and contrary to other authors, a significant effect of particle size was found, which becomes more relevant for smaller particles and increasing suspension density. It was observed that the extension of the heat transfer surface area did not influence the heat transfer coefficient for lengths greater than 0.93 m.The heat transfer surface location did not show any effect, except for the exchanger at the botton of the riser. A simple correlation was proposed to calculate the heat transfer coefficient as a function of particle diameter and suspension density.     

Boiling model for a fluidized bed of particles

A mechanism for boiling of a fluidized bed was examined in [1]. Due to hydrodynamic instability the solid particles acquire random motion, and as a result of collisions between particles part of the energy of random motion is converted to rotation of the particles. A rotating particle experiences a Magnus force which considerably increases the random motion and leads to spontaneous boiling of the layer. For this mechanism there is typically a minimum boiling time , defined basically as the time to develop a hydrodynamic instability. It is shown in this study that besides the spontaneous mechanism there is an induced mechanism for boiling of the bed arising from the generation of random motion in one particle layer. Particles in that layer boil, transmitting a perturbation to the energy of the next layer, and leading to layer boiling in a manner analogous to the propagation of a detonation wave in solids.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 89–94, May–June, 1984.