Two-fluid hydrodynamics of a fluidized bed

Prior to the formulation of specific problems on the motion or processes of transport in a fluidized bed it is necessary to answer two fundamental questions, without the satisfactory resolution of which consistent theoretical study of the fluidized bed is quite impossible. The first question is related to the formulation of the governing equations-the equations of motion of the fluidized bed as a two-phase continuous medium-the second question is concerned with the construction of some model of the interaction of the fluidized bed with the solid surfaces bounding the bed and the consideration of the boundary conditions which must be imposed on the solution of these equations.The present study attempts to solve both of these problems. Equations are presented which describe the motion of the fluidized bed as a continuum with account for the relative slip of the phases, where one group of equations concerns the motion of a ficticious liquid porous medium consisting of particles and a liquid phase frozen in these particles, while the second group describes the filtration of a liquid phase in this porous medium. The influence of the solid walls on the motion of the fluidized bed is described with the aid of concepts on the existence near the walls of a region in which transport of momentum by the liquid phase takes place. The model developed is illustrated using the problem of flow past a solid sphere mounted in an unbounded fluidized bed. This problem also makes it possible to clarify certain unique qualitative features of the motion in a fluidized bed.The author wishes to thank Yu. S. Ryazantsev for helpful comment.     

Convective instability of a homogeneous fluidized bed

Convective motions of the phases in a homogeneous fluidized bed are considered. The motions of the phases are described by a simple model of two ideal interpenetrating interacting fluids. The model admits an increasing concentration of the solid particles with the height, which leads to circulatory flows. Approximate equations of motion of the liquid and the solid particles are obtained, and these are analogous to the Boussinesq approximation in the case of natural convection in a pure liquid. The equations contain a parameter which is analogous to the Rayleigh number and characterizes the stability of the layer. An approximate analytic solution to the corresponding eigenvalue problem is found. The spectrum of Rayleigh numbers and the sizes of the convective cells are determined. The obtained results provide an explanation for the existence of the multicenter circulatory motions of the phases frequently observed in a fluidized beds and make it possible to determine the sizes of the circulatory regions. Information about the Rayleigh number spectrum and the sizes of the regions is needed to solve the problem of the scale transition and also to enable the choice of measures to suppress or intensify the displacement processes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–46, July–August, 1982.     

A new drag model for TFM simulation of gas–solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas–solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with experimental data than those of the Gidaspow drag model did.     

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed （CFB） designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process. Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-offbetween computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient. A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementa- tion is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed （solid flux） is implemented through additional mass source/sink terms in the continuity equations of the two phases, For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations, The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system, The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.     

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed (CFB) designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process.Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-off between computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient.A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementation is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed (solid flux) is implemented through additional mass source/sink terms in the continuity equations of the two phases.For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations. The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system.The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.     

Kinetic model of heat transfer processes in a fluidized bed

In the present paper equations are obtained for determining the temperature field in a fluidized layer. The heat and mass transfer processes in a fluidized bed depend significantly on the motion of the solid particles which form the bed. In any small volume of a fluidized bed with nonuniform thermal conditions there are particles with different average temperatures. Therefore it is natural to resort to the statistical representation of such a system, developed previously in [1, 2], for the study of the heat transfer processes. The expression obtained here for the heat conductivity coefficient of the bed is in good qualitative agreement with the experimental data.The author wishes to thank V. G. Levich for his interest and valuable discussions.     

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.     

A new drag model for TFM simulation of gas-solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas-solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with exoerimental data than those of the Gidasoow dra~ model did.     

Local heat transfer coefficients around a horizontal heated tube immersed in a gas fluidized bed

The heat transfer characteristics around a single horizontal heated tube immersed in air fluidized bed was investigated, to clarify the mechanism of heat transfer in a fluidized bed heat exchanger. The local heat transfer coefficient around the tube was measured at various fluidization velocities and five different solid particles. The experimental values of the local heat transfer coefficient at the minimum fluidization velocity condition were correlated with the particle size in two empirical equations. The predicted results were in good agreement with the experiment data.     

Effect of secondary air on NO emission in a 440 t/h circulating fluidized bed boiler based on CPFD method

The 440 t/h circulating fluidized bed boiler was numerically simulated by the Computational Particle Fluid Dynamics (CPFD) method. The combustion characteristics of circulating fluidized bed boiler and the effect of secondary air on NO emission were investigated. The full-scale three-dimensional model of a 440 t/h circulating fluidized bed boiler was established. The rationality of the grid was validated by the experimental data of material layer resistance. The accuracy of the simulation was validated by measuring the temperature of each measuring point in the dense phase area. The combustion conditions in the furnace under different setting modes were simulated. The effects of secondary air rates on NO formation in fluidized bed were predicted. The results show that when the secondary air rate increases to 27%, the proper secondary air rate has a positive effect on the inhibition of NO generation, and the proper strengthening of the central air supply will improve the permeability of the secondary air and make the combustion more uniform and stable. When the secondary air rate increases to 33%, excessive improvement of air classification and central air distribution will affect the stability of circulating fluidized bed operation. Therefore, air classification and strengthening of central air supply can be used together to inhibit the generation of NO.     

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.     

The basic character of five two‐phase flow model equation sets

Three test problems were simulated using five different two‐phase flow model equation sets from the open literature. The test problems chosen were a fluidized bed, a batch settling, and a horizontal jet impingement on a vertical wall. These three problems demonstrate an important cross‐section of physical phenomena, such as fluidized bed voidage oscillations, phase separation, countercurrent flow, and jet formation. The dispersed flow regime is selected for all three problems. The study was performed to assess the basic character of the five‐field equation sets responding to the same initial and boundary conditions and using the same finite difference numerical scheme. The general performance of the five equation sets was found to be similar, even though one of them was ill posed as an initial‐value problem. Broad trends are the same and quantitative differences could be assessed by examining the fine structure of the results. None of the equation sets could be entirely rejected on the basis of producing physically impossible or unacceptable results. Copyright © 2000 John Wiley & Sons, Ltd.     

Simulation of mass balance behavior in a large-scale circulating fluidized bed reactor

We determine using a compound model the influence of the mass of granular matter on the behavior of a supercritical circulating fluidized bed (CFB) reactor. Population balance enables a stationary-regime modeling of the mass flow of granular matter inside a CFB unit in a large-scale. The simulation includes some important dynamic processes of gas-particle flows in fluidized bed such as attrition, fragmentation, elutriation, and fuel combustion. Numerical calculations with full boiler loading were performed of operational parameters such as furnace temperature, furnace pressure, feeding materials mass flows, and excess air ratio. Furthermore, three bed inventory masses were adopted as experimental variables in the simulation model of mass balance. This approach enables a sensitivity study of mass flows of granular matter inside a CFB facility. Some computational results from this population balance model obtained for a supercritical CFB reactor are presented that show consistency with the operational data for large-scale CFB units.     

Micro/meso simulation of a fluidized bed in a homogeneous bubbling regime

Due to the wide range of spatial scales and the complex features associated to fluid/solid and solid/solid interactions in a dense fluidized bed, the system can be studied at different length scales, namely micro, meso and macro. In this work, we select a flow configuration relevant of a homogeneous liquid/solid fluidization and compare computed results from Particle Resolved Simulation (PRS) with those from locally averaged Euler/Lagrange simulation. PRS at the micro-scale is carried out by a parallel Distributed Lagrange Multiplier (DLM) solver in the framework of fictitious domain methods (Wachs, 2011a, 2015). For meso-scale simulations, the set of mass and momentum conservation equations is averaged in control volumes encompassing few particles and momentum transfer between the two phases is modeled using appropriate drag laws. Both methods are coupled to a Discrete Element Method (DEM) combined with a soft-sphere contact model to solve the Newton–Euler equations with collisions for the particles in a Lagrangian framework (Wachs et al., 2012). A test case of intermediate size with 2000 spheres is chosen as a sensible compromise between size limitations of the meso-scale model for an appropriate averaging process and computational resources required to run micro-scale simulations. These two datasets yield new insight on momentum transfer at different spatial scales in the flow, and question the validity of certain approximations adopted in the meso-scale model. Results demonstrate an acceptable agreement between the micro- and meso-scale predictions on integral measures as pressure drop and bed height. Investigating more detailed features of the flow, it has been shown that particles fluctuations are considerably suppressed in meso-scale simulations and in particular the particles transverse motion is underestimated, regardless of the selected drag law. The origin of these dependencies is carefully investigated by reconstructing the closure laws based on PRS results and comparing them to the closure laws proposed in the literature.     

Heat transfer characteristics in a horizontal swirling fluidized bed

An innovative horizontal swirling fluidized bed (HSFB) with a rectangular baffle in the center of an air distributor and three layers of horizontal secondary air nozzles located at each corner of fluidized bed was developed. Experiments on heat transfer characteristics were conducted in a cold HSFB test model. Heat transfer coefficients between immersed tubes and bed materials in the HSBF were measured with the help of a fast response heat transfer probe. The influences of fluidization velocity, particle size of bed materials, measurement height, probe orientation, and secondary air injection, etc. on heat transfer coefficients were intensively investigated. Test results indicated that heat transfer coefficients increase with fluidization velocity, and reach their maximum values at 1.5-3 times of the minimum fluidization velocity. Heat transfer coefficients are variated along the circumference of the probe, and heat transfer coefficients on the leeward side of the probe are larger than that on the windward side of the probe. Heat transfer coefficients decrease with increasing of measurement height; heat transfer coefficients of the longitudinal probe are larger than that of the transverse probe. The proper secondary air injection and particle size of bed materials can generate a preferred hydrodynamics in the dense zone and enhance heat transfer in a HSFB.     

A Local Thermal Non-Equilibrium Analysis of Fully Developed Forced Convective Flow in a Tube Filled with a Porous Medium

A local thermal non-equilibrium model has been considered for the case of thermally fully developed flow within a constant heat flux tube filled with a porous medium. Exact temperature profiles for the fluid and solid phases are found after combining the two individual energy equations and then transforming them into a single ordinary differential equation with respect to the temperature difference between the solid phase and the wall subject to constant heat flux. The exact solutions for the case of metal-foam and air combination reveal that the local thermal equilibrium assumption may fail for the case of constant heat flux wall. The Nusselt number is presented as a function of the Peclet number, which shows a significant increase due to both high stagnant thermal conductivity and thermal dispersion resulting from the presence of the metal-foam.     

STUDY ON THE OVERALL PRESSURE BALANCE OF A DOWNFLOW CIRCULATING FLUIDIZED BED SYSTEM

A pressure balance model for a circulating fluidized bed unit that incorporates a downer has been proposed. The model predictions were validated with the experimental data obtained from a special cold-model circulating fluidized bed. Comparison of the operation stability between a CFB downer and a CFB riser has been carried out. Only one critical gas velocity exists in the CFB-riser for a given riser solids flux, while there can be many critical gas velocities for the operation of a CFB downer. Therefore, it is possible to achieve high solids concentration in a CFB downer if appropriate operating conditions are used.     

STUDY ON THE OVERALL PRESSURE BALANCE OF A DOWNFLOW CIRCULATING FLUIDIZED BED SYSTEM

A pressure balance model for a circulating fluidized bed unit that incorporates a downer has been proposed. The model predictions were validated with the experimental data obtained from a special cold-model circulating fluidized bed. Comparison of the operation stability between a CFB downer and a CFB riser has been carried out. Only one critical gas velocity exists in the CFB-riser for a given riser solids flux, while there can be many critical gas velocities for the operation of a CFB downer. Therefore, it is possible to achieve high solids concentration in a CFB downer if appropriate operating conditions are used.