Axi-symmetric simulation of a two phase vertical thermosyphon using Eulerian two-fluid methodology

Numerical simulation of steady state operation of a vertical two phase closed thermosyphon is performed using the two-fluid methodology within Eulerian multiphase domain. A full scale axi-symmetric model is developed for computational fluid dynamics simulation of thermosyphon using ANSYS/FLUENT 13.0. The effects of evaporation, condensation and interfacial heat and mass transfer are taken into account within the whole domain. Cooling water jacket is also modelled along with the wall of thermosyphon to simulate the effect of conjugate heat transfer between the wall and fluid phase. The results obtained are presented and compared with available experimental investigations for a similar thermosyphon. It is established that two-fluid methodology can be used effectively for the purpose of simulation of two phase system like a typical thermosyphon.     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

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.     

Extending EMMS-based models to CFB boiler applications

Recently, EMMS-based models are being widely applied in simulations of high-throughput circulating fluidized beds (CFBs) with fine particles. Its use for low flux systems, such as CFB boiler (CFBB), still remains unexplored. In this work, it has been found that the original definition of cluster diameter in EMMS model is unsuitable for simulations of the CFB boiler with low solids flux. To remedy this, we propose a new model of cluster diameter. The EMMS-based drag model (EMMS/matrix model) with this revised cluster definition is validated through the computational fluid dynamics (CFD) simulation of a CFB boiler.     

A CORRELATION EQUATION FOR CALCULATING INCLINED JET PENETRATION LENGTH IN A GAS-SOLID FLUIDIZED BED

Numerical simulation of gas-solid flow in a two-dimensional fluidized bed with an inclined jet was performed. The numerical model is based on the two-fluid model of gas and solids phase in which the solids constitutive equations are based on the kinetic theory of granular flow. The improved ICE algorithm, which can be used for both low and high-velocity fluid flow, were used to solve the model equations. The mechanism of jet formation was analyzed using both numerical simulations and experiments. The emergence and movement of gas bubbles were captured numerically and experimentally. The influences of jet velocity, nozzle diameter, nozzle inclination and jet position on jet penetration length were obtained. A semi-empirical expression was derived and the parameters were correlated from experimental data. The correlation equation, which can be easily used to obtain the inclined jet penetration length, was compared with our experimental data and published correlation equations.     

Smoothed particle hydrodynamics for coarse-grained modeling of rapid granular flow

We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics(SPH) solutions of a set of continuum equations.This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization.We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow,thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization.Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.     

Analysis of the flow in inhomogeneous particle beds using the spatially averaged two-fluid equations

The drag force term appearing in two-fluid models for fluid–particle flows is commonly closed by expressing it as a function of the local quantities, such as the local particle volume fraction, the local slip velocity between the particle and fluid phases, and the local mean-squared fluctuating velocity of the particles. The adequacy of such closures for inhomogeneous suspensions has been debated in the literature and some researchers have suggested the need for additional terms involving spatial gradients in these quantities. To test this proposition, simulations of flow in inhomogeneous steady beds of particles have been performed using the lattice-Boltzmann method. The particle beds consisted of disordered assemblies with a density profile on a scale much larger than the particle radius. Inhomogeneous beds with a controlled density profile were generated in three different ways, (i) by inhomogeneous stretching of the particle bed in one direction, (ii) by applying an inhomogeneous force to the particle phase during random motion of the particles, and (iii) by taking snapshots of a direct simulation of a traveling wave in a fluidization simulation. The global structure of the three beds was comparable, while assessment of the radial distribution functions showed that the three beds exhibited clearly different microscopic structures.     

CFD-simulation of a circulating fluidized bed riser

In the current work, a model of the fluid mechanics in the riser of a circulating fluidized bed （CFB） has been implemented using computational fluid dynamics （CFD）. The model developed shall be used in future as the basis of 3D-reactor model for the simulation of large scale CFB combustors. The two-fluid model （TFM） approach is used to represent the fluid mechanics involved in the flow. The computational implementation is accomplished by the commercial software FLUENT. Different closure formulations are tested on a simplified geometry. Two different turbulence formulations, namely the swirl modified RNG k-e model and the Realizable k-e model, are tested in combination with two different approaches to solid phase turbulence, namely the dispersion and per phase approach. One focus of the current work is put on the study of different drag correlations. Besides the drag correlations by Syamlal et al. [Syamlal, M., Rogers, W., ＆ O＇Brien, T. J. （1993）. MFIX documentation theory guide. Technical Report DOE/METC-9411004, U.S. Department of Energy （DOE）. Morgantown Energy Technology Center： Morgantown, WV] and Gidaspow [Gidaspow, D. （1994）. Multiphaseflow andfluidization. New York： Academic Press] the EMMS model has been used to determine the momentum exchange between the two phases. The resulting formulation is then used to simulate a 1-m × 0.3-m cold CFB setup and is validated by experimental results [Schlichtharle, P. （2000）. Fluid dynamics and mixing of solids and gas in the bottom zone of circulating fluidized beds. Unoublished doctoral dissertation, Technische Universitaet Hamburg-Harburg, Shaker Verlag： Aachen].     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.      

Experimental study on reactor performance of gas–solids low-velocity fluidized beds

Reactor performance of bubbling fluidized bed (BFB) and turbulent fluidized bed (TFB) was carefully examined and systematically compared using catalytic ozone decomposition as a model reaction, based on a complete mapping of local flow structures and spatial distributions of ozone conversion and solids holdup. TFB clearly has a higher conversion and shows better reactor performance than BFB as a result of the vigorously turbulent flow and the relatively homogeneous gas–solids mixing in TEB. Besides, the intensive interaction between gas and solids in TFB leads to greater gas–solids contact efficiency of TFB over that of BFB. Due to gas bypassing and backmixing caused by bubbling behaviours and two-phase structure, BFB deviates significantly from a plug flow reactor and sometimes from a continuously stirred tank reactor. The flow structures essentially dictate the reactor performance in the low-velocity fluidized beds.     

Characterization of heterogeneous solids via wave methods in computational microelasticity

Real solids are inherently heterogeneous bodies. While the resolution at which they are observed may be disparate from one material to the next, heterogeneities heavily affect the dynamic behavior of all microstructured solids. This work introduces a wave propagation simulation methodology, based on Mindlin's microelastic continuum theory, as a tool to dynamically characterize microstructured solids in a way that naturally accounts for their inherent heterogeneities. Wave motion represents a natural benchmark problem to appreciate the full benefits of the microelastic theory, as in high-frequency dynamic regimes do microstructural effects unequivocally elucidate themselves. Through a finite-element implementation of the microelastic continuum and the interpretation of the resulting computational multiscale wavefields, one can estimate the effect of microstructures upon the wave propagation modes, phase and group velocities. By accounting for microstructures without explicitly modeling them, the method allows reducing the computational time with respect to classical methods based on a direct numerical simulation of the heterogeneities. The numerical method put forth in this research implements the microelastic theory through a finite-element scheme with enriched super-elements featuring microstructural degrees of freedom, and implementing constitutive laws obtained by homogenizing the microstructure characteristics over material meso-domains. It is possible to envision the use of this modeling methodology in support of diverse applications, ranging from structural health monitoring in composite materials to the simulation of biological and geomaterials. From an intellectual point of view, this work offers a mathematical explanation of some of the discrepancies often observed between one-scale models and physical experiments by targeting the area of wave propagation, one area where these discrepancies are most pronounced.     

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.     

Investigation of dense slurry suspensions with coaxial mixers: Influences of design variables through tomography and mathematical modelling

The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor. In this research work, the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system (comprised of a close clearance anchor rotating with a low speed and an inner axial impeller rotating with a high speed) was analyzed employing ERT (electrical resistance tomography, a non-intrusive flow visualization technique), and computational fluid dynamics (CFD). The numerical models were validated by comparing the axial solid concentration profiles generated using the ERT data and the CFD simulation results. The influences of various important parameters such as the diameter of the inner axial impeller, the inner impeller type, and the inner impeller spacing on the hydrodynamic characteristics of the slurry suspensions in a coaxial mixing vessel were thoroughly analyzed. The radial and axial velocity profiles of solid particles were generated using the validated mathematical models. The assessment of energy loss due to the solid–solid collisions, the particle–fluid frictions, and the particle–vessel wall collisions was conducted. The evaluation of optimum inner impeller clearance and inner impeller diameter is essential to attain a high degree of solids suspension and dissemination in a coaxial slurry mixing system.     

Analyzing dominant particle-flow structures inside a bubbling fluidized bed

The particle phase of a gas-particle flow inside a bubbling fluidized bed is characterized by strong unsteady flow patterns and intense meso-scale fluctuations that give rise to an intense mixing rate. As such, it is important to gain a deeper insight into how particle-flow structures and the associated fluctuating velocity field contribute to the overall bed dynamics. To this end, advanced post-processing methodologies, i.e., the Proper Orthogonal Decomposition (POD) and the swirling strength criterion, are applied to the particle flow fields predicted by a “two-fluid model” of a cylindrical bubbling bed to identify and analyze the dominant spatio-temporal patterns of the particle phase. Three-dimensional POD results indicate that the dominant particle fluctuating velocity patterns are principally aligned in the axial direction, corresponding to particle mixing by the bubble wakes, with significant laterally directed fluctuating velocity vectors at the bed surface, corresponding to mixing caused by the bubbles bursting. The particle velocity gradient tensor is decomposed based on the swirling strength criterion and reveals formation of extended and flat structures that may be considered as a characteristic feature of the particle vortical motions in bubbling beds.     

CFD study: Effect of pulsating flow on gas–solid hydrodynamics in FCC riser

Gas–solid flow in a fluid catalytic cracking (FCC) riser exhibits poor mixing in the form of a core–annulus flow pattern and a dense bottom/dilute top distribution of solids. To enhance gas–solid mixing, studies on dense fluidized beds have suggested using a pulsating flow of gas. The present study investigates the effect of pulsating flow on gas–solid hydrodynamics inside the FCC riser employing computational fluid dynamics. Two flow conditions are investigated: a cold flow of air-FCC catalyst in a pilot-scale riser and a reactive flow in an industrial-scale FCC riser. In the cold-flow riser, pulsating flows cause the slug flow of solids and thus increase the average solid accumulation in the flow domain and solid segregation towards the wall. In the industrial FCC riser, pulsating flows produce radial profiles that are more homogeneous. Pulsating flows further improve the conversion and yield in the initial few metres of height. At 7 m, the conversion from pulsating flow is 59%, compared with 44% in without pulsating flow. The results and analysis presented here will help optimize flow conditions in the circulating fluidized bed riser, in not only FCC but also applications such as fast pyrolysis and combustion.     

Numerical study on hydrodynamics of gas–solids circulating fluidized bed with L-valve

L-valve is often used as a non-mechanical valve for the circulation of solids in gas–solids fluidized bed (GSFB) due to its advantages in simple construction and easy control. The information on solids circulation rate as well as the hydrodynamics performance of the CFB with L-valve is of great importance for its better control and design. This paper proposes a Eulerian-Eulerian approach based numerical model integrating the computational fluid dynamics (CFD) with turbulent model, the kinetic theory of granular flow (KTGF) and the drag model, thus the solids circulation rate and the local phase velocity as well as solids volume fraction can be predicted simultaneously. With this model, the hydrodynamics performance of the full loop GSCFB with a L-valve is analyzed in detail. It is found that the drag model affects the simulation significantly and the (energy minimization multiscale) EMMS method shows good performance in the full-loop simulation of GSCFB.     

A study on the numerical stability of the two-fluid model near ill-posedness

The two-fluid model is widely used in studying gas–liquid flow inside pipelines because it can qualitatively predict the flow field at low computational cost. However, the two-fluid model becomes ill-posed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the Euler implicit method for the time derivatives in conjunction with the two-fluid model is analyzed. A pressure correction algorithm for the two-fluid model is carefully implemented to minimize its effect on numerical stability. von Neumann stability analysis shows that the central difference scheme is more accurate and more stable than the 1st-order upwind, 2nd-order upwind, and QUICK schemes. The 2nd-order upwind scheme is much more susceptible to instability than the 1st-order upwind scheme and is inaccurate for short waves. Excellent agreement is obtained between the predicted and computed growth rates of harmonic disturbances. The instability associated with the two-fluid model discretized system of equations is related to but quantitatively different from the instability associated with ill-posedness of the two-fluid model. When the computation becomes unstable due to the ill-posedness, the machine roundoff errors from a selected range of short wavelengths, which scale with the grid size, are amplified rapidly to render the computation of any targeted long wavelength variation useless. For the viscous two-fluid model with wall friction and interfacial drag, a small-amplitude long wavelength disturbance grows due to viscous Kelvin–Helmholtz instability without triggering the grid scale short waves when the system remains well posed. Under such a condition, central difference is found to be the most accurate discretization scheme among those investigated.     

Bubble wake solids content in three-phase fluidized beds

It is shown that existing equations for predicting the holdups of wakes behind bubbles in three-phase fluidized beds are not entirely satisfactory. A new model is then developed whereby the wake is treated as the sphere-completing volume of a spherical cap bubble, due allowance being made for hydrodynamic interactions between bubbles. The generalized wake equations of Bhatia & Epstein (1974) are applied to compute the ratio of solids holdup in the wakes to that in the remaining liquid of the bed. Using experimental data from the literature, a rational equation is then generated for predicting this ratio from measured variables, and a mechanism for wake solids entrainment is proposed which is consistent with this equation.