Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part I: Model derivation and numerical implementation

We have derived a new set of closure equations for the rheologic properties of a dense gas-solid fluidised bed consisting of a multi-component mixture of slightly inelastic spheres, using the Chapman-Enskog solution procedure of successive approximations, where the particle velocity distribution of all particle species is assumed to be nearly Maxwellian around the particle mixture velocity with the particle mixture granular temperature. In this theory, differences in the mean velocities (i.e. particle segregation) and granular temperatures of the particle species result from higher order perturbation functions. Special attention is paid to assure thermodynamic consistency between the radial distribution function and the chemical potential of a hard-sphere particle specie appearing in the diffusion driving force when applying the revised Enskog theory, which is often overlooked. In the resulting closure equations, the rheologic properties of the particle mixture are explicitly described in terms of the particle mixture velocity and granular temperature, and the diffusion velocity and granular temperature of the individual particle phases can be computed from the mixture properties, which is a major advantage with respect to the numerical implementation. A new numerical solution strategy has been devised, which is an extension of the well-known SIMPLE algorithm and takes the compressibility of the solids phase directly into account, which allows for much larger time steps (about a factor of 10 larger). In Part 2 the simulation results obtained with the new model are compared with experimental data and discrete particle model (DPM) simulations.     

Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part II: Segregation in binary particle mixtures

Particle mixing and segregation rates in a bi-disperse freely bubbling fluidised bed have been studied with a new multi-fluid model (MFM) based on the kinetic theory of granular flow for multi-component systems (see Part I). The MFM simulation results have been compared with digital image analysis experiments obtained by Goldschmidt et al. [2003. Digital image analysis of bed expansion in dense gas-fluidised beds. Powder Technology 138, 135-159] for bi-disperse mixtures of glass beads. In strong contrast to MFMs previously described in the literature, that strongly overestimate the segregation rates, the new MFM seems to underestimate the segregation rates at longer times. This underprediction of the segregation rate is probably related to the neglect of frictional stresses associated with long-term multiple-particle contacts resulting in an overestimation of the mobility of the emulsion phase, which is corroborated by discrete particle simulations without friction between the particles and the particles and the wall. The level of the granular temperature of the segregating system, as computed with the new MFM, compares reasonably well with the granular temperatures found in the DPM simulation.     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

Model validation for low and high superficial gas velocity bubble column flows

In the present work, gas-liquid flow dynamics in a bubble column are simulated with CFDLib using an Eulerian-Eulerian ensemble-averaging method in a two-dimensional Cartesian system. The two-phase flow simulations are compared to experimental measurements of a rectangular bubble column performed by Mudde et al. [1997. Role of coherent structures on Reynolds stresses in a 2-D bubble column. A.I.Ch.E. Journal 43, 913-926] and a cylindrical bubble column performed by Rampure et al. [2003. Modeling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. The Canadian Journal of Chemical Engineering 81, 692-706] for low and high superficial gas velocities, respectively. The objectives are to obtain grid-independent numerical solutions using CFDLib to reconcile unphysical results observed using FLUENT with increasing grid resolutions [Law, D., Battaglia, F., Heindel, T.J., 2006. Numerical simulations of gas-liquid flow dynamics in bubble columns. In: Proceedings of the ASME Fluids Engineering Division, IMECE2006-13544, Chicago, IL], and to validate computational fluid dynamics (CFD) simulations with experimental data to demonstrate the use of numerical simulations as a viable design tool for gas-liquid bubble column flows. Numerical predictions are presented for the local time-averaged liquid velocity and gas fraction at various axial heights as a function of horizontal or radial position. The effects of grid resolution, bubble pressure (BP) model, and drag coefficient models on the numerical predictions are examined. The BP model is hypothesized to account for bubble stability, thus providing physical solutions.     

基于EMMS模型的气固鼓泡床的模拟及气泡特性的分析

基于EMMS曳力模型,采用双流体的方法对气固鼓泡床内的气固流动特性进行模拟,建立基于图像处理气泡特性的分析方法,重点研究了不同表观气速下气泡在床层内分布特性,包括气泡平均当量直径、气泡速度和气泡球形度的轴向分布,以及气泡的生命周期。研究结果表明,小气泡多集中在床层底部和壁面区域,而大气泡多集中在床层中间区域。随着表观气速的增加,床层高度不断增加,气泡的球形度降低,气泡的大小、出现频率、上升速度以及生命周期均增加;然而,当表观气速增大到一定程度,继续增加气速对气泡的上升速度影响不大。     

CFD simulations of bubbling beds of rough spheres

Hydrodynamics of three-dimensional gas-solid bubbling fluidized beds are numerically analyzed. The particle-particle interactions are simulated from the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere proposed by Lun [1991. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough sphere. Journal of Fluid Mechanics 233, 539-559] to account for rough sphere binary collisions and the frictional stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] to consider the frictional contact forces between particles. The present model is evaluated by measured particle distributions and velocities of Yuu et al. [2001. Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed. Powder Technology 118, 32-44] and experimental bed expansion of Taghipour et al. [2005. Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chemical Engineering Science 60, 6857-6867]. Our computed results indicated that the present model gives better agreement with experimental data than the results from original kinetic theory for frictionless slightly inelastic sphere of Ding and Gidaspow [1990. A bubbling fluidization model using kinetic theory of granular flow. A.I.Ch.E. Journal 36, 523-538] with and without solid friction stress model.     

Experimental study of mass transfer in a dense bubble swarm

We consider the liquid-side mass transfer coefficient k_L in a dense bubble swarm for a wide range of gas volume fraction (0.45%≤α_G≤16.5%). The study is performed for an air–water system in a square column. Bubble size, shape and velocity have been measured for different gas flow rates by means of a high speed camera. Gas volume fraction and bubble velocity have also been measured by a dual-tip optical probe. Both of these measurements show that the bubble vertical velocity decreases when increasing α_G in agreement with previous investigations. The mass transfer is measured from the time evolution of the dissolved oxygen concentration, which is obtained by the gassing-out method. The mass transfer coefficient is found to be very close to that of a single bubble provided the bubble Reynolds number is based on the average equivalent diameter 〈d_eq〉 and the vertical slip velocity 〈V_z〉.     

Dynamic simulation of a 2D bubble column

The present paper demonstrates how 2D, dynamic simulations of a flat bubble column are feasible, applying state-of-the-art dynamic turbulence models, when an appropriate turbulent dispersion term is applied in the conservation equation for the gas volume fraction. The kω turbulence model yielded a better qualitative prediction of the bubble plume than the kε model, due to the low-Reynolds number treatment of the former model. The simple mixing length turbulence model gave the best prediction of the meandering plume, without any dispersion term. The mixing length model is, however, almost identical to a Large-Eddy simulation when run time-dependent on a fine mesh, and should be applied with care due to the use of a constant turbulence length scale and the inherent 3D nature of turbulence. By refining the mesh to the extreme end, it was shown that an apparently grid independent numerical solution was really grid-dependent, even when dynamic turbulence models were applied. The apparently grid independent solution was computed with an increment in the computational mesh that was of the same size as an equilibrium Kolmogorov length scale.     

Hydrodynamic characterization of a needle sparger rectangular bubble column: Homogeneous flow, static bubble plume and oscillating bubble plume

In this work a detailed experimental hydrodynamic characterization of a needle sparger rectangular bubble column has been performed. The liquid velocity profiles and bubble plume oscillation frequency have been measured by means of laser Doppler anemometry (LDA), and the bubble velocity map by particle image velocimetry (PIV). In this way, the influence of the superficial gas velocity, liquid height and aeration pattern on the column flow structure was analysed. A highly uniform upward flow structure with down flow near the walls was obtained by means of a full-length aeration pattern. This flow structure was preserved even for high gas fractions values. The partial-length aeration patterns with the aerated zone (defined as the aerated width divided by the column width) larger than 0.7 provide a bubble plume and two pure liquid vortical structures in the column bottom, although they are static in nature. With aerated zones lower than 0.6, an oscillating bubble plume is obtained. A non-dimensional analysis of bubble plume oscillation frequency shows a dependence of bubble plume behaviour with the aerated zone. In this way, two different types of bubble plume oscillations, namely confined bubble plume oscillation and free bubble plume oscillation, are introduced and analysed.     

Shape oscillations and path transition of bubbles rising in a model bubble column

We investigate experimentally the occurrence of shape oscillations accompanied by path transition of periodically produced air bubbles rising in water. Within the period of bubble formation, the induced velocity is measured to examine bubble-liquid and bubble-bubble interactions. The flow is produced in a small-scale bubble column with square-shaped cross section. A capillary aerator produces bubbles of size 3.4 mm at a frequency of 5 Hz. Measuring techniques employed are high-speed imaging to capture bubble shape oscillations and path geometry, and laser-Doppler anemometry (LDA) to measure the velocity in the liquid near the rising bubbles. The experimentally obtained bubble shape data are expanded in Legendre polynomials. The results show the occurrence of oscillations by the periodicity of the expansion coefficients in space. Significant shape oscillations accompanied by path transition are observed as the second-mode oscillation frequency converges to the frequency of the initial shape oscillations. The mean velocity field in the water obtained by LDA agrees well with potential theory. An analysis of the decay of the induced flow shows that there is no interaction between the flow fields of two succeeding 3.4 mm bubbles in the rectilinear path when the bubble production frequency is lower than 7.4 Hz.     

Insights in distributed secondary gas injection in a bubbling fluidized bed via discrete particle simulations

Experiments have shown that distributed secondary gas injection via a fractal injector in fluidized beds can significantly reduce the bubble size, and may also decrease the bubble fraction. In order to gain insight into the distribution of the gas between the phases and the mechanisms behind these effects simulations of small bubbling fluidized beds with one or two secondary gas injection points were carried out using a discrete particle model. Although the systems are very small, so that wall effects cannot be excluded, the model predicts that the bubble size and bubble fraction both decrease with secondary gas injection, while the gas flow through the dense phase increases. The secondary gas tends to stay in the dense phase, which limits the amount of gas available to form bubbles and is the main contributor to the decrease in the bubble size and fraction. The gas-solid contact improves as a result.     

Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

A phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Investigation of the unsteady two-phase flow with small bubbles in a model bubble column using phase-Doppler anemometry

The unsteady two-phase flow of water laden with small air bubbles in a model bubble column is investigated experimentally. Phase-Doppler anemometry (PDA) is used for measuring the velocities of water and bubbles. The measured sizes of reflecting tracers in the water and of the air bubbles are used to discriminate between water and bubble data. The investigations are focussed on the unsteady behaviour of the flow and on the interaction between the two phases. The measurement of relative (slip) velocities between bubbles and water reveals information about the dynamic behaviour of the two-phase system under the action of buoyancy on the disperse phase. The evaluation of time series of bubble velocities yields insight into typical frequencies at which the flow fluctuates. It is shown that, at all locations in the flow field, the velocity probability density functions of bubbles and liquid can be described by two superimposed Gaussian functions. The bubbles belonging to the two Gaussians exhibit different slip velocities. The probability for the occurrence of bubble collisions is quantified on the basis of the PDA data.     

A second-order moment method of dense gas-solid flow for bubbling fluidization

A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168].     

CFD-DEM modelling of multiphase flow in dense medium cyclones

Dense medium cyclone (DMC) is a high-tonnage device that is widely used to upgrade run-of-mine coal in coal preparation. It is simple in design but the flow pattern within it is complex due to the size and density distributions of the feed and process medium solids, and the turbulent vortex formed. This paper presents a mathematical model to describe this flow system by means of combining Discrete Element Method (DEM) with Computational Fluid Dynamics (CFD). The DEM is used to model the motion of discrete particles by applying Newton's laws of motion. The CFD is used to model the motion of slurry medium by numerically solving the local-averaged Navier-Stokes equations facilitated with the Volume of Fluid (VOF) and Mixture multiphase flow models. The approach is shown to be able to reproduce typical flow phenomena in DMCs. The effect of medium-to-coal ratio and the so-called “surging” phenomenon are analyzed. An attempt is made to explain the observed phenomena in terms of particle-particle, particle-fluid and particle-wall interaction forces. The approach offers a convenient way to examine the flow and performance of DMC in relation to geometric, material and operational conditions.     

A gas holdup model for cocurrent air-water-fiber bubble columns

A gas holdup model is developed for cocurrent air-water-fiber bubble column flows using the drift-flux model. The model coefficients are estimated using a nonlinear least square method and systematically acquired experimental data. The model correlates gas holdup with superficial gas and liquid velocity, and fiber type and mass fraction. The model reproduces most experimental data within ±10% error and all but 3 of the 3839 experimental data points within ±15% error. It also accurately predicts air-water bubble column gas holdup data; these data were not used in estimating the model coefficients. The physical implications of the model coefficients are also discussed.     

Single-phase flow model development for macroscopic liquid flow evaluation in gas–liquid reactors, by computational fluid dynamics

This paper proposes a single-phase flow model to simulate the flow induced in a liquid by the injection of gas dispersed in the form of a bubble curtain. It aims at predicting macroscopic liquid flow and mixing time. This single-phase flow model is developed as an alternative to two-phase flow models. The model is based on the assumption that the liquid flow is induced by a density imbalance between the bulk zone and the bubble curtain zone. The density in the bulk is set to the water density while the density in the bubble curtain corresponds to the air–water mixture density and is assessed by numerical simulations, thanks to an iterative procedure. Only the knowledge of the injected air flow rate and the bubble liquid relative velocity is required. The single-phase flow model is applied to assess the liquid flow and the mixing in open quarries having a complex geometry. The liquid velocities and the flow structure in the open quarries simulated with the single-phase flow model are in good agreement with those predicted by numerical simulations based on a two-phase flow model.