DEM simulation of the particle dynamics in two-dimensional spouted beds

A Discrete Element Method (DEM) is used together with the continuum model of turbulent fluids to simulate the periodic spouting of granular solids in a two-dimensional spouted bed. The bed is contained in a rectangular column of 152 mm width and 15 mm depth with a tapered base. Glass beads with a diameter of 2 mm are used as bed material. Simulations using the DEM together with a low Reynolds number k-ε turbulence model for the fluid phase yield predictions of the unstable spout regime, characterized as a periodic upward-moving particle jet. The simulation results compare well to experimental data obtained using a particle image velocimetry (PIV) technique, including fluid flow fields, time-averaged particle velocity profiles, and spout shape. Finally, DEM predictions for distribution of drag and net force on the particles, particle concentration fields, gas velocity and turbulence field are discussed.     

Granular temperature in a liquid fluidized bed as revealed by diffusing wave spectroscopy

We report granular temperature and solid fraction fields for a thin rectangular bed (20×200 mm cross-section and 500 mm high) of glass particles (mean diameter of 165 μm and density of 2500 kg/m³) fluidized by water for superficial velocities ranging from 0.05U_t, which is approximately double the minimum fluidization velocity, to 0.49U_t, where U_t is the particle terminal velocity estimated by fitting the Richardson-Zaki correlation to the bed expansion data. At superficial velocities below 0.336U_t, the solid fraction and granular temperature are uniform throughout the bed. At higher superficial velocities, the solid fraction tends to decrease with height above the distributor, whilst the granular temperature first increases to a maximum before decaying towards the top of the bed. Correlation of the mean granular temperature with the mean solid fraction and the local granular temperature with the local solid fraction both suggest that the granular temperature in the liquid fluidized bed can be described solely in terms of the solid fraction. The granular temperature increases monotonically with solid fraction to a maximum at φ≈0.18 where it then decreases monotonically as φ approaches the close-packed limit.     

Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Dependence of particle fluctuation velocity on gas flow, and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes

In this paper we present new experimental data on the steady-state, mean squared, fluctuation velocity, or granular temperature, of Geldart B polymer, glass, nickel, and stainless steel monodispersed spheres averaged over the wall of a gas fluidized bed, as a function of gas flow and sphere diameter. The granular temperature is obtained by Acoustic Shot Noise technology—namely power spectral analysis of the steady state vibrational energy of the wall excited by random sphere impact, and calibrated by hammer excitation over the wall. The new data extends to polymer and metallic spheres the experimental discovery of a 1996 paper of Cody et al. that the fluctuation velocity of Geldart B glass spheres when scaled to the gas superficial velocity, U_s, is inversely proportional to sphere diameter, directly proportional to a fundamental length scale, D_o^B, and is a universal function of U = (U_s / U_mf). We also demonstrate that the new data is consistent with the diameter dependence of the fluctuation velocity that can be derived from both the 1997 paper of Menon and Durian, who measured random sphere motion near the wall through the spectroscopy of scattered laser light, and the 1992 paper of Rahman and Campbell, who measured the average granular pressure of random sphere impact on a porous steel membrane. While the inverse scaling of the fluctuation velocity with sphere diameter, and the existence of a fundamental length scale for gas fluidization, D_o^B, had not been a feature of any published fundamental model, or computer simulation, of the steady state granular temperature of spheres in gas fluidized beds, we show that it is a feature of two recent dense kinetic fluidization models published in 1999, by Buyevich and Kapbasov, and Koch and Sangani. Both theories implicitly define a fundamental length scale for the fluctuation velocity, D^? = (μ_f² / ρ_p²g)^1 / 3, where ρ_p is the sphere density, μ_f is the gas viscosity, and g is the laboratory gravitational field. The new data for polymer, glass, nickel and stainless steel spheres presented in this paper, defines D_o^B = (56 ± 2)D^?. We use the Anderson-Jackson stability model to show that the length scale D_o^B, also defines a stability length scale, such that for D < D_o^B(D > D_o^B), the uniform dense phase of the fluidized bed is stable (unstable), against one dimensional, first order fluctuations in sphere concentration. The length scale, D_o^B is thus the theoretical equivalent to the empirical scaling length introduced by Geldart, D_B/A, to distinguish spheres (D > D_B/A) that bubble at fluidization, from spheres (D < D_B/A) that fluidize before bubbling. Finally, we present new experimental data, on the remarkable changes in the granular temperature, bed expansion, and bed collapse time, between Geldart B and Geldart A monodispersed glass spheres, and compare that data to granular temperature, and bed expansion, for Geldart A rough, non-spherical, log-normal dispersed diameter catalytic particles.     

Numerical modeling of particle fluidization behavior in a rotating fluidized bed

In this study, numerical modeling of particle fluidization behaviors in a rotating fluidized bed (RFB) was conducted. The proposed numerical model was based on a DEM (Discrete Element Method)-CFD (Computational Fluid Dynamics) coupling model. Fluid motion was calculated two-dimensionally by solving the local averaged basic equations. Particle motion was calculated two-dimensionally by the DEM. Calculation of fluid motion by the CFD and particle motion by the DEM were simultaneously conducted in the present model. Geldart group B particles (diameter and particle density were 0.5 mm and 918 kg/m³, respectively) were used for both calculation and experiment. First of all, visualization of particle fluidization behaviors in a RFB was conducted. The calculated particle fluidization behaviors by our proposed numerical model, such as the formation, growth and eruption of bubble and particle circulation, showed good agreement with the actual fluidization behaviors, which were observed by a high-speed video camera. The estimated results of the minimum fluidization velocity (U_mf) and the bed pressure drop at fluidization condition (ΔP_f) by our proposed model and other available analytical models in literatures were also compared with the experimental results. It was found that our proposed model based on the DEM-CFD coupling model could predict the U_mf and ΔP_f with a high accuracy because our model precisely considered the local downward gravitational effect, while the other analytical models overpredicted the ΔP_f due to ignoring the gravitational effect.     

Size segregation of spherical nickel pellets in the surface flow of a packed bed: Experiments and Discrete Element Method simulations

The size segregation of binary mixtures of spherical nickel pellets flowing into a packed bed was investigated with Discrete Element Method (DEM) simulations and physical experiments in 30 cm and 60 cm wide rectangular test cells. Each test cell approximates a vertical slice of a cylindrical packed bed, with a rising feed tube on one side of the cell representing the stationary frame of reference in the packed bed. As the feed tube is raised, the pellets flow laterally into the test cell to form a sloping surface inclined to the horizontal by the angle of repose. The lateral flow of pellets is confined near the surface of the packed bed, and was intermittent in character (i.e. surging). Velocity vectors show the detailed flow field in the simulated test cells. The smaller pellets were found to be concentrated near the core of the granular assembly, and the larger pellets segregate to the outer wall farthest from the feed tube. The degree of segregation, or coefficient of variation (variance/mean), is proportional to the diameter ratio α of the pellets and the length of the surface, and inversely proportional to the mass fraction of the smaller pellets within the range of parameters studied. The DEM simulations had an average deviation in mass fraction of 0.07 and maximum deviation of 0.22 from the experimental data.     

Numerical simulations of transfer and transport properties inside packed beds of spherical particles

In this study, we investigate the transport and transfer properties inside packed beds of spherical particles by means of CFD simulations. Heat and mass transfer properties have been computed in packing configurations of increasing complexity at low to moderate Reynolds numbers (1<R_e<80). Only liquid-phase flows are studied (300<S_c<1000). The problem of contact points between particles, which is inherent to finite-volume numerical methods, is solved by applying a contraction of 2% on all the particles of the bed. We show that this treatment has very little influence on the results when analyzed with dimensionless numbers as N_u=f(R_e, P_r) or S_h=f(R_e, S_c). Finally, a very dense packing of spheres was built using a Discrete Element Method and used to represent the real granular media. Transfer predictions by the model are very realistic. Longitudinal and transverse dispersion coefficients are determined inside geometries containing hundreds of particles. Predictions of dispersion coefficients are consistent with literature, but a correction is applied to improve results, because the bed contraction leads to the underestimation of the transverse dispersion coefficient. The model is found to be very promising to study the “near wall channelling” phenomena inside small packed columns induced by the heterogeneity of the porosity profile close to the wall.     

Transitions to vibro-fluidization in a deep granular bed

Granular media subjected to vibration can approximate fluid behavior with sufficient vibration acceleration. Unlike gas fluidization, the transition from a static bed to a liquid-like state is poorly defined and has primarily studied previously in shallow or 2D granular beds. Three granular states are identified in this work: the static, the quasi-static, and the vibro-fluidized state. These states are characterized for a deep granular bed through quantitative measurements of the power or torque required to rotate a vane within the granular media. In this study, the vane is rotated while the bed is subjected to vibration at 10 Hz with acceleration in the range 0 ≤ Γ = ω² x_max/g ≤ 4.0. We define a critical dimensionless vibration acceleration, Γ_c, based on a dramatic decrease in vane power and the absence of a dynamic zero-shear rate torque, as the transition to vibro-fluidization. Typical of granular materials, significant hysteresis is observed in measuring these bed state transitions. These measurements of “granular rheology” provide a quantitative framework for defining these transitions.     

Non-premixed fluidized bed combustion of C1-C4n-alkanes

The non-premixed combustion of C₁-C₄n-alkanes with air was investigated inside a bubbling fluidized bed of inert sand particles at intermediate temperatures: 923 K ? T_B ? 1123 K. For ethane, propane and n-butane, combustion occurred mainly in the freeboard region at bed temperatures below T₁ = 923 K. On the other hand, complete conversion occurred within 0.2 m of the injector at: T₂ = 1073 K. For methane, the measured values of T₁ and T₂ were significantly higher at 1023 K and above 1123 K, respectively. The fluidized bed combustion was accurately modeled with first-order global kinetics and one PFR model to represent the main fluidized bed body. The measured global reaction rates for C₂-C₄n-alkanes were characterized by a uniform Arrhenius expression, while the global reaction rate for methane was significantly slower. Reactions in the injector region either led to significant conversion in that zone or an autoignition delay inside the main fluidized bed body. The conversion in the injector region increased with rising fluidized bed temperature and decreased with increasing jet velocity. To account for the promoting and inhibiting effects, an analogy was made with the concept of induction time: the PFR length (b_i) of the injector region was correlated to the fluidized bed temperature and jet velocity using an Arrhenius expression. These results show that the conversion of C₂-C₄n-alkanes can be estimated with one set of critical bed temperatures and modeled with one Arrhenius kinetics expression.     

Modelling of dense gas-particle flow in a circulating fluidized bed by Distinct Cluster Method (DCM)

Computational Fluid Dynamics (CFD) is a powerful tool to study the dense gas-solid flow in a circulating fluidized bed. Most of the existing methods focus on the microscopic properties of individual particle. Therefore, the simulation scale is significantly limited by the huge number of individual particles, and so far the numbers of particles in most of the reported simulations are less than 10⁵. The hydrodynamics behaviour of particle clustering in a dense gas-solid two-phase flow has been verified by several experimental results. The Distinct Cluster Method (DCM) was proposed in this paper by studying the macroscopic particle clustering behaviour, and comprehensive models for cluster motion, collision, break-up, and coalescence have been well developed. We model the dense two-phase flow field as gas-rich lean phase and solid-rich cluster phase. The particle cluster is directly treated as one discrete phase. The gas turbulent flow is calculated by Eulerian approach, and the particle behaviour is studied by Lagrangian approach. Using the proposed method, a three-dimension dense gas-particle two-phase flow field in a circulating fluidized bed with square-cross-section, with particle number up to 7.162 × 10⁷ are able to be numerically studied, on which few results have been reported. Details on instantaneous and time-averaged distributions are obtained. Developing process of non-uniform particle distribution is visualized. These results are in agreements with experimental observations, which justified the feasibility of using the DCM method to model and simulate dense gas-solid flow in a circulating fluidized bed with large number of particle numbers.     

Mass loss and apparent kinetics of a thermally thick wood particle devolatilizing in a bubbling fluidized bed combustor

This work presents the results of experiments conducted to determine the mass loss characteristics of a cylindrical wood particle undergoing devolatilization under oxidation conditions in a bubbling fluidized bed combustor. Cylindrical wood particles having five different sizes ranging from 10 to 30 mm and aspect ratio (l/d = 1) have been used for the study. Experiments were conducted in a lab scale bubbling fluidized bed combustor having silica sand as the inert bed material and air as the fluidizing medium. Total devolatilization time and mass of wood/char at different stages of devolatilization have been measured. Studies have been carried out at three different bed temperatures (T_bed = 750, 850 and 950 °C), two inert bed material sizes (mean size d_p = 375 and 550 μm) and two fluidizing velocities (u = 5u_mf and u = 10u_mf). Devolatilization time is most influenced by the initial wood size and bed temperature. Most of the mass is lost during the first half of the devolatilization process. There was no clear influence of the fluidization velocity and bed particle size on the various parameters studied. The apparent kinetics estimated from the measured mass history show that the activation energy varied narrowly between 15 and 27 kJ/mol and the pre-exponential factor from 0.11 and 0.45 s⁻¹ for the wood sizes considered.     

CFD–DEM simulations of wet particles fluidization with a new evolution model for liquid bridge

A new model for liquid-bridge evolution with consideration of particle dynamics, is proposed to improve Computational Fluid Dynamics-Discrete Element Method (CFD–DEM) simulations of wet particles fluidization under high liquid loading and viscosity. A liquid bridge is allowed to form and remains stable only when the normal relative velocity of two particles is lower than a critical value v _nc. A large v _nc leads to an increase of liquid-bridge or cohesive force. The model can be reduced to the conventional liquid-bridge model in literature when v _nc = 0 or ∞. With the new model, the prediction of bubble properties including bubble center, aspect ratio, and volume agrees well with the experimental data in literature. In particular, under high liquid loading, bubble disintegration due to particle agglomerating is reasonably captured. The simulations demonstrate the advantage of the new model that can extend the liquid-bridge models and CFD–DEM for high liquid loading and viscosity.     

Three-dimensional numerical simulation of a horizontal rotating fluidized bed

Three-dimensional numerical simulations of a horizontal rotating fluidized bed (RFB) containing glass bead particles (d_s = 82 μm, ρ_s = 2450 kg/m³) and washed alumina (d_s = 89 μm, ρ_s = 1550 kg/m³) were performed. FLUENT 6.1 software was used to carry out our simulation. The numerical results were compared with the experimental data of Qian and Pfeffer et al. [G.H. Qian, I. Bagyi, I.W. Burdick, R. Pfeffer, H. Shaw, Gas-Solid Fluidization in a Centrifugal Field.” AIChE J. 47 (5) (2001) 1022-1034]. The rotating speed of the RFB was set at 325 rpm (34 rad/s), which is equivalent to a centrifugal acceleration of 7 g.The flow behavior of the solid particles was analyzed; the bed thickness and the calculated pressure drop were compared with the experimental results. Our calculated pressure drop agreed very well with the experimental results.     

The rise of a buoyant sphere in a gas-fluidized bed

The rise velocity, V, of a single sphere, released in the bottom of a bed of sand fluidized by air, was measured: the sphere had a diameter of 9.0 or 13.2 mm; its density ranged from 900 to . These experiments with a single sphere used: (i) a bubbling bed, diameter 141 mm, with 1.05<U/U_mf<2.00, (ii) a slugging bed, diameter 24 mm, with 1.70<U/U_mf<3.20. Here U is the fluidizing velocity; U=U_mf at incipient fluidization. It was found that, for each sphere in a given bed, V=V_mf+C(U-U_mf): the constant C was up to 10 times larger for bubbling beds than slugging beds.The rise velocity at incipient fluidization, V_mf, is governed, for both types of bed, by the apparent viscosity of the incipiently fluidized bed. Therefore, Stokes's law was used to predict V_mf, but using an important modification: since each buoyant sphere appears to carry on its top a defluidized ‘hood’ of particles, Stokes's law was applied to the composite ‘particle’ consisting of the sphere plus its hood. Analysis of the measured V_mf then gave the volume of the hood, in agreement with direct measurements of it above a fixed cylinder in a two-dimensional bed. In addition, the analysis gave the apparent viscosity of the incipiently fluidized bed to be 0.66 Pa s, in excellent agreement with the estimate of Grace (Can. J. Chem. Eng. 48 (1970) 30) for similar sand.     

Devolatilization of coals of northeastern India in inert atmosphere and in air under fluidized bed conditions

Devolatilization of five coals having volatile matter in the range of 31 to 41% was studied in argon and in air under fluidized bed conditions. The diameter of the coal particles varied between 4 and 9.5 mm. The variation of devolatilization time with particle diameter was expressed by the correlation, t_v = Ad_vⁿ. The superficial gas velocity was found to have a significant effect on the rate of devolatilization. The devolatilization rate increased with the increase in the oxygen concentration in the fluidizing gas. The correlations developed in this study fitted the mass versus time profiles of the coal particles satisfactorily. The same correlations were found to be appropriate for predicting devolatilization of a batch of coal particles. The correlations developed in the present study will be useful for the design of fluidized bed combustors.     

The influence of DEM simulation parameters on the particle behaviour in a V-mixer

Results are described of simulations based on the discrete element method (DEM) using a code developed by Tsuji, Kawaguchi, and Tanaka (Discrete particles simulation of 2-dimensional fluidized bed. Powder Technology 77 (1993) 79-87). The mechanical interactions between particles and also between particles and the walls in granular flows are modelled by linear springs, dash-pots and friction sliders. The simulation parameters are the restitution coefficient, normal stiffness, friction coefficient between particles and between particles and the walls, and two ratios which relate the normal and tangential stiffness and damping coefficients. Their influence on particle motion in a V-mixer has been evaluated and compared with radioactive tracer measurements of particle motion. A number of quantitative methods for comparing DEM and experimental data were developed. Given the simplified nature of the modelled interactions, the agreement between the predicted and measured data is remarkably close for restitution coefficient values of 0.7 and 0.9, internal friction coefficient values of 0.3 and 0.6 and wall friction coefficient values of 0 and 0.3. The internal and wall friction coefficients are important in determining the initiation of particle movement, while the value of the restitution coefficient has a larger influence on particles in a dynamic state. The simulation of the fully elastic case (coefficient of restitution =1.0) with zero internal and wall friction, gives results that are very different from the experiment data.     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

Heat transfer study in a pilot-plant scale bubble column

The effects of superficial gas velocity on heat transfer coefficient and its time-averaged radial profiles along the bed height have been investigated in a pilot-plant scale bubble column of 0.44 m diameter using air-water system. Notable differences were observed in heat transfer coefficients along the bed axial locations particularly between the sparger (Z/D = 0.28) and the fully developed flow (Z/D = 4.8) regions. In the fully developed flow region larger heat transfer coefficient values were obtained compared to those in the sparger region. About 14-22% increase in heat transfer coefficients measured in the fully developed flow region has been observed compared to those measured in the distributor region when the superficial gas velocity increases from 0.05 to 0.45 m/s. The heat transfer coefficients in the column center for all the conditions studied are about 9-13% larger than those near the wall region. It has been noted that in the fully developed flow region, the axial variation of the heat transfer coefficients was not significant.     

Favorable vibrated fluidization conditions for cohesive fine particles

The present study was performed to clarify the operational range for vibro-fluidization of fine cohesive particles (glass beads, d_p = 6 μm). Decreasing and increasing gas velocity methods were examined to clarify the favorable vibro-fluidization region. The upper limit of the gas velocity for intermittent channel breakage was higher in the case of the increasing gas velocity method than the decreasing gas velocity method. This was because the changes in the bed flow pattern from a favorable (intermittent channel breakage) to an unfavorable fluidization state (stable channels) were moderate in the case of the increasing gas velocity method. In the increasing gas velocity method, two kinds of cross-points were obtained from the relationship between the gas velocity and the bed pressure drop. At one of the gas velocities at these cross-points, the bed void fraction reached its maximum. In the present study, the above-mentioned gas velocity was defined as the upper limit of gas velocity for favorable vibro-fluidization, u_chu. A favorable vibro-fluidization region was determined by combining u_chu with u_chl, which is the lower limit of gas velocity for intermittent channel breakage obtained in a previous study. The value of u_chu was found to have a maximum corresponding to a certain vibration strength.     

The nature of the flow just above the perforated plate distributor of a gas-fluidised bed, as imaged using magnetic resonance

Flow patterns within a 3D bed of oil-containing seeds fluidised by nitrogen have been observed for the first time using magnetic resonance imaging (MRI). Attention was focused on the lower region of the bed, just above the multi-orifice distributor: the orifices were 1.0 or 1.5 mm in diameter with square or triangular layouts, of pitch 7-10 mm. Two sizes of seeds were used: 1.2 and 0.50 mm. Each MRI image was a time-average over and measured the local concentration of seeds. Values of U/U_mf were in the range 0.0-3.6, where U is the superficial gas velocity and U=U_mf at incipient fluidisation. The images revealed:

(1)

There was a substantial ‘jet’ above each orifice in the distributor, remarkably these ‘jets’ were found even when U?U_mf. The length of a ‘jet’ increased with U/U_mf. Because of the time-averaged nature of the measurements, a ‘jet’ could be: (a) a permanent void, (b) a stream of bubbles, or (c) a ‘jet’ followed by bubbles.

(2)

When U/U_mf<1.0, the particles surrounding each ‘jet’ were in motion. This was apparent, particularly as U/U_mf approached 1.0, even though the bed was not fully fluidised at all points.

(3)

When U/U_mf>1.0, the upper parts of the ‘jets’ merged with each other forming a central dilute core. For the first time, a time-averaged velocity map over a horizontal plane was obtained; it demonstrated that the central core was rising upwards and that the surrounding material was descending.

(4)

Between each pair of ‘jets’, there was a small region of motionless particles sitting on the upper surface of the distributor, forming a fixed dead zone. A criterion for the maximum pitch of the orifices, to minimise the volume of this dead zone between pairs of ‘jets’, has been derived.

Simple correlations between dimensionless groups summarise the measurements well, giving the length and half angle of a ‘jet’ in terms of the gas velocity and other variables. These correlations are consistent with published results and include a dependence on the pitch of the orifices, which was found to be important.