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.     

Origin of pressure fluctuations in fluidized beds

The present paper shows a novel approach in interpreting the standard deviation of pressure fluctuations in a fluidized bed with respect to the spectral analysis. Based on several realistic assumptions for a freely bubbling bed, the physical model was proposed for the standard deviation of incoherent part of pressure fluctuations. Using the concept of energy dissipated in a fluidized bed the plausible explanation of linear dependence of standard deviation calculated from the total pressure signal on the excess gas velocity was given and verified experimentally.     

Comparison of decoupling methods for analyzing pressure fluctuations in gas‐fluidized beds

Two methods of decoupling pressure fluctuations in fluidized beds by using the incoherent part (IOP) of absolute pressure (AP) and differential pressure (DP) fluctuations are evaluated in this study. Analysis is conducted first to demonstrate their similarities, differences, and drawbacks. Then, amplitudes, power spectral densities, mean frequencies, coherence functions, and filtering indices of the IOP of AP and DP fluctuations are calculated and compared based on experimental data from a two‐dimensional fluidized column of FCC particles. Derived bubble sizes are also compared with the sizes of bubbles viewed in the two‐dimensional bed. The results demonstrate the similarity of these two methods in filtering out global compression wave components from absolute pressure fluctuations, especially those generated from oscillations of fluidized particles and gas flow rate fluctuations. However, both methods are imperfect. Neither can filter out all the compression wave components and retain all the useful bubble‐related wave components. Their amplitudes can be used to characterize global bubble property and quality of gas–solids contacting in bed, but they do not give accurate measurement of bubble sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Characterization of dynamic behaviour of the continuous phase in liquid fluidized bed

The dynamic behaviour of the continuous phase in liquid solid fluidized bed is characterized through velocity measurements by laser anemometry at the top of the bed. The experiments were conducted using glass particles of 2, 4 and 8 mm diameter fluidized by water. The root mean square (RMS) of axial velocity fluctuations presents a maximum value at porosity around 0.7 and increases with particle diameter. When compared to the fixed bed situation, we observe an enhancement of the agitation probably due to the added mass effect which plays the role of a turbulence promoter. The spectra analysis of the velocity time series has revealed a specific spectral dynamic of liquid fluidized bed for the higher frequency range which does neither follow strictly the Kolmogorov law nor a Brownian process power law. A time frequency-scale decomposition combined to an autocorrelation analysis of velocity signal was pertinent to capture the impact of porosity waves and cooperative movements of particles on the liquid phase dynamic, and to characterize these coherent structures by low frequency scales (below 1 Hz). The results compare well with the available data obtained directly from void propagation studies by light transmission techniques. Moreover, the high frequency scales have been found random and linked to the small scale movements of the particles. We have shown, when possible, the similarity of behaviour between the liquid and the dispersed phase dynamics through the comparison of some characteristics.     

The voidage function and effective drag force for fluidized beds

Here, an experimental investigation on the effective drag force in a conventional fluidized bed is presented. Two beds of different particle size distribution belonging to group B and group B/D powders were fluidized in air in a diameter column. The drag force on a particle has been calculated based on the measurement of particle velocity and concentration during pulse gas tests, using twin-plane electrical capacitance tomography. The validity of the voidage function “correction function”, (1−ε_s)ⁿ, for the reliable estimation of the effective drag force has been investigated. The parameter n shows substantial dependence on the relative particle Reynolds number , and the spatial variation of the effective static and hydrodynamic forces. It is also illustrated that, a simple correlation for the effective drag coefficient as function of the particle Reynolds number (Re_p), expressed implicitly in terms of the interstitial gas velocity, can serve in estimating the effective drag force in a real fluidization process. Analysis shows that, the calculated drag force is comparable to the particle weight, which enables a better understanding of the particle dynamics, and the degree of spatial segregation in a multi-sized particle bed mixture. The analogy presented in this paper could be extended to obtain a generalized correlation for the effective drag coefficient in a fluidized bed in terms of Re_p and the particle physical properties.     

CFD modeling of solid-liquid fluidized beds of mono and binary particle mixtures

CFD simulation of bed expansion of mono size solid-liquid fluidized beds has been performed in creeping, transition and turbulent flow regimes, where Reynolds number (Re_∞=d_pV_S∞ρ_L/μ_L) has been varied from 0.138 to 1718. It has been observed that the predicted values of bed voidage using the drag law of Joshi [1983. Solid-liquid fluidized beds: some design aspects. Chemical Engineering Research and Design 61, 143-161] and Pandit and Joshi [1998. Pressure drop in packed, expanded and fluidized beds, packed columns and static mixers—a unified approach. Reviews in Chemical Engineering 14, 321-371] (which has been derived from the first principals), exhibited an excellent agreement with the Richardson and Zaki equation. CFD simulations have also been performed for the prediction of segregation and/or intermixing of binary particle systems having the ratio of terminal settling velocity over a range from 3.2 to 1.06. The Reynolds number has also been varied over the range of 0.33 to 2080. It has been observed that the present CFD model explains all the qualitative and quantitative observations reported in the published literature (complete segregation, partial segregation, complete intermixing, etc) and these predictions are in good agreement with the experimental results. The present CFD model also predicts successfully the layer inversion phenomena which occur in the binary particle mixtures of different size as well as density. Further, the critical velocity at which the complete mixing of the two particle species occurs has also been predicted.     

Parametric modelling of time series of pressure fluctuations in gas-solid fluidized beds

Applying parametric models on time series of pressure fluctuations recorded in a fluidized bed, this paper shows that the bed dynamics can be expressed in analogy with a mechanical system of a certain degree. Thus, the pressure signal is assumed to be an output of a linear time-invariant system driven by a forcing function. The forcing function represents a number of apparently random events (e.g. formation of bubbles at the air-distributor, bubble eruptions at the surface of the bed) and may thereby be approximated as white noise. Parametric models are advocated for characterization of the dynamics of fluidized beds when, for various reasons, long data records are not available or when the quality of the recorded signal is poor. An autoregressive model (AR) of the time series is proposed, and it is shown that the order of the model identifies a mechanical equivalent of certain fluidization behaviour. The model is applied to four fluidization time series, previously investigated. The result indicates that fluidized beds behave like single second-order systems or multiple higher-order mechanical systems acting in parallel. Parametric methods are also used for estimation of power spectra of pressure fluctuations. The information obtained is presented in the form of Bode plots to accentuate the behaviour of fluidized beds as linear dynamical systems. The results are compared with the corresponding information obtained by nonparametric methods, now predominantly used. Data requirements (number of samples, sampling frequency) for the use of parametric models are discussed.     

Monitoring of fluidized beds hydrodynamics using recurrence quantification analysis

A new method is presented for on‐line monitoring of fluidized beds hydrodynamics using pressure fluctuations signal by recurrence quantification analysis. The experiments were carried out at different gas velocities and sand types. A 95% confidence interval was computed for determinism (Det) of signals obtained from reference state as well as other operating conditions named as unideal states. Det of unideal states was compared with Det of the reference state to reject the null hypothesis that all the signals have been generated from the reference state. It was shown that Det is sensitive to small change in particles size whereas it is not sensitive to minor superficial gas velocity variations, indicating its ability for hydrodynamic on‐line monitoring. Furthermore, in this method it is no need for time series embedding, long‐term data sampling and time‐consuming numerical algorithms. © 2012 American Institute of Chemical Engineers AIChE J, 59: 399–406, 2013     

Prediction of single particle settling velocities through liquid fluidized beds

Single particle settling velocities through water fluidized beds of mono-sized glass spheres (d_p = 0.645, 1.20, 1.94, 2.98 and 5 mm in diameter) were studied experimentally using a column, 40 mm in diameter. The settling spherical particles (D_p = 10 and 19.5 mm) had different densities (1237 to 8320 kg/m³), while the settling particles (D_p = 5 and 2.98 mm) were glass spheres. The pseudo-fluid model, which considers a liquid fluidized bed as a homogenous pseudo-fluid, predicts single particle settling velocities quite well if the ratio D_p/d_p is larger than about 10. With decreasing ratio D_p/d_p, the overall friction between the settling particle and the fluidized media increases. A method for predicting single particle settling velocities through a liquid fluidized bed is proposed and discussed. Following the approach of Van der Wielen et al. [L.A.M. Van der Wielen, M.H.H Van Dam, K.C.A.M. Van Luyben, On the relative motion of a particle in a swarm of different particles, Chem. Eng. Sci. 51 (2006) 995-1008], the overall friction is decomposed into a particle-fluid and a particle-particle component. The effective buoyancy force is calculated using the transition function proposed by Ruzicka [M.C. Ruzicka, On buoyancy in dispersion, Chem. Eng. Sci. 61 (2006) 2437-2446]. A simple model for predicting the collision force is proposed, as well as a correlation for the collision coefficient. The mean absolute deviation between the experimental and calculated slip velocities was 5.08%.     

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.     

Layer inversion and mixing of binary solids in two- and three-phase fluidized beds

Water fluidization in a 210 mm diameter semi-cylindrical acrylic column of a binary solids mixture of 3.2 mm polymer beads (ρ_s=1280 kg/m³) and 0.385 mm glass beads (ρ_s=2500 kg/m³) at superficial liquid velocities from 18.1 to 43.1 mm/s is shown to generate layer inversion at a superficial liquid velocity, U_L, of 33.1 mm/s. Introduction of air with a superficial velocity, U_g, of 1.92 mm/s yielded a layer inversion velocity at U_L=30.4 mm/s. The latter is explainable if it is assumed that the determinant of layer inversion is the interstitial liquid velocity and that therefore the main function of the gas in this respect is to occupy space.Mixing of the binary solids, as quantified by a mixing index applied to measured particle compositions at different levels of the fluidized bed, is shown to be greatest at the layer inversion velocity for liquid fluidization and, in general, to increase as co-current gas flow increases at a fixed value of U_L.     

Prediction of critical fluidization velocity and maximum bed pressure drop for binary mixture of regular particles in gas–solid tapered fluidized beds

The problems associated with conventional (cylindrical) fluidized beds, viz., fluidization of wider size range of particles, entrainment of particles and limitation of fluidization velocity could be overcome by using tapered fluidized beds. Limited work has been carried out to study the hydrodynamics of single materials with uniform size particles in tapered beds. In the present work, an attempt has been made to study the hydrodynamic characteristics of binary mixtures of homogeneous and heterogeneous regular particles (glass bead and sago) in tapered fluidized beds having different tapered angles. Correlations have been developed for critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds for binary mixtures of regular particles. Model predictions were compared with experimental data, which were in good agreement.     

Improved magnetic particle tracking technique in dense gas fluidized beds

Noninvasive monitoring of multiphase flow is rapidly gaining increased interest. More specifically noninvasive particle tracking techniques have received a lot of attention in recent years to study dense granular flow. However, these techniques are usually quite expensive and require strict safety measures. An improved magnetic particle tracking (MPT) technique for dense granular flow will be presented in this article. The improvements of the analysis technique for MPT will be demonstrated and rigorously tested with a three‐dimensional system and two‐dimensional sensor system. The strengths and limitations of the MPT technique will also be reported. Finally, the results of the MPT are compared with data obtained from a combined particle image velocimetry and digital image analysis technique. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3133–3142, 2014     

Correlations for critical fluidization velocity and maximum bed pressure drop for heterogeneous binary mixture of irregular particles in gas–solid tapered fluidized beds

The tapered fluidized bed is a remedial measure for certain drawbacks of the gas–solid system, by the fact that a velocity gradient exists along the axial direction of the bed with increase in cross-sectional area. To study the dynamic characteristics of heterogeneous binary mixture of irregular particles, several experiments have been carried out with varying tapered angles and composition of the mixtures with various particles. The tapered angle of the bed has been found to affect the characteristics of the bed. Models based on dimensional analysis have been proposed to predict the critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds. Experimental values of critical fluidization velocity and maximum bed pressure drop compare well with that predicted by the proposed models and the average absolute errors are well within 15%.     

液速陡变时液固流化床中颗粒浓度的变化模型

在液速陡变时,分别考察了铅直管液固流化床内粒径为225 μm和511 μm的玻璃微珠的体积分数分布随时间变化的规律,发现大小颗粒在不同的液速变化幅度下都呈现出同样的体积分数变化趋势.联立颗粒速度和颗粒的连续方程式模拟颗粒的体积分数变化过程,建立了一个相对简单的颗粒体积分数变化的数学模型.在模型中,用定常状态的空隙率方程...     

Non‐intrusive characterization of particle size changes in fluidized beds using recurrence plots

An on‐line method is developed for monitoring of mean particle size in fluidized beds using pressure fluctuations (PFs) and acoustic emissions (AE) signal by recurrence plot (RP) and recurrence quantification analysis (RQA). PFs and AE signals of a lab‐scale fluidized bed were measured simultaneously at various superficial gas velocities and mean particle sizes. Although the AE signals are often very complicated due to many different acoustic sources in the bed, applying RP analyses showed that small changes in mean particle size can be detected by visual comparison of AE‐RP structures, while this cannot be distinguished by graphical RP analysis of PFs. Moreover, the hydrodynamics of the bed was inspected through RQA analysis of both signals. For this purpose, recurrence rate, determinism, laminarity, average length of diagonal and vertical lines were extracted from RPs showing the effect of an increase in the mean particle size. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3547–3561, 2016     

CFD modelling of liquid fluidized beds in slugging mode

Computational Fluid Dynamics (CFD) modelling has been used to simulate a liquid fluidized bed of lead shot in slugging mode. Simulations have been performed using a commercial code, CFX4.4. The kinetic model for granular flow, which is already available in CFX, has been used during this study. 2D time-dependent simulations have been carried out at different water velocities. Simulated aspects of fluidization such as voidage profiles, slug formation, pressure drop and pressure fluctuations have been analysed. The fluid-bed pressure drop was found to be greater than the theoretical one at all velocities, in agreement with experimental observations reported for fully slugging fluidized beds. Power spectral density analysis of the pressure signal was used to investigate the development of the flow pattern and the structure of the fluid-bed with increasing fluidizing velocity. A comparison between experimental and simulated results is also reported.     

On the relationship between operating pressure and granular temperature: A discrete particle simulation study

Low density polyethylene and polypropylene are produced at large scale via the UNIPOL™ and SPHERIPOL™ process. In this process catalyst particles are fluidized with monomer gas that reacts with the catalyst particles to form polymeric particles up to a size of 1 mm. The process is typically operated at pressures of 20 to 25 bar. Pressure impacts the hydrodynamics of the fluidized bed as it influences the bubble behaviour, particle mixing and heat transfer characteristics. Despite decades of research on fluidized beds these effects are not completely understood.In order to gain more insight in the effects of operating pressure on the fluidization behaviour we have performed full 3D discrete particle simulations. We used a state-of-the-art discrete particle model (DPM) to simulate fluidization behaviour at different pressures. In our model the gas phase is described by the volume-averaged Navier-Stokes equations, whereas the particles are described by the Newtonian equations of motion. The DPM accurately accounts for the gas-particle interaction, which is necessary for capturing the pressure effect.In order to study the pressure effect on the granular temperature, we analysed seven simulations with operating pressures ranging from 1 to 64 bar. It was found that the granular temperature increases with pressure. This is mostly caused by the increased porosity at elevated operating pressures. The granular temperature is anisotropic: it is larger in the vertical direction. Also the pressure dependency of the granular temperature is larger in the vertical direction.     

Critical fluidization velocities and maximum bed pressure drops of homogeneous binary mixture of irregular particles in gas-solid tapered fluidized beds

Recently, tapered fluidized bed has become more attractive because of the problems associated with conventional (cylindrical) beds like fluidization of widely distributed particles, entrainment of particles and limitation of fluidization velocity. There have been some investigations on hydrodynamics of uniform single size particles but there have been no detailed studies of homogeneous binary mixture of particles of different sizes and different particles in tapered beds. In the present work, an attempt has been made to study the hydrodynamic characteristics of homogeneous binary mixture of irregular particles in tapered beds having different tapered angles. Correlations have been developed for important characteristics, especially critical fluidization velocities and maximum bed pressure drops of homogeneous binary mixture of irregular particles in gas-solid tapered fluidized beds. Experimental values of critical fluidization velocities and maximum bed pressure drops have been compared with the developed correlations.     

Granular and gas-particle flows in a channel with a bidisperse particle mixture

Steady state solutions of granular and gas-particle flows in a channel with a bimodal particle mixture have been computed using kinetic theory. For granular channel flows we find granular energy equipartition breaks down with an increase in the system inelasticity and the mass ratio of particles. The effect of the particle size ratio on breakdown of energy equipartition is very small if the two particle species have the same mass. The species segregation in the solid phase is enhanced with a decrease in the system inelasticity, an increase in the average solid fraction or an increase in the size ratio, due to the competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force, and the pressure diffusion force. In addition, we find a competition mechanism exists in the equal density case (particles with equal density but different sizes) since in the equal mass case (particles with equal mass but different sizes) small particles have a higher concentration in low granular energy regions, whereas in the equal size case (particles with equal size but different masses) heavy particles have a higher concentration in low granular energy regions. These findings are in agreement with the results for granular Couette flows. For equal density particles, the segregation of large particles has a transition from the walls to the center when the restitution coefficient (e_p) decreases from 1 to 0.99. This sensitivity is reduced when the system becomes more inelastic. For a given monodisperse granular system, we show that if larger particles are mixed in the system the sensitivity of the total solid distribution to the restitution coefficient is suppressed, while if smaller particles are added in the system the situation reverses. Lastly, we extend our work to gas-particle flows in a channel where particles are fluidized by gas flowing upwards, and find that for the kinetic theory models used in the present study, the solid fraction, the species segregation and the granular energy profiles are quite similar between the granular flows and the gas-particle flows.