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.     

Prediction of pressure fluctuations and minimum fluidization velocity of binary mixtures of geldart group b particles in bubbling fluidized beds

A simple method was proposed to find the pressure fluctuations of binary systems of Geldart Group B particles under bubbling fluidized bed conditions. The pressure fluctuations of binary systems could be predicted from the pressure fluctuations of the individual particles component which comprised the binary systems for completely mixed and partially mixed systems. The predicted pressure fluctuations could be used to calculate the minimum fluidization velocity of the binary systems. The predicted and experimental values of pressure fluctuations and the minimum fluidization velocity of binary systems were in fairly good agreement.     

Pressure and voidage fluctuations in slugging fluidized beds

In fully developed slugging fluidized beds, the maximum amplitude of absolute pressure fluctuations is reached with increasing superficial gas velocity when the slug length reaches a maximum, and the separation distance between successive slugs starts to decrease. U_c, the superficial gas velocity at which absolute pressure fluctuations reach a maximum, thus indicates the early stage of transition from slugging to core-annular flow. U_c, identified based on standard deviations of differential pressure fluctuations or local voidage fluctuations, can be predicted by slug flow models and does not signify a transition to turbulent fluidization.     

Characterization of gas fluidized beds of group C,A and B particles based on pressure fluctuations

Pressure fluctuation data were obtained with a quick response transducer at a sampling frequency of 100 Hz for periods of 100 s (i.e. 10,000 points) in order to characterize the gas-solid flow behaviour of fluidized beds of six powders. For beds of Geldart group B and group A particles, the occurrence and movement of bubbles caused vigourous pressure fluctuations of relatively large scale and weak dominant frequency. For beds of group C particles, on the other hand, pressure fluctuations were significantly smaller in scale and exhibited large dominant frequencies, with no clear formation of bubbles. The standard deviation of pressure fluctuations was markedly higher for the group A particles than for the group C powders. Group C particles could be characterized by gas voids and channels which exhibit periodic behavior, while beds of group A and B particles behaved in a less periodic manner and were dominated by more random and intensive bubble motion. Chaotic time series analysis was carried out for the six different species of particles. The Hurst exponent demonstrated differences between the three different powder groups. The two-phase character of gas-solids flow was more distinguishable for the group B and A powders than for the group C powders.     

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.     

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.     

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.     

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%.     

On trajectory and velocity measurements in fluidized beds using positron emission particle tracking (PEPT)

Positron emission particle tracking (PEPT) is a non-invasive technique that can be used for following the trajectories of particles in fluidized beds, so increasing understanding of solids motion in fluidized bed processes. We describe how PEPT is applied, how its performance is optimized, and how trajectory information can be built up into instantaneous and time-averaged measures of particle movement. Choices and pitfalls in data processing are explained and illustrated by reference to the travelling fluidized bed (TFB) collaboration initiated by Professor John Grace.     

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...