Determination and comparison of rotational velocity in a pseudo 2‐D fluidized bed using magnetic particle tracking and discrete particle modeling

Modeling of dense granular flow has been subject to a large amount of research. Particularly discrete particle modeling has been of great importance because of the ability to describe the strongly coupled dynamics of the fluid and the solids in dense suspensions. Many studies have been reported on the validation of the translational particle velocities predicted by using these models. The rotational motion however has received far less attention, mainly because of the spherical nature of the particles under investigation and the lack of techniques with the capability to study the rotational behavior of the solid phase. In this study, we will for the first time present experimental data on the rotational behavior of particles in a pseudo two‐dimensional fluidized bed setup using Magnetic Particle Tracking. In addition the experimental results are compared to data obtained from discrete particle simulations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3198–3207, 2015     

Numerical and experimental study on multiple-spout fluidized beds

In this paper we study the effect of multiple spouts on the bed dynamics in a pseudo-2D triple-spout fluidized bed, employing the discrete particle model (DPM) and non-intrusive measurement techniques such as particle image velocimetry (PIV) and positron emission particle tracking (PEPT). A flow regime map was constructed, revealing new regimes that were not reported so far. The multiple-interacting-spouts regime (C) has been studied in detail for a double- and triple-spout fluidized bed, where the corresponding fluidization regime for a single-spout fluidized bed has been studied as a reference case. The experimental results obtained with PIV and PEPT agree very well for all the three cases, showing the good performance of these techniques. The DPM simulation results slightly deviate from the experiments which is attributed to particle–wall effects that are more dominant in pseudo-2D beds than in 3D systems. The investigated multiple-interacting-spouts regime is a fully new flow regime that does not appear in single-spout fluidized beds. Two flow patterns have been observed, viz. particle circulation in between the spouts near the bottom of the bed, and an apparent single-spout fluidization motion at a higher location upwards in the bed. These findings show that the presence of multiple spouts in a spout fluidized bed highly affect the flow behaviour, which cannot be distinguished by solely investigating single-spout fluidized beds.     

Experimental data for code validation: Horizontal air jets in a semicircular fluidized bed of Geldart Group D particles

Experiments were conducted with 6 mm plastic beads (Geldart Group D) in a semi‐circular, gas‐fluidized bed with side jets. Attention was paid to particle characterization and bed measurements, making the resulting dataset ideal for CFD‐DEM validation and uncertainty quantification. The bed was operated slightly above and below the minimum fluidization velocity, with additional fluidization provided by one of two pairs of opposing jets located above the distributor near the flat, front face of the unit. Care is taken to report material properties and bed conditions with either measured distribution functions or uncertainty bounds. High‐speed video imaging and particle tracking velocimetry are used to extract bin‐averaged velocity profiles, which are used to extract jet penetration depths. The time‐averaged mean and standard deviation of the bed pressure drop is also reported. Finally, the lower jets are also inserted into the bed until the opposing jets merge to form a spout‐like pattern. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2351–2363, 2018     

Initial particle velocity spatial distribution from 2-D erupting bubbles in fluidized beds

Some results on particle image velocimetry (PIV) in 2-D freely bubbling fluidized beds are presented. The PIV applications were used in order to determine the initial particle velocity of bubble eruptions. A two-dimensional non-reacting fluidized bed was constructed to measure the origin of the ejected particles and the initial particle velocity distribution, using coarse sand particles. The bubble ejection mechanism was observed taking into account the origin of particles ejected, the initial particle velocity distributions as well as the effect of other neighbor exploding bubbles. Our results show that the assumption of linear dependence of initial velocity with the angle predicts the velocity faithfully only for purely vertical-ascent bubbles. Measurements of ejection velocities show that initial velocities in the combined layer are higher than those of the particles in the nose of the leading bubble. Avoiding coalescence of bubbles at the bed surface can lead to less particle entrainment out of the bed and consequently to shorter fluidized beds.     

Experimental study on solid circulation in a multiple jet fluidized bed

Particle image velocimetry was used to investigate the evolution of multiple inlet gas jets located at the distributor base of a two‐dimensional fluidized bed setup. Results were used to estimate the solid circulation rate of the fluidized bed as well as particle‐entrainment into the individual jets. The effects of fluidization velocity, orifice diameter, orifice pitch, particle diameter, and particle density were studied. It was determined from this study that the solid circulation rate linearly increased with an increase in the fluidization velocity until the multiple jet system transitioned from isolated to an interacting system. In the interacting system of jets, the solid circulation increased with fluidization velocity but at a much lower rate. For multiple jet systems, this phenomenon may indicate the presence of an optimum operating condition with high circulation rate and low air input in the bed. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3003–3015, 2012     

Analysis and modeling of particle-wall contact time in gas fluidized beds

Although extensive studies have been conducted on convective heat transfer from a heat exchanger surface to a gas fluidized bed, the contribution through particle convection has not been adequately described, especially in turbulent fluidized beds. In this study, the role that dense bed hydrodynamics play on particle convection has been outlined. The existing models in the literature suggest a constant decrease of particle-wall contact time with an increase in the gas velocity. It has been experimentally demonstrated, however, that the contact time increases, both in bubbling and turbulent regimes, upon increasing the gas velocity. A comprehensive model has been developed to represent such a trend and improve agreement with experimental data presented in literature. The proposed model includes two constants for taking into account the wall effect on bubbles and clusters. The constants of the model have been evaluated based on the radial profiles of the distribution of bubbles and clusters using a radioactive particle tracking technique. A comparison of the predicted results with the experimental data from the literature confirms the validity of the present model for the dense bed region of a fluidized bed of sand particles.     

Pressure drop and gas bypassing in recirculating fluidized beds

The effect of different operating and design parameters on the pressure drop profile for a recirculating fluidized bed has been studied. A mathematical model was developed for the pressure drop in the recirculating fluidized bed. The different parameters considered were flow rate, inventory of solids and spacing between the draft-tube bottom and the distribution plate. Geldart D and B particles were used for the study. The gas bypassing from the jet towards the downcomer was calculated on the basis of the mathematical model and the effect of various parameters on gas bypassing were analyzed.     

A multiple radioactive particle tracking technique to investigate particulate flows

Radioactive particle tracking is a nonintrusive technique that has been successfully used to study the flow dynamics in a wide range of reactors and blenders. However, it is still limited to the tracking of only one tracer at a time. A multiple radioactive particle tracking (MRPT) technique that can determine the trajectory of two free or restricted (attached to the same particle) moving tracers in a system is introduced. The accuracy (<5 mm) and precision (<5 mm) of the proposed technique is evaluated by tracking two stationary tracers and two moving tracers. The results confirm the reliability and validity of the MRPT technique when the two tracers have the same isotope and the distance between them is not too small (>2 cm). The tracking of two sticking tracers at the two ends of a cylindrical particle in a rotating drum is also considered to illustrate the potential of this characterization method. © 2014 American Institute of Chemical Engineers AIChE J, 61: 384–394, 2015     

Granular pressure and particle velocity fluctuations prediction in liquid fluidized beds

A numerical modelling approach for the dynamic simulation of solid-liquid fluidized beds is evaluated. This approach is based on an Eulerian two-fluid formulation of the transport equations for mass, momentum and fluctuating kinetic energy. The solid-phase fluctuating motion model is derived in the frame of granular medium kinetic theory accounting for the viscous drag influence of the interstitial liquid phase. Solid-liquid fluidized bed two-dimensional simulations were performed for flow configurations taken from the experimental work of Zenit et al. [1997. Collisional particle pressure measurements in solid-liquid flows. Journal of Fluid Mechanics 353, 261-283], for three types of solid particles of contrasted inertia in water at high particle Reynolds number (nylon, glass and steel beads). Experimental and numerical granular pressures exhibit a satisfactory agreement with both low and high inertia particles, the best level of prediction being observed with the most inertial particles. Sensitivity of the predictions to the phenomenological laws used in the model is also presented and it appears that, due to non-linear correlations, the average granular pressure in the bed is a less sensitive variable than the fluctuating kinetic energy (or granular temperature). The transport mechanisms of the mean granular temperature in the bed are therefore analyzed as a function of the solid fraction and the particle inertia. At low and moderate Stokes number (nylon and glass beads) and in all range of solid-phase fraction, the dominant production mechanism of fluctuating kinetic energy is due to the mean velocity gradient, whereas the main dissipation term is that induced by the viscous drag. At higher Stokes number (steel beads) and concentration, the production of the granular temperature is controlled by the compressibility effects via the granular pressure. In this case, the dissipation is mainly provided by inter-particle collisions.     

Experimental investigation of particle contact time at the wall of gas fluidized beds

The contact time of particles at the walls of gas fluidized beds has been studied using a radioactive particle tracking technique to monitor the position of a radioactive tracer. The solids used were sand or FCC particles fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. Based on the analysis of tracer positions, the motion of individual particles near the walls of the fluidized bed was studied. The contact time, contact distance and contact frequency of the particles at the wall were evaluated from these experimental data. It was found that in a bed of sand particles, the mean wall contact time of the fluidized bed of sand particles decreases by increasing the gas velocity in the bubbling and increases in the turbulent fluidization. In other words, the particle-wall contact time is minimum at the onset of turbulent fluidization in the bed of sand particles. However, the mean wall contact time is almost constant in both regimes of fluidization in the bed of FCC particles. All the existing models in the literature predict a decreasing contact time when the gas velocity in the bed is increased. It was also shown that the contact distance increases monotonously by increasing the gas velocity in the bed of sand particles, while it is almost constant for the bed of FCC particles. Contact frequency has a trend similar to that of the contact time for both sand and FCC particles.     

Numerical and experimental study on spout elevation in spout‐fluidized beds

The effect of elevating the spout on the dynamics of a spout‐fluidized bed, both numerically and experimentally is studied. The experiments were conducted in a pseudo‐two‐dimensional (2‐D) and a cylindrical three dimensional (3‐D) spout‐fluidized bed, where positron emission particle tracking (PEPT) and particle image velocimetry (PIV) were applied to the pseudo‐2‐D bed, and PEPT and electrical capacitance tomography (ECT) to the cylindrical 3‐D bed. A discrete particle model (DPM) was used to perform full 3‐D simulations of the bed dynamics. Several cases were studied, that is, beds with spout heights of 0, 2, and 4 cm. In the pseudo‐2‐D bed, the spout‐fluidization and jet‐in‐fluidized‐bed regime, were considered first, and it was shown that in the spout–fluidization regime, the expected dead zones appear in the annulus near the bottom of the bed as the spout is elevated. However, in the jet‐in‐fluidized‐bed regime, the circulation pattern of the particles is affected, without the development of stagnant zones. The jet‐in‐fluidized‐bed regime was further investigated, and additionally the experimental results obtained with PIV and PEPT were compared with the DPM simulation results. The experimental results obtained with PIV and PEPT agreed mutually very well, and in addition agreed well wtih the DPM results, although the velocities in the annulus region were slightly over predicted. The latter is probably due to the particle‐wall effects that are more dominant in pseudo‐2‐D systems compared with 3‐D systems. In the jet‐in‐fluidized‐bed regime, the background gas velocity is relatively high, producing bubbles in the annulus that interact with the spout channel. In the case of a non elevated spout, this interaction occurs near the bottom of the bed. As the spout is elevated, this interaction is shifted upwards in the bed, which allows the bubbles to remain undisturbed providing the motion of the particles in the annulus near the bottom of the bed. As a result, no dead zones are created and additionally, circulation patterns are vertically stretched. These findings were also obtained for the cylindrical 3‐D bed; although, the effects were less pronounced. In the cylindrical 3‐D bed the PEPT results show that the effect on the bed dynamics starts at h_spout =1 4 cm, which is confirmed by the ECT results. Additionally, ECT measurements were conducted for h_spout =1 6 cm to verify if indeed the effect happens at larger spout heights. The root mean square of the particle volume fraction slightly increased at h_spout =1 2 cm, whereas a larger increase is found at h_spout = 4 and 6 cm, showing that indeed more bubbles are formed. The presented results have not been reported so far and form valuable input information for improving industrial granulators. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2524–2535, 2012     

A study of solid behavior in spouted beds using 3-D particle tracking

A non-invasive γ-ray emission system, employing eight NaI detectors, has been developed to follow the motion of a single radioactive particle in a three-dimensional spouted bed reactor. The count-rates measured simultaneously by the detectors are converted into tracer coordinates (x, y, z) using a pre-established calibration model which accounts for every physical and geometrical aspects involved in the spouting facility. Typically four hundred thousands successive coordinates, obtained over 3.5 hours of particle tracking, are used for determining the average particle velocity field and other hydrodynamic quantities such as the cycle time distribution, the spout shape and the solid exchange distribution at the spout boundary, which could not be evaluated accurately using any available techniques.     

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.     

Particle tracking velocimetry investigations on density dependent velocity vector profiles of a swirling fluidized bed

Swirling fluidized bed (SFB) is a newer version of the well-known bubbling bed and very little know. An insight study is therefore required for complete understanding of the hydrodynamics of a SFB operation. The current study was conducted on stable regime of a SFB operated at different blade fin angles, blade inclination angles, particle densities and superficial air velocities. Roughly one quarter of the fluidized bed was photographed and its velocity vector field plots were generated using a MATLAB supported particle tracking velocimetry (PTV) technique. At lower superficial velocities, Gaussian distribution of the velocity vectors was predicted along the radius of the bed. Particles in the vicinity of the bed walls moved relatively slower than those marching in the middle of the bed. However, at higher superficial velocities, the particles closer to the cone boundary were moving with velocities comparable to the particles in the middle of the bed. Unlikely, the particles closer to the outer bed wall kept on moving with lower velocities regardless of increasing superficial air velocity. A further look into individual velocity vector profiles revealed negligible influence of smaller blade angles (9° and 12°) on particles’ motion. The overall velocity magnitude decreased by 6% with 3° increase in blade fin angle and by 9% with 5° increase in inclination angle. Contrarily, the particle velocity underwent a monotonic decrease with particle density.     

Scale‐dependent nonequilibrium features in a bubbling fluidized bed

We investigate experimentally the nonequilibrium features in a pseudo 2‐D bubbling fluidized bed. Velocities of individual particles are measured by using a particle tracking velocimetry (PTV) method, and void fractions are obtained with the Voronoi tessellation. A bimodal shape of probability density function (PDF) for particle vertical velocity is found in not only time‐averaged but also time‐varying statistics, which is caused by the transition between the dense and dilute phases and breaks the local‐equilibrium assumption in continuum modeling of fluidized beds. The results of time‐varying radial distribution function and voidage distribution also confirm this finding. Moreover, the analysis of voidage, particle velocity, granular temperature and turbulent kinetic energy of particles shows that there is no scale‐independent plateau over the interface, and it seems hard to find a scale‐independent plateau to separate the micro‐ and meso‐scales of fluidized beds, which require sub‐grid meso‐scale modeling for continuum or coarse‐graining methods of gas‐fluidized systems. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2364–2378, 2018     

Magnetic particle tracking for nonspherical particles in a cylindrical fluidized bed

In granular flow operations, often particles are nonspherical. This has inspired a vast amount of research in understanding the behavior of these particles. Various models are being developed to study the hydrodynamics involving nonspherical particles. Experiments however are often limited to obtain data on the translational motion only. This paper focusses on the unique capability of Magnetic Particle Tracking to track the orientation of a marker in a full 3‐D cylindrical fluidized bed. Stainless steel particles with the same volume and different aspect ratios are fluidized at a range of superficial gas velocities. Spherical and rod‐like particles show distinctly different fluidization behavior. Also, the distribution of angles for rod‐like particles changes with position in the fluidized bed as well as with the superficial velocity. Magnetic Particle Tracking shows its unique capability to study both spatial distribution and orientation of the particles allowing more in‐depth validation of Discrete Particle Models. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 5335–5342, 2017     

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     

Simulation of particle attrition by supersonic gas jets in fluidized beds

Particle breakage by gas jet is encountered in many processes. Quite often it is necessary to evaluate the attrition performance of different equipment configurations at various flow conditions. Therefore, a simulation tool that can be applied for industrial scale devices can be very beneficial for process design and optimization. A mathematical model for particle attrition by high velocity gas jets is developed. The model utilizes an Eulerian–Eulerian approach for the gaseous and particulate phases coupled with the kinetic theory of granular flow and a novel attrition model connecting the solid phase properties and the granular temperature with the breakage rate. Modelling results allow the calculation of the grinding efficiency – a quantitative measure of the attrition performance. For validation purposes, the model is applied to a large number of cases that have been investigated experimentally. Simulation results demonstrate that the increase of the nozzle inlet pressure or the exit diameter for a forward step nozzle produces an increase of the grinding efficiency. In addition, the convergent–divergent nozzle is more efficient in breaking the particles than the nozzle that contains only the convergent section.     

Mixing dynamics in bubbling fluidized beds

Solids mixing affects thermal and concentration gradients in fluidized bed reactors and is, therefore, critical to their performance. Despite substantial effort over the past decades, understanding of solids mixing continues to be lacking because of technical limitations of diagnostics in large pilot and commercial‐scale reactors. This study is focused on investigating mixing dynamics and their dependence on operating conditions using computational fluid dynamics simulations. Toward this end, fine‐grid 3D simulations are conducted for the bubbling fluidization of three distinct Geldart B particles (1.15 mm LLDPE, 0.50 mm glass, and 0.29 mm alumina) at superficial gas velocities U/Umf = 2–4 in a pilot‐scale 50 cm diameter bed. The Two‐Fluid Model (TFM) is employed to describe the solids motion efficiently while bubbles are detected and tracked using MS3DATA. Detailed statistics of the flow‐field in and around bubbles are computed and used to describe bubble‐induced solids micromixing: solids upflow driven in the nose and wake regions while downflow along the bubble walls. Further, within these regions, the hydrodynamics are dependent only on particle and bubble characteristics, and relatively independent of the global operating conditions. Based on this finding, a predictive mechanistic, analytical model is developed which integrates bubble‐induced micromixing contributions over their size and spatial distributions to describe the gross solids circulation within the fluidized bed. Finally, it is shown that solids mixing is affected adversely in the presence of gas bypass, or throughflow, particularly in the fluidization of heavier particles. This is because of inefficient gas solids contacting as 30–50% of the superficial gas flow escapes with 2–3× shorter residence time through the bed. This is one of the first large‐scale studies where both the gas (bubble) and solids motion, and their interaction, are investigated in detail and the developed framework is useful for predicting solids mixing in large‐scale reactors as well as for analyzing mixing dynamics in complex reactive particulate systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4316–4328, 2017