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One of the most crucial steps in the development of fundamental hydrodynamic models is the validation of these models with accurate, detailed experimental data. Therefore a whole-field, non-intrusive digital image analysis technique has been developed which enables measurement of bed expansion and segregation dynamics of coloured particles in dense gas-fluidised beds. The development, calibration and accuracy of the technique are discussed in detail. The image analysis technique traces bubbles and voidage waves accurately, whereas the mixture composition in a fluidised bed could be determined within 10%.Experiments have been carried out with 1.5 and 2.5 mm coloured glass beads, for which particle–particle and particle–wall collision parameters were accurately known. They were performed in pseudo two-dimensional laboratory scale fluidised beds with a simple rectangular geometry and well-defined gas inflow conditions. An extensive set of results obtained with both mono-disperse systems and binary mixtures, suitable for validation of fundamental hydrodynamic models, is presented.

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... The above equation requires closures for the contact forces, the fluid-particle friction coefficient, and the fluid stress. We use a standard linear spring-dashpot model for the contact forces, the model proposed by Beetstra et al. (2010) for the friction coefficient, and a laminar fluid stress model. ...

... Here the diffusion coefficient is computed as D = l smooth ²/t. Note that this smoothing operation is conservative, and has been used in previous work (Capecelatro and Desjardins, 2013;Pirker et al., 2011). ...

... Thus, the characteristic time scale The time step restrictions for integrating the Navier-Stokes equations are summarized in Figure 2 for a freely sedimenting gas-particle suspension. Note that in this figure the particle and fluid relaxation time for dense suspensions at non-zero Reynolds numbers have been computed using the drag model of Beetstra et al. (2010). ...

Euler-Lagrange (EL) simulations are an extremely important tool for academia and industry to better understand gas-particle flows. We present simulation results for various gas-particle flow configurations using a variety of Lagrangian-to-Euler coupling schemes. Specifically, we have combined the idea of smoothing the exchange fields (as proposed by Pirker et al. (2011), as well as Capecelatro and Desjardins (2013)) to design a new generation of robust mapping schemes that allow implicit, explicit or a hybrid implicit/explicit time marching. Our schemes enable EL simulations of highly loaded gas-particle flows in which particles have a broad size distribution. We demonstrate the performance of our mapping schemes for the case of (i) a bubbling bi-disperse fluidized bed, (ii) a freely sedimenting suspension, as well as (iii) particle injection in turbulent cross flow configurations.

... The second category of indices are straightforwardly defined to be or based on various ratios obtained through a statistical analysis of relative information from the mixture (see Table 1). Such ratios include the mass fraction ratio [33][34][35], relative position ratio [36,37], bed height ratio [38,39], particle number ratio [40,41] and contact number ratio [42], etc. Rowe et al. [33] employed a ratio of jetsam mass fraction between the upper part and the whole bed, to describe the mixing state of mixtures in a granular bed. The segregation index used by Xu et al. [34] was a ratio of mass fraction of target particles at a given state to that at the initial state. ...

... Besides, Goldschmidt et al. [38] put forward a segregation index for the description of segregation in fluidized beds, which has incorporated the influence of such parameters as the mass fraction of target small particles and the average bed height ratio between small and large particles. This index was also adopted in the studies of Konan & Huckaby [39]. ...

... In general, the estimation of statistical-ratio-related indices is similar to that for the first type of indices, and it is dependent on the number and size of samples (or subdomains) [33,35,38,40]. The theoretical scope for some indices is beyond the typical range 0-1.0 [34,42]. ...

In present study, we develop a new segregation index having both geometrical and physical significances, on the basis of segregation profile of granular bed. We carry out a DEM simulation to validate this index and analyze the segregation of binary mixture. The DEM analysis reveals that the segregation profile of granular bed subjected to vibration is in general in a reverse “N” mode, which tends to narrow and weaken as vibration continues. At a proper vibration amplitude, the reverse “N” pattern diminishes progressively and the overall segregation profile evolves into a three-line-segment pattern which stands for the ideal state of full segregation. A comparison analysis indicates that the new index proposed in this study is able to give a more proper estimation of segregation phenomenon for binary mixtures, as compared with other indices from the literature.

... In the present study, we vary computational grid refinement in all three dimensions to examine how grid refinement and the pseudo-2D assumption affect accuracy of the simulation results [13] for a fluidized bed. We compare our CFD-DEM simulation results with experimental data published by Goldschmidt et al. [14], for a fluidized bed of binary-sized particles. Bed-height fluctuation frequency, segregation of the fine and coarse particle components, and height fluctuation of the two components are compared with experimental data. ...

... The computational model is designed to represent the pseudo-2D fluidized bed experiment of Goldschmidt et al. [14]. First, a description of the experiment is given, with a listing of all input quantities. ...

... An overview of the computational grids, simulation cases, and postprocessing is also provided. [14] fluidized a binary-sized mixture of particles in a pseudo-2D bed, and reported quantitative data for bed expansion, bed oscillation frequency, and segregation [14]. Input properties for our simulations, including bed dimensions, particle diameters, number of particles, and particle properties, are based on their reported data, as shown in Table 1. ...

Computational fluid dynamics (CFD)-discrete element method (DEM) simulations are designed to model a pseudo-two-dimensional (2D) fluidized bed, in which bed thickness is minimal compared to height and length. Predicted bed behavior varies as the simulations are conducted on increasingly refined computational grids. Pseudo-2D simulation results, in which a single computational cell spans the bed thickness, are compared against fully-three-dimensional (3D) simulations results. Both pseudo-2D and fully-3D simulations exhibit high accuracy when sufficiently refined. Indicators of bed behavior, such as bed height, bed height fluctuation, bubble generation frequency, and segregation, do not appear to converge as the cell size is reduced. The Koch-Hill and Gidaspow drag laws are alternately employed in the simulations, resulting in different trends of results with computational grid refinement. Grid refinement studies are used to quantify the change in results with grid refinement for both three-dimensional, uniform refinement, and for two-dimensional refinement on pseudo-2D computational grids. Grid refinement study results indicate the total drag converges as the computational grid is refined, for both 3D and pseudo-2D approaches. The grid refinement study results are also used to distinguish the relatively grid-independent results using the Koch-Hill drag law from the highly grid-dependent Gidaspow drag law results. Computational cell size has a significant impact on CFD-DEM results for fluidized beds, but the grid refinement study method can be used to quantify the resulting numerical error.

... The rate of segregation was substantiated with the help of the solid hold-up fluctuations. Goldschmidt et al. [14] and Olaofe et al. [15] quantified the segregation and mixing dynamics of binary system differing in size in a pseudo-2D fluidized bed in terms of time-evolution of % segregation, average dispersed bed height of individual solid phases, and bed expansion frequencies obtained through digital image analysis. The effects of several parameters like U G (1.18-1.62 ...

... The effects of several parameters like U G (1.18-1.62 U mf, flotsam ), bed width (W = 15, 30, 57 cm), bed aspect ratio (H b /W = 0.26-2), and bed composition (0.25-0.75 x flotsam ) on segregation rates and bed expansion dynamics were investigated [14,15]. Olaofe et al. [15] attributed the change observed in the segregation behaviour with increase in the bed width to particle-wall frictional and collisional interactions. ...

... Although the segregation and mixing behaviour of binary gas-solids flow differing in size was quantified in terms of time-evolution of % segregation [14,15], the dynamics of binary gas-solids flow differing in density is not reported in the open literature. Further, in order to understand the dynamics of segregation and mixing behaviour, which are primarily influenced by the local bubbling behaviour; it is important to quantify the effects of bubbling behaviour, local bubble-particle interactions on the observed segregation and mixing behaviour. ...

... The extent of segregation depends on the particle properties and operating parameters (gas velocity, volume ratio between particles, etc.). [2,3] A proper understanding of the segregation and mixing behaviour of polydisperse systems is crucial for industrial operation and process optimization. ...

... The segregation and mixing behaviour of binary particles has been extensively investigated through various experiments. [1][2][3][4][5][6][7][8] It is commonly observed that heavier and larger particles (jetsam) tend to accumulate at the bottom of the bed, while the lighter and smaller particles (flotsam) accumulate in the upper part of the bed. [1,5] The extent of segregation is increased with a lower gas velocity, [2,5] a closer mass ratio of the jetsam and flotsam phases, [1,3] and a larger difference in the size and density of the solid phases (density being more important). ...

... [1][2][3][4][5][6][7][8] It is commonly observed that heavier and larger particles (jetsam) tend to accumulate at the bottom of the bed, while the lighter and smaller particles (flotsam) accumulate in the upper part of the bed. [1,5] The extent of segregation is increased with a lower gas velocity, [2,5] a closer mass ratio of the jetsam and flotsam phases, [1,3] and a larger difference in the size and density of the solid phases (density being more important). [5] In recent years, computational fluid dynamics (CFD) has emerged as a powerful tool to improve our understanding of segregation and mixing behaviour in polydisperse systems. ...

The mixing and segregation behaviour of binary solid mixtures has been extensively studied through various experiments, while accurate CFD simulations are difficult to achieve due to process complexity and a lack of reliable constitutive relations. In this study, CFD simulations of a dense fluidized bed with glass and polystyrene particles were performed in order to identify a universal set of simulation parameters and models for simulating binary mixtures with different mixed and segregation behaviour. Through a comparison to experimental data, it was found that the EMMS drag model coupled with the Ma‐Ahmadi solid pressure and radial distribution models predicted more a reasonable axial distribution of solid phases than the Syamlal O´Brien drag model coupled with the Lun et al. solid pressure and radial distribution models. The increase in the solid‐solid drag further improved the simulation results.
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... T he behaviours of mixing and segregation are generally found in fluidized beds, such as mineral processing, [6,7] particles combustion, [8] and thermochemical reaction. [9] To explore the segregation and mixing process of particles, many experimental studies have been conducted; for example, the effects of size and density ratio, [10][11][12][13] gas velocity, [1,[14][15][16][17] particles shape, [18] and nozzle diameter on mixing and segregation have been studied. [19] In addition to these experiments, computational fluid dynamics (CFD) models, including the discrete particle method (DPM) and the Eulerian-Eulerian method have been widely used to test various drag models and study the motion of different particles in fluidized beds. ...

... Besides height index V p,t to calculate the extent of particle segregation, another segregation index introduced by Goldschmidt et al. [14] in the binary particles system was adopted. One segregation index described the degree of segregation of small particles with respect to both large and medium size particles as follows: . ...

The dense gas‐solid fluidized beds with polydisperse particles are commonly encountered in the chemical industry. In this study CFD‐DEM simulation of ternary particles in a bubbling fluidized bed were studied to assess four polydisperse drag correlations, using experimental data from Olaofe et al.¹ as the benchmark. The following was shown: (i) the drag force models of Sakar et al.,² Cello et al.,³ and Rong et al.⁴ can correctly predict the minimum fluidization velocity of the mixture of ternary particles, but Gidaspow's model significantly over‐predicts this;⁵ (ii) no model can accurately predict the experimental segregation degree at different gas velocity, but for the cases that were studied, the models from Cello et al. and Sakar et al. correlated relatively better with Olaofe et al.'s¹ experimental data than others; and (iii) detailed force analysis found that the collisional force of each type of particles is on average not equal to zero, especially for a system that is strongly segregated. In addition, the differences of drag force for different sizes of particles are the key reason for size segregation rather than pressure gradient force. This article is protected by copyright. All rights reserved

... Goldschmidt et al. 1 and Olaofe et al. 2 used a digital imaging technique for the estimation of percentage segregation using measurements of dispersed heights of individual solid phases in a binary gas-solids flows with varying size in a pseudo-2D bed. It was seen that the percentage segregation decreased with the increase in the fraction of smaller particles, initial bed height, and fluidization velocity. ...

... 10 Further, the normalized radial profiles of the net mass flux of unary and binary particles with varying fraction of smaller particles were reported. 9,12 In the aforementioned measurements, segregation behavior was similar as reported by Goldschmidt et al. 1 and Olaofe et al. 2 for pseudo-2D beds with respect to U G , particle compositions and particle diameter ratios. In one of the studies (Upadhyay et al. 11 ), γ-ray dual-source densitometry was used to study the segregation behavior and to measure the distribution of sago and glass beads of the same size (d p = 1.5 mm) along the axial direction. ...

Dynamics of segregation and fluidization of unary particles and binary mixtures in a cylindrical fluidized bed were investigated using temporally‐ and spatially‐resolved measurements of solids volume fraction (αs) performed using Electrical Capacitance Tomography (ECT). Through the comparison with high‐speed imaging, we have shown that ECT can be used to measure the segregation behavior in 3D fluidized beds quantitatively. ECT measurements have been used further to quantify the effects of mixture compositions, particle‐diameter ratio and superficial gas velocity on the bed segregation behavior. Dynamics of fluidization behavior was characterized using the time‐evolution of spatial αs fluctuations, corresponding frequency distribution, and bubble size distribution. Further, a relation between the measured variance of αs fluctuations with the spatial αs distribution and corresponding flow structures under different fluidization conditions was established. The present work helps to understand and to provide a database for Eulerian multi‐fluid CFD simulations of segregation and fluidization of binary mixtures. This article is protected by copyright. All rights reserved.

... Due to this flow, it is possible that small particles are blown away from the debris bed ( Fig. 1). Goldschmidt et al. (2003), Olivieri et al. (2004) and other researchers (Girimonte et al., 2018) investigated the segregation of fluidized bed with binary mixtures. Goldschmidt et al. (2003) Jung, et al. ...

... Goldschmidt et al. (2003), Olivieri et al. (2004) and other researchers (Girimonte et al., 2018) investigated the segregation of fluidized bed with binary mixtures. Goldschmidt et al. (2003) Jung, et al. Nuclear Engineering and Design 363 (2020) 110606 two sizes of colored spherical glass beads. ...

The particle size distribution (PSD) of the debris bed is a major parameter influencing its coolability with respect to the two-phase pressure drop of the porous media. Most studies have focused on representative particle diameter as opposed to size distribution. Based on a severe accident situation (strong two-phase convection), we introduced a rearrangement of small particles and developed a corresponding size distribution formula by modifying the Rosin-Rammler distribution.
A minimum particle diameter model was proposed as a function of dryout heat flux (DHF) based on a minimum fluidization velocity concept. In addition, a truncated Rosin-Rammler distribution was developed and a Sauter Mean Diameter (SMD) was formulated in the form of the gamma function with a new parameter: the minimum particle diameter (Dmin). Sensitivity analysis of DHF in a 1-D top flooded debris bed showed two notable results for the effect of Dmin on coolability. First, Dmin significantly reduced DHF uncertainty due to the distribution constant. Moreover, the calculated DHF increased by introducing the concept of a minimum particle diameter. In conclusion, treatment of small particles in the debris bed is essential for determining debris bed coolability. Additionally, the truncated Rosin-Rammler distribution could be utilized to provide the precise SMD in a porous media.

... Therefore, the bubbling behavior observed in the pseudo-2D beds (typical bed depths of 1−3.5 cm) can be significantly different from industrially used large fluidized beds due to small bed-depth (D b ) to particle-diameter (d s ) ratio. The D b /d s ratio is in the range of 4.3−10 11,12 for the rectangular beds, which is significantly smaller than the commonly used D b /d s of the cylindrical beds (41−184). 13,14 Several researchers have investigated the effect of interphase interaction (drag) force to improve the predictive ability of the Eulerian two-fluid model in terms of bed expansion, timeaveraged phase and velocity distribution, etc. in gas−solid fluidized beds. ...

... It is expected that the bubbling behavior in the pseudo-2D beds will be different from that in the large-depth beds (e.g., cylindrical beds) due to higher particle−wall collisions and higher loss of the particle kinetic energy. Owing to the lower values of D b /d s used in the pseudo-3D beds (4.3−10), 11,12 the bubbling behavior in such beds can be significantly different from that in the cylindrical beds that are typically in the range of 41−184. 13,14 Quantitative predictions of bubbling behavior in such cylindrical beds with higher D b /d s in terms of the bubbling frequency and bubble size distribution continue to be a challenge. ...

... Specifically, the segregation process is preferred in metallurgical industries [21] while the high-efficiency mixing process is required in engineering fields with the aim to achieve uniform heat and mass transfer [22]. As pointed out by experimental measurements, the segregation process is dominant under low gas velocities while the mixing process is dominant under high gas velocities [23]. Lu et al. [24] experimentally and numerically investigated the minimum fluidization velocity by analyzing the pressure drop distribution in a binary mixture fluidized bed and found the mass fraction of small particles in the binary mixture plays an important role in size segregation. ...

... The numerical scheme of CFD-DEM has been well documented in our previous literature [34,41]. The geometry configuration refers to the experimental work conducted by Goldschmidt et al. [23]. The investigated object is a binary BFB with 0.15 m, 0.015 m, and 0.70 m in width, depth, and height, respectively. ...

The behavior of solid mixing dynamic is of profound significance to the heat transfer and reaction efficiencies in energy engineering. In the current study, the solid mixing characteristics of binary particles in the bubbling fluidized bed are further revealed at particle-scale. Specifically, the influences of gas superficial velocity, Sauter mean diameter (SMD) in the system and the range distribution of particle sizes on the performance of mixing index are quantitatively explored using a computational fluid dynamics-discrete element method (CFD-DEM) coupling model. The competition between solid segregation and the mixing of binary particles is deeply analyzed. There is a critical superficial velocity that maximizes the mixing index of the binary mixture in the bubbling fluidized bed. Solid mixing performs more aggressive when below the critical velocity, otherwise solid segregation overtakes mixing when above this critical velocity. Moreover, superficial velocity is a major factor affecting the mixing efficiency in the binary bubbling fluidized bed. Additionally, the mixing behavior is enhanced with the decrease of SMD while it is deteriorated in the binary system with a wide range of particle size distribution. Therefore, it is highly recommended to perform a binary particle system with smaller SMD and closer particle size distribution for the purpose of enhancing the mixing behavior. The significant understanding of mixing characteristics is expected to provide valuable references for the design, operation, and scale-up of binary bubbling fluidized bed.

... By using smaller or denser biomass particles, Cluet et al. [14] showed that bed homogeneity can be enhanced. When the density of the smaller particles in the mixture is higher, these particles segregate downwards at low gas velocity and upwards at high gas velocity [18]. To gain an overview of which component in a bed mixture can segregate up or down when fluidized, Di Renzo et al. [10] proposed an equilibrium model, which depends on the density and size ratios of the particles, and also on the proportion of biomass in the binary mixture. ...

... Moreover, the size variation of the two different biomass types also mimic those used in large-scale biomass gasifiers or combustors. The densities of both wood materials are lower than that of the sand particles, and as a result, segregation of sand and wood particles is expected to occur during fluidization as reported in previous studies [14,18]. ...

For successful operation and design of a bubbling fluidized bed reactor handling a specific biomass, in-depth knowledge about the bed behaviour is paramount. This study compares the behaviour of a bed of sand containing wood pellets with that containing wood chips at different gas velocities and biomass proportions in a cold fluidized bed of diameter, 10.4 cm. The density and volume-equivalent spherical particle diameter of the pellets are 1139 kg/m³ and 8.96 mm, respectively while those of the wood chips are 423 kg/m³ and 6.87 mm, respectively. The results show that at low gas velocities, wood chips segregate upwards while the pellets segregate downwards in their respective beds. The spread of biomass towards the walls is higher in the bed with wood chips than in that with wood pellets. As the biomass load increases, the bubble diameter increases and the transition from bubbling to slugging regime gets smoother, resulting in an increase in the minimum slugging velocity. The minimum gas velocity for effective solids mixing is less dependent on the bed height, but increases with increase in the biomass load and decreases with increase in the bed diameter. However, when slugs flow in the bed, the biomass layer at the bed surface plugs, preventing mixing of particles to be achieved at the desired gas velocity. A mechanistic model is developed for predicting the minimum gas velocity required to achieve an effective mixing at the surface of a segregated bed. Although this study is conducted in a cold bed, this same model is considered important for a hot bed reactor since devolatilization enhances the upward flow of biomass due to reduction of the biomass density.

... Segregation is often studied using segregation indices. For example, to evaluate the extent of segregation in a binary mixture, the following segregation index is proposed (Goldschmidt et al., 2003;Olaofe et al., 2013): Table 7 Summary of CFD-DEM simulations of mixing process. ...

With increasing the computational resources, the number of publications about coupled computational fluid dynamics – discrete element method is in the rise in the recent years. This technique is very useful, especially in simulation of fluid-solid flows in process engineering. This paper provides an introduction to CFD-DEM modeling in process engineering systems, including heat and mass transfer and long range forces, and reviews the major researches in simulation of two-phase processes such as drying, coating, granulation, crystallization, chemical reactions (including combustion, gasification and pyrolysis) and mixing. Details of implementing unresolved CFD-DEM in these applications are explained in details and major assumptions and findings are discussed.

... Active development includes load balancing strategies to improve parallel performance and geometrydependent adaptive mesh refinement for improved wall resolution. Beyond repeating the relatively simple cases considered in this work, future MFiX-Exa V&V work will include extending the benchmarking database to more complex cases, for example considering • integer-disperse material, e.g., Goldschmidt et al. [47], Jiang et al. [48] • simple, non-rectangular geometries, e.g., Boyce et al. [49], Penn et al. [50] • complex geometries, e.g., Xu et al. [32], Fullmer et al. [51], Jalali et al. [52] • ordered pattern formation, e.g., Wu et al. [53], Bakshi et al. [33] ...

MFiX-Exa is a new code being actively developed at Lawrence Berkeley National Laboratory and the National Energy Technology Laboratory as part of the U.S. Department of Energy's Exascale Computing Project. The starting point for the MFiX-Exa code development was the extraction of basic computational fluid dynamic (CFD) and discrete element method (DEM) capabilities from the existing MFiX-DEM code which was refactored into an AMReX code architecture, herein referred to as the preliminary MFiX-Exa code. Although drastic changes to the codebase will be required to produce an exascale capable application, benchmarking of the originating code helps to establish a valid start point for future development. In this work, four benchmark cases are considered, each corresponding to experimental data sets with history of CFD-DEM validation. We find that the preliminary MFiX-Exa code compares favorably with classic MFiX-DEM simulation predictions for three slugging/bubbling fluidized beds and one spout-fluid bed. Comparison to experimental data is also acceptable (within accuracy expected from previous CFD-DEM benchmarking and validation exercises) which is comprised of several measurement techniques including particle tracking velocimetry, positron emission particle tracking and magnetic resonance imaging. The work concludes with an overview of planned developmental work and potential benchmark cases to validate new MFiX-Exa capabilities.

... The biomass particles can be transported to the surface or bottom of the bed due to segregation effect [5], and thus have limited contact time with the bed material supposed to provide the heat required for the reaction. The particle segregation can be brought about by the density difference between biomass and the bed material particles [6], and by the rise of gas bubbles formed around the particles as biomass undergoes devolatilization [7,8]. The mean residence time and residence time distribution characterize the degree of mixing in a non-catalytic fluidized bed reactor [9]. ...

Gasification of biomass in bubbling fluidized beds can be limited by accumulation of unconverted char particles during the process. The amount of unconverted biomass depends on the residence time of the fuel particles. This study demonstrates a method for measuring the biomass residence time over the conversion period at a given air flowrate and a given amount of biomass in a bubbling bed using the variation of bed temperature and fluid pressure recorded over time. The results show that biomass conversion is characterized by the devolatilization and extinction times. The two biomass residence times increase with decreasing air flowrate and increasing amount of biomass charged in the bed. The amount of unconverted char between the two characteristic times also increases with decreasing air flowrate and increasing biomass load. The total heat loss during the devola-tilization is observed to increase with increasing air flowrate and amount of biomass in the bed. Correlations are proposed for predicting the mean biomass residence time, the amount of unconverted char particles and the devolatilization heat loss at a given operating condition. The results of this study can be used in determining the bubbling bed properties and solid circulation rate required to decongest the accumulated char particles in the bed.

... However, it is widely recognized that quantifying these quantities is very limited and challenging both experimentally and numerically, especially in a full-scale 3D high-temperature industrial system like in steelmaking reactors, although several attempts have been reported. [36][37][38] Based upon the foundation of volume of fluid method, the step function determines the portion of each phase in a cell as a n;i ¼ ...

Insights into dispersed phases, such as droplets, and their distribution and evolution in a mechanically agitated ladle like Kanbara reactor (KR), which dramatically increases the contact area between phases/reactants and remarkably intensifies the rate phenomena, are of great significance to refining processes of steelmaking industries, but are still challenging and not fully understood. This work presents a droplet-resolved model (DRM) combined with a scaled-down water model experiment to investigate the dispersion behavior of desulfurization flux into the hot metal, wherein the DRM can directly acquire the small-scale dispersed droplets in the dispersion process and large-scale interface without employing any empirical relations. The study focuses include identifying the dispersion regimes, quantifying the dispersed phase, understanding their temporal and spatial evolution, and optimizing the operating/design parameters to intensify the desulfurization efficiency. Specifically, three dispersed regimes—non-dispersion, local dispersion, and emulsion/complete dispersion regimes—are first identified based on the experiments and numerical simulations. Further, after being validated by these experiments, the DRM model is applied to study a full-scale industrial KR, and two measures for quantifying the dispersed phases—the dispersion rate γ and the interfacial density B—are introduced. The simulation results revealed the developing dispersion process as three stages: non-dispersion, transition, and dynamic equilibria. Also, the effect of the impeller rotation speed, immersion depth, blade dimensions, amount and density of molten desulfurization slag on γ and B, and the spatial distribution variation of the dispersed phase are discussed. Finally, two new correlations for evaluating the dispersion rate and interfacial density are proposed for hot metal desulfurization industrial ladles with mechanically agitated.

... In addition, the mixing quality significantly affects the heat and mass transfer rate and consequently, the efficiency of the process [1]. Mixing of solids in gas fluidization can be studied experimentally using methods such as cameras [2,3], thermal tracers [4], probe sampling [5], and radioactive particle tracking [6]. ...

Shape is one of the most important properties of particles, and can affect particle flow behavior significantly in particulate systems. In the past, extensive studies have been conducted on the effect of particle size and density on the mixing quality of particle mixtures in gas-fluidized beds, but little is known regarding the influence of particle shape. In this work, CFD-DEM approach is used to investigate the mixing of binary mixtures composed of ellipsoids and spheres. A modified drag model suitable for multicomponent mixtures of nonspherical particles is proposed first, and its validity is then verified by comparison to experimental data. The simulation results show that for the cases considered, adding a second component of ellipsoids to spheres results in reducing the minimum fluidization velocity of the mixtures; however, oblate particles in decreasing the minimum fluidization velocity is more significant than prolate particles. The mixing index of all binary mixtures generally increases with increasing gas superficial velocity. The results also show that with the added component varying from spheres to oblate or prolate particles, segregation happens in the bed and becomes more severe with aspect ratio. It is found that the effect of particle shape on the drag force is responsible for the occurrence of particle segregation.

... For this purpose pseudo 2D rectangular fluidized beds are commonly used. Such experimental set ups allow the easy use of non-intrusive techniques for the investigation of bed hydrodynamics [4][5][6], bubble motion [7,8], and solids mixing and segregation [9,10]. The agreement between experimental measurements from pseudo 2D experiments and model predictions from 2D CFD simulations are generally satisfactory with the exceptions of the solids velocity [4,[11][12][13] and the bubble rise velocity [11,14] which have been observed to be over predicted in 2D simulations due to the negligence of friction from the front and back walls. ...

This work explores the ability of the two-fluid-model (TFM) to model the dynamical and turbulent features of a
pseudo 2D gas-solid fluidized bed operated under slugging conditions. 2D and 3D numerical simulations are
performed to investigate the effect of the bed thickness on predicted quantities. Hi fidelity raw pressure drop
and particle velocity data from the NETL small scale challenge problem is processed and used to validate the
CFD model. Our work shows that the differences between 2D and 3D simulations in predicting the fluidized
bed dynamics using pressure fluctuation data is minimal. However the effect of the bed thickness on turbulent
properties namely the normal Reynolds stresses, turbulent kinetic energy, granular temperatures is significant.
Taking into account the bed thickness does not necessarily improve the model predictions of all the dynamic
and turbulent features. Furthermore mean profiles alone are not sufficient to validate TFM models as is quite
common in the open literature. Mixing in the slugging bed is predominantly due to coherent meso-scale structures
(voids and slugs) rather than individual particles as revealed from computed granular temperatures.

... Experimental efforts are reliable sources to validate particle acceleration models. However, limited optical access into fluidized beds limits the applicability of experimental investigations to either dilute suspensions (Lee & Durst 1982;Rogers & Eaton 1991;Sato, Hishida & Maeda 1996;Oakley, Loth & Adrian 1997;Kiger & Pan 2000) or pseudo two-dimensional experimental settings (Goldschmidt et al. 2003;Bokkers, Annaland & Kuipers 2004). Particle-resolved direct numerical simulation (PR-DNS) has emerged as a powerful tool to study turbulent particle-laden suspensions (Balachandar & Eaton 2010;Tenneti & Subramaniam 2014) and hone point-particle models (Tenneti, Garg & Subramaniam 2011). ...

We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with solid-phase volume fraction $\unicode[STIX]{x1D719}=0.001$ in a decaying isotropic turbulent particle-laden flow. The particle diameter $d_{p}$ in the suspension is chosen to be the same as the initial Kolmogorov length scale $\unicode[STIX]{x1D702}_{0}$ ( $d_{p}/\unicode[STIX]{x1D702}_{0}=1$ ) in order to overlap with the regime where PP-DNS is valid. We assess the point-particle acceleration model for two different particle Stokes numbers, $St_{\unicode[STIX]{x1D702}}=1$ and 100. For the high Stokes number case, the Stokes drag model for particle acceleration under-predicts the true particle acceleration. In addition, second moment quantities which play key roles in the physical evolution of the gas–solid suspension are not correctly captured. Considering finite Reynolds number corrections to the acceleration model improves the prediction of the particle acceleration probability density function and second moment statistics of the point-particle model compared with the particle-resolved simulation. We also find that accounting for the undisturbed fluid velocity in the acceleration model can be of greater importance than using the most appropriate acceleration model for a given physical problem.

... For this purpose pseudo 2D rectangular fluidized beds are commonly used. Such experimental set ups allow the easy use of non-intrusive techniques for the investigation of bed hydrodynamics [4][5][6], bubble motion [7,8], and solids mixing and segregation [9,10]. The agreement between experimental measurements from pseudo 2D experiments and model predictions from 2D CFD simulations are generally satisfactory with the exceptions of the solids velocity [4,[11][12][13] and the bubble rise velocity [11,14] which have been observed to be over predicted in 2D simulations due to the negligence of friction from the front and back walls. ...

... Although very little is known on the behavior of mixtures of fully dissimilar solids, in which the effects of density and size segregation overlap, it is recognized that density parameter is more significant than size [28] . In the situation of segregation only by size, generally larger particles tend to act as jetsam [29,30] .Particularly a layer inversion phenomenon, in which the role of species acting as flotsam and jetsam changes, may take place for such type of segregation due to the increase in gas velocity, depending on the composition of components [31] . ...

Numerical simulations of the cold flow of a gas–solid mixture in a G-Volution circulating dual gasification reactor are conducted by using the commercial software package ANSYS FLUENT. Isothermal non-reactive, turbulent, unsteady gas–solid flow is assumed and the Eulerian–Eulerian fluid model is adopted. The effect of restricted cross sections on the pressure gradient and the solids holdup in the fuel reactor of this Circulating Fluidized G-Volution Gasification dispositive is investigated. Computation of the reactor without internals is also conducted for comparison. In addition, segregation in a fluidized binary biomass –sand bed is considered for different inlet velocities.

... All walls have no-slip boundary conditions. The most important conditions and properties of the CFD-DEM simulation are given in Fig. 2. According to [79], values of C fs = 0.15, C fr = 0.001, and e 0 = 0.97 are used for friction and restitution coefficients. Density and fluid viscosity were set to r g = 1.184 kg m -3 and m g = 0.01855 mPa s, respectively. ...

Coarse‐Grained DEM is a relatively new, promising and, efficient method for the numerical simulation of particulate systems. The accuracy of the method relies on appropriate scaling rules for contact and fluid‐particle interaction forces. A variety of scaling rules is reported in the literature, including the additional use of drag correction models. To shed some light on the topic, different contact scaling rules are used and compared with DEM results regarding mean and RMS values of pressure drop and average particle height in a fluidized bed. The results indicated that in terms of averaged values as mean particle position and voidage profile the CFD‐CGDEM approach leads to accurate results for low scaling factors. With increasing scaling factors, deviations get higher. Regarding the particle dynamics, the approach leads to an underestimation of RMS values of particle position indicating a loss of particle dynamics in the system due to coarse‐graining. Furthermore, the results show that temporal discretization and contact scaling rule is not as important as expected. The impact of cell cluster size on drag force calculation is studied by comparing numerical results with experiments. The use of Energy Minimization Multi‐Scale drag correction is investigated, and a reduced mesh dependency and good accuracy are observed.

... To demonstrate the bed expansion dynamic characteristics more clearly, the average particle height in the fluidized bed is calculated from the following expression [53] : ...

A bubble structure‐based drag model developed for the monodispersed system has been extended to simulate bi‐dispersed bubbling fluidized beds. Both dense phase and dilute phase are considered to be comprised of two types of particles with different sizes. The derivation of the structure‐based drag coefficient for individual particle based on the force equilibrium principle is proved to be independent of the volume fractions (&ip.eop; si) of particle i. The multi‐fluid model in the commercial software Ansys Fluent is employed to evaluate the polydispersed drag model for the segregation of binary gas‐particle flows in a bubbling fluidized bed. It is shown that the simulation results predicted by the new structure‐based drag model are in reasonable agreement with experimental data with a 6.34% root mean square error (RMSE). The new structure‐based model can capture the particle distribution at the top region of the fluidized bed well. The bubble behaviour can also be captured by the new model well.
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... The drag law used most frequently was proposed by Gidaspow,22 which is a combination of the empirical equation by Ergun 23 for low porosities and the drag correlation by Wen and Yu 24 for high porosities. Goldschmidt et al. 25 and Bokkers et al. 26 showed that, for binary or polydisperse systems, the traditional drag models need to be modified. Link et al. 27 investigated the performances of three drag laws of Gidaspow, 22 Koch and Hill 28 and minimum of Ergun 23 and Wen and Yu 24 relations in a spout-fluidized bed and pointed out that the modified drag law and the Koch and Hill 28 relation derived from lattice Boltzmann (LBM) simulations were more suitable. ...

Gas-solid flows are widely found in various industrial processes, e.g. chemical engineering and sand ingestion test for aero-engine; the interaction between continuum and discrete particles in such systems always leads to complex phase structures of which fundamental understandings are needed. Within the OpenFOAM, the present work uses the discrete element method combined with the computational fluid dynamics to investigate the gas-solid flow behaviors in a dense fluidized bed under various conditions. A drag law which is for polydisperse systems derived from lattice Boltzmann simulations is incorporated into the computational fluid dynamics-discrete element method framework and its suitability for different flow regimes is investigated. The regimes including, namely slugging bed, jet-in-fluidized bed, spout fluidization, and intermediate, are simulated and validated against experiments. The results show that the lattice Boltzmann drag relation performs well in capturing characteristics of different gas-solid flow regimes. Good agreements are also obtained quantitatively by comparisons of pressure drop fluctuation, and time-averaged gas velocity and particle flux.

... 4,6 The hydrodynamic behavior of this class of powders has been the subject of many experimental investigations. [7][8][9][10][11][12][13][14][15] In addition, researchers have managed to obtain better insights into these systems through simulations. One of the simulation tools that has been in use to study processes based on fluidized bed technology, is computational fluid dynamics (CFD). ...

Fluidized beds are widely used in many industrial processes as they ensure the desirable high-intensity heat and mass
transfers between gas and particles and offer the possibility to perform operations in a continuous mode and powders
recycling. Some of these industrial processes use Geldart D type of powders and operate in the slugging mode. This
paper presents a 3D numerical model of gas-solid flows in a fluidized bed based on the Two-Fluid Model (TFM).
Turbulence modeling (k- e) was used to predict flow behavior in fluidized bed of Geldart D particles. The solid phase
consists of Geldart D powders and the gas flow is in a slug regime. The numerical results are validated against the
experimental work of Azzi et al. Model predictions on flow patterns, bed expansion, volume fraction time series and
pressure drop fluctuations are presented and discussed in details in order to demonstrate the cyclic process of slug
formation (onset, growth, rising and bursting of slugs) and its effects on the overall performance of beds fluidizing
Geldart D type of powders.

... The U mf of the established system is firstly determined using the same method as described in the validation section. It is worth mentioning that U mf is a concept for mono particle systems, but similar characteristic velocities also exist in multivariate systems, and different scholars refer to the corresponding velocity as the complete fluidization velocity, the critical fluidization velocity, or the final fluidization velocity, respectively [46][47][48]. To avoid ambiguity, the initial fluidization velocity of the mono and binary particle systems is both referred as the U mf in this study. ...

The fluidization properties of binary particles in a supercritical water fluidized bed reactor (SCWFBR) are numerically investigated based on coupled Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. The accuracy and effectiveness of the CFD-DEM model is firstly validated via previously published experimental data. Then, the model is adopted to study the effect of flow velocities and sinusoidal pulse on the mixing of the binary particles. Numerical results show that it is effective to promote mixing of binary particles in SCWFBR by introducing external energy pulses, which cannot be achieved by simply increasing the flow velocities without pulses. Compared to high frequency pulses, low frequency pulses are more effective in promoting mixing. Within the parameters considered here, it is also found that the pulse amplitude is almost positively correlated with the effect on the promotion of particle mixing when it is smaller than the fixed flow velocity. In addition, an efficient and economical method based on Fast Fourier Transform (FFT) on the bed pressure drop is given to determine the optimal pulse frequency, which can prevent the waste of manpower and the physical resources from happening. This study can provide technical guidance to achieve optimal mixing of binary particles in SCWFBR and offer theoretical support for the design and optimization.

... Berthiaux et al. developed an IA-based method for the measurement of powder homogeneity of loose materials and proposed their real-time principal component analysis as an on-line methodology adaptable to other techniques [35]. The degree and rate of segregation in polydisperse systems during fluidization can also be monitored with the help of IA [36,37]. ...

In pharmaceutical sciences, visual inspection is one of the oldest methods used for description in pharmacopeias and is still an important part of the characterization and qualification of active ingredients, excipients, and dosage forms. With the development of technology, it is now also possible to take images of various pharmaceutical dosage forms with different imaging methods in a size range that is hardly visible or completely invisible to the human eye. By analyzing high-quality designs, physicochemical processes can be understood, and the results can be used even in the optimization of the composition of the dosage form and in the development of its production. The present study aims to show some of the countless ways image analysis can be used in the manufacturing and quality assessment of different dosage forms. This summary also includes measurements and an evaluation of, amongst others, a less studied dosage form, medicated foams.

... 4,6 The hydrodynamic behavior of this class of powders has been the subject of many experimental investigations. [7][8][9][10][11][12][13][14][15] In addition, researchers have managed to obtain better insights into these systems through simulations. One of the simulation tools that has been in use to study processes based on fluidized bed technology, is computational fluid dynamics (CFD). ...

Fluidized beds are widely used in many industrial processes as they ensure the desirable high-intensity heat and mass transfers between gas and particles and offer the possibility to perform operations in a continuous mode and powders recycling. Some of these industrial processes use Geldart D type of powders and operate in the slugging mode. This paper presents a 3 D numerical model of gas-solid flows in a fluidized bed based on the Two-Fluid Model (TFM). Turbulence modeling (k- e) was used to predict flow behavior in fluidized bed of Geldart D particles. The solid phase consists of Geldart D powders and the gas flow is in a slug regime. The numerical results are validated against the experimental work of Azzi et al. Model predictions on flow patterns, bed expansion, volume fraction time series and pressure drop fluctuations are presented and discussed in details in order to demonstrate the cyclic process of slug formation (onset, growth, rising and bursting of slugs) and its effects on the overall performance of beds fluidizing
Geldart D type of powders.

This article presents an experimental study regarding the behavior of a ball-shaped polyethylene solid particle in vertical air channel. To this effect, we used a laboratory stand, an aerodynamic screen with vertical air flow, and a high-speed camera to study the behavior of the solid particle. The recoding speed of this measurement was 500 frames∙sec ⁻¹ . During this assessment, the movement direction of the solid particle within the vertical air flow was not taken into account, i.e. the particle moved either in the same direction with the air flow or in the opposite direction. After the video recording analysis, a series of physical data of the solid particle have been identified, such as: average travelling speed, distance covered by the solid particle, tracing time, angular speed of the solid particle and its rotation. It has been observed that aforementioned data are in strict accordance with the variation of the speed of the air flow passing through the ascending vertical air channel. © 2018 ALMA MATER Publishing House, “VASILE ALECSANDRI” University of Bacău. All rights reserved.

In the separation process on a gas-solid separation fluidized bed, formation of binary mixtures of fine coal and magnetite is inevitable. Using a high-speed camera system (HSCS), the formation of these binary mixtures was observed, and the mixing mechanism was established. The effects of different factors (e.g. gas velocity and size fraction and mixture ratio of fine coal) on the degree of mixing of binary mixture particles were studied using a combination of factor analysis method and orthogonal test method. The results show that the mixing process of fine coal and magnetite plays a crucial role in the adjustment of the bed density. It is clear that the bed density can maintain their identities only when the fine coal and the magnetite are fully mixed. The degree of mixing of binary particles increased with increasing gas velocity while the value decreased with increasing size fraction and mixing ratio of fine coal. The three factors influencing the mixing efficiency showed the following order as: gas velocity, mixture ratio and size fraction of fine coal. Maximum degree of mixing was obtained for the gas velocity of 9.83 cm/s, particle sizes less than 0.15 mm and mixing ratio of 5%. According to the sorting test, the separation efficiency of the gas-solid separation fluidized bed containing binary mixtures is more obvious under the optimal working conditions, i.e., clean coal is obtained with the ash content reduced by 25.67% compared with raw coal and the probable error (E) is 0.13.

For many fluidized bed applications, the particle movement inside the reactor is accompanied by reactions at the particle scale. The current study presents for the first time in literature a multi-scale modelling approach coupling a one-dimensional volumetric particle model with the dense discrete phase model (DDPM) of ANSYS Fluent via user defined functions. To validate the developed modelling approach, the current study uses experimental data of pressure drop, temperature and gas composition obtained with a lab-scale bubbling fluidized bed biomass gasifier. Therefore, a particle model developed previously for pyrolysis was modified implementing a heat transfer model valid for fluidized bed conditions as well as kinetics for char gasification taken from literature. The kinetic theory of granular flow is used to describe particle–particle interactions allowing for feasible calculation times at the reactor level whereas an optimized solver is employed to guarantee a fast solution at the particle level. A newly developed initialization routine uses an initial bed of reacting particles at different states of conversion calculated previously with a standalone version of the particle model. This allows to start the simulation at conditions very close to stable operation of the reactor. A coupled multi-scale simulation of over 30 s of process time employing 300.000 inert bed parcels and about 25.000 reacting fuel parcels showed good agreement with experimental data at a feasible calculation time. Furthermore, the developed approach allows for an in-depth analysis of the processes inside the reactor allowing to track individual reacting particles while resolving gradients inside the particle.

Multiphase flows are frequently encountered in both nature and large‐scale industrial processes. The inherent multiscale nature of multiphase flows and associated scientific challenges, makes numerical modelling of multiphase flows very complex. In this chapter we will focus on the modelling of gas–liquid, liquid–solid and gas–liquid–solid flows. The different simulation techniques are grouped in terms of Euler–Euler, Euler–Lagrange and fully resolved or Direct Numerical Simulation techniques. Both the governing equations and numerical implementation will be presented, as well as different methods to describe the interfaces between phases. Special attention will be given to the exchange of Momentum, Heat and Mass between the phases. Each subsection will contain a short discussion on the application of the different methods presented.

Fluidization experiments were conducted on a small scale and with a rapid response (short duration) to enable corresponding simulations at low‐computational cost. Rise times are reported for four or fewer polyethylene particles (intruders) in an air‐fluidized bed of ~5,000 Group D glass beads. Experimental inputs were completely characterized–particle properties, system dimensions and operating conditions–which is necessary for validating CFD‐DEM including a comprehensive uncertainty quantification (UQ) analysis. Input uncertainties are reported as bounds or cumulative distribution functions of measured values. The staggering number of simulations required to complete a UQ analysis (~O(104) simulations corresponding to ~5 uncertain inputs) motivates this work. These segregating‐bed experiments are designed to permit analogous CFD‐DEM simulations to complete in less than a day on a single (~2.5 GHz) CPU. Segregation times are reported for several operating conditions, intruder sizes, and initial configurations, providing a rich dataset for numerical model testing, validation and UQ.

Gas-solid fluidized beds have drawn the attention of engineers and researchers as an effective technology for a large variety of applications, and numerical simulations can play an increasingly relevant role in their development and optimization. Although real-time simulations will require substantial progress in the accuracy, capability, and efficiency of numerical models, future developments could herald a new era of so-called virtual reality for process engineering, featuring interactive simulations instead of stepwise experimental scale-up studies and cost-intensive empirical trial-and-error methods. This review paper provides a significant body of knowledge on the developments of CFD mathematical models and how they can be applied in various fluidized-bed systems. The review is divided into three main parts. The first part (Mathematical modeling) describes the state-of-the-art numerical models of gas-solid flows (two-fluid model, soft-sphere model, hard-sphere model, and hybrid model) and their fundamental assumptions (gas-solid, particle-particle, and particle-wall interactions). Special attention is devoted to the forces and the moments of the forces acting on particles, the parcel modeling, the homogeneous and structure-dependent drag models, the non-spherical particle models, the heat and mass transfer, and the turbulence. The second part of this review (State-of-the-art studies) is dedicated to the body of literature, focusing on how these numerical models are applied to fluidized-bed systems used in chemical and energy process engineering. Relevant works on simulation in the literature up to 2021 are analyzed, complemented by an overview of popularly used commercial and in-house simulation codes. Particular attention is paid to those studies that include measurement validation, to achieve a fundamentally competitive comparison between the different numerical models. The pros and cons of applying CFD models to fluidized-bed systems are studied and assessed based on the existing body of literature. The third part of this review (Conclusion and prospects) highlights current research trends, identifying research gaps and opportunities for future ways, in which CFD can be applied to fluidized beds for energetic and chemical processes.

CFD-DEM modeling was conducted to study the particle heat transfer in an oxy-fuel fluidized bed under different gas compositions and operating pressures. In particular, to determine the appropriate operating fluidization velocity for the pressurized oxy-fuel fluidized bed, three fluidizing parameters, the excess velocity Uex, fluidization number FN, and Froude particle number Frp, were evaluated by examining the similarities of the flow patterns and the particle heat transfer. The results revealed that the particle heat transfer is positively correlated with the gas density and specific heat capacity, as well as the fluidization velocity. Increasing the operating pressure augments the particle heat transfer, with the rate of increase being the highest at a constant Uex while being less significant at a constant Frp. Moreover, using the constant Frp under pressurized conditions makes possible an almost constant bed expansion and a more desirable particle temperature distribution, as well as a similar thermal input.

Mixing of binary mixture with small-sized particles component (SC) and large-sized particles component (LC) is simulated using unequal granular temperature-based kinetic theory (UGT-KT) in supercritical carbon dioxide fluid (S-CO2) fluidized bed. Synergy angle is applied to identify the tendency of mixing/segregation of SC and LC binary mixture according to the axial distribution of component volume fractions along bed height of S-CO2 fluidized bed. Three different regions, including segregation (SE) near the bed bottom, transition (TR) near the bed top and dense (DE) between the SE and TR regions along bed height, are discriminated. Large synergy angle reveals the tendency for the SC and LC particles to segregate. Small synergy angles occur with fluidizing velocity and temperature. Defluidization occurred at certain pressure ratio p/pcr of 1.22–1.62, leading to a large synergy angle in S-CO2 fluidized bed.

To study the distribution of ferrous burden (which is a mixture of pellets and sinter) in the blast furnace, the burden must be characterised in terms of input parameters which can be used in discrete element method (DEM) simulations. A methodology is presented to determine these parameters which can help represent the ferrous burden mixture. First, angle of repose experiments are performed and determined for pellet, sinter and their mixtures at different proportions. Using this experimental data, the DEM parameters individually for pellets and sinter using previously determined experimental values and DEM calibration approach are chosen and they are represented accurately. From these, the values of DEM parameters for pellet-sinter contact are taken as the average of their individual counterparts. Using all determined parameters for intra-material as well as inter-material particle contacts, simulations of angle of repose for mixtures at varying proportions are done and a good match is found between experimental and simulation values at all proportions. In this way, binary mixtures are characterised while maintaining the constituents as individual species.

This paper investigates the thermochemical and physical conversion processes in coal gasification numerically with particular interest on calcination in a bubbling fluidized bed furnace. A comprehensive Eulerian-Eulerian three-dimensional model is developed for studying the gasification process. Three calcination cases are carried out under different operating conditions while one inert case is conducted to evaluate the effect of calcination. The presented numerical results aim at determining the mechanism of coal gasification in an air-steam environment with different flowrates. Evidence of particle segregation is found in the bed of coal and limestone due to density reduction and diameter shrinkage. Char conversion is investigated for different air-coal and steam-coal ratios, also the effect of bed temperature, fluid flowrate and fuel feeding rate on the carbon conversion is studied comprehensively. The highest char conversion rate is observed in the airflow rate of 17.0 kg/hr where the bed temperature is found to be maximum. A noticeable impact of calcination is found in the gaseous emission while increasing CO2 concentration. Time averaged solid and gas temperature and species concentration profiles indicate the steady-state condition of numerical simulation.

Mixing of different size and density particles plays a vital role in the hydrodynamics of fluidized beds. In this study, a multiphase model based on the kinetic theory of granular flow has been developed to study the mixing behaviour of biomass and sand particles in a bubbling fluidized bed. After validating the model using available experimental data from the literature, it was used to study the influence of various parameters such as superficial gas velocity, mixture composition and particle size. Emphasis was given on understanding the impact of these parameters on the particle segregation number, which is the parameter used to quantify the segregation behaviour of the fluidized bed. Results are plotted as the change in particle segregation number with respect to time for different mixture compositions, superficial gas velocities and particle diameters. The results show that mixing is promoted with the increase in gas velocities which give lower values of particle segregation number. Increase in ratio of biomass in the mixture leads towards segregation while increase in biomass particle diameter promotes mixing. The results of 2D simulations are also compared with the 3D configuration.

Eulerian-Eulerian modeling is widely applied in simulations of multi-phase flows in fluidized beds. However, the validity of this model is questionable, especially with the limitation of gas-solid drag closures. In this study, CFD simulations were performed to investigate the validity of the numerical model for segregating fluidized bed. The numerical model was tested with experimental data from the literature to select the most appropriate gas-solid drag model. It was found that the Gidaspow drag model is generally better than the Syamlal-O’Brien, the BVK, and the Di Felice models. However, all the drag models showed poor agreement with experimental data of size segregating systems. Also, all the investigated gas-solid drag models mispredicted the minimum fluidization velocity of various fluidized bed systems. The Gidaspow and Di Felice models had an acceptable error, while the BVK and the SB always under-predicted the minimum fluidization velocity with high error. A new correlation was proposed to correct the computational superficial velocity to mitigate the effect of the error of fluidization velocity prediction by the Wen-Yu gas-solid drag model.

Drag force models are one of the most important factors that can affect TFM and CFD-DEM simulation results of two-phase systems. This article investigates the accuracies, implementation issues and limitations of the majority of the drag models for spherical, non-spherical and systems with size distribution and evaluates their performance in various simulations. Around 1888 data points were collected from 19 different sources to evaluate the drag force closures on mono-dispersed spherical particles. The Reynolds number and fluid volume fraction ranges were between 0.01 and 10,000 and between 0.33 and 1, respectively. In addition, 776 data points were collected from seven different sources to evaluate the drag force closures on poly-dispersed spherical particles. The Reynolds numbers were between 0.01 and 500, fluid volume fractions between 0.33 and 0.9, and diameter ratios up to 10. A comprehensive discussion on the accuracy and application of these models is given in the article.

Numerical simulations of a freely bubbling cylindrical fluidized bed are carried out using a coupled computational fluid dynamics and discrete element method (CFD-DEM) model and compared to recent experimental data. The experiments were conducted using high-resolution and high-frequency magnetic resonance imaging providing high-fidelity data of the bubbling within a central 10 mm slice of the bed. Qualitatively, we find more regular (i.e., less chaotic) structures in the simulated beds than observed experimentally. Quantitatively, however, the bubble diameter and number of bubbles as a function of height within the bed is predicted well by the base model. Unfortunately, the regularity in the simulations manifests as a considerable discrepancy in the speed of the (dense) emulsion phase. The simulated velocity probability distribution functions show an accumulation of low-speed regions and deficiency of high-speed regions. A simple parametric study of the base model is also carried out considering many of the most common CFD-DEM modeling parameters. It is found that the fluid grid size, geometry resolution, transfer kernel and drag law did not have a significant effect on bubble or particle dynamics.

Computational Particle Fluid Dynamics (CPFD) simulation was performed to study coal pyrolysis in a Circulating Fluidized Bed (CFB) downer containing binary particles (coal particles and heat carrier particles). A suitable drag model, which considers the cluster effect by assuming dynamic equilibrium for particles in and out cluster, was incorporated into the CPFD model, which shows acceptable accuracy in describing the hydrodynamics of binary particles in the downer. The predicted mixing index of temperature was also in good agreement with experiment, indicating the model can also be used to study heat transfer between binary particles in the downer. The coal pyrolysis kinetics were further incorporated into the model. Simulation results demonstrated that the rapid mixing of coal and heat carrier near the downer inlet was beneficial for the rapid temperature increase of coal particle. The predicted coal pyrolysis behaviors further demonstrated that the gas-solids can flow uniformly with short residence time and low back-mixing in the downer, which facilitates the rapid pyrolysis of coal. It was concluded that the CPFD modeling can provide reasonable simulation results with respect to hydrodynamics, heat transfer and chemical reactions in the downer for coal pyrolysis.

Purpose
The purpose of this paper is to present a computational fluid dynamic simulation for the investigation of the particles segregation phenomenon in the gas–solid fluidized beds.
Design/methodology/approach
These particles have the same size and different densities. The k – ε model and multiphase particle-in-cell method have been utilized for modeling the turbulent fluid flow and solid particles behaviors, respectively. The coupled equations of the velocity and pressure have been solved by using a combination of SIMPLE and PISO algorithms. After validating the simulation, different mixing indices, with different calculation bases, have been investigated, and it has been found that the Lacey mixing index, which was defined based on statistical concepts, is suitable to investigate the segregation/mixing phenomena of this bed in different conditions. Finally, the effects of parameters such as velocity, particle density ratio, jetsam concentration, and initial arrangement on the segregation/mixing behaviors of the bed have been studied.
Findings
The results show that the increase in the superficial gas velocity decreases the mixing index to a minimum value and then increases this index in the beds with mixed initial condition, unlike the beds with separated initial condition. Moreover, an increase in the particle density ratio increases the minimum fluidization velocity of the bed, and also the amount of segregation, and increase in the jetsam concentration increases the value of the mixing index.
Originality/value
A computational fluid dynamics simulation has been presented for the particles segregation phenomenon in the gas–solid fluidized beds.

MFIX-Exa is a computational fluid dynamics–discrete element model (CFD-DEM) code designed to run efficiently on current and next-generation supercomputing architectures. MFIX-Exa combines the CFD-DEM expertise embodied in the MFIX code—which was developed at NETL and is used widely in academia and industry—with the modern software framework, AMReX, developed at LBNL. The fundamental physics models follow those of the original MFIX, but the combination of new algorithmic approaches and a new software infrastructure will enable MFIX-Exa to leverage future exascale machines to optimize the modeling and design of multiphase chemical reactors.

In this work, mixing and segregation of binary mixtures involving biomass materials in a fluidized bed was experimentally investigated. A frozen bed method was employed to investigate both axial and radial distribution of biomass particles in silica sand. Three different biomass materials were studied: willow sawdust, pelletized soy and oat hull materials. Biomass loading investigated ranged from 5% to 30% by weight. The extent of mixing for each of the biomass composition was investigated using Lacey’s mixing index which is based on the standard deviations of the sample at different axial positions in the bed. The radial composition was also investigated by means of digital imaging analysis using a high-resolution digital camera. The experiments revealed the differences in the extent of particle distribution for pelletized biomass materials vs non-densified materials as a result of differences in particle size, density and importantly, the particle shape of the materials utilized. The results showed an increase in the extent of mixing as the fluidizing velocity increased for both pellet materials while the mixing index for sawdust decreased beyond a loading of 20%. With an increase in biomass loading, an increase in mixing index was found for the two pellet materials. A similar trend was observed for sawdust at the lower loading level. However, the mixing index started to decrease at higher loading level beyond 20%. The results greatly contributed to the understanding of the hydrodynamics of binary and multicomponent mixtures involving biomass materials, especially pelletized materials in fluidized beds.

Traditional methods for measuring the residence time distribution (RTD) of particles in a fluidized bed are complex and time-consuming. To this regard, the present work proposes a new measurement method with remarkable efficiency based on digital image analysis. The dyed tracers are recognized in the images of the samples due to the difference of colors from bed materials. The HSV and the well-known RGB color space were employed to distinguish the tracers. By enhancing the Saturation and the Value in HSV and adjusting the gray range of images, the recognition error is effectively reduced. Then the pixels representing the tracers are distinguished, based on which the concentration of the tracers and RTD are measured. The efficiency, accuracy and repeatability of the method were validated by RTD measurements experiments. The method is also fit for distinguishing the target particles from multi-component systems consisting of particles of different colors.

The segregation behavior of a mixture of silica-coated titanium dioxide (TiO2) particles of three different sizes in a pseudo two-dimensional fluidized bed was studied experimentally by the freeze–sieving method and numerically by the multi-fluid model (MFM). Three-dimensional computational fluid dynamics (CFD) simulations were carried out to evaluate the effects of the solid wall boundary conditions on particle segregation in terms of specularity and particle–wall restitution coefficients. The quantitative indexes of segregation tendency and segregation degree were used to determine the axial segregation of the mixture in triangular coordinates. The simulation results revealed that the axial segregation increased with the specularity coefficient, whereas the particle–wall restitution coefficient had a minor effect on axial segregation. Comparison of the simulation results with experimental data showed that the appropriate value of the specularity coefficient used in the CFD model depended on superficial gas velocity. The study of the effects of superficial gas velocity on segregation behavior demonstrated that the greatest segregation was obtained at minimum fluidization velocity and the segregation decreased as the gas velocity gradually increased.

Binary mixture fluidization is an important operation type of fluidized bed. The regularity of mixing and segregation of binary mixture is the key to process research and development. In this paper, a new experimental method for the measurement of mixing and segregation of binary mixture is proposed by combining gas cutting-off method and Electrical Capacitance Volume Tomography (ECVT). While inheriting the advantage of high applicability of gas cutting-off method, this method can be of high spatial resolution with the application of ECVT. This combination can not only obtain detailed particle component distribution information, but also reduce the experimental labor intensity. Based on the measuring principle of ECVT and Maxwell Garnett mixing model, the calibration relationship between voxel value and particle mixing ratio was deduced. An experimental binary mixture system was employed to validate the calibration relationship. The result showed that the calculated calibration curve was in good agreement with the experimental calibration curve, which indicates the rationality and feasibility of the method. On this basis, mixing process of the same particle system was quantitatively characterized and analyzed at a given air flow rate.

Oil shale is a high-value fuel resource and its global output is gradually increasing with time. Based on the analysis of physical properties of oil shale, a sorting process for high-density dense-phase gas-solid separation using fluidized bed is proposed. During the separation process in a gas-solid separation fluidized bed, a binary mixture of oil shale's mineral powder and ferrosilicon powder is formed. This paper systematically analyzes the separation characteristics of ferrosilicon powder. Furthermore, the influence of different factors (fluidization number N, and oil shale's powder grade)on the degree of mixing of particles in the binary mixture and the influence of binary heavy medium ratio on the stability of bed are also studied. The results show that the weight of ferrosilicon is prone to stratification and grading in the fluidized bed due to its own particle size composition. The mixing process of oil shale mineral powder and ferrosilicon powder plays a crucial role in the adjustment of bed density. The density gradually narrows with the increase in the value of fluidization number. For the same fluidization number, the bed density decreases with the increase in the mass fraction of oil shale's mineral powder. The oil shale is separated under optimized operating conditions (particle size of 0.5–0.9 mm, mixing ratio of 10%, and fluidization number of 1.4). The yield of concentrate is 27.18%, while the oil content is 10.76%. Furthermore, the yield of tailings is 77.61%, whereas the oil content is 1.46%. Additionally, the separation precision (possible error)E has the value of 0.113.

ABSTRACT In this paper a state-of-the-a rt review will be presented on hydrodynamic,modeling,of dense gas-particle flows as encountered in the fluid bed,family of gas-solid contactors. After a brief introduction ,the different classes of fundamental,hydrodynamic,models,will be discussed together with their physical basis and,mutual,advantages,and,disadvantages. Thereafter some,typical results will be pr e- sented on first principles modeling,of dense gas-fluidized beds. Finally the conclusions will be presented ,and,areas which ,need substantial further attention will be indicated.

Non-invasive monitoring of multiphase flows is a result of the latest advances realized in non-invasive measurement of multiphase systems by means of various tomographic and velocimetric techniques. The book reviews in 15 chapters the theoretical background and the physics of the measurement process for each of a number of techniques. In addition, the mathematical modeling related to the measured property, such as in the image reconstitution problem for tomography, successful application of the techniques for measurement in various multiphase systems and their advantages and limitations are described.

This chapter discusses the use of non-intrusive digital image analysis methods for the study of the behavior of bubbles and solid phases in two-dimensional beds. A bubbling fluidized bed is a two-phase gas–solid contacting device. According to the two-phase theory of fluidization, gas flow in excess of that required to maintain the dense phase at minimum fluidization (bubbling) conditions, flows through the bed in the form of gas pockets or bubbles. These bubbles exert the dominant influence on the mixing, heat/mass transfer, and reactant conversion capabilities of the fluidized bed. Such beds have been used very often in the past to obtain qualitative and quantitative information on bubble characteristics. However, photographic techniques employed to extract quantitative information on bubbles are laborious and require subjective interpretation in the delineation of bubble–solid phase boundaries. The labor-intensive effort reduces the motivation for obtaining sufficient data for making reasonable statistical inferences. Two-dimensional beds have also been used to study the influence of bubble motion on the motion of solids in the bed.

A two-dimensional multi-fluid Eulerian CFD model with closure laws according to the kinetic theory of granular flow has been applied to study the influence of the coefficient of restitution on the hydrodynamics of dense gas-fluidised beds. It is demonstrated that hydrodynamics of dense gas-fluidised beds (i.e. gas bubbles behaviour) strongly depend on the amount of energy dissipated in particle–particle encounters. It is concluded that, in order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is of prime importance to correctly take the effect of energy dissipation due to non-ideal particle–particle encounters into account.

Several types of submersible probes have been employed in the measurement of bubble velocity and size in gas-fluidized beds. Dual-tipped probes can measure only the pierced length of a bubble, since the central axis of the rising bubble need not be aligned with that of the probe. The distribution of the measured pierced lengths is then used to deduce, from geometrical probability procedures, the distribution of bubble diameters if the shape of the bubble is known. However, the signal interpretation methods used for such probes invariably assume that all bubbles rise vertically. From observations in a two-dimensional bed, it appears that bubbles move in an intricate pattern influenced both by other bubbles in the vicinity as well as the local solids flow pattern; the assumption of vertical bubble rise clearly needs further examination. Multiple-tipped probes have also been used; the data collection algorithms for such probes contain criteria which detect and reject the non-vertically rising bubbles. Whether such selection methods influence the measured statistics of bubble populations does not appear to have been established.

In this paper a review will be presented on the application of Computational Fluid Dynamics (CFD) to the field of Chemical Reaction Engineering (CRE). After a brief introduction and explanation of the traditional approaches followed within the field of CRE, the CFD discipline and its historical development will be briefly discussed. Some important areas of application will also be mentioned. Subsequently the theoretical framework will be expanded on and the techniques involved in the numerical solutions will be briefly outlined. Throughout this paper the authors have found it useful to make a distinction between i) Single Phase systems and ii) Multiphase Systems. In our review a brief section has been incorporated on experimental validation which is considered to constitute a critical action to pave the way for more widespread acceptance of CFD in the chemical engineering community, especially in connection with multiphase flow applications. The authors have used this opportunity to present some of the results which have been obtained during their own research activities. Finally some recommendations for future actions will be given.

This chapter presents a new emerging tool that is a combination of fluid dynamics (CFD) and numerical mathematics backed up by the immense growth of computer power: computational fluid dynamics. CFD offers great potential for the chemical engineer and that this rapidly emerging new hybrid science of mathematics and mechanics at present already has a profound impact on chemical reaction engineering. It is expected that the role of CFD in the future design of chemical reactors will increase substantially and that CFD can reduce the experimental effort required to develop industrial reactors. A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the “complete velocity distribution map” is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of a piece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. Applications of CFD may be divided into broad categories—those involving single-phase systems and those involving multiphase systems. Within single-phase systems, a further distinction can be made between systems involving laminar flows, turbulent flows, flows with complex rheology, and fast chemical reactions. In many processes encountered in industrial practice, multiphase flows are encountered and, it can be stated that, because of the inherent complexity of such flows, general applicable models and related CFD codes are nonexistent.

Submersible probes are often used to study the local bubble properties in gas-fluidized beds. Since the axes of the intercepted bubbles need not be aligned with the probe axis of the probe, simple probes measure only the pierced length of the bubbles; and the deduction of the diameters of the bubbles is not simple. Geometrical probability offers an elegant solution to the conversion of the distribution of pierced lengths to that of bubble size measures. However, the theory has not been verified experimentally so far. In this investigation, digital image analysis techniques were used to obtain the pierced length and several size measures (maximum horizontal and vertical dimensions, circumference and area equivalent diameter) of bubbles intercepted at an ‘imaginary’ probe in a thin two-dimensional fluidized bed. The measured pierced lengths, along with assumed bubble shapes, were used to obtain theoretical predictions of the bubble size measures using geometrical probability. The comparison of the predictions with experimental data, for the first time, enables assessment of the geometrical probability approach and bubble shape assumptions in the prediction of bubble size from measurements on bubble pierced lengths. The results indicate that the use of spherical and ellipsoidal (aspect ratio = 0.77) bubble shapes with geometrical probability leads to good agreement between theory and experiment.

The state of mixing in a gas fluidised bed of sand of a continuous size distribution has been investigated at various fluidisation velocities. The results are shown mainly as axial concentration profiles of the individual size fractions obtained by sieving. It was found that the local size distribution of the bed material was strongly non-uniform axially due to segregation up to fluidisation velocities significantly higher than the minimum fluidisation velocity. Moreover, the segregated bed exhibited a pattern which can be described roughly as two superimposed layers, each of approximately constant powder composition axially. This is similar to what has been found in beds containing binary mixtures of powders. In contrast to binary systems, however, defluidisation of the bottom of the bed was not seen under any of the conditions investigated. An attempt at a qualitative, and in some measure quantitative, explanation of the obtained results has been made.

The formation of segregation patterns in initially homogeneous, fluidized, binary
mixtures of particles has been studied. The adjustment of the bed depends on the
proportions of fine and coarse particles in the mixture and the gas flow rate relative to
the minimum fluidization velocities of the two components. The particles are immobile
until the gas flow rate is sufficiently large to fluidize the mixture of particles. When the
gas flow rate exceeds this critical value, alternating vertical bands of coarse and fine
particles form. At a second critical gas velocity this pattern breaks down and the more
familiar pattern of a mixed horizontal band on top of a layer of coarse particles forms.
A phase diagram, constructed from experimental observations, shows the conditions
for which each of these regimes exists. Its structure is explained in terms of the
fluidization and consequent mobility of the mixture components. When horizontal
bands are present, the thickness of the lower layer of coarse particles decreases with
increasing gas flow rate depending on the proportion of fine particles in the bed.
This, and its development, can be understood by analogy with the sedimentation
of particles through a turbulent fluid. The experiments imply that the efficiency of
mixing by the bubbles in the fluidized bed is very much less than that expected from
gas bubbles in a liquid.

The rate of particle separation was studied in a 7. 0 cm diameter fluidized bed using crushed acrylic plastic particles as flotrsam and dolomite particles as jetsam. The separation fluidizing velocities employed in the studies ranged from velocities slighty higher than the minimum fluidization velocity of the flotsam to higher than that of the jetsam, and the test duration ranged from 3 to 120 s. For mixtures of different jetsam concentrations, the rate and degree of particle separation were different, but the process of particle separation was generally completed in less than 15 s in all cases. A mechanistic model has been developed to explain the particle separation phenomenon for this highly segregating system.

The aim of this paper is to describe an experimental facility to measure the low velocity impact behaviour of spherical particles with high accuracy. Measurements have been made of particle rotation, normal restitution coefficient to within of glancing incidence, and tangential restitution coefficient to within of normal impact, with very low scatter. The results are accurate enough to be used for quantitative comparison to theoretical studies. Achievement of a high level of precision and reproducibility has involved detailed attention to all aspects of the experiment design, construction, control and computer-based image measurement.

The particle concentration profiles and minimum fluidizing velocity of ternary mixtures were investigated experimentally. All the experiments were carried out in an 88 mm I.D. transparent acrylic column containing fluidized beds of ternary particles of different sizes, densities and shape. Mixing/segregation patterns were visualized under different operating conditions. The experimental results are compared with empirical relationships for mixing index and take-off velocity. A new definition of the mixing index, including particle minimum fluidizing velocity and density predicted the mixing/segregation behaviour reliably. The proposed correlation of take-off velocity agrees with the experimental results very well.
On a étudié de manière expérimentale les profils de concentration de particules et la vitesse minimum de fluidisation de mélanges ternaires. Toutes les expériences ont été menées dans une colonne acrylique transparente de 88 mm de diamètre intérieur contenant des lits fluidisés de particules ternaires de tailles, densités et formes différentes. On a visualisé des modèles de mélange/ségrégation dans des conditions de fonctionnement variées. Les résultats expérimentaux ont été comparés à des relations empiriques d'indice de mélange et de vitesse de déversement. Une nouvelle définition de l'indice de mélange, incluant la vitesse minimum de fluidisation des particules et la masse volumique, prédit de façon satisfaisante le comportement de mélange/ségrégation. La corrélation proposée pour la vitesse de déversement concorde parfaitement avec les résultats expérimentaux.

Bubble size is an important parameter in the design of fluidized bed reactors. A novel method based upon digital image analysis has been developed to automate the measurement of bubble properties in gas-fluidized beds. In order to identify the bubbles, the gray-level image is segmented by applying a global threshold. The distributions of various bubble properties as a function of bed position and fluidizing velocity are presented. Results are compared with theoretical predictions using a population balance model The study shows that the model in which coalescence is considered as the dominant growth mechanism may not be adequate.

The application of tomographic and other imaging techniques to the investigation of fluidized beds is reviewed. A majority of the work in the past has focused on the developing technology in radiation absorption imaging, but recent advances in electrical tomography are beginning to be exploited. The work on fluidized bed systems has shown that there are many other applications of tomographic techniques to process engineering, and that similarity extensive research and development should be encouraged.

A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid–solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Microscale processes such as particle–particle collisions, droplet–particle coalescence and agglomeration are directly taken into account by simple closure models. Simulations of the hydrodynamic behaviour of a batch granulation process are presented to demonstrate the potential of the model for creating insight into the influence of several key process conditions such as fluidisation velocity, spray rate and spray pattern on powder product characteristics.

A hard-sphere discrete particle model of a gas-fluidised bed was used in order to simulate segregation phenomena in systems consisting of particles of different sizes. In the model, the gas-phase hydrodynamics is described by the spatially averaged Navier–Stokes equations for two-phase flow. For each solid particle, the Newtonian equations of motion are solved taking into account the inter-particle and particle–wall collisions. The (2D) model was applied to a binary system consisting of particles of equal density, but different sizes where the homogeneous gas inflow velocity was equal to the minimum fluidisation velocity of the bigger particles. Segregation was observed over a time scale of several seconds although it did not become complete due to the continuous back mixing of the bigger particles by the bubbles. An analysis of the dynamics of the segregation in terms of mass fraction distributions is presented. When the particle–particle and particle–wall interactions were assumed to be perfectly elastic and perfectly smooth, segregation occurred very fast and was almost complete due to the absence of bubbles.

An automated non-intrusive image analysis method has been developed for following the course of solids mixing in two-dimensional bubbling fluidized beds. In this investigation, experimental data have been obtained on the axial mixing of uniform solids. Oscillations in the concentration response, resulting from the gross circulation of the solids, have been observed experimentally. These oscillations become increasingly more prominent as the bed particle size increases. These measurements have been used to evaluate the three-phase counter-current back-mixing model (Gwyn et al.). The bubble parameters required for the model were obtained from independent experiments conducted as a part of this investigation; the exchange coefficient however, was found by parameter estimation using the solids mixing data. With this choice of parameters, the counter-current flow model has been found to predict the experimental trends reasonably well. The estimated values for the exchange coefficient do not compare favourably with the predictions of the models available in the literature (Yoshida and Kunii, and Chiba and Kobayashi). These models predict that the wake exchange coefficient should increase with increase in the minimum fluidization of the bed particles. Our results, on the other hand, show that the wake exchange coefficient increases with UO/Umf for UO/Umf < 3 and the values, in this region are independent of the particle size. In line with these results, the experimental measurements of Chiba and Kobayashi, for injected bubbles in a two-dimensional fluidized bed of particles smaller than those used in this investigation, are found to be in excellent agreement with the lower bound of our estimations.

Thesis (doctoral)--Universiteit Twente, 2000.

Particle impact tests were performed on three types of orbiter surface with a micrometeoroid facility. The test equipment electrostatically accelerated micron sized particles to high velocities simulating micrometeoroid impacts. Test particles were titanium diboride with typical velocities in the range 1 to 2.3 km x sec/1 and equivalent particle diameters in the range 4 to 16 microns. Impact angles to the material surface were 90, 60 and 30 degrees. The particle impact sites were located on the sample surfaces and craters were photographed with a magnification of 400X.

Results of particle impact tests, Impact Research Group IRG 13, The Open University

- D A Gorham
- A H Kharaz

D.A. Gorham, A.H. Kharaz, Results of particle impact tests, Impact Research Group IRG 13, The Open University, Milton Keynes, UK, 1999.

1364 hh small i [m] 0.1846 0

- Large

hh large i [m] 0.1330 0.1237 0.1316 0.1364 0.1340 0.1364 hh small i [m] 0.1846 0.1985 0.1948 0.2038 0.2118 0.2059 RMS hh large i [m] 0.0032 0.0067 0.0052 0.0109 0.0082 0.0095 RMS hh small i [m] 0.0055 0.0091 0.0096 0.0125 0.0144 0.0121 50 – 60 s

13 Bed expansion dynamics for a binary mixture (x small = 0.50, h b = 22.5 cm) Fluidisation velocity 1

- A Table

Table A.13 Bed expansion dynamics for a binary mixture (x small = 0.50, h b = 22.5 cm) Fluidisation velocity 1.10 m/s 1.15 m/s 0 – 10 s

5 Fluidisation velocity 1.30 m/s 1.35 m/s 1.40 m

- A Fig

Fig. A.5 Fluidisation velocity 1.30 m/s 1.35 m/s 1.40 m/s 20 – 30 s