Mesh sensitivity analysis on hydrodynamics behavior of a fluidized bed containing silver oxide nanoparticle agglomerates: Transition from bubbling to slugging and turbulent flow regimes

Accepted Manuscript Mesh sensitivity analysis on hydrodynamics behavior of a fluidized bed containing silver oxide nanoparticle agglomerates: Transition from bubbling to slugging and turbulent flow regimes

Shohreh Hamidifard, Alireza Bahramian, Mojtaba Rasteh PII: DOI: Reference:

S0032-5910(18)30185-2 doi:10.1016/j.powtec.2018.03.002 PTEC 13233

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

24 August 2017 5 February 2018 2 March 2018

Please cite this article as: Shohreh Hamidifard, Alireza Bahramian, Mojtaba Rasteh , Mesh sensitivity analysis on hydrodynamics behavior of a fluidized bed containing silver oxide nanoparticle agglomerates: Transition from bubbling to slugging and turbulent flow regimes. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Ptec(2017), doi:10.1016/j.powtec.2018.03.002

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ACCEPTED MANUSCRIPT Mesh Sensitivity Analysis on Hydrodynamics Behavior of a Fluidized Bed Containing Silver Oxide Nanoparticle Agglomerates: Transition from Bubbling to Slugging and Turbulent Flow Regimes Shohreh Hamidifard, Alireza Bahramian*and Mojtaba Rasteh

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Department of Chemical Engineering, Hamedan University of Technology, Hamedan, P.O.

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Box, 65155-579, Iran Abstract

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The fluidization characteristics of silver oxide nanoparticles (NPs) were studied in a bench-scale fluidized bed in this research. Hydrophobic NPs adhere to each other and form nanoagglomerates because of inter-particle forces, leading to bed channeling. The hydrodynamic

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behavior of the two-phase flow was investigated to gain insights into the transition from bubbling to slugging and from slugging to turbulent flow regimes. To check the mesh

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configuration, simulations of the triangular and tetrahedral grid cells were performed using the

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two-fluid model (TFM). The simulation results revealed that the first transition occurs over a range of velocities rather than at a specific velocity, while the second transition occurs due to the upward-movement of bubbles along the bed’s length. The simulation outputs showed that the

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increasing gas velocity reduces the bed’s solid volume fraction mainly because it enhances the

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area occupied by the slugs in the slugging regime, which were identified by optical fiber experiments. The simulation results of fine mesh with the tetrahedral grid cell and near-wall mesh refinement showed a reasonably good agreement with the experimental data, but the results

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deviated when the mesh structure was triangular without the near-wall mesh strategy. The validation of the simulation results was discussed based on experimental observations, optical technique, and pressure measurements.

Keywords: Mesh sensitivity analysis, fluidized bed, hydrodynamic characteristics, bubbling regime, turbulent fluidization, nanoparticle agglomerates. * Corresponding author. Tel.: +98 081 38411502; Fax: +98 081 383852040. E-mail address: [email protected] (A. Bahramian). 1

ACCEPTED MANUSCRIPT 1. Introduction Over the past years, the high specific surface area of microparticles (MPs) and nanoparticles (NPs) has been enhanced especially due to the development of technology in the pharmaceutical, chemical, and petrochemical industries [1, 2]. Typically, ultrafine particles have been used to

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improve the physical and chemical properties of materials, polymers, and dyes and the progress

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of health-related industries, as well as water and wastewater treatment plants [3, 4]. Different

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hydrothermal methods, such as evaporation at high temperature and vapor-phase deposition [5, 6], mechanical techniques like grinding and drilling [7], and liquid-phase methods like micro-

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emulsion have been developed to commercially produce NPs [8]. Metal oxide NPs are produced

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by the sol-gel chemical route [9, 10], followed by the drying of wet particles through freezedrying [11] or heating by fluidized bed dryers [12, 13]. Due to the high cost and the operational

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limitations, industrial-scale manufacturing is not feasible in practice by the freeze-drying

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method. Fluidized beds provide isothermal conditions, good mixing and high gas-solid contact efficiency for the production of large volumes of fine powders and NPs [14-16]. Static imaging

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by scanning electron microscopy (SEM) [17, 18] and dynamic imaging by optical fiber probe

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and laser technique have shown that the hydrodynamic behavior of MPs and NPs in the fluidized beds is significantly dissimilar [19, 20]. Wang et al. [21], classified the fluidization behavior of

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the NP agglomerate into agglomerate particulate fluidization (APF) and agglomerate bubbling fluidization (ABF). They demonstrated that the APF regime shows homogeneous fluidization, low Umf, large bed expansion (typically three to five times the initial bed height), and negligible bubbling even in high gas velocities, whereas the ABF regime exhibits channels and difficulties in fluidization in low gas velocities. Liu et al. [22] proposed a numerical model to simulate the NP agglomerate fluidization. They showed that the qualitative mechanisms could be revealed

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ACCEPTED MANUSCRIPT from their model. According to their finding, in the absence of a cohesive force, the bed shows an almost uniform fluid-like regime or APF-type fluidization, and the bed expansion ratio reaches around 5. In the presence of a cohesive force, the bed represents a bubbling regime or ABF-type fluidization, and the bed expansion ratio is almost 2.

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Typically, gas-solid fluidization is divided into homogeneous and heterogeneous types.

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Homogeneous fluidization occurs in a velocity range between the minimum fluidization velocity,

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Umf, and the minimum bubbling velocity, Umb. A heterogeneous fluidization regime with large bubbles could be seen for dense NPs for Ug>Umb. Depending on the gas velocity and the Geldart

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classification of particles, the heterogeneous fluidization regime of the bed varies among

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bubbling, slugging, and turbulent fluidization [23]. For Ug>Umb, bubbles form and disrupt the homogeneous structure of the expanded bed. The bed height decreases because the dense-phase

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voidage decreases and the bubble hold-up increases, which indicates the bubbling fluidization

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regime. In the bubbling regime, the pressure drop remains constant even with an increase in gas velocity. The drop in the bed pressure decreases when the gas velocity is above the terminal

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velocity of the particles [24]. Yang [25] proposed that the slugging regime appears in the

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fluidized beds with aspect ratios (H0/D) greater than 2. This indicates that the bubbles have enough time to coalesce into bigger bubbles called “slugs”, which grow to two-third the size of

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the bed diameter and show slugging regime or bed channeling. Lim et al. [26] showed that turbulent fluidization occurs when Ug is increased and a point is reached in which the slugs or bubbles begin to break down instead of continuing to grow. Their results indicated that turbulent fluidization is not uniform in the axial and radial direction, showing a non-uniformity of the flow structure.

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ACCEPTED MANUSCRIPT Computational fluid dynamics (CFD) has proven to be effective in clarifying the hydrodynamic characteristics of fluidized beds [27-31]. CFD encompasses the continuum (Eulerian−Eulerian) models [27, 30] and discrete particle (Eulerian−Lagrangian) models [29, 31]. The Eulerian−Eulerian or two-fluid models (TFMs) are developed for large-scale

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simulations, in which the controlling equations resemble the Navier-Stokes equations for an

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ordinary gas flow. Unlike the continuum model, the discrete particle model (DPM) is used to

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study the detailed physics of granular flow based on the analysis of motion for individual

continuum-based constitutive equations [32, 33].

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particles. It does not need global assumptions on particles, such as steady-state behavior and/or

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The effect of mesh configuration is an important issue in CFD analysis of the gas-solid fluidized bed because of its influence on simulation accuracy and computational time. The

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related theoretical aspects of mesh configuration have been referred to as “mesh strategy” in the

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literature [34]. In most cases, the rate of convergence to a mesh-independent solution is the key issue, with the computation time dependent on the mesh strategy [35, 36]. Tarelho et al. [37]

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performed a mesh sensitivity analysis on the prediction of the bubble size and the momentum

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exchange between the bubble and emulsion phases. Souza Braun et al. [38] studied the dependence of computational mesh size and diffusion effects in the numerical discretization of

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the convection terms in the CFD simulation of a fluidized bed using the TFM approach. They showed that the first-order upwind (FOU) method was extremely diffusive and needed refined meshes, while the second-order upwind (SOU) method was a successful discretization scheme. Their results also demonstrated that the use of a high-order method, such as the “Superbee” scheme, presented better agreement with the reported data of Kuipers et al. [39] and permitted the use of a coarser mesh in the simulation.

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ACCEPTED MANUSCRIPT This paper focuses on the hydrodynamic behavior of poly-disperse dry silver oxide NP agglomerates in a bench-scale fluidized bed. At first, the hydrodynamic behavior of the bed, such as pressure drop and homogenous bed expansion, was studied experimentally. Then, the numerical studies focused on the analysis of the reliability of predictions affected by mesh

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configuration and resolution. To simulate the gas-solid flow in the bed, a numerical simulation

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with a TFM approach was performed based on the modified Syamlal-O’Brien drag function [40]

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by using triangular and tetrahedral mesh configurations and different numbers of cells. The results are presented in three parts, describing (a) the transition from bubbling to slugging and

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from slugging to turbulent flow regimes, (b) mesh sensitivity effects, and (c) the mesh

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refinement effects on the hydrodynamic behavior of the NP agglomerates, by comparing the simulation results with the experimental data. The present work can be extended to an industrial-

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scale fluidized bed to study the fluidization characteristics of hydrophobic NP agglomerates.

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2. Experimental section

Fluidization experiments were conducted on a bench-scale Plexiglas fluidized bed. Figures

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1A and 1B schematically demonstrate the experimental apparatus and bed dimensions

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respectively. A cylindrical vessel, 0.06 m in diameter and 1.0 m in height, was used in the fluidization experiments. A porous stainless plate of 3 mm thickness (standard mesh No. 635),

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was used as the gas distributor to prevent the fine particles from escaping. Four nylon membrane filters with a pore size of 0.45 µm filtered the exhaust gas. Experimental runs were carried out in different gas velocities to identify steady state bed pressure drop, minimum fluidization velocity, bed expansion ratio (H/H0), and the transition from bubbling to slugging and from slugging to turbulent flow regimes. Figure 1. (A) Experimental apparatus. 1: Compressor, 2: Valves, 3: Rotameter, 4: Electrical heating element, 5: Probe thermometer, 6: Perforated plate distributor, 7: Manometers, 8: 5

ACCEPTED MANUSCRIPT Fluidized bed, 9: Cylindrical vessel, 10: Bag filters, 11: Nd-YAG solid-state laser, 12: Detectors, 13: Amplifier, 14: Computer and monitor, 15: Cyclone. (B) Dimensions of the column. Dried hydrophobic silver oxide NPs with an average initial size of 28 nm, bought from Degussa Company, were used in the experiments. The hydrodynamic behavior of silver oxide

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particles can be classified as Geldart B group [41]. Each experimental run was repeated at least

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twice with new particles to confirm the reproducibility of the data. Figures 2A and 2B show

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TEM and high-magnification SEM images of the primary silver oxide NPs. The silver oxide NPs abruptly adhere to each other to form nano-agglomerates during fluidization because of attractive

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inter-particle forces such as van der Waals interaction. The silver oxide nano-agglomerates have sphericity ranging between 0.84 and 0.91. Figure 2C presents a low-magnification SEM image of

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silver oxide nano-agglomerates after the fluidization process. A low-magnification SEM image

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of micron-sized particles is also shown in Figure 2D, which represents that the silver oxide NPs

the agglomerates in the bed.

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are nearly spherical in shape. The ImageJ software was used to determine the size and shape of

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Figure 2. Microscopic images of silver oxide NPs, NP agglomerates and micro-particles. (A) TEM image of primary NPs; (B) high-magnification SEM image of NPs; (C) low-magnification SEM image of NP agglomerates; (D) low-magnification SEM image of micron sized particles. Table 1 shows the size distribution of the silver oxide NP agglomerates sieved after

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fluidization. A mean diameter of 175 µm was determined based on the analysis of the weight fractions for each sieve opening. Table 2 shows the physical properties of the silver oxide nanoagglomerates. The Brown and Richard method was used to determine the initial solid packing [42]. Table 1. Particle size distribution of silver oxide NP agglomerates used in this study Table 2. Physical properties of silver oxide nano-agglomerates 6

ACCEPTED MANUSCRIPT The experiments were carried out in a fluidized bed unit with a static bed height, H0, of 0.04 m, and the Ug, ranged from 0 to 650 mm s-1. Nitrogen at a temperature of 60 °C was used as the fluidizing gas. In all the experiments, the gas velocity first increased from the fixed-bed state to the completely fluidized bed, and then decreased until the initial state was reached. The gas flow

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meter (Brooks® mass flow meter 5863S) was used to measure the volumetric flow rate of the

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gas, and the bed pressure drop was measured by a differential pressure transducer (RS 286-686).

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An optical probe modulation technique was employed to determine the bed solid volume fraction in different axial positions. An r-z translator was used to insert the probe in certain

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locations. An Nd-YAG laser served as the light source, with a frequency of 50 Hz. Light signals

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were collected by a photodiode, converted to a voltage ranging from 1 to 100 mV, and passed through an amplifier (resulting in signals ranging from -12V to +12V). A 12V source transmitted

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light to the emitting fiber, and a filter controlled the beam intensity. An analog/digital signal

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interface sent the information to a computer for the statistical analysis and processing by MATLAB 7.1. Further details of the experimental system and procedure are available elsewhere

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[20, 43-47].

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3. Simulation procedure and CFD modeling 3.1. Numerical Procedure and Modeling

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The Eulerian-Eulerian approach (TFM model) was used for the gas and solid phases. Silver oxide particles and nitrogen at a temperature of 60°C and atmospheric pressure respectively were considered as the solid and gas phases. The governing equations of TFM have been summarized in Appendix A (Eqs. A.1-4). The constitutive equations for the solid stress tensor, shear viscosity, solid pressure, collisional dissipation energy, solid-phase momentum, granular temperature, and the related parameters have been presented in Appendix B (Eqs. B.1-11). Based

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ACCEPTED MANUSCRIPT on previous literature, use of the modified Syamlal-O’Brien [40] drag model in the simulations gives the lowest value of the mean relative error for the prediction of solid volume fraction and bed expansion ratio among other drag models [2, 22, 46]. In particular, in the dense region (Ug0.8.

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This is in agreement with the results of Herzog et al. (2011). In the dilute region (Ug>Umf), the

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Syamlal–O’Brien model gives more accurate predictions than the Gidaspow drag model does.

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The value of αs in the present study was 0.85 (αg=0.15); that is, the drag coefficient was neglected by the Gidaspow drag model in the transition from a dense to a diluted regime.

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Therefore, the modified Syamlal-O’Brien drag model was applied to all the CFD simulations.

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The modified Syamlal-O’Brien model and the corresponding correlation, including the interphase momentum exchange, coefficient have been summarized in Appendix C (Eqs. C.1-3).

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Since the volume fraction of particles is a key factor in calculating the effective viscosity of a

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two-phase flow, the granular solid viscosity (µs) should be used to determine the mixture viscosity, which is presented in Appendix B. The volume-weighted average viscosity

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incorporates the shear viscosity arising from particle momentum exchange due to the particles’

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collision.

The gas-solid flow was simulated using a commercial package ANSYS-Fluent as a CFD

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solver and ANSA as a pre-processor. The ANSA was selected because a structured hexahedral mesh can be generated with HexaBlock tools even for quite complex geometries [47]. The SIMPLE solution method was applied to simultaneously solve the coupled pressurevelocity equations for the two phases in a segregated state. All partial differential equations were solved using a SOU discretization scheme.

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ACCEPTED MANUSCRIPT To compare the simulation results with the experimental data, all the simulation runs were set to the properties similar to those of silver oxide agglomerates with a diameter of 175 μm (according to the average particle diameter obtained in the experiments). A restitution coefficient (ess) of 0.9 was applied to the simulations. Depending on the convergence of the solutions, the

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time step for unsteady simulations varied from 5×10-5 to 1×10-4 s to minimize the total

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computing time. The simulation time of 3.0 s was sufficient to obtain independent results for the

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averaging time. The real time for CFD simulations varied from ~18 to 54 hours, depending on

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the mesh strategy applied to a PC with a 4-GHz 8-core processor. 3.2. Assumptions and Boundary Conditions

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The assumptions and the boundary conditions used in the present study were:

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1. The continuous phase was treated as an ideal gas.

diameter of 175 µm.

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2. The silver oxide particles were assumed to have a spherical shape with an average

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3. At the inlet, the gas velocity was assigned in the range of 8 to 650 mm s-1. The inlet solid velocity was set to zero.

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4. The outlet pressure was equal to the atmospheric condition.

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5. At the wall, the no-slip boundary condition was used for the gas-phase, while the partial slip condition developed by Johnson and Jackson was applied for the solid-phase [43]. 3.3. Mesh Configurations and Grid Sizes To evaluate the effects of mesh strategy, five mesh configurations were considered. Table 3 demonstrates the configurations and the number of grid cells used in the simulations. The wall region (0.4–0.5 r/R range, in which r is the radial direction and R the bed radius) near the distributor (z≤2 cm, in which z is the axial direction) is subject to a near-wall mesh strategy

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ACCEPTED MANUSCRIPT because this zone is more sensitive to the mesh size due to the adhesion between the particles and the wall [45]. At the bottom of the bed, where the solid volume fraction is relatively high, a mesh as fine as (2.3-4.5)dagg, avg (i.e., 0.4-0.8 mm) was tested. At the top of the bed, coarser mesh sizes, such as 1.0 mm×1.0 mm and 1.5 mm×1.5 mm, were applied to reduce the

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computational time. Figure 3 shows the typical mesh configurations. The magnified images are

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placed next to each one for a better understanding.

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Table 3. Grid properties and mesh configurations used in the simulations

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Figure 3. Mesh configurations and grid cells used in the simulations 3.4. Mesh Independence Analysis

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To verify the mesh independence strategy, the pressure drop across the bed was studied based

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on different numbers of cells. Five meshes, based on tetrahedral and triangular configuration with different numbers of cells, were used for this analysis. Figure 4 shows the bed pressure drop

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versus the number of meshes at Ug=220 mm s-1 for each configuration. The optimum mesh was

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selected in each case, in which no improvement was seen in the errors by increasing the mesh

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number.

Figure 4. The bed pressure drop profile versus number of cells

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Figure 5 shows the results of mesh-independent studies to check the computational performance of each mesh arrangement. An analysis of variance was used to show the independence of the predictions from the mesh number based on the different mesh strategies, which is mentioned in Table 3. A mesh-independent solution was obtained for each mesh arrangement to study the hydrodynamic behavior of the bed based on optimal mesh. For example, in the case of mesh #1, after refining the grid from cells 62200, the results did not vary

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ACCEPTED MANUSCRIPT significantly. So, cells 62200 were used for further analysis in this mesh. The computational time required for meshes #1 and #3 (tetrahedral geometry) were ~28 hours and ~33 hours respectively. The corresponding values for the computational time for meshes #4 and #5 (triangular geometry) were ~40 hours and ~54 hours respectively.

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Figure 5. The mesh independency analysis

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When the number of grid cells in a mesh with a specific configuration increases, the calculation error is reduced, while the rounding error increases. This happens because of the

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reduction in the discretization error for small meshes, while the greater number of repetitive

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operations increases the rounding error. Among the simulations with tetrahedral cells, the use of the near-wall strategy in the TFM simulation is also acceptable in terms of computational time

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and calculation error.

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4. Results and discussion

4.1. Transition from Fixed Bed to Bubbling Regime

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The transition from a fixed-state to bubbling flow regime happens by increasing the size of

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the bubbles and the coherent structures in the bed by increasing the gas velocity [48, 49]. Uniform bubble distribution and relatively smooth particle circulation are seen over the cross-

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sectional area of the bed in the bubbling flow regime. The experimental procedure to determine minimum bubbling velocity (umb) is based on the appearance of the “first obvious bubble” with a gradual increase in the gas velocity. Geldart and Wong [48] experimentally described the way bubbles destroyed the fixed-bed structure by increasing the gas velocity slightly above umb, implying a transition regime. In our experimental observations, a fixed-bed regime was established for Ug<14.0 mm s–1, while small bubbles appeared at 16.0 mm s–1, and the bubbling regime was seen up to Ug≈28.0 11

ACCEPTED MANUSCRIPT mm s–1 for H0=0.04 m. The transition between the two regimes was gradual and obviously evident. From the simulation viewpoint, “bubble” is characterized in literature as a zone with a solid volume fraction of less than either 0.15 [48] or 0.2 [50]. In this work, the solid volume fraction

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for the characterization of the bubbling regime was selected at 0.15 as a threshold value. The

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value of umb corresponded to the lowest velocity for which one or more cells in the contour plots

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were detected with a solid volume fraction less than the threshold value. The visual method was usually used to determine the umb from the transient simulation in the first 1.5 to 2.5 s of the

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simulation time. Figure 6 shows the typical fine mesh simulation (mesh #3) contour plots of the

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bed containing silver oxide particles. A pseudo-steady-state simulation was reached before 2.0 s; hence, the fluidization time of 3.0 s was selected for the bubble detection. The contour plots

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show the bed expansion associated with the transition from the homogeneous to the bubbling

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regime in the velocity range of 8.0 mm s-1 (Fig. 6a) to 16.0 mm s-1 (Fig. 6e). The simulation contour plots obviously show the appearance of diluted zones, which can be

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defined as the zones of changed voidage which overcome the homogeneous structure of the bed.

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As it can be seen, the diluted zones appeared around 12 mm s-1 (Fig. 6c), while the bed uniformity was maintained for Ug≤10 mm s-1 (Figs. 6a-b). Hence, the diluted zones visibly

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disrupted the bed uniformity, thereby creating local voidage fluctuations. It was clearly visible that multiple bubbles appeared at 14 mm s-1 (Fig. 6d), and this velocity indicated the breakout of heterogeneous structures in the bed, leading to a bubbling regime, which was assigned as the bubbling velocity (ub) [36]. An observation of the defined multiple bubbles at 12 mm s-1 was also reported from the DEM simulations [51].

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ACCEPTED MANUSCRIPT For TFM simulations, the transition to the bubbling regime apparently occurred over a velocity range (umb−ub) rather than in a single velocity, implying a transition regime to the bubbling state. The value of umb obtained by the visual method and the simulation results for different mesh strategies were only around 12−14 mm s-1. Even for a fine mesh strategy (mesh

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#3), the small domain contour plots exhibited the onset of diluted zones, showing that a small

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domain had a homogeneous particle distribution. The transition regime from 9−12 mm s-1 seems

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to be supported by the DEM simulation contour plots of Renzo and Maio (dp=70 μm, ρs=1.0 g cm-3) [51]. The value of umb obtained in this study, (14 mm s-1), was slightly greater than that of

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the others reported from DEM simulations [51]. This might be explained as a consequence of the

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increasing Geldart B characteristics of the particles due to the high ρs value of silver oxide particles (2.92 g cm-3) compared to other related studies that used particles with ρs values of 1-2.8

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g cm-3 and dp=70 μm [51]. However, it must be noted that the empirical correlation of

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Abrahamsen and Geldart gives no change of umb with ρs [52].

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Figure 6. Typical fine mesh simulation (mesh #3) contour plots of the bed containing silver oxide particles at pseudo-steady-state (transition from fixed state to bubbling regime (a-f), bubbling to slugging regime (g-j) and turbulent flow (k). [(a): 8, (b) 10, (c) 12, (d) 14, (e) 16, (f) 24, (g) 30, (h) 48, (i) 54, (j) 62, (k) 85 mm s-1]. 4.2. Transition from Bubbling to Slugging and Turbulent Flow Regimes

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Experimentally, the slugging state of the bed is identified by using a visual method from the outside of the bed. The transition from the bubbling to the slugging flow regime is identified by a rapid process known as the “choking phenomenon”. In this phenomenon, a small change in the gas velocity leads to a big change in the bed’s hydrodynamic behavior, such as a pressure drop, or in the bed expansion ratio [32]. Although the initiation of choking is reflected in the pressure drop profile of the time-series pressure drop signals, little is known about the mechanics of the choking transition for Group B particles based on internal flow structure variations. 13

ACCEPTED MANUSCRIPT Experimental observations showed that a transition from the bubbling to the slugging regime occurred when the gas velocity was beyond the minimum slugging velocity, ums, 28 mm s–1. A distinct variation was seen during the choking transition, in which wall slugs/gas intervals formed for Ugums. After the transition, the

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bed experienced slugging fluidization and the wall slugs were created. During transition from the

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bubbling to the slugging regime, the slugs with various irregular shapes moved upward across

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the center of the bed. This made the particles’ movement in the slugging regime more violent compared to the bubbling regime. In the slugging regime, a low percentage of gas flow

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penetrated the particles’ near wall due to the large size of the slug in the bed’s central region.

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The bubbles were stretched due to the bed wall effects and their interaction. And then, they moved upwards, leading to larger bubbles. These bubbles burst and split when they reach the top

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of the bed. There were upward particles rising in the bed center and downward particles falling

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on the walls, leading to a heterogeneous particle circulation and mixing flow. Figure 6 (g–j) shows the fine mesh simulation results of the transition from the bubbling to

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the slugging regime. The slugging fluidization regime could be seen at a gas velocity ranging

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from 28 to 62 mm s-1, in which ums was determined to be 28.0 mm s-1 (Fig. 6g). For Ug>ums, the bubbles with irregular shapes and various sizes rose in a spiral motion and became large enough

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to spread through the bed of particles. At Ug=62 mm s-1 (Fig. 6j), the bubbles were detached from the bottom and a sharp lifting of the particles was observed. When the gas velocity was further increased, the upper surface of the bed disappeared and, instead of irregular bubbles, a turbulent motion of particles was observed. A transition from the slugging to the turbulent regime was seen at a velocity utr of around 85 mm s-1 (Fig. 6k), and for Ug>utr, a turbulent flow occurred.

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ACCEPTED MANUSCRIPT 4.3. Mesh Sensitivity Effects on the Bed Hydrodynamics in a Turbulent Regime Figure 7 shows fine mesh simulation (mesh #3) contour plots of the simulated solid volume fraction in a fluidized bed in a turbulent flow regime (Ug=220 mm s-1) based on the modified Syamlal-O’Brien drag model. Experimental observations clearly showed that after the fixed

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state, the bed was expanded at t=0.2 s, associated with flocculation and the formation of bubbles.

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At t=0.4 s, the bed expansion ratio increased mainly because of the bubbles coalescing at the top

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of the bed. At t=0.6 s, the bed appeared to be in a stable wavelike fluidization regime, and large agglomerates adhered to the distributor plate. However, at the time of 0.6 s, the hydrodynamics

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of the simulated bed were in a semi-stable wavelike state (Fig. 7). For the 0.8≤t≤1.8 s interval,

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channeling appeared in the bed center, which is called a “spout zone” in the literature, and gas bubbles passed through this region until the whole bed was gradually fluidized [50, 51]. For

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t≥0.6 s, the system reached a pseudo-steady state, and no substantial changes were observed in

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the flow regime. During fluidization, a greater gas flow was observed through the spout zone, with channeling through the core of the bed, while less gas flowed through the near-wall annular

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zone. The particle velocity was higher in the spout zone than in the annular zone.

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Although the contour plots were reasonably consistent with our experimental observations, the following points should be noted: (1) Compared to the simulation, fluidization was delayed

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in the experimental runs, probably due to the stronger inter-particle forces. In addition, the significant difference between the simulation results and experimental data can be attributed to the effects of the gas distributor, which is not included in the CFD simulation. (2) The contour plots exhibited a transition from bubbling to turbulent fluidization. Although the modified Syamlal- O’Brien model predicted small bubbles near the bottom of the bed, in real conditions, the bubbles grew due to coalescence and rose to the top of the bed. (3) There were variations in

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ACCEPTED MANUSCRIPT the instantaneous bubble dynamics predicted by a fine mesh strategy. (4) The fine mesh simulation showed that the solid volume fraction varied considerably in the axial direction. (5) The application of a fine near-wall mesh strategy (mesh #3) led to particle homogeneity in the bed.

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Figure 7. Fine mesh simulation (mesh #3) results of solid volume fraction profile for 2-D bed over 0.0–3.0 s interval at Ug=220 mm s-1.

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Figure 8 shows the experimental data (A) and simulation results (B) of the bed pressure drop as a function of time for Ug=220 mm s-1. As it has been shown, the bed pressure drop decreased

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rapidly within just a few seconds. The reason for this transition can be explained by the fact that

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the bed pressure drop is initially greater than the particles’ weight in the bed per unit of the crosssectional area, which is called “overpressure” [44, 53]. This overpressure is necessary to

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overcome the friction force between the particles and the wall and the adhesion force between

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the particles and the gas distributor. Pressure fluctuations in the bed continued, especially for the ABF flow regime, though the amplitude of the pressure fluctuations decreased with time. After a

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few seconds, bed channeling took place with time, which gave way to a decrease in the pressure

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drop fluctuation. The greatest deviations between the experimental data and the simulation results were seen at the bottom of the bed due to the interaction between gas and large

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agglomerates, in which a high adhesion force exists between the particles and the distributor plate, and a high friction force exists among the particles. Although the modified SyamlalO’Brien drag model provides great deviations at the bed bottom, the Gidaspow drag model may accurately predict the drag coefficient only when αg>0.8. The simulation results were obtained using the modified Syamlal-O’Brien drag model by applying the five meshes introduced in Table 3. For t <0.4 s, all the simulations predicted a sharp peak of the bed pressure drop, though the pressure drop eventually reached the bed weight per 16

ACCEPTED MANUSCRIPT unit area [22, 51, 54, 55]. For 0.6
T

t=3.0 s was a good time to extract data from the CFD simulations. It should be noted that despite

IP

the long time of simulation, the bubbling regime also created significant fluctuations, and a rise

CR

in the gas velocity increased these fluctuations.

US

Figure 8. The variation of bed pressure drop as a function of time at Ug=220 mm s-1. (A) The experimental data, (B) predicted results for different mesh strategies.

AN

Figure 9 shows the experimental data and the simulation results of the bed pressure drop as a function of the gas velocity for the five meshes introduced previously. Experimental

M

observations showed that for Ug~80 mm s-1, the bed was in a wave-like state. According to

ED

Figure 9, the experimental value of Umf, corresponding to the change in pressure drop behavior, is 90 mm s-1. At this point, the total weight of the particles is balanced with the pressure drop.

PT

The experimental data showed that the pressure drop remained more or less constant, around 700

CE

Pa, for Ug>100 mm s-1. For Ug≥90 mm s-1, the pressure drop increased abruptly, indicating that the turbulent fluidization was achieved in the bed. The experimental results also showed a

AC

transition from the slugging to the turbulent regime and a reverse flow regime with time, giving rise to slight variations in the bed pressure drop. The simulation result showed the value of Umf close to the experimental value (±10%), though some variations can be seen in the bed pressure drop. This deviation happened because of the inter-particle cohesive forces at work between the silver oxide NPs, especially near the wall, which are not considered by the simulations. It should

17

ACCEPTED MANUSCRIPT be noted that the simulated values of pressure drop were obtained by averaging the data across the bed for t=3 s. Figure 9. Pressure drop vs. superficial gas velocity for fluidized bed. [Simulation results were obtained at t=3 s for five different meshes as introduced in Table 3].

T

The value of utr, which was previously introduced as the transition velocity from the

IP

slugging to the turbulent fluidization regime, is an important parameter for the hydrodynamic

CR

behavior of fluidized beds [56]. Based on Figure 9, the experimental value of utr was determined to be 120 mm s-1 for H0=0.04 m. The relative error (%) between the experimental data and the

US

predicted values of the utr for the different meshes is shown in Table 4. As it can be seen, the use

AN

of the structured tetrahedral configuration mesh in the simulation caused less deviation from the experimental data compared to the triangular configuration. Using the fine near-wall strategy

M

(mesh #3) could help reduce the relative error (%) in the structured tetrahedral configuration.

ED

Table 4. The relative error (%) between experimental data and simulated values of the utr for different mesh configuration

PT

Figure 10 compares the experimental data and the simulation results of the bed expansion

CE

ratio for all the five studied meshes as a function of the inlet gas velocity. The CFD results were obtained at t=3 s for five different meshes. As observed in the experimental data, for Ug
AC

bed was not expanded considerably and the bed expansion ratio was close to unity. As the gas velocity increased (Ug>utr), the bed slowly expanded and fluidized in the upper part, while the bottom of the bed was in a wave-like state. This could be due to the formation of agglomerates during fluidization or the creation of large agglomerates at the bottom of the bed. A reason for this was that dense agglomerates probably formed during the fluidization of the bed under the bubbling flow regime because near the bottom of the bed, the agglomerates consisted of polydispersed micrometric particles in sizes that naturally needed a higher inlet gas velocity [8, 54]. 18

ACCEPTED MANUSCRIPT However, as the inlet gas velocity increased, channeling gradually disappeared and the bed began to be fully fluidized [49, 51, 52, 57, 58]. Figure 10. Comparison of the experimental and simulated bed expansion ratio [Simulation results are obtained at t=3 s for five different meshes as introduced in Table 3].

T

Table 5 provides the relative errors (in %) between the experimental data and the

IP

simulation results of the bed expansion ratio at different gas velocities. The deviations between

CR

the experimental data and the simulation results may have happened due to high inter-particle

US

friction forces and particle-particle collisions that cannot be applied to the TFM simulations. The simulation results showed that when a coarse mesh was used (meshes #1 and 4), the relative

AN

error (in %) value of the simulated bed expansion ratio increased. The relative error values indicated that the simulation results for mesh refinement strategy (mesh #3) provided a better

M

agreement with the experimental data, which was verified by previous studies [30, 32, 33, 44,

ED

59]. McKeen and Pugsley [32] revealed that the bed expansion for FCC particles at Ug=100 mm s-1 was about 70 % greater than the experimental value for a 10 mm×10 mm grid, and 35%

PT

greater for a 2.5 mm×2.5 mm grid, indicating that a mesh refinement strategy played an

CE

important role in CFD simulation. In a later study on the same system Parmentier et al. [55] overestimated the bed expansion by about 24% while using a 1 mm×1 mm grid. They indicated

AC

that the simulation results approached the experimental data, when fine grids were used. Table 5 also suggests that meshes with a tetrahedral structure (meshes #1–3) exhibited a smaller relative error than those based on triangular cells (meshes #4 and 5). The use of near-wall mesh strategy for the prediction of bed expansion ratio for Ug=650 mm s-1 was not approved, which contributes to high energy dissipation of large particles at a high gas velocity in the real state. Table 5. The relative error values (in %) between experimental data and simulation results of the bed expansion ratio 19

ACCEPTED MANUSCRIPT Figure 11 shows the experimental data and the simulation results of the radial distribution of solid volume fraction profile at z=0.08 m and gas velocities of 30, 48, 54 and 62 mm s-1. The time-averaged simulation results were obtained for five different meshes, as shown in Table 3. The simulation results of the solid volume fraction are time-averaged from 0.2 to 3 seconds. The

T

time-averaged results across the bed are expected to be asymmetrical. Both the experimental data

IP

(Fig. 11a) and the simulation results (Fig. 11b) indicated that the solid volume fraction is

CR

increased near the wall region. Visual observations demonstrated that the increase in gas velocity reduces the bed solid volume fraction mainly because of an enhancement of the area occupied by

US

the slugs in the slugging regime. A mesh sensitivity analysis showed that the inhomogeneous bed

AN

structures can be recognized better when the mesh resolution increases (mesh #2). The case with the finer mesh represents more solid volume fraction fluctuation, probably because more

M

computing performances are required for the time-averaging procedure. By increasing the mesh

ED

resolution (mesh #2), more particles are moved to the centre of the bed, which results in a decrease in the solid volume fraction close to the walls as the mass flux of particles remains

PT

constant. By applying the mesh-refinement strategy (mesh #3), the predicted values of solid

CE

volume fraction can be found to be in good agreement with the experimental data. Figure 11. Experimental data (a) and simulation results (b) of the radial distribution of solid

AC

volume fraction profile at z=0.08 m and gas velocities of 30, 48, 54 and 62 mm s-1 [timeaveraged Simulation results are obtained at Ug=48 mm s-1 and H=0.08 m for five different meshes as introduced in Table 3].

Figure 12 compares the experimental data and simulation results of the axial solid volume fraction profile in different gas velocities of 220, 425, 531, and 650 mm s-1 for the five mesh strategies. The simulation results were obtained at t=3 s for different mesh strategies. The experimental data showed that the solid volume fraction decreased with the bed height, reaching 20

ACCEPTED MANUSCRIPT zero at the top of the bed. The results followed a reverse S-shaped trend with the bed height. As observed in Figure 12, with the increase in the bed height, the solid volume fraction reduced sharply. In addition, the distribution of the solid volume fraction across the bed was wider at Ug=650 mm s-1 compared to that at 220 mm s-1. The simulated values were obtained from

T

averaging the solid volume fractions in all the computational cells at different bed heights. The

IP

trend of the simulation values was reasonably similar to the experimental data. It is noteworthy

CR

that accurate measurements may not be established with certainty close to the gas distributor, in which considerable deviations were seen. Particularly, the particles tend to stick around the

US

corner of the distributor plate, and the gas flow is blocked due to a strong binding between the

AN

particles and the distributor plate. In addition, the dense phase at the gas distributor had a high circulation rate of particles due to the high downward solid flow. Furthermore, intense

M

fluctuations between the solid volume fractions can be identified by the difference between

ED

<αsUs>ρs and <αs>˂Us>ρs terms (Appendix A), which indicates that the turbulent diffusion plays a key role in the dense flow [52]. The lack of balance between the effective gravity and the

PT

pressure drop is due to sudden changes in the bulk particle density and the bed pressure drop,

CE

which leads to the local channels, as well as measurement difficulties and errors caused by the

AC

processing of the data.

Figure 12. Experimental data and simulated values of the axial solid volume fraction profile at gas velocities of (a) 220, (b) 425, (c) 531, and (d) 650 mm s-1 [Simulation results are obtained for five different meshes as introduced in Table 3] Table 6 shows the relative errors (%) between the experimental data and the simulation results of the solid volume fraction across the bed at different gas velocities. The presented results were obtained by averaging the solid volume fraction data at any particular height of the bed. It was found that the CFD simulation results gained by applying the mesh #3 were more 21

ACCEPTED MANUSCRIPT accurate for the solid volume fraction along with the axial distance of the bed. The results also confirmed that the simulation results gained by applying structured tetrahedral configuration exhibited less deviation from the experimental data compared to that of the triangular cells. In addition, choosing the wall refinement strategy (mesh #3) led to a reduction in the relative error

IP

T

(%) compared to the other mesh configurations.

CR

Table 6. The relative error values (%) between the experimental data and simulation results of the solid volume fraction across the bed height at the different gas velocities 5. Conclusion

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The fluidization characteristics of the silver oxide NPs with a primary diameter of 28 nm were

AN

studied in a fluidized bed. Experimental measurements were performed by using the optical fiber modulation technique and the pressure drop analysis to study the hydrodynamic behavior of the

M

bed at different gas velocities. Silver oxide NPs with a hydrophobic property adhere together to

ED

form nano-agglomerates because of the inter-particle forces. This leads to the formation of cracks and channeling in the bed. The hydrodynamic behavior of the two-phase flow was studied

PT

to gain insights into the transition from fixed-state to bubbling, from bubbling to slugging, and

CE

from slugging to turbulent flow regimes. Subsequently, a numerical approach based on the Eulerian-Eulerian approach (TFM) was carried out by the triangular and tetrahedral grid cells.

AC

The TFM simulations clearly revealed that the transition from the fixed-bed to bubbling flow regime occurred by an increase in the size of bubbles and coherent structures by an increase in the gas velocity. Hence, rather than a discrete minimum bubbling velocity, a “transition regime” (umb−ub) was clarified by diluted zones in the bed, implying a transition regime to a bubbling state. The values of umb obtained by the visual method and the simulation results by different mesh strategies were only around 12−14 mm s-1. The simulation results showed the low amplitude of pressure fluctuations, resulting from the disappearance of bed voids. Experimental 22

ACCEPTED MANUSCRIPT observations showed that the transition from the bubbling to slugging regime occurs when the gas velocity is beyond the minimum slugging velocity of 28 mm s–1. During the transition from the bubbling to the slugging regime, the slugs with irregular shapes move upward across the bed center. It makes the particles in the slugging regime move more violently compared to those in

T

the bubbling regime. The transition regime from the slugging to the turbulent fluidization was

IP

characterized by an upward-movement of the bubbles along the length of the bed. A transition

CR

regime from the slugging to the turbulent flow occurs at a transition velocity of 85 mm s-1. To evaluate the effects of the mesh structure quality on the TFM simulation results, two

US

strategies, including the triangular and the tetrahedral grid cells associated with the mesh

AN

refinement, were studied, and the relevant results were compared with the experimental data. Finding the optimal mesh size allows a highly accurate simulation closer to the experimental

M

data. The CFD results obtained for the transition velocities (i.e. umb and utr) and the solid volume

ED

fraction in the radial and axial directions showed that the tetrahedral mesh configuration associated with the near-wall mesh refinement strategy was more consistent with the

PT

experimental data than the other mesh configurations. Although the effect of the near-wall

CE

refinement strategy on the transition velocity and the solid volume fraction profiles was significant, its influence on the bed pressure drop and bed expansion ratio was trivial, while the

AC

use of this strategy for the prediction of the bed expansion ratio was not approved. The cost-time simulation analysis showed that the triangular cells needed more computational time than the tetrahedral mesh configuration did. In addition, the computing time was saved significantly by choosing a coarser mesh strategy because of a reduction in the rounding error. However, by applying finer mesh simulations, the calculation error can be reduced. The results of this study

23

ACCEPTED MANUSCRIPT can be extended to evaluate the different mesh strategies to analyze the fluidization characteristics of industrial-scale fluidized beds containing hydrophobic NPs. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval

IP

T

to the final version of the manuscript.

CR

Acknowledgments

The authors would like to thank the Hamedan University of Technology (Grant No. E. 28234,

US

2017) and Laser and Optic Research Institute of Iran for optical experiments and processing. The authors also thank Ms. Mina Molaei for producing 3D illustrations by 3D Max Studio modelling.

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Notation and abbreviations

M

Symboles

drag coefficient, dimensionless

d

diameter, m

ess

particle-particle and particle-wall restitution coefficient, dimensionless

H

expanded bed height, m

Ho

static bed height, m

k

turbulent kinetic energy, kg.m-1.s-3

P

PT

CE

AC

kθs

ED

CD

diffusion coefficient for granular energy, kg/ms pressure, Pa

r

radial coordinate, m

R

column radius, m

Re

Reynolds number, dimensionless

t

time, s 24

ACCEPTED MANUSCRIPT U, u

velocity, m.s-1

xi

weight fraction

z

height above distributor

Greek letters volume fraction, dimensionless

β

momentum inter-phase exchange coefficient, dimensionless

Ф

particle shape factor, dimensionless

μ

shear viscosity, kg/ms



density, kg.m-3

θ

granular temperature, m2/s2

average

b

bulk

g

gas

i

general index

mb

minimum bubbling

ms

minimum slugging

AC

CE

PT

ED

M

avg

s

particle solid

tr

transition regime

w

wall

Abbreviations CFD

CR US

AN

Subscripts

p

IP

T



computational fluid dynamics

25

ACCEPTED MANUSCRIPT MPs

micro-particles

NPs

nano-particles

SEM

scanning electron microscope

TEM

transmission electron microscope

T

Acknowledgments

IP

The authors thank Hamedan University of Technology and Laser and Optic Research School of

CR

Iran for use of optical equipment and digital analysis under Project No. CE. 2015-6879. we

US

would also like to thank Professor John R. Grace for reviewing this manuscript. Appendix A

AN

Governing equation and conservation laws for gas/solid flows:

  ( i .i )  .( i .i . v i )  0 t

M

Mass conservation for phase i (i = g for gas and s for solid)

(A.1)

ED

Linear momentum balance for gas and solid phases

PT

      ( g .g . Ug )  .( g .g . U g . U g )   g P  . g   (U g  v s )   g .g . g t       ( s .s . v s )  .( s .s . v s . v s )   sP  . s  Ps   (U g  v s )   s .s . g t

(A.2) (A.3)

CE

Transport equation for the solid phase granular temperature (A.4)

AC

  3  s .s .θs   . s .s . vs .θs   (Ps I  s ) : . vs  .  k ..θs   γ  gs  2  t 

Appendix B

Constitutive equations of gas-solid flow: Solid stress tensor =  2       τs =s   vs  ( vs )T    s  s  . vs 3    

(B.1)

where solid shear viscosity is μs  s,col + s,kin + s,fr

(B.2)

26

ACCEPTED MANUSCRIPT The collisional contribution to shear viscosity is

θ 4 s ,col   s .s .g 0 ,ss 1  e ss  s 5 

(B.3)

The kinetic contribution to shear viscosity

s , kin 

10 s .ds θs .

96s 1  e ss  g 0 ,ss

 4  1  5 g 0 ,ss .s 1  ess   

2

(B.4)

T

The frictional contribution to shear viscosity

IP

s , fr  pf sin( ) 2 I 2 D

4 3

s  s2 .s .ds .g0,ss 1  ess 

CR

Solid phase bulk viscosity

θs π

12 (1  e ss2 ) g 0,ss

s . s2 .θs3/ 2

ds π

Solid pressure

Thermal energy diffusion coefficient

M

Ps   s .s .θs  2 s 1  ess  s2 .g 0,ss .θs

AN

 

US

Collision dissipation energy

ED

25 s .d s s .  6 θ  k  . 1  .s .g 0,ss . 1  e ss   2s .s2 .d s 1  e ss  g 0,ss s 64 1  e ss  .g 0,ss  5  

    1   s    s,max 

(B.6)

(B.7)

(B.8)

2

(B.9)

1/3 -1

  

   

(B.10)

CE

g 0,ss

PT

Radial distribution function

(B.5)

Dissipation of granular temperature by gas damping

gs  3 .θs

AC

(B.11)

Appendix C

The modified Syamlal-O'Brien model and the corresponding correlation including inter-phase momentum exchange coefficient. Syamlal-O’Brien proposed a drag coefficient model based on measuring the particle terminal velocity in fluidized beds:



 Re 3 s . g . g C D . s 2 v 4 v r ,s .d s  r ,s

  . v s U g 

(C.1)

Drag coefficient 27

ACCEPTED MANUSCRIPT 2

  4.8  C D   0.63    Re v s r ,s   vr,s is the terminal velocity correlation for the solid phase: 0.5  A  0.06Res  

 0.06Res 

2

(C.2)

 0.12Res  2B  A   A 2  

(C.3)

where

 g  0.85

B   Qg

 g  0.85

IP

B  P  1g.28

T

A   g4.14

CR

The procedure for specifying the parameters P and Q for the minimum fluidization velocity corresponds

US

to the modified Syamlal-O'Brien model.

AN

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[37] L.A.d.C. Tarelho, D.S.F. Neves, M.A.A. Matos, Forest biomass waste combustion in a pilot-scale bubbling fluidised bed combustor, Biomass and bioenergy, 35 (2011) 1511-1523.

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[38] M.P. de Souza Braun, A.T. Mineto, H.A. Navarro, L. Cabezas-Gomez, R.C. Da Silva, The

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effect of numerical diffusion and the influence of computational grid over gas–solid two-phase flow in a bubbling fluidized bed, Mathematical and Computer Modelling, 52 (2010) 1390-1402.

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[39] J. Kuipers, K. Van Duin, F. Van Beckum, W.P.M. van Swaaij, Computer simulation of the

(1993) 839-858.

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hydrodynamics of a two-dimensional gas-fluidized bed, Computers & chemical engineering, 17

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[40] M. Syamlal, T.J. O’Brien, Computer simulation of bubbles in a fluidized bed, AIChE Symp. Ser, 1989, pp. 22-31. [41] D. Geldart, Types of gas fluidization, Powder technology, 7 (1973) 285-292. [42] R. Brown, J.C. Richards, Principles of powder mechanics, (1970).

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ACCEPTED MANUSCRIPT [43] A. Bahramian, M. Olazar, Profiling solid volume fraction in a conical bed of dry micrometric particles: measurements and numerical implementations, Powder technology, 212 (2011) 181-192. [44] A. Bahramian, M. Olazar, Fluidization of micronic particles in a conical fluidized bed:

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experimental and numerical study of static bed height effect, AIChE Journal, 58 (2012) 730-744.

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[45] A. Bahramian, M. Olazar, G. Ahmadi, Effect of slip boundary conditions on the simulation

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of microparticle velocity fields in a conical fluidized bed, AIChE Journal, 59 (2013) 4502-4518. [46] A. Bahramian, H. Ostadi, M. Olazar, Evaluation of drag models for predicting the

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fluidization behavior of silver oxide nanoparticle agglomerates in a fluidized bed, Industrial &

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Engineering Chemistry Research, 52 (2013) 7569-7578.

[47] Y.L. He, S.Z. Qin, C. Lim, J. Grace, Particle velocity profiles and solid flow patterns in

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spouted beds, The Canadian Journal of Chemical Engineering, 72 (1994) 561-568.

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[48] D. Geldart, A. Wong, Fluidization of powders showing degrees of cohesiveness—I. Bed expansion, Chemical Engineering Science, 39 (1984) 1481-1488.

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[49] P.C. Johnson, R. Jackson, Frictional–collisional constitutive relations for granular materials,

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with application to plane shearing, Journal of fluid Mechanics, 176 (1987) 67-93. [50] P.C. Sande, S. Ray, Fine mesh computational fluid dynamics study on gas-fluidization of

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Geldart A particles: Homogeneous to bubbling bed, Industrial & Engineering Chemistry Research, 55 (2016) 2623-2633. [51] A. Di Renzo, F.P. Di Maio, Homogeneous and bubbling fluidization regimes in DEM–CFD simulations: hydrodynamic stability of gas and liquid fluidized beds, Chemical Engineering Science, 62 (2007) 116-130.

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ACCEPTED MANUSCRIPT [52] D. Geldart, A.R. Abrahamsen, Homogeneous fluidization of fine powders using various gases and pressures, Powder Technology, 19 (1978) 133-136. [53] M. Olazar, M.a.J. San José, M.A. Izquierdo, A.O. de Salazar, J. Bilbao, Effect of operating conditions on solid velocity in the spout, annulus and fountain of spouted beds, Chemical

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Engineering Science, 56 (2001) 3585-3594.

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[54] P. Lettieri, D. Newton, J. Yates, Homogeneous bed expansion of FCC catalysts, influence of

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temperature on the parameters of the Richardson–Zaki equation, Powder Technology, 123 (2002) 221-231.

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[55] J.F. Parmentier, O. Simonin, O. Delsart, A functional subgrid drift velocity model for

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filtered drag prediction in dense fluidized bed, AIChE Journal, 58 (2012) 1084-1098. [56] G.R. Caicedo, M.G.a. Ruiz, J.J.P. Marqués, J.G. Soler, Minimum fluidization velocities for

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gas–solid 2D beds, Chemical Engineering and Processing: Process Intensification, 41 (2002)

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761-764.

[57] J. Li, J. Kuipers, Gas-particle interactions in dense gas-fluidized beds, Chemical

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Engineering Science, 58 (2003) 711-718.

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[58] L. Mazzei, P. Lettieri, CFD simulations of expanding/contracting homogeneous fluidized beds and their transition to bubbling, Chemical Engineering Science, 63 (2008) 5831-5847.

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[59] C. Wen, Y. Yu, A generalized method for predicting the minimum fluidization velocity, AIChE Journal, 12 (1966) 610-612.

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ACCEPTED MANUSCRIPT Figure captions Figure 1. (a) Experimental apparatus. 1: Compressor, 2: Valves, 3: Rotameter, 4: Electrical heating element, 5: Probe thermometer, 6: Perforated plate distributor, 7: Manometers, 8: Fluidized bed, 9: Cylindrical vessel, 10: Bag filters, 11: Nd-YAG solid-state laser, 12: Detectors, 13: Amplifier, 14: Computer and monitor, 15: Cyclone. (b) Dimensions of the column.

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Figure 2. Microscopic images of silver oxide NPs, nano-agglomerates and micro-particles. (A) TEM image of primary NPs; (B) high-magnification SEM image of NPs; (C) low-magnification SEM image of nano-agglomerates; (D) low-magnification SEM image of micron sized particles.

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Figure 3. Mesh configurations and grid cells used in the simulations.

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Figure 4. The bed pressure drop profile versus number of cells. Figure 5. The mesh independency analysis

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Figure 6. Typical fine mesh simulation (mesh #3) contour plots of the bed containing silver oxide particles at pseudo-steady-state (transition from fixed state to bubbling regime (a-f), bubbling to slugging regime (g-j) and turbulent flow (k). [(a): 8, (b) 10, (c) 12, (d) 14, (e) 16, (f) 24, (g) 30, (h) 48, (i) 54, (j) 62, (k) 85 mm s-1].

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Figure 7. Fine mesh simulation (mesh #3) results of solid volume fraction profile for 2-D bed over 0.0–3.0 s interval at Ug =220 mm s-1.

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Figure 8. The variation of bed pressure drop as a function of time at Ug=220 mms-1. (A) The experimental data, (B) predicted results for different mesh strategies.

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Figure 9. Pressure drop vs. superficial gas velocity for fluidized bed. [Simulation results were obtained at t=3 s for five different meshes as introduced in Table 3].

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Figure 10. Comparison of the experimental and simulated bed expansion ratio [Simulation results are obtained at t=3 s for five different meshes as introduced in Table 3]. Figure 11. Experimental data (a) and simulation results (b) of the radial distribution of solid volume fraction profile at z=0.08 m and gas velocities of 30, 48, 54 and 62 mm s-1 [timeaveraged Simulation results are obtained at Ug=48 mm s-1 and H=0.08 m for five different meshes as introduced in Table 3]. Figure 12. Experimental data and simulated values of the axial solid volume fraction profile at gas velocities of (a) 220, (b) 425, (c) 531, and (d) 650 mms-1 [Simulation results are obtained for five different meshes as introduced in Table 3].

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ACCEPTED MANUSCRIPT Tables

20-25

2.79*10-2

1.49*10-3

25-32

3.14*10

-2

-4

28

32-45

3.23*10

-2

45-53

8.78*10-3

53-63

7.13*10

-2

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8.78*10

-2

74-90

5.91*10

-2

90-106

63-74

125-200

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6.84*10

-4

22

5.71*10-4

49

4.98*10

-4

58

1.32*10

-4

68 82

8.94*10-2

6.03*10-4

98

3.02*10-1

5.04*10-4

115

1.76*10-1

5.78*10-4

163

1.14*10-1

4.39*10-4

225

-3

175

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200-250

dp,avg (µm)

-4

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106-125

1

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Total

1.12*10

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Sieve opening, dpi

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(x/dp)i

(µm)

Weight fraction, xi

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Table 1. Particle size distribution of silver oxide nano-agglomerates used in this study

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1.17*10

5.72*10

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Table 2. Physical properties of silver oxide agglomerates Property

symbol (unit)

value

Primary particle size

dp, primary (nm)

28

Average agglomerate size

dagg, avg (µm)

175

solid density

ρs (g cm )

2.92

Maximum packing limit

αp,max

0.67

Initial solid packing

αp,initial

0.85

Average shape factor

φ

-3

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(H0=0.04 m)

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0.88

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ACCEPTED MANUSCRIPT Table 3. Grid properties and mesh configurations used in the simulations.

Structured tetrahedral

Top

1.0×1.0

Bottom

1.0×0.6

Top

0.6×1.0

Bottom

0.6×0.4 Near wall

Top 3

No. of grid cells 62,200 106,900

0.5×1.0

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2

Structured tetrahedral

Grid size (Δx×Δy (mm2))

Other parts 1.0×1.0

Structured tetrahedral / finer grid near wall Bottom

Near wall

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Mesh configuration

77,300

0.5×0.5

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Mesh No.

Other parts 1.0×0.5 1.5×1.5

Bottom

0.8×0.8

Top

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Structured triangle

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1.0×1.0 0.6×0.6

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Bottom

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Structured triangle

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4

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38,700 82,400

ACCEPTED MANUSCRIPT Table 4. The relative error (%) between the experimental data and simulation results of the utr for different mesh configurations Mesh 1

Mesh 2

Mesh 3

Mesh 4

Mesh 5

Experimental data

utr (m s-1)

81.0

83.0

85.0

79.0

76.0

90

Relative error (%)

10.0

7.8

5.5

12.2

15.5

-

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Mesh

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Mesh 1

Mesh 2

Mesh 3

Mesh 4

Mesh 5

0

0

0

0

0

0

220

8.730

8.730

4.100

15.079

9.391

425

6.818

15.909

2.272

7.954

13.068

531

3.571

1.020

3.571

7.653

17.347

650

12.264

1.415

13.679

25.943

12.736

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Ug (mm s-1)

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Table 5. The relative error values (in %) between experimental data and simulation results of the bed expansion ratio

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ACCEPTED MANUSCRIPT Table 6. The relative error values (%) between the experimental data and simulation results of the solid volume fraction across the bed height at different gas velocities Mesh 1

Mesh 2

Mesh 3

Mesh 4

Mesh 5

220

25.168

14.373

26.545

24.375

54.931

425

21.550

43.300

14.690

26.753

23.851

531

29.168

14.439

19.458

29.753

19.200

650

21.444

16.564

16.426

33.847

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Ug (mm s-1)

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14.391

ACCEPTED MANUSCRIPT Figures

Air

Outlet

13

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Particle

8 6 5

1

3

2

(B)

Inlet

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4

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(A)

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0.06 m

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2

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1.0 m

12

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Figure 1. (a) Experimental apparatus. 1: Compressor, 2: Valves, 3: Rotameter, 4: Electrical

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heating element, 5: Probe thermometer, 6: Perforated plate distributor, 7: Manometers, 8: Fluidized bed, 9: Cylindrical vessel, 10: Bag filters, 11: Nd-YAG solid-state laser, 12: Detectors,

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13: Amplifier, 14: Computer and monitor, 15: Cyclone. (b) Dimensions of the column.

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ACCEPTED MANUSCRIPT (A)

(B)

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50 nm

(D)

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(C)

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Figure 2. Microscopic images of silver oxide NPs, nano-agglomerates and micro-particles. (A) TEM image of primary NPs; (B) high-magnification SEM image of NPs; (C) lowmagnification SEM image of nano-agglomerates; (D) low-magnification SEM image of micron sized particles.

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mesh 1

mesh 2

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mesh 3

mesh 4

mesh 5

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Figure 3. Mesh configurations and grid cells used in the simulations.

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ACCEPTED MANUSCRIPT 800

600 500 400 300

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Mesh 1 Mesh 2

200

Mesh 3 Mesh 4 Mesh 5

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Bed pressure drop (Pa)

700

0 100

300

500

700

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100

900

1100

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No. of Cells (*100)

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Figure 4. The bed pressure drop profile versus number of cells.

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ACCEPTED MANUSCRIPT 80 Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5

60 50 40

Optimized mesh

30

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Difference (%)

70

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20

32000

52000

72000

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0 12000

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10

92000

112000

No. of Meshes

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Figure 5. The mesh independency analysis

c

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b

d

e

f

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a

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g

h

i

j

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k

Figure 6. Typical fine mesh simulation (mesh #3) contour plots of the bed containing silver

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oxide particles at pseudo-steady-state (transition from fixed state to bubbling regime (a-f), bubbling to slugging regime (g-j) and turbulent flow (k). [(a): 8, (b) 10, (c) 12, (d) 14, (e) 16, (f)

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24, (g) 28, (h) 48, (i) 54, (j) 62, (k) 85 mm s-1].

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Figure 7. Fine mesh simulation (mesh #3) contour plots of solid volume fraction profile for 2-D

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over 0.0–3.0 s interval at Ug = 220 mm s-1

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ACCEPTED MANUSCRIPT 3.5

2.5 2

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1.5 1

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Pressure (kPa)

3

0 0

0.5

1

1.5

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0.5

2

2.5

3

3.5

4

Time (sec)

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(A)

(B) Figure 8. The variation of bed pressure drop as a function of time. (A) Experimental data, (B) predicted results for different mesh strategies at Ug=220 mm s-1.

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Umf

Figure 9. Pressure drop vs. superficial gas velocity for fluidized bed [Simulation results

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are obtained at t=3 s for five different meshes as introduced in Table 3].

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Gas velocity (m/s)

Figure 10. Comparison of experimental and simulated bed expansion ratio [Simulation results

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are obtained at t=3 s for five different meshes as introduced in Table 3].

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ACCEPTED MANUSCRIPT 1 0.8

Ug, mm s-1 30

(b)

(a) 48

54

62

0.7 0.6 0.5 0.4

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0.3 0.2

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Solid volume fraction (-)

0.9

0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

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r /R (-)

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0.1

Figure 11. Experimental data (a) and simulation results (b) of the radial distribution of solid

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volume fraction profile at z=0.08 m and gas velocities of 30, 48, 54 and 62 mm s-1 [timeaveraged Simulation results are obtained at Ug=48 mm s-1 and H=0.08 m for five different

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meshes as introduced in Table 3].

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(b)

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(a)

(c)

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(d)

Figure 12. Experimental data and simulation results of the axial solid volume fraction profile at gas velocities of (a) 220, (b) 425, (c) 531, and (d) 650 mm s-1 calculated for the five mesh strategies [Simulation results are obtained for five different meshes as introduced in Table 3].

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ACCEPTED MANUSCRIPT Appendix A Governing equation and conservation laws for gas/solid flows: Mass conservation for phase i (i = g for gas and s for solid)   ( i .i )  .( i .i . v i )  0 t

(A.1)

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Linear momentum balance for gas and solid phases (A.2)

      ( s .s . v s )  .( s .s . v s . v s )   sP  . s  Ps   (U g  v s )   s .s . g t

(A.3)

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Transport equation for the solid phase granular temperature

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      ( g .g . Ug )  .( g .g . U g . U g )   g P  . g   (U g  v s )   g .g . g t

(A.4)

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  3  s .s .θs   . s .s . vs .θs   (Ps I  s ) : . vs  .  k ..θs   γ  gs  2  t 

Solid stress tensor

2        s  s  . vs 3   

(B.1)

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=    τs =s   vs  ( vs )T 

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Constitutive equations of gas-solid flow:

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Appendix B

where solid shear viscosity is

μs  s,col + s,kin + s,fr

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(B.2)

The collisional contribution to shear viscosity is

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θ 4 s ,col   s .s .g 0 ,ss 1  e ss  s 5 

(B.3)

The kinetic contribution to shear viscosity

s , kin 

10 s .ds θs .

96s 1  e ss  g 0 ,ss

 4  1  5 g 0 ,ss .s 1  ess   

2

(B.4)

The frictional contribution to shear viscosity

s , fr  pf sin( ) 2 I 2 D

(B.5)

Solid phase bulk viscosity

4 3

s  s2 .s .ds .g0,ss 1  ess 

θs π

(B.6)

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ACCEPTED MANUSCRIPT Collision dissipation energy

 

12 (1  e ss2 ) g 0,ss

s . s2 .θs3/ 2

ds π

(B.7)

Solid pressure Ps   s .s .θs  2 s 1  ess  s2 .g 0,ss .θs

(B.8)

Thermal energy diffusion coefficient

25 s .d s s .  6 θ  k  . 1  .s .g 0,ss . 1  e ss   2s .s2 .d s 1  e ss  g 0,ss s 64 1  e ss  .g 0,ss  5   1/3 -1

  

   

Dissipation of granular temperature by gas damping

(B.10)

(B.11)

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gs  3 .θs

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g 0,ss

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Radial distribution function

    1   s    s,max 

(B.9)

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Appendix C

The modified Syamlal-O'Brien model and the corresponding correlation including inter-phase momentum exchange coefficient.

 Re 3 s . g . g C D . s 2 v 4 v r ,s .d s  r ,s

  . v s U g 

(C.1)

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

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Syamlal-O’Brien proposed a drag coefficient model based on measuring the particle terminal velocity in fluidized beds:

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Drag coefficient

2

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  4.8  C D   0.63    Re v s r ,s   vr,s is the terminal velocity correlation for the solid phase: 2 0.5  A  0.06Res   0.06Res   0.12Res  2B  A   A 2    where A   g4.14 B  P  1g.28

 g  0.85

B   Qg

 g  0.85

(C.2)

(C.3)

The procedure for specifying the parameters P and Q for the minimum fluidization velocity corresponds to the modified Syamlal-O'Brien model.

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ACCEPTED MANUSCRIPT Graphical abstract

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Ug

Mesh generation Bubbling fluidization

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Slugging fluidization

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Turbulent fluidization

ACCEPTED MANUSCRIPT Highlights  Fluidization experiments were performed in a fluidized bed containing silver oxide NPs.  A CFD model was presented to study the mesh sensitivity to size and shape.  Computational grids and the effects of mesh refinement were studied.

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 The bed transition regimes from bubbling to slugging and turbulent flow were discussed.

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 The near-wall refinement strategy on each of the transition velocities was studied.

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