Computational study of particle temperature in a bubbling spout fluidized bed with hot gas injection

    Computational study of particle temperature in a bubbling spout fluidized bed with hot gas injection A.V. Patil, E.A.J.F. Peters, J.A.M. Kuipers PII: DOI: Reference:

S0032-5910(15)00546-X doi: 10.1016/j.powtec.2015.07.014 PTEC 11131

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

13 February 2015 26 June 2015 14 July 2015

Please cite this article as: A.V. Patil, E.A.J.F. Peters, J.A.M. Kuipers, Computational study of particle temperature in a bubbling spout fluidized bed with hot gas injection, Powder Technology (2015), doi: 10.1016/j.powtec.2015.07.014

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Computational study of particle temperature in a bubbling spout fluidized bed with hot gas injection

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A. V. Patila , E. A. J. F. Petersa,∗, J. A. M. Kuipersa

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a Multiphase Reactors Group, Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, the Netherlands.

Abstract

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CFD-DEM simulations of a hot gas jet issuing into a pseudo 2D gas-solid fluidized bed of glass particles is reported. A novel CFD-DEM model accounting for fluid-particle heat transfer has been developed and used for this particular

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research. In this work the background gas is maintained at minimum fluidization velocity and room temperature (300 K) while a hot gas jet (500 K) is injected

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from the center of a pseudo 2D bed. Three different particle sizes have been studied (1 mm, 2 mm and 3 mm). The hot gas jet causes continuous bubble

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formation and propagation in the bed thus creating a circulation pattern of particles. Using the detailed simulation data various kinds of analysis are presented

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on the particle temperature statistics like standard deviation and distribution profiles of time-averaged particle density, volume flux and temperature variation about the mean. Further, a tracer particle analysis is presented that shows the variation of particle temperatures about the mean for different particle sizes. Keywords: spout fluidized bed, temperature distribution, heat transfer

1. Introduction Spouted fluidized beds are widely used in processes such as granulation, drying and coating. Some of the products produced by such processes are detergents, pharmaceuticals, food and fertilizers. These products need to be ∗ Corresponding

author. Tel: +31 40 247 3122; Fax: +31 40 247 5833 Email address: [email protected] (E. A. J. F. Peters)

Preprint submitted to Powder Technology

June 23, 2015

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produced with specific properties such as size, mechanical strength (for ease of

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handling) and chemical composition (purity). Fluidization using spouted beds is widely considered to be the most suited mode of operation to produce granu-

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lar products. This has resulted in a large amount of research on spout fluidized bed applications in literature [1, 2, 3, 4].

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The spout, which has a high speed gas jet compared to the background fluidization gas, avoids creation of slugs and thus facilitates a well defined particle circulation pattern. This is believed to facilitate optimal and uniform particulate processing making this processing method one of the most popular and promis-

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ing methods. A large number of experimental investigations have been carried out on spout fluidization to understand overall particle flow dynamics and their regimes of operations in spout fluidization; see [5, 6, 7, 8, 9, 10]. Besides this,

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the spectral analysis of pressure drop fluctuations has been exhaustively stud-

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ied in literature [11, 12, 13]. Hydrodynamics of spouted fluidized beds has been studied extensively both experimentally and computationally in the past using

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relatively simple one dimensional models [14, 15, 16]. Early modeling works on spout fluidizations involved many kinds of theoretical and population balance models for size distributions [17, 18]. Individual

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particle flow modeling first became possible with the advent of the discrete particle modeling method (DEM) by Tsuji et al. [19]. The application of discrete particle models to study spout fluidized beds was introduced by Kawaguchi et al. [20]. This further led to many studies using improved gas-particle and particleparticle modeling methods for spout fluidized beds which is now known as the computational fluid dynamics - discrete particle model (CFD-DEM) technique [21, 22, 23]. CFD-DEM is an Euler-Lagrange based modeling tool which is best suited for medium scale studies of gas-solid fluidized bed systems; see Link [24]. Thus it is often used to assess the impact of closures for fluid-particle and particle-particle interaction models in various spouting regimes backed up by novel experimental techniques [25, 26]. Some recent works with CFD-DEM have focussed on improving particle-particle interaction models that produce results that better 2

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correspond to experimental observations [27, 28]. Experimental validations of

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spouted fluidized beds have also been extended to multiple and elevated spout studies [29].

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In CFD-DEM the gas phase is treated as a continuum (Eulerian) whereas the particulate phase as discrete (Lagrangian) fashion. Through two-way-coupling

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both phases experience each other through momentum exchange. Particle collisions mechanics is accounted for using the soft sphere model first proposed by Cundall and Strack [30]. CFD-DEM models have been extended with heat transfer descriptions where the continuous phase is modeled by a convection-

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diffusion equation whereas the discrete phase is treated using a thermal energy equation for each particle.

Heat transfer to the emulsion phase in spouted fluidized beds is of great

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importance as it determines the efficiency of various process operations like

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drying, coating, etc. With the extension of energy transfer in DEM heat transfer in spout fluidized bed systems Xiao et al. [31], Patil et al. [32] can be studied

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in detail. Development of new infrared techniques has lead to possibilities of experimental validations of these models using detailed temperature distributions [33, 34, 35].

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Studies of spout fluidized beds are not limited to thermal aspects but can be extended to include the motion (mixing) of individual particles. The motion of tracer particles in fluidized beds have been researched extensively in literature using PEPT measurements [36, 37, 38]. However these studies are limited to individual particle motion measurement. So for studying particle temperature variations during these motions or circulations the CFD-DEM approach can be used. CFD-DEM with heat transfer brings many possiblities of studies in spout fluidized beds such as particles size effects on both hydrodynamic and thermal behaviour. In this work we study heat transfer to the particle emulsion from a hot gas jet that is injected at the centre bottom of a pseudo 2D fluidized bed. A typical spouting process has various regimes of operations and here we study the continuous bubbling regime. In this regime continuous formation of hot 3

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gas bubbles takes place at the nozzle. Once the bubble reaches a certain size

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it detaches and rises through the bed. Depending on the particle size and background gas velocity the injected bubbles exchange heat with the emulsion

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phase at different rates.

This paper aims to study variations in particle distribution profiles for spout

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fluidization in bubbling regime operation as a function of particle size. Properties of particles like overall particle temperature standard deviation and spatial distribution have been studied. These properties in general were observed to increase with increasing particle size.

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Tracer particle study is a novel method that has been previously employed in experiments and simulations [39, 40]. Mostly these studies have been limited to tracer particle position study and did not involve properties like temperature

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of particles. Here a tracer particle study was performed to study individual

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particle behaviour with respect to the mean particle temperature. We will start with stating the governing equations in §2 and provide details

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of the spout injection system used for our study in §3. In §4 the main results will be presented, the main conclusions will be summarised in §5

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2. Governing Equations 2.1. Gas phase modeling In our CFD-DEM model the gas phase is treated as a continuum. The volume-averaged conservation equations for mass and momentum are respectively given by, ∂ (εf ρf ) + ∇ · (εf ρf u) = 0, ∂t

(1)

∂ (εf ρf u) + ∇ · (εf ρf uu) = −εf ∇p − ∇ · (εf τ f ) + Sp + εf ρf g, ∂t

(2)

where Sp denotes the source term for momentum transfer from the particulate phase and is given by Sp =

X βVa (va − u) δ(r − ra ) ≡ α − β u. 1 − εf a 4

(3)

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Here β represents the volumetric drag coefficient for particles due to gas flow

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whereas α is the momentum felt by the gas phase per unit volume due to the overall particle motion. The particle properties are distributed on the Eulerian

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grid using smoothed Dirac-delta functions. The drag coefficient, β, is obtained from the Ergun [41] equation for the dense regime and the Wen and Yu [42]

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equation for the dilute regime;   150 1−εf + 1.75 (1 − εf ) Rep 2 β dp εf = Fdrag =  µ  3 CD Rep (1 − εf ) ε−2.65 f 4

if εf < 0.8

(4)

if εf > 0.8

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The gas phase flow solver uses the semi-implicit projection method. The details of this method can be found in Patil et al. [32] and hence will not be reported here.

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The thermal energy equation for the gas phase is given by,

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∂ (ǫf ρf Cp,f T ) + ∇ · (ǫf ρf uCp,f T ) = ∇ · ǫf kfeff ∇T + Qp , ∂t

(5)

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where Qp represents the source term from heat coupling with the particulate phase and kfeff is the effective thermal conductivity of the gas phase which is re-

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lated to the intrinsic fluid thermal conductivity given by the following equation, p 1 − 1 − ǫf eff (6) kf . kf = ǫf This equation was first proposed by Syamlal and Gidaspow [43]. The fluidparticle heat transfer can be obtained by summing the contributions of all particles belonging to a particular Eulerian cell using a smoothed delta-function as, Qp = −

X a

Qa δ(r − ra ) =

X

hf p Aa (Ta − Tf ) δ(r − ra ).

(7)

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Where Qa is the heat transferred from the gas to particle a and hf p is the gasparticle heat transfer coefficient for which we use the empirical correlation given by Gunn [44],

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  0.33 Nup = (7 − 10 ǫf + 5 ǫ2f ) 1 + 0.7 Re0.2 p Pr

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+ (1.33 − 2.40 ǫf + 1.20 ǫ2f ) Re0.7 Pr0.33 where,

dp ǫf ρf |u − v| µf Cp,f hf p d p , Rep = and Pr = . kf µf kf

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Nup =

(9)

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2.2. Discrete particle phase

(8)

The modeling of the particle phase flow is based on the Cundall and Strack [30] model of the resultant force acting on individual spherical particles due to

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various contributing factors. Any given particle a with mass ma and moment

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of inertia Ia is described by Newton’s equations: d2 ra βVa = −Va ▽ p + (u − va ) + ma g + Fcontact,a 2 dt 1 − εf ωa dω = τa , Ia dt

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ma

(10) (11)

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where ra is the position. The forces on the right-hand side of Eq. (10) are the pressure gradient, drag, gravity and contact forces due to collisions, τa is the torque, and ω a the angular velocity vector. The major contributions to the torque on a particle are the tangential forces experienced while colliding with other particles.

The heat transfer rate from the fluid to the particles is evaluated as the product of the fluid-particle heat transfer coefficient and the driving force (Tf − Ta ) where, Tf , is interpolated from the Eulerian grid using volume weighing. The heat balance for particle a gives an evolution-equation for its temperature, Ta , Qa = ρa Va Cp,p

dTa = hf p Aa (Tf − Ta ). dt

(12)

It is assumed that the temperature in the particle is uniform, i.e., Bi = 0. In a previous paper [45] we included direct heat-transfer between particles during 6

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collisions. This mode of heat transport was found to be negligible and is not

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included in the current simulations. Also the small contribution of radiative

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heat-transfer was neglected.

3. Bubble formation and rise

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3.1. Gas jet injection setting

The continuous gas jet injection study was performed with particle sizes of 1 mm, 2 mm and 3 mm. To enable a comparison of relative effects of particle

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sizes the cross sectional dimensions of the beds were kept the same (0.24 m × 0.75 m). The particle and gas properties used for the simulations are tabulated in Table 1 and particle collision properties are summarized below in Table 2.

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The collision model is based on the spring/dashpot/slider description proposed by Cundall and Strack [30]. A detailed description of the model relations

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can be found in previous literature [46].The normal and tangential spring stiffnesses are not related to material properties such as the elastic modulus, but

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follow from numerical criteria. One criterion is that a collision is fast compared to the other characteristic times in the system, but slow enough such that not

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too small time steps are needed for computing the particle trajectories. Another requirement is that the overlap increase due to a relatively low normal spring stiffness is negligible. This stiffness is chosen such that the maximum particle overlap is always less than 1 % of the particle diameter. Damping coefficients are tuned to assure that binary collisions reproduce the normal and tangential restitution coefficients given in Table 1. A detailed description of the method to obtain the model parameters is described by van der Hoef et al. [47]. The size of the injection nozzle size was fixed to 2 cm in width and equal to the bed thickness in the depth direction. The gas mass flux through the injection nozzle was maintained at 11.67 kg/m2 s at a temperature of 500 K. The remainder of the bed was maintained at minimum fluidization velocity with cold background gas entering with a temperature of 300 K.

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The dimensions of the bed are provided in Table 2 where it can be seen that

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the depth of the bed is the only changing factor. This was done in order to give the particles enough space in the depth direction at changing particle size. The

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bed depth for the 1, 2 and 3 mm particle sizes were 1 cm, 1.5 cm and 1.8 cm respectively. The bed mass for each particle size was adjusted such that the

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same bed height is generated in a fixed bed state. Thus the resulting number of particles for 1 mm, 2 mm and 3 mm particles amounted 700000, 130000 and 60000 respectively.

The choice of domain dimensions used was motivated from similar earlier

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simulation conducted by Patil et al. [32] and Olaofe et al. [48]. The details of the applied boundary conditions are similar to those used for the single bubble injection study made in the earlier work Patil et al. [32]. The surrounding walls

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are represented as no slip and adiabatic boundaries. The bottom boundary is

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defined by a prescribed mass flux profile at the background gas inlet and the central nozzle. The top boundary condition consists of prescribed pressure and

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constant temperature gradient for the gas flowing out.

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4. Results and discussion 4.1. Bubbling regime operation The spout injection into a gas-solid fluidized bed generates a distinctive particulate flow pattern. In this kind of operation particles in the dense emulsion at the sides of the spout are sucked into the wake of intermittently forming gas bubbles. The particles move fast along the centre line in the vertical direction. The particles are ejected into the freeboard once they reach the top of the bed. The particles then slowly move downwards through the dense emulsion phase from the sides. Due to the central position of the jet this is the circulation pattern that is generally observed in such spout fluidized beds. The hot gas injection causes the temperature of the particles in the bed to rise. The particles coming close to the jet receive most of the heat and momentum. These particles thus experience a sharp rise in temperature and

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(vertical) velocity as they rise quickly through the centre of the bed. The

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relatively slow moving particles which descend near the sides of the spout slowly cool due to the cold percolating background gas. Particles which manage to

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reach the bottom of the dense bed at the sides become the coldest particles in the bed. This is obviously because of the fresh cold background gas supplied to

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these particles.

Fig. 1 shows a set of instantaneous images at times t=20 s, 100 s and 800 s of a jet issuing into the bed of particle size 1 mm. At each of these times 3 different images are shown where the first image shows the gas temperature

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profile, the second shows the particle temperature profile and the third shows the superimposed images of gas and particles. From the images it can be seen that during the early stage of heating of the bed hot particles settle in layers

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at the sides of the jet. This is because of the formation and detachment of

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bubbles at the nozzle. However as time proceeds this effect is reduced as the bed temperature increases and the bed temperature becomes more uniform.

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As the particles reach a higher temperature, the cold layer of particles at the bottom of the bed besides the spout are much more clearly visible, which can be observed in the image at 800 s time.

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The particle size also influences the hydrodynamics and hence the transfer of heat to the emulsion phase. This can be nicely observed in Fig. 2 which shows instantaneous images of the superimposed gas phase and particle temperature fields for 3 different particle sizes at 2 different times (t=25 s, 35 s and steady state). The hot gas bubbles generated by the jet exchange heat with the surrounding particles in the emulsion phase as the bubbles rise through the bed. It can be seen that in the 1 mm particle size bed the bubbles formed are bigger in size. Also the bubbles are carrying hotter gas compared to bubbles for larger particles sizes (2 mm and 3 mm). As an example, in the images shown in Fig. 2 it can be seen that for the 1 mm particle bed some of the bubbles that have reached the top of the bed contain hot gas, as compared to 2 mm particles where bubbles are warm only up to half way the bed height. Similarly, bubbles in the 3 mm particle bed are cooling faster than in the smaller, two particles sizes. This 9

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is happening because of the increased convective heat exchange between the hot

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gas bubble and emulsion phase for large particles. Due to the relatively low heat exchange between the bubbles and the emulsion phase for smaller particles the

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bubbles reaching the top of the bed are relatively warm leading to less efficient fluid-particle heat transfer. The gas leakage from the bubble to emulsion phase

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is lower for smaller particles because of the dense packing of small particles. This leads to a lower bubble-to-emulsion heat transfer coefficient. This has been shown in a single bubble simulation study previously [32].

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4.2. Unsteady state heat transfer analysis

Our simulations produce detailed information on positions, velocities and temperatures of all the individual particles in the bed as a function of time.

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Using this detailed data the mean particle temperature was calculated and is

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shown in Fig. 3 as a function of time. In this plot it can be observed that the rate of heating of the particles is different for bubble injections at different particles sizes. This is because of

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the different background gas velocity for each of the particle sizes (0.58 m/s for 1 mm, 1.1 m/s for 2 mm and 1.4 m/s for 3 mm) and the bed mass which

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was different for different particle sizes in order to keep the bed size nearly the same. This also influences the equilibration temperature of particles which attains steady state at different particle temperatures (Tp,ss = 401 K for 1 mm particles, Tp,ss = 373 K for 2 mm particles and Tp,ss = 359 K for 3 mm particles). This temperature is nearly equal to the cup mixing temperature of inlet gas (including background and spout injection gas, Tg,ss ) as particles in the bed attain near thermal equilibrium with the gas. It can be observed that the time needed to attain steady state is also different for different particle sizes. For smaller particle sizes it takes more time to reach steady state. This is also due to the same reasons as explained above (lower background gas velocity and larger bed mass for smaller particle size). A simplified energy balance model on the system was developed in order to be able to study the profile for a theoretical ideally mixed system. In the 10

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simulations the rate of energy injected into the system per unit time is known

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for each of the cases and it is also known that the exit gas temperature is nearly at equilibrium with the mean particle temperature in the bed. So for

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the approximate (thermal) calculation it was assumed that the injected gas and solids ideally mix and thermally equilibrate, leading to an exit gas which is at

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thermal equilibrium with the particle phase. Thus the energy balance for such a system is given by Eq. 13. Here the rate of change of the temperature of particles in the bed is equated to the total energy entering the system from the inlet boundary condition minus the energy leaving the system from the outlet

mp Cp,p

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gas after it has completely equilibrated with the particle phase, dTp,m = ρg,b Ab ug,b Cp,g Tg,b + ρg,N AN ug,N Cp,g Tg,N − m ˙ g,F Cp,g Tpm , dt (13)

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where m ˙ g,F is the overall mass flow rate of the gas passing through the fluidized

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bed which is given by ρg,b Ab ug,b + ρg,N AN ug,N . Upon integration of this

obtain Eq. 14.

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equation, with the initial condition that at t = 0 s, Tp,m0 = 300 K = Tg,b we t

Tp,m = Tg,ss + ( Tg,p − Tg,ss )e(− τ ) ,

(14)

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where Tg,ss and τ are constants representing the thermal steady state temperature and a thermal time constant respectively. These quantities are respectively given by;

Tg,ss =

mp Cp,p (ρg,b Ab ug,b Tg,b + ρg,N AN ug,N Tg,N ) and τ = . m ˙ g,F m ˙ g,F Cp,g

(15)

It should be noted that at steady state where thermal equilibrium is attained, the particle mean temperature at steady state Tg,ss is equal to the exit gas temperature at steady state Tp,ss . So in the above equations Tg,ss and Tp,ss can be used interchangeably. Eq. 14 gives the particle temperature profile Tp,m versus time for the assumed assumed ideally mixed system which is included in Fig. 3 (represented by dotted line). It reveals that for the 3 mm particle bed the theoretical data and simulation data match perfectly. This is because the bubbles generated in 11

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this case thermally equilibrate with the bed before leaving the bed. The theo-

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retical profile has a slightly faster changing profile compared to simulations for 2 mm and 1 mm particle beds. This shows the slight heat transfer resistance

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that exists for gas-particle heat exchange for 2 mm and 1 mm particle beds. The individual particle temperature data saved at every 0.25 s time steps

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was used to process and obtain the particle temperature distribution. Fig. 4 shows an instantaneous particle temperature distribution semilog plot for the 3 particle sizes when the mean particle temperature equals 351 K. The width of the distribution as can be seen here has a narrow sharp peak close the mean

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temperature 351 K for all the 3 particle sizes where the normalized density distribution exceeds 0.1. Outside this range of about 4 to 6 K temperature the normalized density distribution values are very small. It was observed that this

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peak for each particle size fluctuates somewhat with respect to spread while the

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height of the peaks for all particle sizes varied between 0.5 and 0.8. However, an interesting observation was made outside of the peak region of

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the distribution where a low value of normalized density exists. As can be seen in Fig. 4 for 1 mm particle size the distribution spread exists between temperatures ranging from 342 K to 368 K. Outside the narrow peak region here (which is

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approximately between 348 K and 354 K) the density distribution is very low at times going below 10−3 . This is obviously because of small number of particles having temperatures outside the peak region. Similarly for 2 mm particle size the distribution spread ranges from 315 K to 354 K and for 3 mm particle size the distribution spread stretches further from 302 K to 358 K. It was observed from these distribution spreads that for small particle size (1 mm) the spread stretched more above the mean particle temperature or temperature distribution peak, while for larger particle sizes (2 mm and 3 mm) the distribution spread was more below the mean particle temperature. This was primarily because we know that heat transport from bubble to emulsion phase is low for small particles. So, particles at the bubble emulsion interface tend to absorb more heat causing some of these interfacial particles to 12

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reach a high temperature relative to the mean particle temperature. Due to the

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high background gas velocity, for large particle size (2 mm and 3 mm) beds, the particles close to the gas inlet experience very low temperatures. This causes

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the density distribution spread of particle temperatures to stretch more below the mean particle temperature.

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Using this temperature distribution data that was obtained for every 0.25 s the evolution of the standard deviation of the particle temperature distribution was evaluated as well. This standard deviation was recorded against the mean particle temperature that was obtained at the given instant of time for all par-

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ticle sizes. This plot is shown in Fig. 5. As can be seen for small particle size of 1 mm the standard deviation varied little with increasing mean temperature of particles. However for larger the particle sizes (2 mm and 3 mm) the stan-

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dard deviation increased with increasing mean temperature of particles. This is

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due to the higher background gas velocity which causes the spread of particle temperature distribution to extend more below the mean particle temperature.

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The simulations also provide information on instantaneous particle densities, velocities and temperature distributions. The time-averaged data for the particle density, solids volume flux and temperature distribution about the mean

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was calculated from the simulation data. These averaged quantities are defined respectively in equations 16, 17 and 18.

1 X εp (t, i, j) Nt t 1 X Φ p (i, j) = εp (t, i, j) vp (t, i, j) Nt t εp (i, j) =

Γp (i, j) = P

X 1 εp (t, i, j) (Tp (t, i, j) − hTp (t)iε ) t εp (t, i, j) t

(16) (17)

(18)

Using these equations distribution plots have been made which are shown in Fig. 6. As discussed earlier larger bubbles are formed for smaller particles near the nozzle and they grow to become larger bubbles as they rise through the bed. This can be seen in Fig. 6a compared to Fig. 6b and Fig. 6c. Due 13

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to larger bubble formation near the nozzle for 1 mm particles the exchange

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of heat between hot gas and particles is lower. This influences the particle temperature distribution plot as shown in Fig. 6g. It can be seen as well that

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above the nozzle the temperature distribution in the hot zones is uniform for 2 and 3 mm particles whereas for 1 mm particles the distribution indicates colder

4.3. Steady state heat transfer analysis

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zones above the nozzle and hotter zones at the sides.

The heat transfer process eventually reaches a stage where the mean particle

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temperature in the bed becomes more or less constant. Due to the reduced driving force the rate of change of the mean temperature of particles becomes less than a certain threshold (0.002 K/s) after which we consider the system at

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steady state.

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The spatial distribution of the time-averaged particle temperature is shown in Fig. 7. From this figure it can be seen that the temperature distribution in the central and upper part of the bed is close to uniform, but there exists a sharp

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low temperature profile close to the bottom plate where the cold background gas is entering. Furthermore a specific narrow zone is formed, starting at the

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nozzle and moving up along the central axis. This cold zone is caused by colder particles from the sides that are being sucked into the gas jet. As the particles receive high amount of heat from the jet they quickly heat up as they rise along the direction of the jet. So this narrow jet zone as can be seen in Fig. 7 leaves a trail which has patches created by the hot particles in the time-averaging. Most of these hot particles from bubbles tend to percolate into the tail of the bubble creating a trail of hot particles as the bubble moves up. This narrow jet zone formation is more pronounced for the larger particles (2 mm and 3 mm particles) as can be seen in Fig. 7b and Fig. 7c. But for 1 mm particles it gets more diffused from a point slightly above the nozzle itself (see Fig. 7a). The reason for this pattern of the smaller 1 mm particles is that the bubbles forming near the nozzle are larger in size compared to that for larger particles. 14

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This can be observed by comparing the instantaneous images of Fig. 2. Larger

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bubbles of the 1 mm particle bed disturb the trail left behind by a previous bubble. However, this does not happen so much for larger particles which have

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smaller bubbles that disturb the trail of hot particle less.

The bubble dynamics has its own unique effect in fluidized beds. As the

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bubbles rise in the bed they tend to grow in size. The smaller particle bed bubbles, due to their lower leakage of gas from the bubbles, tend to grow faster. For larger particles on the other hand the leakage is higher which does not allow the bubble to grow much in size as they rise in the bed. This can be also

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inferred from the time-averaged solid density distribution given in Fig. 6. This further supports the nozzle jet pattern formation behaviour in the temperature

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4.4. Tracer particle study

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time-averaging at steady state as discussed here in this section.

In this section we will study the heat transfer process from a Lagrangian perspective with the aid of tracer particles which are tracked starting from

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several initial positions in the bed. The 3 individual particles that were chosen from an initial position of bottommost left, centre left and topmost left of the

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bed. The initial positions of these particles have been indicated in Fig. 8. The particles are represented with red, blue and green color where the same colors have been used in the subsequent plots to visualise the temperature histories experienced by the particles. These 3 particles are specifically chosen from 3 different parts inside the bed to illustrate the effect of their initial position. Fig. 9 shows the behaviour of the tracer particles in each type of bed with respective particle size. It can be seen that the tracer particle which was at the bottommost corner shows a very different profile in comparison with the 2 mm and 3 mm particle size bed. In the case of 2 mm particle size the particle has a much lower initial temperature. Since this particle did not move from its initial bottom left position and mix in the bed its temperature did not change. However, as soon as it was carried into the jet the temperature of this particle increased fast and approaches the mean temperature of particles. The same 15

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behaviour is observed for the 3 mm particle in case it does not move from its

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position throughout the simulation.

The tracer particles 2 and 3 show similar behaviour in all the 3 particle

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size plots. These tracer particles mostly follow temperatures very close to the mean temperature of the particles. These particle temperature profiles observe

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sudden peaks that appear randomly in each of the plots. Particles during their circulation in the bed are suddenly heated when they come close to the hot injection gas. These sudden peaks are representative of the given tracer particle moving in the vicinity of the hot jet environment of the bed. The particles

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along with energy also gain high momentum close to the jet and hence are pushed away from the jet in upward direction. After these tracer particles gain this high momentum the particles move out

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into the dense sides of the jet and recirculate back towards the jet. The particles,

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when they recirculate, they either take a short path like the purple curved line or they take a long path represented by the yellow line in Fig. 8. It can be

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imagined that the close consecutive peaks are due to the shorter recirculation paths taken by the particles. Conversely when the particles take a longer path the consecutive peaks are further apart with a fairly stable temperature profile

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in between.

Rarely, reverse peaks are observed where the particle temperature suddenly declines below the mean temperature and then slowly returns back to the mean temperature of particles. In this case the particles, while taking longer circulation paths (like the yellow line), are thrown far away close to the side walls. So, these particles while re-circulating move very close to the cold gas inlet zone at the bottom of the bed. When these particles approach the lowermost layer of particles where the particle comes in direct contact with fresh background gas entering the system such reverse peaks might be occurring. Since the number of particles taking this long path is low the reverse peaks are rarely observed for the tracer particles. Some characteristic patterns could be observed in these peaks. When closely examined the peaks in 1 mm particle tracers are sharper compared to others. 16

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After attaining their peak the 1 mm particles re-equilibrated in temperature

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with other particles more quickly. It can be observed that comparatively 2 mm and 3 mm take longer times on an average to re-equilibrate.

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Further, the temperature of tracer particle 2’s deviation with respect to the mean particle temperature was evaluated. This is shown in Fig. 10 where

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deviations for each of the particle sizes can be observed. Here it can be clearly seen that the particles mostly tend to experience positive peaks and a few negative peaks. Smaller particles fluctuate less compared to larger particles and the peaks re-equilibrate faster compared to larger particles.

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The spacing between the peaks seems random but when more closely examined for 1 mm particle size it is higher compared to 2 mm and 3 mm. The spacing between peaks with respect to time was evaluated and plotted as a his-

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togram for each of the particle size. This is shown in Fig. 11 where the time

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spacing between peaks is plotted against number of occurrences of the given time spacing. Here in the first histogram shown in Fig. 11a it can be seen that

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the time between peaks is more evenly spread from lowest time spacing of less than 5 s to some very high time spacings between peaks at 80 s. However for 2 and 3 mm particle beds time between peaks are more concentrated below

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10 s. Therefore, for smaller particles larger number of peaks are observed per unit time. Further this is an indication that for larger particles there is a faster recirculation of particles in the same size bed compared to smaller particles.

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5. Conclusion

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Hot gas jet injection into a particulate bed at minimum fluidization was

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studied in detail using DEM with 3 particle sizes (1 mm, 2 mm and 3 mm). The heating and thermal equilibration of particles with the incoming gas was studied. Due to higher minimum fluidization velocity and lower bed mass for

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larger particles a higher standard deviation of particle temperature and a more pronounced spatial distribution of the particle temperature was observed. In addition tracer particles data in each particle size bed were extracted and studied. They were obtained from 3 different initial regions of the bed to

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quantify the temperature dynamics in the bed. The tracer particles showed characteristic behaviour for each particle size. Mostly the particle temperatures followed the mean particle temperature closely. However, the tracer particle

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initially close to the bottom took a long time to catch up and at all times sudden

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temperature peaks occurred. For smaller particles the peaks were sharper and they re-equilibrated with the mean particle temperature much faster. Also the

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peaks were more densely spaced for larger particles indicating faster circulation. In conclusion the tracer particles showed very intermittent deviations from

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the average behavior. These deviations can have important consequences when temperature sensitive processes occur in the particles (such as catalytic reactions). Therefore more extensive investigations of Lagrangian statistics is recommended for future studies. Acknowledgments The authors would like to thank the European Research Council for its financial support, under its Advanced Investigator Grant scheme, contract number 247298 (Multiscale Flows). References [1] K. B. Mathur, N. Epstein, Spouted Beds, Academic Press Incorporated,U.S., 1974. 18

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[2] J. R. Grace, J. Matsen, Fluidization, Plenum Press Engineering Foundation

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(U.S.), 1980.

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[3] J. Litster, B. Ennis, L. Lian, The Science and Engineering of Granulation Processes, Particle Technology Series, Springer, 2004.

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[4] N. Epstein, J. R. Grace, Spouted and Spout-Fluid Beds: Fundamentals and Applications, Cambridge University Press, 2010. [5] S. Alpert, D. Keairns, Fluidization and fluid-particle systems, AIChE sym-

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posium series, American Institute of Chemical Engineers, 1974. [6] A. Salman, M. Hounslow, J. Seville, Granulation, Handbook of Powder Technology, Elsevier Science, 2006.

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[7] W. Sutanto, N. Epstein, J. R. Grace, Hydrodynamics of spout-fluid beds,

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Powder Technology 44 (1985) 205 – 212. [8] F. Berruti, J. R. Muir, L. A. Behie, Solids circulation in a spout-fluid bed

919–923.

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with draft tibe, The Canadian Journal of Chemical Engineering 66 (1988)

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[9] J. Zhao, C. Lim, J. R. Grace, Flow regimes and combustion behaviour in coal-burning spouted and spout-fluid beds, Chem. Engg. Sci. 42 (1987) 2865 – 2875.

[10] N. Epstein, J. R. Grace, Handbook of Powder Science and Technology, Springer US, 1997. [11] A. Nagarkatti, A. Chatterjee, Pressure and flow characteristics of a gas phase spout-fluid bed and the minimum spout-fluid condition, The Canadian Journal of Chemical Engineering 52 (1974) 185–195. [12] J. Xu, X. Bao, W. Wei, G. Shi, S. Shen, H. Bi, J. Grace, C. Lim, Statistical and frequency analysis of pressure fluctuations in spouted beds, Powder Technology 140 (2004) 141 – 154.

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[13] J. Link, L. Cuypers, N. G. Deen, J. A. M. Kuipers, Flow regimes in a

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spout-fluid bed: A combined experimental and simulation study, Chem.

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Engg. Sci. 60 (2005) 3425 – 3442.

[14] C. Lim, A. Watkinson, G. Khoe, S. Low, N. Epstein, J. R. Grace, Spouted, fluidized and spout-fluid bed combustion of bituminous coals, Fuel 67

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[15] B. Ye, C. J. Lim, J. R. Grace, Hydrodynamics of spouted and spoutfluidized beds at high temperature, Can. J. Chem. Eng. 70 (1992) 840–847.

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[16] M. L. Passos, A. S. Mujumdar, G. Vijaya, V. G. Raghavan, Spouted and spout-fluidized beds for gram drying, Drying Technology 7 (1989) 663–696.

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[17] M. Hounslow, The population balance as a tool for understanding particle

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rate processes, KONA Powder and Particle Journal 16 (1998) 179–193. [18] S. Morooka, T. Okubo, K. Kusakabe, Recent work on fluidized bed process-

105 – 112.

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ing of fine particles as advanced materials, Powder Technology 63 (1990)

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[19] Y. Tsuji, T. Kawaguchi, T. Tanaka, Discrete particle simulation of twodimensional fluidized bed, Powder Technology 77 (1993) 79 – 87. [20] T. Kawaguchi, M. Sakamoto, T. Tanaka, Y. Tsuji, Quasi-three-dimensional numerical simulation of spouted beds in cylinder, Powder Technology 109 (2000) 3 – 12. [21] W. Zhong, Y. Xiong, Z. Yuan, M. Zhang, DEM simulation of gas-solid flow behaviors in spout-fluid bed, Chem. Engg. Sci. 61 (2006) 1571 – 1584. [22] J. Link, C. Zeilstra, N. G. Deen, J. A. M. Kuipers, Validation of a discrete particle model in a 2-D spout-fluid bed using non-intrusive optical measuring techniques, The Canadian Journal of Chemical Engineering 82 (2004) 30–36.

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[23] M. S. van Buijtenen, N. G. Deen, S. Heinrich, S. Antonyuk, J. A. M.

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Kuipers, Discrete particle simulation study on the influence of the restitution coefficient on spout fluidized-bed dynamics, Chemical Engineering

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and Technology 32 (2009) 454–462.

[24] J. Link, Development and validation of discrete particle model of spout

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fluidbed granulator, PhD thesis, University of Twente, 2006. [25] J. Link, W. Godlieb, N. G. Deen, J. A. M. Kuipers, Discrete element study of granulation in a spout-fluidized bed, Chem. Engg. Sci. 62 (2007) 195 –

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207.

[26] M. S. van Buijtenen-Tiemersma, Multiphase flow in spout fluidized bed granulator, PhD thesis, Eindhoven university of technology, 2011.

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[27] C. Goniva, C. Kloss, N. G. Deen, J. A. M. Kuipers, S. Pirker, Influence

(2012) 582 – 591.

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of rolling friction on single spout fluidized bed simulation, Particuology 10

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[28] D. Jajcevic, E. Siegmann, C. Radeke, J. G. Khinast, Large-scale CFD-DEM simulations of fluidized granular systems, Chem. Engg. Sci. 98 (2013) 298

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– 310.

[29] M. S. van Buijtenen, W. J. van Dijk, N. G. Deen, J. A. M. Kuipers, T. Leadbeater, D. Parker, Numerical and experimental study on multiple-spout fluidized beds, Chem. Engg. Sci. 66 (2011) 2368 – 2376. [30] P. Cundall, O. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [31] R. Xiao, M. Zhang, B. Jin, Y. Huang, H. Zhou,

High-temperature

air/steam-blown gasification of coal in a pressurized spout-fluid bed, Energy and Fuels 20 (2006) 715–720. [32] A. V. Patil, E. Peters, T. Kolkman, J. A. M. Kuipers, Modeling bubble heat transfer in gas-solid fluidized beds using DEM, Chem. Engg. Sci. 105 (2014) 121 – 131. 21

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[33] T. Tsuji, T. Miyauchi, S. Oh, T. Tanaka, Simultaneous measurement of

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particle motion and temperature in two-dimensional fluidized bed with heat

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transfer, KONA Powder and Particle Journal 28 (2010) 167–179. [34] S. L. Brown, B. Y. Lattimer, Transient gas-to-particle heat transfer measurements in a spouted bed, Experimental Thermal and Fluid Science 44

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(2013) 883 – 892.

[35] A. V. Patil, E. Peters, V. S. Sutkar, N. G. Deen, J. A. M. Kuipers, A study of heat transfer in fluidized beds using an integrated DIA/PIV/IR

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technique, Chem. Engg. J. 259 (2015) 90 – 106.

[36] M. Stein, Y. Ding, J. Seville, D. Parker, Solids motion in bubbling gas

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fluidised beds, Chem. Engg. Sci. 55 (2000) 5291 – 5300. [37] M. V. de Velden, J. Baeyens, J. Seville, X. Fan, The solids flow in the riser

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of a circulating fluidised bed (CFB) viewed by positron emission particle

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tracking (PEPT), Powder Technology 183 (2008) 290 – 296. [38] F. Depypere, J. Pieters, K. Dewettinck, PEPT visualisation of particle motion in a tapered fluidised bed coater, Journal of Food Engineering 93

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(2009) 324 – 336.

[39] J. A. Laverman, I. Roghair, M. van Sint Annaland, J. A. M. Kuipers, Investigation into the hydrodynamics of gas-solid fluidized beds using particle image velocimetry coupled with digital image analysis, The Canadian Journal of Chemical Engineering 86 (2008) 523–535. [40] N. Mostoufi, J. Chaouki, Local solid mixing in gas-solid fluidized beds, Powder Technology 114 (2001) 23 – 31. [41] S. Ergun,

Fluid flow through packed columns,

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Progress 48 (1952) 89–94. [42] Y. Wen, Y. Yu, Mechanics of fluidization, Chemical Engineering Progress Symposium Series 62 (1966) 100–111. 22

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[43] M. Syamlal, D. Gidaspow, Hydrodynamics of fluidization: Prediction of

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wall to bed heat transfer coefficients, AIChE J. 31 (1985) 127–135.

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[44] D. Gunn, Transfer of heat or mass to particles in fixed and fluidised beds, Int. J. Heat and Mass Transfer 21 (1978) 467–476.

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[45] A. V. Patil, E. Peters, J. A. M. Kuipers, Comparison of CFDDEM heat transfer simulations with infrared/visual measurements, Chem. Engg. J. 277 (2015) 388 – 401.

[46] N. Deen, M. van der Hoef, M. van Sint Annaland, J. Kuipers, Numerical

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simulation of dense gas-particle flows using the euler-lagrange approach, Progr. Comput. Fluid Dyn. 7 (2007) 153 – 163.

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[47] M. van der Hoef, M. Ye, M. van Sint Annaland, A. Andrews, S. Sundaresan,

31 (2006) 65–149.

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J. Kuipers, Multi-scale modeling of gas-fluidized beds, Adv. Chem. Engg.

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[48] O. Olaofe, M. A. van der Hoef, J. A. M. Kuipers, Bubble formation at a single orifice in a 2d gas fluidised beds, Chem. Engg. Sci. 66 (2011)

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2764–2773.

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Table 1: Standards for DEM simulations.

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Geldart D glass

particle diameter

1-3 mm

particle density

2526 kg/m3

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particle type

normal coeff. of restitution

0.97

tangential coeff. of restitution

0.33 0.1

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friction coeff. heat capacity of gas

1010 J/kgK

thermal conductivity of gas

0.025 W/mK

2.5 × 10−5 s

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time step (flow solver)

840 J/kgK

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heat capacity of particles

2.5 × 10−6 s

dp

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time step (particles e.o.m.)

(mm)

Table 2: Properties and settings for DEM.

ubg

Normal

Tangential

Number of

grid

size

bed

(m/s)

spring

spring

particles

[width×depth

[width×depth

stiffness

stiffness

×height]

×height]

(N/m)

(N/m)

size

(m×m×m)

1

0.6

7000

2248.9

700000

48×2×150

0.24×0.01×0.75

2

1.1

10000

3212.7

130000

48×2×150

0.24×0.015×0.75

3

1.45

19000

6104.1

60000

48×2×150

0.24×0.018×0.75

24

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Figure 1: Instantaneous images showing temperature profiles at time t=20 s, 100 s and 800 s. For each of the times images shown are gas temperature field, particle temperature field and the superimposed temperature field of both gas and particles.

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t =25 s

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t =35 s

dp =1mm

dp =3mm

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dp =2mm

Figure 2: Instantaneous images showing temperature profiles at time t=25 s and 35 s. For

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each of the times the images show the superimposed gas phase and particle temperature fields

Mean temperature of particles, K

420

400

380

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where the same temperature scale has been used for all the images.

360 dp = 3mm simulations dp = 2mm simulations

340

dp = 1mm simulations dp = 1mm theoretical

320

dp = 2mm theoretical dp = 3mm theoretical

300 0

100

200

300

400

500 time t, s

600

700

800

900

1000

Figure 3: Mean particle temperature against time plot for different particle sizes. The nozzle mass flux =11.7 kg/(m2 s).

26

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0

10

d = 1mm

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p

dp = 2mm

−1

10

d = 3mm p

−2

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10

−3

10

−4

10

−5

10

−6

10

300

310

320

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normalized density distribution of particles, [−]

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330 340 Particle temperature, K

350

360

370

Standard deviation of particle temperature distribution, K

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particle temperature of 351 K

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Figure 4: Temperature distribution of particles for varying particle size at the same mean

5

d = 1mm p

4.5

d = 2mm

4

dp = 3mm

p

3.5 3

2.5 2 1.5 1 0.5 0

300

310

320

330 340 350 360 370 Mean Averaged temperature of particles, K

380

390

400

Figure 5: Standard deviation against mean temperature of particles plot

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Figure 6: Time-averaged data for the 3 different particle sizes. The columns correspond to results for particle size 1,2 and 3 mm. The 3 rows show time-averaged solids volume fraction, solids volume flux and particle temperature deviation about the mean.

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380 K

0,3

0.3

0.3

0 0

0.1

400

0.1 x, [m]

0 0

395

0.2

365

(a) dp =1 mm

z, [m]

370

0.2

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0,1

0.2

0.1 x, [m]

0.2

360

(b) dp =2 mm

0 0

0.1 x, [m]

365

360

355

0.1

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405

375

z, [m]

z, [m]

410

0,2

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415 K

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350

0.2

345

(c) dp =3 mm

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Figure 7: Time-averaged particle temperature distribution at steady state.

24cm

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1cm-1.8cm

75cm Tp0 = 300K

ubg =umf Tbg =300K ubg =umf msp = 11.67kg/m2s Tsp = 500K Figure 8: Schematic representation showing the 3 individual tracer particles in red, blue and green color studied.

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400

370

Tp,mean

360

Tp,tr1

350

Tp,tr2

340

T

p,tr3

330

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320 320 300 0

100

200

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Tp,mean and Tp,tr, K

380

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390

300

400

time t, s

500

(a) Tracer particles 1, 2, 3 and mean particle temperature against time for particle

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size 1 mm. 370

350

T

p,mean

D

340 330

T

p,tr1

Tp,tr2

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Tp,mean and Tp,tr, K

360

320

300 0

100

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310

200

T

p,tr3

300

400

500

time t, s

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(b) Tracer particles 1, 2, 3 and mean particle temperature against time for particle size 2 mm. 360

Tp,mean and Tp,tr, K

350

Tp,mean

340

Tp,tr1

330

T

p,tr2

T

320

p,tr3

310 300 0

100

200

300 time t, s

400

500

600

(c) Tracer particles 1, 2, 3 and mean particle temperature against time for particle size 3 mm. Figure 9: Comparison plot showing the tracer particles profile alongside with the mean particle temperature.

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p

d = 2mm p

d = 3mm

D

p

TE

0

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Tp,tr−Tmean, K

5

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−5

−10 0

d = 1mm

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10

50

100

150

200

250 300 time t, s

350

400

450

500

Figure 10: Deviation with respect to mean temperature of particles for tracer particle 2 for the beds with different particle size (i.e. 1 mm, 2 mm, 3 mm).

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25

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15

10

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number of occurance

20

5

0 0

10

20

30 40 50 time period between peaks, τ, s

60

70

80

70

80

70

80

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(a) 1 mm.

25

D TE

15

10

5

25

number of occurance

20

10

20

30 40 50 time period between peaks, τ, s

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0 0

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number of occurance

20

60

(b) 2 mm.

15

10

5

0 0

10

20

30 40 50 time period between peaks, τ, s

60

(c) 3 mm. Figure 11: Histogram of the time interval between peaks for the 3 different particle sizes.

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Graphical abstract

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+LJKOLJKWV

CFD-DEM study of heat-transfer in pseudo 2D fluidized bed

·

Continuous bubbling due to hot gas injected in an incipient fluidized bed

·

Influence of particle size on the heat-transfer mechanism is investigated

·

Time-averaged as well as particle-tracing data are presented

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·