Modeling 3D Bubble Heat Transfer in Gas–Solid ... - ACS Publications

Nov 2, 2015 - ABSTRACT: Computational fluid dynamics discrete element method simulations of a 3D fluidized bed at nonisothermal conditions are ...
1 downloads 0 Views 4MB Size
Download PDF
Article pubs.acs.org/IECR

Modeling 3D Bubble Heat Transfer in Gas−Solid Fluidized Beds Using the CFD-DEM A. V. Patil,† E. A. J. F. Peters,*,† Y. M. Lau,‡ and J. A. M. Kuipers† †

Multiphase Reactors Group, Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands ‡ Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, 01314 Dresden, Germany ABSTRACT: Computational fluid dynamics discrete element method simulations of a 3D fluidized bed at nonisothermal conditions are presented. Hot gas injection into a colder bed that is slightly above minimum fluidization conditions is modeled in a 3D square bed containing up to 8 million particles. In this study, bubbles formed in monodisperse beds of different glass particle sizes (0.25, 0.5, 0.75, and 1 mm) and using hot-gas-injection temperatures ranging from 700 to 1100 K are analyzed. Bubble heat-transfer coefficients in 3D fluidized beds are reported and compared with theoretical predictions on the basis of the Davidson and Harrison model.

■

INTRODUCTION Gas−solid fluidized beds are used in a variety of industries because of their unique properties such as solids mobility and excellent mass- and heat-transfer characteristics. Important applications include the manufacture of polymers, pharmaceuticals, fertilizers, etc., where efficient gas−solid contact is desired. Many gas−solid fluidized-bed processes involve energyintensive operations. For instance, in energy-transfer processes such as coal gasification, hot air or steam is injected through nozzles in fluidized beds.1−4 In some other processes such as gas-phase polymerization, energy produced by reactions is absorbed by cold inlet gas entering the system.5 Thus, a complex interplay between the hydrodynamics and mass- and heat-transfer processes occurs during fluidized-bed operation. In processes like these, mass and heat exchange between gas bubbles and the emulsion phase is important. A thorough understanding of the interplay of mass, momentum, and heat transport is clearly of high practical relevance. The hydrodynamics of gas−solid fluidized beds has been studied extensively using both experimental and computational approaches.6−11 However, in many processes, (combined) mass and heat transfer between the gas and solid phases prevail and need to be accounted for as well. Some studies on the hydrodynamics combined with heat and mass transfer using the computational fluid dynamics discrete element method (CFDDEM) have been reported.12−17 However, only in recent times have heat-transfer extensions to the CFD-DEM been used for bubble-to-emulsion transfer studies in pseudo-2D beds.18 In the current paper, we want to enhance the understanding of the interplay of momentum and heat transport by simulating real 3D heat transfer in the bubbling fluidization regime, as opposed to pseudo-2D, because bubbles in fluidized beds are, of course, 3D. The focus will be on bubble-to-emulsion heat transfer for a single bubble. Clearly, the detailed CFD-DEM modeling is much more assumption-free than, e.g., the classical theoretical model of ref 19, which has many severe assumptions. Therefore, the simulations can be used to assess the validity © 2015 American Chemical Society

of the modeling assumption of simplified theoretical models. The knowledge of where simple models go wrong (or not) enhances insight into the basic mechanism of bubble-toemulsion heat transfer. Comparative studies for a single bubble have also been done experimentally using novel IR measuring techniques for mass transfer.20 However, such noninvasive radiative techniques are limited to pseudo-2D bed studies and cannot be used for 3D beds. Fluidized-bed hydrodynamics in 3D has been studied experimentally using emission-computed and X-ray tomography techniques.21,22 Furthermore, measurements utilizing probes have been performed to study heat transfer in rising bubbles in 3D fluidized beds, e.g., by ref 23. In their study, heattransfer coefficients for rising bubbles in fluidized beds of smaller particles in the range 250−500 μm were reported. However, the measurement of spatial thermal fields has been primarily limited to pseudo-2D systems.24 Because of the difficulties of 3D experiments, our approach for creating insight into heat transfer in real 3D beds is a twostep approach. First, a detailed CFD-DEM model is constructed and validated experimentally using pseudo-2D experimental data. Second, the validated code is used to generate insight into full 3D behavior that is experimentally hard to obtain. The pseudo-2D simulation of bubble-toemulsion heat transfer was presented by Patil et al.18 and the experimental validation by Patil.25 In the current work, we extend the CFD-DEM simulation study on bubble-to-emulsion heat transfer to real 3D systems that are practically relevant. A CFD-DEM study is capable of providing full spatial and temporal information on all hydrodynamic and thermal properties with ease and reasonable accuracy. In the CFDDEM approach, the gas phase is treated as a continuum (Eulerian) and the particulate phase as a discrete phase Received: Revised: Accepted: Published: 11466

August 4, 2015 October 23, 2015 November 2, 2015 November 2, 2015 DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research (Lagrangian). Through two-way coupling, the mass, momentum, and energy exchange has been accounted for. Eulerian grid dimensions in the CFD-DEM are about only 2−5 times larger than the particle diameter, which gives the right scale for accurate fluidized-bed single-bubble studies. With recent advances, CFD-DEM studies have been extended with parallelization, which has led to studies of relatively large 3D fluidized beds.26−28 Large-scale CFD-DEM simulations of 3D fluidized-bed systems have, as far as the authors know, never been used to study single-bubble injection in fluidized bed to obtain bubbleto-emulsion heat-transfer coefficients. To be able to simulate 3D systems, a large number of particles are needed. The simulations presented in the current paper contain up to 8 million particles. The efficient simulation of these large systems is made possible by the algorithmic optimizations presented by Patil.29 In our simulations, different injection temperatures and particle sizes are used. This work presents a study of the formation and rise of hot-gas bubbles in a 3D beds. The bubbleinjection mass flux through the nozzle, nozzle size, and domain size is scaled based on the particle size being used. The temperature of the injection is set at values of 300 , 700, and 1100 K. Heat-transfer coefficients are determined from the simulations and compared with theoretical and experimental predictions.

Table 1. Settings Used for Bubble-Injection Simulations (a) Basic Simulation Settings particle type ρp normal coefficient of restitution tangential coefficient of restitution Cp,f Cp,p Δt (Eulerian) Δt (Lagrangian) no. of particles (b) Particle Properties dp (mm)

Geldart type

0.25 0.5 0.75 1.0

normal spring stiffness (N/m)

THEORY AND SETTINGS Governing Equations. The governing equations and correlations used in this paper are the same as those presented by Patil et al.18 for the simulation of heat transfer in a pseudo2D fluidized bed. As in a conventional CFD-DEM, a smoothed continuum description for the gas velocity field is used and particle trajectories are modeled by solving Newton’s equations. The dynamics of gas and particles are two-way-coupled by using a drag correlation. To model the heat transfer, a convection−conduction equation is solved for the gas phase. The temperature profile in the particles is assumed to be homogeneous (Bi = 0), and the particle−gas heat transfer is modeled using the Gunn correlation30 for the particle-to-gas Nusselt number. In another publication by Patil et al.,25 we also modeled particle−particle heat transfer when particles collide. There we concluded that this mode of heat transfer was negligibly small, so we did not include it here. Simulation Settings. Hot-gas injection into an incipiently fluidized 3D bed was simulated using a CFD-DEM approach. For the simulations, a square channel was considered with noslip wall-boundary conditions on all of the vertical sides inlet at the bottom and outlet boundary condition at the top. The Eulerian grid consists of a structured block mesh, whereas the particulate motion was described by moving (Lagrangian) points. For the incipient fluidization, the background gas was maintained slightly above the minimum fluidization velocity, at a value ubg given in Table 2, and the inlet temperature of the background gas was 300 K in all of the simulations. A central injection nozzle with a set inlet mass flux (see Table 1c) was used to generate a gas bubble in the bed. A square nozzle, of size 2 × 2 or 3 × 3 cells, was used to inject the bubble. Depending on the time needed for necking of the bubble to occur, the injection time was set for each particle size. Cold gas with the same background velocity as that used elsewhere was fed from the nozzle after bubble injection was

tangential spring stiffness (N/m)

B 3200 1025 B 7000 2249 D 10000 3212 D 19000 6104 (c) Quantities Different for Each Temperature

mass flux [kg/(m2 s)]

T (K)

ρf (kg/m3)

uinj (m/s)

17.55

300 700 1100 300 700 1100

1.1700 0.5014 0.319 1.1700 0.5014 0.319

15.0 35.0 45.0 10.0 23.33 30.0

11.7

■

glass 2526 kg/m3 0.97 0.33 1010 J/(kg K) 840 J/(kg K) 2.5 × 10−5 s 2.5 × 10−6 s 8 × 106

Table 2. Summary of the Bubble-Injection Data dp (mm)

ubg (m/s)

nozzle size (mm2)

injection time (s)

0.25

0.05

19.5

0.06

0.5

0.22

39

0.08

0.75

0.42

56.25

0.1

1.0

0.58

100

0.1

bed size (m × m × m) 0.05 × 0.05 0.15 0.10 × 0.10 0.3 0.15 × 0.15 0.525 0.2 × 0.2 ×

× × × 0.7

grid size 24 × 24 70 48 × 48 140 40 × 40 140 40 × 40 140

× × × ×

completed. After detachment, the bubble rose in the fluidized bed, exchanging heat with the surrounding emulsion phase. Table 1a summarizes the basic data of the gas and particles and simulation settings that were used in the simulations. There were four sizes of glass particles used: 1, 0.75, 0.5, and 0.25 mm. These particles are of various types in the Geldart classification. The particle collision parameters and fluidization velocities used for these simulations are given in Table 1b. The spring stiffness is selected such that, at the maximum relative velocity of particles (close to 1 m/s), the particle overlap is less than 1% of the particle diameter. The injection mass flux through the central nozzle used was 17.55 kg/(m2 s) for the 1 mm and 0.75 mm particles and 11.7 kg/(m2 s) for the 0.5 mm and 0.25 mm particles. For each of the particle sizes, three gas-injection temperatures were considered, namely, 300, 700, and 1100 K, all at the same mass flux. In order to keep the injection mass flux the same, the injection velocity was varied. Table 1c gives the respective gas densities and injection velocities used for the simulations at each injection temperature and injection mass flux. The size of the bed was varied according to the sizes of the particles. Thus, system settings like the bed size, grid size, 11467

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research

The images in Figure 1 show the particulate phase where almost 2−3 million particles of the CFD-DEM simulation are visualized. The domain of the bed is cut in half so that the gas bubble in the interior of the bed can be seen. The gas-phase data are visualized on a plane that is perpendicular to the cut plane. Only the high-gas-temperature regions on the Eulerian grid are shown. The low-temperature region in the sliced grid was made transparent so that the internal shape of the bubble is visible. From the scale of the gas temperature, the temperature profiles inside the bubble on the sliced grid can be inferred. During the injection, the high-temperature hot-gas jet strikes the ceiling of the bubble, facilitating expansion of the bubble. The hot gas after impinging on the ceiling either penetrates into the emulsion phase or moves to the sides in the radial direction, which is shown in Figure 1 at time t = 0.04 and 0.07 s. As the injection stops, a pocket of gas has accumulated at the top of the bubble, as can be seen at time t = 0.07 s of Figure 1. The part of the hot gas that is convected through the ceiling immediately cools because of contact with the cold particles. Right after injection, also a hot pocket of gas remains at the top inside the bubble. Now, cold background gas rises through the center of the bubble that convects this hot gas to the stagnant sides, which leads to the formation of a ring-shaped hightemperature zone. This ring-shaped high-temperature zone is similar to the high-temperature pockets forming on the sides of the bubble in pseudo-2D fluidized beds; see work by Patil et al.18 The hot zone is cooled because of the nearby cold particles at the bubble boundary by means of a combination of heat convection and conduction. With further rising of the bubble, the hot pocket zone cools and disappears. Figure 2 shows the contour of the high-gas-temperature zones for bubble injection in a 0.5 mm particle bed with an injection temperature of 1100 K. The boundary of the contour is represented by a temperature threshold of 350 K. The color on the contour surface represents the pressure field. During the time of injection (t = 0.08 s), as can be seen in Figure 2, a highpressure zone exists at the top of the bubble. This high-pressure zone in the center top of the bubble reduces in size as the bubble gets detached from the nozzle (t = 0.12 s in Figure 2). The pressure reduces because the high-pressure gas convects out from the roof of the bubble into the emulsion phase as the bubble rises through the bed. Thus, a flow pattern in the bubble is developed, where the background gas entering from the

nozzle size, and injection time were adjusted for each of the particle sizes. These data are summarized in Table 2.

■

RESULTS AND DISCUSSION Bubble Injection and Rise. A sample bubble injection and subsequent rise image captured in 3D using the Paraview imaging tool is shown in Figure 1. This is a single bubble-

Figure 1. Hot-gas injection and rise of a bubble for the particle size 0.25 mm with an injection mass flux of 11.7 kg/(m2 s) and a gasinjection temperature of 1100 K.

injection example for the particle size 0.25 mm and a gasinjection temperature of 1100 K. This figure shows snapshots at times of 0.04, 0.07, and 0.08 s, where the injection time is 0.06 s. As the injection of gas is stopped, the bubble necks and detaches from the nozzle and rises through the particulate bed (at incipient fluidization).

Figure 2. Hot-gas injection and rise of a bubble for the particle size 0.5 mm with an injection mass flux of 11.7 kg/(m2 s) and a gas-injection temperature of 1100 K. The contour boundary is represented by a gas-temperature threshold of 350 K. The color scheme on the contour represents the pressure field along this interface. 11468

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research bottom flows toward the center of the bubble and moves out from the top roof of the bubble. Figure 3 shows top views of the bubble depicted in Figure 1 for time t = 0.08 s. The porosity field can be observed in Figure

of 80%. Previously, Olaofe et al.31 and Patil et al.18 used the same value (threshold) in pseudo-2D bed DEM studies. The traced bubble region was used to obtain the size of the bubble, mean temperature of the bubble, and gas velocity in the bubble from the Eulerian grid data. Thus, variation of these parameters could be tracked in time. Using the computed bubble volume, the equivalent diameter of the bubble was obtained assuming a spherical shape. During the gas-injection stage, the growth of the bubble with time is governed by the bubble dynamics. One of the most successful theoretical models for bubble growth is that of Caram and Hsu.32 Here the motion of the particles is purely inertial and driven by the gas pressure. The leakage of the gas out of the bubble is described as Darcy flow with respect to the emulsion phase. Previously, Olaofe et al.31 matched pseudo-2D DEM and two-fluid model (TFM) simulations with this model to validate them under isothermal conditions. Verma et al.33 compared 3D TFM simulation of bubble formation with the Caram and Hsu 32 model. Similar hydrodynamics validations were performed here as well, considering 3D bubble injection in isothermal conditions using our CFD-DEM code. The results in Figure 5 show that also in the 3D case the predicted (isothermal) hydrodynamics match well with the theoretical model.

Figure 3. Cross-sectional top view of a bubble rising through the bed at time t = 0.08 s. The profiles are taken for the particle size 0.25 mm at a height of 0.03 m above the bottom, which is approximately at the middle of this specific bubble. The intensity plots of three fields are shown: (a) porosity; (b) temperature; (c) upward gas velocity.

3a. Figure 3b shows the temperature profile forming in the bubble where the white line marks the contour boundary of 80% porosity. From this figure, it can be seen that the 80% porosity boundary marking not just the bubble area but also the high-temperature ring that is formed in the bubble stays within its limits. The velocity field of the gas in the bubble is shown in Figure 3c. By a comparison of the set of figures in Figure 3, it can be seen how the high-temperature ring tries to accommodate itself between the central high-gas-velocity zone (z direction) and the surrounding emulsion phase of the bubble. The cross-sectional front views of this bubble’s porosity and temperature profile are shown in Figure 4. This profile looks very similar to the pseudo-2D fluidized-bed profiles that were shown earlier in the literature.18

Figure 5. Bubble diameter plot versus time for several particle sizes during gas injection at isothermal conditions. The simulation results are compared with the results obtained from the Caram and Hsu32 model.

Figure 4. Cross-sectional front views of the porosity and temperature fields of a bubble with the particle size 1 mm, an injection mass flux of 23.4 kg/(m2 s), and an injection temperature of 1100 K.

In the nonisothermal case, as the mass flux is fixed and gas is injected at an elevated temperature, the resulting bubble size is slightly larger depending on the injection temperature. This can be observed from Figure 6, which shows gas injection at an

The particles initially at the top of the bubble receive the strongest supply of heat from the hot-gas jet. These hot particles move downward along the circumference of the spherical bubble. The hot particles are only present in the fine layer of particles at the interface because of their high heat capacity. This has also been observed in the pseudo-2D fluidized-bed case.18 As the bubble rises, the hot particles collect in the wake of the bubble. The cold gas moving through the bubble next starts to gain heat from these particles before flowing into the bubble. This effect was also observed for pseudo-2D beds18 for larger particles. Similarly here also for 1 mm particles, it can be observed as shown in Figure 4. Bubble Diameter and Velocity. Gas injection into the fluidized bed creates a single gas bubble that rises through the dense particulate phase. This void bubble region consisting of primarily gas and a very small amount of particles was traced during postprocessing to construct a constant porosity contour. The bubble region was defined using a threshold porosity value

Figure 6. Bubble diameter versus time for several injection temperatures and a constant particle size of 0.5 mm. 11469

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research isothermal temperature of 300 K and elevated temperatures of 700 and 1100 K at the same fixed mass flux of 11.7 kg/(m2 s) for varying particle sizes of 0.5 mm. This is due to the higher momentum flux provided by hot-gas injection, which is given by ρug,n2. From the Eulerian data, cells belonging to the bubble area can be identified, and thus the centroid can be calculated. Using this procedure, the rate of change of the position of the center of mass with respect to time was calculated and plotted against time to give the bubble velocity plot. This plot is shown in Figure 7 for the particle sizes 0.5 and 1 mm. The detachment

Figure 8. Bubble mean temperature versus time for a particle size of 0.5 mm and an injection mass flux of 11.7 kg/(m2 s).

where Te represents the temperature of the emulsion phase. Here it is assumed that heat transfer from the bubble to the emulsion phase can be described by a constant heat-transfer coefficient. The analytical solution of this equation gives an exponential decay according to ⎡ − h A (t − t ) ⎤ Tb(t ) − Te 0 ⎥ = exp⎢ b b Tb(t0) − Te ⎢⎣ ρf VbCp,f ⎥⎦ Figure 7. Bubble rise velocity versus time for particle sizes of 0.5 and 1 mm after detachment.

The mean bubble temperature was thus nondimensionalized and plotted against time to give the data plot that can be fitted with eq 3 to obtain the heat-transfer coefficient. The series of fits that were obtained is shown in Figure 9 for all of the particle sizes (0.25, 0.5, 0.75, and 1 mm). This computed heat-transfer coefficient will be compared to the theoretical expression of the Davidson and Harrison19 model given by

time was 0.08 s for 0.5 mm particles and 0.1 s for 1 mm particles. The plot thus shows the rise velocity starting from 0.1 s when the bubble in the 1 mm particle bed detached. After detachment, the bubble shape at the bottom changed quickly from convex to concave, which caused a slight fluctuation in the bubble velocity before it stabilized. Once completely detached and stabilized, the bubble rose with a nearly constant velocity. The mean velocity of the bubble after detachment will be used later for calculation of the theoretical bubble heat-transfer coefficients from the Davidson−Harrison bubble model. The bubble rise velocity, urv, of a bubble according to Davidson and Harrison19 as given by urv = 0.711(gdb)0.5

hb,DH

dTb = −hbAb(Tb − Te) dt

(kgρg Cp,g)0.5 g 0.25 4.5 = umf ρf Cp,f + 5.85 db db 0.25

(4)

for a spherical bubble. In Table 3, the heat-transfer coefficients obtained from simulations are compared with those of the Davidson−Harrison model given by eq 4. Also, the experiments reported in ref 23 for 0.25 and 0.5 mm sand particles have been included in Table 3 for comparison. It can be observed that the simulations give much higher values in comparison with the values obtained from the Davidson and Harrison19 bubble model (approximately twice as large). Hence, a further investigation was undertaken to find out what the reason was for this difference and will be presented subsequently. The bubble heat-transfer coefficient is a function of the gas velocity inside the bubble. The Davidson and Harrison19 bubble model predicts that the mean velocity of gas inside an isolated 3D bubble in a fluidized bed is 3umf. This theoretical result is used to obtain the expression for the heat-transfer coefficient given by eq 4. To check whether in the simulations a value of 3umf is also found, the mean velocity of gas inside the bubble was calculated using the cross-sectional Eulerian data of the gas velocity field. As an example, for a 0.25 mm particle, it was observed that the mean gas velocity was 0.63 m/s. From these numbers, we can obtain the gas velocity relative to the bubble rise velocity by subtracting the bubble rise velocity. This relative mean gas velocity in the rising bubble was divided by the minimum fluidization velocity umf to obtained the required factor. These numbers are tabulated in Table 4. Here it can be u −u seen that the factor g rv is much higher than 3 (about a factor

(1)

The rise velocities obtained by time-averaging the results of Figure 7 compare well with this correlation. This is shown in the third and fourth columns of Table 4, where the computed bubble rise velocities are compared with eq 1. Bubble Temperature of the Gas Phase. The nonisothermal bubble injected possesses an internal temperature profile, which can be seen in Figure 4. Knowing the traced bubble area from the Eulerian data, the mean temperature of the gas phase in the bubble was also calculated. A sample plot of the mean bubble temperature with respect to time is shown in Figure 8 for the particle size 0.5 mm. As indicated in Table 2, the injection stops after 0.08 s and the cooling curve has a kink. The mean temperature of the bubble reduces with time. This cooling of the bubble is due to convective transport of the gas phase originating from the background that carries the hot gas into the emulsion phase. A simple energy balance for the gas inside the bubble, after the injection has stopped, is given by ρf VbCp,f

(3)

u mf

(2)

2 higher). This explains the deviation between the computed 11470

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research

Figure 9. Model fit for all particle sizes of nondimensionalized bubble mean temperature with respect to time: (a) for the particle size 0.25 mm and an injection mass flux of 11.7 kg/(m2 s); (b) for the particle size 0.5 mm and an injection mass flux of 11.7 kg/(m2 s); (c) for the particle size 0.75 mm and an injection mass flux of 23.4 kg/(m2 s); (d) for the particle size 1.0 mm and an injection mass flux of 23.4 kg/(m2 s).

predicted value is that the gas velocity in a 3D bubble is larger than the gas velocity predicted by Davidson and Harrison.19 What remains to be elucidated is why this 3D gas velocity is higher than that predicted. The basic assumptions of the Davidson−Harrison model are that the particle velocity field obeys the potential flow and the gas flow relative to the particle phase is governed by Darcy’s law. As shown by Davidson and Harrison,19 it follows from these assumptions that, for a spherical bubble in an unbounded emulsion phase, the relative mean gas velocity is 3umf. According to the theory, this gas velocity is found for a bubble where the emulsion phase flows according to the potential flow but also for the case where the emulsion phase is fixed and a spherical cavity is present. To investigate where the assumptions of the Davidson− Harrison model are too restrictive and thus to explain the deviation from the simulation results, several tests were performed. We will now discuss these tests one by one. We will first focus on the effect of wall confinement on the gas dynamics because the Davidson−Harrison model assumes the bubble to be present in an infinite domain. In our first test, a fixed spherical cavity inside a nonmoving emulsion phase is considered. The Eulerian cells in the emulsion are given a porosity value of 0.38, and the spherical cavity or bubble, corresponding to a region of porosity 1, is fixed at the center of the domain. To investigate possible wallconfinement effects, two geometries were considered. For the first geometry, we considered a very large domain of 0.2 m × 0.2 m and a spherical cavity with a diameter of 0.027 m. This was the same size as that of injected bubbles while rising through the bed for 0.25 mm particles. So, here the geometry approximates the case of an isolated bubble in an infinite domain. Thus, it can be assumed that there are no wall effects in this particular case. Figure 10a shows a top view of the gas velocity profile at the central plane. The gas velocity sharply rises near the center of the bubble, giving a maximum velocity of 0.29 m/s in the bubble. By comparing Figures 10a and 3c, one sees the differences between the gas flow in stationary and moving

Table 3. Bubble Heat-Transfer Coefficient Calculation for Several Particle Sizes dp (mm)

mass flux [kg/(m2 s)]

Ab hb/ρf Vb Cp,f (s−1)

hb,sim [W/ (m2 K)]

hb,DH [W/ (m2 K)]

hexpt,WA [W/(m2 K)]

1.0 0.75 0.5 0.25

23.4 23.4 11.7 11.7

48.8 34.4 33.1 57.0

931 510 403 267

468 344 189 61

60−200 80−300

Table 4. Bubble Characteristics for Different Particle Sizes bubble rise velocity (m/s) ug − u rv

dp (mm)

min fluidization velocity (m/s)

sim

DH

mean gas velocity ug (m/s)

1.0 0.75 0.5 0.25

0.58 0.42 0.18 0.05

0.9 0.75 0.6 0.35

0.83 0.73 0.59 0.36

4.1 3.3 1.7 0.63

u mf

(m/s) 5.5 6.1 6.2 6.6

heat-transfer coefficient and the Davidson and Harrison19 model heat-transfer coefficient. As shown in the previous section, the bubble rise velocity computed by the simulation compares well with the theoretical prediction in eq 1. Therefore, the deviation is solely due to the computed ug. These differences are unexpected because a similar comparison made earlier by Patil et al.18 showed good agreement for the pseudo-2D case. For 2D bubbles, the Davidson and Harrison19 model predicts that the mean gas velocity inside the bubble is 2umf. This was checked for the data reported by Patil et al.18 Our calculations revealed that the gas velocity inside the bubble matched well with that predicted from the model19 for the earlier reported 2D case, and also the computed heat-transfer coefficients agreed with the theoretical predictions. The likely explanation for the fact that the computed heattransfer coefficient in 3D is larger than the theoretically 11471

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research

correspondence with the Davidson−Harrison prediction, but for the moving bubble, the computed gas velocity is much higher than that in the theoretical prediction. We therefore conclude that confinement effects are small and cannot explain the deviation from the Davidson−Harrison prediction. Because wall confinement cannot explain the unexpectedly high gas through-flow, we hypothesize that the motion of the particulate phase is the reason for it. To investigate this hypothesis, we compared simulation results to the theoretical model. The assumption of Darcy flow for the gas in the Davidson−Harrison model seems very similar to what is included in the detailed CFD-DEM model. Therefore, it is not expected that this assumption causes the large deviation between the simulation and Davidson−Harrison model. This is also confirmed by the fact that the computations and model agree for a fixed spherical cavity. The Davidson−Harrison model assumes that the particulate velocity field obeys the potential flow. This assumption might be at the root of the disagreement found for the moving 3D bubble. Combining this potential flow assumption for the particulate phase with Darcy’s law for the gas flow indicates that the gaspressure field around a bubble is given by the same equation (namely, the solution of a Laplace equation with the same boundary conditions) irrespective of the motion of the bubble, i.e., fixed cavity or particulate potential flow. The pressure profile, as found in the simulations of the rising bubbles, is shown in Figure 11 together with the theoretical expression.

Figure 10. Comparison between the gas velocity fields at the center of a fixed void or bubble for confined and unconfined domain systems.

bubbles, respectively. The mean gas velocity in the stationary bubble equals 0.16 m/s, which is approximately 3 times the minimum fluidization velocity of 0.05 m/s. This agrees with the Davidson−Harrison prediction for a stationary bubble phase. For the second geometry, the same domain size and bed height as those of the simulations reported earlier for bubble injection in a 0.25 mm particle bed were used. So, obviously confinement effects exist here. The same-sized spherical cavity as that in the first geometry was placed at the center. Figure 10b shows the top-view flow velocity profile for the confined domain with the stationary bubble at its center. It can be seen that in this case the maximum velocity of gas inside the bubble amounts to 0.23 m/s. The mean gas velocity in this fixed bubble, however, was also found to be 3umf. When the profiles in parts a and b of Figure 10 are compared, they reveal small differences, indicating the influence of confinements. However, in both cases, the mean velocity is nearly the same. Therefore, we conclude that, if the particles are kept fixed, the mean gas flow is not influenced much by wall confinement. An ideal test for the moving bubble case would be to consider a much bigger fluidized-bed domain and the same bubble size injection as before. However, because of the computational limitation on the maximum number of particles (i.e., the size of the domain), we decided to inject a smaller bubble and check the mean velocity of gas in the bubble. So, we used an injection mass flux of 2.9 kg/(m2 s) for the simulations of 0.25 mm particles, where originally we had injected gas with a mass flux of 11.7 kg/(m2 s). Now the bubble formed was onefourth the size of that shown in Figure 3. With a substantially smaller bubble injected, the bubble−emulsion interface was relatively far away from the confining wall, and hence any confinement effect would be expected to be small. The mean velocity of gas relative to the bubble calculated for the smaller bubble equals that of the larger bubble. So, this test ascertains that the wall confinement did not change the through-flow in the bubble much. The observation that confinement does not seem to severely influence the gas through-flow even for moving bubbles is likely due to the fact that confinement also does not severely influence the particulate motion. In the work of Collins,34 an analogous potential flow derivation for a bubble rising in confinement has been made. This equation is limited to 2D systems, and a derivation for a 3D bubble rising in a square duct has not been made. However, the results for the pseudo-2D bed from the Collins34 model were compared with the simulation results of Patil et al.,18 and it was observed that it also matched equally well with the simulation for the Davidson and Harrison19 model. In conclusion, in both cases, i.e., for the fixed and moving 3D bubble, confinement does not significantly change the gas velocity inside the bubble. For the fixed case, there is

Figure 11. Axial pressure profile for a rising bubble plot for the particle size 0.25 mm indicating pressure profiles above, below, and inside the bubble.

This plot clearly shows a difference in the shape of the pressure curve in the wake of the bubble. So, here the Davidson− Harrison model indeed seems to break down. To more clearly access what the velocity field of the solids look like, we compared the velocity field obtained from the simulation to that predicted by Davidson and Harrison, i.e., assuming potential flow around a sphere. Figure 12a shows the Davidson−Harrison flow field of particles in a reference frame moving with the bubble. The streamlines look qualitatively different from those of Figure 12c,d, which are obtained from the 3D bubble CFD-DEM simulations at gas-injection mass fluxes of 11.7 and 2.9 kg/(m2 s), respectively. In both of these figures, a red dotted line has been used to indicate the bubble boundary. The black dotted lines define a region outside of which the flow resembles the potential flow predicted by the theoretical model. In between the red and black dotted lines, a circulating flow pattern is found that is very different from the theoretical prediction. This qualitative difference in the particulate flow pattern was not observed in the pseudo-2D 11472

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research

The formation of a bubble under isothermal conditions was compared with the Caram and Hsu32 model. The heat-transfer coefficient for the single-bubble rise simulation was found to be twice that of the Davidson and Harrison19 model. The possible reasons for this difference were probed in detail. The rise velocity of the single bubble matched well with that of the Davidson and Harrison19 model. However, the through-flow of gas in the bubble was found to be twice that predicted by the Davidson and Harrison19 model. A detailed study attributes this difference to the particulate flow field in the inner-shell region around the bubble between the simulation and theoretical model. This flow pattern of particles causes drag on the gas, which leads to higher recirculation of gas through the bubble, thus producing a higher heat-transfer coefficient for the bubble rising through the fluidized bed.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the European Research Council for its financial support, under its Advanced Investigator Grant scheme [Contract 247298 (Multiscale Flows)]. The authors also thank Ivo Roghair for providing help with Paraview visualization.

Figure 12. Streamlines of the particular phase viewed in a reference frame moving along with the bubble: (a) streamlines around a spherical bubble according to the Davidson−Harrison model; (b) computed streamlines for a pseudo-2D bubble at the indicated injection mass flux; (c and d) computed streamlines for a 3D bubble for two injection mass fluxes.

■

REFERENCES

(1) Lee, J. M.; Kim, Y. J.; Lee, W. J.; Kim, S. D. Coal-gasification kinetics derived from pyrolysis in a fluidized-bed reactor. Energy 1998, 23, 475−488. (2) Xiao, R.; Zhang, M.; Jin, B.; Huang, Y.; Zhou, H. HighTemperature Air/Steam-Blown Gasification of Coal in a Pressurized Spout-Fluid Bed. Energy Fuels 2006, 20, 715−720. (3) Weber, R.; Orsino, S.; Lallemant, N.; Verlaan, A. Combustion of natural gas with high-temperature air and large quantities of flue gas. Proc. Combust. Inst. 2000, 28, 1315−1321. (4) Ye, B.; Lim, C. J.; Grace, J. R. Hydrodynamics of spouted and spout-fluidized beds at high temperature. Can. J. Chem. Eng. 1992, 70, 840−847. (5) Floyd, S.; Choi, K. Y.; Taylor, T. W.; Ray, W. H. Polymerization of olefines through heterogeneous catalysis IV. Modeling of heat and mass transfer resistance in the polymer particle boundary layer. J. Appl. Polym. Sci. 1986, 31, 2231−2265. (6) Foka, M.; Chaouki, J.; Guy, C.; Klvana, D. Gas phase hydrodynamics of a gas-solid turbulent fluidized bed reactor. Chem. Eng. Sci. 1996, 51, 713−723. (7) 16th International Conference on Chemical Reactor Engineering: Goldschmidt, M. J. V.; Kuipers, J. A. M.; van Swaaij, W. P. M. Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow: effect of coefficient of restitution on bed dynamics. Chem. Eng. Sci. 2001, 56, 571−578. (8) Huilin, L.; Yurong, H.; Gidaspow, D. Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow. Chem. Eng. Sci. 2003, 58, 1197−1205. (9) First International Workshop on Granulation: Bokkers, G. A.; van Sint Annaland, M.; Kuipers, J. A. M. Mixing and segregation in a bidisperse gas-solid fluidised bed: a numerical and experimental study. Powder Technol. 2004, 140, 176−186. (10) Taghipour, F.; Ellis, N.; Wong, C. Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chem. Eng. Sci. 2005, 60, 6857−6867. (11) Laverman, J. A.; Roghair, I.; van Sint Annaland, M.; Kuipers, H. Investigation into the hydrodynamics of gas-solid fluidized beds using

bed study in Patil et al.18 In Figure 12b, streamlines for a pseudo-2D simulation are shown and no particulate circulation zone is seen. Streamlines correspond reasonably well to the 2D potential flow, except that streamlines end abruptly near the roof of the bubble. This is because of the phenomenon of raining of the particle in the bubble for pseudo-2D beds. If we ignore this small effect, we can conclusively say that the pseudo-2D particulate flow field matches much better to the potential flow predictions than the 3D particulate flow field does. This explains why we find a significant deviation from the model predictions for the gas flow through the bubble in 3D but not in 2D. The 3D nonpotential circulating-flow pattern around the bubble causes a drag force on the gas moving out of the roof of the bubble. Because of this, the gas in the emulsion phase close to the bubble boundary experiences a higher downward drag, causing a higher recirculation of gas back into the bubble. The reason why the potential flow assumption failed for 3D beds is not well-understood. Because in a 3D system the bulk particle−particle interaction and shear is higher, this could be causing the observed flow pattern. In a pseudo-2D bed, this feature is not that significant because of a thin layer of particle− particle interaction but does become dominant in 3D beds.

■

CONCLUSION The CFD-DEM technique was successfully used to study heat transfer through a hot-gas bubble injection in a 3D fluidizedbed system. The large 3D-system-based study was made possible through an improved collision handling technique. 11473

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474

Article

Industrial & Engineering Chemistry Research particle image velocimetry coupled with digital image analysis. Can. J. Chem. Eng. 2008, 86, 523−535. (12) Ninth Congress of the French Society of Chemical Engineering: Zhou, H.; Flamant, G.; Gauthier, D.; Flitris, Y. Simulation of Coal Combustion in a Bubbling Fluidized Bed by Distinct Element Method. Chem. Eng. Res. Des. 2003, 81, 1144−1149. (13) Zhou, H.; Flamant, G.; Gauthier, D. DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure. Chem. Eng. Sci. 2004, 59, 4193−4203. (14) Limtrakul, S.; Boonsrirat, A.; Vatanatham, T. DEM modeling and simulation of a catalytic gas-solid fluidized bed reactor: a spouted bed as a case study. Chem. Eng. Sci. 2004, 59, 5225−5231. (15) Zhou, Z. Y.; Yu, A. B.; Zulli, P. A new computational method for studying heat transfer in fluid bed reactors. Powder Technol. 2010, 197, 102−110. (16) Wu, C.; Cheng, Y.; Ding, Y.; Jin, Y. CFD-DEM simulation of gas-solid reacting flows in fluid catalytic cracking (FCC) process. Chem. Eng. Sci. 2010, 65, 542−549. (17) Bluhm-Drenhaus, T.; Simsek, E.; Wirtz, S.; Scherer, V. A coupled fluid dynamic-discrete element simulation of heat and mass transfer in a lime shaft kiln. Chem. Eng. Sci. 2010, 65, 2821−2834. (18) Patil, A. V.; Peters, E. A. J. F.; Kolkman, T.; Kuipers, J. A. M. Modeling bubble heat transfer in gas-solid fluidized beds using DEM. Chem. Eng. Sci. 2014, 105, 121−131. (19) Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: Cambridge, U.K., 1963. (20) Dang, T. Y. N.; Kolkman, T.; Gallucci, F.; van Sint Annaland, M. Development of a novel infrared technique for instantaneous, wholefield, non invasive gas concentration measurements in gas-solid fluidized beds. Chem. Eng. J. 2013, 219, 545−557. (21) Mudde, R. F. Bubbles in a fluidized bed: A fast X-ray scanner. AIChE J. 2011, 57, 2684−2690. (22) Verma, V.; Deen, N. G.; Padding, J. T.; Kuipers, J. A. M. Twofluid modeling of three-dimensional cylindrical gas-solid fluidized beds using the kinetic theory of granular flow. Chem. Eng. Sci. 2013, 102, 227−245. (23) Wu, W.; Agarwal, P. K. Heat Transfer to an isolated bubble rising in a high temperature incipiently fluidised bed. Can. J. Chem. Eng. 2004, 82, 399−405. (24) Patil, A. V.; Peters, E. A. J. F.; Sutkar, V. S.; Deen, N. G.; Kuipers, J. A. M. A study of heat transfer in fluidized beds using an integrated DIA/PIV/IR technique. Chem. Eng. J. 2015, 259, 90−106. (25) Patil, A.; Peters, E.; Kuipers, J. Comparison of CFD-DEM heat transfer simulations with infrared/visual measurements. Chem. Eng. J. 2015, 277, 388−401. (26) Papers presented at the Fifth World Conference of Particle Technology (WCPT5), Orlando, FL, April 23−27, 2006: Chu, K. W.; Yu, A. B. Numerical simulation of complex particle-fluid flows. Powder Technol. 2008, 179, 104−114. (27) Chu, K. W.; Wang, B.; Xu, D. L.; Chen, Y. X.; Yu, A. B. CFDDEM simulation of the gas-solid flow in a cyclone separator. Chem. Eng. Sci. 2011, 66, 834−847. (28) Yang, S.; Luo, K.; Fang, M.; Zhang, K.; Fan, J. Parallel CFDDEM modeling of the hydrodynamics in a lab-scale double slotrectangular spouted bed with a partition plate. Chem. Eng. J. 2014, 236, 158−170. (29) Patil, A. V. Heat transfer in gas−solid fluidized beds. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2015. (30) Gunn, D. J. Transfer of heat or mass to particles in fixed and fluidised beds. Int. J. Heat Mass Transfer 1978, 21, 467−476. (31) Olaofe, O. O.; van der Hoef, M. A.; Kuipers, J. A. M. Bubble formation at a single orifice in a 2D gas fluidised beds. Chem. Eng. Sci. 2011, 66, 2764−2773. (32) Caram, H. S.; Hsu, K.-K. Bubble formation and gas leakage in fluidized beds. Chem. Eng. Sci. 1986, 41, 1445−1453. (33) Verma, V.; Padding, J. T.; Deen, N. G.; Kuipers, J. Bubble formation at a central orifice in a gas-solid fluidized bed predicted by

three-dimensional two-fluid model simulations. Chem. Eng. J. 2014, 245, 217−227. (34) Collins, R. An extension of Davidson’s theory of bubbles in fluidized beds. Chem. Eng. Sci. 1965, 20, 747−755.

11474

DOI: 10.1021/acs.iecr.5b02865 Ind. Eng. Chem. Res. 2015, 54, 11466−11474