Heat Transfer from an Immersed Tube in a ... - ACS Publications

Article pubs.acs.org/IECR

Heat Transfer from an Immersed Tube in a Bubbling Fluidized Bed Zhongyuan Hau and Eldin Wee Chuan Lim* Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585 S Supporting Information *

ABSTRACT: An Eulerian−Eulerian approach was used to investigate the effects of particle size and immersed tube temperature on bubbling and heat transfer behaviors in a gas fluidized bed. Large gas bubbles were observed to split into smaller bubbles that flowed around the immersed tube during the fluidization process. The formation of pockets of gas around the immersed tube led to a lower heat transfer coefficient. Heat transfer between the immersed tube and particles was facilitated by a phenomenon of particle renewal. Larger gas bubbles formed in the gas fluidized bed containing larger particles and this resulted in lower heat transfer coefficients due to the formation of more gas pockets around the immersed tube. When the temperature of the immersed tube was increased, the sensitivity of the heat transfer process toward formation of gas pockets around the immersed tube was observed to increase.

1. INTRODUCTION Fluidized bed systems are extensively used in industrial unit operations due to their excellent heat and mass transfer characteristics. Fluidization of particles is applied in many industrial processes such as drying, mixing, granulation, coating, heating and cooling. A fluidized bed promotes good heat transfer between particles and the fluid as well as between the bulk phase and heat transfer surfaces immersed in the bed. Good understanding of heat transfer in fluidized bed systems with or without immersed tubes can aid in the designs and operations of such systems for various industrial applications. With the advent of computational capabilities, computational fluid dynamics (CFD) has been increasingly used as a tool to model the multiphase hydrodynamics in fluidized bed systems. However, although many research studies have been reported on simulations of fluidization behaviors, studies on coupled effects of hydrodynamics with heat transfer have been limited in the current literature. Heat transfer in a gas fluidized bed system is almost always studied in unison with the hydrodynamics of the system. This is due to the strong coupling between hydrodynamics and heat transfer. Molerus1 defined a two-phase Prandtl number for prediction of maximum heat transfer coefficients in bubbling fluidized beds which takes into consideration the thermal and hydrodynamic properties of particles and fluid. He subsequently developed six correlations for calculating maximum heat transfer rate based on excess gas velocity.2 The hydrodynamics of bubbling fluidized beds has been investigated using the Eulerian−Eulerian approach, providing predictions on instantaneous solid volume fraction as well as particle velocity profiles. Schmidt and Renz3 applied the Eulerian approach for numerical simulations of two-phase flow in a fluidized bed with an immersed tube. The empirical models of Gunn4 and Kuipers et al.5 were used to derive the interphase heat transfer and © 2016 American Chemical Society

thermal conductivity of the solid phase respectively and were applied in the simulations yielding results that suggested a strong correlation between solid volume fraction and heat transfer coefficient around the heated tube. Schmidt and Renz3 also discussed the approach by Hunt6 that predicted thermal conductivity based on a model that is a function of granular temperature. According to Hunt,6 the thermal conductivity is highly sensitive toward granular temperature. However, high granular temperature was found to be located in dilute particulate regions whereby the void fraction was high and there were no significant differences in the values predicted by other models. Schmidt and Renz7 subsequently applied the Eulerian approach to investigate heat transfer and fluid dynamics in a fluidized bed with immersed tubes. The packet theory was used to describe the heat transfer process between the walls of the immersed tubes and particles that contacted the wall. Heat transfer coefficients obtained using the standard and kinetic approaches were compared with those calculated using empirical models and derived experimentally. The results were compared with penetration theory and proved to be consistent. Schimdt and Renz8 investigated heat transfer in a fluidized bed with Geldart type B particles. Two approaches were used to model the heat conduction process in the solid phase. The first was the standard approach of deriving the effective thermal conductivity from an ideal arrangement of particles whereas the second was based on kinetic theory. They found that fluxes of particles around the heated tube wall contributed to high heat transfer coefficient and this was in agreement with experimental studies conducted by Mickley et al.9 Received: Revised: Accepted: Published: 9040

May 1, 2016 July 1, 2016 August 2, 2016 August 2, 2016 DOI: 10.1021/acs.iecr.6b01682 Ind. Eng. Chem. Res. 2016, 55, 9040−9053

Article

Industrial & Engineering Chemistry Research Behjat et al.10 conducted simulations of a gas−solid fluidized bed based on the Eulerian description of the phases to study mass and heat transfer phenomena. Gas and solid temperature distributions were computed for two different reactor geometries and varying gas velocities. The results indicated that higher gas velocities would result in a higher gas temperature and lower solid phase temperature that could be attributed to higher heat transfer coefficient. Hamzehei and Rahimzadeh11 conducted experimental and computational studies on effects of particle size on hydrodynamic behavior and heat transfer between the gas and solid phases in a gas fluidized bed system. The simulation results showed that larger particle size would result in lower solid phase temperature. This was an indication that heat transfer was poorer with larger particle size as the overall surface area was decreased. It was also noted that instantaneous solids temperatures were higher at higher bed heights and this was due to a larger temperature gradient between solids and gas, which resulted in greater rate of heat transfer. Hamzehei et al.12 conducted computer simulations with various drag models to investigate their effects on the hydrodynamics as well as heat transfer of a two-dimensional gas fluidized bed system. The simulation studies were able to replicate the temperature distribution obtained from experiments and exhibited an inverse relationship between gas temperature and gas velocities. It was also observed from the numerical and experimental studies that gas temperatures were lower at larger bed heights whereas particle temperatures were higher. Lungu et al.13 applied the Eulerian−Eulerian model to study flow structure and heat transfer in a bubbling fluidized bed with a central jet. The existence of three solid flow regions referred to as the jetting region, wall region and freeboard region was observed. Maximum instantaneous fluid-to-particle heat transfer coefficients occurred in the wakes of bubbles whereas maximum averaged heat transfer coefficients occurred near the wall. More recently, Ngoh and Lim14 investigated the effects of fluidization behaviors on heat transfer in bubbling fluidized beds with the Eulerian−Eulerian approach. It was deduced that an optimal set of operating conditions existed where heat transfer was most efficient as overfluidization led to poor heat transfer due to channeling while under-fluidization resulted in poor convective heat transfer between the two phases. Zhou et al.15 coupled the discrete element method (DEM) with computational fluid dynamics (CFD) to study interparticle and particle−fluid heat transfer in a bubbling fluidized bed and packed bed. The various modes of heat transfer were investigated to determine the impact of each mode on the overall heat transfer. For a model of spheres in contact, it was found that particle−fluid convective heat transfer had the highest contribution at low superficial velocities and the contribution to overall heat transfer decreased as superficial velocity increased. On the other hand, a model of noncontact spheres exhibited an opposite trend, with low particle−fluid heat transfer contribution for low superficial gas velocity and an increased contribution to overall heat transfer at higher superficial gas velocity. Hou et al.16 conducted numerical studies on heat transfer in a gas-fluidized bed with an immersed horizontal tube. A discrete particle simulation coupled with CFD was used to model the system. Simulated results were compared with experimental studies conducted by Wong and Seville17 for model validation and heat transfer coefficient values from computational studies were found to be in good agreement with the experimental results. Hou et al.18 applied

the CFD-DEM approach to examine the various powder types and their heat transfer characteristics in gas fluidization. They established that although both Geldart groups A and B powders had different heat transfer characteristics, convective heat transfer was the primary mechanism of heat transfer, whereas conductive heat transfer accounted for 20% of the overall heat transfer. Radiative heat transfer was only significant when the bed temperature was high. Patil et al.19 applied the CFD-DEM approach to model heat transfer in gas−solid bubbling fluidized beds. The heat transfer coefficient for single-bubble rise was found to be twice that predicted by the Davidson and Harrison model and this was attributed to solids flow behaviors in the inner-shell region around the bubble assumed by the theoretical model and simulated using the CFD-DEM approach. More recently, Hou et al.20 combined the CFD-DEM approach with heat transfer models to investigate the effects of material properties and geometry of a tube array on heat transfer characteristics in fluidized beds with tubes. It was reported that convective and conductive heat transfers were dominant for large, noncohesive particles and small, cohesive particles, respectively. The effect of the tube array geometry was complex as conduction was dependent on contacts between particles and tubes whereas convection was dependent on local porosity. Apart from computational studies, several experimental studies of heat transfer in various types of fluidized bed systems have also been reported in the literature. Yusuf et al.21 carried out experimental and computational studies to verify the wall-to-bed heat transfer capabilities in a bubbling gas−solid fluidized bed. A pseudo-two-dimensional fluidized bed with a jet near a heated wall was used as the experimental setup and a three-dimensional, finite volume, in-house code was used for numerical simulations. It was reported that an accurate estimation of solid thermal conductivity especially at nearwall regions was important for a realistic prediction of thermal conductivity. The same group of researchers also investigated the effects of immersed horizontal tube-banks on heat transfer in a fluidized bed reactor.22 They sought to address the lack of understanding of complex tube geometries in fluidized beds and overprediction of tube-to-bed heat transfer coefficients. The simulations were compared to an experimental rig conducted by Olsson and Almstedt23 to measure the local instantaneous bed-to-tube heat transfer coefficient in a cold pressurized laboratory-scale fluidized bed. An experimental study was conducted by Merzsch et al.24 to investigate heat transfer in fluidized beds with a single horizontal tube using extreme poly dispersed materials. In industries, this kind of pressurized steam fluidized bed was commonly used for drying of lignite. Similar to vertically immersed heating surfaces and nearly monodisperse particles, an increase in lignite particle diameter size corresponded to a lower heat transfer coefficient and superficial velocity had to be increased to offset this behavior. Yoshie et al.25 applied a novel method for measuring the temperature history of hot ferromagnetic particles in a binary mixture flowing in a downer. The experimental measurements were used to calculate cross-sectional averaged particle-to-bed heat transfer coefficients and the results showed that there was a strong correlation between these coefficients with normalized collision frequency. More recently, Zhang et al.26 measured heat transfer coefficients for different types of powders flowing in a circulating fluidized bed and compared their measurements with empirical predictions. Immersed surfaces such as fins, horizontal and vertical tubes facilitate heat transfer in fluidized bed systems. However, the 9041

DOI: 10.1021/acs.iecr.6b01682 Ind. Eng. Chem. Res. 2016, 55, 9040−9053

Article

Industrial & Engineering Chemistry Research introduction of such additional fittings into a fluidized bed would alter the hydrodynamics and flow patterns of the fluid− solid system. Heat transfer between these immersed surfaces and the fluid−solid phases within the fluidized bed are coupled with the hydrodynamics of the fluidization process and not fully understood to date. In particular, most studies to date have focused on fluidized bed systems with fixed particle sizes and immersed tube temperatures. The effects of particle size on fluidization and bubbling behaviors and the effects of these on heat transfer behaviors have not been addressed adequately to date. The current study serves to fill the gaps in current understanding of coupled effects between hydrodynamics and heat transfer in such fluidized bed systems with an immersed tube. In the following section, the computational model and physical system of interest will be described. The simulation results obtained for the various physical conditions considered in this study will then be discussed and a summary of the conclusions derived will be presented in the Conclusions section.

μs = μs,col + μs,kin + μs,fr

The collisional viscosity μs,col is ⎛ θ ⎞0.5 μs,col = 0.8εsρs dsg0,ss(1 + ess)⎜ s ⎟ ⎝π⎠

μs,kin =

μs,fr =

96εS(3 − ess)g0,ss

[1 + 0.8g0,ssεs(1 + ess)]2

(10)

Pssin ϕ 2 I2D

(11)

where ϕ is the angle of internal friction and I2D is the second invariant of the deviatoric stress tensor. The solids pressure is ps = εsρs Θs + 2ρs (1 + ess)εs 2g0,ssΘs

(12)

27

The drag model by Gidaspow was used to evaluate momentum exchange coefficients. The momentum exchange coefficients based on the Gidaspow drag model are ⎧ ρ |⇀ v −⇀ vg |ϵs ϵ 2μ ⎪150 s g + 1.75 g s , ϵg ≤ 0.8 ⎪ ds ϵg ds 2 ⎪ β=⎨ ⎪ 3 3 ϵsϵg ρg |⇀ vs − ⇀ vg | ⎪ CD ϵ−g 2.65, ϵg > 0.8 ⎪ 4 4 d ⎩ s

(13)

The energy equations for gas and solids phases are ∂ (ϵg ρg hg ) + ∇·(ϵg ρg ⇀ vg hg ) ∂t ⎡∂ ⎤ = ∇ϵg⇀ qg + α(Ts − Tg) + τg̿ ·∇⇀ vg + ϵg ⎢ P + ⇀ vg ∇P ⎥ ⎣ ∂t ⎦

(2)

(14)

∂ (ϵsρs ) + ∇·(ϵsρs ⇀ vs ) = 0 ∂t

∂ (ϵsρs hs) + ∇·(ϵsρs ⇀ vs hs) ∂t

(3) ⎯⇀

⇀

where ρg and ρs are the densities and vg and vs are the velocities of the gas-phase and solid-phase, respectively. The momentum equations for gas and solids phases are ∂ (ϵg ρg ⇀ vg ) + ∇·(ϵg ρg ⇀⇀ vg vs ) = ∇· τg − ϵg ∇P + ϵg ρg⇀ g ∂t + β(⇀ v −⇀ v) g

⎡∂ ⎤ = ∇ϵs⇀ qs + α(Tg − Ts) + τs̿ ·∇⇀ vs + ϵs⎢ P + ⇀ vs ∇P ⎥ ⎣ ∂t ⎦ (15)

The granular temperature, Θ, expresses the fluctuating velocity of individual solid particles and is a function of the solids pressure and stress tensors. The granular temperature is defined as

(4)

∂ (ϵsρs ⇀ vs ) + ∇·(ϵsρs ⇀⇀ vg vs ) = ∇·τs̿ − ϵs∇P − ∇ps + ϵg ρg⇀ g ∂t + β(⇀ v −⇀ v) g

10ρs ds ϑsπ

The frictional viscosity is

where ϵg and ϵs are the gas-phase and solid-phase volume fractions. The continuity equations for gas (g) and solids (s) phases are

s

(9)

The kinetic viscosity is

2. COMPUTATIONAL MODEL An Eulerian−Eulerian approach was applied for transient simulations of heat transfer and hydrodynamics in gas fluidized beds with an immersed tube. The commercial CFD software Ansys Fluent R16.2 was used in this study to solve the governing equations of mass, momentum and energy conservation. The kinetic theory of granular flow was used for the closure of solid stress terms. The governing equations are summarized as follows. The sum of volume fractions of the phases is unity: ϵg + ϵs = 1 (1)

∂ (ϵg ρg ) + ∇·(ϵg ρg ⇀ vg ) = 0 ∂t

(8)

s

Θ=

(5)

(6)

1 ⇀ Di = [∇⇀ vi + (∇⇀ vi )T ] 2

(7)

(16)

⎯u ′ is the random fluctuating velocity of the particle and where → s → ⎯ ⎯ → ⟨ us′· us′⟩ represents ensemble averaging of the fluctuating particle velocities. The fluctuating energy of the solids phase can be described by the following equation:

where ⎛ 2 ⎞ Di + ⎜λ i* − μ*i ⎟ ·tr(⇀ Di )I τi̿ = 2μ*i ⇀ ⎝ 3 ⎠

1 ⟨us⃗′·us⃗′⟩ 3

3⎡ ∂ ⇀⎤ ⎢ (ϵsρs Θs) + ∇·(ϵsρs Θs) vs ⎥⎦ = ( −Ps*I + τs̿ ) 2 ⎣ ∂t : ∇⇀ vs + ∇·(k Θ*∇Θs) − γ * + Φ*Θ

The shear viscosity, μi* is the sum of the collisional, kinetic and frictional components:

Θ

9042

(17)


Article

Industrial & Engineering Chemistry Research The diffusion coefficient for granular energy k*Θ is k Θ* =

15dsρs ϵs π Θs ⎡ 12 2 η (4η − 3)ϵsg0,ss ⎢⎣1 + 4(41 − 33η) 5 ⎤ 16 (41 − 33η)ηϵsg0,ss⎥ + ⎦ 15π

coupling terms were fully incorporated into the pressure correction equation. The linearized equations were solved using a block algebraic multigrid method. Each set of simulation was conducted for 10.0 s physical time. This was deemed sufficient as it allowed about 3 to 4 cycles of bubbling within the fluidized beds where one cycle was generally defined as one group of bubbles rising from the bottom to the surface of the bed.

(18)

1

where η = 2 (1 + ess). g0,ss is the radial distribution function that describes the probability of particle−particle collisions: g0,ss

−1 ⎡ ⎛ ε ⎞1/3⎤ = ⎢1 − ⎜⎜ s ⎟⎟ ⎥ ⎢ ⎝ εs,max ⎠ ⎦⎥ ⎣

3. RESULTS AND DISCUSSION 3.1. Comparisons with Experimental and 2D Simulation Results. The simulation results obtained in the initial phase of this study were compared with experimental and 2D simulation results reported by Schmidt and Renz8 based on a similar fluidized bed system. Schmidt and Renz8 observed vigorous bubbling in their CFD simulations of a 2D fluidized bed system with an immersed tube (refer to Figure 2 of Schmidt and Renz8). Figure 1 shows that the bubbling

(19)

The dissipation of fluctuating energy, γΘ* as a result of inelastic particle collisions is γΘ* =

12(1 − ess 2)g0,ss ds π

ρs ϵs 2Θs1.5

(20)

The exchange of fluctuating energy between the solids and gas phases is given by Φ*Θ = −3β Θs

(21)

The above governing equations were solved using a finite volume approach. The fluidized bed model used in this study was based on the one investigated by Schmidt and Renz8 and the initial set of simulations conducted were also based on the same operating conditions applied by the previous researchers as shown in Table 1. A sensitivity analysis was carried out Table 1. Material Properties and Operating Parameters particle density gas density particle diameter restitution coefficient initial solids packing bed width bed height bed thickness static bed height mesh size time step fluidizing gas temperature initial temperature of bed particles immersed tube diameter immersed tube temperature immersed tube elevation

2660 kg/m3 1.225 kg/m3 500, 700, 900 μm 0.9 0.6 185 mm 500 mm 10 mm 210 mm 1 mm 10−4 s 293 K 293 K 40 mm 373, 453, 533 K 150 mm

during the initial phase of this study to investigate the effect of mesh size, time step size, and convergence criterion on the final simulation results. Table 1 shows the values of these parameters derived from this sensitivity analysis study. To ensure convergence at every time step of the simulations, the number of iterations per time step was specified to be 1000. The phasecoupled SIMPLE (PC-SIMPLE) algorithm, which is an extension of the SIMPLE algorithm to multiphase flows, was applied for the pressure−velocity coupling. In this algorithm, the coupling terms were treated implicitly and formed part of the solution matrix. The pressure−velocity coupling was based on total volume continuity and the effects of the interfacial

Figure 1. Bubbling behavior of gas fluidized bed with an immersed tube. The color contours represent solid volume fraction extracted from the midplane of the bed along the spanwise direction for visualization of bubbling behaviors within the bed.

behaviors obtained from CFD simulations of a 3D equivalent of the same fluidized bed system in this study were in good agreement with those presented by the previous researchers. This 3D fluidized bed model will be used for all subsequent investigations of heat transfer behaviors and parametric analyses of the system throughout this study. 9043


Article

Industrial & Engineering Chemistry Research

Figure 2. Time-averaged distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube. The 90° and 270° positions correspond to the top and bottom of the tube, respectively. Gas flows in the upward direction from the bottom toward the top of the tube.

Figure 3. Solid velocity vectors and flow of gas bubbles around the immersed tube.

volume fraction distributions obtained in the current and previous studies (refer to Figures 9 and 10 of Schmidt and Renz8). Solid volume fraction was observed to be higher at the top of the tube than at the bottom. The heat transfer behaviors around the immersed tube as observed from the time-averaged and instantaneous heat transfer coefficient distributions could be understood by analyses of the flow behaviors of both particles and gas bubbles around the tube. Figure 3 shows that as a bubble flowed around the immersed tube, particles with higher temperatures were displaced from the surface of the tube. Some particles were entrained in the wake of the bubbles during this process and replaced by particles with lower temperatures near the tube surface. This gave rise to a phenomenon of particle renewal near the tube surface during which particles with lower temperatures were transported to come into contact with the immersed tube for heat transfer to these particles to take place. It could also be observed that there was a tendency for a single large bubble rising up over the immersed tube to split into two smaller bubbles which then rose, one on each side of the tube.

Figure 2 shows the time-averaged heat transfer coefficient, granular temperature and solid volume fraction distributions around the immersed tube. The 90° and 270° positions correspond to the top and bottom of the tube, respectively. In comparison with the corresponding distributions presented by Schmidt and Renz8 (refer to Figure 8 in their paper), the heat transfer coefficient distribution obtained in the current work was more uniform and exhibited better agreement with the experimentally measured distribution reported by the previous researchers. This was likely due to the larger number of computational cells (1 021 493 cells) applied to mesh the fluidized bed geometry and the 3D model used in the current study which was a better representation of the actual fluidized bed system used by Schmidt and Renz8 in their experimental investigations. The time-averaged granular temperature distribution obtained in the current simulation exhibited qualitatively lower granular temperature values near the bottom of the immersed tube than those obtained by the previous researchers in their 2D simulations while good quantitative agreement was obtained between the time-averaged solid 9044


Article


Figure 4. Instantaneous distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube at (a) 2.0 s, (b) 2.1 s, (c) 2.2 s, (d) 2.3 s, (e) 2.4 s and (f) 2.5 s.

This allowed for particle renewal, whereby particles with higher and lower temperatures were transported away from and toward the tube surface respectively, and efficient heat transfer to take place on both sides of the immersed tube. Such a

particle renewal mechanism for heat transfer between particles and an immersed tube in a fluidized bed observed in the current study was consistent with the conclusions derived by Mickley and Fairbanks28 in their experimental investigations. They 9045


Article


Figure 5. Time evolutions of average heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube during the initial 1.5 s of fluidization for beds with particle sizes 500, 700 and 900 μm.

bubbling fluidization. Based on the studies of Molerus,1,2 the hydrodynamic contribution to heat transfer rates in bubbling fluidized beds was predominantly the excess gas velocity. In this part of the current study, this hydrodynamic contribution was deemed to be maintained constant via a fixed ratio of inlet gas velocity to minimum fluidization velocity so as to investigate the effect of a material property, particle size, on heat transfer behaviors. It was observed that the size of bubbles increased with increasing particle size (refer to figures shown in the Supporting Information). This was consistent with a recent study by Ngoh and Lim14 who investigated the effect of particle size on heat transfer in bubbling fluidized beds. When larger bubbles collided with the immersed tube, the time interval during which the immersed tube was surrounded by a gas pocket was longer. The frequency of bubble formation and rise was also correspondingly lower with larger bubble size. During the onset of fluidization, Figure 5 shows that strong correlations existed between the time evolutions of heat transfer coefficients, granular temperatures and solid volume fractions around the immersed tube for all particle sizes considered. As particles started to become fluidized and the bed expanded, solid volume fractions decreased during the first 1.5 s of the fluidization process. This corresponded with a decrease in heat transfer coefficients as parts of the bed around the immersed tube lost physical contact with the tube, which led to poorer heat transfer in comparison with heat transfer by conduction from the immersed tube to a stationary packed bed. In addition, this phase of fluidization was characterized by increases in granular temperatures as particles gained kinetic energy and exhibited greater fluctuations in velocities. Figure 6 shows that the mechanism of particle renewal had already been initiated 0.5 s after the start of gas flow. As the bed expanded, particles originally in contact with the immersed tube which had been heated up were transported upward and replaced by

reported that the dominant resistance against heat or mass transfer from surfaces to fluidized beds were the layers of particles next to those surfaces and the rate of transfer was limited by the rate of replacement of parts of these layers of particles. Figure 4 shows a strong correlation between the instantaneous heat transfer coefficient and solid volume fraction distributions around the immersed tube and supports the mechanism of particle renewal coupled with heat transfer described above. The large fluctuations in heat transfer coefficient between high and low values at the bottom of the immersed tube corresponded well with similar fluctuations in solid volume fraction at the same position over a time interval of 0.5 s, and this corresponded with the flow of a gas bubble over the tube as seen in the previous figure. The solid volume fraction at the top of the tube remained fairly high throughout this time interval but some particle renewal could nevertheless be observed from the previous figure. This resulted from entrainment of particles near the top of the tube in the wake of bubbles and led to moderate values of heat transfer coefficient at this position. The instantaneous distributions of granular temperature indicated large fluctuations in particle velocities especially on the two sides of the immersed tube and this corroborated well with the phenomenon of splitting of a single large bubble into two smaller bubbles which then rose over the two sides of the tube, thereby giving rise to vigorous particle renewal at those positions. 3.2. Effects of Particle Size on Heat Transfer from an Immersed Tube. The effects of particle size on heat transfer from an immersed tube to a fluidized bed were investigated by repeating the earlier simulations with particle sizes of 700 and 900 μm. In each case, as with the earlier simulation with a particle size of 500 μm, an inlet gas velocity that was twice the minimum fluidization velocity of the bed was applied to induce 9046


Article


Figure 6. Instantaneous distributions of heat transfer coefficient and corresponding solid velocity vectors (colored by solid temperature) around the immersed tube at 0.5 s after the start of gas flow for beds with particle sizes 500, 700 and 900 μm.

about 0.33, 0.31 to 0.28 with increasing particle sizes. Figure 7 shows that the time-averaged distributions of heat transfer coefficient and solid volume fraction around the immersed tube exhibited similar trends. The decreasing solid volume fraction resulted from formation of larger bubbles in beds with larger particle sizes. Larger bubbles in turn led to larger pockets of gas around the immersed tube, which then reduced the rate of conductive heat transfer between the immersed tube and solid particles. These observations were consistent with those reported by Hou et al.16 who showed that conductive heat flux was dominant in regions with low porosity (higher solid volume fraction) while low heat flux corresponded to instances of low solid volume fraction when a bubble passed a heated tube. In the current simulations, these effects were most

particles with lower temperatures. The instantaneous distributions of heat transfer coefficients around the immersed tube exhibited by the three beds with particle sizes 500, 700 and 900 μm were qualitatively and quantitatively similar at this stage of the fluidization and heat transfer process. In general, it may be concluded that there were no significant differences in fluidization or heat transfer behaviors of the beds with different particle sizes during this initial phase of fluidization. After the initial phase of fluidization, it was observed that the average heat transfer coefficients around the immersed tube between 1.5 to 5.0 s after the start of gas flow decreased from about 95, 88 to 77 W m−2 K−1 with increasing particle sizes from 500, 700 to 900 μm, respectively. Correspondingly, the average solid volume fraction during this period decreased from 9047


Article


Figure 7. Time-averaged distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube between 1.5 and 5.0 s after the start of gas flow.

was lower while heat transfer coefficient was higher all around the tube. 3.3. Effects of Immersed Tube Temperature on Heat Transfer. The effects of surface temperature of the immersed tube on heat transfer to particles in the fluidized bed were investigated by repeating the simulations with tube temperatures of 373, 453 and 533 K while maintaining all other parameters constant. The particle size and inlet gas velocity applied were 500 μm and 0.56 m s−1 respectively for all three cases. Figure 10 shows the instantaneous solid velocity vectors and contours of air temperature at 0.5 s for the three cases with immersed tube temperatures of 373, 453 and 533 K. It may be seen that solid flow behaviors were similar, implying that fluidization behaviors were not significantly affected by the differences in tube temperature. In contrast, the temperature of gas around the immersed tube was significantly different between the three cases. This was expected as the driving force for heat transfer from the immersed tube increased with increasing temperature of the tube. In the vicinity of the immersed tube, temperature of gas was higher with higher tube temperature. However, the gas temperature decreased fairly rapidly with distance away from the tube indicating heat transfer from the heated gas to particles. Figure 11 shows the time-averaged distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube with different tube temperatures. It was observed that distributions of granular temperature and solid volume fraction did not vary significantly with tube temperature. This was consistent with the observation of similar fluidization behaviors between the three cases with immersed tube temperatures of 373, 453 and 533 K in terms of their instantaneous solid velocity vectors and contours of air temperature at 3.5 s (Figure 12). Solid volume fractions were higher near the top of the tube than near the bottom whereas granular temperatures were higher on the two sides. These were characteristics of the bubble splitting and particle renewal phenomena discussed earlier, which would promote heat transfer between particles and the immersed tube for all three cases. On the other hand, the average heat transfer coefficients around the immersed tube increased from about 107, 198 to 280 W m−2 K−1 with increasing tube temperatures from 373, 453 to 533 K, respectively. The higher rate of heat transfer at higher tube temperature could thus be attributed to the larger driving force present for both conductive and

significant at the bottom of the immersed tube where largest differences in heat transfer coefficients and solid volume fractions between the beds with different particle sizes were observed. Figure 7 shows that the time-averaged distributions of granular temperature around the immersed tube increased with increasing particle size. This was due to the formation of larger gas bubbles in the beds with larger particle sizes. The gas bubbles split into smaller bubbles which flowed around both sides of the immersed tube and entrained particles in their wakes. During this particle renewal process, larger bubbles entrained more particles and gave rise to greater fluctuations in their velocities. Figure 8 shows the instantaneous distributions of heat transfer coefficient, granular temperature and solid volume fractions around the immersed tube during this phase of the fluidization process for the three particle sizes. It was observed that solid volume fractions were generally higher at the top and bottom of the immersed tube and lower on the two sides. This corresponded with higher heat transfer coefficients and lower granular temperatures at the top and bottom of the immersed tube. This was due to the phenomenon of splitting of gas bubbles into two smaller bubbles, which then flowed past the two sides of the immersed tube as discussed earlier. The smaller bubbles entrained particles on the two sides of the tube, resulting in greater fluctuations in particle velocities and thus higher granular temperatures at those positions. With frequent passing of bubbles on the two sides of the tube, solid volume fractions at those positions were lower than at the top and bottom and this gave rise to poorer conductive heat transfer between particles and the immersed tube. An example of the above phenomenon could be observed in the instantaneous distributions of heat transfer coefficient and granular temperature and velocity vectors of particles around the immersed tube at two instants of time for the bed with 700 μm particles. Figure 9 shows that as two split bubbles moved past the two sides of the immersed tube at 2.3 s, particles were entrained in their wakes and transported upward with the bubbles. This gave rise to high granular temperatures in these particles at the positions of the wakes of the bubbles. At the same time, solid volume fractions at the positions of the two bubbles were low and this resulted in low heat transfer coefficients on the two sides of the immersed tube. When these two bubbles had flowed past the tube at 2.4 s and the tube was surrounded almost entirely by particles, granular temperature 9048


Article


Figure 8. Instantaneous distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube at (a) 2.3 s, (b) 2.4 s, (c) 2.5 s and (d) 2.6 s.

increasing tube temperature. In other words, the sensitivity of the heat transfer process toward solid volume fraction distribution around the immersed tube had been increased at higher tube temperature. This was also manifested as a larger difference in gas temperatures at the top and bottom of the immersed tube seen in the previous figure. It would thus be prudent to consider both heat transfer efficiencies and sensitivity toward solid distributions when designing the operating conditions of such fluidized bed systems with immersed tubes.

convective heat transfer between particles and the immersed tube. In addition, it may be seen that heat transfer coefficients were generally higher near the top of the immersed tube than near the bottom and this could be attributed to formation of gas pockets by bubbles near the bottom which reduced direct, physical contact between particles and the tube. Interestingly, the difference in heat transfer coefficients between the top and bottom of the immersed tube increased significantly with increasing tube temperatures despite similar solid volume fraction distributions for the three cases. This implied that the effect of gas pocket formation near the bottom of the tube leading to lower heat transfer rates was amplified with 9049


Article


Figure 9. Instantaneous distributions of heat transfer coefficient and granular temperature and solid velocity vectors around the immersed tube at 2.3 s (left) and 2.4 s (right) for the bed with 700 μm particles.

Figure 10. Instantaneous solid velocity vectors superimposed on air temperature contours at 0.5 s with immersed tube temperature of (a) 373 K, (b) 453 K and (c) 533 K.

4. CONCLUSIONS The coupled effects of local hydrodynamics on heat transfer from an immersed tube in a fluidized bed were investigated computationally in this study. An Eulerian−Eulerian approach was used to model bubbling fluidization, and the effects of particle size and tube temperature on hydrodynamics and heat transfer were investigated. Due to the formation of gas bubbles that flowed around the immersed tube, the solid volume fraction at the bottom of the tube was low and this resulted in low heat transfer coefficient at that position. There was a tendency for large gas bubbles to split into two smaller bubbles that then flowed around both sides of the immersed tube. Particles were entrained by the gas bubbles and this led to the phenomenon of particle renewal whereby particles at higher

temperatures near the tube surface were transported away and replaced by particles at lower temperatures. Although the solid volume fraction at the top of the tube was fairly high due to the formation of a cluster of particles at that position, some particles were observed to be entrained in the wakes of bubbles flowing past the immersed tube. The mechanism of convective heat transfer via the phenomenon of particle renewal played an important role in heat transfer from the immersed tube to particles in the fluidized bed. When the size of particles was increased, larger gas bubbles were observed to form in the fluidized bed. This led to the formation of more gas pockets around the immersed tube and consequently lower heat transfer coefficient. Higher granular temperatures were observed around the tube indicating larger 9050


Article


Figure 11. Time-averaged distributions of heat transfer coefficient, granular temperature and solid volume fraction around the immersed tube with tube temperature of 373, 453 or 533 K.

Figure 12. Instantaneous solid velocity vectors superimposed on air temperature contours at 3.5 s with immersed tube temperature of (a) 373 K, (b) 453 K and (c) 533 K.

■

fluctuations in particle velocities resulting from entrainment of particles by larger gas bubbles. There was a minimal effect of the temperature of the immersed tube on fluidization and bubbling behaviors. A higher tube temperature provided a larger driving force for conductive and convective heat transfer to the gas and particles around the tube and this gave rise to higher gas temperatures. Heat was transferred from the gas to particles as the temperature of the gas decreased gradually away from the immersed tube. The sensitivity of the heat transfer process toward formation of gas pockets around the immersed tube increased with increasing tube temperature. This was manifested as a larger difference in heat transfer coeffcient between the top and bottom of the immersed tube at higher tube temperature. In view of the significant effect of particle size on fluidization, bubbling and heat transfer behaviors in such systems, it would be pertinent to extend the current study to consider effects of polydispersity on coupled effects of hydrodynamics and heat transfer in bubbling fluidized beds with an immersed tube. The study, design and optimization of fluidized bed systems with a bank of immersed tubes which can function as an integrated fluidized bed reactor-heat exchanger system can also be a subject of future investigations applying the methods of analysis presented in this study.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b01682.

■

Bubbling behaviors of gas fluidized beds showing that the size of bubbles increased with increasing particle size (PDF).

AUTHOR INFORMATION

Corresponding Author

*E. W. C. Lim. Tel.: (65) 6516 4727. Fax: (65) 6779 1936. Email address: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

This study has been supported by the National University of Singapore (NUS). The authors gratefully acknowledge the presentation of a FoE 30th Innovation & Research Award by the Faculty of Engineering of NUS. 9051


Article


■

NOMENCLATURE B = Factor of deformation CD = Drag coefficient ds = Diameter of solid particle (m) ess = Particle restitution coefficient g = Gravitational acceleration (m s−2) g0,ss = Radial distribution function hg = Gas phase enthalpy (J kg−1) hs = Solids phase enthalpy (J kg−1) I = Unit tensor I2D = Second invariant of deviatoric stress tensor kg = Turbulent kinetic energy for gas phase (m2 s−2) k = Thermal conductivity (W m−1 K−1) Nu = Nusselt number P = Pressure (Pa) Pg = Gas pressure (Pa) Ps = Solid pressure (Pa) Ps,total = Total solid pressure (Pa) Pr = Prandtl number ⎯⇀ ⎯ qg = Gas phase heat flux (W m−2)

τg̿ = Gas viscous stress tensor τs̿ = Solid viscous stress tensor ΦΘ* = Energy exchange between fluid and solid phase (W m−3) ϕ = Internal angle of friction

■

REFERENCES

(1) Molerus, O. Heat transfer in gas fluidized beds Part 1. Powder Technol. 1992, 70, 1−14. (2) Molerus, O. Heat transfer in gas fluidized beds Part 2. Dependence of heat transfer on gas velocity. Powder Technol. 1992, 70, 15−20. (3) Schmidt, A.; Renz, U. Eulerian computation of heat transfer in fluidized beds. Chem. Eng. Sci. 1999, 54, 5515−5522. (4) Gunn, D. Transfer of heat or mass to particles in fixed and fluidized-beds. Int. J. Heat Mass Transfer 1978, 21, 467−476. (5) Kuipers, J.; Prins, W.; Vanswaaij, W. P. M. Numerical-calculation of wall-to-bed heat-transfer coefficients in gas-fluidized beds. AIChE J. 1992, 38, 1079−1091. (6) Hunt, M. L. Discrete element simulations for granular material flows: effective thermal conductivity and self-diffusivity. Int. J. Heat Mass Transfer 1997, 40, 3059−3068. (7) Schmidt, A.; Renz, U. Numerical prediction of heat transfer in fluidized beds by a kinetic theory of granular flows. Int. J. Therm. Sci. 2000, 39, 871−885. (8) Schmidt, A.; Renz, U. Numerical prediction of heat transfer bewteen a bubbling fluidized bed and an immersed tube bundle. Heat Mass Transfer 2005, 41, 257−270. (9) Mickley, H. S.; Fairbanks, D. F. Hawthorn R. D. The relation between the heat transfer coefficient and thermal fluctuations in fluidized-bed heat transfer. Chem. Eng. Progr. Symp. Ser. 1961, 57, 51− 60. (10) Behjat, Y.; Shahhosseini, S.; Hashemabadi, S. H. CFD modelling of hydrodynamic and heat transfer in fluidized bed reactors. Int. Commun. Heat Mass Transfer 2008, 35, 357−368. (11) Hamzehei, M.; Rahimzadeh, H. Experimental and numerical study of hydrodynamics with heat transfer in a gas-solid fluidized-bed reactor at different particle sizes. Ind. Eng. Chem. Res. 2009, 48, 3177− 3186. (12) Hamzehei, M.; Rahimzadeh, H.; Ahmadi, G. Computational and experimental study of heat transfer and hydrodyanmics in 2D gas-solid fluidzed bed reactor. Ind. Eng. Chem. Res. 2010, 49, 5110−5121. (13) Lungu, M.; Wang, J.; Yang, Y. Numerical simulations of flow structure and heat transfer in a central jet bubbling fluidized bed. Powder Technol. 2015, 269, 139−152. (14) Ngoh, J.; Lim, E. W. C. Effects of particle size and bubbling behavior on heat transfer in gas fluidized beds. Appl. Therm. Eng. 2016, 105, 225−242. (15) Zhou, Z. Y.; Yu, A. B.; Zulli, P. Particle scale study of heat transfer in packed and bubbling fluidized beds. AIChE J. 2009, 55, 868−884. (16) Hou, Q. F.; Zhou, Z. Y.; Yu, A. B. Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube. AIChE J. 2012, 58, 1422−1434. (17) Wong, Y. S.; Seville, J. P. K. Single-particle motion and heat transfer in fluidized beds. AIChE J. 2006, 52, 4099−4109. (18) Hou, Q. F.; Zhou, Z. Y.; Yu, A. B. Computational study of the effects of material properties on heat transfer in gas fluidization. Ind. Eng. Chem. Res. 2012, 51, 11572−11586. (19) Patil, A. V.; Peters, E. A. J. F.; Lau, Y. M.; Kuipers, J. A. M. Modeling 3D bubble heat transfer in gas-solid fluidized beds using the CFD-DEM. Ind. Eng. Chem. Res. 2015, 54, 11466−11474. (20) Hou, Q. F.; Zhou, Z. Y.; Yu, A. B. Gas-solid flow and heat transfer in fluidized beds with tubes: effects of material properties and tube array settings. Powder Technol. 2016, 296, 59−71. (21) Yusuf, R.; Halvorsen, B.; Melaaen, M. C. An experimental and computational study of wall to bed heat transfer in a bubbling gas− solid fluidized bed. Int. J. Multiphase Flow 2012, 42, 9−23.

⎯⇀ ⎯

qs = Solid phase heat flux (W m−2) Tg = Gas temperature (K) Ts = Solid temperature (K) Umf = Minimum fluidizing velocity (m s−1) → ⎯u ′ = Fluctuating velocity of particles (m s−1) s ⎯⇀ vg = Gas velocity (m s−1) ⇀ vs = Solid velocity (m s−1)

Greek Symbols

α = Volumetric interphase heat transfer coefficient (W m−2 K−1) αgs = Fluid-particle heat transfer coefficient (W m−2 K−1) β = Coefficient of thermal expansion γ*Θ = Dissipation of kinetic energy via inelastic particle collision (W m−2 K−1) εg = Turbulent dissipation for gas phase (m2 s−3) ϵg = Volume fraction of gas phase ϵs = Volume fraction of solid phase ϵs,max = Packing limit Θ = Granular temperature (m2 s−2) θs = Solid granular temperature (m2 s−2) κfluid = Fluid thermal conductivity (W m−1 K−1) κg = Gas phase thermal conductivity (W m−1 K−1) κg* = Eulerian gas phase thermal conductivity (W m−1 K−1) κpm = Particle material thermal conductivity (W m−1 K−1) κs = Solid phase thermal conductivity (W m−1 K−1) κ*s = Eulerian solid phase thermal conductivity (W m−1 K−1) λg = Gas phase bulk viscosity (Pa s) λs = Solid phase bulk viscosity (Pa s) μg = Gas phase shear viscosity (Pa s) μm = Mixture viscosity (Pa s) μs,col = Solid collisional viscosity (Pa s) μs,fr = Solid frictional viscosity (Pa s) μs,kin = Solid kinetic viscosity (Pa s) μs = Solid phase shear viscosity (Pa s) μt = Eddy viscosity (Pa s) ρg = Gas density (kg m−3) ρm = Mixture density (kg m−3) ρs = Solid density (kg m−3) σk = Turbulent Prandtl number for k σε = Turbulent Prandtl number for ε 9052


Article

Industrial & Engineering Chemistry Research (22) Yusuf, R.; Halvorsen, B.; Melaaen, M. C. Eulerian-Eulerian simulation of heat transfer between a gas-solid fluidized bed and an immersed tube-bank with horizontal tubes. Chem. Eng. Sci. 2011, 66, 1550−1564. (23) Olsson, S. E.; Almstedt, A. E. Local instantaneous and timeaveraged heat-transfer in a pressurized fluidized-bed with horizontal tubes - influence of pressure, fluidization velocity and tube-bank geometry. Chem. Eng. Sci. 1995, 50, 3231−3245. (24) Merzsch, M.; Lechner, S.; Krautz, H. J. Heat-transfer from single horizontal tubes in fluidized beds: Influence of tube diameter, moisture and diameter-definition by Geldart C fines content. Powder Technol. 2013, 235, 1038−1046. (25) Yoshie, Y.; Ishizuka, M.; Guan, G. Q.; Fushimi, C.; Tsutsumi, A. A novel experimental technique to determine the heat transfer coefficient between the bed and particles in a downer. Adv. Powder Technol. 2013, 24, 487−494. (26) Zhang, H. L.; Baeyens, J.; Degreve, J.; Brems, A.; Dewil, R. The convection heat transfer coefficient in a circulating fluidized bed (CFB). Adv. Powder Technol. 2014, 25, 710−715. (27) Gidaspow, D. Multiphase flow and fluidization; Academic Press: London, 1994. (28) Mickley, H. S.; Fairbanks, D. F. Mechanisms of heat transfer to fluidized beds. AIChE J. 1955, 1, 374−384.

9053


Heat Transfer from an Immersed Tube in a ... - ACS Publications

Recommend Documents