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Heat transfer from immersed tubes in a pulsating fluidized bed
Powder Technology 327 (2018) 500–511
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Heat transfer from immersed tubes in a pulsating fluidized bed Emily Min Li Sin, Eldin Wee Chuan Lim ⁎ Department of Chemical and Biomolecular Engineering, National University of Singapore, 117585, Singapore
a r t i c l e
i n f o
Article history: Received 6 July 2017 Received in revised form 10 November 2017 Accepted 30 December 2017 Available online 10 January 2018 Keywords: Computational fluid dynamics Pulsating fluidized bed Heat transfer Immersed tubes
a b s t r a c t Heat transfer through immersed tubes in pulsating fluidized beds was investigated computationally using an Eulerian-Eulerian approach. The effects of pulsating frequency and configuration of the immersed tubes were studied. At low pulsating frequency, more orderly bubbling behaviors were observed and these gave rise to more uniform heat transfer rates from all tubes. An interesting heat transfer behavior whereby the heat transfer coefficient distribution around an immersed tube alternated between a needle-like and a wide fan-shaped pattern was observed for the first time in this study. An increase in pulsating frequency caused the fluidized bed to exhibit fluctuating heat transfer rates. The staggered tube configuration considered in this study was observed to aid in the development of more orderly bubbling behaviors, with heat transfer coefficient of tubes in the bottom row exhibiting similar oscillation amplitudes. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Fluidization has been established as an important operation in a variety of industrial processes. Due to excellent heat transfer characteristics, fluidized bed reactors and dryers have been applied in various industries. One of the approaches for transferring energy into or out of a gas fluidized bed is through the use of immersed tubes. Heat transfer takes place between the gas and solids of the fluidized bed and a utility fluid within the immersed tubes. In many of these processes, efficient heat transfer between the immersed tubes and solids is essential to the operation of the fluidized bed but may be difficult to achieve. Pulsed fluidization is a special mode of fluidized bed operation where the gas flow rate is varied periodically with time. The benefits of pulsed fluidization include reduced gas by-passing and channeling and enhanced gassolid contact. However, the effect of pulsed fluidization on heat transfer through immersed tubes is poorly understood even today. Although many research studies have been reported on simulations of fluidization behaviors, studies on coupled effects of gas pulsation with heat transfer from immersed tubes in fluidized bed systems have been limited to date. Schmidt and Renz [1] conducted numerical simulations to understand the heat transfer behavior between a heated surface and bed particles. They then explored the validity of two different approaches – standard and kinetic – to describe the thermal conductivity of the solid phase [2]. Subsequently, Schmidt and Renz [3] conducted numerical simulations to analyze heat transfer between a fluidized bed of Geldart B particles and an immersed tube and showed that the correlation ⁎ Corresponding author. E-mail address: [email protected] (E.W.C. Lim).
https://doi.org/10.1016/j.powtec.2017.12.095 0032-5910/© 2018 Elsevier B.V. All rights reserved.
between heat transfer coefficient and the bed hydrodynamics was in theoretical agreement with the packet theory developed by Mickley and Fairbanks [4]. Wong and Seville [5] adopted the packet theory and analyzed heat transfer behavior with particle convection as the dominant mode of heat transfer. Behjat et al. [6] investigated the effect of monodispersed and bimodal solid mixtures on hydrodynamics and the effect of varying gas velocities on gas and solid temperature distributions and found that heat transfer between solids and gas increased with increasing gas velocity. Zhou et al. [7] conducted simulations using the combined Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) to analyze particle-particle and particle-fluid heat transfer behaviors by quantifying the contribution to heat transfer coefficient via convection, conduction and radiation. Hamzehei and Rahimzadeh [8] applied an Eulerian-Eulerian model coupled with the kinetic theory for solid particles to simulate industrial fluidized-bed reactors and found that a decrease in particle sizes led to an overall increase in heat transfer rate due to increased gas-solid contact. Subsequently, Hamzehei et al. [9] extended this study by incorporating an additional k-ε turbulence model to simulate heat conducting gas-solid flow in fluidized beds. Hou et al. [10] conducted computer simulations to study heat transfer in a fluidized bed with an immersed tube using the CFD-DEM approach and observed that increasing particle thermal conductivity resulted in an increase in conductive flux but had limited impact on improving heat transfer coefficient. Hou et al. [11] continued the above study to investigate the effect of particle properties, namely Hamaker constant and particle size, on heat transfer in a fluidized bed and observed that an increase in Hamaker constant resulted in convective and conductive heat flux increasing to a maximum at minimum bubbling velocity. More recently, Hau and Lim [12] simulated the fluidized bed system investigated by Schmidt and Renz [3] and conducted 3D
E.M.L. Sin, E.W.C. Lim / Powder Technology 327 (2018) 500–511
CFD simulations to investigate how heat transfer coefficient between solid particles and a heated tube varied with particle size and temperature of the heated tube. Ngoh and Lim [13] showed that the size of bubbles formed exhibited an inverse relation with particle size. Wahyudi et al. [14] conducted 3D simulations of a fluidized bed with an immersed tube to study hydrodynamics and heat transfer behavior using CFD-DEM and were able to reproduce general hydrodynamic and heat transfer trends, such as pressure drop and the correlation between heat transfer coefficient with varying superficial gas velocity. Gan et al. [15] applied CFD-DEM to study heat transfer behavior in fluidized beds containing non-spherical particles and found that spherical particles had the lowest effective thermal conductivity while ellipsoidal particles gave rise to lower convective heat transfer but higher conductive heat transfer rates. Ireland et al. [16] provided a comprehensive review of pulsed flow fluidization and the key findings in recent research and development in this field of study. Coppens and van Ommens [17] investigated three methods, via application of an alternating AC electric field, fractal injectors and pulsed flow, to introduce order into a fluidized bed which was characterized as a chaotic system. In a DEM study conducted by Wang and Rhodes [18], they investigated the relationship between pulsed flow and formation of regular bubble patterns and concluded that low pulse frequencies were not favorable in forming regular bubble patterns due to prolonged periods of high and low gas velocities which resulted in an intermittently fluidized and unsteady bed. Gui and Fan [19] performed 2D numerical simulations of a pulsed fluidized bed using DEM-LES to investigate the effect of pulsed flow frequency and immersed tube arrangements on particle interactions with the fluid and immersed tubes. Bizhaem and Tabrizi [20] conducted experiments to study the effect of particle properties, pulse frequency and gas velocity on the hydrodynamics of a pulsed fluidized bed. Dong et al. [21] adopted a novel approach towards dry beneficiation of fine coal by applying flow pulsation in a dense medium fluidized bed. Ali et al. [22] conducted experiments to study the hydrodynamics of pulsed flow fluidized bed consisting of nanoparticles by analyzing the bed collapse behavior exhibited at different air velocities. In an experimental study conducted by Saidi et al. [23], the effect of pulsed air flow on separation efficiency of a binary mixture of dissimilar sized particles in a gas-solid fluidized bed was investigated. In a subsequent simulation study conducted by Saidi et al. [24], a pulsed, spouted fluidized bed was modeled using CFD-DEM. Most studies to date have focused on either the effects of gas pulsation on bubbling behaviors in fluidized bed systems or mixing behaviors. The possibility of applying gas pulsation to enhance heat transfer in fluidized beds containing multiple immersed tubes arranged in different tube configurations have not been explored to date. From an industrial application perspective, the application of gas pulsation to improve heat transfer efficiencies in large-scale fluidized bed reactors or dryers where heat supply or removal is critical to the operation of the fluidized bed may represent a promising approach for process intensification that has not been explored to date. The current study serves to fill this gap in current understanding of coupled effects between gas pulsation and heat transfer in fluidized bed systems containing immersed tubes. 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. 2. Computational model A multiphase Eulerian-Eulerian model was used to simulate a pulsating fluidized bed with immersed tubes. The solids phase was modeled as a continuum and the kinetic theory of granular flow was used as closure for the solids stress tensor. The governing equations for conservation of mass, momentum and energy were solved using
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Fig. 1. Configurations of immersed tubes comprising (a) six in-line tubes and (b) five staggered tubes.
the commercial CFD software Ansys Fluent R18 and are summarized as follows. The continuity equations for gas and solids phases are: ∂ ! ðεs ρs Þ þ ∇∙ εs ρs vs ¼ 0 ∂t
ð1Þ
∂ ! ε g ρg þ ∇∙ εg ρg vg ¼ 0 ∂t
ð2Þ
! ! where ρs and ρg are densities and vs and vg are the velocities of the solids and gas phases respectively. The sum of solids volume fraction, εs and gas volume fraction, εg is unity. Table 1 Material properties and operating parameters. Particle density Gas density Gas viscosity Particle diameter Restitution coefficient Initial solids packing Bed width Bed height Bed thickness Static bed height Fluidizing gas temperature Initial bed temperature Immersed tube diameter Immersed tube temperature Tubes configuration Immersed tube elevation Pulsating gas frequency
2660 kg/m3 1.225 kg/m3 1.8 × 10−5 Pa·s 500 μm 0.9 0.6 320 mm 800 mm 10 mm 400 mm 293 K 293 K 40 mm 373 K 5 tubes staggered, 6 tubes in-line 150 mm (bottom row), 230 mm (top row) 0, 5, 20 Hz
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The solid shear viscosity, μ i is the sum of the collisional, kinetic and frictional viscosities:
The momentum equations for gas and solids phases are: ∂ ! ! ! !! ! ! εs ρs vs þ ∇∙ ε s ρs vs vg ¼ ∇∙τ s −εs ∇P þ ε s ρs g þ β vs −vg ∂t
ð3Þ
∂ ! ! !! ! ! ! εg ρg vg þ ∇∙ εg ρg vs vg ¼ ∇∙ τ g −εg ∇P þ εg ρg g þ β vg −vs ð4Þ ∂t ! ! where β is the gas-solid drag coefficient and τs and τg are stress tensors for the respective phases. The drag model by Ding and Gidaspow [25] was used in this study. The gas-solid drag coefficients used in the Gidaspow drag model are: 8 ! ! εs 2 μ g > ρg vs −vg εs > > þ 1:75 ; εg ≤0:8 < 150 2 d εs ds β ! ! s > > 3 εs εG ρs vs −vg −2:65 > : CD εg ; εg N0:8 4 ds
ð5Þ
D⃑ i ¼
i 1h ! T ∇vI þ ð∇! vI Þ 2
0:5 4 θs εs ρs ds g 0;ss ð1 þ εss Þ 5 π pffiffiffiffiffiffiffi
2 P s sinϕ 10ρs ds θs π þ 1 þ 0:8g 0;ss εs ð1 þ ε ss Þ þ pffiffiffiffiffiffiffi 96εs ð3−εss Þg 0;ss 2 I 2D
ð6Þ
ð7Þ
ð8Þ
where ϕ is the angle of internal friction, I2D is the second invariant of the deviatoric stress tensor and Ps is the solids pressure. The solids pressure is: (9) Ps = εs ρs Ξs þ 2ρs ð1 þ εss Þεs 2 g0;ss Ξs The energy equations for gas and solids phases are ∂ ! ! ! ε g ρg hg þ ∇∙ εg ρg vg hg ¼ −∇εg qg þ α T s −T g þ τ g ∙∇vg ∂t
∂ ! þ εg P þ vg ∇P ∂t
The stress tensor is described as: 2 ! τ i ¼ 2μ i D⃑ iþ λi − μ i ∙tr D⃑ i I 3
μs ¼
∂ ! ! ! ðεs ρs hs Þ þ ∇∙ εs ρs vs hs ¼ −∇εs qs þ α T g −T s þ τs ∙∇vs ∂t
∂ ! P þ vs ∇P þ εs ∂t
ð10Þ
ð11Þ
Fig. 2. Bubbling behaviors of fluidized beds with in-line tube configuration subjected to a pulsating frequency of (a) 0 Hz, (b) 5 Hz, (c) 20 Hz, and staggered tube configuration subjected to a pulsating frequency of (d) 0 Hz, (e) 5 Hz, (f) 20 Hz.
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Fig. 2 (continued).
The balance of the solids phase granular energy can be described by the following equation:
3 ∂ ! ! ðεs ρs Ξs Þ þ ∇∙ðεs ρs Ξs Þvs ¼ ð−P s I þ τs Þ∇vs 2 ∂t þ ∇∙ðkΞ ∇Ξs Þ−γ Ξ þ −3βΞs
ð12Þ
The diffusion coefficient for granular energy kΞ is given by:
kΞ ¼
pffiffiffiffiffiffiffiffiffi 15ds ρs εs Ξs π 12 2 16 1þ η ð4η−3Þεss g 0;ss þ ð41−33ηÞηε ss g 0;ss 4ð41−33ηÞ 5 15π ð13Þ
where η ¼ 12 ð1 þ εss Þ. g0, ss is the radial distribution function that describes the probability of particle-particle collisions and is expressed as: " g 0;ss ¼ 1−
εs
13 #−1
εs;max
ð14Þ
The dissipation of fluctuating energy, γ Ξ is: γΞ ¼
12 1−εss 2 g 0;ss pffiffiffi ρs εs 2 Ξs 1:5 ds π
ð15Þ
The granular temperature, Ξs represents the kinetic energy of the fluctuating solid phase particles and is a variable of the solids pressure and stress tensors. The granular temperature is defined as Ξs ¼
1 2 v0s 3
ð16Þ
where v′s is fluctuating velocity. The velocity profile for pulsating flow of gas used by Gui and Fan [19] was applied at the inlet of the fluidized bed: U ðt Þ ¼ U 0 þ U S sinð2πft Þ
ð17Þ
where U0 is the mean superficial gas velocity, US is the amplitude of pulsation and f is the pulsating frequency. The frequency range explored in this study was 0–20 Hz. Values of the mean velocity U0 was selected such that the resulting gas velocity would always be higher than the minimum fluidization velocity of the fluidized bed. A User Defined Function (UDF) was written in the C language to implement the above pulsating gas velocity profile and the program code was compiled with the CFD model developed. The fluidized bed model used in this study was based on the one investigated by Hau and Lim [12], while tube configuration dimensions were based on those investigated by Gui and Fan [19] (Fig. 1). The initial set of simulations conducted was based on the same operating conditions applied by the previous researchers
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Fig. 2 (continued).
respectively. Table 1 shows the material properties and operating parameters applied in the current study. All material properties were assumed to be independent of temperature in the simulations conducted. A sensitivity analysis was carried out during the initial phase of this study to investigate the effects of mesh size, time step size, and convergence criterion on the final simulation results. The mesh size and time step size that were derived through this analysis to ensure simulation results were independent of these parameters were 2.5 mm and 10−4 s respectively. 1000 iterations per time step was specified to ensure that simulations converged at every time step. The phase coupled SIMPLE (PC-SIMPLE) algorithm, which is an extension of the SIMPLE algorithm for multiphase flows, was applied for the pressure-velocity coupling. The velocities were solved coupled by phases in a segregated fashion. Fluxes were reconstructed at the faces of the control volume and then a pressure correction equation was built based on total continuity. The coefficients of the pressure correction equations came from the coupled per phase momentum equations. The linearized equations were solved using a block algebraic multigrid method. For postprocessing of the simulation results, instantaneous values of heat transfer coefficient at various positions along the circumference of the immersed tubes were extracted and Matlab programs were written to generate plots of heat transfer coefficient distributions in polar coordinates as well as to compute average heat transfer coefficient values.
3. Results and discussion 3.1. Effects of pulsation on fluidization behaviors The simulation results obtained in the initial phase of this study showed general agreement with simulation results obtained in various studies conducted by other researchers. When the bed was subjected to continuous flow of gas at a superficial gas velocity greater than the minimum fluidization velocity, vigorous bubbling was observed. As shown in Fig. 2a and d, typical vigorous bubbling behavior characterized by expansion of the fluidized bed, small bubbles at the inlet, coalescence of bubbles during ascent and eruption of gas bubbles at the bed surface were observed. These observations were similar to those reported by Hau and Lim [12]. Coppens and van Ommen [17] recognized that gases injected into pulsating fluidized beds form uniform but staggered rows of bubbles which suppress vigorous bubbling. Fig. 2b and e show the fluidization behavior of the same bed when subjected to low frequency pulsating flow at 5 Hz. It could be observed that unilateral and staggered rows of gas bubbles formed which gave rise to regular patterns of bubbles which were relatively smaller and more uniform. When the frequency of pulsation was increased to 20 Hz (Fig. 2c and f), the regular bubble patterns previously observed during low frequency pulsation were no longer observed. This behavior was congruent with that reported by Wang and Rhodes [18] who suggested that this might have occurred
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Fig. 3. Solids velocity vectors colored by solids temperature with red and blue representing high and low temperatures respectively at 1.5, 1.6 and 1.7 s for in-line tube configuration subjected to a pulsating frequency of (a) 5 Hz and (b) 20 Hz.
as the gas-flow variation was too fast for the structure of the bed to respond, thereby diminishing the formation of horizontal channel-like structures near the distributor plate. However, it may be observed that bubbles were still more regularly spaced near the inlet at high frequency gas pulsation compared to those generated in a bed that was subjected to continuous flow. The phenomenon of particle renewal was observed whenever heated solids around the tubes were displaced by cooler solids due to the rising bubble motion. Fig. 3 shows the occurrences of particle renewal for in-line tubes subjected to low and high pulsating frequencies. The upward force generated by the bubbles pushed the heated solids (colored red to green) upwards and away from the tubes. This created voids which were then filled by adjacent cooler solids (colored blue) thus ensuring continuous and efficient heat transfer between the tubes and the solids. The particle renewal behavior for the staggered tube configuration was observed to be qualitatively similar to that for the in-line tube configuration and so has not been shown for brevity. This phenomenon was first observed in the study by Mickley and Fairbanks [4] who reported that the rate of heat transfer is dependent on the rate of displacement of solid particles around an immersed heated tube. At high pulsation frequency, bubbles with different sizes were generated and rose through the bed at different velocities. This disparity in rising velocities resulted in mixing of solids especially near the top of the fluidized bed. At low pulsation frequency, the solids generally moved upwards as a result of more uniform sizes of bubbles. However, at high pulsation frequency, solids were observed to move outwards towards the walls when there were significant differences in the sizes of bubbles. Larger bubbles were able to force solids to be pushed
downwards and outwards, thereby further impacting the solids volume fraction distributions around tubes in the top section of the bed. This was observed to be particularly significant for tubes in the top row within the staggered tube configuration. The high gas velocity caused the bulk of heat transfer to occur at regions above the tubes. Fig. 4 shows the time averaged solids volume fraction distributions and corresponding heat transfer coefficient distributions around different tubes when subjected to pulsating frequencies of 0 Hz and 5 Hz. Solids volume fractions were high around tubes in the top section of the tube bundle and low in the bottom section. This corresponded with high heat transfer and low granular temperatures in the top section, which indicated that solids thermal conduction was the primary mode of heat transfer from the heated immersed tubes to the solids. The bottom of each tube was in constant contact with rising air bubbles which split into smaller bubbles that flowed along the sides of the tubes. Granular temperatures were higher due to large fluctuations in solids motion while solids volume fraction was correspondingly low. As the fluidizing air was a poor medium for conductive heat transfer, the heat transfer coefficients of the tubes with low solids volume fractions were lower. These observations were consistent with those reported by Hau and Lim [12] who investigated heat transfer from a single immersed tube in a bubbling fluidized bed with continuous gas flow. The observed differences in fluidization behaviors in the absence and presence of pulsating gas flow gave rise to significant differences in heat transfer behaviors between the immersed tubes and surrounding solids. With continuous gas flow (pulsating frequency of 0 Hz), the heat transfer coefficient varied significantly with circumferential position around each immersed tube. In contrast, when low frequency pulsating flow was applied,
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much more uniform heat transfer coefficient distributions could be achieved for all immersed tubes. It could also be observed from Fig. 4 that heat transfer coefficients decreased and heat transfer coefficient distributions became narrower with low frequency pulsating flow. This was expected as larger volumes of air were injected into the system. However, heat transfer coefficients of tubes located in the top section (tubes 5 and 6) decreased more significantly than those of tubes in the bottom section (tube 2). The initial huge bubble was broken into smaller bubbles upon contact with tubes in the bottom section. Bubbles flowing near the center of the fluidized bed were relatively smaller than those flowing near the walls. This resulted in generation of relatively more uniform, small bubbles for both tube configurations when subjected to either continuous or pulsating flow. As such, the impact of pulsating flow affecting heat transfer rate was smaller, as evidenced by the comparisons of heat transfer coefficient distributions of tube 2 across all cases in Fig. 4. The differences in bubbling behaviors were more evident near the top section of the fluidized bed. With continuous flow, air bubbles
remained small near the center of the bed but grew in size near the walls. Growth of air bubbles near the center of the bed was disrupted by the tubes which caused splitting of gas bubbles as described earlier. Bubbles flowing near the walls coalesced with other air bubbles and grew along the bed height. Larger bubbles had a tendency to coalesce with smaller bubbles, which was the phenomenon that resulted in the disparity in heat transfer rates for tubes in the top section of the bed. Fig. 5 shows the granular temperature distributions of solids around tubes 2, 5 and 6 which reveal the effects of the above bubbling behaviors on fluctuating motions of solids. The splitting of bubbles around tubes at the bottom resulted in fairly symmetrical solids motion around tube 2. In contrast, asymmetrical solids motion was observed around tube 6. There was lower likelihood of contact between air bubbles and tube 5 compared with contact with tube 6 because bubbles near the center of the bed were smaller than the tube spacing and they exhibited greater tendencies to flow towards the sides to coalesce with larger bubbles. On the other hand, tubes 4 and 6 were exposed to larger bubbles that had coalesced and grew, and hence the tube surfaces were largely in
Fig. 4. Time averaged solids volume fraction distributions and heat transfer coefficient (kW/m2 K) distributions around tubes 2, 5 and 6 when subjected to a pulsating frequency of 0 Hz or 5 Hz in (a) in-line and (b) staggered tube configurations.
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Fig. 4 (continued).
contact with air. This would inhibit effective heat transfer between the tubes and solids. When low frequency pulsating flow was applied in either tube configurations, symmetrical granular temperature distributions were achieved for all tubes. This was a result of more even splitting of air bubbles characteristic of pulsating flow. This explained the relatively similar heat transfer coefficient distributions obtained for all tubes as seen earlier in Fig. 4. 3.2. Effects of pulsating frequency on heat transfer It was interesting to note that a unique “on-and-off” pattern was observed for the heat transfer coefficient distribution around the tubes when the bed was fluidized with low frequency pulsation. This is a new observation of heat transfer behavior in a gas fluidized bed containing immersed tubes subjected to pulsating flow which has not been reported in the literature to date. Fig. 6 shows the instantaneous heat transfer coefficient distribution of the tubes after the initial fluidization phase when low frequency pulsation was applied. A distinct, alternating pattern emerged comprising a needle-like distribution and a wide fan-shaped distribution. This corresponded to the
coalescence of air bubbles downstream of the tubes and the splitting of air bubbles along the tube sides respectively. The resulting timeaveraged heat transfer rates for the tubes in either configuration were of similar magnitude and distribution as those shown in Fig. 4 previously. Fig. 7 presents another representation of the same phenomenon with plots of average tube heat transfer coefficient across a 2 s period. As can be observed from the figure, the bed subjected to continuous flow did not exhibit the distinct, alternating pattern that is characteristic of one subjected to pulsating flow. When subjected to pulsating flow, sinusoidal oscillations of average tube heat transfer coefficient with respect to time were observed to develop at both low and high pulsating frequencies. An initial fluidization phase where heat transfer coefficient values dropped from an initially high value was observed when the bed was subjected to either low or high pulsating frequency. A structured fluidized bed was assumed to have been developed after this initial fluidization phase of 0.6 s based on the development of these sinusoidal patterns that characterized the fluctuation of heat transfer coefficient values between a maximum and minimum. In other words, these maximum and minimum heat transfer coefficient values corresponded
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Fig. 5. Granular temperature distributions (m2/s2) for (a) in-line and (b) staggered tube configurations when subjected to a pulsating frequency of 0 Hz and (c) in-line and (d) staggered tube configurations when subjected to a pulsating frequency of 5 Hz.
to the alternating needle-like and wide fan-shaped distributions, as discussed previously, respectively. The large bubbles that were observed resembled those of round-nosed gas slugs that are usually formed with bed materials that fluidize easily such as Geldart Groups A and B particles. The gas slugs rose at regular intervals and divided the main part of the fluidized bed into alternating regions of dense and lean phases. The presence of these large bubbles, as a result of
coalescence, was useful in ensuring that there was continuous circulation of solids, especially in stagnant regions around the tubes in the top section of the bed. It could be observed that the range over which heat transfer coefficient values fluctuated decreased with increasing pulsating frequency. When subjected to a pulsating frequency of 5 Hz, the heat transfer coefficient values ranged from 100,000 W/m2 K to 300,000 W/m2 K.
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Fig. 6. Instantaneous heat transfer coefficient distributions for pulsating flow at 5 Hz for in-line and staggered tube configurations showing a distinct, alternating pattern between a needlelike distribution and a wide fan-shaped distribution.
This range decreased to within 150,000 W/m2 K and 200,000 W/m2 K for a pulsating frequency of 20 Hz, indicating a decrease in the maximum value accompanied with an increase in the minimum value of heat transfer coefficient attainable. At a higher pulsating frequency, air was injected into the bed more regularly and this reduced the contact time between the solids and heated tube surfaces, resulting in an overall decrease in maximum heat transfer coefficient value. Wang and Rhodes [18] mentioned in their study that pulsed flow at high frequency resulted in regular fluidization reverting to chaotic bubbling that was similar to fluidization with continuous flow. Based on the solids volume fraction profiles observed in the current study, vigorous
bubbling was observed and the random fluctuations in heat transfer coefficient values were indicative of such a transition, especially at positions near the top section of the bed. 3.3. Effects of tube configuration on heat transfer A staggered tube configuration could be designed as an additional feature of a fluidized bed with immersed tubes to enhance the regularity of fluidization, on top of applying pulsating flow. Fig. 8 shows a comparison of the heat transfer performance of tubes in the top and bottom rows within a staggered or in-line tube configuration. The heat transfer
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Fig. 7. Time evolution of average heat transfer coefficient for in-line and staggered tube configurations when subjected to a pulsating frequency of (a) 0 Hz, (b) 5 Hz and (c) 20 Hz.
coefficient values obtained when the bed was subjected to low frequency pulsating flow fluctuated fairly periodically for tubes in both the top and bottom rows within both tube configurations but these periodic fluctuations were lost at high pulsating frequency in all cases except for tubes in the bottom row within the staggered configuration. High frequency pulsating flow (20 Hz) destroyed the orderly bubbling behavior observed at low frequency and caused the fluidized bed to revert back to a disorderly system, reminiscent of one subjected to continuous flow. Interestingly, the staggered configuration of the tubes helped to alleviate some of the destructive effect of high frequency pulsation on orderly bubbling albeit this was restricted to tubes in the bottom row. The period of fluctuation of the heat transfer coefficient was observed to increase after 1.5 s, and this contrasted with the more random fluctuations observed for tubes in the top row. The positioning of tubes in a staggered configuration restricted the growth of air bubbles especially during instances when the gas velocity was high. This constrained the sizes of air bubbles to be within a certain range, thereby reducing their influence on solids volume fraction distributions around tube 2. A regular fluctuation in heat transfer coefficient distribution could thus be maintained throughout the fluidization process. The above effect was not observed for the fluidized bed with an inline tube configuration. The channels between tubes through which rising bubbles could flow allowed vigorous bubbling to develop and caused regularity to be diminished. However, tubes in the in-line configuration were observed to have better heat transfer rates when subjected to high frequency pulsation compared to those in the staggered configuration. This was particularly so for tubes in the top row within the in-line configuration. The positions of the tubes might have contributed to this phenomenon. The three evenly spaced tubes in the top section of the bed reduced the amount of free space through which air bubbles could rise and coalesce to form larger bubbles. As such, the sizes of bubbles formed in the bed with in-line tube configuration were relatively smaller than those formed in the bed with staggered tube configuration. The smaller bubbles had less impact on the immediate surroundings of the top row of tubes and so better heat transfer rates from the tubes could be achieved.
Fig. 8. Time evolution of average heat transfer coefficient for tubes in the (a) top and (b) bottom rows within the in-line or staggered tube configuration when subjected to a pulsating frequency of 5 Hz (○) or 20 Hz (●).
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4. Conclusions
Acknowledgment
The coupled effects of local hydrodynamics on heat transfer from immersed tubes in a fluidized bed were investigated computationally in this study. An Eulerian-Eulerian approach was used to model bubbling fluidization and the effects of pulsating frequency and tube configuration on hydrodynamics and heat transfer were investigated. Low solids volume fractions at the bottom and sides of the tubes were associated with the rise and splitting of air bubbles around the tubes. This led to low heat transfer coefficients and high granular temperatures at those positions. Regions with high heat transfer coefficients also had high solids volume fractions, which suggested that the dominant mode of heat transfer was via solid-solid thermal conduction between heated surfaces and solids. When the fluidized bed was subjected to low frequency pulsation at 5 Hz, orderly rows of bubbles at regular intervals were formed. The intermittent injection of gas into the system removed gas channels and suppressed the coalescence of air bubbles. Uniform rows of small sized air bubbles that rose along the sides of the tubes and coalesced into bigger bubbles resulted in a distinct pattern of alternating needle-like and fan-shaped heat transfer coefficient distributions. The average heat transfer coefficient of the tubes fluctuated within a fixed range. This orderly fluctuating pattern was destroyed with higher pulsation frequency. At a pulsating frequency of 20 Hz, some orderly bubbling could be observed whereby small bubbles were produced near the inlet of the bed but these were completely absent for the case of continuous gas flow. However, the orderly behavior was observed to revert back to vigorous bubbling with the progression of time and along the bed height. Tube configurations were also found to aid in structuring fluctuations in heat transfer behaviors in such fluidized bed systems, such as in a bed with tubes in a staggered configuration subjected to high pulsating frequency. The heat transfer coefficient of tubes in the bottom row exhibited similar oscillation amplitudes. This effect was not observed for tubes in the top row within the same fluidized bed system. This could be due to the tubes in the top row causing direct obstructions to the rising air bubbles and hence enforcing some structure in the flow pattern. It would be pertinent to investigate the underlying mechanisms of this phenomenon in fluidized beds with immersed tubes subjected to pulsating gas flow in a future study. In addition, based on the qualitative differences in bubbling behaviors observed at the low and high pulsation frequencies considered in this study and the resulting qualitatively different heat transfer behaviors observed, it would be important to conduct more detailed parametric analyses of pulsation frequency to possibly derive an empirical relationship between pulsation frequency and heat transfer coefficient.
This study has been supported by the National University of Singapore under Grant No. R-279-000-497-114. References [1] A. Schmidt, U. Renz, Eulerian computation of heat transfer in fluidized beds, Chem. Eng. Sci. 54 (1999) 5515–5522. [2] A. Schmidt, U. Renz, Numerical prediction of heat transfer in fluidized beds by a kinetic theory of granular flows, Int. J. Therm. Sci. 39 (2000) 871–885. [3] A. Schmidt, U. Renz, Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle, Heat Mass Transf. 41 (2005) 257–270. [4] H.S. Mickley, D.F. Fairbanks, Mechanisms of heat transfer to fluidized beds, AICHE J. 1 (1955) 374–384. [5] Y.S. Wong, J.P.K. Seville, Single-particle motion and heat transfer in fluidized beds, AICHE J. 52 (2006) 4099–4109. [6] Y. Behjat, S. Shahhosseini, S.H. Hashemabadi, CFD modelling of hydrodynamic and heat transfer in fluidized bed reactors, Int. Commun. Heat Mass Transfer\ 35 (2008) 357–368. [7] Z.Y. Zhou, A.B. Yu, P. Zulli, Particle scale study of heat transfer in packed and bubbling fluidized beds, AICHE J. 55 (2009) 868–884. [8] M. Hamzehei, H. Rahimzadeh, Experimental and numerical study of hydrodynamics with heat transfer in a gas-solid fluidized-bed reactor at different particle sizes, Ind. Eng. Chem. Res. 48 (2009) 3177–3186. [9] M. Hamzehei, H. Rahimzadeh, G. Ahmadi, Computational and experimental study of heat transfer and hydrodyanmics in 2D gas-solid fluidzed bed reactor, Ind. Eng. Chem. Res. 49 (2010) 5110–5121. [10] Q.F. Hou, Z.Y. Zhou, A.B. Yu, Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube, AICHE J. 58 (2012) 1422–1434. [11] Q.F. Hou, Z.Y. Zhou, A.B. Yu, Computational study of the effects of material properties on heat transfer in gas fluidization, Ind. Eng. Chem. Res. 51 (2012) 11572–11586. [12] Z. Hau, E.W.C. Lim, Heat transfer from an immersed tube in a bubbling fluidized bed, Ind. Eng. Chem. Res. 55 (2016) 9040–9053. [13] J. Ngoh, E.W.C. Lim, Effects of particle size and bubbling behavior on heat transfer in gas fluidized beds, Appl. Therm. Eng. 105 (2016) 225–242. [14] H. Wahyudi, K. Chu, A.B. Yu, 3D particle-scale modeling of gas–solids flow and heat transfer in fluidized beds with an immersed tube, Int. J. Heat Mass Transf. 97 (2016) 521–537. [15] J. Gan, Z. Zhou, A.B. Yu, Particle scale study of heat transfer in packed and fluidized beds of ellipsoidal particles, Chem. Eng. Sci. 144 (2016) 201–215. [16] E. Ireland, K. Pitt, R. Smith, A review of pulsed flow fluidisation; the effects of intermittent gas flow on fluidised gas–solid bed behaviour, Powder Technol. 292 (2016) 108–121. [17] M.-O. Coppens, J.R. van Ommen, Structuring chaotic fluidized beds, Chem. Eng. J. 96 (2003) 117–124. [18] X. Wang, M. Rhodes, Pulsed fluidization—a DEM study of a fascinating phenomenon, Powder Technol. 159 (2005) 142–149. [19] N. Gui, J. Fan, Numerical simulation of pulsed fluidized bed with immersed tubes using DEM–LES coupling method, Chem. Eng. Sci. 64 (2009) 2590–2598. [20] K.H. Bizhaem, B.H. Tabrizi, Experimental study on hydrodynamic characteristics of gas– solid pulsed fluidized bed, Powder Technol. 237 (2013) 14–23. [21] L. Dong, Y. Zhao, C. Duan, Z. Luo, B. Zhang, X. Yang, Characteristics of bubble and fine coal separation using active pulsing air dense medium fluidized bed, Powder Technol. 257 (2014) 40–46. [22] S.S. Ali, M. Asif, A. Ajbar, Bed collapse behavior of pulsed fluidized beds of nano-powder, Adv. Powder Technol. 25 (1) (2014) 331–337. [23] M. Saidi, H.B. Tabrizi, S. Chaichi, M. Dehghani, Pulsating flow effect on the segregation of binary particles in a gas–solid fluidized bed, Powder Technol. 264 (2014) 570–576. [24] M. Saidi, H.B. Tabrizi, J.R. Grace, C.J. Lim, G. Ahmadi, Hydrodynamic and mixing characteristics of gas–solid flow in a pulsed spouted bed, Ind. Eng. Chem. Res. 54 (2015) 7933–7941. [25] J. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow, AICHE J. 36 (1990) 523–538.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Heat transfer from immersed tubes in a pulsating fluidized bed Emily Min Li Sin, Eldin Wee Chuan Lim ⁎ Department of Chemical and Biomolecular Engineering, National University of Singapore, 117585, Singapore
a r t i c l e
i n f o
Article history: Received 6 July 2017 Received in revised form 10 November 2017 Accepted 30 December 2017 Available online 10 January 2018 Keywords: Computational fluid dynamics Pulsating fluidized bed Heat transfer Immersed tubes
a b s t r a c t Heat transfer through immersed tubes in pulsating fluidized beds was investigated computationally using an Eulerian-Eulerian approach. The effects of pulsating frequency and configuration of the immersed tubes were studied. At low pulsating frequency, more orderly bubbling behaviors were observed and these gave rise to more uniform heat transfer rates from all tubes. An interesting heat transfer behavior whereby the heat transfer coefficient distribution around an immersed tube alternated between a needle-like and a wide fan-shaped pattern was observed for the first time in this study. An increase in pulsating frequency caused the fluidized bed to exhibit fluctuating heat transfer rates. The staggered tube configuration considered in this study was observed to aid in the development of more orderly bubbling behaviors, with heat transfer coefficient of tubes in the bottom row exhibiting similar oscillation amplitudes. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Fluidization has been established as an important operation in a variety of industrial processes. Due to excellent heat transfer characteristics, fluidized bed reactors and dryers have been applied in various industries. One of the approaches for transferring energy into or out of a gas fluidized bed is through the use of immersed tubes. Heat transfer takes place between the gas and solids of the fluidized bed and a utility fluid within the immersed tubes. In many of these processes, efficient heat transfer between the immersed tubes and solids is essential to the operation of the fluidized bed but may be difficult to achieve. Pulsed fluidization is a special mode of fluidized bed operation where the gas flow rate is varied periodically with time. The benefits of pulsed fluidization include reduced gas by-passing and channeling and enhanced gassolid contact. However, the effect of pulsed fluidization on heat transfer through immersed tubes is poorly understood even today. Although many research studies have been reported on simulations of fluidization behaviors, studies on coupled effects of gas pulsation with heat transfer from immersed tubes in fluidized bed systems have been limited to date. Schmidt and Renz [1] conducted numerical simulations to understand the heat transfer behavior between a heated surface and bed particles. They then explored the validity of two different approaches – standard and kinetic – to describe the thermal conductivity of the solid phase [2]. Subsequently, Schmidt and Renz [3] conducted numerical simulations to analyze heat transfer between a fluidized bed of Geldart B particles and an immersed tube and showed that the correlation ⁎ Corresponding author. E-mail address: [email protected] (E.W.C. Lim).
https://doi.org/10.1016/j.powtec.2017.12.095 0032-5910/© 2018 Elsevier B.V. All rights reserved.
between heat transfer coefficient and the bed hydrodynamics was in theoretical agreement with the packet theory developed by Mickley and Fairbanks [4]. Wong and Seville [5] adopted the packet theory and analyzed heat transfer behavior with particle convection as the dominant mode of heat transfer. Behjat et al. [6] investigated the effect of monodispersed and bimodal solid mixtures on hydrodynamics and the effect of varying gas velocities on gas and solid temperature distributions and found that heat transfer between solids and gas increased with increasing gas velocity. Zhou et al. [7] conducted simulations using the combined Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) to analyze particle-particle and particle-fluid heat transfer behaviors by quantifying the contribution to heat transfer coefficient via convection, conduction and radiation. Hamzehei and Rahimzadeh [8] applied an Eulerian-Eulerian model coupled with the kinetic theory for solid particles to simulate industrial fluidized-bed reactors and found that a decrease in particle sizes led to an overall increase in heat transfer rate due to increased gas-solid contact. Subsequently, Hamzehei et al. [9] extended this study by incorporating an additional k-ε turbulence model to simulate heat conducting gas-solid flow in fluidized beds. Hou et al. [10] conducted computer simulations to study heat transfer in a fluidized bed with an immersed tube using the CFD-DEM approach and observed that increasing particle thermal conductivity resulted in an increase in conductive flux but had limited impact on improving heat transfer coefficient. Hou et al. [11] continued the above study to investigate the effect of particle properties, namely Hamaker constant and particle size, on heat transfer in a fluidized bed and observed that an increase in Hamaker constant resulted in convective and conductive heat flux increasing to a maximum at minimum bubbling velocity. More recently, Hau and Lim [12] simulated the fluidized bed system investigated by Schmidt and Renz [3] and conducted 3D
E.M.L. Sin, E.W.C. Lim / Powder Technology 327 (2018) 500–511
CFD simulations to investigate how heat transfer coefficient between solid particles and a heated tube varied with particle size and temperature of the heated tube. Ngoh and Lim [13] showed that the size of bubbles formed exhibited an inverse relation with particle size. Wahyudi et al. [14] conducted 3D simulations of a fluidized bed with an immersed tube to study hydrodynamics and heat transfer behavior using CFD-DEM and were able to reproduce general hydrodynamic and heat transfer trends, such as pressure drop and the correlation between heat transfer coefficient with varying superficial gas velocity. Gan et al. [15] applied CFD-DEM to study heat transfer behavior in fluidized beds containing non-spherical particles and found that spherical particles had the lowest effective thermal conductivity while ellipsoidal particles gave rise to lower convective heat transfer but higher conductive heat transfer rates. Ireland et al. [16] provided a comprehensive review of pulsed flow fluidization and the key findings in recent research and development in this field of study. Coppens and van Ommens [17] investigated three methods, via application of an alternating AC electric field, fractal injectors and pulsed flow, to introduce order into a fluidized bed which was characterized as a chaotic system. In a DEM study conducted by Wang and Rhodes [18], they investigated the relationship between pulsed flow and formation of regular bubble patterns and concluded that low pulse frequencies were not favorable in forming regular bubble patterns due to prolonged periods of high and low gas velocities which resulted in an intermittently fluidized and unsteady bed. Gui and Fan [19] performed 2D numerical simulations of a pulsed fluidized bed using DEM-LES to investigate the effect of pulsed flow frequency and immersed tube arrangements on particle interactions with the fluid and immersed tubes. Bizhaem and Tabrizi [20] conducted experiments to study the effect of particle properties, pulse frequency and gas velocity on the hydrodynamics of a pulsed fluidized bed. Dong et al. [21] adopted a novel approach towards dry beneficiation of fine coal by applying flow pulsation in a dense medium fluidized bed. Ali et al. [22] conducted experiments to study the hydrodynamics of pulsed flow fluidized bed consisting of nanoparticles by analyzing the bed collapse behavior exhibited at different air velocities. In an experimental study conducted by Saidi et al. [23], the effect of pulsed air flow on separation efficiency of a binary mixture of dissimilar sized particles in a gas-solid fluidized bed was investigated. In a subsequent simulation study conducted by Saidi et al. [24], a pulsed, spouted fluidized bed was modeled using CFD-DEM. Most studies to date have focused on either the effects of gas pulsation on bubbling behaviors in fluidized bed systems or mixing behaviors. The possibility of applying gas pulsation to enhance heat transfer in fluidized beds containing multiple immersed tubes arranged in different tube configurations have not been explored to date. From an industrial application perspective, the application of gas pulsation to improve heat transfer efficiencies in large-scale fluidized bed reactors or dryers where heat supply or removal is critical to the operation of the fluidized bed may represent a promising approach for process intensification that has not been explored to date. The current study serves to fill this gap in current understanding of coupled effects between gas pulsation and heat transfer in fluidized bed systems containing immersed tubes. 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. 2. Computational model A multiphase Eulerian-Eulerian model was used to simulate a pulsating fluidized bed with immersed tubes. The solids phase was modeled as a continuum and the kinetic theory of granular flow was used as closure for the solids stress tensor. The governing equations for conservation of mass, momentum and energy were solved using
501
Fig. 1. Configurations of immersed tubes comprising (a) six in-line tubes and (b) five staggered tubes.
the commercial CFD software Ansys Fluent R18 and are summarized as follows. The continuity equations for gas and solids phases are: ∂ ! ðεs ρs Þ þ ∇∙ εs ρs vs ¼ 0 ∂t
ð1Þ
∂ ! ε g ρg þ ∇∙ εg ρg vg ¼ 0 ∂t
ð2Þ
! ! where ρs and ρg are densities and vs and vg are the velocities of the solids and gas phases respectively. The sum of solids volume fraction, εs and gas volume fraction, εg is unity. Table 1 Material properties and operating parameters. Particle density Gas density Gas viscosity Particle diameter Restitution coefficient Initial solids packing Bed width Bed height Bed thickness Static bed height Fluidizing gas temperature Initial bed temperature Immersed tube diameter Immersed tube temperature Tubes configuration Immersed tube elevation Pulsating gas frequency
2660 kg/m3 1.225 kg/m3 1.8 × 10−5 Pa·s 500 μm 0.9 0.6 320 mm 800 mm 10 mm 400 mm 293 K 293 K 40 mm 373 K 5 tubes staggered, 6 tubes in-line 150 mm (bottom row), 230 mm (top row) 0, 5, 20 Hz
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The solid shear viscosity, μ i is the sum of the collisional, kinetic and frictional viscosities:
The momentum equations for gas and solids phases are: ∂ ! ! ! !! ! ! εs ρs vs þ ∇∙ ε s ρs vs vg ¼ ∇∙τ s −εs ∇P þ ε s ρs g þ β vs −vg ∂t
ð3Þ
∂ ! ! !! ! ! ! εg ρg vg þ ∇∙ εg ρg vs vg ¼ ∇∙ τ g −εg ∇P þ εg ρg g þ β vg −vs ð4Þ ∂t ! ! where β is the gas-solid drag coefficient and τs and τg are stress tensors for the respective phases. The drag model by Ding and Gidaspow [25] was used in this study. The gas-solid drag coefficients used in the Gidaspow drag model are: 8 ! ! εs 2 μ g > ρg vs −vg εs > > þ 1:75 ; εg ≤0:8 < 150 2 d εs ds β ! ! s > > 3 εs εG ρs vs −vg −2:65 > : CD εg ; εg N0:8 4 ds
ð5Þ
D⃑ i ¼
i 1h ! T ∇vI þ ð∇! vI Þ 2
0:5 4 θs εs ρs ds g 0;ss ð1 þ εss Þ 5 π pffiffiffiffiffiffiffi
2 P s sinϕ 10ρs ds θs π þ 1 þ 0:8g 0;ss εs ð1 þ ε ss Þ þ pffiffiffiffiffiffiffi 96εs ð3−εss Þg 0;ss 2 I 2D
ð6Þ
ð7Þ
ð8Þ
where ϕ is the angle of internal friction, I2D is the second invariant of the deviatoric stress tensor and Ps is the solids pressure. The solids pressure is: (9) Ps = εs ρs Ξs þ 2ρs ð1 þ εss Þεs 2 g0;ss Ξs The energy equations for gas and solids phases are ∂ ! ! ! ε g ρg hg þ ∇∙ εg ρg vg hg ¼ −∇εg qg þ α T s −T g þ τ g ∙∇vg ∂t
∂ ! þ εg P þ vg ∇P ∂t
The stress tensor is described as: 2 ! τ i ¼ 2μ i D⃑ iþ λi − μ i ∙tr D⃑ i I 3
μs ¼
∂ ! ! ! ðεs ρs hs Þ þ ∇∙ εs ρs vs hs ¼ −∇εs qs þ α T g −T s þ τs ∙∇vs ∂t
∂ ! P þ vs ∇P þ εs ∂t
ð10Þ
ð11Þ
Fig. 2. Bubbling behaviors of fluidized beds with in-line tube configuration subjected to a pulsating frequency of (a) 0 Hz, (b) 5 Hz, (c) 20 Hz, and staggered tube configuration subjected to a pulsating frequency of (d) 0 Hz, (e) 5 Hz, (f) 20 Hz.
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503
Fig. 2 (continued).
The balance of the solids phase granular energy can be described by the following equation:
3 ∂ ! ! ðεs ρs Ξs Þ þ ∇∙ðεs ρs Ξs Þvs ¼ ð−P s I þ τs Þ∇vs 2 ∂t þ ∇∙ðkΞ ∇Ξs Þ−γ Ξ þ −3βΞs
ð12Þ
The diffusion coefficient for granular energy kΞ is given by:
kΞ ¼
pffiffiffiffiffiffiffiffiffi 15ds ρs εs Ξs π 12 2 16 1þ η ð4η−3Þεss g 0;ss þ ð41−33ηÞηε ss g 0;ss 4ð41−33ηÞ 5 15π ð13Þ
where η ¼ 12 ð1 þ εss Þ. g0, ss is the radial distribution function that describes the probability of particle-particle collisions and is expressed as: " g 0;ss ¼ 1−
εs
13 #−1
εs;max
ð14Þ
The dissipation of fluctuating energy, γ Ξ is: γΞ ¼
12 1−εss 2 g 0;ss pffiffiffi ρs εs 2 Ξs 1:5 ds π
ð15Þ
The granular temperature, Ξs represents the kinetic energy of the fluctuating solid phase particles and is a variable of the solids pressure and stress tensors. The granular temperature is defined as Ξs ¼
1 2 v0s 3
ð16Þ
where v′s is fluctuating velocity. The velocity profile for pulsating flow of gas used by Gui and Fan [19] was applied at the inlet of the fluidized bed: U ðt Þ ¼ U 0 þ U S sinð2πft Þ
ð17Þ
where U0 is the mean superficial gas velocity, US is the amplitude of pulsation and f is the pulsating frequency. The frequency range explored in this study was 0–20 Hz. Values of the mean velocity U0 was selected such that the resulting gas velocity would always be higher than the minimum fluidization velocity of the fluidized bed. A User Defined Function (UDF) was written in the C language to implement the above pulsating gas velocity profile and the program code was compiled with the CFD model developed. The fluidized bed model used in this study was based on the one investigated by Hau and Lim [12], while tube configuration dimensions were based on those investigated by Gui and Fan [19] (Fig. 1). The initial set of simulations conducted was based on the same operating conditions applied by the previous researchers
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Fig. 2 (continued).
respectively. Table 1 shows the material properties and operating parameters applied in the current study. All material properties were assumed to be independent of temperature in the simulations conducted. A sensitivity analysis was carried out during the initial phase of this study to investigate the effects of mesh size, time step size, and convergence criterion on the final simulation results. The mesh size and time step size that were derived through this analysis to ensure simulation results were independent of these parameters were 2.5 mm and 10−4 s respectively. 1000 iterations per time step was specified to ensure that simulations converged at every time step. The phase coupled SIMPLE (PC-SIMPLE) algorithm, which is an extension of the SIMPLE algorithm for multiphase flows, was applied for the pressure-velocity coupling. The velocities were solved coupled by phases in a segregated fashion. Fluxes were reconstructed at the faces of the control volume and then a pressure correction equation was built based on total continuity. The coefficients of the pressure correction equations came from the coupled per phase momentum equations. The linearized equations were solved using a block algebraic multigrid method. For postprocessing of the simulation results, instantaneous values of heat transfer coefficient at various positions along the circumference of the immersed tubes were extracted and Matlab programs were written to generate plots of heat transfer coefficient distributions in polar coordinates as well as to compute average heat transfer coefficient values.
3. Results and discussion 3.1. Effects of pulsation on fluidization behaviors The simulation results obtained in the initial phase of this study showed general agreement with simulation results obtained in various studies conducted by other researchers. When the bed was subjected to continuous flow of gas at a superficial gas velocity greater than the minimum fluidization velocity, vigorous bubbling was observed. As shown in Fig. 2a and d, typical vigorous bubbling behavior characterized by expansion of the fluidized bed, small bubbles at the inlet, coalescence of bubbles during ascent and eruption of gas bubbles at the bed surface were observed. These observations were similar to those reported by Hau and Lim [12]. Coppens and van Ommen [17] recognized that gases injected into pulsating fluidized beds form uniform but staggered rows of bubbles which suppress vigorous bubbling. Fig. 2b and e show the fluidization behavior of the same bed when subjected to low frequency pulsating flow at 5 Hz. It could be observed that unilateral and staggered rows of gas bubbles formed which gave rise to regular patterns of bubbles which were relatively smaller and more uniform. When the frequency of pulsation was increased to 20 Hz (Fig. 2c and f), the regular bubble patterns previously observed during low frequency pulsation were no longer observed. This behavior was congruent with that reported by Wang and Rhodes [18] who suggested that this might have occurred
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Fig. 3. Solids velocity vectors colored by solids temperature with red and blue representing high and low temperatures respectively at 1.5, 1.6 and 1.7 s for in-line tube configuration subjected to a pulsating frequency of (a) 5 Hz and (b) 20 Hz.
as the gas-flow variation was too fast for the structure of the bed to respond, thereby diminishing the formation of horizontal channel-like structures near the distributor plate. However, it may be observed that bubbles were still more regularly spaced near the inlet at high frequency gas pulsation compared to those generated in a bed that was subjected to continuous flow. The phenomenon of particle renewal was observed whenever heated solids around the tubes were displaced by cooler solids due to the rising bubble motion. Fig. 3 shows the occurrences of particle renewal for in-line tubes subjected to low and high pulsating frequencies. The upward force generated by the bubbles pushed the heated solids (colored red to green) upwards and away from the tubes. This created voids which were then filled by adjacent cooler solids (colored blue) thus ensuring continuous and efficient heat transfer between the tubes and the solids. The particle renewal behavior for the staggered tube configuration was observed to be qualitatively similar to that for the in-line tube configuration and so has not been shown for brevity. This phenomenon was first observed in the study by Mickley and Fairbanks [4] who reported that the rate of heat transfer is dependent on the rate of displacement of solid particles around an immersed heated tube. At high pulsation frequency, bubbles with different sizes were generated and rose through the bed at different velocities. This disparity in rising velocities resulted in mixing of solids especially near the top of the fluidized bed. At low pulsation frequency, the solids generally moved upwards as a result of more uniform sizes of bubbles. However, at high pulsation frequency, solids were observed to move outwards towards the walls when there were significant differences in the sizes of bubbles. Larger bubbles were able to force solids to be pushed
downwards and outwards, thereby further impacting the solids volume fraction distributions around tubes in the top section of the bed. This was observed to be particularly significant for tubes in the top row within the staggered tube configuration. The high gas velocity caused the bulk of heat transfer to occur at regions above the tubes. Fig. 4 shows the time averaged solids volume fraction distributions and corresponding heat transfer coefficient distributions around different tubes when subjected to pulsating frequencies of 0 Hz and 5 Hz. Solids volume fractions were high around tubes in the top section of the tube bundle and low in the bottom section. This corresponded with high heat transfer and low granular temperatures in the top section, which indicated that solids thermal conduction was the primary mode of heat transfer from the heated immersed tubes to the solids. The bottom of each tube was in constant contact with rising air bubbles which split into smaller bubbles that flowed along the sides of the tubes. Granular temperatures were higher due to large fluctuations in solids motion while solids volume fraction was correspondingly low. As the fluidizing air was a poor medium for conductive heat transfer, the heat transfer coefficients of the tubes with low solids volume fractions were lower. These observations were consistent with those reported by Hau and Lim [12] who investigated heat transfer from a single immersed tube in a bubbling fluidized bed with continuous gas flow. The observed differences in fluidization behaviors in the absence and presence of pulsating gas flow gave rise to significant differences in heat transfer behaviors between the immersed tubes and surrounding solids. With continuous gas flow (pulsating frequency of 0 Hz), the heat transfer coefficient varied significantly with circumferential position around each immersed tube. In contrast, when low frequency pulsating flow was applied,
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much more uniform heat transfer coefficient distributions could be achieved for all immersed tubes. It could also be observed from Fig. 4 that heat transfer coefficients decreased and heat transfer coefficient distributions became narrower with low frequency pulsating flow. This was expected as larger volumes of air were injected into the system. However, heat transfer coefficients of tubes located in the top section (tubes 5 and 6) decreased more significantly than those of tubes in the bottom section (tube 2). The initial huge bubble was broken into smaller bubbles upon contact with tubes in the bottom section. Bubbles flowing near the center of the fluidized bed were relatively smaller than those flowing near the walls. This resulted in generation of relatively more uniform, small bubbles for both tube configurations when subjected to either continuous or pulsating flow. As such, the impact of pulsating flow affecting heat transfer rate was smaller, as evidenced by the comparisons of heat transfer coefficient distributions of tube 2 across all cases in Fig. 4. The differences in bubbling behaviors were more evident near the top section of the fluidized bed. With continuous flow, air bubbles
remained small near the center of the bed but grew in size near the walls. Growth of air bubbles near the center of the bed was disrupted by the tubes which caused splitting of gas bubbles as described earlier. Bubbles flowing near the walls coalesced with other air bubbles and grew along the bed height. Larger bubbles had a tendency to coalesce with smaller bubbles, which was the phenomenon that resulted in the disparity in heat transfer rates for tubes in the top section of the bed. Fig. 5 shows the granular temperature distributions of solids around tubes 2, 5 and 6 which reveal the effects of the above bubbling behaviors on fluctuating motions of solids. The splitting of bubbles around tubes at the bottom resulted in fairly symmetrical solids motion around tube 2. In contrast, asymmetrical solids motion was observed around tube 6. There was lower likelihood of contact between air bubbles and tube 5 compared with contact with tube 6 because bubbles near the center of the bed were smaller than the tube spacing and they exhibited greater tendencies to flow towards the sides to coalesce with larger bubbles. On the other hand, tubes 4 and 6 were exposed to larger bubbles that had coalesced and grew, and hence the tube surfaces were largely in
Fig. 4. Time averaged solids volume fraction distributions and heat transfer coefficient (kW/m2 K) distributions around tubes 2, 5 and 6 when subjected to a pulsating frequency of 0 Hz or 5 Hz in (a) in-line and (b) staggered tube configurations.
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507
Fig. 4 (continued).
contact with air. This would inhibit effective heat transfer between the tubes and solids. When low frequency pulsating flow was applied in either tube configurations, symmetrical granular temperature distributions were achieved for all tubes. This was a result of more even splitting of air bubbles characteristic of pulsating flow. This explained the relatively similar heat transfer coefficient distributions obtained for all tubes as seen earlier in Fig. 4. 3.2. Effects of pulsating frequency on heat transfer It was interesting to note that a unique “on-and-off” pattern was observed for the heat transfer coefficient distribution around the tubes when the bed was fluidized with low frequency pulsation. This is a new observation of heat transfer behavior in a gas fluidized bed containing immersed tubes subjected to pulsating flow which has not been reported in the literature to date. Fig. 6 shows the instantaneous heat transfer coefficient distribution of the tubes after the initial fluidization phase when low frequency pulsation was applied. A distinct, alternating pattern emerged comprising a needle-like distribution and a wide fan-shaped distribution. This corresponded to the
coalescence of air bubbles downstream of the tubes and the splitting of air bubbles along the tube sides respectively. The resulting timeaveraged heat transfer rates for the tubes in either configuration were of similar magnitude and distribution as those shown in Fig. 4 previously. Fig. 7 presents another representation of the same phenomenon with plots of average tube heat transfer coefficient across a 2 s period. As can be observed from the figure, the bed subjected to continuous flow did not exhibit the distinct, alternating pattern that is characteristic of one subjected to pulsating flow. When subjected to pulsating flow, sinusoidal oscillations of average tube heat transfer coefficient with respect to time were observed to develop at both low and high pulsating frequencies. An initial fluidization phase where heat transfer coefficient values dropped from an initially high value was observed when the bed was subjected to either low or high pulsating frequency. A structured fluidized bed was assumed to have been developed after this initial fluidization phase of 0.6 s based on the development of these sinusoidal patterns that characterized the fluctuation of heat transfer coefficient values between a maximum and minimum. In other words, these maximum and minimum heat transfer coefficient values corresponded
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Fig. 5. Granular temperature distributions (m2/s2) for (a) in-line and (b) staggered tube configurations when subjected to a pulsating frequency of 0 Hz and (c) in-line and (d) staggered tube configurations when subjected to a pulsating frequency of 5 Hz.
to the alternating needle-like and wide fan-shaped distributions, as discussed previously, respectively. The large bubbles that were observed resembled those of round-nosed gas slugs that are usually formed with bed materials that fluidize easily such as Geldart Groups A and B particles. The gas slugs rose at regular intervals and divided the main part of the fluidized bed into alternating regions of dense and lean phases. The presence of these large bubbles, as a result of
coalescence, was useful in ensuring that there was continuous circulation of solids, especially in stagnant regions around the tubes in the top section of the bed. It could be observed that the range over which heat transfer coefficient values fluctuated decreased with increasing pulsating frequency. When subjected to a pulsating frequency of 5 Hz, the heat transfer coefficient values ranged from 100,000 W/m2 K to 300,000 W/m2 K.
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Fig. 6. Instantaneous heat transfer coefficient distributions for pulsating flow at 5 Hz for in-line and staggered tube configurations showing a distinct, alternating pattern between a needlelike distribution and a wide fan-shaped distribution.
This range decreased to within 150,000 W/m2 K and 200,000 W/m2 K for a pulsating frequency of 20 Hz, indicating a decrease in the maximum value accompanied with an increase in the minimum value of heat transfer coefficient attainable. At a higher pulsating frequency, air was injected into the bed more regularly and this reduced the contact time between the solids and heated tube surfaces, resulting in an overall decrease in maximum heat transfer coefficient value. Wang and Rhodes [18] mentioned in their study that pulsed flow at high frequency resulted in regular fluidization reverting to chaotic bubbling that was similar to fluidization with continuous flow. Based on the solids volume fraction profiles observed in the current study, vigorous
bubbling was observed and the random fluctuations in heat transfer coefficient values were indicative of such a transition, especially at positions near the top section of the bed. 3.3. Effects of tube configuration on heat transfer A staggered tube configuration could be designed as an additional feature of a fluidized bed with immersed tubes to enhance the regularity of fluidization, on top of applying pulsating flow. Fig. 8 shows a comparison of the heat transfer performance of tubes in the top and bottom rows within a staggered or in-line tube configuration. The heat transfer
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Fig. 7. Time evolution of average heat transfer coefficient for in-line and staggered tube configurations when subjected to a pulsating frequency of (a) 0 Hz, (b) 5 Hz and (c) 20 Hz.
coefficient values obtained when the bed was subjected to low frequency pulsating flow fluctuated fairly periodically for tubes in both the top and bottom rows within both tube configurations but these periodic fluctuations were lost at high pulsating frequency in all cases except for tubes in the bottom row within the staggered configuration. High frequency pulsating flow (20 Hz) destroyed the orderly bubbling behavior observed at low frequency and caused the fluidized bed to revert back to a disorderly system, reminiscent of one subjected to continuous flow. Interestingly, the staggered configuration of the tubes helped to alleviate some of the destructive effect of high frequency pulsation on orderly bubbling albeit this was restricted to tubes in the bottom row. The period of fluctuation of the heat transfer coefficient was observed to increase after 1.5 s, and this contrasted with the more random fluctuations observed for tubes in the top row. The positioning of tubes in a staggered configuration restricted the growth of air bubbles especially during instances when the gas velocity was high. This constrained the sizes of air bubbles to be within a certain range, thereby reducing their influence on solids volume fraction distributions around tube 2. A regular fluctuation in heat transfer coefficient distribution could thus be maintained throughout the fluidization process. The above effect was not observed for the fluidized bed with an inline tube configuration. The channels between tubes through which rising bubbles could flow allowed vigorous bubbling to develop and caused regularity to be diminished. However, tubes in the in-line configuration were observed to have better heat transfer rates when subjected to high frequency pulsation compared to those in the staggered configuration. This was particularly so for tubes in the top row within the in-line configuration. The positions of the tubes might have contributed to this phenomenon. The three evenly spaced tubes in the top section of the bed reduced the amount of free space through which air bubbles could rise and coalesce to form larger bubbles. As such, the sizes of bubbles formed in the bed with in-line tube configuration were relatively smaller than those formed in the bed with staggered tube configuration. The smaller bubbles had less impact on the immediate surroundings of the top row of tubes and so better heat transfer rates from the tubes could be achieved.
Fig. 8. Time evolution of average heat transfer coefficient for tubes in the (a) top and (b) bottom rows within the in-line or staggered tube configuration when subjected to a pulsating frequency of 5 Hz (○) or 20 Hz (●).
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4. Conclusions
Acknowledgment
The coupled effects of local hydrodynamics on heat transfer from immersed tubes in a fluidized bed were investigated computationally in this study. An Eulerian-Eulerian approach was used to model bubbling fluidization and the effects of pulsating frequency and tube configuration on hydrodynamics and heat transfer were investigated. Low solids volume fractions at the bottom and sides of the tubes were associated with the rise and splitting of air bubbles around the tubes. This led to low heat transfer coefficients and high granular temperatures at those positions. Regions with high heat transfer coefficients also had high solids volume fractions, which suggested that the dominant mode of heat transfer was via solid-solid thermal conduction between heated surfaces and solids. When the fluidized bed was subjected to low frequency pulsation at 5 Hz, orderly rows of bubbles at regular intervals were formed. The intermittent injection of gas into the system removed gas channels and suppressed the coalescence of air bubbles. Uniform rows of small sized air bubbles that rose along the sides of the tubes and coalesced into bigger bubbles resulted in a distinct pattern of alternating needle-like and fan-shaped heat transfer coefficient distributions. The average heat transfer coefficient of the tubes fluctuated within a fixed range. This orderly fluctuating pattern was destroyed with higher pulsation frequency. At a pulsating frequency of 20 Hz, some orderly bubbling could be observed whereby small bubbles were produced near the inlet of the bed but these were completely absent for the case of continuous gas flow. However, the orderly behavior was observed to revert back to vigorous bubbling with the progression of time and along the bed height. Tube configurations were also found to aid in structuring fluctuations in heat transfer behaviors in such fluidized bed systems, such as in a bed with tubes in a staggered configuration subjected to high pulsating frequency. The heat transfer coefficient of tubes in the bottom row exhibited similar oscillation amplitudes. This effect was not observed for tubes in the top row within the same fluidized bed system. This could be due to the tubes in the top row causing direct obstructions to the rising air bubbles and hence enforcing some structure in the flow pattern. It would be pertinent to investigate the underlying mechanisms of this phenomenon in fluidized beds with immersed tubes subjected to pulsating gas flow in a future study. In addition, based on the qualitative differences in bubbling behaviors observed at the low and high pulsation frequencies considered in this study and the resulting qualitatively different heat transfer behaviors observed, it would be important to conduct more detailed parametric analyses of pulsation frequency to possibly derive an empirical relationship between pulsation frequency and heat transfer coefficient.
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