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Numerical study of particle injection into a gas-solid fluidized bed
PTEC-14684; No of Pages 11 Powder Technology xxx (2019) xxx
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Numerical study of particle injection into a gas-solid fluidized bed Ying Liu a, Sihang Tian a, Shaoshuo Li a, Yao Yang a, Zhengliang Huang a, Jingyuan Sun a,⁎, Zuwei Liao a, Jingdai Wang a, Yongrong Yang a, Jian Yang b a b
State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China Institute of Pharmaceutical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China
a r t i c l e
i n f o
Article history: Received 13 November 2018 Received in revised form 14 February 2019 Accepted 6 September 2019 Available online xxxx Keywords: Computational fluid dynamics Gas-solid fluidized bed Particle injection Flow behaviors Solid mixing
a b s t r a c t The flow and dispersion behaviors of the fine particle injection in a gas-solid fluidized bed were studied numerically based on the two-dimensional multi-fluid model. The injection path and flow pattern of the flotsam solids were investigated. A distinct pair of counter-rotating vortices of flotsam particles appeared in the middle and upper parts of the fluidized bed. Higher injection rate was preferred for faster flotsam dispersion. The effects of flotsam injection on bed hydrodynamics were investigated with regard to the velocity distribution and volume fraction of bulk materials and the bubble size. Consequently, the mixing properties of the flotsam particles and bulk solids were quantified by the fluid-free flotsam fraction profile and the standard deviation. The fluidized bed was mixed acceptably with modest local segregation for all the conditions simulated. Lower injection velocity made contributions to better mixing especially for the duration of injection. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Gas-solid fluidized beds provide high heat and mass transfer rates as well as intense mixing and contact of different phases in a number of industrial processes, including traditional processes such as combustion, gasification, oil refining, olefin polymerization, calcination, drying and granulation, as well as emerging fields such as biotechnology, pharmaceutical manufacturing and environmental industries [1,2]. These transfer behaviors mainly originate from the solid circulation inside the fluidized bed, in which the solid motion is induced by gas bubbles and streams rising through the bed. The solid flow pattern is also a significant factor that impacts other bed characteristics such as the chemical reaction degree and the particle growth rate and it varies with operation parameters like the superficial gas velocity, bed aspect ratio, solid phase properties and the configurations of gas distributor. Moreover, many processes involve solid feeding through the side inlet, with physical properties different from the bulk materials, for instance, catalyst injection in manufacturing of polyolefins and reactant feeding in biomass combustion. In the gas phase olefin polymerization process, a few fine catalyst particles are usually injected into the dense section of the fluidized bed reactor with gas flow. These highly active particles quickly disperse inside the bed while catalyzing the polymerization of gas phase monomers, resulting in significant local heat generation. The fines penetrate into the system and are then entrained by the bulk solid circulation which mainly governs the heat removal via convective heat ⁎ Corresponding author. E-mail address: [email protected] (J. Sun).
transfer. If the particles are not well dispersed, the heat transfer would be hindered and particle agglomeration may be prone to occur. Therefore, it is of vital importance to understand the way in which the solid particles enter the fluidized bed and then disperse and mix with the bed materials in order to control the reaction intensity and heat transfer, so that an efficient design and operation of fluidized bed can be achieved. Considerable experimental investigations have been carried out to explore the underlying mechanisms of the solid flow patterns as well as gas jet penetration and mixing in fluidized beds [3–6]. Li et al. obtained the solid and gas flow patterns using positron emission particle tracking (PEPT). The impact of particle properties, bed design and operation conditions were investigated and four different solid flow patterns were founded under various conditions [7]. Panariello et al. employed X-ray imaging technique to observe the jets penetration length and their evolution through horizontal nozzles at industrial scale. An empirical correlation was proposed to predict the jet penetration, measured at various jet velocities for different particle materials and sizes [8]. However, limited studies are focused on the solid particles injection and motion due to the difficulty of tracking the injected particles and bulk solids simultaneously inside dense-phase fluidized beds. A comprehensive characterization of the dynamic behavior of the solid injection and its interaction with bed materials and fluidization gas is lacked, which is of interest to this study. With the increase of computing capability, computational fluid dynamics (CFD) has become an effective tool for the investigation of many complex phenomena in multiphase flows. Khan et al. have reviewed the application of CFD in various aspects of the fluidized bed and popular softwares with their framework. CFD modeling
https://doi.org/10.1016/j.powtec.2019.09.010 0032-5910/© 2019 Elsevier B.V. All rights reserved.
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helps to provide detailed information of multiphase flows which are challenging or impossible to be estimated experimentally [9,10]. In the present study, the multi-fluid Euler-Euler approach is adopted to numerically characterize the hydrodynamic properties of a fluidized bed with solid injection through the side inlet. The effects of various injection conditions on the overall hydrodynamic behaviors of the fluidized bed are studied. In addition, the dispersion and mixing characteristics of the injected flotsam (lighter and smaller particles that tend to float to the top of the bed) [11] with the bulk jetsam solid phase are investigated through numerical results. 2. Numerical method and procedure In this work, a two-dimensional multi-fluid Euler-Euler model was applied to simulate the fluidized bed with solid injection through the side inlet. In this approach, different phases are treated as interpenetrating continuums and a single pressure is shared by all phases [12]. Conservation equations are derived for each phase and linked by interphase momentum transfer coefficients and pressure. Solid phase properties are obtained through kinetic theory of granular flows.
CD ¼
3
8 0:687 i 24 h > > ; Rep ≤1000 <α Re 1 þ 0:15 α p Rep p
> > :
Rep ¼
p
ð8Þ
; Rep N1000
0:44
ρg up −ug dp μg
ð9Þ
The interaction of jetsam and flotsam is so complicated that no generally accepted empirical equation has been achieved. Syamlal's expression [14] was used in this study and the solid-solid exchange coefficient is of the form π 2 π2 α j ρ j α f ρ f d j þ d f g 0;jf 3 1 þ ejf þ C fr;jf 8 2 u j −u f βjf ¼ 3 3 2π ρ j d j þ ρ f d f
ð10Þ
2.1. Governing equations
Constitutive relations for solid phases are derived based on the kinetic theory of granular flows. The solids pressure is composed of a kinetic term and a second term due to particle collisions:
Hydrodynamic models of gas-solid fluidized beds are based on the conservation of mass and momentum. As neither reaction nor mass transfer occur in the studied system, the continuity equations for gas, jetsam and flotsam phases are given by
pp ¼ α p ρp Θp þ
∂ ðα i ρi Þ þ ∇ ðα i ρi ui Þ ¼ 0 ∂t
ð1Þ
where αg + αj + αf = 1, i = g, j, f. Momentum conservation equations for three phases are expressed as ∂ α g ρg ug þ ∇ α g ρg ug ug ¼ −α g ∇p þ ∇ τg þ α g ρg g ∂t X þ βpg up −ug
ð2Þ
∂ α j ρ j u j þ ∇ α j ρ j u j u j ¼ −α j ∇p−∇p j þ ∇ τ j þ α j ρ j g ∂t þβgj ug −u j þ βfj u f −u j
ð3Þ
∂ α f ρ f u f þ ∇ α f ρ f u f u f ¼ −α f ∇p−∇p f þ ∇ τ f þ α f ρ f g ∂t þβgf ug −u f þ βjf u j −u f
ð4Þ
g 0;pp ¼
1 þ 2:5α s þ 4:59α 2s þ 4:52α 3s 1 X α p þ dp 3 0:678 dp 2 1− α s =α s; max
ð12Þ
g 0;qp ¼
dp g 0;qq þ dq g 0;pp dp þ dq
ð13Þ
where αs = αj + αf. The collisional and kinetic parts, and the frictional part, are added to give the solids shear viscosity:
2 þ α g λg − μ g ∇ ug I 3
ð5Þ
2 þ α p λp − μ p ∇ u p I 3
ð6Þ
μ p:col
rffiffiffiffiffiffi Θp 4 αp ¼ α p ρp dp g 0;pp 1 þ epp π 5
μ p;kin ¼ 2.2. Constitutive equations Gidaspow's drag model [13] was applied to evaluate the momentum exchange coefficient between the gas and solid phases since it's suitable for dense fluidized beds, which combined Ergun's equation and the Wen and Yu model as follows:
β pg
ð15Þ
The kinetic part takes the expression from Gidaspow et al. [13] as
where p = j, f.
8 α p 1−α g μ g ρg α p up −ug > > þ 1:75 ; α g ≤0:8 150 > < 2 dp α g dp ¼ > 3 α p α g ρg up −ug −2:65 > > : CD αg ; α g N0:8 dp 4
ð14Þ
The collisional part of the shear viscosity is modeled as
τp ¼ α p μ p ∇ up þ uTp
ð11Þ
The radial distribution function is calculated from Ma and Ahmadi's [15] equation
μ p ¼ μ p;col þ μ p;kin þ μ p;fr
τg ¼ α g μ g ∇ ug þ uTg
X dp þ dq 3 2 1 þ eqp g 0;qp α p α q ρp Θp 2dp
pffiffiffiffiffiffiffiffiffi
2 10ρp dp Θp π 4 1 þ g 0;pp α p 1 þ epp α p 5 96α p 1 þ epp g 0;pp
ð16Þ
Particle-particle coefficient of restitution is an important physical parameter of the particle which shows the proportion of energy dissipated through interparticle collisions. And it was designated 0.90 according to earlier simulations investigating its influence on the solid flow pattern (Supplementary Fig. S1). The frictional viscosity is included using Schaeffer's [16] expression:
ð7Þ μ p;fr ¼
pp sinφ pffiffiffiffiffiffiffi 2 I 2D
ð17Þ
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To obtain the frictional pressure, the Johnson and Jackson [17] model is adopted: 2 α p −α p; min P fr ¼ 0:05 5 α p; min −α p
ð18Þ
The granular temperature for the solids phase is proportional to the kinetic energy of the particles' random motion. It can be expressed as Θp ¼
1 up;i up;i 3
ð19Þ
where up,i represents the ith component of the fluctuating solids velocity in the Cartesian coordinate system. The transport equation derived from kinetic theory has the following form:
3 ∂ α p ρp Θp þ ∇ α p ρp up Θp 2 ∂t ð20Þ ¼ −pp I þ τp : ∇up þ ∇ kΘp ∇Θp −γΘp þ φgp The model of Gidaspow et al. [13] was adopted to obtain the diffusion coefficient for granular energy kΘp
pffiffiffiffiffiffiffiffiffi 150ρp dp Θp π ¼ 384 1 þ epp g 0;pp rffiffiffiffiffiffi
2 6 Θp 1 þ α p g 0;pp 1 þ ep þ 2ρp α 2p dp 1 þ epp g 0;pp π 5
ð21Þ
The shear force at the wall is interpreted in the following form: qffiffiffiffiffiffi π pffiffiffi αp τp ¼ − ρ g Θp up;j 3ϕ α p; max p 0 6
ð22Þ
Fig. 1. Time-averaged solid velocity field, (a) predicted, (b) observed.
As discerned from the figures, the solid flow pattern predicted agreed well with the experimental data according to Fig. 1. Two pairs of counter-rotating vortices appeared in the solid velocity profile. In the upper part of the bed, particulate flow ascends in the central region while falls down along the walls. At the bottom of the bed, the direction of particle movement is completely reversed. This phenomenon can be attributed to bubble flow which has been shown in Fig. 2. Bubbles are uniformly generated on the gas distributor and tend to move toward central region when going upward, which induces particulate flow to rise near the walls and shift to the center in the lower part of the bed. Then a downflow of particles is expected in the central region due to
Here ϕ is the specularity coefficient which characterizes the friction between particles and the wall, depending on the roughness of the wall. It got assigned the value of 0.5 according to earlier simulation research about the effect on the solid flow pattern (Supplementary Fig. S1). 2.3. Simulation setup The numerical simulations performed in the present study were based on the experimental settings reported by Laverman et al. [18]. The experiment was carried out in a cylindrical bed with an inner diameter of 0.30 m, using air as fluidizing agent. Initially, particles were packed uniformly to the height of 0.30 m. More detailed simulation conditions are summarized in Table 1. After the gas-solid flow reached the fully developed state and the numerical results became stable, the general hydrodynamics were analyzed by examining the time-averaged solid velocity field and voidage distribution as shown in Figs. 1 and 2.
Table 1 Material properties and simulation settings [16]. Parameter
Value
Solid density (kg/m3) Particle diameter (μm) Minimum fluidization velocity (m/s) Interparticle restitution coefficient Internal friction angle Specularity coefficient Particle-wall restitution coefficient Gas density (kg/m3) Gas viscosity (Pa·s) Superficial gas velocity
2500 485 0.18 0.9 28.5 0.5 1.0 1.225 1.79e-5 0.63
Fig. 2. Time-averaged voidage contour predicted.
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Table 2 Physical properties of the binary mixture [17]. Property
Silica sand(Flotsam)
Glass beads(Jetsam)
Sauter mean diameter (μm) Size (μm) Sphericity Density (kg/m3) Geldart group Terminal velocity (m/s) Minimum fluidization velocity (m/s)
125 100–150 ≈1 2600 B 0.80 0.017
500 400–600 1 2540 B 4.10 0.220
the continuity of the flow. At certain bed height, the gathered bubbles coalesce and continue to ascend in the central region until reaching the bed surface. Therefore, the upper pair of solid vortices consequently forms. To investigate the behavior of particles entering the system and its impact on the overall hydrodynamics, the feed was introduced with low and high gas velocities of 1 m/s and 5 m/s respectively through a nozzle with the diameter of 3 mm along the bed side located at the heights of 0.04 m, 0.09 m, 0.13 m and 0.30 m above the distributor. The batch modes were performed with the respective injection duration of 5 s and 1 s for both low and high gas flow rates to maintain the same amount of the particles injected and another 10 s of simulations were then conducted for postprocessing. Under the low flow rate, a continuous injection mode was also simulated. Silica sand was adopted as the injected flotsam material, properties of which are shown in Table 2.
Fig. 3. Spatial profile of the gas fraction.
Fig. 4. Axial profile of average jetsam fraction.
3. Results and discussion 3.1. Model verification Several simulation runs were carried out to assess the capability of the multi-fluid model for the prediction of the dynamic behaviors of the experimental polydisperse fluidized mixtures reported by Marzocchella et al. [19]. The fluidized bed simulated was set to mimic as closely as possible the conditions in the experiments which were conducted in a gas-solid fluidized bed with the inner diameter of 0.12 m and the height of 1.5 m. The physical properties of the binary mixture are listed in Table 2. Fig. 3 provides a snapshot of the spatial profile of the gas phase volume fraction after the particulate phases in the bed have been fully fluidized. The axial distribution of average jetsam fraction predicted was in good agreement with the experimental data with total average error of 6.3%, according to Fig. 4. Particles mixed well along the vertical axis of
Fig. 5. Schematic diagram of the fluidized bed divided into four separate zones.
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Fig. 6. Time variation of flotsam concentration in different zones of the bed.
the bed except for the bottom part of the bed where the error of simulation prediction increased to about 15.4%. The larger discrepancy may arise from the different ways to determine the fluid-free jetsam concentrations. Computationally, jetsam volume fractions were calculated while the mixtures were still fluidized. However, a bed freezing procedure was adopted experimentally. The bed was “frozen” by suddenly shutting off the fluidizing gas flow after the preset fluidization time
expired. Then size distributions of solids in six individual segment were directly obtained by sieve analysis. Though the bed collapses within a quite short time, particles in the bottom center may be pushed downwards to the edge while those around the edge would ascend along the walls. In addition, the deviation of the axial profile of average jetsam fraction may occur as a result of insufficient simulation time which can be diminished by extending the time.
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Fig. 7. Time-averaged volume fraction and velocity distributions of flotsam.
Fig. 8. Time-averaged jetsam velocity fields for HJ = 0.04 m, (a) VJ = 1 m/s continuous mode, (b) VJ = 1 m/s batch mode, (c) VJ = 5 m/s batch mode.
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Fig. 9. Time-averaged lateral profiles of axial jetsam velocity at different bed heights for VJ = 5 m/s batch mode, solid lines HJ = 0.04 m, dash lines HJ = 0.09 m, dot lines HJ = 0.13 m, dash dot lines HJ = 0.30 m.
3.2. Flow and dispersion behaviors of flotsam particles The flotsam particles injected through the side inlet penetrated only a short distance into the fluidized bed before entrained by the strong gas and flotsam flow existed due to its relatively low initial momentum and then detached from the injection region and traveled further, getting into the global solid circulation. As the purpose of flotsam injection is to inject catalysts or feed reactants to the reactor, it is helpful for the optimization of the injectors through research of the injection and dispersion behaviors of flotsam particles, which was studied by analyzing the response of divided zones of the fluidized bed, time-averaged velocity field and spatial distribution of flotsam under different conditions. The fluidized bed was divided vertically at symmetry axis and horizontally at height of 0.09 m above the distributor into four zones based on the two pairs of counter-rotating vortices of jetsam
phase as shown in Fig. 5. The evolution of flotsam concentration within different zones implied the dispersion route on entering the fluidized bed. Since the dispersion paths of jetsam particles injected by both the batch way and the continuous way were the same at relatively low flow rate and the flotsam accumulated in all zones with consistently increasing concentration under continuous injection, comparison of batch processes at different rates were made as follows. It can be observed from Fig. 6 that flotsam particles spread through the following sequence of zone 1, zone 2, zone 3 and zone 4 when the injection ports were located at the height 0.04 m and 0.90 m above the distributor. The situation varied for higher injection ports in the upper pair of jetsam vortices. The flotsam path was in the order of zone 2, zone 1, zone 3 and zone 4 if injected at 0.13 m and changed to be in the order of zone 2, zone 3, zone 1 and zone 4 for the injector located at 0.30 m. Flotsam particles rapidly spread to the entire bed under either high or low injection rates. For zone 2 and zone 3, subject to the control of the stronger upper pair of jetsam vortices, flotsam concentration achieved the steady state faster than that in zone 1 and zone 4, with smoother fluctuations at the same time. Under low injection rate, the flotsam particles dispersed in a relatively weak but gentle way, the concentration of which almost became stable right at the end of the injection. While injected at higher flow rate, the flotsam phase gained more momentum initially causing larger transient concentration in the injection region, and longer time was needed to reach the steady state than the injection period. But on the whole, increasing injection rate helps flotsam particles to disperse quickly and tend to the steady distribution with a less fluctuated range. Time-averaged analysis of volume fraction and velocity distributions of flotsam phase were also conducted to characterize the flotsam flow pattern. On the whole, a distinct pair of counter-rotating vortices appeared in the middle and upper parts of the fluidized bed under different conditions, where flotsam particles ascended in the central region and descended near the walls, according to Fig. 7. The symmetry of flotsam vortices induced by continuous injection was
Fig. 10. Time- averaged jetsam volume fraction HJ = 0.04 m VJ = 1 m/s continuous mode.
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Fig. 11. Time variation of equivalent bubble diameter for HJ = 0.09 m, VJ = 1 m/s, batch mode.
Fig. 12. Time variation of equivalent bubble diameter for HJ = 0.30 m, VJ = 5 m/s, batch mode.
lower than that of batch operation. Flotsam motion in the bottom of the bed was comparatively random within the limited simulation time because of the unilateral injection and low flotsam concentration within this region. According to the time-averaged concentration distribution of flotsam, similar to the jetsam phase, flotsam particles tended to accumulate on the walls arising from the fact that bubbles tend to move upward away from the wall toward the center and coalesce at the intermediate part of the bed, then continue to rise along the centerline until break up at the bed surface. Flotsam concentration near the opposite side of the bed from the injection port changed little under various injection conditions due to rapid momentum loss after detaching the injection region and the control of the bulk jetsam vortices. The flotsam particles tended to be similarly distributed within the range from the height of 0.15 m to 0.40 m on that wall. Apart from the injection zone, the high concentration region of flotsam was mainly located in the outside and bottom parts of the vortices. In some processes, for example, the newly injected fine additives or fly ash produced of biomass and wastes combustion in bubbling fluidized beds is easy to accumulate and stick to the walls which may destroy the fluidization and affect the normal operation of the reactor [20]. Taking the predicted distribution features of flotsam particles into account, an improvement in blowing policy can be established to solve the problem efficiently.
3.3.1. Bulk solids flow field The injection of flotsam had little impact on the bulk jetsam flow pattern under various circumstances according to the time-averaged jetsam velocity field and axial jetsam velocity after injection. Fig. 8 shows that two pairs of jetsam vortices remained in the fluidized bed. The average axial velocity of jetsam in Fig. 9 for all conditions is approximately the same at certain height, with a slightly larger deviation for the central and near-wall regions. As the amount and initial velocity of flotsam released are relatively small, the momentum of these particles dissipated rapidly after entering the fluidized bed. Then the movement of flotsam mainly depends on the flow regime of the fluidization gas and bulk jetsam and thus its effect on the average axial jetsam velocity is limited. In addition, the time- averaged jetsam volume fraction spatial profiles haven't changed much as it can be seen from Fig. 10. Except that the steady feeding of flotsam particles disrupted the jetsam solid phase distribution right beside the side inlet along the wall under continuous injection at low velocity.
3.3. Effects of flotsam injection on hydrodynamics General hydrodynamics were analyzed by examining the mean flow field of bulk solids as previously mentioned in the numerical procedure part and two pairs of counter-rotating vortices formed in the fluidized bed of bulk solid phase were observed. Flotsam particles were then fed through a side inlet and penetrated into the system before they were entrained by the bulk jetsam flow, affecting both the bulk solids and gas phases. Table 3 Time-averaged bubble sizes at low injection rate in different periods for both modes.
HJ = 0.04 m HJ = 0.09 m HJ = 0.13 m HJ = 0.30 m
During injection
After injection Continuous
Batch
0.1207 0.1195 0.1182 0.1106
0.1203 0.1200 0.1191 0.1165
0.1130 0.1099 0.1099 0.1061
3.3.2. Gas flow field Bubble flow behavior is the essence of the hydrodynamics in bubbling fluidized beds. The bubble characteristics which involve size, shape, rise velocity, etc. can profoundly influence the movement of the particulate phases and are closely related to the mixing and segregation of homogeneous and/or heterogeneous particles [21]. Hence, it is important to analyze the bubble properties, mainly referring to bubble size here. However, the contribution of flotsam injection to bubble behaviors is immensely complex, affected by a lot of factors. As for the gas included in the feed injection, it may form tiny individual bubbles, leading to reduced average bubble size. On the other hand, the injected gas can be dragged into the bubbles passing by or split and pierce into them with enough energy [22]. With respect to the particles injected, the addition of flotsam may cause decrease of the average bubble size, allowing more interstitial gas to pass through at the expense of the bubble phase
Table 4 Time-averaged bubble sizes at high injection rate in different periods.
HJ = 0.04 m HJ = 0.09 m HJ = 0.13 m HJ = 0.30 m
During injection
After injection
0.1414 0.1518 0.1474 0.1428
0.1244 0.1371 0.1403 0.1224
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Fig. 13. Profiles of flotsam fraction of total solids under batch-wise injection for (a) low flow rate and (b) high flow rate.
[23,24]. Moreover, the flotsam injection is a kind of disturbance to the bubbles in the vicinity which may contributes to bubble breakup. In the present study, bubble boundaries were set by a threshold value of 0.8 for the gas volume fraction from numerical results. The time-average equivalent bubble diameter calculated without flotsam injection was 0.1305 m. Comparison of bubble sizes under various conditions are summarized as follows. For flotsam injection at relatively low rate, as depicted in Fig. 11 and Table 3, the average bubble sizes all declined slowly during the initial feeding period. As the overall influence of gas injected was rather weak, the bubble shrinking was mainly caused by the addition of flotsam. The equivalent bubble diameters continued to reduce as the simulation proceeded and then tended to a certain value. A sharper drop under batch-wise operation was observed in continuous feeding. Furthermore, higher injection port led to larger decrease in average bubble size. Since bubbles grow when moving upward, the bubble diameter increases with bed height [25]. Besides, the poor stability of larger bubbles makes it easier to breakup sheared by the flotsam injection, resulting in more significant decrease of the average bubble size. For flotsam injection at higher flow rate, as depicted in Fig. 12 and Table 4, the average bubble sizes were boosted right after the feeding and then began to decrease until reaching near the steady state in the limited simulation time. When the flotsam injection ports were located at HJ = 0.04 m and 0.30 m, the equivalent bubble diameters became smaller than that of previous flow field without flotsam injection. At the same time, bubbles were slightly enlarged while the flotsam was injected at height of 0.09 m and 0.13 m above the distributor. For bubbles in the middle section of bed have grown up a little and start to coalesce. As higher injection rate reinforced the role of injected gas phase
and promoted the growth of voids, the interaction of which was strengthened with surrounding bubbles particularly for the coalescence, bringing about the increase of the average bubble sizes. In the long term, the average bubble sizes for both batch processes should be similar on account of the same addition amount of flotsam particles but it took time for the inlet effects to dissipate. 3.4. Mixing properties of flotsam and jetsam particles The solid mixing is of great importance to selectivities and conversions for gas-solid reactions in the fluidized bed which affects the gas-solid contacting, degree of catalyst deactivation, convective heat transfer via particulate phases, etc. [26]. Hence it is of practical importance to investigate the mixing of injected flotsam particles with bulk jetsam materials inside the fluidized bed qualitatively and quantitatively. Fig. 13 exhibits the fluid-free flotsam concentration at different levels above the distributor under both batch processes. In general, the flotsam mixed acceptably with the bulk jetsam phase, with mild segregation in the bottom of the fluidized bed which became more serious as the injection port was raised higher. On top of this, reducing the injection rate may improve the mixing degree particularly for the bottom part. The mixing homogeneity of a binary mixture was usually estimated by the relative standard deviation in the literature, defined as the ratio of the standard deviation to the mean composition [27], the standard deviation based on flotsam concentration was adopted in the current study. RSD ¼
σ C
ð23Þ
Fig. 14. Time variations of σ at low flow rate for (a) continuous mode and (b) batch mode.
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impacts of flotsam injection were examined through time-averaged analysis on solid velocity and concentration profiles which was found to be relatively weak and limited in the injection region. The equivalent bubble diameter was calculated so that proper injection setting can be chosen with desired size for specific applications. Finally, the mixing homogeneity was characterized by the standard deviation based on flotsam concentration. The mixing quality reduced during the injection period and then recovered soon after the injection was terminated. Lower injection flow rate was believed to contribute to better mixing especially for the duration of injection. Therefore, quick dispersion and better mixing need to be balanced to determine the proper injection condition accordingly. Nomenclature
Fig. 15. Time variations of σ at high flow rate.
σ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP 2 u N t i¼1 C−C i N−1
ð24Þ
where RSD is the relative standard deviation, C is the mean composition of flotsam in particle mixture and σ is the standard deviation in which the decrease of its value means the increase of mixing homogeneity. As shown in Fig. 14, during the initial injection period at low flow rate, the standard deviations of injection ports at the height of 0.04 m and 0.30 m maintained a level lower than those of other two injection sites, indicating better mixing of flotsam injected with bulk jetsam phase. In the continuous way adopted, all the standard deviations kept increasing with the addition of flotsam particles and the differences among them were narrowed after about 5 s. The condition varied under the batch process. The standard deviations reached their peaks at the end of flotsam injection and then began to decrease until achieving the steady state. However, the differences of the standard deviations were shrunk likewise and the similar mixing quality was obtained under different situations finally. Under higher injection rate, as shown in Fig. 15, the standard deviations for injection ports at different levels increased sharply at the beginning and then rapidly decreased once the injection was terminated, with a slightly higher peak when injected at the height of 0.3 m. At last, the standard deviations became stable and attained a similar value, implying similar mixing degree. Comparing the time variations of the standard deviations under different injection rates, it was found that increasing injection rate led to narrower peak and higher peak value. Therefore, high injection rate helps the system to reach the steady mixing state rapidly while low injection rate offers the procedure relatively high mixing homogeneity. 4. Conclusions Euler - Euler simulations based on the kinetic theory of granular flow have been performed in a gas-solid fluidized bed with horizontal injection of flotsam particles to investigate the effects on the general flow hydrodynamics as well as mixing with the bulk materials. A comprehensive research was carried out to study the flotsam flow behaviors. Time variation of flotsam concentration in four bed zones provided deeper understanding of flotsam path on entering the system. For faster and steadier dispersion, high injection rate at the upper pair of vortices was preferred. Mean flotsam concentration distribution needs to be considered in design and operation of fluidized beds. For all operation conditions simulated, the bed materials were mixed acceptably well except in the bottom section and decreasing injection rate at the lower pair of vortices helps to improve the mixing condition. In addition, the
Letters Cfr CD d e g g0 I2D kΘ p Re t u
the coefficient of friction drag coefficient particle diameter the coefficient of restitution gravitational acceleration radial distribution function second invariant of the deviatoric stress tensor the diffusion coefficient for granular energy pressure Reynolds number time velocity
Greek symbols α volume fraction β interphase exchange coefficient the collisional dissipation of granular energy γΘ λ bulk viscosity μ shear viscosity ρ density φ the angle of internal friction ϕ specularity coefficient Θ granular temperature τ stress tensor Subscripts g gas phase j jetsam phase f flotsam phase Supplementary data to this article can be found online at https://doi. org/10.1016/j.powtec.2019.09.010. Acknowledgements The authors gratefully acknowledge financial support from the Project of National Natural Science Foundation of China (Grant No. 91434205), the National Science Fund for Distinguished Young (Grant No. 21525627), the National Natural Science Foundation for Young (Grant No. 21808198), the Science Fund for Creative Research Groups of National Natural Science Foundation of China (Grant No. 61621002), and the Fundamental Research Funds for the Central Universities (2017QNA4029). References [1] D. Kunii, O. Levenspiel, Fluidization Engineering, John Wiley & Sons, 1969. [2] D. Agba, A.D. Salman, M.J. Hounslow, Fluidized bed applications preface, Chem. Eng. Sci. 62 (2007) 1. [3] G.N. Ahuja, A.W. Patwardhan, CFD and experimental studies of solids hold-up distribution and circulation patterns in gas-solid fluidized beds, Chem. Eng. J. 143 (2008) 147–160.
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[16] D.G. Schaeffer, Instability in the evolution equations describing incompressible granular flow, J. Diff. Eq. 66 (1987) 19–50. [17] P.C. Johnson, R. Jackson, Frictional-collisional constitutive relations for granular materials with application to plane shearing, J. Fluid Mech. 176 (1987) 67–93. [18] J.A. Laverman, X. Fan, A. Ingram, M.v.S. Annaland, D.J. Parker, J.P.K. Seville, J.A.M. Kuipers, Experimental study on the influence of bedmaterial on the scaling of solids circulation patterns in 3D bubbling gas–solid fluidized beds of glass and polyethylene using positron emission particle tracking, Powder Technol. 224 (2012) 297–305. [19] A. Marzocchella, P. Salatino, V. Di Pastena, L. Lirer, Transient fluidization and segregation of binary mixtures of particles, AICHE J. 46 (11) (2000) 2175–2182. [20] G. Pifer, Bubbling fluidized-bed technology serves combustion need for biomass, Pulp. Pap. 79 (1) (2005) 54–57. [21] B. Du, L.-S. Fan, F. Wei, W. Warsito, Gas and solid mixing in a turbulent fluidized bed, AICHE J. 48 (2002) 1896–1909. [22] R. Jan de Korte, J.C. Schouten, C.M. Van den Bleek, Controlling bubble coalescence in a fluidized-bed model using bubble injection, AICHE J. 47 (2001) 851–860. [23] G.C. Brouwer, E.C. Wagner, J.R. van Ommen, R.F. Mudde, Effects of pressure and fines content on bubble diameter in a fluidized bed studied using fast X-ray tomography, Chem. Eng. J. 207–208 (2012) 711–717. [24] Y.L. Gu, A. Ozel, S. Sundaresan, Numerical studies of the effects of fines on fluidization, AICHE J. 62 (7) (2016) 2271–2281. [25] S. Mori, C.Y. Wen, Estimation of bubble diameter in gaseous fluidized beds, AICHE J. 21 (1975) 109–115. [26] M. Askarishahi, M.S. Salehi, H.R. Godini, G. Wozny, CFD study on solids flow pattern and solids mixing characteristics in bubbling fluidized bed: effect of fluidization velocity and bed aspect ratio, Powder Technol. 274 (2015) 379–392. [27] W.J. Thiel, P.L. Stephenson, Assessing the homogeneity of an ordered mixture, Powder Technol. 31 (1982) 45–50.
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Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Numerical study of particle injection into a gas-solid fluidized bed Ying Liu a, Sihang Tian a, Shaoshuo Li a, Yao Yang a, Zhengliang Huang a, Jingyuan Sun a,⁎, Zuwei Liao a, Jingdai Wang a, Yongrong Yang a, Jian Yang b a b
State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China Institute of Pharmaceutical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China
a r t i c l e
i n f o
Article history: Received 13 November 2018 Received in revised form 14 February 2019 Accepted 6 September 2019 Available online xxxx Keywords: Computational fluid dynamics Gas-solid fluidized bed Particle injection Flow behaviors Solid mixing
a b s t r a c t The flow and dispersion behaviors of the fine particle injection in a gas-solid fluidized bed were studied numerically based on the two-dimensional multi-fluid model. The injection path and flow pattern of the flotsam solids were investigated. A distinct pair of counter-rotating vortices of flotsam particles appeared in the middle and upper parts of the fluidized bed. Higher injection rate was preferred for faster flotsam dispersion. The effects of flotsam injection on bed hydrodynamics were investigated with regard to the velocity distribution and volume fraction of bulk materials and the bubble size. Consequently, the mixing properties of the flotsam particles and bulk solids were quantified by the fluid-free flotsam fraction profile and the standard deviation. The fluidized bed was mixed acceptably with modest local segregation for all the conditions simulated. Lower injection velocity made contributions to better mixing especially for the duration of injection. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Gas-solid fluidized beds provide high heat and mass transfer rates as well as intense mixing and contact of different phases in a number of industrial processes, including traditional processes such as combustion, gasification, oil refining, olefin polymerization, calcination, drying and granulation, as well as emerging fields such as biotechnology, pharmaceutical manufacturing and environmental industries [1,2]. These transfer behaviors mainly originate from the solid circulation inside the fluidized bed, in which the solid motion is induced by gas bubbles and streams rising through the bed. The solid flow pattern is also a significant factor that impacts other bed characteristics such as the chemical reaction degree and the particle growth rate and it varies with operation parameters like the superficial gas velocity, bed aspect ratio, solid phase properties and the configurations of gas distributor. Moreover, many processes involve solid feeding through the side inlet, with physical properties different from the bulk materials, for instance, catalyst injection in manufacturing of polyolefins and reactant feeding in biomass combustion. In the gas phase olefin polymerization process, a few fine catalyst particles are usually injected into the dense section of the fluidized bed reactor with gas flow. These highly active particles quickly disperse inside the bed while catalyzing the polymerization of gas phase monomers, resulting in significant local heat generation. The fines penetrate into the system and are then entrained by the bulk solid circulation which mainly governs the heat removal via convective heat ⁎ Corresponding author. E-mail address: [email protected] (J. Sun).
transfer. If the particles are not well dispersed, the heat transfer would be hindered and particle agglomeration may be prone to occur. Therefore, it is of vital importance to understand the way in which the solid particles enter the fluidized bed and then disperse and mix with the bed materials in order to control the reaction intensity and heat transfer, so that an efficient design and operation of fluidized bed can be achieved. Considerable experimental investigations have been carried out to explore the underlying mechanisms of the solid flow patterns as well as gas jet penetration and mixing in fluidized beds [3–6]. Li et al. obtained the solid and gas flow patterns using positron emission particle tracking (PEPT). The impact of particle properties, bed design and operation conditions were investigated and four different solid flow patterns were founded under various conditions [7]. Panariello et al. employed X-ray imaging technique to observe the jets penetration length and their evolution through horizontal nozzles at industrial scale. An empirical correlation was proposed to predict the jet penetration, measured at various jet velocities for different particle materials and sizes [8]. However, limited studies are focused on the solid particles injection and motion due to the difficulty of tracking the injected particles and bulk solids simultaneously inside dense-phase fluidized beds. A comprehensive characterization of the dynamic behavior of the solid injection and its interaction with bed materials and fluidization gas is lacked, which is of interest to this study. With the increase of computing capability, computational fluid dynamics (CFD) has become an effective tool for the investigation of many complex phenomena in multiphase flows. Khan et al. have reviewed the application of CFD in various aspects of the fluidized bed and popular softwares with their framework. CFD modeling
https://doi.org/10.1016/j.powtec.2019.09.010 0032-5910/© 2019 Elsevier B.V. All rights reserved.
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helps to provide detailed information of multiphase flows which are challenging or impossible to be estimated experimentally [9,10]. In the present study, the multi-fluid Euler-Euler approach is adopted to numerically characterize the hydrodynamic properties of a fluidized bed with solid injection through the side inlet. The effects of various injection conditions on the overall hydrodynamic behaviors of the fluidized bed are studied. In addition, the dispersion and mixing characteristics of the injected flotsam (lighter and smaller particles that tend to float to the top of the bed) [11] with the bulk jetsam solid phase are investigated through numerical results. 2. Numerical method and procedure In this work, a two-dimensional multi-fluid Euler-Euler model was applied to simulate the fluidized bed with solid injection through the side inlet. In this approach, different phases are treated as interpenetrating continuums and a single pressure is shared by all phases [12]. Conservation equations are derived for each phase and linked by interphase momentum transfer coefficients and pressure. Solid phase properties are obtained through kinetic theory of granular flows.
CD ¼
3
8 0:687 i 24 h > > ; Rep ≤1000 <α Re 1 þ 0:15 α p Rep p
> > :
Rep ¼
p
ð8Þ
; Rep N1000
0:44
ρg up −ug dp μg
ð9Þ
The interaction of jetsam and flotsam is so complicated that no generally accepted empirical equation has been achieved. Syamlal's expression [14] was used in this study and the solid-solid exchange coefficient is of the form π 2 π2 α j ρ j α f ρ f d j þ d f g 0;jf 3 1 þ ejf þ C fr;jf 8 2 u j −u f βjf ¼ 3 3 2π ρ j d j þ ρ f d f
ð10Þ
2.1. Governing equations
Constitutive relations for solid phases are derived based on the kinetic theory of granular flows. The solids pressure is composed of a kinetic term and a second term due to particle collisions:
Hydrodynamic models of gas-solid fluidized beds are based on the conservation of mass and momentum. As neither reaction nor mass transfer occur in the studied system, the continuity equations for gas, jetsam and flotsam phases are given by
pp ¼ α p ρp Θp þ
∂ ðα i ρi Þ þ ∇ ðα i ρi ui Þ ¼ 0 ∂t
ð1Þ
where αg + αj + αf = 1, i = g, j, f. Momentum conservation equations for three phases are expressed as ∂ α g ρg ug þ ∇ α g ρg ug ug ¼ −α g ∇p þ ∇ τg þ α g ρg g ∂t X þ βpg up −ug
ð2Þ
∂ α j ρ j u j þ ∇ α j ρ j u j u j ¼ −α j ∇p−∇p j þ ∇ τ j þ α j ρ j g ∂t þβgj ug −u j þ βfj u f −u j
ð3Þ
∂ α f ρ f u f þ ∇ α f ρ f u f u f ¼ −α f ∇p−∇p f þ ∇ τ f þ α f ρ f g ∂t þβgf ug −u f þ βjf u j −u f
ð4Þ
g 0;pp ¼
1 þ 2:5α s þ 4:59α 2s þ 4:52α 3s 1 X α p þ dp 3 0:678 dp 2 1− α s =α s; max
ð12Þ
g 0;qp ¼
dp g 0;qq þ dq g 0;pp dp þ dq
ð13Þ
where αs = αj + αf. The collisional and kinetic parts, and the frictional part, are added to give the solids shear viscosity:
2 þ α g λg − μ g ∇ ug I 3
ð5Þ
2 þ α p λp − μ p ∇ u p I 3
ð6Þ
μ p:col
rffiffiffiffiffiffi Θp 4 αp ¼ α p ρp dp g 0;pp 1 þ epp π 5
μ p;kin ¼ 2.2. Constitutive equations Gidaspow's drag model [13] was applied to evaluate the momentum exchange coefficient between the gas and solid phases since it's suitable for dense fluidized beds, which combined Ergun's equation and the Wen and Yu model as follows:
β pg
ð15Þ
The kinetic part takes the expression from Gidaspow et al. [13] as
where p = j, f.
8 α p 1−α g μ g ρg α p up −ug > > þ 1:75 ; α g ≤0:8 150 > < 2 dp α g dp ¼ > 3 α p α g ρg up −ug −2:65 > > : CD αg ; α g N0:8 dp 4
ð14Þ
The collisional part of the shear viscosity is modeled as
τp ¼ α p μ p ∇ up þ uTp
ð11Þ
The radial distribution function is calculated from Ma and Ahmadi's [15] equation
μ p ¼ μ p;col þ μ p;kin þ μ p;fr
τg ¼ α g μ g ∇ ug þ uTg
X dp þ dq 3 2 1 þ eqp g 0;qp α p α q ρp Θp 2dp
pffiffiffiffiffiffiffiffiffi
2 10ρp dp Θp π 4 1 þ g 0;pp α p 1 þ epp α p 5 96α p 1 þ epp g 0;pp
ð16Þ
Particle-particle coefficient of restitution is an important physical parameter of the particle which shows the proportion of energy dissipated through interparticle collisions. And it was designated 0.90 according to earlier simulations investigating its influence on the solid flow pattern (Supplementary Fig. S1). The frictional viscosity is included using Schaeffer's [16] expression:
ð7Þ μ p;fr ¼
pp sinφ pffiffiffiffiffiffiffi 2 I 2D
ð17Þ
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To obtain the frictional pressure, the Johnson and Jackson [17] model is adopted: 2 α p −α p; min P fr ¼ 0:05 5 α p; min −α p
ð18Þ
The granular temperature for the solids phase is proportional to the kinetic energy of the particles' random motion. It can be expressed as Θp ¼
1 up;i up;i 3
ð19Þ
where up,i represents the ith component of the fluctuating solids velocity in the Cartesian coordinate system. The transport equation derived from kinetic theory has the following form:
3 ∂ α p ρp Θp þ ∇ α p ρp up Θp 2 ∂t ð20Þ ¼ −pp I þ τp : ∇up þ ∇ kΘp ∇Θp −γΘp þ φgp The model of Gidaspow et al. [13] was adopted to obtain the diffusion coefficient for granular energy kΘp
pffiffiffiffiffiffiffiffiffi 150ρp dp Θp π ¼ 384 1 þ epp g 0;pp rffiffiffiffiffiffi
2 6 Θp 1 þ α p g 0;pp 1 þ ep þ 2ρp α 2p dp 1 þ epp g 0;pp π 5
ð21Þ
The shear force at the wall is interpreted in the following form: qffiffiffiffiffiffi π pffiffiffi αp τp ¼ − ρ g Θp up;j 3ϕ α p; max p 0 6
ð22Þ
Fig. 1. Time-averaged solid velocity field, (a) predicted, (b) observed.
As discerned from the figures, the solid flow pattern predicted agreed well with the experimental data according to Fig. 1. Two pairs of counter-rotating vortices appeared in the solid velocity profile. In the upper part of the bed, particulate flow ascends in the central region while falls down along the walls. At the bottom of the bed, the direction of particle movement is completely reversed. This phenomenon can be attributed to bubble flow which has been shown in Fig. 2. Bubbles are uniformly generated on the gas distributor and tend to move toward central region when going upward, which induces particulate flow to rise near the walls and shift to the center in the lower part of the bed. Then a downflow of particles is expected in the central region due to
Here ϕ is the specularity coefficient which characterizes the friction between particles and the wall, depending on the roughness of the wall. It got assigned the value of 0.5 according to earlier simulation research about the effect on the solid flow pattern (Supplementary Fig. S1). 2.3. Simulation setup The numerical simulations performed in the present study were based on the experimental settings reported by Laverman et al. [18]. The experiment was carried out in a cylindrical bed with an inner diameter of 0.30 m, using air as fluidizing agent. Initially, particles were packed uniformly to the height of 0.30 m. More detailed simulation conditions are summarized in Table 1. After the gas-solid flow reached the fully developed state and the numerical results became stable, the general hydrodynamics were analyzed by examining the time-averaged solid velocity field and voidage distribution as shown in Figs. 1 and 2.
Table 1 Material properties and simulation settings [16]. Parameter
Value
Solid density (kg/m3) Particle diameter (μm) Minimum fluidization velocity (m/s) Interparticle restitution coefficient Internal friction angle Specularity coefficient Particle-wall restitution coefficient Gas density (kg/m3) Gas viscosity (Pa·s) Superficial gas velocity
2500 485 0.18 0.9 28.5 0.5 1.0 1.225 1.79e-5 0.63
Fig. 2. Time-averaged voidage contour predicted.
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Table 2 Physical properties of the binary mixture [17]. Property
Silica sand(Flotsam)
Glass beads(Jetsam)
Sauter mean diameter (μm) Size (μm) Sphericity Density (kg/m3) Geldart group Terminal velocity (m/s) Minimum fluidization velocity (m/s)
125 100–150 ≈1 2600 B 0.80 0.017
500 400–600 1 2540 B 4.10 0.220
the continuity of the flow. At certain bed height, the gathered bubbles coalesce and continue to ascend in the central region until reaching the bed surface. Therefore, the upper pair of solid vortices consequently forms. To investigate the behavior of particles entering the system and its impact on the overall hydrodynamics, the feed was introduced with low and high gas velocities of 1 m/s and 5 m/s respectively through a nozzle with the diameter of 3 mm along the bed side located at the heights of 0.04 m, 0.09 m, 0.13 m and 0.30 m above the distributor. The batch modes were performed with the respective injection duration of 5 s and 1 s for both low and high gas flow rates to maintain the same amount of the particles injected and another 10 s of simulations were then conducted for postprocessing. Under the low flow rate, a continuous injection mode was also simulated. Silica sand was adopted as the injected flotsam material, properties of which are shown in Table 2.
Fig. 3. Spatial profile of the gas fraction.
Fig. 4. Axial profile of average jetsam fraction.
3. Results and discussion 3.1. Model verification Several simulation runs were carried out to assess the capability of the multi-fluid model for the prediction of the dynamic behaviors of the experimental polydisperse fluidized mixtures reported by Marzocchella et al. [19]. The fluidized bed simulated was set to mimic as closely as possible the conditions in the experiments which were conducted in a gas-solid fluidized bed with the inner diameter of 0.12 m and the height of 1.5 m. The physical properties of the binary mixture are listed in Table 2. Fig. 3 provides a snapshot of the spatial profile of the gas phase volume fraction after the particulate phases in the bed have been fully fluidized. The axial distribution of average jetsam fraction predicted was in good agreement with the experimental data with total average error of 6.3%, according to Fig. 4. Particles mixed well along the vertical axis of
Fig. 5. Schematic diagram of the fluidized bed divided into four separate zones.
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Fig. 6. Time variation of flotsam concentration in different zones of the bed.
the bed except for the bottom part of the bed where the error of simulation prediction increased to about 15.4%. The larger discrepancy may arise from the different ways to determine the fluid-free jetsam concentrations. Computationally, jetsam volume fractions were calculated while the mixtures were still fluidized. However, a bed freezing procedure was adopted experimentally. The bed was “frozen” by suddenly shutting off the fluidizing gas flow after the preset fluidization time
expired. Then size distributions of solids in six individual segment were directly obtained by sieve analysis. Though the bed collapses within a quite short time, particles in the bottom center may be pushed downwards to the edge while those around the edge would ascend along the walls. In addition, the deviation of the axial profile of average jetsam fraction may occur as a result of insufficient simulation time which can be diminished by extending the time.
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Fig. 7. Time-averaged volume fraction and velocity distributions of flotsam.
Fig. 8. Time-averaged jetsam velocity fields for HJ = 0.04 m, (a) VJ = 1 m/s continuous mode, (b) VJ = 1 m/s batch mode, (c) VJ = 5 m/s batch mode.
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Fig. 9. Time-averaged lateral profiles of axial jetsam velocity at different bed heights for VJ = 5 m/s batch mode, solid lines HJ = 0.04 m, dash lines HJ = 0.09 m, dot lines HJ = 0.13 m, dash dot lines HJ = 0.30 m.
3.2. Flow and dispersion behaviors of flotsam particles The flotsam particles injected through the side inlet penetrated only a short distance into the fluidized bed before entrained by the strong gas and flotsam flow existed due to its relatively low initial momentum and then detached from the injection region and traveled further, getting into the global solid circulation. As the purpose of flotsam injection is to inject catalysts or feed reactants to the reactor, it is helpful for the optimization of the injectors through research of the injection and dispersion behaviors of flotsam particles, which was studied by analyzing the response of divided zones of the fluidized bed, time-averaged velocity field and spatial distribution of flotsam under different conditions. The fluidized bed was divided vertically at symmetry axis and horizontally at height of 0.09 m above the distributor into four zones based on the two pairs of counter-rotating vortices of jetsam
phase as shown in Fig. 5. The evolution of flotsam concentration within different zones implied the dispersion route on entering the fluidized bed. Since the dispersion paths of jetsam particles injected by both the batch way and the continuous way were the same at relatively low flow rate and the flotsam accumulated in all zones with consistently increasing concentration under continuous injection, comparison of batch processes at different rates were made as follows. It can be observed from Fig. 6 that flotsam particles spread through the following sequence of zone 1, zone 2, zone 3 and zone 4 when the injection ports were located at the height 0.04 m and 0.90 m above the distributor. The situation varied for higher injection ports in the upper pair of jetsam vortices. The flotsam path was in the order of zone 2, zone 1, zone 3 and zone 4 if injected at 0.13 m and changed to be in the order of zone 2, zone 3, zone 1 and zone 4 for the injector located at 0.30 m. Flotsam particles rapidly spread to the entire bed under either high or low injection rates. For zone 2 and zone 3, subject to the control of the stronger upper pair of jetsam vortices, flotsam concentration achieved the steady state faster than that in zone 1 and zone 4, with smoother fluctuations at the same time. Under low injection rate, the flotsam particles dispersed in a relatively weak but gentle way, the concentration of which almost became stable right at the end of the injection. While injected at higher flow rate, the flotsam phase gained more momentum initially causing larger transient concentration in the injection region, and longer time was needed to reach the steady state than the injection period. But on the whole, increasing injection rate helps flotsam particles to disperse quickly and tend to the steady distribution with a less fluctuated range. Time-averaged analysis of volume fraction and velocity distributions of flotsam phase were also conducted to characterize the flotsam flow pattern. On the whole, a distinct pair of counter-rotating vortices appeared in the middle and upper parts of the fluidized bed under different conditions, where flotsam particles ascended in the central region and descended near the walls, according to Fig. 7. The symmetry of flotsam vortices induced by continuous injection was
Fig. 10. Time- averaged jetsam volume fraction HJ = 0.04 m VJ = 1 m/s continuous mode.
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Fig. 11. Time variation of equivalent bubble diameter for HJ = 0.09 m, VJ = 1 m/s, batch mode.
Fig. 12. Time variation of equivalent bubble diameter for HJ = 0.30 m, VJ = 5 m/s, batch mode.
lower than that of batch operation. Flotsam motion in the bottom of the bed was comparatively random within the limited simulation time because of the unilateral injection and low flotsam concentration within this region. According to the time-averaged concentration distribution of flotsam, similar to the jetsam phase, flotsam particles tended to accumulate on the walls arising from the fact that bubbles tend to move upward away from the wall toward the center and coalesce at the intermediate part of the bed, then continue to rise along the centerline until break up at the bed surface. Flotsam concentration near the opposite side of the bed from the injection port changed little under various injection conditions due to rapid momentum loss after detaching the injection region and the control of the bulk jetsam vortices. The flotsam particles tended to be similarly distributed within the range from the height of 0.15 m to 0.40 m on that wall. Apart from the injection zone, the high concentration region of flotsam was mainly located in the outside and bottom parts of the vortices. In some processes, for example, the newly injected fine additives or fly ash produced of biomass and wastes combustion in bubbling fluidized beds is easy to accumulate and stick to the walls which may destroy the fluidization and affect the normal operation of the reactor [20]. Taking the predicted distribution features of flotsam particles into account, an improvement in blowing policy can be established to solve the problem efficiently.
3.3.1. Bulk solids flow field The injection of flotsam had little impact on the bulk jetsam flow pattern under various circumstances according to the time-averaged jetsam velocity field and axial jetsam velocity after injection. Fig. 8 shows that two pairs of jetsam vortices remained in the fluidized bed. The average axial velocity of jetsam in Fig. 9 for all conditions is approximately the same at certain height, with a slightly larger deviation for the central and near-wall regions. As the amount and initial velocity of flotsam released are relatively small, the momentum of these particles dissipated rapidly after entering the fluidized bed. Then the movement of flotsam mainly depends on the flow regime of the fluidization gas and bulk jetsam and thus its effect on the average axial jetsam velocity is limited. In addition, the time- averaged jetsam volume fraction spatial profiles haven't changed much as it can be seen from Fig. 10. Except that the steady feeding of flotsam particles disrupted the jetsam solid phase distribution right beside the side inlet along the wall under continuous injection at low velocity.
3.3. Effects of flotsam injection on hydrodynamics General hydrodynamics were analyzed by examining the mean flow field of bulk solids as previously mentioned in the numerical procedure part and two pairs of counter-rotating vortices formed in the fluidized bed of bulk solid phase were observed. Flotsam particles were then fed through a side inlet and penetrated into the system before they were entrained by the bulk jetsam flow, affecting both the bulk solids and gas phases. Table 3 Time-averaged bubble sizes at low injection rate in different periods for both modes.
HJ = 0.04 m HJ = 0.09 m HJ = 0.13 m HJ = 0.30 m
During injection
After injection Continuous
Batch
0.1207 0.1195 0.1182 0.1106
0.1203 0.1200 0.1191 0.1165
0.1130 0.1099 0.1099 0.1061
3.3.2. Gas flow field Bubble flow behavior is the essence of the hydrodynamics in bubbling fluidized beds. The bubble characteristics which involve size, shape, rise velocity, etc. can profoundly influence the movement of the particulate phases and are closely related to the mixing and segregation of homogeneous and/or heterogeneous particles [21]. Hence, it is important to analyze the bubble properties, mainly referring to bubble size here. However, the contribution of flotsam injection to bubble behaviors is immensely complex, affected by a lot of factors. As for the gas included in the feed injection, it may form tiny individual bubbles, leading to reduced average bubble size. On the other hand, the injected gas can be dragged into the bubbles passing by or split and pierce into them with enough energy [22]. With respect to the particles injected, the addition of flotsam may cause decrease of the average bubble size, allowing more interstitial gas to pass through at the expense of the bubble phase
Table 4 Time-averaged bubble sizes at high injection rate in different periods.
HJ = 0.04 m HJ = 0.09 m HJ = 0.13 m HJ = 0.30 m
During injection
After injection
0.1414 0.1518 0.1474 0.1428
0.1244 0.1371 0.1403 0.1224
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Fig. 13. Profiles of flotsam fraction of total solids under batch-wise injection for (a) low flow rate and (b) high flow rate.
[23,24]. Moreover, the flotsam injection is a kind of disturbance to the bubbles in the vicinity which may contributes to bubble breakup. In the present study, bubble boundaries were set by a threshold value of 0.8 for the gas volume fraction from numerical results. The time-average equivalent bubble diameter calculated without flotsam injection was 0.1305 m. Comparison of bubble sizes under various conditions are summarized as follows. For flotsam injection at relatively low rate, as depicted in Fig. 11 and Table 3, the average bubble sizes all declined slowly during the initial feeding period. As the overall influence of gas injected was rather weak, the bubble shrinking was mainly caused by the addition of flotsam. The equivalent bubble diameters continued to reduce as the simulation proceeded and then tended to a certain value. A sharper drop under batch-wise operation was observed in continuous feeding. Furthermore, higher injection port led to larger decrease in average bubble size. Since bubbles grow when moving upward, the bubble diameter increases with bed height [25]. Besides, the poor stability of larger bubbles makes it easier to breakup sheared by the flotsam injection, resulting in more significant decrease of the average bubble size. For flotsam injection at higher flow rate, as depicted in Fig. 12 and Table 4, the average bubble sizes were boosted right after the feeding and then began to decrease until reaching near the steady state in the limited simulation time. When the flotsam injection ports were located at HJ = 0.04 m and 0.30 m, the equivalent bubble diameters became smaller than that of previous flow field without flotsam injection. At the same time, bubbles were slightly enlarged while the flotsam was injected at height of 0.09 m and 0.13 m above the distributor. For bubbles in the middle section of bed have grown up a little and start to coalesce. As higher injection rate reinforced the role of injected gas phase
and promoted the growth of voids, the interaction of which was strengthened with surrounding bubbles particularly for the coalescence, bringing about the increase of the average bubble sizes. In the long term, the average bubble sizes for both batch processes should be similar on account of the same addition amount of flotsam particles but it took time for the inlet effects to dissipate. 3.4. Mixing properties of flotsam and jetsam particles The solid mixing is of great importance to selectivities and conversions for gas-solid reactions in the fluidized bed which affects the gas-solid contacting, degree of catalyst deactivation, convective heat transfer via particulate phases, etc. [26]. Hence it is of practical importance to investigate the mixing of injected flotsam particles with bulk jetsam materials inside the fluidized bed qualitatively and quantitatively. Fig. 13 exhibits the fluid-free flotsam concentration at different levels above the distributor under both batch processes. In general, the flotsam mixed acceptably with the bulk jetsam phase, with mild segregation in the bottom of the fluidized bed which became more serious as the injection port was raised higher. On top of this, reducing the injection rate may improve the mixing degree particularly for the bottom part. The mixing homogeneity of a binary mixture was usually estimated by the relative standard deviation in the literature, defined as the ratio of the standard deviation to the mean composition [27], the standard deviation based on flotsam concentration was adopted in the current study. RSD ¼
σ C
ð23Þ
Fig. 14. Time variations of σ at low flow rate for (a) continuous mode and (b) batch mode.
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impacts of flotsam injection were examined through time-averaged analysis on solid velocity and concentration profiles which was found to be relatively weak and limited in the injection region. The equivalent bubble diameter was calculated so that proper injection setting can be chosen with desired size for specific applications. Finally, the mixing homogeneity was characterized by the standard deviation based on flotsam concentration. The mixing quality reduced during the injection period and then recovered soon after the injection was terminated. Lower injection flow rate was believed to contribute to better mixing especially for the duration of injection. Therefore, quick dispersion and better mixing need to be balanced to determine the proper injection condition accordingly. Nomenclature
Fig. 15. Time variations of σ at high flow rate.
σ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP 2 u N t i¼1 C−C i N−1
ð24Þ
where RSD is the relative standard deviation, C is the mean composition of flotsam in particle mixture and σ is the standard deviation in which the decrease of its value means the increase of mixing homogeneity. As shown in Fig. 14, during the initial injection period at low flow rate, the standard deviations of injection ports at the height of 0.04 m and 0.30 m maintained a level lower than those of other two injection sites, indicating better mixing of flotsam injected with bulk jetsam phase. In the continuous way adopted, all the standard deviations kept increasing with the addition of flotsam particles and the differences among them were narrowed after about 5 s. The condition varied under the batch process. The standard deviations reached their peaks at the end of flotsam injection and then began to decrease until achieving the steady state. However, the differences of the standard deviations were shrunk likewise and the similar mixing quality was obtained under different situations finally. Under higher injection rate, as shown in Fig. 15, the standard deviations for injection ports at different levels increased sharply at the beginning and then rapidly decreased once the injection was terminated, with a slightly higher peak when injected at the height of 0.3 m. At last, the standard deviations became stable and attained a similar value, implying similar mixing degree. Comparing the time variations of the standard deviations under different injection rates, it was found that increasing injection rate led to narrower peak and higher peak value. Therefore, high injection rate helps the system to reach the steady mixing state rapidly while low injection rate offers the procedure relatively high mixing homogeneity. 4. Conclusions Euler - Euler simulations based on the kinetic theory of granular flow have been performed in a gas-solid fluidized bed with horizontal injection of flotsam particles to investigate the effects on the general flow hydrodynamics as well as mixing with the bulk materials. A comprehensive research was carried out to study the flotsam flow behaviors. Time variation of flotsam concentration in four bed zones provided deeper understanding of flotsam path on entering the system. For faster and steadier dispersion, high injection rate at the upper pair of vortices was preferred. Mean flotsam concentration distribution needs to be considered in design and operation of fluidized beds. For all operation conditions simulated, the bed materials were mixed acceptably well except in the bottom section and decreasing injection rate at the lower pair of vortices helps to improve the mixing condition. In addition, the
Letters Cfr CD d e g g0 I2D kΘ p Re t u
the coefficient of friction drag coefficient particle diameter the coefficient of restitution gravitational acceleration radial distribution function second invariant of the deviatoric stress tensor the diffusion coefficient for granular energy pressure Reynolds number time velocity
Greek symbols α volume fraction β interphase exchange coefficient the collisional dissipation of granular energy γΘ λ bulk viscosity μ shear viscosity ρ density φ the angle of internal friction ϕ specularity coefficient Θ granular temperature τ stress tensor Subscripts g gas phase j jetsam phase f flotsam phase Supplementary data to this article can be found online at https://doi. org/10.1016/j.powtec.2019.09.010. Acknowledgements The authors gratefully acknowledge financial support from the Project of National Natural Science Foundation of China (Grant No. 91434205), the National Science Fund for Distinguished Young (Grant No. 21525627), the National Natural Science Foundation for Young (Grant No. 21808198), the Science Fund for Creative Research Groups of National Natural Science Foundation of China (Grant No. 61621002), and the Fundamental Research Funds for the Central Universities (2017QNA4029). References [1] D. Kunii, O. Levenspiel, Fluidization Engineering, John Wiley & Sons, 1969. [2] D. Agba, A.D. Salman, M.J. Hounslow, Fluidized bed applications preface, Chem. Eng. Sci. 62 (2007) 1. [3] G.N. Ahuja, A.W. Patwardhan, CFD and experimental studies of solids hold-up distribution and circulation patterns in gas-solid fluidized beds, Chem. Eng. J. 143 (2008) 147–160.
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Please cite this article as: Y. Liu, S. Tian, S. Li, et al., Numerical study of particle injection into a gas-solid fluidized bed, Powder Technol., https://doi. org/10.1016/j.powtec.2019.09.010