Experimental investigation on gas-solid

Powder Technology 307 (2017) 175–183

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Experimental investigation on gas-solid hydrodynamics of coarse particles in a two-dimensional spouted bed He Zhang, Malin Liu, Tianjin Li ⁎, Zhiyong Huang, Xinming Sun, Hanliang Bo, Yujie Dong Key Laboratory for Advanced Reactor Engineering and Safety of Ministry of Education, Institute of Nuclear and New Energy Technology, Collaborative Innovation Center for Advanced Nuclear Energy Technology, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 15 September 2016 Received in revised form 5 November 2016 Accepted 15 November 2016 Available online 30 November 2016 Keywords: Flow pattern Particle velocity Spout diameter Coarse particle Two-dimensional spouted bed CFD-DEM coupling

a b s t r a c t The gas-solid hydrodynamics of coarse particles in a two-dimensional spouted bed (2DSB) are measured using 6 mm glass beads to obtain quantitative experimental results. A one-dimensional mathematical model based on gas-solid mass and momentum balance is used to characterize the spout-annulus interaction and to further interpret the experimental results. The superficial velocity and static bed height are in the range of 2.58 to 4.39 m/s and 8.0 to 13.3 cm, respectively. Pressure fluctuation periodicity of the bed pressure drop is characterized by power spectral density (PSD) analysis. The whole-field particle velocity profiles in 2DSB are obtained by high speed CCD camera and PIV technique. The results show that particle motion in the spout in the present 2DSB experiments is dominated by the balance of drag force, solid stress and gravitation. The existence of obvious solid stress from particle impaction and friction leads to energy dissipation, which limits the increase of vertical particle velocity along the spout axis (vyc) in the spout and results in a flat stage of vyc with slight fluctuation near the bottom of the fountain. The solid stress also contributes to the nearly flat peak of lateral profile of downward particle velocity in the annulus. These detailed results are helpful for understanding the gas hydrodynamics and particle motion behavior of coarse particles in 2DSB, and for verification of the extended CFD-DEM coupling method for particle size approaching fluid cell size. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Spouted beds have been studied for handling coarse particles in many areas, such as drying, granulation, particle coating, gasification, pyrolysis and combustion [1]. The development of draft tube spouted beds also provides a new kind of non-mechanical solids feeder, i.e. the spouted bed feeder [2–4], for vertical pneumatic conveying of coarse particles. A novel non-mechanical solids feeding device, called draft tube type feeder (DTF) which is based on the combination of draft tube technique and local fluidization principle, has been developed by our group [5,6] for application in absorber sphere pneumatic conveying in pebble bed High Temperature Gas-Cooled Reactor (HTGR or HTR). HTGR is the Generation IV advanced nuclear reactor, which has the advantages of inherent safety, high efficiency and multiple purpose application potential [7–9]. Absorber sphere conveying in pebble bed HTGR is a special application of pneumatic conveying technique in nuclear engineering [10,11]. Our group has studied absorber sphere pneumatic conveying for many years [6,12]. The main features of absorber sphere pneumatic conveying are as follows: (a) coarse particles (e.g. particle ⁎ Corresponding author at: Institute of Nuclear and New Energy Technology, Tsinghua University, 30 Shuangqing Rd, Haidian, Beijing 100084, China. E-mail address: [email protected] (T. J. Li).

http://dx.doi.org/10.1016/j.powtec.2016.11.024 0032-5910/© 2016 Elsevier B.V. All rights reserved.

diameter dp = 6 mm), (b) small ratio of riser internal diameter to particle diameter (Dt/dp) in the range of 6 to 10, (c) high pressure helium gas used as conveying gas, and (d) high temperature environment for feeder operation (about 250 °C, requires non-mechanical feeder for high reliability). Although the draft tube type feeder developed in our previous work meets the need of project requirements, there are still strong demands on interpretation the mechanism of coarse particle entrainment and vertical conveying for the design optimization of the feeder and conveying process. The accurate prediction of particle motion behavior and gas flow hydrodynamics is important for the system design and process optimization for the absorber spheres conveying in pebble bed HTGR. CFD-DEM coupling simulation is an effective method at particle scale for understanding the relationship between macroscopic behavior and microscopic properties of gas-solid flow system [13–19]. The common CFD-DEM coupling is based on the momentum exchange in each discretized fluid flow cell, in which the particle-induced force on the fluid flow is treated as a body force. This method fails when particle size approach (including larger than) the fluid cell size. The absorber spheres conveying through the draft tube type feeder and riser pipe (featured with dp = 6 mm and Dt/dp of about 8) in pebble bed HTGR is such an example in engineering practice. The demand from the engineering practice promotes the research of CFD-DEM coupling simulation for particle size approaching fluid cell size.

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H. Zhang et al. / Powder Technology 307 (2017) 175–183

There are two types of strategy reported in literature to deal with the problem of particle size approaching fluid cell size in CFD-DEM coupling simulation. One strategy is to decrease flow field resolution by using rough fluid cell size to meet the requirement of common CFD-DEM method. This strategy is used by Yang et al. [20] in the simulation study of gas-solid flow of soybeans in spouted bed with draft tube (equivalent dp = 6 mm, draft tube diameter of 35 mm). The other strategy is to develop extended CFD-DEM method by modifying the interphase coupling calculation method. Several kinds of concept have been proposed in developing the extended CFD-DEM method, e.g. the local averaging concept [21], porous media concept [22,23], two-grid concept [24–28], distribution function concept [29], diffusion-based concept [30,31] and particle meshing method concept [32]. The verification of prediction accuracy of these extended CFD-DEM method for gas-solid flow is insufficient, since the choice of proper parameters remains an open question (e.g., the distribution width in distribution function, which strongly affects the distribution of the force of a particle on the fluid to an appropriate volume of the fluid) [31]. The particle diameter and Reynolds number are two important factors for choosing the proper distribution parameters [31]. There are only a few open publications on quantitative experimental study on particle motion behavior of coarse particles (dp N 4 mm) in gassolid flow system. These publications are mainly in the study of pneumatic conveying and spouted beds. Vasquez et al. [33] measured the plug velocity and plug length of four types of coarse particles in horizontal plug conveying (dp in the range of 4 to 5.41 mm, Dt ~ 50 mm). Neto et al. [34] reported experiments of soybeans (equivalent dp = 6 mm) in a 3-Dimensional (3D) spouted bed with draft tube (inner diameter 35 mm), in which only pressure drop was measured. Neuwirth et al. [35] reported the particle motion behavior of spherical polymer particles with a mean diameter of 6 mm in a 3D rotor granulator with the Magnetic Particle Tracking technique. Chen et al. [36] investigated distribution of particle velocity of corn (equivalent volume diameter 6.6 mm) in a 3D conical cylindrical spouted bed with the slightly-invasive optical fiber endoscope measurement. Olazar et al. [37] reported the particle motion behavior of dp = 4 and 5 mm coarse particle in 3D spouted beds with the slightly-invasive optical fiber probes measurement. The measurement results might be unrealistic because of the improper application of the optical fiber probes [38]. The two-dimensional spouted bed (2DSB) have the advantage in obtain whole-field detailed information of particle motion behavior with the non-invasive PIV techniques [39–41]. However, the particle diameter are all no N 2.5 mm in the reported conical 2DSB [42] and the flat bottomed 2DSB experiments [22,38]. The main purpose of this study is to make a better understanding of gas-solid hydrodynamics of coarse particles in a 2DSB, and to obtain detailed whole-field experimental results of particle motion behavior of coarse particle for verification of the extended CFD-DEM method. Section 2 describes the experimental setup and procedure. In Section 3, we describe the flow pattern and measure the velocity profiles of the coarse particles in the 2DSB. Furthermore, a one-dimensional mathematical model based on gas-solid mass and momentum balance is used to characterize the spout-annulus interaction and to further interpret the experimental results. 2. Experimental setup 2.1. Apparatus The experimental system (shown in Fig. 1) is mainly composed of a 2DSB, air compressor, pressurizer, rotameter, PIV measuring system and high frequency pressure acquisition system. Geometric parameters of the 2DSB and particle properties are summarized in Table 1. To ensure the bed operates at a ‘two-dimensional’ not a ‘slot-rectangular’ mode, the ratio of column thickness to column width (Lz/Lc) used in this study is small enough to eliminate the third-dimensional effects along

Fig. 1. Schematic diagram of the two-dimensional spouted bed experimental system.

bed thickness [43]. The ratio of column thickness to particle diameter (Lz/dp) is larger than the critical value of 5 to reduce the wall friction effects [44]. 2DSB is made of plexiglass to observe and film particle movement. Spherical glass beads of dp = 6 mm and particle density ρp = 2518 kg/m3 are used in the experiments. Glass beads are loaded into 2DSB at a low gas velocity to inhibit particles falling into the gas inlet slot. Six different mass loadings of 400, 500, 600, 700, 800 and 900 g are considered, which approximately correspond to the static bed height (Hb) of 8.0, 9.2, 10.4, 11.4, 12.4 and 13.3 cm in the wedge section of the bed, respectively. Ambient air is used as the source gas. Gas inlet flow rate (Q0) is controlled and measured by the rotameter, which is increased slowly to the value of operating condition. Superficial gas velocity Ug with respect to the bed column cross section of 210 × 36 mm is in the range of 2.58 to 4.39 m/s. The experimental condition of Ug = 4.39 m/s and different static bed height of 12.4, 10.4 and 8.0 cm are referred as case 1, 2 and 3, respectively, for convenience. Images of particle movement are recorded by a high speed CCD camera during stable spouting. The camera provides 670 pixel × 900 pixel resolution at 1000 fps (frames per second) and can continuously record for several seconds for these parameters. The flow field of the recorded section is illuminated by two identical 150 W LED lights symmetrically placed beside the bed at an angle smaller than 45° to avoid undesirable reflections [22,23]. 2.2. Pressure measurement The pressure measurement point is at the side wall of gas inlet slot and 30 mm below the bed bottom. The sampling time is 10 s with a Table 1 Geometric parameters of the 2DSB and particle properties. Items

Unit

Values

Column width, Lc Included angle, θ Column thickness, Lz Slot width, λ Bottom width, Li Column height, Hc Particle diameter, dp Particle density, ρp

mm ° mm mm mm m mm kg/m3

210 60 36 30 45 1.2 6 2518


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3. Results and discussion

friction between particles. The spout “neck” in case 3 seems relatively weak (Fig. 2(b)). It might be attributed to the flow pattern transition near the dilute spouting regime as reported by Olazar et al. [48] and Barrozo et al. [49], since the average voidage for the entire bed with particles is estimated to be 0.80 in case 3. Fig. 3(a) illustrates the typical time sequence of the bed pressure drop in case 1. PSD analysis of the pressure drop in case 1 shows a dominant frequency Fd at 4.88 Hz (Fig. 3(b)), which equals to the dominant frequency of the periodic particle motion of incoherent spouting (shown in Fig. 2(a)). The effect of static bed height Hb on dominant frequency of bed pressure drop at Ug = 4.39 m/s is shown in Fig. 3(c). The dominant frequency almost linearly decreases from 6.10 to 4.64 Hz with static bed height increasing from 8.0 to 13.3 cm, which is owing to the slower response to the gas flow at a deeper bed in 2DSB [39]. Previous work with dp = 2 mm [39] and dp = 1.44 mm [47] glass beads in 2DSB showed that the dominant frequency slightly increased with increasing superficial gas velocity (along arrow direction for each Hb in Fig. 3(c)). It can be found that when the particle diameter increased, the dominant frequency decreased at the same static bed height, even with the increased superficial gas velocity.

3.1. Flow pattern

3.2. Time-averaged particle velocity profiles

Incoherent spouting with a dynamic changing of the spout shape is observed. Fig. 2(a)–(b) show the images of flow patterns within one cycle T in case 1 and 3, respectively. It can be found that the cycle time of the incoherent spouting for the two cases is 0.204 and 0.168 s (i.e. frequency 4.90 and 5.95 Hz), respectively. Similar incoherent spouting in 2DSB with dp = 2 mm [39–41], 2.5 mm [42] and 1.44 mm [47] glass beads have also been reported in the literature. The outermost particles in fountain descending zone collide with the column side wall in case 1 (Fig. 2(a)) as a result of the large particle size and small ratio of Lc/dp. With Hb increasing from 8.0 to 12.4 cm, particles in the annulus and fountain increase, which makes the fountain denser. It is noted that the spout “neck” in case 1 seems quite dense (t = 0.051 and 0.102 s in Fig. 2(a)), which may result in strong impaction and

3.2.1. Particle velocity field of entire bed Fig. 4 illustrates a typical time-averaged particle velocity field of the entire bed for case 1. It is seen that the phenomena of particles colliding with the column side wall in fountain descending zone have also been obviously observed. Two vortex are observed. Particles rapidly accelerate in the low part of the spout, gradually decelerate in the fountain upward core, and accelerate again in the fountain descending zone. Before further discussion on particle velocity profile, the spout length should be defined. It is noted that the boundary between spout and fountain along spout axis in conical 2DSB is not as clear as in 3D cylindrical spouted bed, since the bed surface is inclined and dynamically changing with incoherent spouting in conical 2DSB. There were two definitions of the spout length in conical 2DSB reported in literature.

sampling frequency of 1 kHz for each experiment. The periodicity of bed pressure drop can be used as an index of gas-solid flow dynamic in a 2DSB. Power spectral density (PSD) is used to analyze frequency distributions of the pressure drop. 2.3. Particle image velocimetry (PIV) PIV technique is originally used for fluid flow measurement. It has been applied to obtain particle velocities in two-dimensional granular flow systems [38,39,42,45]. The direct normalized cross-correlation (DNCC) algorithm is chosen in the commercial PIV software. The interrogation window (IW) size is recommended to be 16 pixel × 32 pixel with a 50% overlap for entire bed according to Adrian and Westerweel's conclusion [46] and the flow characteristics in the 2DSB. To obtain particle motion behavior more precisely, 1000 sequence images with time interval Δt = 1 ms and 750 sequence images with Δt = 4 ms are used in each case in the PIV analysis for the dilute zones (spout or fountain) and dense zones (annulus), respectively.

Fig. 2. Flow patterns of 6 mm coarse particles in: (a) Ug = 4.39 m/s and Hb = 12.4 cm (case 1); (b) Ug = 4.39 m/s and Hb = 8.0 cm (case 3).

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Fig. 4. Typical particle velocity field of the entire bed in Ug = 4.39 m/s and Hb = 12.4 cm (case 1).

in the fountain usually fall back to impact with the particles moving upward in case 1 and 2. It results in a slight fluctuation of vyc in the flat stage for these two cases. The fluctuation of vyc in the flat stage is also the reason why we do not choose the height of the maximum vyc as the definition of spout length. The flat peak were previously observed in the 2DSB experiments with dp = 2 mm [39–41] and 2.5 mm [42] glass beads, but the slight fluctuation of vyc found in the present study have not been previously observed. It is an obvious characteristic of the larger particles falling back in the fountain in 2DSB. Swasdisevi et al. [50] observed the 8 mm

Fig. 3. The characteristics of bed pressure drop of coarse particles in 2DSB: (a) typical results of pressure drop changing with time in Ug = 4.39 m/s and Hb = 12.4 cm (case 1); (b) PSD analysis of bed pressure drop in case 1; (c) effect of static bed height Hb on dominant frequency Fd at Ug = 4.39 m/s and comparison with literature.

One definition was the height of “vortex core” used by Liu et al. [39]. The other was the height corresponding to the maximum vertical particle velocity along spout axis [42], after which particles began to monotonically decelerate. The former definition is adopted in the present study, since it gives a height approximately equal to the lower part of the inclined bed surface. 3.2.2. Particle velocity in the spout or fountain Fig. 5(a) shows the longitudinal profile of vertical particle velocity along the spout axis (vyc) in case 1 to 3. Particles are rapidly accelerated from bed level zero to about 5 cm, and then particle velocity increases slowly to a nearly flat stage with a maximum value of near 1.2 m/s in case 1. The acceleration of particles in the lower part of spout is quite similar for the three cases with the same superficial velocity. vyc in case 2 is the maximum one in the three cases at the bed level below about 3 cm. With Hb increasing from 8.0 to 12.4 cm, the maximum vyc slightly increases, while the height of flat stage and the height of bed expansion also increase. It is observed from the CCD images that particles

Fig. 5. Longitudinal profiles of vertical particle velocity along spout axis: (a) Ug = 4.39 m/s, (b) Hb = 8.0 cm.


coarse particles falling back in the spout at low superficial velocity in the CFD-DEM simulation of a 2DSB with draft plate. The phenomena of particles falling back and reacceleration in the fountain have also been reported by Liu et al. [51] in the CFD-DEM simulation of high-density Fe particles in a 2DSB. The falling back of large particles or high-density particles are attributed to the larger gravitational force than the drag force in that region. Fig. 5(b) shows the longitudinal profile of vertical particle velocity along the spout axis under three superficial gas velocity Ug = 3.20, 3.72 and 4.39 m/s and an identical static bed height Hb = 8.0 cm. It is seen that vyc is obviously affected by Ug. With Ug increasing from 3.20 to 4.39 m/s, the maximum vyc increases from 0.68 to 1.08 m/s. The height of nearly flat stage and bed expansion also obviously increases with increasing Ug. Liu et al. [39] was the first one to argue that the lateral profiles of vertical particle velocity in the spout exhibit self-similarity of a third-degree polynomial function in 2DSB experiments using dp = 2 mm particles. This flow self-similarity has been subsequently found in 2DSB experiments with dp = 2.5 mm wet particles. It is found that 6 mm coarse particles still obey the self-similarity of a third-degree polynomial function in our 2DSB experiments. Fig. 6(a) illustrates the lateral profiles of vertical particle velocity (vy) in the spout for case 1. The vertical particle velocity increases with increasing the bed level, while it decreases from the maximum vyc at the spout axis to zero at the spout-annulus interface at each bed level. Fig. 6(b) shows the relationship between dimensionless velocity vy/vyc and dimensionless lateral position x/rs in case 1, where rs is the spout radius or spout half width corresponding to bed level y. The solid line represents the fitted cubical function among bed levels of 3.85 to 10.45 cm with the correlation coefficient R2 = 0.9884. The inset represents a fitted cubical function of a single bed level of 7.15 cm, which shows a slightly better cubical function with R2 = 0.9986.

179

3.2.3. Particle velocity in the annulus Fig. 7 shows the lateral profiles of the downward vertical particle velocity in the annulus at various bed levels in case 1 and 3. With the lateral distance increases from the spout-annulus interface, the vertical particle velocity rapidly increases from zero to a maximum value around 0.16 and 0.12 m/s for the two cases, respectively. A nearly flat peak appears with the bed level y in the range of 7.15 to 10.45 cm and 6.05 to 7.15 cm in case 1 and 3, respectively. This flat peak enlarges with increasing the bed level in case 1 and 3, and similar results are obtained in case 2 (not shown). The reason for the emergence of this flat peak will be further explained by the solid stress from the one-dimensional model prediction results in the following section. The vertical particle velocity rapidly decreases as it approaches the conical bed wall. The maximum vertical particle velocity slightly increases with increasing the bed level in case 3, while it slightly decreases from 0.163 m/s to 0.156 m/s with increasing the bed level from 4.95 to 7.15 cm and remains constant with further increasing the bed level to 10.45 cm in case 1. Liu et al. [39] investigated the lateral profiles of the downward vertical particle velocity in the annulus in a 2DSB experiments with dp = 2 mm particles. It was reported that the maximum vertical particle velocity in the annulus obviously increased with increasing the bed level. San Jose et al. [52] drew the opposite conclusion in the previous study of cylindrical bed with dp = 3.5 mm particles. They reported that the maximum downward vertical particle velocity in the annulus decreased with increasing the bed level, since the cross-sectional area of the annulus became smaller in the lower bed level. Experimental results in our present study show that the variation of the maximum vertical particle velocity in the annulus with the bed level are affected by the operation conditions. 3.3. Spout-annulus interaction In this section, we use a one-dimensional (1D) mathematical model based on gas-solid mass and momentum balance to characterize the spout-annulus mixing and flow split of coarse particles in 2DSB, and

Fig. 6. Lateral profiles of vertical particle velocity in the spout at various bed levels in Ug = 4.39 m/s and Hb = 12.4 cm (case 1): (a) original; (b) normalized, vy by vyc and x by rs.

Fig. 7. Lateral profiles of the vertical particle velocity in the annulus at various bed levels in: (a) Ug = 4.39 m/s and Hb = 12.4 cm (case 1); (b) Ug = 4.39 m/s and Hb = 8.0 cm (case 3).

180


to further interpret the experimental results. This 1D model has been previously reported by Zhu et al. [42] to analyze the effects of cohesion on the granular acceleration behavior in the dilute spout of a 2DSB. Porosity, gas velocity and pressure gradient are assumed to be uniform in the 1D model at each bed level. Before further discussion on spout-annulus interaction, the spout width xs should be analyzed, since it represents the characteristics of spout-annulus interface. Spout width is identified as the boundary of spout-annulus interface where the vertical particle velocity is zero and the bed level below spout length. Fig. 8 shows the variation of spout width along spout axis for case 1 to 3. It can be seen that spout width xs increases first linearly and then rapidly with increasing bed level y. xs decreases with increasing Hb at the bed level above about 3.6 cm. Below the bed level of about 3.6 cm, xs in case 2 turns to be the smallest one. The relatively smaller xs might be a possible reason for the slightly higher vyc at the low bed level shown in Fig. 5(a). The dimensionless annulus width (single side of the bed) to particle diameter is 10.6, 9.0 and 7.9 near the spout end in case 1 to 3, respectively. The small dimensionless annulus width might contribute to the nearly flat peak in the lateral profiles of the downward vertical particle velocity in the annulus. Similar trend of the spout width increasing first linearly and then rapidly with increasing the bed level were also reported in the previous study with dp = 2 mm [39–41] and 2.5 mm [42] dry glass beads in a 2DSB. The spout width in the previous studies were obviously smaller, owing to a smaller slot inlet width of 9 mm. With the spout width xs, mean particle vertical velocity in the spout (vs) and particle lateral velocity at spout-annulus interface (vxi) determined by PIV measurements, the porosity in the spout (εs) are numerically obtained by solving the solid phase mass conservation of the spout (Eq. (1)). ρp xs

d½ð1−εs Þvs dGs ¼ ¼ 2vxi ð1−εa Þρp dy dyLz

ð1Þ

where Gs is the solid circulation rate defined as the integral of particle mass flux and interface area along the bed height. vs is represented by vyc/2 because of the cubical function between vy/vyc and x/rs in the spout. The annulus voidage εa is estimated to be 0.39 according to the previous work [49] and our experimental measurements of glass beads random loose packing in the 2DSB. Fig. 9 shows the results of porosity distributions in the spout for case 1 to 3. The porosity εs is unity when y equals to zero, since there is no particles at the inlet of 2DSB. εs decreases with bed level increasing, owing to particle entrainment along the whole spout length. The higher static bed height Hb gives a lower porosity for the same bed level. One of the reasons is that more particles are entrained into the spout from the annulus with higher static bed height. Another reason is the decrease of spout width with increasing Hb at bed level above about 4.0 cm (shown

Fig. 9. The longitudinal profile of porosity distributions in the spout predicted by onedimensional model for Ug = 4.39 m/s and different Hb of 12.4, 10.4 and 8.0 cm (case 1 to 3).

in Fig. 8), which contributes to the further decreasing of porosity. Near the spout end, the porosity decreases to 0.53, 0.72 and 0.79 for case 1 to 3, respectively, which clearly shows the transition from the dense to relatively dilute flow in the spout. It is noted that the particle concentration near the spout end in case 1 increases to 0.47, which is near the random loose packing fraction of about 0.61 for 6 mm coarse particles in the 2DSB. With εs obtained above, interstitial gas velocity in the spout (us), superficial gas velocity in the annulus (Ua) and pressure gradient in the spout (dp/dy) can be obtained by the combination of the gas phase momentum conservation of the spout (Eq. (2)), integral form for the mass conservation of gas phase (Eq. (3)) and Ergun equation. Ergun equation is simplified as Eq. (4) in the 1D model, in which it is determined by the viscous resistance due to the relatively low slip velocity in the annulus, since the pressure drop in the spout equals to that in the annulus at the same bed level. ρf

d εs u2s dp þ βðvs −us Þ ¼ −εs dy dy

ð2Þ

U a Aa ¼ Q 0 −εs us As dp ¼ dy

ð3Þ

dp ð1−εa Þ2 η f ≈ −150 U 2 a dy a ε3a d

ð4Þ

p

where ρf, ηf and Q0 are the gas density, gas viscosity and gas flow rate, Aa and As represents the area of the annulus and the spout, respectively. It should be noted that the interphase momentum transfer coefficient (β) is based on the correlation proposed by Koch and Hill [53] from the Lattice-Boltzmann method (LBM), since it is more suitable for gassolid flow of coarse particles [22]. It is slightly different from the interphase momentum transfer coefficient chosen in the previous study of Zhu et al. [42]. β¼

18η f ε2s εp 2

dp

1 F 0 εp þ F 3 εp Rep 2

8 pffiffiffiffiffiffiffiffiffiffi 135 > > < 1 þ 3 εp =2 þ 64 εp ln εp þ 16:14εp F 0 εp ¼ 1 þ 0:681εp −8:48ε2p þ 8:16ε3p > > : 10εp =ε3s

Fig. 8. Variation of spout width along spout axis for Ug = 4.39 m/s with different Hb of 12.4, 10.4 and 8.0 cm (case 1 to 3).

ð5:1Þ

εp b0:4

ð5:2Þ

εp ≥0:4

F 3 εp ¼ 0:0673 þ 0:212εp þ 0:0232=ε 5s

ð5:3Þ

Rep ¼ εs ρ f jus −vs jdp =η f

ð5:4Þ

where εp = 1 – εs and Rep is the particle Reynolds number. Substituting


Eq. (3) into Eq. (4) and then finally into Eq. (2), us can be numerically solved for the known εs and vs. The solutions of Ua and dp/dy are also obtained. Fig. 10 shows the predicted results for the interstitial gas velocity in the spout (us) for case 1 to 3. The interstitial gas velocity in the spout decreases with increasing bed level due to the flow split from the spout to annulus. The interstitial gas velocity near the spout end are 4.8, 8.9 and 13.4 m/s, respectively, for case 1 to 3. An obvious slow decrease of the interstitial gas velocity for case 1 is observed for the bed level near the spout end. The overall gas fraction from the spout to annulus till bed level y can be expressed as fy = (1 – εsusxsLz/Q0) × 100% with proper unit. The evolution characteristics of xs (shown in Fig. 8), εs (shown in Fig. 9) and us result in the overall gas fraction from the spout to annulus near the spout end (fse) increasing from 23% to 79% (3.43 times) with increasing static bed height Hb from 8.0 to 12.4 cm (1.55 times) (shown in inset of Fig. 10). The results indicate that the static bed height Hb is an important parameter to influence the gas fraction from spout to annulus. Zhao et al. [41] reported the gas fraction near the spout end of about 20% for dp = 2 mm particles in the CFD-DEM simulation of a 2DSB with Ug = 1.58 m/s and Hb = 10 cm. Zhu et al. [42] reported the gas fraction near the spout end of 35.7% for dp = 2.5 mm dry particles in a 2DSB experiments with Ug = 1.08 m/s and Hb = 7 cm. Takeuchi et al. [54] reported that 25% gases flow into the annulus from the spout in the simulation of a 3D spouted beds. Spreutels et al. [55] reported that the overall gas fraction from spout to annulus increases from 70% to 90% (about 1.3 times) as the static bed height increases from 15 to 25 cm (1.67 times) in the experiments of a 3D conical spouted bed using 3 mm glass beads. These results indicate that the gas fraction behavior in spouted bed is complex. Further work are needed to make a better understanding of the gas fraction characteristics especially when predicting heat and mass transfer performance in a spouted bed. With the solutions of us, εs, dp/dy and the measured vs, the contribution of various terms to the acceleration of particles in the spout are further analyzed by employing conservation of the solid-phase momentum [42,56]:

d ð1−ε s Þv2s dp ¼ −ð1−εs Þ þ βðus −vs Þ−ð1−εs Þ ρp dy dy dσ s ρp −ρ f g− dy

ð6Þ

The solid stress term dσs/dy is obtained by numerically solving Eq. (6). The dimensionless solid stress, (−dσs/dy)/((1 – εs)ρpg), gives as large as –4 at the bottom of the spout in case 1 to 3, while the dimensionless drag with respect to gravitation is estimated to be 6. The ratio of pressure gradient force to gravitational force, (−dp/dy)/(ρpg), has a magnitude of 0.1 or much lower, which implies that the pressure-gradient force is too low to overcome the gravitation. It should be pointed out

Fig. 10. The longitudinal profile of interstitial gas velocity in the spout predicted by onedimensional model for Ug = 4.39 m/s with different Hb of 12.4, 10.4 and 8.0 cm (case 1 to 3).

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that the solid stress in the spout is fairly appreciable in case 1 to 3 in the present study. It is quite different from the previous work of Zhu et al. [42] with dp = 2.5 mm particles in a 2DSB, where the solid stress almost vanished in the dilute spout. We notice a weak reverse flow of gas above the inlet from the annulus to the spout in the 1D model prediction results. A maximum reverse flow of about 6% of Q0 at the bed level of 2.2 cm is obtained in case 3. No reverse flow is obtained in case 1 which has higher static bed height. The small reverse gas flow from the annulus to the spout just above the inlet has been previously reported in the CFD-DEM simulation of 3D spouted bed [57] and in the review article of spouting of biomass particles [58]. The 1D model prediction results reveal that particle motion in the spout in the present 2DSB experiments is dominated by the balance of drag force, solid stress and gravitation. The existence of obvious solid stress from particle impaction and friction leads to energy dissipation, which limits the increase of vyc in the spout and results in a flat stage of vyc with slight fluctuation near the bottom of the fountain (shown in Fig. 5(a)). The obvious solid stress may spread to the spout-annulus interface. It results in confinement of the downward particle flow in the annulus, which further result in the nearly flat peak of the lateral profile of the vertical particle velocity in the annulus in the present study (shown in Fig. 7). The prediction results from the one-dimensional mathematical model are helpful for understanding the gas hydrodynamics and particle motion behavior of coarse particles in 2DSB. These detailed results of flow pattern and particle velocity profile are also helpful for verification of the extended CFD-DEM coupling simulation. 4. Conclusion The gas-solid hydrodynamics of coarse particles in a 2DSB were measured by using dp = 6 mm glass beads to obtain detailed quantitative experimental results. A one-dimensional mathematical model based on gas-solid mass and momentum balance is used to investigate the spout-annulus interaction and to further interpret the experimental results. The superficial velocity and static bed height are in the range of 2.58 to 4.39 m/s and 8.0 to 13.3 cm, respectively. Some different characteristics are observed owing to coarse particles. The conclusions are as follows. (1) The dominant frequency linearly decreases from 6.10 to 4.64 Hz with static bed height increasing from 8.0 to 13.3 cm for Ug = 4.39 m/s. The phenomena of particles collide with the side wall are observed in fountain descending zone, owing to the larger particle size and smaller ratio of bed column width to particle diameter. (2) The vertical particle velocity along the spout axis vyc shows a fast increase followed by a nearly flat stage with increasing bed level. Slight fluctuation of vyc in the flat stage is observed, owing to particles in the fountain region falling back to impact with the particles moving upward. It is an obvious characteristic of the large particles falling back near the bottom of the fountain in 2DSB. The 6 mm coarse particles still obey the flow self-similarity of vertical particle velocity in the spout of a third-degree polynomial function. (3) A nearly flat peak appears in the lateral profiles of the downward vertical particle velocity in the annulus. The variation of maximum downward vertical particle velocity in the annulus with the bed level is affected by the operation conditions. (4) The static bed height is an important parameter to influence the overall gas fraction from spout to annulus. With increasing static bed height Hb for case 1 to 3, the evolution characteristics of xs, εs and us result in the gas fraction near the spout end increasing from 23% to 79%. (5) The 1D model prediction results reveal that particle motion in the spout in the present 2DSB experiments is dominated by the

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balance of drag force, solid stress and gravitation. Solid stress plays important roles on particle motion behavior of coarse particles in the 2DSB. The existence of obvious solid stress from particle impaction and friction leads to energy dissipation, which limits the increase of vyc in the spout and results in a flat stage of vyc with slight fluctuation near the bottom of the fountain. The spreading of solid stress from the spout to the spout-annulus interface may confine the downward particle flow in the annulus, which results in the emergence of the nearly flat peak of the lateral profile of downward particle velocity in the annulus. Nomenclature Lc column width, mm θ included angle, ° Lz column thickness, mm λ slot width, mm Li bottom width, mm Hc column height, m Dt pipe internal diameter, mm dp particle diameter, mm ρp particle density, kg/m3 Hb static bed height, cm Q0 gas inlet flow rate, m3/s Ug superficial gas velocity, m/s Fd dominant frequency, Hz vyc vertical particle velocity along spout axis, m/s vy vertical particle velocity, m/s rs spout radius or spout half width, mm xs spout width, mm vs mean particle vertical velocity in the spout, m/s vxi particle lateral velocity at spout-annulus interface, m/s εs porosity in the spout, – Gs solid circulation rate, kg/s εa annulus voidage, – us interstitial gas velocity in the spout, m/s Ua superficial gas velocity in the annulus, m/s dp/dy pressure gradient in the spout, Pa/m ρf gas density, kg/m3 Aa area of the annulus, m2 As area of the spout, m2 Rep particle Reynolds number, – fy overall gas fraction from spout to annulus till bed level y, % fse overall gas fraction near spout end, % σs solid stress, Pa Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51506113 and No. 21306097). We would like to thank the National S&T Major Project (Grant No. ZX06901) for the partial financial support of the two-dimensional spouted bed. The author Tianjin Li is very grateful to Prof. Shuiqing Li, Dr. Xianglong Zhao, Dr. Guanqing Liu, Dr. Runru Zhu and Associate Prof. Nan Gui at Tsinghua University for helpful discussions. References [1] N. Epstein, J.R. Grace, Spouted and Spout-Fluid Beds: Fundamentals and Applications, Cambridge University Press, 2011. [2] M.C. Ferreira, E.M.V. Silva, J.T. Freire, Analysis of a one-dimensional fluid dynamic model for dilute gas-solid flow in a pneumatic dryer with a spouted bed type solid feeding system, Dry. Technol. 16 (1998) 1971–1985. [3] I.A. Costa, M. do Carmo Ferreira, J.T. Freire, Analysis of regime transitions and flow instabilities in vertical conveying of coarse particles using different solids feeding systems, Can. J. Chem. Eng. 82 (2004) 48–59. [4] R.C. Sousa, A.R.F. de Almeida, M.C. Ferreira, J.T. Freire, Analysis of fluid dynamics and thermal behavior using a vertical conveyor with a spouted bed feeder, Dry. Technol. 28 (2010) 1277–1287.

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