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Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet
PTEC-14651; No of Pages 10 Powder Technology xxx (2019) xxx
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Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet S. Shrestha, J.Q. Gan, Z.Y. Zhou ⁎ ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, VIC 3800, Australia
a r t i c l e
i n f o
Available online xxxx Keywords: Fluidization Bubble coalescence Bubble properties Single jet CFD-DEM
a b s t r a c t Advancement in the knowledge of bubble dynamics and properties can significantly aid to improve the design and operation of gas-solid fluidized beds. In this work, bubble properties in a single jet fluidized bed were studied by the combined approach of CFD and DEM. The results illustrated that the process of the continuous injection of a central air jet to the bed was successfully reproduced, with the formation of a series of bubbles which rise through the bed and burst at the bed top. During this process, the series of bubbles align vertically which show coalescence in three different levels of the bed. However, the coalescence patterns depend upon jet velocity and are fairly regular. The bubbles are categorized into two types: primary/leading bubbles and trailing bubbles. The size of primary bubbles keeps increasing with bed height while the size of trailing bubbles decreases since trailing bubbles coalesce with primary bubbles. Primary bubbles, although formed at different times, are of similar shape at different heights of the bed while trailing bubbles are generally elongated in shape. Trailing bubbles have a higher velocity than primary bubbles. The spatial analysis of pressure gradient, drag, and particle-fluid interaction force shows that the presence of bubbles leads to different particle flow zones where forces vary significantly. Moreover, the bubble passage can be delineated by the temporal variation of the particle-fluid interaction force. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Fluidization technology has been widely used in many industrial applications such as food, pharmaceuticals, energy, and environment since they are associated with good heat and mass transfer. The flow behavior in gas-solid fluidized beds is very complex because of the strong fluidparticle and particle-particle interactions. In bubbling fluidized beds, the bubbles govern the hydrodynamics, induce gas-solid mixing and promote heat and mass transfer [1,2]. Thus, a good understanding of bubble formation from an orifice and bubble dynamics is essential to aid in the design and development of gas-solid fluidized beds. Various experimental studies have been carried out in this direction [3] and some theoretical models have been established [4,5]. Additional experimental techniques were applied to study the time evolution of bubble characteristics [3], the pressure wave propagation and attenuation behavior [6], bubble-induced particle mixing [7], the effect of electrostatics [8] and the characteristics of bubble, cloud and wake [9]. In recent years, different numerical techniques have been widely used to study gas-solid fluidized beds and have become a significant approach to characterize bubble behavior. Numerical techniques can be either continuum- or discrete-based with respect to the solid phase. The ⁎ Corresponding author. E-mail address: [email protected] (Z.Y. Zhou).
former is often called the two-fluid model (TFM), where both gas and solid phases are considered continuous and fully interpenetrating. The latter is commonly referred to as coupled CFD-DEM where the particle phase is modeled as a discrete phase and the gas phase as continuous. Several researchers have used TFM to study bubble formation at a single orifice and bubble dynamics for different operational and design conditions [10–15]. However, CFD-DEM simulations have advantages over TFM simulations because the solid phase is modeled more accurately with respect to friction [16–18]. CFD-DEM studies on single jet fluidized beds show that the size of a bubble is sensitive to the cohesive interparticle force [18], gas injection velocities, particle properties (size, shape, and density) and bed dimensions [17–20]. Some studies made efforts to depict bubble-induced particle mixing [21], and formulate models for bubble to emulsion phase mass transfer [22]. Nevertheless, the CFD-DEM investigations carried out previously mainly focussed on a single bubble by injecting a single pulse of the jet. When a gas is continuously injected into the bed through a central orifice, the process leads to the periodical formation of a series of bubbles. The bubble formation starts after the detachment of the initial bubble from the distributor which is followed by the chain of the bubbles. For such a system, as shown in our previous work [23], the effect of jet velocity on bubble properties such as size and shape of the initial bubble (the first bubble generated from an orifice) and averaged bubble properties in the whole bed was investigated. However, in this process, the
https://doi.org/10.1016/j.powtec.2019.08.091 0032-5910/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Table 1 Components of forces and torques acting on particle i. Forces and torques Normal elastic force (fcn,ij) Normal damping force (fdn,ij)
Equations pffiffiffiffiffi −4=3E R δ3=2 n n pffiffiffiffiffiffiffiffiffiffi 1=2 −cn ð8mij E R δn Þ vn;ij
Coulomb friction force (ft,ij)
μ s jf cn;ij j ð1−ð1−δt =δt;max Þ3=2 Þ^δt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij j f cn;ij j 1−δt =δt; max =δt; max Þ vt;ij ^ −μ jf cn;ij j δt
Torque by tangential force (Mt,ij) Rolling friction torque (Mr,ij)
Rc, ij(fct, ij + fdt, ij) ^ nij μ r;ij jf cn;ij j ω
Fluid drag force (fd,i)
0.125Cd, 0, iρfπd2piε2i ∣ui − vi∣ (ui − vi)ε−χ i
Tangential elastic force (fct,ij) Tangential damping force (fdt,ij)
s
^ nij ¼ ωnij = jωnij j; ^δt ¼ δt = jδt j; δt,max = μs Where, 1/mij = 1/mi + 1/mj, E ∗ = E/2(1 − ν2), ω (2 − ν)/2(1 − ν)μδn, vij = vj − vi + ωjRc, ji − ωiRc,ij, vn, ij = (vij. n). n, vt, ij = (vij. n). n, εi = 1 − ∑k1cVi/ΔV, χ = 3.7 − 0.65 exp [−(1.5 − log10Rei)2/2], 2 Cd,0,i = (0.63 + 4.8/Re0.5 i ) , Rei = ρfdpiεi|ui − vi|/μf. Note that tangential forces (fct,ij + fdt,ij) should be replaced by ft,ij when δt ≥ δt, max.
bubble behavior is dynamic. For example, during bubble rising, phenomena such as bubble coalescence and bubble split occur which alters bubble properties and trajectories. In connection with the previousd work [23], this work focusses on the changes of bubble properties during bubble rising process in a continuous gas jet from a single orifice. Firstly, the flow pattern is examined to analyze the bubble rising process followed by the investigation of the bubble properties such as size, shape and velocity. Finally, the temporal and spatial distributions of different interaction forces are examined to further understand the behavior of particles around bubbles. 2. Models and simulation conditions 2.1. CFD-DEM governing equations In CFD-DEM, the solid phase is based on the DEM and the gas phase is treated as a continuum phase in a similar way to the two fluid model (TFM). The governing equations for particle i with mass mi and moment of inertia Ii can be written as: mi
dvi ki ¼ f pf ;i þ ∑ j¼1 f c;ij þ f d;ij þ mi g dt
i dωi X ¼ Mt;ij þ Mr;ij dt j¼1
ð1Þ
k
Ii
ð2Þ
where vi and ωi are the translational and angular velocities of the particle, respectively, and ki is the number of particles interacting with the particle. The forces involved are particle-fluid interaction force fpf,i, the gravitational force mig, and the inter-particle forces between the particles, which include elastic force fc,ij and viscous damping force fd,ij. The torques acting on particle i by particle j include: Mt,ij generated by the tangential force and Mr,ij commonly known as the rolling friction torque. The equations and the component of the forces and torques are listed in Table 1. This approach has been widely used in the literature, for example, [24]. The governing equations for gas phases are given as: ∂ε f þ ∇∙ ε f u ¼ 0 ∂t ∂ ρf εf u ∂t
þ ∇∙ ρ f ε f uu ¼ −∇p− Fpf þ ∇∙ ε f τ þ ρ f ε f g
ð3Þ
ð4Þ
where u, ρf and p are the fluid velocity, density and pressure, respecPc tively.Fpf ¼ ðð ki¼1 f pf ;i Þ=ΔV) is the volumetric particle-fluid interaction force in a computational CFD cell of volume, ΔV. Note that in this study
the particle-fluid interaction force fpf,i includes drag force fd,i (as shown in Table 1) and pressure gradient force f∇p,i ( = −∇ p ⋅ Vi), which usually are two dominant forces in gas fluidization. τ and εf are the fluid viscous stress tensor and local porosity, which are respectively given as τ = μf Pc [(∇u) + (∇u)−1] and ε f ¼ 1−ð ki¼1 V p;i Þ=ΔV, where Vp,i is the volume of particle i (or part of the volume if the particle does not fully occupy the cell), and kc is the number of particles in the computational cell. μf is the fluid molecular viscosity. The methods for a numerical solution and CFD and DEM coupling scheme of have been well established in the literature [25–28]. The same coupling algorithm is used in this work. At each time step, DEM will give information such as the positions and velocities of individual particles. From these, the porosity and volumetric fluid-particle interaction force in each computational cell are calculated. CFD then uses the information to determine the gas flow field, from which the fluid drag forces acting on individual particles are calculated. Incorporation of the resulting forces into DEM will produce information about the motion of the individual particles for the next time step.
2.2. Simulation conditions The bed geometry used in this work is a slot model with periodic boundary conditions applied to the front and rear walls. For such a geometry, two-dimensional CFD and three dimensional DEM are employed as used elsewhere [23,24,29,30]. Particles are generated randomly at different heights and allowed to come to rest to form a bed. Then, the bed is fluidized by gas jet from the central orifice at the bottom which is of size 4 CFD cells (0.001 m). Table 2 lists the parameters including the bed geometry, physical properties of particles and fluid used in the simulation. Note that in this study our major aim is to investigate the bubbling phenomenon without the influence of cohesive forces, thereby, van der Waals force is not considered. The effect of van der Waals force on bubble dynamics will be reported in the future. Several interphase boundary/threshold values (0.70–0.85) of voidage can be used to describe bubbles [31]. In this study, the threshold value of porosity of 0.8 is used. The regions where porosities are b0.8 are considered as the emulsion phase, and the regions where porosities are greater than or equal to 0.8 are considered as bubbles. The data from the simulation were saved every 0.0033 s and then imported into Tecplot, a data visualization software. In Tecplot, to visualize a clear bubble boundary, the voidage contour level was cut-off at the threshold value
Table 2 Various parameters used in CFD-DEM simulation. Variable
Values
Bed geometry Bed width (x) Bed height (z) Bed thickness (y) CFD cells (x, z) CFD cell size (Δx, Δz)
0.02 m 0.08 m 0.0004 m 322 × 82 cells 0.00025 m
Particle properties Particle shape Number of Particles, Np Particle size, dp Particle density, ρp Normal damping coefficient, cn Tangential damping coefficient, ct Friction coefficient, μ Rolling friction coefficient Young's modulus, E Poisson ratio, ν Time step, Δt
Spherical 200,000 100 μm 2450 kg/m3 0.3 0.3 0.4 0.3% dp 1 × 107 Pa 0.3 1.6 × 10−6 s
Particle properties Density Viscosity
1.205 kg/m3 1.8 × 10−5 Pa s
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 1. Bubble formation and trajectory snapshots for a jet velocity of 0.25 m/s.
of 0.8. The image was then analyzed by using the MATLAB Image Processing Toolbox to determine the geometric properties of bubbles. The bubble boundary is not extrapolated and the procedure of obtaining bubble properties is similar to the one used by Busciglio et al. [2]. The equivalent bubble diameter is defined as the diameter of the circle possessing the same area as the numerically computed area pffiffiffiffiffiffiffiffiffiffiffi for which voidage N0.8, and calculated by db ¼ 4A=π , where A is the bubble area. The shape of the bubble is characterized by aspect ratio, β [32]. The bubble aspect ratio is defined as the ratio of the maximum distance in the vertical distance to the maximum distance in the horizontal section, and given by β = dy/dx, where dy and dx are the vertical and horizontal maximum of the bubble dimensions. The bubble rising velocity is calculated by evaluating the displacement of
its centroid between two subsequent frames. Note that only axial displacement (ΔY) was considered in this study to evaluate the axial bubble rising velocity (Ub = ΔY/Δt). 3. Results and discussion 3.1. Bubble split and coalescence phenomenon Generally, when a gas jet is injected from a central orifice into a bed maintained at the minimum fluidization state, the gas starts to penetrate through the bed. After a certain period, accumulation of gas gradually leads to the formation of a bubble atop the distributor which then disengages. This bubble is termed the initial bubble and the time this
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
Fig. 2. Motion of chain of bubbles for jet velocities of (a) 0.15 m/s and (b) 0.25 m/s (straight lines indicate primary bubbles and dotted lines indicate trailing bubbles).
Fig. 3. Bubble diameter at different positions at a jet velocity of 0.25 m/s.
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Fig. 4. Bubble shape at different positions at a jet velocity of 0.25 m/s.
bubble disengages the distributor is termed the bubble detachment time. Previous studies have shown that the size of the initial bubble increases with the intensity of the jet velocity, however, the time of detachment remains unaffected [18]. After disengagement from the distributor, the initial bubble starts to rise through the bed and finally erupts at the top. This is the case when only a single bubble or a pulse of the jet is injected into the bed. However, with continuous gas injection, the scenario is different. After the formation and detachment of an initial bubble, it is accompanied by an elongated jet which then merges with the bubble at a certain height above the distributor and the merged bubble rises through the bed [18]. This phenomenon is depicted in Fig. 1 (0.043 s–0.0164 s). In general, continuous injection of a central air jet to the bed features with the gradual formation of a series of bubbles. This is consistent with the literature reported by Tsukada and Horio [33]. Fig. 1 shows bubble formation and trajectory snapshots at various times. It can be observed that several bubbles are present in the bed at different locations, thus distinguishing the process to be a multibubble system. In our previous work, the average bubble properties in this multi-bubble system due to continuous gas injection have been investigated and reported [23]. For example, the average bubble size increases with the height of the bed and jet velocity, and the bubble generation frequency of small and large bubbles also increases with the jet velocity. Moreover, the bubble shape characterized by shape factor and aspect ratio follows a normal distribution. However, the bubble behavior such as bubble coalescence and split phenomenon and bubble
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Fig. 6. Bubble velocity at different positions at a jet velocity of 0.25 m/s.
properties during the bubble rising process were not analyzed in detail, and particle-fluid interaction forces around bubbles were not presented in the work of Shrestha et al. [21]. These are the main targets of the present work. For clarity, in Fig. 1, bubbles are numbered according to their formation and detachment time. The plus sign indicates the merging/coalescence of two or three bubbles. More details can be observed from Fig. 2 which shows the motion of chain of bubbles for jet velocities of 0.15 and 0.25 m/s, respectively. The rising behavior of these chain of bubbles has been known to be contradistinctive [34]. Therefore, the bubbles are categorized into two types: primary/leading bubbles and trailing bubbles, as shown in Fig. 2, where straight lines represent primary bubbles and dotted lines represent trailing bubbles. The primary bubbles are defined as the bubbles whose motion are not affected by the bubbles ahead of them but they affect the succeeding bubbles. The trailing bubbles are those bubbles whose motion is affected by the primary bubbles. For example, from Figs. 1 and 2(b), bubble 1 (B1) is a primary bubble and B2 is a trailing bubble, similarly, B3 is a primary bubble and B4 and B5 are trailing bubbles. There are 32 and 33 bubbles generated for jet velocities of 0.15 and 0.25 m/s, respectively during the simulation time of 1.1 s. Among the 32 bubbles generated for the jet velocity of 0.15 m/s, only 14 bubbles are identified as primary bubbles while the rest of the bubbles are identified as trailing bubbles. At the jet velocity of 0.25 m/s, only 8 bubbles are observed as primary bubbles. The number of primary bubbles decreases with an increase of jet velocity, while the number of trailing bubbles attached to the
Fig. 5. Bubble shape from porosity images at a jet velocity of 0.25 m/s: (a) primary bubble (bubble 6) at different locations of the bed and (b) different trailing bubbles.
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 7. Spatial distribution of different forces (top: drag force, middle: pressure gradient force and bottom: particle-fluid interaction force) at a jet velocity of 0.25 m/s.
primary bubbles increases with jet velocity. At 0.15 m/s, only three primary bubbles (B5, B8, and B12) have more than one trailing bubble and the rest only have one trailing bubble. Whereas, at the jet velocity of 0.25 m/s, only primary bubble B1 and B17 have one trailing bubble while the rest of the primary bubbles have more than one trailing bubble. Also, from Fig. 2(b) it can be seen that the bubble split is not so significant and only observed in a few occasions [Fig. 1 (0.234, 0.257 and 0.378 s)]. The bubble splits happen mainly due to the raining of particles from the bubble cloud at the nose of
the bubble. At lower height, when the bubble splits, it recoalesces. At the top of the bed, the bubble breaks up to erupt. However, the coalescence phenomenon is observed to be occurring and dominating the process. Generally, the trailing bubbles catch up with the primary bubble at some height in the bed and then coalesce. The coalescence observed for the bubbles formed mainly consists of a leading-trailing type of coalescence [35]. Leading-trailing coalescence describes the scenario where two bubbles form consecutively rather than simultaneously. As they
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 8. Spatial distribution of flow fields at a jet velocity of 0.25 m/s (top: fluid flow field and porosity distribution and bottom: particle velocity field).
rise, the leading bubble slows down due to its interaction with the trailing bubble. The trailing bubble will then ‘catch’ and ‘coalesce’ with the leading bubble. The coalesced bubble will move up in the remaining height of the bed as a single bubble or may coalesce with other bubbles. There are three positions where coalescence occurs as shown in Fig. 2. The first position is near the distributor just after bubble detachment at a bed height of 0.005–0.008 m, and the bubble is sequentially followed by a jet which merges to form a larger bubble. The second coalescence occurs at the center of the bed (0.008–0.016 m for 0.15 m/s and 0.013–0.016 m for 0.25 m/s). The third coalescence occurs near the top of the bed at a bed height of N0.022 m where the merged bubbles erupt concurrently. It is observed that generally only one or two of the three types of coalescence happens during the rise of primary bubbles. At the jet velocity of 0.15 m/s, the second type of coalescence prevails; while at the jet velocity of 0.25 m/s a combination of the first and third type of coalescence is dominant. The development of the bubble coalescence pattern is observed to be fairly regular but significantly affects bubble properties. 3.2. Bubble properties The ambiguous behavior of primary and trailing bubbles may result in different bubble properties such as diameter, shape and velocity. Fig. 3 shows the bubble diameter at different bubble nose positions. Three primary bubbles (B3, B6, and B10) with their trailing bubbles at a jet velocity of 0.25 m/s are investigated. Fig. 3(a–c) show the change in bubble diameter with bubble nose position for both primary and trailing bubbles. It can be seen that the increase in bubble diameter is because of bubble coalescence while the decrease in bubble diameter is due to bubble splitting. In this process, the size of the primary bubble keeps increasing while the size of the trailing bubble decreases since the trailing bubble is coalescing with the primary bubble. Fig. 3(d) shows the change in bubble diameters of three primary bubbles at the different bubble nose position. It can be seen that the bubble diameter and its change for the primary bubbles at different bed heights are similar
indicating the growth of primary bubbles are comparable as they ascend through the bed. Fig. 4 shows the bubble shape characterized by aspect ratio at different bubble positions, and Fig. 5 shows the bubble shape obtained from porosity images for primary bubbles (top) and trailing bubbles (bottom). The figures clearly show the differences of bubble shapes for primary and trailing bubbles. The primary bubbles, although formed at different times, maintain a similar shape as they rise through the bed. During bubble rising at the lower level of the bed, it expands in the vertical direction and thereby becomes elongated (i.e. prolate shaped with aspect ratio N 1). After the bubble is detached, the bubble stretches in the horizontal direction due to the development of a wake, resulting in the decrease of aspect ratio. At the mid-level of the bed, the bubble is almost circular (aspect ratio = 1). As the bubble rises towards the top of the bed, it stretches in the horizontal direction and becomes oblately shaped (aspect ratio b 1) before the eruption. However, the shape of the trailing bubbles follows a different trend. The trailing bubbles are generally elongated in shape (aspect ratio NN 1). This is because their motion is under the influence of the primary bubbles. When the trailing bubbles move into the vortex of the primary bubbles, they accelerate and catch up with and finally merge with the primary bubble resulting in an elongated bubble (Fig. 5(b)). From Fig. 1 it can be seen that the bubble B1 at 0.043 s is just above the distributor which then rises and merges with bubble B2 and finally erupts at 0.17 s. Similar rising time length is also observed for bubbles B3 and B6, and so on and so forth. It is deduced that the primary bubble takes around 0.15 s to rise and then erupt at the top. Fig. 6 shows the bubble velocity for different nose positions of the bubble. It is evident from the figure that the bubble velocity is distinctly different for primary and trailing bubbles. The bubble velocity for primary bubbles initially increases as it rises through the bed then remains constant (at mid-level of the bed) until it falls rapidly at the top of the bed during the eruption. On the contrary, trailing bubbles have very high bubble velocity around 1.5–2 times the velocity of primary bubbles. The increased velocity of the trailing bubble is due to the interaction effect, that is
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 9. Different forces acting on the bed at different times at a jet velocity of 0.25 m/s for different bed height (axial direction): (a) H = 0.005 m, (b) H = 0.01 m, (c) H = 0.015 m, and (d) H = 0.02 m.
trailing bubbles accelerate to catch up with and merge with primary bubbles which are at a higher level. It should be noted that the bubble properties reported above is for two dimensional bubbles and the simulation setup is a slot model with a bed thickness 4dp. In this study, periodic boundary condition is used to eliminate the front and rear wall effects, as used elsewhere [36,37]. However, the bed thickness may affect the simulation results, even with the use of periodic boundary condition. It might be a potential future study to investigate this effect. 3.3. Particle-fluid interaction force analysis One of the important forces in the process of fluidization is the particle-fluid interaction force. In CFD-DEM, it is obtained as the sum
of the fluid drag force and pressure gradient force as discussed in Section 2. These forces can vary spatiotemporally. As an example, the spatial distribution of various forces (top – drag force; middle – pressure gradient force; and bottom – particle-fluid interaction force) at different times is depicted in Fig. 7. It should be noted that the force ratio is used by normalizing forces with particle gravity mg. It can be observed that these forces around gas bubbles are significantly different from other areas. The forces are generally large in the dense areas around the gas bubbles, and relatively weak in the loose areas in the sides of bubbles or far from bubbles. These forces are maximum in the area between the bubbles (i.e., above the nose of bubbles), and minimum in close vicinity around the bubbles. This force difference in different areas can be primarily attributed to the difference in porosity and permeability [27]. Fig. 8 shows the spatial distributions of porosity, fluid and particle
Fig. 10. Particle fluid interaction force acting on the bed: (a) axially averaged at different radial direction vs time, and (b) radially averaged along the height of the bed.
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 11. Change in particle-fluid interaction force with the bubble movement.
velocity flow field. It can be seen that the force distribution is minimum at the bubble cloud and wake where porosity is in a range of 0.6–0.8. The distribution of the force is higher in the emulsion region where the bed is loosely packed (porosity = 0.4–0.5) than when densely packed (porosity = 0.3–0.4). Also, it is noteworthy to mention that the region where the force distribution is maximum is corresponding to the region where the gas flows from the nose of the bottom bubble towards the base of the top bubble and also the region where the particle velocity is maximum. Fig. 9 shows the temporal variation of drag force, pressure gradient force and particle-fluid interaction force at different axial bed heights. It can be seen that the pressure gradient force is greater than the drag force at any level of the bed. Moreover, the magnitude of the forces decreases as the bed height increases, which is due to the loss of energy retained by the bubbles as the bed height increases. It can be observed that the peak plateaus as the bed height increases. This is because of the bubble coalescence discussed in Section 3.1. At a lower level of the bed, there is no significant bubble coalescence, however as the bed level increases there is significant bubble coalescence present. Therefore, the interval between the two rising bubbles increases, leading to the increased presence of solid materials in loosely packed state. As a consequence, the increased magnitude of the relative forces resides for a longer period of time forming a plateau. Fig. 10(a) shows the temporal variation of particle-fluid interaction forces for different radial locations and Fig. 10(b) shows the radially averaged particle-fluid interaction force along the height of the bed. It can be seen that the magnitude and fluctuations of the particle-fluid interaction force are high at the center of the bed, and decrease towards the wall. The bubble trajectory follows the centreline since the gas injection is through the central orifice which results in the inconsistency in porosity leading to the fluctuations of the force. In the central region of the lower level of the bed, the particle-fluid interaction force is higher than gravitational force but decreases linearly as the bed height increases, and finally levels off at the top of the bed. At the wall region, the solids are moving down slowly in a packed state, therefore the particle-fluid interaction force is less than the gravitational force. In addition, the peaks illustrated in Figs. 9 and 10 are due to the bubble passage. The maximum represents when the bubble has passed the point while the minimum represents when the bubble centroid is at that point. This information can be clearly visualized in Fig. 11 which shows how the particle-fluid interaction force changes when different parts of the bubble passes through a point. Four points a, b, c, and d are assigned to a bubble, ‘a’ represents the top of the bubble cloud, ‘b’ and ‘c’ represent the top and bottom of the bubble, respectively, and ‘d’ represents the bottom of bubble wake. These positions of a bubble exhibit different magnitude of particle-fluid interaction force, for example, large at locations ‘a’ and ‘d’ while small in locations ‘b’ and ‘c’. Similar
results for local porosity time-series data were shown by Huang and Lu [9], who conducted experiments in jetting fluidized bed by using a capacitance probe. In their case, ‘b’ and ‘c’ locations have higher porosity while ‘a’ and ‘d’ have lower porosity. The porosity and particle-fluid interaction force are inter-related in gas-solid fluidized beds. For example, higher porosity leading to a lower particle-fluid interaction force and lower porosity to a higher particle-fluid interaction force. This finding shows that the particle-fluid interaction force can be used to represent the bubble passage. 4. Conclusion Formation of a series of bubbles in a gas-solid fluidized bed operated with a single continuous jet was studied using CFD-DEM to study the bubble characteristics such as bubble size, shape, and velocity. The results illustrate that the bubbles coalesce at three different bed heights and the pattern of the bubble coalescence is fairly regular but dependent on the jet velocity. The bubbles are categorized into two types: primary/ leading bubbles and trailing bubbles, where primary bubbles are defined as the bubbles whose motion are not affected by the bubbles ahead of them but they affect the succeeding bubbles, and trailing bubbles are those bubbles whose motion is affected by the primary bubbles. The trailing bubbles catch up with the leading bubbles at some height in the bed, thereby coalescing. The size of primary bubble increases at the cost of trailing bubbles. The variation in the size of primary bubbles with bed height are almost identical. The shape of the primary bubbles change from prolate to circular to oblate as it escalates through the bed while the trailing bubbles are elongated in shape. The rising velocity of primary bubbles is 1.5 to 2 times smaller compared to the rising velocity of the trailing bubbles due to the effect of bubble interaction. The drag force, pressure gradient force and particle-fluid interaction force are high in the areas where particles are loosely packed. For example, in the region between the gas bubbles. The forces are relatively weak in the vicinity of bubbles and areas far from the bubbles where particles are densely packed. The temporal variation of particle-fluid interaction force delineates a sharp peak at the lower bed levels and a plateaued peak at the higher bed levels. In addition, particle-fluid interaction forces vary with the bubble positions such as cloud, bubble and wake. Insights generated from this study are helpful to allow a better understanding of bubble dynamics and the hydrodynamics of complex gas-solid fluidized bed behaviour. Acknowledgements The authors are grateful for the financial support from the Australian Research Council Industrial Transformation Research Hubs Scheme (Project Number IH140100035). This research was undertaken with
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet S. Shrestha, J.Q. Gan, Z.Y. Zhou ⁎ ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, VIC 3800, Australia
a r t i c l e
i n f o
Available online xxxx Keywords: Fluidization Bubble coalescence Bubble properties Single jet CFD-DEM
a b s t r a c t Advancement in the knowledge of bubble dynamics and properties can significantly aid to improve the design and operation of gas-solid fluidized beds. In this work, bubble properties in a single jet fluidized bed were studied by the combined approach of CFD and DEM. The results illustrated that the process of the continuous injection of a central air jet to the bed was successfully reproduced, with the formation of a series of bubbles which rise through the bed and burst at the bed top. During this process, the series of bubbles align vertically which show coalescence in three different levels of the bed. However, the coalescence patterns depend upon jet velocity and are fairly regular. The bubbles are categorized into two types: primary/leading bubbles and trailing bubbles. The size of primary bubbles keeps increasing with bed height while the size of trailing bubbles decreases since trailing bubbles coalesce with primary bubbles. Primary bubbles, although formed at different times, are of similar shape at different heights of the bed while trailing bubbles are generally elongated in shape. Trailing bubbles have a higher velocity than primary bubbles. The spatial analysis of pressure gradient, drag, and particle-fluid interaction force shows that the presence of bubbles leads to different particle flow zones where forces vary significantly. Moreover, the bubble passage can be delineated by the temporal variation of the particle-fluid interaction force. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Fluidization technology has been widely used in many industrial applications such as food, pharmaceuticals, energy, and environment since they are associated with good heat and mass transfer. The flow behavior in gas-solid fluidized beds is very complex because of the strong fluidparticle and particle-particle interactions. In bubbling fluidized beds, the bubbles govern the hydrodynamics, induce gas-solid mixing and promote heat and mass transfer [1,2]. Thus, a good understanding of bubble formation from an orifice and bubble dynamics is essential to aid in the design and development of gas-solid fluidized beds. Various experimental studies have been carried out in this direction [3] and some theoretical models have been established [4,5]. Additional experimental techniques were applied to study the time evolution of bubble characteristics [3], the pressure wave propagation and attenuation behavior [6], bubble-induced particle mixing [7], the effect of electrostatics [8] and the characteristics of bubble, cloud and wake [9]. In recent years, different numerical techniques have been widely used to study gas-solid fluidized beds and have become a significant approach to characterize bubble behavior. Numerical techniques can be either continuum- or discrete-based with respect to the solid phase. The ⁎ Corresponding author. E-mail address: [email protected] (Z.Y. Zhou).
former is often called the two-fluid model (TFM), where both gas and solid phases are considered continuous and fully interpenetrating. The latter is commonly referred to as coupled CFD-DEM where the particle phase is modeled as a discrete phase and the gas phase as continuous. Several researchers have used TFM to study bubble formation at a single orifice and bubble dynamics for different operational and design conditions [10–15]. However, CFD-DEM simulations have advantages over TFM simulations because the solid phase is modeled more accurately with respect to friction [16–18]. CFD-DEM studies on single jet fluidized beds show that the size of a bubble is sensitive to the cohesive interparticle force [18], gas injection velocities, particle properties (size, shape, and density) and bed dimensions [17–20]. Some studies made efforts to depict bubble-induced particle mixing [21], and formulate models for bubble to emulsion phase mass transfer [22]. Nevertheless, the CFD-DEM investigations carried out previously mainly focussed on a single bubble by injecting a single pulse of the jet. When a gas is continuously injected into the bed through a central orifice, the process leads to the periodical formation of a series of bubbles. The bubble formation starts after the detachment of the initial bubble from the distributor which is followed by the chain of the bubbles. For such a system, as shown in our previous work [23], the effect of jet velocity on bubble properties such as size and shape of the initial bubble (the first bubble generated from an orifice) and averaged bubble properties in the whole bed was investigated. However, in this process, the
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Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Table 1 Components of forces and torques acting on particle i. Forces and torques Normal elastic force (fcn,ij) Normal damping force (fdn,ij)
Equations pffiffiffiffiffi −4=3E R δ3=2 n n pffiffiffiffiffiffiffiffiffiffi 1=2 −cn ð8mij E R δn Þ vn;ij
Coulomb friction force (ft,ij)
μ s jf cn;ij j ð1−ð1−δt =δt;max Þ3=2 Þ^δt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij j f cn;ij j 1−δt =δt; max =δt; max Þ vt;ij ^ −μ jf cn;ij j δt
Torque by tangential force (Mt,ij) Rolling friction torque (Mr,ij)
Rc, ij(fct, ij + fdt, ij) ^ nij μ r;ij jf cn;ij j ω
Fluid drag force (fd,i)
0.125Cd, 0, iρfπd2piε2i ∣ui − vi∣ (ui − vi)ε−χ i
Tangential elastic force (fct,ij) Tangential damping force (fdt,ij)
s
^ nij ¼ ωnij = jωnij j; ^δt ¼ δt = jδt j; δt,max = μs Where, 1/mij = 1/mi + 1/mj, E ∗ = E/2(1 − ν2), ω (2 − ν)/2(1 − ν)μδn, vij = vj − vi + ωjRc, ji − ωiRc,ij, vn, ij = (vij. n). n, vt, ij = (vij. n). n, εi = 1 − ∑k1cVi/ΔV, χ = 3.7 − 0.65 exp [−(1.5 − log10Rei)2/2], 2 Cd,0,i = (0.63 + 4.8/Re0.5 i ) , Rei = ρfdpiεi|ui − vi|/μf. Note that tangential forces (fct,ij + fdt,ij) should be replaced by ft,ij when δt ≥ δt, max.
bubble behavior is dynamic. For example, during bubble rising, phenomena such as bubble coalescence and bubble split occur which alters bubble properties and trajectories. In connection with the previousd work [23], this work focusses on the changes of bubble properties during bubble rising process in a continuous gas jet from a single orifice. Firstly, the flow pattern is examined to analyze the bubble rising process followed by the investigation of the bubble properties such as size, shape and velocity. Finally, the temporal and spatial distributions of different interaction forces are examined to further understand the behavior of particles around bubbles. 2. Models and simulation conditions 2.1. CFD-DEM governing equations In CFD-DEM, the solid phase is based on the DEM and the gas phase is treated as a continuum phase in a similar way to the two fluid model (TFM). The governing equations for particle i with mass mi and moment of inertia Ii can be written as: mi
dvi ki ¼ f pf ;i þ ∑ j¼1 f c;ij þ f d;ij þ mi g dt
i dωi X ¼ Mt;ij þ Mr;ij dt j¼1
ð1Þ
k
Ii
ð2Þ
where vi and ωi are the translational and angular velocities of the particle, respectively, and ki is the number of particles interacting with the particle. The forces involved are particle-fluid interaction force fpf,i, the gravitational force mig, and the inter-particle forces between the particles, which include elastic force fc,ij and viscous damping force fd,ij. The torques acting on particle i by particle j include: Mt,ij generated by the tangential force and Mr,ij commonly known as the rolling friction torque. The equations and the component of the forces and torques are listed in Table 1. This approach has been widely used in the literature, for example, [24]. The governing equations for gas phases are given as: ∂ε f þ ∇∙ ε f u ¼ 0 ∂t ∂ ρf εf u ∂t
þ ∇∙ ρ f ε f uu ¼ −∇p− Fpf þ ∇∙ ε f τ þ ρ f ε f g
ð3Þ
ð4Þ
where u, ρf and p are the fluid velocity, density and pressure, respecPc tively.Fpf ¼ ðð ki¼1 f pf ;i Þ=ΔV) is the volumetric particle-fluid interaction force in a computational CFD cell of volume, ΔV. Note that in this study
the particle-fluid interaction force fpf,i includes drag force fd,i (as shown in Table 1) and pressure gradient force f∇p,i ( = −∇ p ⋅ Vi), which usually are two dominant forces in gas fluidization. τ and εf are the fluid viscous stress tensor and local porosity, which are respectively given as τ = μf Pc [(∇u) + (∇u)−1] and ε f ¼ 1−ð ki¼1 V p;i Þ=ΔV, where Vp,i is the volume of particle i (or part of the volume if the particle does not fully occupy the cell), and kc is the number of particles in the computational cell. μf is the fluid molecular viscosity. The methods for a numerical solution and CFD and DEM coupling scheme of have been well established in the literature [25–28]. The same coupling algorithm is used in this work. At each time step, DEM will give information such as the positions and velocities of individual particles. From these, the porosity and volumetric fluid-particle interaction force in each computational cell are calculated. CFD then uses the information to determine the gas flow field, from which the fluid drag forces acting on individual particles are calculated. Incorporation of the resulting forces into DEM will produce information about the motion of the individual particles for the next time step.
2.2. Simulation conditions The bed geometry used in this work is a slot model with periodic boundary conditions applied to the front and rear walls. For such a geometry, two-dimensional CFD and three dimensional DEM are employed as used elsewhere [23,24,29,30]. Particles are generated randomly at different heights and allowed to come to rest to form a bed. Then, the bed is fluidized by gas jet from the central orifice at the bottom which is of size 4 CFD cells (0.001 m). Table 2 lists the parameters including the bed geometry, physical properties of particles and fluid used in the simulation. Note that in this study our major aim is to investigate the bubbling phenomenon without the influence of cohesive forces, thereby, van der Waals force is not considered. The effect of van der Waals force on bubble dynamics will be reported in the future. Several interphase boundary/threshold values (0.70–0.85) of voidage can be used to describe bubbles [31]. In this study, the threshold value of porosity of 0.8 is used. The regions where porosities are b0.8 are considered as the emulsion phase, and the regions where porosities are greater than or equal to 0.8 are considered as bubbles. The data from the simulation were saved every 0.0033 s and then imported into Tecplot, a data visualization software. In Tecplot, to visualize a clear bubble boundary, the voidage contour level was cut-off at the threshold value
Table 2 Various parameters used in CFD-DEM simulation. Variable
Values
Bed geometry Bed width (x) Bed height (z) Bed thickness (y) CFD cells (x, z) CFD cell size (Δx, Δz)
0.02 m 0.08 m 0.0004 m 322 × 82 cells 0.00025 m
Particle properties Particle shape Number of Particles, Np Particle size, dp Particle density, ρp Normal damping coefficient, cn Tangential damping coefficient, ct Friction coefficient, μ Rolling friction coefficient Young's modulus, E Poisson ratio, ν Time step, Δt
Spherical 200,000 100 μm 2450 kg/m3 0.3 0.3 0.4 0.3% dp 1 × 107 Pa 0.3 1.6 × 10−6 s
Particle properties Density Viscosity
1.205 kg/m3 1.8 × 10−5 Pa s
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
S. Shrestha et al. / Powder Technology xxx (2019) xxx
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Fig. 1. Bubble formation and trajectory snapshots for a jet velocity of 0.25 m/s.
of 0.8. The image was then analyzed by using the MATLAB Image Processing Toolbox to determine the geometric properties of bubbles. The bubble boundary is not extrapolated and the procedure of obtaining bubble properties is similar to the one used by Busciglio et al. [2]. The equivalent bubble diameter is defined as the diameter of the circle possessing the same area as the numerically computed area pffiffiffiffiffiffiffiffiffiffiffi for which voidage N0.8, and calculated by db ¼ 4A=π , where A is the bubble area. The shape of the bubble is characterized by aspect ratio, β [32]. The bubble aspect ratio is defined as the ratio of the maximum distance in the vertical distance to the maximum distance in the horizontal section, and given by β = dy/dx, where dy and dx are the vertical and horizontal maximum of the bubble dimensions. The bubble rising velocity is calculated by evaluating the displacement of
its centroid between two subsequent frames. Note that only axial displacement (ΔY) was considered in this study to evaluate the axial bubble rising velocity (Ub = ΔY/Δt). 3. Results and discussion 3.1. Bubble split and coalescence phenomenon Generally, when a gas jet is injected from a central orifice into a bed maintained at the minimum fluidization state, the gas starts to penetrate through the bed. After a certain period, accumulation of gas gradually leads to the formation of a bubble atop the distributor which then disengages. This bubble is termed the initial bubble and the time this
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
Fig. 2. Motion of chain of bubbles for jet velocities of (a) 0.15 m/s and (b) 0.25 m/s (straight lines indicate primary bubbles and dotted lines indicate trailing bubbles).
Fig. 3. Bubble diameter at different positions at a jet velocity of 0.25 m/s.
S. Shrestha et al. / Powder Technology xxx (2019) xxx
Fig. 4. Bubble shape at different positions at a jet velocity of 0.25 m/s.
bubble disengages the distributor is termed the bubble detachment time. Previous studies have shown that the size of the initial bubble increases with the intensity of the jet velocity, however, the time of detachment remains unaffected [18]. After disengagement from the distributor, the initial bubble starts to rise through the bed and finally erupts at the top. This is the case when only a single bubble or a pulse of the jet is injected into the bed. However, with continuous gas injection, the scenario is different. After the formation and detachment of an initial bubble, it is accompanied by an elongated jet which then merges with the bubble at a certain height above the distributor and the merged bubble rises through the bed [18]. This phenomenon is depicted in Fig. 1 (0.043 s–0.0164 s). In general, continuous injection of a central air jet to the bed features with the gradual formation of a series of bubbles. This is consistent with the literature reported by Tsukada and Horio [33]. Fig. 1 shows bubble formation and trajectory snapshots at various times. It can be observed that several bubbles are present in the bed at different locations, thus distinguishing the process to be a multibubble system. In our previous work, the average bubble properties in this multi-bubble system due to continuous gas injection have been investigated and reported [23]. For example, the average bubble size increases with the height of the bed and jet velocity, and the bubble generation frequency of small and large bubbles also increases with the jet velocity. Moreover, the bubble shape characterized by shape factor and aspect ratio follows a normal distribution. However, the bubble behavior such as bubble coalescence and split phenomenon and bubble
5
Fig. 6. Bubble velocity at different positions at a jet velocity of 0.25 m/s.
properties during the bubble rising process were not analyzed in detail, and particle-fluid interaction forces around bubbles were not presented in the work of Shrestha et al. [21]. These are the main targets of the present work. For clarity, in Fig. 1, bubbles are numbered according to their formation and detachment time. The plus sign indicates the merging/coalescence of two or three bubbles. More details can be observed from Fig. 2 which shows the motion of chain of bubbles for jet velocities of 0.15 and 0.25 m/s, respectively. The rising behavior of these chain of bubbles has been known to be contradistinctive [34]. Therefore, the bubbles are categorized into two types: primary/leading bubbles and trailing bubbles, as shown in Fig. 2, where straight lines represent primary bubbles and dotted lines represent trailing bubbles. The primary bubbles are defined as the bubbles whose motion are not affected by the bubbles ahead of them but they affect the succeeding bubbles. The trailing bubbles are those bubbles whose motion is affected by the primary bubbles. For example, from Figs. 1 and 2(b), bubble 1 (B1) is a primary bubble and B2 is a trailing bubble, similarly, B3 is a primary bubble and B4 and B5 are trailing bubbles. There are 32 and 33 bubbles generated for jet velocities of 0.15 and 0.25 m/s, respectively during the simulation time of 1.1 s. Among the 32 bubbles generated for the jet velocity of 0.15 m/s, only 14 bubbles are identified as primary bubbles while the rest of the bubbles are identified as trailing bubbles. At the jet velocity of 0.25 m/s, only 8 bubbles are observed as primary bubbles. The number of primary bubbles decreases with an increase of jet velocity, while the number of trailing bubbles attached to the
Fig. 5. Bubble shape from porosity images at a jet velocity of 0.25 m/s: (a) primary bubble (bubble 6) at different locations of the bed and (b) different trailing bubbles.
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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S. Shrestha et al. / Powder Technology xxx (2019) xxx
Fig. 7. Spatial distribution of different forces (top: drag force, middle: pressure gradient force and bottom: particle-fluid interaction force) at a jet velocity of 0.25 m/s.
primary bubbles increases with jet velocity. At 0.15 m/s, only three primary bubbles (B5, B8, and B12) have more than one trailing bubble and the rest only have one trailing bubble. Whereas, at the jet velocity of 0.25 m/s, only primary bubble B1 and B17 have one trailing bubble while the rest of the primary bubbles have more than one trailing bubble. Also, from Fig. 2(b) it can be seen that the bubble split is not so significant and only observed in a few occasions [Fig. 1 (0.234, 0.257 and 0.378 s)]. The bubble splits happen mainly due to the raining of particles from the bubble cloud at the nose of
the bubble. At lower height, when the bubble splits, it recoalesces. At the top of the bed, the bubble breaks up to erupt. However, the coalescence phenomenon is observed to be occurring and dominating the process. Generally, the trailing bubbles catch up with the primary bubble at some height in the bed and then coalesce. The coalescence observed for the bubbles formed mainly consists of a leading-trailing type of coalescence [35]. Leading-trailing coalescence describes the scenario where two bubbles form consecutively rather than simultaneously. As they
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
S. Shrestha et al. / Powder Technology xxx (2019) xxx
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Fig. 8. Spatial distribution of flow fields at a jet velocity of 0.25 m/s (top: fluid flow field and porosity distribution and bottom: particle velocity field).
rise, the leading bubble slows down due to its interaction with the trailing bubble. The trailing bubble will then ‘catch’ and ‘coalesce’ with the leading bubble. The coalesced bubble will move up in the remaining height of the bed as a single bubble or may coalesce with other bubbles. There are three positions where coalescence occurs as shown in Fig. 2. The first position is near the distributor just after bubble detachment at a bed height of 0.005–0.008 m, and the bubble is sequentially followed by a jet which merges to form a larger bubble. The second coalescence occurs at the center of the bed (0.008–0.016 m for 0.15 m/s and 0.013–0.016 m for 0.25 m/s). The third coalescence occurs near the top of the bed at a bed height of N0.022 m where the merged bubbles erupt concurrently. It is observed that generally only one or two of the three types of coalescence happens during the rise of primary bubbles. At the jet velocity of 0.15 m/s, the second type of coalescence prevails; while at the jet velocity of 0.25 m/s a combination of the first and third type of coalescence is dominant. The development of the bubble coalescence pattern is observed to be fairly regular but significantly affects bubble properties. 3.2. Bubble properties The ambiguous behavior of primary and trailing bubbles may result in different bubble properties such as diameter, shape and velocity. Fig. 3 shows the bubble diameter at different bubble nose positions. Three primary bubbles (B3, B6, and B10) with their trailing bubbles at a jet velocity of 0.25 m/s are investigated. Fig. 3(a–c) show the change in bubble diameter with bubble nose position for both primary and trailing bubbles. It can be seen that the increase in bubble diameter is because of bubble coalescence while the decrease in bubble diameter is due to bubble splitting. In this process, the size of the primary bubble keeps increasing while the size of the trailing bubble decreases since the trailing bubble is coalescing with the primary bubble. Fig. 3(d) shows the change in bubble diameters of three primary bubbles at the different bubble nose position. It can be seen that the bubble diameter and its change for the primary bubbles at different bed heights are similar
indicating the growth of primary bubbles are comparable as they ascend through the bed. Fig. 4 shows the bubble shape characterized by aspect ratio at different bubble positions, and Fig. 5 shows the bubble shape obtained from porosity images for primary bubbles (top) and trailing bubbles (bottom). The figures clearly show the differences of bubble shapes for primary and trailing bubbles. The primary bubbles, although formed at different times, maintain a similar shape as they rise through the bed. During bubble rising at the lower level of the bed, it expands in the vertical direction and thereby becomes elongated (i.e. prolate shaped with aspect ratio N 1). After the bubble is detached, the bubble stretches in the horizontal direction due to the development of a wake, resulting in the decrease of aspect ratio. At the mid-level of the bed, the bubble is almost circular (aspect ratio = 1). As the bubble rises towards the top of the bed, it stretches in the horizontal direction and becomes oblately shaped (aspect ratio b 1) before the eruption. However, the shape of the trailing bubbles follows a different trend. The trailing bubbles are generally elongated in shape (aspect ratio NN 1). This is because their motion is under the influence of the primary bubbles. When the trailing bubbles move into the vortex of the primary bubbles, they accelerate and catch up with and finally merge with the primary bubble resulting in an elongated bubble (Fig. 5(b)). From Fig. 1 it can be seen that the bubble B1 at 0.043 s is just above the distributor which then rises and merges with bubble B2 and finally erupts at 0.17 s. Similar rising time length is also observed for bubbles B3 and B6, and so on and so forth. It is deduced that the primary bubble takes around 0.15 s to rise and then erupt at the top. Fig. 6 shows the bubble velocity for different nose positions of the bubble. It is evident from the figure that the bubble velocity is distinctly different for primary and trailing bubbles. The bubble velocity for primary bubbles initially increases as it rises through the bed then remains constant (at mid-level of the bed) until it falls rapidly at the top of the bed during the eruption. On the contrary, trailing bubbles have very high bubble velocity around 1.5–2 times the velocity of primary bubbles. The increased velocity of the trailing bubble is due to the interaction effect, that is
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Fig. 9. Different forces acting on the bed at different times at a jet velocity of 0.25 m/s for different bed height (axial direction): (a) H = 0.005 m, (b) H = 0.01 m, (c) H = 0.015 m, and (d) H = 0.02 m.
trailing bubbles accelerate to catch up with and merge with primary bubbles which are at a higher level. It should be noted that the bubble properties reported above is for two dimensional bubbles and the simulation setup is a slot model with a bed thickness 4dp. In this study, periodic boundary condition is used to eliminate the front and rear wall effects, as used elsewhere [36,37]. However, the bed thickness may affect the simulation results, even with the use of periodic boundary condition. It might be a potential future study to investigate this effect. 3.3. Particle-fluid interaction force analysis One of the important forces in the process of fluidization is the particle-fluid interaction force. In CFD-DEM, it is obtained as the sum
of the fluid drag force and pressure gradient force as discussed in Section 2. These forces can vary spatiotemporally. As an example, the spatial distribution of various forces (top – drag force; middle – pressure gradient force; and bottom – particle-fluid interaction force) at different times is depicted in Fig. 7. It should be noted that the force ratio is used by normalizing forces with particle gravity mg. It can be observed that these forces around gas bubbles are significantly different from other areas. The forces are generally large in the dense areas around the gas bubbles, and relatively weak in the loose areas in the sides of bubbles or far from bubbles. These forces are maximum in the area between the bubbles (i.e., above the nose of bubbles), and minimum in close vicinity around the bubbles. This force difference in different areas can be primarily attributed to the difference in porosity and permeability [27]. Fig. 8 shows the spatial distributions of porosity, fluid and particle
Fig. 10. Particle fluid interaction force acting on the bed: (a) axially averaged at different radial direction vs time, and (b) radially averaged along the height of the bed.
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Fig. 11. Change in particle-fluid interaction force with the bubble movement.
velocity flow field. It can be seen that the force distribution is minimum at the bubble cloud and wake where porosity is in a range of 0.6–0.8. The distribution of the force is higher in the emulsion region where the bed is loosely packed (porosity = 0.4–0.5) than when densely packed (porosity = 0.3–0.4). Also, it is noteworthy to mention that the region where the force distribution is maximum is corresponding to the region where the gas flows from the nose of the bottom bubble towards the base of the top bubble and also the region where the particle velocity is maximum. Fig. 9 shows the temporal variation of drag force, pressure gradient force and particle-fluid interaction force at different axial bed heights. It can be seen that the pressure gradient force is greater than the drag force at any level of the bed. Moreover, the magnitude of the forces decreases as the bed height increases, which is due to the loss of energy retained by the bubbles as the bed height increases. It can be observed that the peak plateaus as the bed height increases. This is because of the bubble coalescence discussed in Section 3.1. At a lower level of the bed, there is no significant bubble coalescence, however as the bed level increases there is significant bubble coalescence present. Therefore, the interval between the two rising bubbles increases, leading to the increased presence of solid materials in loosely packed state. As a consequence, the increased magnitude of the relative forces resides for a longer period of time forming a plateau. Fig. 10(a) shows the temporal variation of particle-fluid interaction forces for different radial locations and Fig. 10(b) shows the radially averaged particle-fluid interaction force along the height of the bed. It can be seen that the magnitude and fluctuations of the particle-fluid interaction force are high at the center of the bed, and decrease towards the wall. The bubble trajectory follows the centreline since the gas injection is through the central orifice which results in the inconsistency in porosity leading to the fluctuations of the force. In the central region of the lower level of the bed, the particle-fluid interaction force is higher than gravitational force but decreases linearly as the bed height increases, and finally levels off at the top of the bed. At the wall region, the solids are moving down slowly in a packed state, therefore the particle-fluid interaction force is less than the gravitational force. In addition, the peaks illustrated in Figs. 9 and 10 are due to the bubble passage. The maximum represents when the bubble has passed the point while the minimum represents when the bubble centroid is at that point. This information can be clearly visualized in Fig. 11 which shows how the particle-fluid interaction force changes when different parts of the bubble passes through a point. Four points a, b, c, and d are assigned to a bubble, ‘a’ represents the top of the bubble cloud, ‘b’ and ‘c’ represent the top and bottom of the bubble, respectively, and ‘d’ represents the bottom of bubble wake. These positions of a bubble exhibit different magnitude of particle-fluid interaction force, for example, large at locations ‘a’ and ‘d’ while small in locations ‘b’ and ‘c’. Similar
results for local porosity time-series data were shown by Huang and Lu [9], who conducted experiments in jetting fluidized bed by using a capacitance probe. In their case, ‘b’ and ‘c’ locations have higher porosity while ‘a’ and ‘d’ have lower porosity. The porosity and particle-fluid interaction force are inter-related in gas-solid fluidized beds. For example, higher porosity leading to a lower particle-fluid interaction force and lower porosity to a higher particle-fluid interaction force. This finding shows that the particle-fluid interaction force can be used to represent the bubble passage. 4. Conclusion Formation of a series of bubbles in a gas-solid fluidized bed operated with a single continuous jet was studied using CFD-DEM to study the bubble characteristics such as bubble size, shape, and velocity. The results illustrate that the bubbles coalesce at three different bed heights and the pattern of the bubble coalescence is fairly regular but dependent on the jet velocity. The bubbles are categorized into two types: primary/ leading bubbles and trailing bubbles, where primary bubbles are defined as the bubbles whose motion are not affected by the bubbles ahead of them but they affect the succeeding bubbles, and trailing bubbles are those bubbles whose motion is affected by the primary bubbles. The trailing bubbles catch up with the leading bubbles at some height in the bed, thereby coalescing. The size of primary bubble increases at the cost of trailing bubbles. The variation in the size of primary bubbles with bed height are almost identical. The shape of the primary bubbles change from prolate to circular to oblate as it escalates through the bed while the trailing bubbles are elongated in shape. The rising velocity of primary bubbles is 1.5 to 2 times smaller compared to the rising velocity of the trailing bubbles due to the effect of bubble interaction. The drag force, pressure gradient force and particle-fluid interaction force are high in the areas where particles are loosely packed. For example, in the region between the gas bubbles. The forces are relatively weak in the vicinity of bubbles and areas far from the bubbles where particles are densely packed. The temporal variation of particle-fluid interaction force delineates a sharp peak at the lower bed levels and a plateaued peak at the higher bed levels. In addition, particle-fluid interaction forces vary with the bubble positions such as cloud, bubble and wake. Insights generated from this study are helpful to allow a better understanding of bubble dynamics and the hydrodynamics of complex gas-solid fluidized bed behaviour. Acknowledgements The authors are grateful for the financial support from the Australian Research Council Industrial Transformation Research Hubs Scheme (Project Number IH140100035). This research was undertaken with
Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091
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Please cite this article as: S. Shrestha, J.Q. Gan and Z.Y. Zhou, Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.091