Simulation of Bubble Behavior Characteristics in a Rolling Fluidized Bed with the Addition of Longitudinal Internal Members

Abstract

To address the effect of a ship’s rolling on the fluidization quality of fluidized beds, in this study, a simulation of a rolling fluidized bed with longitudinal internal members added (R-FBLIM) was carried out and compared with that of a rolling fluidized bed without internal members added (R-FBWIM). The transient motion, as well as the behavioral characteristics of the bubbles within the R-FBLIM, was analyzed; the variation patterns of the number of bubbles, as well as the equivalent diameter of the bubbles, were compared for different apparent gas velocities, oscillation periods, and amplitudes; and the mechanism of the action of the longitudinal internal members was investigated. The results show that the structural design of the longitudinal internal members can effectively improve the gas–solid fluidization quality of the rolling fluidized bed. The horizontal support plate and the cap hole structure can effectively break the air bubbles, the cap hole structure promotes the radial mixing of the gas–solid fluid, and the internal and outer rings of the curved surface plate roll in rows, which inhibit the aggregation behavior of the gas–solid fluid to the two sides of the oscillating planes, respectively, by cooperating with the cap hole structure. Compared with R-FBWIM, the gas–solid phase within R-FBLIM is more spatially distributed, with the number of bubbles increasing by about 2–4 times and the mean diameter decreasing by about 50–60%. The number of bubbles increases with the gas velocity but decreases with the rolling amplitude; the mean diameter decreases with the gas velocity but responds less to the rolling amplitude change.

1. Introduction

At present, the number of exploitable oil fields on land is declining, while marine oil and gas resources are abundant. Therefore, it is of great significance to promote the development and utilization of marine oil and gas resources. However, whether it is the transport of crude oil and natural gas from the sea to the land for processing or the transport of finished fuel oil and gas products from the land to the sea for use by power equipment, the time and economic costs of long-distance transport are factors that should not be ignored [1]. In recent years, offshore floating platforms such as FPSO (floating production, storage, and offloading) have been more and more widely used due to their high flexibility and adaptability. Based on floating production, storage, and offloading units (FPSOs) and other offshore floating platforms and ocean-going mining vessels, gas–solid bubble fluidization technology has been applied to marine floating platforms. On the one hand, this can carry out the processing of far-offshore oil and gas resources and solid waste treatment and reduce the cost of long-distance transportation while expanding the functions of floating platforms [2]; on the other hand, it can open up a new way for solid waste minimization and marine environmental protection under marine conditions.

Until now, a large number of researchers and scholars have conducted in-depth studies on gas–solid fluidized beds under conventional stationary conditions. These include bubble dynamics [3,4], flow pattern transition and identification [5], particle agglomeration properties [6], and heat and mass transfer [7,8,9]. Based on the above studies on the gas–solid flow characteristics within a conventional static fluidized bed, some researchers believe that the fluid flow characteristics within a gas–solid fluidized bed under conventional static upright conditions can be altered by the addition of internal components [10,11] and the mixing and heat exchange between gas and particles within the bed can be increased [12]. In addition, by reasonably designing the arrangement form and parameters of the internal components, the radial distribution of bubbles in the gas–solid bubbling fluidized bed can be changed, so that the distribution of bubbles in the bed is more uniform and the radial inhomogeneity of bubbles and particles can be attenuated [13,14]. This change in gas–solid flow characteristics is conducive to enhancing the gas–solid two-phase flow uniformity and improving the heat transfer, mass transfer, and reaction performance of the reactor.

However, when fluidization technology is applied to the marine environment, the gas–solid flow characteristics within a wobbling fluidized bed are different from those of a cabinet static fluidized bed [15,16]. The researchers found that in the rolling plane, under the influence of rolling, the bubbles will be aggregated to one side of the wall of the bed, and the particle aggregation wall is in the opposite direction of the bubble aggregation, resulting in the separation of gas–solid two-phase media. In addition, rolling changes the trajectory and shape of the air bubbles near the bed walls [17], and the large bubbles generated during rolling will form large cavities, which will make the gas–solid contact inhomogeneous and change the stability of the fluidized bed [11]; this inhomogeneous distribution will reduce the heat and mass transfer within the fluidized bed [18]. The particle volume distribution also exhibits periodic variations affected by the bubble motion [19], and the particle descent rate exhibits asymmetry under the influence of the rolling amplitude [20]. Therefore, an in-depth study of the bubble behavior characteristics within the rolling fluidized bed is necessary.

Concerning the optimization scheme for gas–solid flow in a conventional static upright fluidized bed, the addition of internal components should also be a viable way to improve the quality of fluidization in a fluidized bed under rolling conditions. In gas–solid fluidized beds under conventional upright conditions, the internal member structure is dominated by the transverse baffle type [10,21,22,23]. Such transverse internal members have an optimizing effect on the gas–solid flow characteristics in fluidized beds when within a certain operating range. However, under rolling conditions, the inertial force, as well as the radial component of the gravitational force, will dynamically change in the time domain, and the attachment of the gas–solid flow to the wall, as well as the reverse aggregation phenomena, are obvious. The radial force of the transverse internal member for the material inside the fluidized bed is small, and it is difficult to attenuate the phenomenon of gas–solid reverse wall aggregation, which is not universally applicable when directly applied to the rolling condition, and on the contrary, it may deteriorate the characteristics of the gas–solid flow in the fluidized bed.

Therefore, based on the gas–solid flow law under rolling conditions, a new type of longitudinal internal member is designed by referring to the structural type of the internal member under conventional stationary conditions. By analyzing and discussing the bubble behavior characteristics in a rolling fluidized bed with the addition of longitudinal internal members (R-FBLIM) and comparing them with those in a rolling fluidized bed without the addition of longitudinal internal members (R-FBWIM), the effectiveness of the longitudinal endmember is examined and, at the same time, an insight into the bubble behavior characteristics within the R-FBLIM is gained. However, it is difficult to accurately capture the bubble behavior inside the fluidized bed through experiments, and this difficulty can be solved by the method of numerical simulation. Through numerical simulation study, the flow characteristics of the medium inside the rolling fluidized bed can be better grasped, and this study is expected to provide relevant methodological references for the improvement of the fluidization quality and inter-phase contact efficiency of the rolling fluidized bed and to provide a theoretical basis for subsequent industrial applications.

2. Numerical Simulation

2.1. Experimental

A three-dimensional gas–solid rolling fluidized bed experimental device consists of a three-dimensional fluidized bed body, rolling platform, gas supply device, high-speed camera, pressure signal acquisition device, and other components; the experimental device is shown in Figure 1a. The main body of the three-dimensional fluidized bed includes a straight bed, expansion section, variable diameter section, distribution plate, gas chamber, and pressure measurement hole. For easy observation, this experiment was carried out in a three-dimensional cylindrical Plexiglas body with a diameter of Φ300 mm. The height of the straight bed is 1000 mm, and the dilatation section and reducer section are installed on the straight bed. The internal diameter of the expanding section is Φ500 mm, the height of the reducing section is 100 mm, and the height of the reducing section is 200 mm. In addition, the gas outlet is equipped with a filter screen to remove dust. Ventilation holes with a diameter of Φ4 mm are uniformly opened on the distribution plate, with an opening rate of 0.94%. The lower part of the distribution plate is equipped with a gas chamber so that the gas can enter the fluidized bed stably and uniformly. The pressure measuring hole is used to connect the pressure probe of the pressure signal acquisition device. The rocking motion of the fluidized bed is controlled by the rocking platform fixed at its bottom, and the required rocking amplitude and rocking period can be obtained by controlling the stroke parameters of the electric cylinder through the program matching with the rocking platform. The gas supply device consists of a blower, a valve, a rotor flowmeter, and other parts. In the experiment, the blower blows out air, controls the gas velocity through the valve, and flows into the fluidized bed after being measured by the rotor flowmeter. Concerning the rocking amplitude and rocking period range of the actual ship movement [24,25], a rocking amplitude of 5~13° and a rocking period of 8~16 s were selected for the experiment, and the operating gas velocity of 0.25~0.4 m/s was selected for the experiment, considering the operating gas velocity range of the bubbling fluidized bed [2,11].

After the gas–solid bubbling fluidized bed is applied to rolling environments such as floating platforms and ships in the ocean, the rolling amplitude, rolling period, and apparent gas velocity will affect the bubble behavior [15]. Considering the periodic effects of the rolling process on the gas–solid flow in the fluidized bed [19], as well as the gas–solid interactions, a novel longitudinal internal member was designed, as shown in Figure 2a [26], which was mounted at the position shown in Figure 1a, with its bottom 100 mm from the bottom of the fluidized bed. As shown in Figure 2a, the longitudinal internal members consist of a lower support plate structure, a middle curved plate structure, and an upper support plate structure. As shown in Figure 2b, the upper and lower support plates are composed of 12 slats with L × W × H = 150 mm × 20 mm × 5 mm and two reinforcing rings with a thickness of 5 mm, and their structures are similar to the transverse member. The lower support plate is used to break bubbles moving in the axial direction and plays the role of supporting the upper curved plate structure as well as the upper support plate; the upper support plate is used to break bubbles growing in the axial direction through the curved plate. As shown in Figure 2c, the overall structure of the curved plate consists of two circles of curved plates, one inside and one outside, each with the same dimensions, a height of 350 mm, and a bending angle of 90°. Figure 2d shows the details of the arrangement of the internal and outer curved panels. There are three curved panels in the same circle, and they are uniformly arranged along the circumference, with their total circumferential arc length accounting for three-quarters of the circumference of the circle in which they are located. In addition, considering that the two gas–solid phases will be, respectively, aggregated to the side wall region during the bed rolling process, the resulting separation movement of the two gas–solid phases along the radial direction and the rolling spacing arrangement between different circles of the curved surface plates can prevent the movement of the gas–solid phase medium along the radial direction, and the gaps between the curved surface plates of the same circle can provide a certain radial mixing condition. In addition, each curved surface plate is provided with a cap hole, and an opening is provided at the location where the cap hole is connected to the curved surface plate; the total opening rate of the curved surface plate is 21.5%. In the same axial line of the surface plate, the cap holes are evenly arranged along the surface plate; in the adjacent two different axial lines, the cap holes are rolling up and down, and the opening direction is reversed, relative to the surface plate facing inward/outward arrangement. On the one hand, the fluidized bed axial and radial movement of gas bubbles breaks through the cap hole structure; on the other hand, the growth in gas residence time in the bed through the different directions and rolling arrangement of the form promotes the radial mixing of the fluid medium.

In the experiments, the gas phase used was room temperature air with density ρ_g = 1.205 kg/m³, viscosity μ_g = 1.79 × 10⁻⁵ Pa·s, and apparent air velocity U_g = 0.25–0.40 m/s. The solid medium used was Geldart B spherical glass bead particles with an initial packing height of H_b = 0.50 m, a particle density of ρ_p = 2350 kg/m³, a packing density of ρ_b = 1402.3 kg/m³, a particle size range from 0.283 to 1.125 mm, and an average particle size of d_p = 0.57 mm.

2.2. Numerical Simulation Models and Meshing Methods

In this experiment, Solidworks 2021 drawing software was used to draw the model, and the Mat format file was exported to the meshing module of Workbench for meshing. As shown in Figure 3a, to ensure the effectiveness of the simulation and reduce the simulation calculation time, the simulation model is the straight bed part of the experimental equipment, with an internal diameter of Φ300 mm and a height of 1000 mm. As shown in Figure 3b, the simulated dimensions of the longitudinal internal members are consistent with the actual dimensions of the internal components. Each unit of the internal member is modeled and assembled, and each unit is saved separately to facilitate the subsequent assembly of each unit structure into the straight bed for simulation. The results of R-FBWIM and R-FBLIM meshing are shown in Figure 3c and Figure 3d, respectively. The mesh at the edge wall of the internal members in the R-FBLIM is encrypted during the meshing to improve the computational accuracy, and the encrypted details of the local position of the edge wall of the internal members are given in Figure 3d.

2.3. Simulation Setting

Simulations were carried out using the CFD software Fluent 2021 using the Eulerian–Eulerian two-fluid model [13], with wall conditions of no slip for the gas phase and partial slip for the particulate phase [27], where the solids are assumed to be anthropomorphic, an assumption that satisfies the continuous medium assumption. Its physical quantities such as velocity, temperature, and pressure have a continuous distribution in space and change slowly enough to obey the assumption of local equilibrium. The RNG k-epsilon flow model is used in the R-FBLIM, and the turbulent viscosity used takes into account the rotational flow in the mean flow, and the addition of a term reflecting the fluid strain rate in the ε equations allows for the treatment of flows with high strain rates, as well as a large degree of streamline curvature. The continuity equation and the interphase momentum transfer equation are calculated by the Gidaspow drag model [28]. The gas phase inlet is set as the velocity inlet and the outlet as the pressure outlet. The control equations are shown in

Table 1. Control equations.

Conservation of momentum of gas and solid	$\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left({\alpha }_g{\rho }_g\overrightarrow{v_g}\right)+\nabla \left({\alpha }_g{\rho }_g\overrightarrow{v_g}\right)=-{\alpha }_g\nabla p+\nabla \left(\stackrel{̿}{{\tau }_g}\right)+{\alpha }_g{\rho }_g\overrightarrow{g}-\beta \left(\overrightarrow{v_g}-\overrightarrow{v_s}\right)$
	$\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left({\alpha }_s{\rho }_s\overrightarrow{v_s}\right)+\nabla \left({\alpha }_s{\rho }_s\overrightarrow{v_s}\right)=-{\alpha }_s\nabla p-\nabla p_s+\nabla \left(\stackrel{̿}{{\tau }_s}\right)+{\alpha }_s{\rho }_s\overrightarrow{g}-\beta \left(\overrightarrow{v_g}-\overrightarrow{v_s}\right)$
Continuity equations of gas and solid	$\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left({\alpha }_i{\rho }_i\right)+\nabla \left({\alpha }_i{\rho }_i\overrightarrow{v_i}\right)=0$
Granular temperature equation	$\frac{3}{2}\left[\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left({\alpha }_s{\rho }_s{\theta }_s\right)+\nabla \left({\alpha }_s{\rho }_s\overrightarrow{v_s}{\theta }_s\right)\right]=\left(-P_{SD}\stackrel{̿}{I}+\stackrel{̿}{{\tau }_s}\right):\nabla \overrightarrow{v_s}+\nabla \left(K_{{\theta }_s}\nabla {\theta }_s\right)-{\gamma }_{{\theta }_s}+{\varphi }_{g_s}$
Solid-phase stress	$p_s={\alpha }_s{\rho }_s{\theta }_s+2{\rho }_s\left(1+e\right){{\alpha }_s^{2}g}_0{\theta }_s$
Solid-phase kinetic viscosity	${\mu }_{s,kin}=\frac{10{\rho }_s{d}_s\sqrt{{\theta }_s\pi }}{96{\alpha }_s\left(1+e\right)g_0}\left[1+\frac{2}{5}\left(1+e\right)\left(3e-1\right)g_0{\alpha }_s\right]$
Solid-phase bulk viscosity	${\lambda }_s=\frac{4}{3}{{\alpha }_s{\rho }_s{d}_{s}g}_0\left(1+e\right)\sqrt{\frac{{\theta }_s}{\pi }}$

, and the bed rolling program is integrated into the Fluent 2021 R1 using a custom function (UDF).

In the simulation, the time step is set to 0.0005 s. To ensure time precision and accuracy, the rolling process is analyzed and calculated after the flow field is stabilized. The gas–solid physical properties and the simulation start time are consistent with the experiments, the gas phase is room temperature air, the solid phase is spherical glass beads, and the calculation time is set to be one rolling cycle, with the maximum angle of the left tilt as the zero point of the start timing. Considering the limitations of the experimental conditions, a broader operating condition was adopted in the simulation, with the simulated apparent gas velocity taken as U_g = 0.30~0.70 m/s, the rolling amplitude taken as Θ = 5~20°, and the rolling period taken as T = 8~16 s. The simulation time was set to be one rolling cycle, and the zero point of the start timing was set at the maximum angle of leftward tilt.

2.4. Meshing and Model Validation

2.4.1. Grid Independence

The tetrahedral meshing method is adopted to mesh the R-FBLIM and R-FBWIM, respectively, by the Patch Conforming algorithm, which is a point-and-body meshing method that can consider all faces and boundaries, and the quality of the meshing is higher than that of the Patch Independent algorithm, which can obtain more accurate calculation results. Six different mesh sizes are constructed for the R-FBLIM, which are 5 mm, 6 mm, 7 mm, 9 mm, 10 mm and 12 mm, and the corresponding numbers of the meshes are 4676933, 3493297, 2451211, 1644294, 1504528, and 1369669; five different global mesh sizes are constructed for the R-FBWIM, which are 6 mm, 7 mm, 9 mm, 10 mm, and 12 mm, and the corresponding grid numbers are 2110644, 1428010, 1051200, 837765, and 625041.

Ensuring mesh independence is an effective way to improve the computational accuracy of the model. As shown in Figure 4, grid-independence validation is performed for R-FBWIM and R-FBLIM, respectively. It can be noticed that the bed pressure drop is less affected by the change in grid size when the grid size is small. Within the R-FBLIM, the absolute values of the magnitude of change in bed pressure drop are ≤1.23%, 2.36%, 5.72%, 5.93%, and 9.12% for models with grid sizes of 6, 7, 9, 10, and 12 mm, respectively, when compared to the size of 5 mm; within the R-FBWIM, the models with grid sizes of 7, 9, 10, and 12 mm showed bed pressure drop changes of ≤2.31%, 3.13%, 10.02%, and 7.49% in absolute terms, respectively, when compared to the 6 mm size. Therefore, based on ensuring the accuracy and timeliness of the simulation, the global grid size of R-FBLIM was determined to be 7 mm and the number of grids was determined to be 2451211; the global grid size of R-FBWIM was determined to be 9 mm, and the number of grids was determined to be 1051200.

2.4.2. Model Validation

In Figure 5, the pre-simulation of the R-FBLIM and R-FBWIM by the selected model, respectively, with U_g = 0.30 m/s, Θ = 10°, and T = 8 s as an example, is shown, as well as the cloud maps of the solidity distribution in the fluidized bed for the three transient attitudes obtained by simulation and pictures of the particle distribution obtained by experimental means. Among them, in the solidity distribution cloud diagram, dark blue is the gas phase aggregation area (bubbles) and red is the particle aggregation area; in the particle distribution picture obtained by the experiment, dark grey is the gas phase aggregation area (bubbles). The comparison shows that the phenomena such as bubble distribution and aggregation trend observed in the simulation and experiment are in good agreement with the R-FBLIM and R-FBWIM. At different axial heights for the three transient attitudes (t = 1/4T, t = 1/2T, and t = 3/4T), the bubble distribution and sizes obtained from the experiments and simulations are similar, and it is also found that the transient tilt of the bed (t = 1/2T) exhibits a clear bubble aggregation feature in both the particle distribution pictures and the simulated solid content ratio distribution cloud maps.

The pressure signal fluctuation is related to the gas–solid hydrodynamics in the fluidized bed [11]. Figure 6 takes the pressure signal value at the P3 measuring point as an example and gives the change curve of the instantaneous pressure signal with time at the height of the Z2 and Z3 cross sections. It can be seen that the fluctuation law of the pressure signal obtained from the experiment and the simulation is basically the same, and the pressure signal fluctuates drastically in the R-FBWIM during the instantaneous attitude transformation (t = 2.0 s, t = 4.0 s, t = 6.0 s). The pressure signal fluctuations within the R-FBLIM are less affected by the rolling attitude transformation, and the experimental and simulation results are closer.

The time-averaged pressures of R-FBLIM and R-FBWIM at different axial heights of P1 and P2 measurement points are given in Figure 7, in which the time-averaged pressures obtained from experiments and simulations decrease with increasing axial heights, and the error of simulations relative to experiments is within 20%. This shows that the models used in this study for R-FBLIM and R-FBWIM are reliable and can satisfy the simulation of gas–solid two-phase flow under rolling conditions.

2.5. Bubble Image Processing Method

The gas phase in the fluidized bed mainly exists in the form of gas bubbles and interstitial gases in the particles in the emulsified phase. Now, based on the X-Z oscillating plane, the gas–solid distribution in the plane is extracted. The threshold value of the bubble phase under the instantaneous flow field is set to 0.8 [29,30,31]; that is, it is considered that when the volume fraction of the gas phase is higher than 0.8 (the volume fraction of the solids is lower than 0.2), the gas phase mainly exists in the form of bubbles, while the one lower than 0.8 (the volume fraction of the solids is higher than 0.2) mainly exists in the interstitial space of the particles, and the physical characteristics such as the velocity of the bubble phase can be obtained from the flow field data at this time.

The image needs to be greyscaled prior to image processing [32]. As shown in Figure 8, the cloud map obtained from the simulation is processed by Matlab 2021 software, and the cloud map is the rolling plane passing through the central axis of the bed. Firstly, the cloud map is converted to greyscale by grey scale processing through the Rgb2gray function, and then the greyscale map is binarized through the Imbinarize function, and the greyscale map is converted to the binarized map. At this time, the image has only two colors, black and white, which is convenient for the extraction of bubble information. As shown in Figure 8c, based on the threshold setting, the black area, except for the upper part of the fluidized bed, is the bubble phase and the white is the emulsion phase. Finally, the connectivity region where the bubble phase is located is identified by the Bwlabel function, and the bubble size and the number of bubbles at the moment where each cloud is located are recorded using the Regionprops function and the Length function, respectively, with the number of bubbles denoted by S. The bubble size and the number of bubbles at the moment where each cloud is located are recorded by the Bwlabel function. The bubble mean equivalent diameter Db is obtained by averaging the bubble sizes at each moment.

3. Results and Discussion

3.1. Characteristics of Transient Bubble Distribution inside the R-FBLIM Bed and Comparison with R-FBWIM

Figure 9 shows the gas inclusion rate distribution characteristics of R-FBWIM and R-FBLIM at the wall and inside the bed in a gas–solid fluidized bed under rolling conditions with U_g = 0.40 m/s, Θ = 10°, and T = 8 s.

The high gas velocity region above the bed (red-filled section) contains almost no particles, so it is not focused. In the lower bed region, on the other hand, different gas velocity distribution characteristics can be observed from the figure, by which the distribution characteristics of the bubbles can be discerned. Compared with the analysis of the wall bubble characteristics in the experimental part of Section 3, it can be found that the simulation results are similar to the experimentally observed wall bubble movement patterns. Inside the R-FBLIM, it can be observed that the number of bubbles in the middle and lower parts of the bed increases significantly after the breaking of the internal components. Those aggregated bubbles that reach a certain height are re-broken and uniformly distributed in the radial direction. In contrast, within the R-FBWIM, a larger range of bubble-attached aggregation can be observed, especially in the region of the upper wall of the inclined bed. This leads to particle aggregation towards the lower wall region of the inclined bed, exhibiting a low gas velocity distribution pattern in the lower wall region of the inclined bed. A comparison of the R-FBLIM and R-FBWIM reveals that the presence of the internal member inhibits the continuous bubble aggregation and growth due to the transient tilting of the bed.

The periodic transition of the bed body transiently in the tilted and upright attitudes is the main feature in the operation process of the rolling fluidized bed, and it is also an important factor affecting the gas–solid motion. Therefore, to deeply analyze the influence of attitude transition on the bubble motion in the bed, the bubble distribution cloud map during the transition between upright and tilted attitudes of the bed is binarized according to the bubble image processing method introduced in Section 2.5. Among them, the velocity distribution cloud map comes from the plane located along the rolling direction passing through the center axis of the bed (the plane where the X-Z coordinate axes are located), and the time interval of cloud map extraction is 0.20 s. Taking U_g = 0.40 m/s, Θ = 10°, T = 8 s as an example, Figure 10a–c show the bubble distribution after binarization during the process from instantaneous upright to the maximum tilt angle on the right side (t = 2.0~4.0 s corresponding to t = T/4~T/2), where the right side of Figure 10b 1→2 and 3→4 show the local enlargement of the motion of bubbles in the R-FBLIM before and after passing through the cap holes on the curved surface plate.

Observing Figure 10a,b, it can be found that the bubbles entering into the R-FBLIM are more uniformly distributed along the axial direction at different moments, and the number of bubbles in the bed is larger and the diameter is smaller. From the bubble movement process of 1→2, 3→4, it can be seen that the cap holes on the longitudinal curved plate can crush the aggregated bubbles step by step. In addition, the crushed bubbles have a velocity in the direction of the cap-hole constraints, which makes the bubbles more uniformly distributed along the radial direction. Observing Figure 10c, in the R-FBWIM, the bed has just completed the attitude transition from left-tilted to upright at t = 2.0 s. In the period of t = 2.0~2.6 s, even though the tilted attitude transition (transient right-tilted attitude) has occurred, according to the bubble movement process of 1→2 in the R-FBWIM, it can be seen that some of the bubbles are still aggregated in the lower wall region on the right side of the bed, and with the emergence of the phenomenon of “bubble attachment transition lag” [33], there was also a bubble transition delay of 0.60 s. However, the “bubble attachment transition lag” disappeared in the t = 2.8–4.0 s range during bed motion. The transition of the bed tilt attitude caused a shift in the bubble wall aggregation region, and the bubbles tended to concentrate in the upper wall region of the tilted bed, which had larger diameters, while almost no bubbles were generated in the lower wall region of the tilted bed.

Figure 11a–c show the binarized bubble distribution during the process from the maximum tilt angle on the right side of the transient to upright motion (t = 4.0~6.0 s corresponding to t = T/2~3T/4), where the right side of Figure 11b shows a local zoom in 3, 4→5 for the movement of bubbles within the R-FBLIM before and after they pass through the cap holes on the curved plate.

As can be seen in Figure 11a,b, the bed tilted significantly during the period of t = 4.0~4.8 s. The wall-attached aggregation behavior of some bubbles was also accompanied by the R-FBLIM, but the size of the wall-attached bubbles has been significantly reduced compared with the R-FBWIM. Meanwhile, as shown in labels 1 and 3, the bubble distribution tends to move towards the mid-axis side of the bed. In addition, as can be seen from label 2, reaching the upper support plate action region corresponding to the height of Z3, the large bubbles are also cut into several individual bubbles with small differences in diameter after passing through the support plate. Observing the bubble movement process of 4→5 circled in the figure, the cap hole also plays a crushing role. As can be seen from Figure 11c, in the range of t = 2.6~3.2 s within the R-FBWIM, some bubbles rise along the attached wall region to the height region of Z2~Z3 to complete an agglomeration, which is conical in shape and breaks up and overflows when it reaches the position of Z3.

In summary, the cap holes provided in the curved surface plate of the internal member can continuously crush the gas bubbles during the bed rolling process and give some of the gases radial constraints, which, to a certain extent, inhibit the gases from gathering and aggregating the amount of gases directly to the wall area. At the same time, the upper support plate also crushes the gas bubbles, increases the number of gas bubbles, and reduces their diameters, making the distribution of gas bubbles in the R-FBLIM more uniform. In addition, during the transient upright to transient right-tilting swaying process, there is no phenomenon of continuous aggregation of gas bubbles attached to the wall.

3.2. Patterns of Change in Bubble Behavior within R-FBLIM and Comparison with R-FBWIM

To further analyze the bubble motion characteristics inside the R-FBLIM bed and the influence of internal components, the bubble parameter information in the X-Z coordinate plane along the rolling direction is extracted, and the instantaneous number of bubbles inside the R-FBLIM and R-FBWIM beds in one cycle is counted and analyzed according to the bubble image processing method given in Section 2.5.

Taking U_g = 0.40 m/s, Θ = 10°, and T = 8 s as an example, Figure 12 demonstrates the change rule of the number of bubbles S in the X-Z axis coordinate plane along the rolling direction of R-FBLIM and R-FBWIM with time. As can be seen from the figure, the number of bubbles in the R-FBLIM stays between 11 and 22 throughout the process, and the number of bubbles is higher than 13 at most moments, which is much more than the number of bubbles in the R-FBWIM. It is worth noting that within the R-FBWIM, due to the effect of rolling, the number of bubbles rises significantly when the bed is in the vicinity of the upright attitude (t = 2.0 s and t = 6.0 s), while in the transiently tilted attitude, the number of bubbles is lower. As shown in Figure 13, this is because the transient tilting leads to a decrease in the circulation area in the vertical direction of the bubbles, and in the case where the bubble aggregation behavior is dominant, the bubble diameter increases and aggregates with bubbles that have risen to a certain altitude to form attached bubbles that begin to rise along the side walls. From the curve of bubble number versus time, it can be observed that the number of bubbles in the R-FBWIM decreases abruptly due to the aggregation and growth behavior of multiple bubbles during the period of t = 2.0–3.0 s. The bubble number of the R-FBWIM increases with the growth of the bubble. By comparing the average number of bubbles in the R-FBLIM and R-FBWIM beds, the average number of bubbles in the R-FBLIM is about 3–4 times that of the R-FBWIM, which suggests that the internal member has a cutting and crushing effect on large bubbles in the bed and also inhibits the aggregation of small bubbles to the wall area to form large bubbles.

To further analyze the bubble kinematic properties inside the R-FBLIM bed and the influence of internal components, the bubble parameter information in the X-Z axis coordinate plane along the rolling direction is extracted, and the instantaneous bubble means equivalent diameters, D_b, inside the R-FBLIM and R-FBWIM beds in one cycle, are statistically counted and analyzed according to the bubble image processing method given in Section 2.5.

The average equivalent diameter of bubbles, D_b, is an important indicator for assessing the effectiveness of gas–solid contact in fluidized beds. In a gas–solid bubbling fluidized bed, the bubble phase and the emulsion phase do not exist in isolation, but gas-phase exchange occurs continuously on the contact surface between the bubble phase and the emulsion phase. Therefore, the size of the bubble diameter in the fluidized bed affects the exchange efficiency of the wrapped gases, and a larger bubble diameter implies a larger amount of wrapped gases, resulting in a portion of the wrapped gases not being able to be exchanged promptly, which affects the quality of the fluidization. Figure 14 demonstrates the distribution of the average equivalent diameter of bubbles in the X-Z plane of the R-FBLIM and R-FBWIM beds over the entire rolling cycle. As can be seen from the figure, in R-FBLIM, the bubble mean equivalent diameter does not change significantly with the bed swaying, and the bubble mean equivalent diameter in the X-Z plane along the swaying direction is maintained between 0.015 m and 0.033 m. In R-FBWIM, the bubble mean equivalent diameter in the X-Z plane is between 0.015 m and 0.033 m. In R-FBWIM, however, the bubble mean equivalent diameter changes significantly with the rolling of the bed. When the bed is transiently in leftward inclination (t = 0.0 s to t = 1.0 s), some bubbles are aggregated and obvious, resulting in a sudden increase in the bubble mean equivalent diameter at a certain moment. When the bed transient attitude is close to upright (t = 2.0 s), the aggregation behavior of the bubbles is weakened and the mean equivalent diameter of the bubbles decreases. However, when the bed is tilted again, bubble aggregation occurs again and this aggregation behavior persists after the transient upright motion, with some bubbles still having larger diameters. In other words, the phenomenon of “bubble attachment transition hysteresis” described in Section 3.1 leads to a cumulative effect of bubble aggregation in time, which prolongs the cumulative time for the presence of large-sized bubbles.

By comparing the average bubble size in the R-FBLIM and R-FBWIM beds, the average bubble equivalent diameter in the R-FBLIM beds is about 50–60% of that in the R-FBWIMs, which also indicates that the internal member has a cutting and crushing effect on the large bubbles inside the beds and also inhibits the aggregation of small bubbles to the wall area to form large bubbles.

3.3. Changing Law of Bubble Behavior with Operating Parameters

3.3.1. Changing Law of Bubble Behavior in R-FBLIM with Apparent Gas Velocity

As shown in Figure 15, the number of bubbles S and the average equivalent diameter of bubbles D_b for R-FBLIM and R-FBWIM at different apparent gas velocities are given, with the number of bubbles and the average equivalent diameter of bubbles coming from the X-Z coordinate plane along the rolling direction. Comparing the R-FBLIM and R-FBWIM, it can be seen from the figure that at all gas velocities, the overall number of bubbles in the bed of the R-FBLIM is larger than that of the R-FBWIM, and the average equivalent diameter of the bubbles is smaller than that of the R-FBWIM, which indicates that the longitudinal internal members are effective in suppressing the gas aggregation to the wall area and improving the gas–solid contact efficiency.

From the change rule of the average equivalent diameter of bubbles with apparent gas velocity, the average equivalent diameter of bubbles in R-FBWIM shows a tendency to increase and then decrease with the increase in gas velocity; when the apparent gas velocity U_g ≤ 0.50 m/s, the bubbles near the wall are mainly aggregated, and when U_g > 0.50 m/s, the increase in gas velocity also enhances the tendency of bubble crushing, which leads to the consequent decrease in the size of the bubbles. Within the R-FBLIM, the average equivalent diameter of bubbles generally shows a slow decreasing trend with increasing gas velocity, and this change is characterized mainly by the ability of the internal members to fragment large bubbles, thus limiting the growth of bubble size. In addition, with the increase in apparent gas velocity, the average equivalent diameter of bubbles in the R-FBWIM shows a pattern of increasing and then decreasing, which is consistent with the conclusion of Hao [33] in the non-coherent analysis of pressure signals.

In terms of the number of bubbles, the overall number of bubbles in the R-FBWIM does not change much with the gas velocity; when the gas velocity is low, the number of bubbles generated is small and there is a tendency to merge with the wall area, while when the gas velocity is high, the rate of merging to the wall is accelerated, so the overall number of bubbles does not change much with the gas velocity. In the R-FBLIM, the overall number of bubbles shows an increasing trend with the increase in gas velocity due to the constraints of the longitudinal internal members and the crushing effect on the bubbles.

3.3.2. Patterns of Change in the Oscillation Period of Bubble Behavior within the R-FBLIM

In addition to the apparent gas velocity, the rolling parameter is also a condition that affects the bubble behavior. Taking U_g = 0.40 m/s and Θ = 10° as an example, Figure 16 shows the number of bubbles S and the mean equivalent diameter of bubbles D_b in R-FBLIM and R-FBWIM under different rolling cycles. It can be seen from the figure that, under different rolling cycles, the action of the internal member makes the number of bubbles in R-FBLIM increase significantly and the mean equivalent diameter of bubbles is smaller than that of R-FBWIM. However, the effect of the rolling cycle on the number of bubbles and the mean equivalent diameter of bubbles is smaller. The equivalent diameter and the average equivalent diameter and number of bubbles in R-FBLIM and R-FBWIM did not change significantly with the rolling period.

3.3.3. Patterns of Bubble Behavior within the R-FBLIM as a Function of Oscillation Amplitude

Figure 17 shows the number of bubbles, S, and the bubble mean equivalent diameter, D_b, for the R-FBLIM and R-FBWIM at three different sway amplitudes with U_g = 0.40 m/s and T = 8 s. It can be observed that the bubble mean equivalent diameter in the R-FBLIM is unaffected by sway amplitude, and the number of bubbles decreases when the sway amplitude is increased. Unlike the R-FBLIM, the mean equivalent diameter of bubbles in the R-FBWIM decreases with increasing rolling amplitude, while the number of bubbles slightly increases.

With the increase in rolling amplitude, the overall tendency of gas aggregation to the wall is enhanced. For R-FBLIM, the degree of gas aggregation to the wall is limited by the constraints of the longitudinal internal members, but with the increase in rolling amplitude, some gas aggregation is also generated in the wall region, and thus the distribution of the number of bubbles S is shown to be decreased with the increase in rolling amplitude. As for the R-FBWIM, compared with the R-FBLIM, because it does not have the constraint effect of the longitudinal internal members, the gas phase produces obvious wall aggregation at a small rolling amplitude, so the number of bubbles does not change greatly with the rolling amplitude.

The difference in the trend of the average equivalent diameter of R-FBLIM and R-FBWIM bubbles with the rolling amplitude is mainly caused by the difference in the material level height at the bed interface of the two. Normally, with the increase in rolling amplitude, the difference in bed material level height between two sides of the bed tilted in the rolling direction increases, which leads to the different resistance of the gas phase in the wall area on both sides of the rolling direction, and the resistance in the low material level area is smaller, so the gas phase is more inclined to pass through the area with low resistance. For the R-FBWIM, with the increase in rolling amplitude, the height of the material level on the gas-phase aggregation side decreases, and the decrease in the material level also shortens the gas-phase circulation distance, which shortens the bubble aggregation time and thus leads to the decrease in the average equivalent diameter of the bubbles with the increase in the rolling amplitude. In the R-FBLIM, the bed level is less affected by the rolling amplitude due to the constraints of the longitudinal internal members on the gas and particles, so the bubble mean equivalent diameter curve is nearly horizontal.

In the above Figure 15, Figure 16 and Figure 17, in comparison to R-FBWIM, from the change rule of the average equivalent diameter of the bubbles in R-FBLIM with the operating conditions, it can be seen that the average equivalent diameter of the bubbles under the action of the internal member does not change with the rolling amplitude, which shows that the internal member improves the effect of the change in rolling amplitude on the behavior of the bubbles, and the guiding and crushing effect of the cap holes improves the contacting efficiency of the solids in the bed, and, at the same time, the curved surface plate also inhibits the bubbles from gathering and growing on the side of the attached wall.

The curved surface plate also inhibits the bubbles from aggregating and growing up at the side of the attached wall; in addition, it can be found that the number of bubbles in the R-FBLIM increases significantly compared with that in the R-FBWIM, and the number of bubbles in the R-FBLIM is about 2–4 times that of the bubbles in the R-FBWIM, and the average equivalent diameter of the bubbles is about 50–60% of that in the R-FBWIM.

3.4. Mechanism of Action of Longitudinal Internal Members

Previous studies have shown that the fluidized bed rolling motion has a greater effect on the distribution of internal gas and particles within the bed; after adding the longitudinal internal members designed in this paper, the tendency of gas aggregation to the side wall is suppressed to a certain extent, and the homogeneity of the gas–solid distribution is improved. To investigate this mechanism of action of the longitudinal internal members, this paper will use numerical simulation research methods to reveal this mechanism of action by analyzing the detailed information of the local flow field of the R-FBLIM bed.

Firstly, the bed was cut along the plane where the X-Z coordinates of the bed rolling direction are located, and the bed was divided into two parts equally to show the details of the gas–solid flow inside the bed of the R-FBLIM through the cut surface, as shown in Figure 18a–c.

Figure 18a shows the schematic diagram of the equipment in the area of the installed longitudinal internal members, where the blue part is the longitudinal internal member and the transparent part is the fluidized bed cylinder; Figure 18b shows the sectional structure after cutting the plane where the X-Z coordinates of the R-FBLIM are located; Figure 18c shows the clouds of gas–solid distribution based on the plane, and with the center line of the bed in the vertical direction as the reference, the section on the left side of the center line contains the curved surface plate in the internal rim of the longitudinal internal members, as well as the cap-hole structure, and the profile to the right of the center line contains the longitudinal internal member’s outer ring curved plate and the cap-hole structure.

In conjunction with the longitudinal internal member’s structure, shown in Figure 2 in Section 2, the support plate is equivalent to a horizontal internal member in addition to its role in fixing the curved surface plate.

Figure 19 shows the gas–solid distribution cloud diagram of the upper support plate region of the longitudinal internal members. Figure 19a,b, respectively, give the gas–solid distribution cloud diagrams under two adjacent instantaneous moments when the fluidized bed is swaying, and it can be found from the 1→2 bubble movement marked out in Figure that, after the bubbles under the support plate are aggregated and crushed by the vertical slat structure of the support plate, the bubble sizes are all reduced. Analysis found that when the diameter of the bubble through the slat gap, due to the existence of the slats, is larger, then the slat spacing will be divided by the slats; when the bubble through the slat structure is compared to the longitudinal internal members above, the bubble diameter is smaller than the slat spacing to achieve the effect of crushing. It can thus be shown that under the rolling condition, the support plate portion on the longitudinal internal members can also have a crushing effect on the air bubbles in its area of action.

The above analysis shows that the slat structure of the upper and lower support plates of the longitudinal internal members can play a role in breaking up the bubbles. To analyze the role of the curved surface plate, which is the core component of the longitudinal internal members, Figure 20 gives a cloud map of the oscillating plane gas–solid distribution of the region where the curved surface plate of the fluidized bed acts in the R-FBLIM at a certain transient attitude.

The above analysis shows that the slat structure of the upper and lower support plates of the longitudinal internal members can play a role in breaking up the bubbles. To analyze the role of the curved surface plate, which is the core component of the longitudinal internal members, Figure 20 gives a cloud map of the oscillating plane gas–solid distribution of the region where the curved surface plate of the fluidized bed acts in the R-FBLIM at a certain transient attitude. Two neighboring instantaneous moments are given for both instantaneous attitudes. First of all, Figure 20a,b are the moments when the bed is transiently in tilt, but there are bubbles in both wall regions of the bed, which indicates that the curved surface plate can have a certain restraining effect on the gathering of gas phases existing in the original R-FBWIM towards the upper wall region of the tilted bed, which reduces the amount of gas in the upper wall region of the original R-FBWIM and correspondingly enhances the amount of gas in the lower wall region of the bed, which improves the homogeneity of the distribution of the gas bubbles in the bed. Secondly, observe the surface plate in the figure on both sides of the cap hole; when the support plate is similar, the cap hole structure can also play a role in breaking the bubbles. As can be seen from the figure, part of the large bubbles move through the cap hole before the cap hole is cut by the edge of the cap hole and are broken into different sizes of small bubbles, due to the influence of the oscillation. Also, part of the cap hole along the edges of the cap hole from the outside of the cap hole moves in an upward manner, and a part of the hat hole moves through the hat hole into the cap hole where the interior of the curved surface plate is; so, respectively, the movement towards the surface of the plate on both sides of the cap hole has a guiding effect on the bubbles.

Based on the above analyses, to further observe the gas flow in the vicinity of the curved plate of the longitudinal internal members and the cap hole, the gas velocity vector passing through the longitudinal inner member, as well as the solid volume fraction cloud, is given in Figure 21. Figure 21a shows the gas-phase motion trajectory passing through the longitudinal internal members, and for easy observation, a local magnification of the white boxed area is given on the right side of Figure 21a, which corresponds to the gas-phase flow trajectory near the outer ring of cap holes of the curved plate and that near the internal ring of cap holes of the curved plate, respectively. Figure 21b gives a cloud view of the gas velocity vector, as well as the solid volume fraction distribution in the rocking plane, with the white part of the figure showing the planar region occupied by the longitudinal internal members.

From Figure 21a, it can be seen that around the curved plate, the gas-phase flow traces from bottom to the top, showing the form of upward flow close to the outer wall of the curved plate and the cap hole, and when it flows to the vicinity of the cap hole, part of the gas phase enters into the internal part of the cap hole, and the rest of the gas phase flows upward along the outer wall of the curved plate. Additionally, it can be found that the flow trajectory is in a curved “S” shape, it is in the same circle of surface plate spacing area, the gas phase exists inside and outside the flow behavior, and different circles of the surface plate rolling set up and form part of the gas close to the surface plate wall in an upward movement; at this time part, of the gas can not be entered into the other circle of the surface plate in time to block the area or the longitudinal component of the internal members. This shows that the longitudinal internal members with the circle of the surface plate spacing set can not only restrain the gas flow directly to the wall area aggregation but also provide a channel for the radial mixing of gas and particles. From Figure 21b, it can be further seen that, under the action of the longitudinal internal members, the gas upward trajectory shows an “S”-shaped flow trajectory similar to that of Figure 21a, and after the guiding action of the cap holes, the gas has a tendency to move in the radial direction, and the gas phase between the internal and outer surface plates continues to be exchanged in the process of upward movement through the cap holes. Combined with the solid volume fraction distribution cloud diagram, it can be found that there is a gas-phase aggregation region with a low solid volume fraction at the node of the gas velocity vector, but under the action of the curved plate, the gas aggregation will not continue to occur but is in the axial direction in the “aggregation separation”, which, to a certain extent, restricts the growth of the bubbles, and this is the reason why the bubble growth in the R-FBLIM is limited by the fact that the gas phase is not in the radial direction. This limits the growth of bubbles to some extent, which is one of the reasons for the reduction in bubble diameter in R-FBLIM.

The above analysis shows that the longitudinal internal members designed in this paper, the upper and lower support plates, and the cap-hole structure on the longitudinal curved plate can realize the shear crushing of the gas bubbles, and the internal and outer circles of the longitudinal curved plate are set at intervals, which on the one hand can have a certain restraining effect on the gathering of gases directly to the wall area and on the other hand can also provide a channel for the radial mixing of gases and solids.

The influence of the above structure on the gas–solid flow in the bed is the reason why the gas–solid distribution in the R-FBLIM is more uniform than that in the R-FBWIM, which also confirms that the longitudinal internal members proposed in this paper are effective at improving the gas–solid fluidization quality in the rolling fluidized bed.

4. Conclusions

(1) Compared with R-FBWIM, the uniformity of gas–solid spatial distribution inside the bed of R-FBLIM is improved, and the time-dependent fluctuation of gas–solid flow parameters during the rolling cycle is reduced. The number of bubbles inside R-FBLIM is increased, which is about 2–4 times that of R-FBWIM; the average equivalent diameter of the bubbles is reduced, which is about 50–60% of that of R-FBWIM.

(2) Within the R-FBLIM bed, the number of bubbles increases with apparent gas velocity and decreases with rolling amplitude; the mean equivalent diameter of bubbles decreases with apparent gas velocity and varies to a lesser extent with rolling amplitude; and the rolling period has a small effect on both the number of bubbles and the mean equivalent diameter.

(3) The longitudinal internal members designed in this paper, the upper and lower support plates, and the cap hole structure on the longitudinal curved plate can realize the shear crushing of gas bubbles, and the internal and outer circles of the longitudinal curved plate are set at intervals, which can have a certain restraining effect on the direct gathering of gases to the wall area and also provide a channel for the radial mixing of gases and solids. Additionally, the influence of the above-mentioned structure on the flow of gases and solids in the bed is the main reason that the gas–solid spatial distribution within the R-FBLIM is more even than that of the R-FBWIM and the flow parameter fluctuation amplitude is smaller than that of the R-FBWIM.