Investigation of fluidization behavior of high density particle in spouted bed using CFD–DEM coupling method

    Investigation of fluidization behavior of high density particle in spouted bed using CFD-DEM coupling method Malin Liu, Yuanyun Wen, Rongzheng Liu, Bing Liu, Youlin Shao PII: DOI: Reference:

S0032-5910(15)00327-7 doi: 10.1016/j.powtec.2015.04.042 PTEC 10952

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

4 August 2014 13 February 2015 20 April 2015

Please cite this article as: Malin Liu, Yuanyun Wen, Rongzheng Liu, Bing Liu, Youlin Shao, Investigation of fluidization behavior of high density particle in spouted bed using CFD-DEM coupling method, Powder Technology (2015), doi: 10.1016/j.powtec.2015.04.042

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Investigation of fluidization behavior of high density

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particle in spouted bed using CFD-DEM coupling method

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Malin Liu1, Yuanyun Wen, Rongzheng Liu, Bing Liu, Youlin Shao

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(Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing 100084 China)

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Abstract：CFD-DEM coupling simulation method is used to study the fluidization behavior of particle with different densities in the spouted bed. The simulation results show that the particle spouting behavior is incoherent and periodic in the stable spouting state. The cycle periods of the whole bed and single particle are obtained from particle trajectory and compared with experimental results. The relationships between the minimum spouting gas velocity, the steady pressure drop and the particle density are obtained. It can be found that the gas velocity range of stable spouting state expands when the particle density increases. The dual, single and multiple dominant frequencies are found in the stable spouting process of high density particle. Through detailed analysis on the mechanism of spouting dominant frequency, the flow pattern map with different superficial gas velocities and particle densities is given and can be divided into five regions: fixed bed with internal spouting, transitional stable spouting state with dual dominant frequency, main stable spouting state with single dominant frequency, transitional stable spouting state with multiple dominant frequency, and unstable spouting state. The stable spouting gas velocity is influenced by the particle density, while the dominant frequency of the particle spouting process will keep invariant even the particle density increases, as long as Ug/Ums is not changed. The influence of particle density on the particle residence time distribution in the spout region, which can be used to characterize the gas solid contact efficiency, is also discussed based on simulation results. Key words：Spouted bed; CFD-DEM; High density particle; Spout frequency; Flow pattern map

1. Introduction Gas-solid fluidized bed can achieve a high rate of mass and heat transfer and is suitable for particle uniform mixing and continuous mass production. It has been widely used in various

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Corresponding author. Tel.: +86 10 89796092; Fax: +86 10 69771464.

Email address: [email protected](Malin Liu)

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process industries. As a kind of special fluidized bed which was suitable to treat Geldart D-type particles, spouted bed has been applied in many areas such as particle coating, drying and surface modification since it was invented in 1955[1]. Efficiency of spouted bed depends on the efficiency of gas-solid mixing and interaction. The enhancement of the gas turbulence and the fluctuation intensity of the solid motion will have a significant influence on the efficiency. The fluidized bed-chemical vapor deposition (FB-CVD) technique can be used for the preparation of nuclear fuel UO2 coated particles and it is the key technology for the guarantee of nuclear reactor safety[2]. The contact efficiency of gas and solid phase in the coating process in spouted bed can be seriously influenced by unstable spouting state and particle agglomeration. The particle density of nuclear fuel UO2 (ρp~10.80 g/cm3) is much larger than that of general particles used in chemical engineering, such as glass beads (GB, ρp~2.60 g/cm3), thus the impact of particle density on the fluidization behavior is important and should be investigated systematically. There have been lots of literature reports on the study of spouted bed on both experimental and theoretical aspects[3], and related monographs have also been published[4, 5], while most of which mainly focus on the low density particle (ρp<3.0 g/cm3). For example, Zhou et al.[6] gave a systematic summarization on the spout fluidizing behavior of different particles such as silica gel beads, polymers, grain, glass beads (GB), pulverized coal, activated carbon and ceramic particles. 25 formulas for calculating the minimum spouting gas velocity were obtained with particle density in the range of 0.40~2.98 g/m3. There are also a few reports on the study of fluidization behavior of high density particles. Zhou et al.[6] studied the minimum spouting gas velocity, gas pressure drop, fountain height and gas velocity distribution of ZrO2 particle (ρp= 5.6 g/cm3) experimentally and hydrodynamic equations were established, but detailed analysis on the effects of particle density on particle fluidization behavior was not given for lack of systematic numerical simulation. Sari[7] investigated the fluidization behavior of high density particles (ZrO2, dp= 0.5, 1 mm) using high speed camera in spouted bed with the diameter of 15 mm and the taper angle of 30°, 45° and 60°. The investigation indicated that after the beginning of external spouting, the intermittent spouting area exists in the range of Ums~1.2Ums and steady spouting state exists in the range of 1.2Ums~2.1Ums . Then jet spouting region appeared as Ug increased continuously, which shows different flow pattern transition from low density particle. Alekhine[8] made an investigation on the brass particles (ρp=8.9 g/cm3) and developed the flow pattern transition rules of high density particles. Saayman[9] paid attention to high density particle (FeSi, ρp=6.69 g/cm3) and pointed out that the reaction performance increases as the bubble become smaller in size in the fluidizing process of high density particle. In the research by Pannala[10], the fluidizing process of ZrO2 particle was numerically simulated, and it is pointed out that periodic particle entrainment exists in the spouting process. It can be found that the above research mainly focus on one kind of high density particles. So far no detailed studies on the effects of high density particles on the spouting process were reported. The numerical simulation methods for studying particle fluidization in the gas-solid system generally include the Euler-Euler method based on Two-Fluid model and the Euler-Lagrange method based on CFD-DEM (Computational Fluid Dynamics–Discrete Element Model)[11]. The hydrodynamic behavior of gas-solid phase in spouted bed was numerically simulated with Two-Fluid model by Hosseini[12]. The particle concentration distribution and velocity field distribution in the jetting region, annulus region and fountain region was given. DEM has been

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widely used for providing the detailed information on particle scale[13, 14]. Salikov[15] has investigated the Al2O3 particle (ρp=1.04g/cm3) dynamics in a prismatic spouted bed using CFD-DEM model. Zhao[16] carried out numerical CFD-DEM simulation study on the flow and mixing behavior in the 2-dimensional riser and downer, and the transient behavior of particle agglomeration was given. Zhong[17] developed the CFD-DEM method and applied it to the study of the particle mixing behavior in the spout-fluid bed. Also, the fluidization behavior of glass beads in the two-dimensional spouted bed was numerically simulated with CFD-DEM method by Zhao[18]. Especially, CFD-DEM coupling method was used in the numerical simulation of film coating process in a novel rotating fluidized bed by using an assumption that a particle was coated only when a particle existed within a spray zone[19]. It can be found that CFD-DEM simulation can give more detailed information about particle fluidization behavior. From the above, FB-CVD is the key technology in the fabrication of nuclear fuel coated particles, and particle fluidization behavior is important for coating layer preparation[20]. The particle density in spouted bed is generally less than 3.0 g/cm3, while particle density in the nuclear fuel coating process can be more than 10.0 g/cm3. In order to study the impact of particle density on the fluidization behavior of particles in spouted bed, CFD-DEM coupling method was used to simulate the fluidization behavior of particles with different densities (GB: 2.60g/cm3, ZrO2: 5.60g/cm3, Fe: 7.80g/cm3, UO2: 10.80g/cm3) in this paper. The effects of the particle density on the spouting process are analyzed, among which the influences of the particle density on the minimum spouting gas velocity, pressure drop, spout dominant frequency, particle entrainment and gas-solid contact efficiency will be paid more attention here.

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2. Numerical simulation 2.1 Mathematical modeling

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DEM can simulate the movement behavior of single particle and the collision process between particles, and the velocity and position of particles at any time can be obtained. The heart of the method is the contact force model. When two particles collide, they actually deform. However, in the soft sphere model, the overlap displacement is assumed instead of considering deformation. The larger the displacement, the larger the repulsive force. In such a particle-particle interaction, the particles lose kinetic energy. The normal force has a spring to provide the repulsive force and a dashpot to provide the inelasticity in the collision. The tangential force has a spring that models tangential elastic deformation of the contacting surfaces and a dashpot to model plastic deformation. The tangential force is limited by the Coulomb friction. This is the limiting friction that can be withstood by the contact before sliding of one particle over the other commences. Considering the above physical mechanisms, Hertz-Mindlin (H-M) model, which is a kind of the soft sphere models, is chosen to describe the collision between particles as shown in Table 1. Table 1 The particle equation and relevant physics used in H-M model In table 1, Yeq, Req, meq, δ, Sn, St, μs, μr are the equivalent Young’s Modulus, the equivalent radius, the equivalent mass, the particle overlap, the normal stiffness, the tangential stiffness, the coefficient of sliding friction and the coefficient of rolling friction respectively. β is the damping factor, which is a function of the restitution coefficient e. The restitution coefficient can be

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2.2 CFD-DEM method

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The gas-solid two phase flow can be numerically simulated by DEM model coupling with CFD solutions. In the CFD-DEM coupling model, the gas flow is described by the local averaged Navier-Stokes equations, while the motion of particles can be obtained by Newton second law and rotation equation. The detailed coupling principle of CFD-DEM model can be found in the related literature[13, 14, 17]. The gas phase hydrodynamics are described with the continuity equation and the momentum conservation equation as follows. Mass conservation equation (Continuity equation) for fluid phase g: (1)

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  g  g      g  g u g   0 t

Momentum conservation equation (Movement equation) for fluid phase g:

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 (2)  g g u g      g g u g u g    g Pg  Fpg     g τ g    g g g t in which Pg is the fluid phase pressure, ug is the fluid velocity, εg is the void fraction, τg is the gas-phase stress tensor and ρg is the fluid density. Fp-g is the source term for momentum, representing the interaction between particle and fluid. The k-ε mixture turbulence model is used for calculated the gas phase turbulence. The Di Felice model is chosen to characterize the coupling effect of gas-solid phase, mainly referring to the drag force between gas and particles. Then for particle i, the translational motion function:

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ni dVi  FDrag ,i  mi g    Fn,ij  Ft ,ij  dt j 1

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the rotation motion function:

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dωi ni    τ t ,ij  τ r ,ij  dt j 1

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in which I is the particle rotational inertia, ω is the rotation velocity, τt and τr is the tangential torque and rolling friction torque respectively. The CFD-DEM simulation scheme is given in Fig.1 to show the simulation process briefly. First, the flow field of the gas phase is resolved by the CFD solver. When a stable solution is obtained, the flow field is passed to the coupling module, where the relative velocity between each particle and the surrounding gas is calculated in order to obtain the drag force. The drag force acting on each particle is then passed to the DEM solver which will update the particle positions in a loop, until the end of the CFD time step is reached. The new particle positions are transferred back to the coupling module, which will update the fluid cell porosities and calculate the momentum sink term for each mesh cell. The CFD solver iterates over the next time step until the flow field again converges to a stable solution. The commercial software EDEM coupled with Fluent which have been validated in literature[21] are used here. Fig. 1 The CFD-DEM simulation scheme

2.3 Simulation parameters

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Fig. 2 The geometric parameters of the 2-dimensional spouted bed Table 2 Geometric and simulation parameters

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3. Results and discussion 3.1 Stable spouting state

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The configuration of the 2-dimensional spouted bed is shown in Fig. 2. The geometric parameters include inverted cone angle (γ), nozzle size (D0), bottom width (Di), bed width (Dc), bed thickness (L). The particle parameters include packed height (H0), particle diameter (dp), particle density (ρp). The geometric and simulation parameters are shown in Table 2. The velocity boundary condition is set at the gas inlet. The free pressure boundary condition is used for the gas outlet. The no-slip boundary condition is used for the walls. The inlet gas velocity Uin is between 0 - 90m/s (corresponding superficial gas velocity Ug ~ 0-5.4m/s).

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In the stable spouting state, it can be found clearly that the periodic particle entrainment phenomena exists as shown in Fig. 3, which shows the ZrO2 particle spouting process with the inlet gas velocity of 45 m/s. It can be seen that the particle transport in the jetting region is in the form of cluster, which is generated around the nozzle, namely the bottom of the jetting region. The volume and density of particle cluster increase as the gas rises in spouted bed for gathering particles from the annulus region continuously. The particle cluster becomes a larger agglomeration when it arrives at the export of the jetting region. Then the particle agglomeration is blown apart by the gas flow, which is called fountain region, and particles scatter over the top of the annulus region. The interspaces between the two particle clusters consists of relatively dilute phase. The process mentioned above is then repeated periodically. The global cycle period can be obtained from the simulation results and the value is around 190ms (1.38s - 1.57s - 1.76s). Fig. 3 The periodical change of particle movement in the spouting process

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Zhao[18, 22] and his colleagues have given a detailed analysis on the spouting process of glass beads, which can be used for verifying the reliability of the simulation method in this paper. In their research[23], the global cycle period is around 160 ms with the packed height of 100 mm and the inlet gas velocity 26.0 m/s (Ug=1.58 m/s), which is close to our simulation results (165 ms) in the glass beads spouting process. For the same glass beads system, Hosseini[24] used the Euler-Euler model to simulate the particle spouting process with the inlet gas velocity of 32.5 m/s (Ug=1.95 m/s), and the results show that the maximum velocity of particles in vertical direction is around 1.38 m/s. From our simulation results, the maximum velocity of particles in vertical direction is 1.42 m/s under the same conditions. It can be found that the present study agrees well with the experimental and simulation results in the previous reports, so the models and parameters used in this paper are reliable.

3.2 Particle cycle time The trajectory of single particle and the detailed information of the particle movement behavior can be obtained from the CFD-DEM simulation results. The typical schematic diagram of the particle trajectory of ZrO2 particle with inlet gas velocity of 45 m/s is shown in Fig. 4. It can be found that single particle finished 4.65 cycles within 4 s, namely that the cycle period of single

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particle is about 860 ms, which is 4.5 times of the whole bed cycle period of 190 ms as mentioned above. Furthermore, it can be found that the particle residence time in the jetting region is around 110 ms in one cycle period, which means that 87% of particles residence time is in the annulus region and fountain region. The results can be helpful for understanding the mechanism of particle spouting coating process. The traditional spouted bed with single nozzle should be modified for improving gas solid contact efficiency, because the gas, especially reactive gas mainly exists in the jetting region and only little gas can disperse into the annulus region. In this case, most reactive gas will escape from the jetting region before completely contacting with particles, resulting in a low coating efficiency and low yield of coated particle. Fig.4 The particle movement trajectory in the spouting process (1s-5s, ZrO2)

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3.3 Minimum spouting gas velocity

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The minimum spouting gas velocity (Ums) is the minimum gas velocity to maintain the stable spouting state in spouted bed, which is represented by the minimum superficial gas velocity in this paper. For the particle coating process, in order to obtain the uniform coating thickness and properties, the superficial gas velocity should be larger than minimum spouting gas velocity, for obtaining good mixing of the whole bed and sufficient gas-solid contact efficiency. Thus, it is necessary to investigate the impact of particle density on the minimum spouting gas velocity. The simulation results showed that the pressure drop of four kinds of particles with different densities changed with the superficial gas velocity, as shown in Fig. 5. Then the minimum spouting gas velocity (Ums) and pressure drop (ΔP) at stable spouting state can be obtained.

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Fig.5 Pressure drop vs superficial gas velocity

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As can be seen from Fig. 5, the minimum spouting gas velocity (Ums) and pressure drop (ΔP) is different for particles with different density, both of them increase rapidly with the particle density. There are many literature reports on the study of the minimum spouting gas velocity and pressure drop at stable spouting state and different calculation equations are given. Zhong et al.[25] made an investigation on the particle spouting process with densities of 1.0, 1.5, 2.0 and 2.503 g/cm3, and indicated that the minimum spouting gas velocity can be calculated as follows:

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 d 3.48   0.40  s   Dc 

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 H 0   Dc       Dc   Di 

  p  g   g

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in which SI unit system is used for all variables. Here the effect of particle density is focused on, so the above equation can be simplified as follows:

U ms  k1 p 0.67

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in which k1 is the parameter related to the geometric parameters of spouted bed, particle diameter and particle packed height, which keeps invariant and can be regarded as a constant here. The relationship between the minimum spouting gas velocity and the particle density can be obtained from Fig. 4. It can be found that the minimum spouting gas velocity is proportional to ρp0.67 from CFD-DEM simulation results as shown in Fig.6, which is in good agreement with the literature.

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Also the value of k1 can be calculated from the equation 5 and it is about 0.35. The simulation result of k1 is 0.38 according to Fig.6, which is also close to equation 5. Similarly, the pressure drop at stable spouting state is found to be proportional to ρp1.20 as can be seen from Fig. 6. Namely that ΔP=k2ρp1.20, k2 is also a constant parameter related to the geometric parameters of spouted bed, particle diameter and particle packed height. The simulation result of k2 is about 0.52 according to Fig. 6.

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Fig.6 The minimum spouting velocity (a) and pressure drop at stable spouting state (b) vs particle density

3.4 Stable spouting region

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As can be seen from Fig. 5, the particle stable spouting regions of different densities are between the dashed lines. The stable spouting range of GB particle, ZrO2 particle, Fe particle and UO2 particle is about 0.72-1.85m/s, 1.08-2.5m/s, 1.44-3.67m/s, and 1.8-4.5m/s respectively. It can be seen that the stable spouting range expands with the particle density increasing, which means there is a larger velocity adjust range that can be chosen from initial spouting to the end of stable spouting state. This is helpful for the practical application of high density particle coating process, because there will be more choice to set the ratio of reactive gas and fluidizing gas for maintaining the stable spouting state.

3.5 Spout dominant frequency

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From the simulation results, it can be found that the particle average velocity in vertical (z-) direction (up,z) changing with time indicates a good periodicity. The the periodicity of the particle average velocity in vertical (z-) direction is the same as the periodicity of the pressure in the jetting region, as been validated in the experimental data[23]. up,z can be obtained from the CFD-DEM simulation results, which is suitable to characterize the periodic pattern of particle spouting. up,z of Fe particle changing with time under different superficial gas velocities (Ug) is shown in Fig. 7.

Fig. 7 Typical curve of up,z vs time at different superficial gas velocities (Fe particle)

Frequency domain analysis of a sampled signal can be performed using discrete Fourier transform (DFT) which indicates the frequency content of a discrete time signal. Power spectral density (PSD) distribution can be used for the analysis on the frequency domain characteristics of time domain signal. PSD represents the energy distribution of signal in frequency domain, which is suitable for investigating the fluctuation characteristics and periodicity of particle velocity[26, 27]. Fig. 8 shows the power spectral density distribution of the time domain signal of particle instantaneous velocity in vertical direction (up,z) under different gas velocity. As can be seen from the simulation results, the dual dominant frequency (2.87 Hz, 5.77 Hz) exists when the gas velocity is slightly larger than the minimum spouting gas velocity (Ums). The phenomenon is similar with the experimental study in literature reports[28]. Zhou[28] did experiment with the ZrO2 particle (d=0.5 mm), and he found that the dual dominant frequency appeared when Ug/Ums is around 1.2. The dual dominant frequency appeared when Ug was slightly larger than Ums, but

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disappeared when the gas velocity increased continuously in experiments [28]. Because the particle loading and particle diameter in experiments[28] is not the same with the present simulation, only qualitatively comparison can be given, but the origination mechanism of the dual dominant frequency is the same. The single dominant frequency of 2.5Ums is 5.3 Hz in Fig. 8-b. When the gas velocity continues increasing, the dominant frequency changes to multiple dominant frequencies, as shown in Fig. 7-c, which means the periodicity of particle velocity disappears.

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Fig. 8 Typical PSD curve of up,z (Fe particle)

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It is noteworthy that dual dominant frequency exists only when the particle density is high enough. Dual dominant frequency also exists for ZrO2 and UO2 particle, but it can not be easily found in the spouting process of glass beads, as can be seen from Fig. 9. The simulation results show that only the single dominant frequency can be found in the stable spouting state of glass beads.

Fig. 9 Dual dominant frequency in the spouting process of ZrO2 and UO2 particle

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The origination mechanism of dual dominant frequency can be explained as in Fig. 10-a. There are two small gas bubbles in the jetting region simultaneously when the gas velocity (Ug) is slightly larger than the minimum spouting gas velocity (Ums). In this case, the high particle density and the small particle entrainment velocity make that two incoherent particle acceleration process exist in the jetting region at one spout cycle, resulting in dual dominant frequency, while this phenomenon can not be easily found for low density particles such as polymer sphere and glass beads. The velocity range of dual dominant frequency will also expand when the particle density is increased. When the gas velocity is increased continuously, there is only one gas bubble in the jetting region, so there is only one particle acceleration process in a spout cycle, resulting in single dominant frequency, as shown in Fig.10-b. In this case, only one kind of particle cluster exists and the frequency domain signal is strong which means a good periodicity, as shown in Fig. 8-b.

Fig.10 Different particle behavior (left) and gas holdup profiles (right) at different kinds of dominant frequency in the spouting process of high density particle If the gas velocity is increased continuously, the incoherent spouting will transfer into coherent spouting. The gas is coherent in the jetting region, so the periodicity is not so clear in this spout state, as shown in Fig.10-c. In this situation, the particle cluster can not exist stably, so the significant dominant frequency will not maintain. The periodicity disappears gradually and the strength of frequency domain signal decreases. In the periodical spout process, the particle rising in the jetting region and falling in the annular region is alternate and not synchronous. When the gas velocity is increased, the periodicity disappears. The rising velocity of particle in jetting region is increased, but the falling velocity of particle in the annular region is increased synchronously, so the average value of particle velocity of the whole bed is decreased on the contrary, as shown in Fig. 7.

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With continuously increasing the gas velocity, the particle spouting is changed to unstable state and the particle entrainment is irregular. Therefore, according to a series of the simulation results, the relationship between the particle spouting process under different particle densities and gas velocities can be summarized in a flow pattern map, which can be divided into five regions: fixed bed with internal spouting, transitional stable spouting state with dual dominant frequency, main stable spouting state with single dominant frequency, transitional stable spouting state with multiple dominant frequency, and unstable spouting state, as shown in Fig.11. It can be found that there are two transitional areas between static bed (internal spouting), unstable spouting state and stable spouting state when the particle density is high enough. It will be helpful to understand how to maintain the stable spouting state in practical fluidization process of high density particles.

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Fig.11 Flow pattern map of different particle densities and superficial gas velocities

3.6 The effect of particle density on spout dominant frequency

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From the simulation results, it can be found that the dominant frequency of the particle spouting will keep invariant (5.3 Hz) in the range of stable spouting even the particle density increasing, as long as Ug/Ums keeps unchanged, as shown in Fig. 12. Similar results have been found in experiments with different particle loading heights[28]. It was found that the spouting dominant frequency would keep invariant in the range of stable spouting when the particle loading increases, as long as Ug/Ums was unchanged. It can be explained as follows. The spout dominant frequency is determined by the particle movement process. When the particle density increases, the minimum spouting gas velocity is increased as a result. Then if the spout gas velocity increases by the same proportion, the particle spouting height keeps unchanged, thus the particle acceleration process and the deceleration process in one spout cycle are almost consistent. The variety trends of particle velocity are analogous, resulting in the same particle periodic entrainment frequency, which is around 5.3Hz, as shown in Fig.12. But the spout dominant frequency decreases significantly with the particle density increasing if only Ug keeps unchanged, because the particle acceleration process is limited by the high density particle. Fig.12 The power spectral density of up,z of different density particle at Ug＝2.5Ums

3.7 The effect of particle density on gas solid contact efficiency In order to analyze its advantages and disadvantages of the particle fluidizing behavior on the particle coating process, many criteria have been proposed such as the particle circulation time, the particle spouting height and the cycle number of single particle[29]. Recently, the coupled CFD-DEM approach was used to model fluidized bed spray coating system at an individual particle level[30]. The trajectory and more detailed information of each single particle can be obtained from CFD-DEM simulation results. Therefore, the particle residence time distribution (RTD) in the effective gas deposition region can be used as a more accurate description of the gas solid contact efficiency. For a given time, if the residence time of all the particles in the effective deposition region is consistent, the materials will deposit on the surface of all particles uniformly.. How to define the effective gas deposition region is still a open question, here the jetting region was used as assumption analogy to the spraying coating simulation for simplification[30].

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The residence time distribution of particles with different densities at the same gas velocity within the spouting time of 2.5 s is then obtained, as shown in Fig. 13. It can be seen that the average residence time decreases with the particle density (Fe: taverage =0.46s, UO2: taverage =0.35s) and the residence time distribution broadens, which means an uneven particle coating when the superficial gas velocity is not changed. The particle residence time distribution in the effective deposition region of different density particles at Ug/Ums=2.5 within the spouting time of 2.5s is obtained from simulation results, as shown in Fig. 14. It can be found that the particle residence time distribution of different densities in the effective deposition region is almost the same (taverage= 0.35s,) at the spout gas velocity of 2.5Ums, which agrees with the spout dominant frequency, as shown in Fig. 12. In the future work, the residence time distribution will be used for investigating the coating efficiency and quality in FB-CVD process in different configurations of spout reactors further. Fig.13 The residence time distribution of different density particle at the same superficial gas

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Fig.14 The residence time distribution of different density particle at Ug=2.5Ums

4. Conclusions

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The spouting processes of different density particles are studied using the CFD-DEM coupling method. The particle cycle time, spout behavior, spout dominant frequency and gas-solid contact efficiency are discussed. Some conclusions can be drawn out as follows. 1) The periodic and incoherent spouting behavior was found in the particle spouting process. The detailed information such as the cycle period of the whole bed and single particle can be obtained using the CFD-DEM simulation method. The cycle period of single particle is much longer than the cycle period of the whole bed in stable spouting state. 2) The minimum spouting gas velocity and pressure drop increases rapidly with the particle density. The minimum spouting gas velocity and the steady pressure drop is proportional to ρp0.67 and ρp1.2 respectively. 3) The gas velocity range of stable spouting state increases with the particle density increasing, which is helpful for choosing the suitable gas velocity to maintain the stable spouting state in the real coating process. 4) The flow pattern map under different densities and different gas velocities is obtained and can be divided into five regions: fixed bed with internal spouting, transitional stable spouting state with dual dominant frequency, main stable spouting state with single dominant frequency, transitional stable spouting state with multiple dominant frequency, and unstable spouting state. Dual dominant frequency exists in the spouted bed with high density particle. The mechanism is owned to the existence of two gas bubbles in the incoherent jetting region simultaneously. 5) Dominant frequency and the cycle period of the particle spouting process will keep invariant in the stable spouting state when the particle density increases, as long as Ug/Ums keeps unchanged. 6) The average residence time decreases when the particle density increases and the superficial gas velocity keeps unchanged, but the average residence time do not change even the particle

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density increases, as long as Ug/Ums keeps unchanged. The CFD-DEM coupling method and the particle residence time distribution in the effective deposition region can be used for investigating the coating efficiency and quality in FB-CVD process in different configurations of spout reactors further.

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Acknowledgements

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The authors would like to thank the National Natural Science Foundation of China (21306097), Tsinghua University Initiative Scientific Research Program (2011Z02159), the Specialized Research Fund for the Doctoral Program of Higher Education (20110002120023), Higher Education Young Elite Teacher Project of Beijing (YETP0155) for the financial support provided.

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Notations Cone included angle, -

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Bed thickness, m

Do

Inlet diameter, m

Di

Diameter of the bed bottom, m

Dc

Column diameter, m

Hc

Height of conical part, m

Ho

Static bed height, m

dp

Particle diameter, m

ρp

Particle density, kg/m3

ρg

Fluid density, kg/m3

Re

Reynolds number, -

Ums

Minimum spout velocity, m/s

Ug

Superficial gas velocity, m/s

Uin

Inlet gas velocity, m/s

∆P Y

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up,z

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γ

Particle velocity in z-direction, m/s Pressure drop at stable spouting state, Pa

eq

The equivalent Young’s Modulus, -

eq

The equivalent particle radius, -

eq

The equivalent mass, -

R

m δ

The particle overlap, -

Sn

The normal stiffness, -

St

The tangential stiffness, -

μs

The coefficient of sliding friction, -

μr

The coefficient of rolling friction, -

β

The damping factor, -

e

The restitution coefficient, -

Reference

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K B Mathur, P E Gishler, A technique for contacting gases with coarse solid particles, AIChE J. 1 (1955) 157-164.

[2]

E Lopez-Honorato, P J Meadows, P Xiao, G Marsh, T J Abram, Structure and mechanical properties of pyrolytic carbon produced by fluidized bed chemical vapor deposition, Nuclear

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Engineering and Design 238 (11) (2008) 3121-3128. C R Duarte, M Olazar, V V Murata, M A S Barrozo, Numerical simulation and experimental

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study of fluid-particle flows in a spouted bed, Powder Technology 188 (3) (2009) 195-205. N Epstein, J R Grace, Spouted and spout-fluid beds: fundamentals and applications 2011, New

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York, Cambridge University Press. [5]

K B Mathur, N Epstein, Spouted Beds. 1974, New York, Academic Press.

[6]

J Zhou, D D Bruns, Minimum spouting velocity of dense particles in shallow spouted beds, The Canadian Journal for Chemical Engineering 90 (2012) 558-564. S Sari, G Kulah, M Koksal, Characterization of gas–solid flow in conical spouted beds

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operating with heavy particles, Experimental Thermal and Fluid Science 40 (2012) 132-139. [8]

F Alekhine. Gas-particles flow transitions for high density powder. Proceedings of the World

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Congress on Engineering. 2012.

J Saayman, N Ellis, W Nicol, Fluidization of high-density particles: The influence of fines on reactor performance, Powder Technology 245 (2013) 48-55.

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S Pannala, C S Daw, C E A Finney, D Boyalakuntla, M Syamlal, T J O'Brien, Simulating the N Almohammed, F Alobaid, M Breuer, B Epple, A comparative study on the influence of the

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dynamics of spouted-bed nuclear fuel coaters, Chemical Vapor Deposition 13 (2007) 481-490. gas flow rate on the hydrodynamics of a gas-solid spouted fluidized bed using Euler-Euler and Euler-Lagrange/DEM models, Powder Technology 264 (2014) 343-364. S H Hosseini, G Ahmadi, M Olazar, CFD simulation of cylindrical spouted beds by the kinetic

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theory of granular flow, Powder Technology 246 (2013) 303-316. [13]

Y Tsuji, T Kawaguchi, T Tanaka, Discrete particle simulation of 2-dimensional fluidized-bed,

[14]

B H Xu, A B Yu, Numerical simulation of the gas-solid flow in a fluidized bed by combining

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Powder Technology 77 (1993) 79-87. discrete particle method with computational fluid dynamics, Chemical Engineering Science 52 (16) (1997) 2785-2809. V Salikov, S Antonyuk, S Heinrich, V S Sutkar, N G Deen, J A M Kuipers, Characterization and CFD-DEM modelling of a prismatic spouted bed, Powder Technology (2014) in press. [16]

Y Zhao, Y Cheng, Y Ding, Y Jin, CFD-DEM simulation of flow and mixing behavior in downers with different entrance structures, Journal of Chemical Industry and Engineering 58 (6) (2007) 1396-1403.

[17]

W Zhong, Y Xiong, Z Yuan, M Zhang, DEM simulation of gas-solid flow behaviors in spout-fluid bed, Chemical Engineering Science 61 (5) (2006) 1571-1584.

[18]

X Zhao, S Li, G Liu, Q Yao, J Marshall, DEM simulation of the particle dynamics in two-dimensional spouted beds, Powder Technology 184 (2008) 205-213.

[19]

H Nakamura, T Iwasaki, S Watano, Numerical simulation of film coating process in a novel rotating fluidized bed, Chemical and Pharmaceutical Bulletin 54 (6) (2006) 839-846.

[20]

M L Liu, Review on application of fluidized bed technology in industry of uranium fuel cycle, Chemical Industry and Engineering Progress 32 (3) (2013) 508-514.

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L Fries, S Antonyuk, S Heinrich, D Dopfer, S Palzer, Collision dynamics in fluidized bed granulators: A DEM-CFD study, Chemical Engineering Science 86 (2013) 108-123.

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X Zhao, S Li, G Liu, Q Song, Q Yao, Flow patterns of solids in a two-dimensional spouted bed with draft plates: PIV measurement and DEM simulations, Powder Technology 183 (2008)

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79-87. G Liu, S Li, X Zhao, Q Yao, Experimental studies of particle flow dynamics in a

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two-dimensional spouted bed, Chemical Engineering Science 63 (2008) 1131-1141. S H Hosseini, G Ahmad, B S Razavi, W Zhong, Computational fluid dynamic simulation of

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hydrodynamic behavior in a two-dimensional conical spouted bed, Energy Fuels 24 (2010) 6086-6098. [25]

W Zhong, X Liu, J R Grace, N Epstein, B Ren, B Jin, Prediction of minimum spouting Engineering 91 (2013) 1809-1814.

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velocity of spouted bed by CFD-TFM: scale-up, The Canadian Journal for Chemical E Piskova, L Morl, Characterization of spouted bed regimes using pressure fluctuation signals, Chemical Engineering Science 63 (9) (2008) 2307-2316. J Xu, X Bao, W Wei, G Shi, S Shen, H T Bi, J R Grace, C J Lim, Statistical and frequency

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analysis of pressure fluctuations in spouted beds, Powder Technology 140 (2004) 141-154. [28]

J Zhou, Characterizing and modeling the hydrodynamics of shallow spouted beds, in Chemical Engineering. 2008, PhD dissertation in The University of Tennessee: Knoxville. S Pannala, C S Daw, D Boyalakuntla, C E A Finney, Process modeling phase I summary

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report for the advanced gas reactor fuel development and qualification program. 2006, Acdamic reports in Oak ridge national laboratory: Oak Ridge, Tennessee. J E Hilton, D Y Ying, P W Cleary, Modelling spray coating using a combined CFD-DEM and

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spherical harmonic formulation, Chemical Engineering Science 99 (2013) 141-160.

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ACCEPTED MANUSCRIPT Figures Fig.1 The CFD-DEM simulation scheme Fig.2 The geometric parameters of the 2-dimensional spouted bed

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Fig.3 The periodical change of particle movement in the spouting process

Fig.4 The particle movement trajectory in the spouting process (1s-5s, ZrO2)

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Fig.5 Pressure drop vs superficial gas velocity

Fig.6 The minimum spouting velocity (a) and pressure drop at stable spouting state (b) vs particle density

Fig.8 Typical PSD curve of up,z (Fe particle)

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Fig.7 Typical curve of up,z vs time at different superficial gas velocities (Fe particle)

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Fig.9 Dual dominant frequency in the spouting process of ZrO2 and UO2 particle Fig.10 Different particle behavior (left) and gas holdup profiles (right) at different kinds of

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dominant frequency in the spouting process of high density particle

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Fig.11 Flow pattern map of different particle densities and superficial gas velocities Fig.12 The power spectral density of up,z of different density particle at Ug＝2.5Ums

velocity

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Fig.13 The residence time distribution of different density particle at the same superficial gas

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Fig.14 The residence time distribution of different density particle at Ug=2.5Ums

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Fig. 1 The CFD-DEM simulation scheme

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Fig. 2 The geometric parameters of the 2-dimensional spouted bed

1.38s

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1.48s

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Fig. 3 The periodical change of particle movement in the spouting process

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(ZrO2, Red: high particle velocity; Blue: low particle velocity)

1.76s

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(a) (b) Fig.4 The particle movement trajectory in the spouting process (1s-5s, ZrO2)

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Fig.5 Pressure drop vs superficial gas velocity

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(b) Fig.6 The minimum spouting velocity (a) and pressure drop at stable spouting state (b) vs particle density

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b）Ug=2.5 Ums

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a） Ug=1.875 Ums

c）Ug=3.3Ums Fig.7 Typical curve of up,z vs time at different superficial gas velocities (Fe particle)

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a）Ug=1.875 Ums

b）Ug=2.5 Ums

c）Ug=3.3Ums Fig.8 Typical PSD curve of up,z (Fe particle)

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a) ZrO2 (Ug=1.67 Ums)

b) UO2 (Ug=1.9 Ums) Fig.9 Dual dominant frequency in the spouting process of ZrO2 and UO2 particle

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a) Dual dominant frequency, Ug=1.875 Ums

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b) Single dominant frequency, Ug=2.5 Ums

c) Multiple dominant frequency, Ug=3.3Ums Fig.10 Different particle behavior (left) and gas holdup profiles (right) at different kinds of dominant frequency in the spouting process of high density particle

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Fig.11 Flow pattern map of different particle densities and superficial gas velocities

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Fig.12 The power spectral density of up,z of different density particle at Ug＝2.5Ums

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Fig.13 The residence time distribution of different density particle at the same superficial gas velocity

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Fig.14 The residence time distribution of different density particle at Ug=2.5Ums

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Table 1 The particle equation and relevant physics used in H-M model Table 2 Geometric and simulation parameters

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Table 1 The particle equation and relevant physics used in H-M model Variable

Equations 3 4 Fn s  kn δn2 , kn  Y eq R eq 3

Normal damping force

Fnd  2

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Normal spring force

1 5 ln e kn meq δn 4 vnrel ,   4 ln 2 e   2

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 F s  Ft d , if Ft  s Fn , in which  Ft   t    s Fn , if Ft  s Fn

For tangential forces, Tangential spring forces

Ft s  St δt , St  8G eq Req n

Tangential damping force

Ft d  2

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5 ln e  St meq vtrel ,   6 ln 2 e   2

τ r  r Fn Ri ωi

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Rolling friction torque

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For Normal forces,

Table 2 Geometric and simulation parameters value

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Parameter Geometry parameters Spout nozzle diameter (Do)

9mm

Inverted cone angle (γ)

60

Bottom width (Di)

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Bed width (Dc) Bed thickness (L)

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Gas properties Density (ρg) Viscosity (μ) Particle properties Particle loading (H0)

150mm 15mm

1.225 g/cm3 1.72×10-5 Pas

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100mm

Diameter (dp)

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Density (ρp)

2mm 3

GB：2.60g/cm ，ZrO2：5.60g/cm3，Fe：7.80g/cm3，UO2：10.80g/cm3

Simulation parameters

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Poisson’s ratio, -

0.25

-2

Young’s modulus, Nm

108

Restitution coefficient, -

0.5

Sliding Friction coefficient, -

0.5

Rolling friction coefficient, -

10-5

CFD time step (∆t), s

10-5

DEM time step (∆t), s

10-6

CFD mesh, -

300×50

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Fig.11 Flow pattern map of different particle densities and superficial gas velocities GRAPHICAL ABSTRACT

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Highlights 1. The relationship between Ums, ∆P and ρp is numerically investigated.. 2. The origination of dual frequency in stable spouting process of high density particle. 3. The flow pattern map of different superficial gas velocities & particle densities. 4. The effect of Ug and ρp on the dominant frequency of particle spouting process. 5. The effect of ρp on particle residence time distribution in the spout region.