Numerical and experimental study on the particle erosion and gas-particle hydrodynamics in an integral multi-jet swirling spout-fluidized bed

Wenbin Li ,Feng Wu,,Liuyun Xu ,Jipeng Sun ,Xiaoxun Ma

1 School of Chemical Engineering, Northwest University, Xi’an 710069, China

2 Luoyang Jianguang Special Equipment Co., Ltd, Luoyang 471003, China

Keywords:Integral multi-jet swirling spout-fluidized bed Gas-particle hydrodynamics Axial swirl vane Uneven Erosion

ABSTRACT In this paper,using the computational fluid dynamics based on Euler Lagrange and the commercial software Barracuda VR,the gas-particle hydrodynamics and the erosion of particles on the inner wall and internal components of the spouted bed in the integrated multi-jet swirling spout-fluidized bed(IMSSFB) are studied.Erosion experiments have obtained the characterization of particle erosion on internal components and verified the relevant numerical models.The results show that:the particle distribution within the IMSSFB is uneven due to the cyclonic effect of the axial swirl vane(ASV),resulting in particle erosion for the ASV being concentrated on one side;when the gas reaches the top,too high an erosion gas velocity leads to gas backflow.As the filling height increases,there is a tendency for the erosion position of the particles on the ASV to expand upwards.However,the effect of increasing gas velocity on the erosion position is insignificant.

1.Introduction

As the leading energy in China,the proportion of coal consumption has decreased yearly,but it still accounts for about 60%[1].In the power generation industry,coal-fired power generation accounts for 70% of the total power generation [2,3].The emission of SO2and other pollutants caused by a tremendous amount of coal combustion has exceeded the environmental carrying capacity.In order to achieve sustainable social and economic development and ensure the construction of ecological civilization,it is crucial to solve the problem of acid rain caused by SO2emissions.Therefore,under the current environmental protection demand,how to effectively deal with and curb SO2pollution in the atmosphere and develop new and efficient desulfurization process equipment are still the focus of environmental protection and scientific research in China.

There are three kinds of sulfur dioxide treatment technologies in flue gas: wet flue gas desulfurization,dry flue gas desulfurization,and semi-dry flue gas desulfurization [4].People are widely concerned about the semi-dry desulfurization process for its significant advantages of less investment,small land occupation,low operation cost,and no wastewater discharge [5,6].In the semidry flue gas desulfurization process,the powder particle spray bed semi-dry flue gas desulfurization technology has significant advantages in the desulfurization effect and utilization of desulfurized[7-10].At present,most powder particle spouted bed equipment still adopts the traditional column cone structure,and its bed structure design and desulfurization efficiency need to be further improved.In the face of strict requirements and intense supervision of environmental protection policies,developing new and efficient semi-dry powder particle spouted bed desulfurization equipment has become an inevitable demand of the new situation.

As an efficient reactor,the spouted bed is widely used in coating,granulation,biomass pyrolysis,gasification,flue gas desulfurization,and many vital fields [11-15].With the development of spouted bed technology,researchers have put forward many improvement schemes to improve the efficiency of spouted beds,such as multi-jet spouted beds,spouted fluidized beds,guide tube spouted beds [16-22],etc.Multi-jet spouted bed can double the total particle handling capacity,but its particle and fluid movement law still sustain the traditional spouted bed form [16].The spouted fluidized bed can eliminate the dead flow zone at the bottom of the spouted bed,but it is necessary to add bypass gas supply equipment to maintain the spouted fluidized state [17-20].The guide tube spouted bed is designed to control the gas residence time under specific process conditions.Compared with the traditional spouted bed,it limits the radial mixing of gas and particles in the jet zone and annulus [21,22].In addition,the particle fluidization range of the spouted fluidized bed is limited to the vicinity of the cone region,which has little effect on the radial fluidization movement of particles in the cylinder annulus region.In the existing literature reports,there is no overall strengthening method for the movement of particles in the cone region and annulus region of the spouted fluidized bed.Given the above situation,a new integrated multi-jet axial swirl spout-fluidized bed (IMSSFB)structure is proposed in this study,as shown in Fig.1.

Fig.1.Structural diagrams of integral multi-jet axial swirl spouting fluidized bed (unit: mm): (a) IMSSFB,(b) ASV,(c) SNDP.

Compared with the conventional spouted bed,the IMSSFB is designed with a spout fluidization component combining the axial swirl vane (ASV) and the side nozzle distribution plate (SNDP)(Fig.1(b),(c)).The strengthening internals is welded with the upper edge of the cone of the spouted bed to form an integral multi-jet structure,which realizes that the main nozzle and the side nozzle share an air inlet(bypass air supply equipment is omitted),and the particles in the cone area and the annular gap area have an integrated fluidization.The main nozzle is a vertical guide to the central airflow to form a jet zone.The SNDP is provided with a specific size,quantity,and layout of the side nozzle structure(Fig.1(c)).The local fluidization of particles in the conical area of the spouted bed is realized through the side nozzle to eliminate the flow dead zone.In addition,to optimize the side nozzle’s fluidization effect on particles,the spatial distribution of the side nozzle is designed as a dense bottom and sparse top structure[23].The ASV structure is designed to solve the problem of dense particles in the annulus.The ASV guides the inlet gas of the main nozzle to fluidize the particles in the annulus periodically in a swirling motion during the rising process and strengthens the radial mixing of particles and gas in the spout area and the annulus.

As a wear phenomenon caused by particle flow scouring equipment or pipelines,erosion widely exists in the chemical,energy,and coal industries.However,there are few reports on the erosion research of chemical vessel equipment,and they mainly focus on the fluidized bed gas-particle multiphase reaction equipment[24-27].Caoet al.[28]studied the influence of material stress state caused by internal and external forces on pipeline erosion rate.They found that the joint action of erosion and material internal stress helps determine the effective resistance of vulnerable parts of the pipeline system.Parsiet al.[29] comprehensively reviewed the application of the solid particle erosion model in oil and gas wells and pipelines,described the key factors affecting erosion,reviewed the existing erosion equations,and discussed the experience and mechanism models used for corrosion prediction in pipelines.Zhanget al.[30] used computational fluid dynamic (CFD),particle tracking program,and erosion equation to predict erosion damage and compared the particle velocity and erosion obtained from simulation and experiment in gas-particle two-phase flow,respectively.However,there is no report about the particle erosion process in the spouted bed,especially in the powder particle spouted bed.

After carefully reviewing the existing literature,it is found that there is no similar study on gas-particle hydrodynamics and particle erosion process in IMSSFB.Therefore,a three-dimensional CFD model based on the Euler-Lagrange method is established in this study to study the gas-particle hydrodynamics in IMSSFB and quantitatively analyze the erosion process of its internal particles on the wall and internal components.In addition,the erosion situation of this kind of spouted bed is learned through this study,which has a particular guiding significance for its industrial application.The position with serious erosion can be reinforced to avoid unnecessary loss.

2.Experimental Apparatus and Results

The experiment in this study uses a GX4FF-10 compressor(Atlas Copco,Sweden) to provide air,as shown in Fig.2.The material used for the experiments is transparent plexiglass,and the internal components of the bed are made of white resin.The particles are non-spherical silica particles with a 1-1.25 mm diameter and set two filling heights as 34 mm and 54 mm,respectively.The airflow is measured by a D07-60B flowmeter (Seven Stars,China).A layer of oily blue ink was applied to the surface of ASV before the experiment began so that the blue ink would be removed when the particles collided and rubbed against the surface of the internal components.During the experiment,the gas produced by the air compressor enters through the spouted bed inlet,and the control valve adjusts the gas flow.The gas velocity is adjusted to 12,13,14,and 15 m·s-1,respectively,for the erosion experiment.

Fig.2.Partial experimental apparatus.

The erosion was concentrated in the lower half of the internal component ASV,so only the erosion morphology of the lower half is being analyzed here.As shown in Fig.3,the degree of particle erosion on the inner component ASV increases with increasing gas velocity.At an air velocity of 13 m·s-1and a filling height of 54 mm,the ASV surface shows complete removal of the bluepurple ink,presumed to be the critical air velocity for ring breakage of the inner part.As the filling height of the particles increases,there is a tendency for the particle erosion of the inner parts to extend to the upper section.Also,at the same position on the ASV,the particle erosion extends laterally as the filling height increases.In addition,due to the influence of the axial swirl vane,the gas has radial kinetic energy,and the gas moves in an upward spiral direction.The radial kinetic energy of the particles makes the erosion of the particles to the ASV have a huge difference in the transverse direction,resulting in serious erosion impact on the left part.

Fig.3.Erosion morphology on internals ASV.

3.Numerical Modeling

3.1.Computational geometry and model setup

The computational geometric models of IMMSFB and its internal ASV and SNDP are shown in Fig.1.See Table 1 for various settings of simulation calculation.Since the solver will reduce the time step to the minimum due to the CFL (Current-Friedrichs-Le wy) value,temperature or other stability control,three differenttime steps are set in the simulation to improve the calculation accuracy of the simulation process.In this simulation,the gasphase fluid flows from bottom to top in the bed,and the filling height of solid particles(SiO2beads)is 54 mm.The particle density was 2200 kg·m-3,and the average particle size was 1-1.25 mm.During the simulation,the gas phase temperature is always 300 K.Previous studies have been carried out in the cold flow model by the multiphase particle in cell (MP-PIC) method,which focuses on gas-particle hydrodynamics and wall erosion [31,32].In addition,the chemical reaction is not involved in the study,so the solid phase temperature is not considered in the current computational particle fluid dynamics (CPFD) simulation.

Table 1 Simulation parameter and boundary conditions for numerical simulation

In order to verify the consistency between the existing CFD model and the experimental results,pressure sensors were used to measure the pressure drop in IMSSFB at different gas velocities and compared it with the simulated values.After verification,further simulation analysis was carried out to obtain the internal gasparticle two-phase flow characteristics and erosion morphology,and erosion experiments were carried out under different gas velocities to obtain the erosion morphology of the internal component ASV surface and compared with the erosion program obtained by simulation calculation.

3.2.Computational methods

In the numerical simulation,the CPFD method based on MP-PIC uses the Euler-Lagrange method to solve the gas-solid flow characteristics.This method treats the fluid as a continuous phase,describes it using the Navier-Stoke equation,treats particles as discrete phases,and calculates it using the MP-PIC method under the Lagrange framework [33].It can simulate the gas-particle two-phase flow with any discrete solid particles and particle size distribution [34],which helps to reflect the specific situation in the spout fluidized bed truly.The fluid information is interpolated into a single particle,and the average statistical value of the particle information in the Euler grid is mapped back to the Euler grid.Then,the continuous fluid phase and discrete particles are coupled through the interphase drag force [35].

MP-PIC particle model packs particles with the same material properties into ‘‘numerical particles” during calculation,which can track the motion characteristics of each particle under complex particle size distribution conditions,simplifying the particle system and significantly improving the calculation efficiency.In addition,numerical particles are created in the control volume,where fluid properties are treated as constants.The drag model adopts the Wen-Yu model[36].Relevant governing equations and constitutive models are shown below [37].

The equations of continuity

The mass conservation equation of fluid phase

The momentum conservation equation of fluid phase

The constitutive equations of fluid phase (for stress tensor)

The distribution of particle phase in space is solved by Liouville equation

wherefis the probability distribution function.

The motion equation of solid particle

where θ is the interphase drag coefficient.The equation describes particle acceleration according to aerodynamic resistance,pressure gradient,gravity and particle normal stress gradient.

The selection of the drag model of gas-solid two phases mainly depends on the particle and local fluid flow characteristics.This paper mainly focuses on particle erosion and adopts the Wen-Yu drag model to meet the actual particle flow characteristics.The interphase resistance coefficient of Wen-Yu is given by

whereCdis the drag coefficient andrsis the particle radius.

In the CPFD method,the particle interaction is modeled by the particle stress function,as shown below.

wherePsis a constant with always set to the default value of 1 Pa,αcpis the particle phase volume fraction at close packing,β is a constant and the recommended value is between 2 and 5,and ε is a minimal number for eliminating singularity.

The effect of the particle stress model with the recommended value of the model constant on the behavior of particles in the dilute phase can be ignored.When the volume fraction of particles in a region begin to approach close packing,the stress model will affect the particles in or moving toward the region.Ideally,the stress model should prevent particles from entering areas where the particle volume fraction is close.In this case,particles moving toward the tightly packed area will be redirected.The maximum momentum redirection of the collision parameter specifies the nature of particle redirection.

According to the law of volume conservation,the sum of volume fractions of fluid and particles is unified,that is,

The fluid momentum equation implicitly coupled fluid and particles through a phase-to-phase momentum transfer.The interface momentum transfer coefficient is

3.3.Erosion model

The wall erosion model in Barracuda VR collects data on particle-wall collisions to study the walls’ erosion and wear.Wall erosion is a function of particle mass,particle speed,and the angle at which particles strike the wall,the form of which is dependent on the wall materials.The magnitude of the erosion valueIpis calculated for each particle as,wherempis the particle mass,upis the particle velocity,aandbare user-specified constants,and ω is a weighting factor that is a function of the erosion angle,θp.

The wear model creates an erosion index for each wall patch on the model surface.The erosion is calculated from the wear model for each particle hitting the wall patch and added to the index.The total index is normalized by the area of the wall patch and then annualized when output to the post-processing files.Therefore,the unit of erosion variable in Barracuda VR has:

aandbare the mass index and velocity index of particles,respectively.Their values are set by selecting the required values from the mass index and velocity index list.Generally,the quality index is between 1 and 5,and the speed index is between 2.5 and 5 [38].In this study,the mass index and velocity index set by simulation calculation are 1.5 and 3.5,respectively,to estimate the erosion of particles on the wall of IMSSFB and its internals ASV.

In Barracuda software,the weighting function can be specified by changing the weighting value of each angle.Angular correlation is an essential characteristic of wall material in the erosion model,so setting the relevant parameters according to the corresponding wall material and erosion characteristics is necessary.Table 2 shows the erosion angle of the default model given in the software and the corresponding weighted values.This study uses this default model for calculation.Among them,the default erosion model in Table 2 has been normalized,so the weight of the maximum erosion angle is 1.00.

Table 2 The default weighted value of erosion angle

3.4.Simulation program

The simulation is carried out through the commercial software Barracuda VR.Consider using the finite volume method to solve the conservation equation,in which staggered scalars and momentum nodes are used.The density,pressure,and velocity of the fluid are coupled by a semi-implicit pressure connection equation derived from the fluid mass conservation equation.The fluid’s conjugate gradient solver is selected to solve the momentum,energy,and pressure equations.The flow chart of the simulation setup is shown in Fig.4.This figure can be obtained from previous studies[39].

Fig.4.Flowchart of the simulation program.

3.5.Mesh model and grid independent analyses

As we all know,mesh type is a critical parameter in CFD modeling,affecting numerical diffusion and simulation quality.As the mesh becomes finer,CFD methods will perform more accurate calculations.Therefore,before starting the numerical verification and further simulation,the number of grids,the grid structure,and the time step of the simulation are changed to check their impact on the flow characteristics in IMSSFB.Generally,there are two traditional mesh geometries,hexahedron and tetrahedron,but the hexahedron element considered in the current CFD research may be suitable for models with higher accuracy requirements [40-42].The grid structure used in IMSSFB in this study is shown in Fig.5.Due to the irregular structure of the internal component ASV (Fig.1(b)),the number of grids may be uneven,which willaffect the numerical stability.Therefore,the grid around it is appropriately encrypted (Fig.5(b)) so that the number of grids is homogenized to ensure numerical stability.

Fig.5.Computational grids used for CFD simulation.

In addition,the stability of grid is checked after local encryption,and the grid inspection diagram shown in Fig.6 is generated.From Fig.6,it can be seen that the uniformity of the number of grids after local encryption has been strengthened.The details of the grid size and number used in this CFD study are shown in Table 3.

Table 3 Grid independence test

Fig.6.The diagram of grid check.

As shown in Fig.7,the mass flow of fluid varies axially with different grid masses.However,the fluctuation trend of fluid mass flow is the same within the same height range.The lowest point of the fluctuation in the figure is located at the section at the top of the cone area.The particle stacking density at this section is the largest and produces the maximum gas resistance.In addition,after a detailed study of the grid independence analysis,it is found that there is no significant difference between the mass flow in IMSSFB with medium and fine grid types,indicating that grid independence has been achieved.However,since the number of fine grids is much larger than that of medium grids,this will increase computing time and waste resources.Therefore,it was decided to use the medium mesh type in the subsequent CPFD simulation.

Fig.7.Axial average mass flux of fluid with different mesh type.

4.Results and Discussion

4.1.CFD model validation

In order to verify the CFD model,the pressure sensor (see Table 4) is used to measure the bed pressure drop at different gas velocities,and the values obtained by simulation are compared.

Table 4 The partial parameters of pressure sensor

As shown in Fig.8,the bed pressure drop obtained by simulation and experiment increases with the increase of gas velocity,with the same trend.With the increase in gas flow rate,the deviation between the experimental and the simulated values becomes more prominent,but the maximum deviation is about 5%.From the verification perspective,the bed pressure drop simulation results are very close to the experimental values so the actual jet state of IMSSFB is roughly predicted by the CFD model and can be used for the subsequent analysis.

Fig.8.The bed pressure drop at different gas velocities.

4.2.Flow characteristic

When the fluid flow reaches a stable state,the simulation results of particle volume fraction in IMSSFB at different gas velocities are shown in Fig.9.The gas-particle two-phase flow in the traditional spouted bed is usually divided into three areas: dilute phase spout area,fountain area and annulus area.The particles in the spout area are entrained by high-speed gas and make downstream contact with the gas.When the particles fall back from the fountain area to the annulus area,they slowly move down and make countercurrent contact with the gas in the annulus area.That is,the medium particles in the spouted bed have prominent characteristics of internal and external stratified flow[43].However,in IMSSFB,due to the internal component ASV,the fountain area in the three-zone structure basically disappeared,or its center shifted after the spout stabilized,but dilute phase spout area and annulus area still exist.

Fig.9.Contours average particle volume fraction (50 s).

At the same time,the internal component ASV guides the gas at the inlet of the main nozzle to fluidize the particles in the annulus periodically in a swirling motion during the rising process,strengthening the radial mixing of particles and gas in the spout area and the annulus,and improving the accumulation of particles in the air inlet.In addition,due to the swirling effect produced by the internal component ASV,the radial pulsation on one side is strengthened,making the particles unevenly distributed on both sides of the spray area,and most of the particles are concentrated on one side,aggravating the loss of internal energy,which also confirms that the erosion phenomenon in Fig.3 is only severe on one side of the internals ASV.This is also confirmed by the concentration of particle erosion for the ASV on one side in Fig.3.

Fig.10 shows the average volume fraction on the longitudinal grid withi=12 andj=21 inside IMSSFB(iandjare the grid positions in theXandYdirections).It can be seen from the figure that the variation trend of the internal average volume fraction is roughly the same at different speeds,and there is only a difference ath=0.054 m (filling height).Different speeds may lead to inconsistent states at the beginning of the spout,resulting in different particle mixing states at this place.In addition,due to the double strengthening of the internals ASV and SNDP,the movement of particles around the inlet intensifies.

Fig.10.The average particle volume fraction at different heights.

According to the distribution of the average particle volume fraction given in Figs.9 and 10,it is found that the movement trend of particles under different gas velocities is roughly the same,so only the average radial velocity of particles and gas when the gas velocity is 14 m·s-1is explained here.As shown in Fig.11,comparing the radial velocity distribution of particles and gas,it is found that the radial velocity of particles is roughly symmetrically distributed along the central axis,and the direction is opposite.However,the radial velocity distribution of gas has no symmetrical distribution trend,which may be due to the swirling effect caused by the internal component ASV,but the radial velocity direction on both sides of the central axis is also opposite.

Fig.11.Contours of the radial velocity distribution: (a) particle and (b) gas(Vgas=14 m·s-1).

Fig.12(a)shows the average axial velocity distribution of particles when the inlet gas velocity is 14 m·s-1.It can be seen from the figure that the axial velocity of particles in the annulus is lower than that in the jet zone,and it increases first and then decreases gradually along the center line of the bed.The increase in the axial velocity of particles is due to the gas’s driving force at the inlet of the main nozzle.With the increase in height,when the gravity of particles is higher than the driving force,the velocity gradually decreases.Fig.12(b) shows the average axial velocity distribution of gas when the inlet gas velocity is 14 m·s-1.It is found that the axial velocity of the gas in the annulus region is much smaller than that in the spout region,and there is a trend of first increasing and then decreasing.In addition,due to the large gas velocity required for erosion in this study,a certain degree of reflux occurred when the gas reached the top.The axial velocity direction of the whole is opposite inside and outside,consistent with the apparent internal and external stratified flow of particles in the spouted bed.

Fig.12.Contours of the axial velocity distribution: (a) particle and (b) gas(Vgas=14 m·s-1).

In both Figs.11 and 12,the radial velocities and maximum values of the particles and gas appear on the left side of the ASV.The experimentally obtained particles have severe erosion on the surface of the ASV on the left side,so the erosion profile obtained by numerical simulation should also be concentrated on the left side of the ASV.

4.3.Particle mixing

The particles at two positions are defined to obtain the mixing conditions of particles in the cone area and above the cone area of the spouted bed.The cloud map of the mixing situation of particles in the initial 1 s was obtained,as shown in Fig.13.It can be seen from the figure that at 0.1 s,the movement and mixing of particles in the cone area is more intense due to the double strengthening of internal components ASV and SNDP.Due to the swirling effect of the internal component ASV,the driving force generated by the gas is asymmetric on the left and right sides.The particles on the left fall because their gravity is greater than the driving force,while the particles on the right suffer from a driving force more extraordinary than their gravity,so they move upward.At 0.3 s,because the particles in the spout area are entrained by high-speed gas and fall after reaching a certain height,the gravity of the particles in the upper layer gradually increases,and the particles on both sides in the annulus begin to move down slowly.At 0.5 s,the spouting in IMSSFB began to stabilize.

Fig.13.Contours of particle mixing within initial 1 s (Vgas=14 m·s-1).

4.4.Erosion analysis on IMSSFB

4.4.1.Model validation

When solid particles hit the wall and rebound due to the driving force of gas,erosion will occur in the gas-particle reactor,and the dominant force on the particles is usually the surface contact force.This has a noticeable impact on the operation of coal gasification and fluidization pipelines and the use of fluidized bed reactors.According to the description of the erosion model in Section 3.3,the wall erosion model in the commercial software Barracuda VR can collect data on particle wall collision to study wall erosion and wear.The amount of erosion is a function of particle mass,velocity,and the angle of particle impacting the wall,and its form depends on the wall material.

In this paper,the wall-related erosion angle weights are used as software defaults,and the values are shown in Table 2.Due to the complexity of erosion characteristics,the validation of the erosion model in this paper can only be completed through erosion morphology.The erosion profiles obtained from the numerical simulations generally agree with the experiments.The particles erode on the same side of the ASV surface and at approximately the exact locations of severe erosion.The erosion model can therefore be used for subsequent studies.

4.4.2.Erosion analysis on internal wall

As shown in Fig.11,the radial velocity near the inner wall surface of the IMSSFB does not fluctuate significantly.Its maximum value is mainly distributed to the left of the ASV,resulting in a significant difference in the amount of erosion on the wall surface and the ASV.Therefore,the erosion of the two parts is discussed separately in this paper.As shown in Fig.14,under different gas velocities,the erosion morphology on the internal wall is roughly the same.However,the erosion amount increases with the gas velocity,and the erosion phenomenon is concentrated above the filling height (54 mm).

Fig.14.Contours of erosion on internal wall (unit: kg1.5·(m·s-1)3.5·m-2·a-1).

The erosion area in the middle section of IMSSFB is widely distributed,which may be due to the internal component ASV,which strengthens the radial pulsation of particles in this section.The erosion morphology also presents the distribution of vortex line shape due to the swirl effect.Because of the large erosion gas velocity and the asymmetric distribution of the flow field caused by the internals,the particles continuously scour a specific area on the top section,resulting in partial erosion on the top.In addition,the erosion pattern in the middle section of the IMSSFB is discontinuous point erosion.

4.4.3.Erosion analysis on ASV

The erosion on the ASV is more severe than that on the inner wall,so this study focuses on analyzing the erosion on the internals.As shown in Fig.15,the erosion conditions on the internal component ASV under different air velocities are compared here only for the most severe erosion position under each air velocity.The erosion amount of other positions will be described later.The figure shows that the maximum erosion point under each gas velocity is roughly at the same position.It can be seen that the impact of the increase of gas velocity on the erosion position can be ignored.However,the erosion amount still increases with the increase of gas velocity.

Fig.15.Contours of erosion on ASV (unit: kg1.5·(m·s-1)3.5·m-2·a-1).

In combination,the erosion of the internal component ASV is concentrated on the left side.At the same time,the maximum values of the radial velocity of the particles are also concentrated on the left side,and the particles with higher axial velocities are also biased to the left side,which may be due to the presence of the ASV giving the flow field a specific cyclonic effect.In addition,the erosion pattern on the ASV shows a longitudinal distribution on the left side,which may be because the axial velocity of the particles is significantly greater than the radial velocity.

Based on the erosion clouds obtained with the Barracuda VR software,it was found that the erosion of the particles to the ASV occurred mainly at heights between 0.05 and 1.2 m.Therefore,a point was taken every 0.01 m in this range,and the erosion intensity was obtained to that point.Thus,the curve of particle erosion intensity varying with bed height under different gas velocities is obtained.As shown in Fig.16,the trend of erosion intensity with height is approximately the same for each gas velocity.However,the maximum erosion increases with increasing gas velocity,and the maximum erosion location is approximately 0.07 m.In conjunction with the erosion heights shown in Fig.16,the maximum spray height for IMSSFB is approximately 0.12 m,and the steady spray height is approximately 0.07 m.

Fig.16.The erosion intensity in different height.

5.Conclusions

In this study,the erosion morphology of the inner member ASV was obtained experimentally at different filling heights,and the gas-particle hydrodynamics within the IMSSFB and the erosion on the inner member ASV and the inner wall surface were investigated using the Euler-Lagrange based model.This model investigated the radial and axial distribution of particles and the mixing of particles at different locations using the MP-PIC-based approach.In summary,the following conclusions are drawn:

(1) The experiment shows that with the increase of gas flow rate,the erosion intensity on the internal component ASV increases,and the maximum erosion point increases with the increase of filling height.

(2) The erosion on the inner wall surface is concentrated in the middle area.The top outlet of IMSSFB and the erosion morphology in the middle area is mainly dotted or flaky and relatively dispersed.

(3)The middle section of the spouted bed and the lower section of the internals can be reinforced in industrial applications to avoid unnecessary product loss.

Data Availability

The data that has been used is confidential.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (22178286) and Shaanxi Qin Chuangyuan ‘‘scientist and engineer” team construction project (2022KXJ-041).

Nomenclature

Cddrag coefficient

ggravitational acceleration,m·s-2

Iparticle interaction

Ipmagnitude of the erosion value,kga·(m·s-1)b·m-2·a-1

Kfsgas-particle drag coefficient

mpparticle mass,kg

Ppressure,Pa

ReReynolds number

upparticle velocity,m·s-1

Vvelocity,m·s-1

α volume fraction

αcpvolume fraction at close packing

β a constant and the recommended value is between 2 and 5

θ interphase resistance coefficient

θperosion angle,°

ε a very small number for eliminating singularity

μ shear viscosity,kg·(m·s)-1

ν velocity vector,m·s-1

ρ density,kg·m-3

τ stress tensor,N·m-1

ω weighting factor

Subscripts

f fluid

p particle

s solid