Fluid Dynamics Investigation in a Cold Flow Model of Internal Recycle Quadruple Fluidized Bed Coal Pyrolyzer

: Internal recycle quadruple fluidized bed pyrolyzer (IR-QFBP) consists of a dual fluidized bed pyrolyzer and a dual fluidized bed combustor and is proposed in this work. It is a new kind of efficient fluidized bed with high pyrolysis and energy efficiency. IR-QFBP may attract extensive attention because of its compact structure. Cold hydrodynamic characteristics of IR-QFBP are the bases of modeling and designing for the hot one. To fully understand the hydrodynamic characteristics of IR-QFBP, a cold flow model on a laboratory scale was designed and set up; furthermore, the two-fluid model (TFM) based simulation was also carried out. The pressure profiles, fluidization states, velocity profiles, and circulation rates of a solid powder at different operation conditions in IR-QFBP were investigated. The results showed that the stable internal circulation of solid powder can be achieved in IR-QFBP. And different circulation characteristics can be obtained by adjusting the operating conditions.


Introduction
Coal is an important energy resource in the world.And a large portion of coal in the world is low-rank coal [1,2].Hence, advanced technologies for the efficient utilization of low-rank coal are urgently required.Coal pyrolysis has been considered as an attractive method of using this low-rank coal [2][3][4][5].Thus, it was necessary to reduce the energy consumption of the coal pyrolysis process, which would be more beneficial for saving energy and reducing cost in the downstream industry.
A number of studies have been proposed in coal pyrolysis, such as the multi-generation technologies coupling pyrolysis with combustion developed by Zhejiang University, the MRF process of China Coal Science and Technology Group Limited Company, the DG technology of Dalian University of Technology, and others [2,6].Most of the above studies have the problems of high energy consumption or low heating rates [2,6].
So far, the main types of pyrolysis reactors that have been developed include fixed bed [7][8][9], bubbling fluidized bed [10][11][12], circulating fluidized bed [13][14][15], entrained flow [16,17], etc.Among them, circulating fluidized bed shows technological and commercial superiority for coal pyrolysis due to short residence time, fast heat transfer, and fast separation of volatiles and char [18,19], although it has some disadvantages such as requiring more fuel conditioning and capital investment [20].Inspired by the advantage of the circulating fluidized bed, the dual fluidized bed (DFB) conversion technologies are proposed, which have a characteristic of using two fluidized bed (FB) reactors that are interconnected with circulated heat carrier particles for higher heating rates [21][22][23][24][25][26][27][28].Based on the DFB technology, quadruple fluidized bed (QFB) system regarded as a cost-effective method is proposed [29][30][31][32].However, it still belongs to the external circulating system, which may lead to an increase in the equipment costs and reduction in heat transfer efficiency to a certain extent.Thus, there is still room to improve the circulating fluidized bed coal pyrolysis technology.
In this work, an internal recycle quadruple fluidized bed pyrolyzer (IR-QFBP) was first proposed [20,33], and the scheme of IR-QFBP is shown in Figure 1.IR-QFBP is divided into two zones including a pyrolysis zone (two axisymmetric high-speed beds) and a combustion zone (two axisymmetric low-speed beds).The circulating powder transports the heat of combustion from the combustion reactor to the pyrolysis reactor to meet the required temperature of pyrolysis.
Processes 2024, 12, x FOR PEER REVIEW 2 of 15 which may lead to an increase in the equipment costs and reduction in heat transfer efficiency to a certain extent.Thus, there is still room to improve the circulating fluidized bed coal pyrolysis technology.
In this work, an internal recycle quadruple fluidized bed pyrolyzer (IR-QFBP) was first proposed [20,33], and the scheme of IR-QFBP is shown in Figure 1.IR-QFBP is divided into two zones including a pyrolysis zone (two axisymmetric high-speed beds) and a combustion zone (two axisymmetric low-speed beds).The circulating powder transports the heat of combustion from the combustion reactor to the pyrolysis reactor to meet the required temperature of pyrolysis.Hot coke powder is produced by air combustion with some coal powder in the lowspeed bed, which enters the high-speed bed through the lower connection channel at the bottom and thus provides heat for the high-speed bed.The pulverized coal in the highspeed bed provides heat for the pyrolysis reaction.The pyrolyzed coal flows into the lowspeed bed from the higher connection channel to form intra solid particle circulation and heat transfer.Coke powder as a product can be discharged from the bottom of the lowspeed bed.The low-speed bed and the high-speed bed are separated by partitions, and only coke powder, at a high temperature, flows and generates heat exchange between the high-speed bed and the low-speed bed.The fluid flow direction of gas phase and solid phase in IR-QFBP is shown schematically in Figure 2. In the practical production, coal gas can be used as the carrier gas in the high-speed bed to avoid contact with air, which can improve the concentration of raw coal gas and reduce the subsequent separation cost.Oxygen or oxygen-enriched combustion is avoided in the low-speed bed, which can cancel the process of air separation process for oxygen production.Hot coke powder is produced by air combustion with some coal powder in the lowspeed bed, which enters the high-speed bed through the lower connection channel at the bottom and thus provides heat for the high-speed bed.The pulverized coal in the high-speed bed provides heat for the pyrolysis reaction.The pyrolyzed coal flows into the low-speed bed from the higher connection channel to form intra solid particle circulation and heat transfer.Coke powder as a product can be discharged from the bottom of the low-speed bed.The low-speed bed and the high-speed bed are separated by partitions, and only coke powder, at a high temperature, flows and generates heat exchange between the high-speed bed and the low-speed bed.The fluid flow direction of gas phase and solid phase in IR-QFBP is shown schematically in Figure 2. In the practical production, coal gas can be used as the carrier gas in the high-speed bed to avoid contact with air, which can improve the concentration of raw coal gas and reduce the subsequent separation cost.Oxygen or oxygen-enriched combustion is avoided in the low-speed bed, which can cancel the process of air separation process for oxygen production.
The problems for most of the previous studies on the industrial process of the utilization technology of low-rank pulverized coal are the serious waste of a large amount of sensible heat at high temperature, the inability to deal with a large amount of wastewater generated by ammonia water cooling [34,35], the bonding between the cooling tar and pulverized coal or coal ash, and the limited development of the tar-processing industry [36,37].
To solve these problems, we proposed a new idea for the utilization of low-rank pulverized coal, that is, coupling the low-order pulverized coal pyrolysis with the pyrolysis gas cracking in the subsequent operation.The problems for most of the previous studies on the industrial process of the utilization technology of low-rank pulverized coal are the serious waste of a large amount of sensible heat at high temperature, the inability to deal with a large amount of wastewater generated by ammonia water cooling [34,35], the bonding between the cooling tar and pulverized coal or coal ash, and the limited development of the tar-processing industry [36,37].To solve these problems, we proposed a new idea for the utilization of low-rank pulverized coal, that is, coupling the low-order pulverized coal pyrolysis with the pyrolysis gas cracking in the subsequent operation.
The main content of the new idea is to pyrolyze low-rank pulverized coal through a coal pyrolysis reactor (IR-QFBP), and the pyrolysis products are the raw gas (gas and gaseous tar mixture at high temperature) and coke.Coke can be collected, sold, or used as a product.Raw gas is no longer cooled, but directly enters a high-temperature reactor (Utube reactor), where the gaseous tar is directly decomposed into small molecules such as methane, CO, or H2 through high-temperature cracking, partial oxidation, or steam reforming reactions.Small molecules can be burned for heating or participate in chemical reactions, which can maximize energy utilization efficiency.
The advantages of this new idea are summarized as follows: (1) the direct decomposition of the gaseous tar can produce H2, which can provide sufficient raw materials for the hydrogen energy industry; (2) the post-treatment process of raw gas abandons the traditional ammonia water cooling process and no longer produces phenol-containing wastewater, which can reduce the cost of the treatment of phenol-containing wastewater by chemical enterprises; (3) the direct high-temperature reaction of the raw gas can make the full use of sensible heat in the raw gas, which improves the energy utilization efficiency; and (4) the tar in the coal gas is directly cracked, and thus, the tar and dust does not bond to cause pipeline obstruction.
In this idea, IR-QFBP is used as the low-rank pulverized coal pyrolysis reactor, and the U-tube reactor is used as the tar pyrolysis reactor.As the IR-QFBP is the key equipment in the whole process, we mainly focused on the characteristics of IR-QFBP in this work.The cold flow models under ambient conditions are widely applied to study the fluid dynamics for a new system [29,[38][39][40].And the hydrodynamic characteristics of IR- The main content of the new idea is to pyrolyze low-rank pulverized coal through a coal pyrolysis reactor (IR-QFBP), and the pyrolysis products are the raw gas (gas and gaseous tar mixture at high temperature) and coke.Coke can be collected, sold, or used as a product.Raw gas is no longer cooled, but directly enters a high-temperature reactor (U-tube reactor), where the gaseous tar is directly decomposed into small molecules such as methane, CO, or H 2 through high-temperature cracking, partial oxidation, or steam reforming reactions.Small molecules can be burned for heating or participate in chemical reactions, which can maximize energy utilization efficiency.
The advantages of this new idea are summarized as follows: (1) the direct decomposition of the gaseous tar can produce H 2 , which can provide sufficient raw materials for the hydrogen energy industry; (2) the post-treatment process of raw gas abandons the traditional ammonia water cooling process and no longer produces phenol-containing wastewater, which can reduce the cost of the treatment of phenol-containing wastewater by chemical enterprises; (3) the direct high-temperature reaction of the raw gas can make the full use of sensible heat in the raw gas, which improves the energy utilization efficiency; and (4) the tar in the coal gas is directly cracked, and thus, the tar and dust does not bond to cause pipeline obstruction.
In this idea, IR-QFBP is used as the low-rank pulverized coal pyrolysis reactor, and the U-tube reactor is used as the tar pyrolysis reactor.As the IR-QFBP is the key equipment in the whole process, we mainly focused on the characteristics of IR-QFBP in this work.The cold flow models under ambient conditions are widely applied to study the fluid dynamics for a new system [29,[38][39][40].And the hydrodynamic characteristics of IR-QFBP system are the bases of modeling and designing of a hot reactor.To fully understand the hydrodynamic characteristics, a cold flow model of IR-QFBP system on a laboratory scale was designed and set up in this work.The aluminum oxide particles were used as the solid materials.Meanwhile, the numerical model for IR-QFBP system was also established.Based on the experimental and numerical methods, the characteristics of fluidization state in IR-QFBP can be obtained.The effects of fluidization velocity on the volume fraction of solid phase, pressure profiles, and solid circulation rate were investigated.In order to verify the possibility of the pilot system of IR-QFBP, the hydrodynamic characteristics of the system were explored in this work, thus providing some ideas for reactor design.

Experiments 2.1. IR-QFBP Apparatus
As shown in Figure 3, the designed IR-QFBP for the experimental investigation is cylindrical in shape, and it is divided into three regions from the bottom to the top: the gas supply region, the reaction region, and the exhaust region.The gas supply region mainly includes four gas supply pipelines and a gas buffer chamber.The inner diameter of the air supply pipe is 45 mm, and the air is introduced from the side of the gas buffer chamber.The diameter and the height of the gas buffer chamber are 300 mm and 200 mm, respectively, and the gas buffer chamber is divided into four disconnected areas by the gas chamber cross baffle.A gas distributor is designed at the connection between the top of the gas buffer chamber and the bottom of the reaction region, and the gas distributor has been made with small holes with a diameter of 2 mm, as shown in the detailed drawing of Figure 3.The bubble cap distributor was used in our work, which can guarantee that the gas distributes uniformly when the equipment is operating, and the solid materials do not leak when the equipment shuts down.The diameter of the reaction region is 300 mm, the height is 1000 mm, and the thickness of the outer wall is 5 mm.The whole body is made of transparent plexiglass, and the copper wire mesh is set close to the inner wall of the plexiglass tube, which can remove static electricity.The interior of the reaction region is divided into four parts by a cross baffle, corresponding to the four parts of the gas buffer chamber.The reaction zone is divided into two high-speed bed zones and two low-speed bed zones.The two high-speed bed zones are centrally symmetrical, and the two low-speed bed zones are also centrally symmetrical.The connecting holes between the high-speed beds and low-speed beds are 80 mm long and 50 mm high and arranged at upper and lower intervals in a clockwise order.The exhaust region is composed of four plexiglass tubes with a diameter of 45 mm, which correspond to the four reaction areas.Four pressure-monitoring points are set at the top (z = 0.9 m) of the two high-speed beds and two low-speed beds, respectively.U-tube differential pressure gauges are used to measure the pressure difference between the high-speed bed and low-speed bed in this work.The main dimensions of IR-QFBP are summarized in Table 1.

Materials
Aluminum oxide particles are used as solid materials in IR-QFBP as it shows low toxicity, easy observation, and the similar physical properties of the low-rank pulverized coal, as shown in Table 2.

Materials
Aluminum oxide particles are used as solid materials in IR-QFBP as it shows low toxicity, easy observation, and the similar physical properties of the low-rank pulverized coal, as shown in Table 2.

Methodology
All the four parts of the reaction region of IR-QFBP are filled with aluminum oxide particles before the beginning of the experiment.The fluidization air for the four parts of the reaction region of IR-QFBP are supplied by four air compressors, respectively.During the experiment, the inlet velocity of high-speed beds and low-speed beds are varied, which can be adjusted by the air compressors.
In order to determine the inlet velocity of high-speed beds and low-speed beds, the minimum fluidization velocity of the aluminum oxide particles shown in Table 2 should be measured firstly.For this purpose, a pilot device was built, which mainly included a lifting tube, a gas chamber, a gas distributor, an air compressor, a buffer tank, and a U-tube differential pressure gauge.A plexiglass tube with a height of 3 m and an inner diameter of 30 mm is used as the lifting tube.A gas chamber is installed at the lower part of the lifting tube.A breathable sintering plate is used as the gas distributor.Flange connection is adopted to connect the above parts.The air compressor is connected to the buffer tank to supply the gas required for fluidizing the particles.The U-tube differential pressure gauge is connected to the lower part of the lifting tube to measure the pressure difference between the system and the outside.The minimum fluidization velocity was measured by the velocity-increasing method and the velocity-decreasing method at the same time.The steps of the measure experiment can be found in the reference of Kunii and Levenspiel [41].
Based on the minimum fluidization velocity obtained from the above methods, the inlet velocity of high-speed beds and low-speed beds can be roughly determined, which are usually several times larger than the minimum fluidization velocity [29].

Physical Model
The hydrodynamics for the gaseous and liquid phases in IR-QFBP was simulated.The reaction region of IR-QFBP shown in Figure 1 was mainly investigated.The detailed geometry and fluid physical parameters used in this simulation are summarized in Tables 1 and 2, respectively.

Numerical Model
In this study, the computational simulations are performed by KTGF (Kinetic Theory of Granular Flow)-based Euler-Euler TFM (two-fluid model) approaches.It is assumed that the aluminum oxide powder is composed of spherical particles with same size and density as shown in Table 2.The temperatures of the air and particles are constant in the absence of chemical reactions, suggesting that both equations of energy conservation are neglected for simplicity.The inter-phase momentum exchange between gas and solid phases is calculated using the Gidaspow gas-solid drag model [42].The governing equations and constitutive relations used in this study are summarized in Table 3 [43].The subscripts f and s represent the gas and the solid phases, respectively.More details about the model can be found in the Fluent 16 manual.

Simulation Settings
ANSYS Fluent 16 commercial package was used to model the gas-solid flow phenomena in IR-QFBP.The Pressure-Based type solver was used to solve the hydrodynamics equations.The computational domain was divided into about 130,000 cells.The calculation was performed on an HP workstation with 24 parallel 2.40 GHz Intel Xeon Silver 4214R processors.
The velocity inlet boundary condition was applied to the bottom boundary of the computational domain as a uniform velocity profile with u f,z = 0.1 m/s for the high-speed beds and u f,z = 0.04 m/s, 0.06 m/s, and 0.08 m/s for the low-speed beds.At the outlet boundary, the pressure outlet boundary condition was applied.The no slip conditions were set on the walls.The transient model was selected, and the time step was set as 0.001 s.

Minimum Fluidization Velocity
As shown in Figure 4, the curves measured by the velocity-increasing method and the velocity-decreasing method are not same, and the former in the range of pressure drop is greater than the opposite process.This is because when the fixed bed is converted to the fluidized bed, additional energy must be supplied to break the cohesion forces between the particles, and thus, the pressure drop peak is formed at the moment of flush out.However, the conclusion can be drawn that the minimum fluidization velocity is about 0.01 m/s from these two methods.
Processes 2024, 12, x FOR PEER REVIEW 8 of 15 beds and uf,z = 0.04 m/s, 0.06 m/s, and 0.08 m/s for the low-speed beds.At the outlet boundary, the pressure outlet boundary condition was applied.The no slip conditions were set on the walls.The transient model was selected, and the time step was set as 0.001 s.

Minimum Fluidization Velocity
As shown in Figure 4, the curves measured by the velocity-increasing method and the velocity-decreasing method are not same, and the former in the range of pressure drop is greater than the opposite process.This is because when the fixed bed is converted to the fluidized bed, additional energy must be supplied to break the cohesion forces between the particles, and thus, the pressure drop peak is formed at the moment of flush out.However, the conclusion can be drawn that the minimum fluidization velocity is about 0.01 m/s from these two methods.

Pressure Profiles
The pressure profile can vividly show the operation condition of the fluidized bed.Thus, the inner pressure profile in IR-QFBP was first investigated.The simulated pressure profiles when the fluid flow is fully developed with the inlet velocity of 0.1 m/s in highspeed beds and 0.04 m/s, 0.06 m/s, and 0.08 m/s in low-speed beds are shown in Figures 5-7.
The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s in low-speed beds are shown in Figure 5.Both the pressures in the high-speed bed and in the low-speed bed are reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the low-speed bed at 0 m < z < 0.3 m, while, the pressure in the high-speed bed is higher than that in the low-speed bed at 0.3 m < z < 0.9 m, which can maintain the fluid flow from the low-speed bed to the high-speed bed through the lower connection hole and from the high-speed bed to the low-speed bed through the higher connection hole.
The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.06

Pressure Profiles
The pressure profile can vividly show the operation condition of the fluidized bed.Thus, the inner pressure profile in IR-QFBP was first investigated.The simulated pressure profiles when the fluid flow is fully developed with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s, 0.06 m/s, and 0.08 m/s in low-speed beds are shown in Figures 5-7.
m/s in low-speed beds are shown in Figure 7. Same as the results in Figures 5 and 6, the pressures in the high-speed bed and in the low-speed bed are reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the lowspeed bed at 0 m < z < 0.5 m, while the pressure in the high-speed bed is higher than that in the low-speed bed at 0.5 m < z < 1.0 m, which also maintain the stable internal circulation of solid materials.m/s in low-speed beds are shown in Figure 7. Same as the results in Figures 5 and 6, the pressures in the high-speed bed and in the low-speed bed are reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the lowspeed bed at 0 m < z < 0.5 m, while the pressure in the high-speed bed is higher than that in the low-speed bed at 0.5 m < z < 1.0 m, which also maintain the stable internal circulation of solid materials.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s in low-speed beds are shown in Figure 5.Both the pressures in the high-speed bed and in the low-speed bed are reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the low-speed bed at 0 m < z < 0.3 m, while, the pressure in the high-speed bed is higher than that in the low-speed bed at 0.3 m < z < 0.9 m, which can maintain the fluid flow from the low-speed bed to the high-speed bed through the lower connection hole and from the high-speed bed to the low-speed bed through the higher connection hole.By comparing these three figures, the pressure differences between the high-speed bed and the low-speed bed in Figure 6 are larger than those in Figures 5 and 7, which may generate greater driving force for the internal circulation.Therefore, the operation conditions with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds were mainly investigated in the following study.
The experimental pressure differences between the high-speed bed and the lowspeed bed can be measured through the method shown in Section 2.1.The simulated pressure differences at z = 0.9 m were selected, as the pressure-monitoring points were set near this location of the apparatus.The results for the three cases are summarized in Table 4.As can be seen, the simulated values are close to the experimental values, which can verify the accuracy of the simulation model used in our work.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds at different times are shown in Figure 8.At the beginning of fluidization, the pressures in the high-speed bed and in the low-speed bed are almost the same.As the fluidization proceeds, pressure differences between the high-speed bed and the low-speed bed begin to appear.When the pressure differences are almost constant, fluidization is considered to be fully developed, and the time of which is about 16 s.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds are shown in Figure 6.Same as the results in Figure 5, the pressures in the high-speed bed and in the low-speed bed are also reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the low-speed bed at 0 m < z < 0.4 m, while the pressure in the high-speed bed is higher than that in the low-speed bed at 0.4 m < z < 1.0 m, which also maintain the stable internal circulation of solid materials in IR-QFBP.
The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.08 m/s in low-speed beds are shown in Figure 7. Same as the results in Figures 5 and 6, the pressures in the high-speed bed and in the low-speed bed are reduced with the increase in the height along z.The pressure in the high-speed bed is lower than that in the low-speed bed at 0 m < z < 0.5 m, while the pressure in the high-speed bed is higher than that in the low-speed bed at 0.5 m < z < 1.0 m, which also maintain the stable internal circulation of solid materials.
By comparing these three figures, the pressure differences between the high-speed bed and the low-speed bed in Figure 6 are larger than those in Figures 5 and 7, which may generate greater driving force for the internal circulation.Therefore, the operation conditions with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds were mainly investigated in the following study.
The experimental pressure differences between the high-speed bed and the low-speed bed can be measured through the method shown in Section 2.1.The simulated pressure differences at z = 0.9 m were selected, as the pressure-monitoring points were set near this location of the apparatus.The results for the three cases are summarized in Table 4.As can be seen, the simulated values are close to the experimental values, which can verify the accuracy of the simulation model used in our work.
The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds at different times are shown in Figure 8.At the beginning of fluidization, the pressures in the high-speed bed and in the low-speed bed are almost the same.As the fluidization proceeds, pressure differences between the high-speed bed and the low-speed bed begin to appear.When the pressure differences are almost constant, fluidization is considered to be fully developed, and the time of which is about 16 s.

Fluidization State
The fluidization state of the solid phase can be used as the indicator for achieving stable internal circulation.The instantaneous solid volume fractions in IR-QFBP with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds are shown in Figure 9.

Fluidization State
The fluidization state of the solid phase can be used as the indicator for achieving stable internal circulation.The instantaneous solid volume fractions in IR-QFBP with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds are shown in Figure 9.

Fluidization State
The fluidization state of the solid phase can be used as the indicator for achieving stable internal circulation.The instantaneous solid volume fractions in IR-QFBP with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds are shown in Figure 9.As shown in Figure 9, as time goes on, the bed heights of both high-speed bed and low-speed bed are growing.The expansion ratio of the bed begins to decrease at t = 10 s, while the bed heights are almost unchanged at t = 16 s.The solid volume fraction in the low-speed bed is higher than that in the high-speed bed after t = 5 s, especially around the top part of the lower connection between the two beds.With the increase in bed height, the solid volume fractions of the two beds are decreased.When the flow is fully developed, i.e., at t = 16 s, the bed height of the high-speed bed is higher than that of the low-speed bed because of the higher pressure at the top of the high-speed bed as shown in Figure 8.

Velocity Profiles of Solid Phase
In order to examine the flow characteristics in IR-QFBP, the streamline and velocity profiles of solid phase are shown in Figure 10.It can be seen clearly in Figure 10 that the solid particles in the high-speed bed enter the low-speed bed from the connecting hole in the upper part of the high-speed bed, while the solid particles in the low-speed bed enter the high-speed bed from the connecting hole in the lower part of the low-speed bed, which shows that the internal recycling is achieved between the two beds.Moreover, there are several flow vortexes formed in the beds, which can enhance mass transfer between the gas phase and the solid phase [44,45].
As shown in Figure 9, as time goes on, the bed heights of both high-speed bed and low-speed bed are growing.The expansion ratio of the bed begins to decrease at t = 10 s, while the bed heights are almost unchanged at t = 16 s.The solid volume fraction in the low-speed bed is higher than that in the high-speed bed after t = 5 s, especially around the top part of the lower connection between the two beds.With the increase in bed height, the solid volume fractions of the two beds are decreased.When the flow is fully developed, i.e., at t = 16 s, the bed height of the high-speed bed is higher than that of the lowspeed bed because of the higher pressure at the top of the high-speed bed as shown in Figure 8.

Velocity Profiles of Solid Phase
In order to examine the flow characteristics in IR-QFBP, the streamline and velocity profiles of solid phase are shown in Figure 10.It can be seen clearly in Figure 10 that the solid particles in the high-speed bed enter the low-speed bed from the connecting hole in the upper part of the high-speed bed, while the solid particles in the low-speed bed enter the high-speed bed from the connecting hole in the lower part of the low-speed bed, which shows that the internal recycling is achieved between the two beds.Moreover, there are several flow vortexes formed in the beds, which can enhance mass transfer between the gas phase and the solid phase [44,45].

Solid Circulation Rate
In this section, we investigated the solid circulation rate through the connection holes between the high-speed beds and low-speed beds, which can be used to measure the amount of the solid particle circulation and has a direct influence on the mean particle residence time [29].The results of the solid particle circulation rates are shown in Table 5. Solid particle circulation rate through the lower connection is the same with that through the higher connection between the two beds.And, with the increase in the inlet velocity of low-speed bed, the solid particle circulation rates are increased.However, there is a small amount of the solid particles flowing out from the outlet of the high-speed bed (about 0.0002 kg/s) when the inlet velocity of the low-speed bed is 0.08 m/s, which can affect the subsequent process and increase the post-processing difficulty.

Solid Circulation Rate
In this section, we investigated the solid circulation rate through the connection holes between the high-speed beds and low-speed beds, which can be used to measure the amount of the solid particle circulation and has a direct influence on the mean particle residence time [29].The results of the solid particle circulation rates are shown in Table 5. Solid particle circulation rate through the lower connection is the same with that through the higher connection between the two beds.And, with the increase in the inlet velocity of low-speed bed, the solid particle circulation rates are increased.However, there is a small amount of the solid particles flowing out from the outlet of the high-speed bed (about 0.0002 kg/s) when the inlet velocity of the low-speed bed is 0.08 m/s, which can affect the subsequent process and increase the post-processing difficulty.

Conclusions
In this work, IR-QFBP, which can enable the coupling and heat transfer between different reactions, was proposed.It has potential for efficient reaction and energy utilization.The cold hydrodynamic characteristics of IR-QFBP, including the pressure profiles, fluidization states, velocity profiles, and circulation rates of the solid phase at different operation conditions were mainly investigated in this work.All the four cases (the cases with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s, 0.06 m/s, and 0.08 m/s in low-speed beds) focused on in the present work can achieve the stable internal circulation of solid materials.The case with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds has the maximal solid circulating driving force.The case with the inlet velocity of 0.1 m/s in high-speed beds and 0.08 m/s can generate the highest solid circulation rate, but at the same time, they can give rise to a certain amount of solid material loss at the top outlet of IR-QFBP.Cold hydrodynamic characteristics' investigation of IR-QFBP in this work can provide the bases for modeling and designing of the corresponding hot reactor.

Figure 2 .
Figure 2. Schematic of the fluid flow direction in IR-QFBP.

Figure 2 .
Figure 2. Schematic of the fluid flow direction in IR-QFBP.

Figure 4 .
Figure 4. Relationship between pressure drop and fluidization velocity by velocity-increasing method and velocity-decreasing method.

Figure 4 .
Figure 4. Relationship between pressure drop and fluidization velocity by velocity-increasing method and velocity-decreasing method.

Figure 5 .Figure 6 .
Figure 5.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s in low-speed beds.

Figure 5 .
Figure 5.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s in low-speed beds.

Figure 5 .Figure 6 .
Figure 5.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.04 m/s in low-speed beds.

Figure 6 .
Figure 6.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.06 m/s in low-speed beds.

Figure 7 .
Figure 7.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.08 m/s in low-speed beds.

Figure 7 .
Figure 7.The pressure profiles with the inlet velocity of 0.1 m/s in high-speed beds and 0.08 m/s in low-speed beds.

Figure 10 .
Figure 10.Streamline and velocity profiles of solid phase in IR-QFBP (plane x = 0.075 m).

Figure 10 .
Figure 10.Streamline and velocity profiles of solid phase in IR-QFBP (plane x = 0.075 m).

γ
Collisional dissipation of energy, J/(m 3 •s) θ s Granular temperature, m 2 /s 2 λ s Solid phase bulk viscosity, Pa•s µ f Gas and solid viscosity, Pa•s µ s Solid viscosity, Pa•s µ s,col Collisional part of solid viscosity, Pa•s µ s,kin Kinetic part of solid viscosity, Pa•s µ s,fr Frictional part of solid viscosity, Pa•s ρ f Gas density, kg/m 3 ρ s Solid density, kg/m 3 τ f Gas phase stress tensor, Pa τ s Solid phase stress tensor, Pa

Table 2 .
Comparison of particle properties of aluminum oxide particles and low-rank pulverized coal.

Table 2 .
Comparison of particle properties of aluminum oxide particles and low-rank pulverized coal.

Table 3 .
Governing equations and constitutive laws of TFM simulations.

Table 4 .
Simulated and experimental results comparison of pressure differences between the highspeed bed and the low-speed bed.

Table 4 .
Simulated and experimental results comparison of pressure differences between the highspeed bed and the low-speed bed.

Table 5 .
Results of solid circulation rate through the connection hole.