Xiaoyi Chen ,Danyang Song ,Dong Zhang ,Xiaogang Jin ,Xiang Ling,*,Dongren Liu

1 School of Mechanical and Power Engineering,Nanjing Tech University,Nanjing 211816,China

2 School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China

3 Mechanical Engineering College,Yangzhou University,Yangzhou 225009,China

Keywords:Thermochemical energy storage CaCO3/CaO Reactors Simulation Two-phase flow Energy-minimization multi-scale model(EMMS)

ABSTRACT According to environmental and energy issues,renewable energy has been vigorously promoted.Now solar power is widely used in many areas but it is limited by the weather conditions and cannot work continuously.Heat storage is a considerable solution for this problem and thermochemical energy storage is the most promising way because of its great energy density and stability.However,this technology is not mature enough to be applied to the industry.The reactor is an important component in the thermochemical energy storage system where the charging and discharging process happens.In this paper,a spiral coil is proposed and used as a reactor in the thermochemical energy storage system.The advantages of the spiral coil include simple structure,small volume,and so on.To investigate the flow characteristics,the simulation was carried out based on energy-minimization multi-scale model (EMMS) and Eulerian two-phase model.CaCO3 particles were chosen as the reactants.Particle distribution was shown in the results.The gas initial velocity was set to 2 m·s-1,3 m·s-1,and 4 m·s-1.When the particles flowed in the coil,gravity,centrifugal force and drag force influenced their flow.With the Reynold numbers increasing,centrifugal and drag force got larger.Accumulation phenomenon existed in the coil and results showed with the gas velocity increasing,accumulation moved from the bottom to the outer wall of the coil.Besides,the accumulation phenomenon was stabilized when φ ＞720°.Also due to the centrifugal force,a secondary flow formed,which means solid particles moved from the inside wall to the outside wall.This secondary flow could promote turbulence and mixing of particles and gas.In addition,when the particle volume fraction is reduced from 0.2 to 0.1,the accumulation at the bottom of the coil decreases,and the unevenness of the velocity distribution becomes larger.

1.Introduction

As fossil fuel consumption increases,the energy and environmental problem are becoming more serious,limiting the development of industry,technology,and economy.The utilization of clean and renewable energy has attracted much attention[1].Solar energy is considered as the most promising solution because of its abundance and applicability.Currently,solar energy has been widely used in the aspects of generation,industry,and heat supply,but challenges still exist [2].Heat provided from solar energy is limited by the weather conditions so it cannot work continuously,such as the diurnal,seasonal,and regional variations.Thus heat storage system is significant for reliable and stable operation of the solar power system [3].

Three heat storage forms are widely used:sensible heat,latent heat,and thermochemical energy [4].The first form is to store energy by the temperature change of the medium.Common materials used in sensible heat storage are molten salts.Disadvantages are obvious that the thermal conductivity and heat density is very low.A better choice is latent heat storage.When the phase of material changes,latent heat will be absorbed or released.The heat density and thermal conductivity are higher than that of sensible heat storage [5].However,these materials are hard to be saved in long periods.Compared with sensible and latent heat storage,thermochemical energy storage has more benefits [6].The energy density is highest in these three heat storage ways.And energy can be stably stored in the chemical bond in reactants.These reactants can be stored for a long time with little heat loss and can be transported to other locations where needs energy supply [7].

Materials that adapt to thermochemical energy storage systems are various.It can be roughly divided into these four types:metal oxide [8],metal hydride [9],metal hydroxide [10],metal sulfate[11],and metal carbonate [12].In this study,the CaCO3/CaO system is taken as reaction materials.The advantages are clear like it is non-toxic,the initial material can be easily got from limestone with low cost and the reaction temperature is high enough for high-temperature solar energy storage [13].

Though the thermochemical energy storage system seems to be a promising technology,it is still not mature and cannot be applied in industry.Many aspects of researches like materials,integrated processes,and reaction processes have been done [6,14,15].However,reactor design is one of the main challenges for the thermochemical energy storage system [16].CaCO3/CaO system is also used in CO2capture [17].The reaction principle is the same so the reactor design is of valuable reference for the heat storage system.However,it should be noted that some reaction conditions like temperature,pressure,gas flow,and so on are different [18].

For solar thermal energy storage,fixed and fluidized beds are two common types of reactors.Yanet al.[19]tested the heat storage and release process of CaO/Ca(OH)2system using a fixed bed and pumped out the air to reduce the impact of air.The large volume and unmovable materials is a shortcoming of a fixed bed,leading to the terrible heat and mass transfer in the reactor.Schmidtet al.[20] presented and experimentally tested an indirectly heated reaction bed consisting of one single heat exchanger plate.2.4 kg of Ca(OH)2storage material was filled into the frame.Then further studies for wider temperature and pressure range were done[21].Comparatively,a fluidized bed is more suitable for high temperature concentrated solar power (CSP) plants [22].In 1980,Badieet al.[23]studied the thermal efficiency for the decarbonization of CaCO3in both fluidized beds(15%)and rotary kiln(7%).Shimizuet al.[24] designed a twin fluid-bed reactor based on the CaCO3/CaO system.The turbine efficiency was 46.6%and it reduced to 42.6%after the second cycle.Recently Tregambiet al.[25]studied the CaL-CSP integrated process using a directly irradiated fluidized bed reactor.The peak value of radiative fluxes was about 3000 kW·m-2,causing overheating in the upper section of the bed.Then further researches were done in 2019 using the same reactor [26].Cosquillo Mejiaet al.[27] designed a novel moving bed reactor,two encapsulated storage materials flowed through several straight tubes and were heated by the heat transfer fluid outside the tubes.The reactor was experimentally and successfully demonstrated.Esenceet al.[28] designed a shallow cross-flow compartmented fluidized-bed reactor.It was tested in a 1-MW Odeillo’s solar furnace (France),using dolomite (CaMg(CO3)2) as the reactant.The particle temperature was 1073 K when the decomposition reaction reached a steady state.Otherwise,a numerical model was established to simulate the energy balance,mass balance,and reaction kinetics.This model was successfully matched with experimental data.Other types of reactors are also investigated.Meieret al.[29,30]designed and tested a 10-kW solar rotary kiln reactor,processing 1-5 mm limestone particles.95%or higher purity lime could be produced.This reactor reliably operated for more than 100 h for a total of 24 sunny days.Abanadeset al.[31] developed a new novel solar reactor concept for high temperature (773-1873 K) thermochemical reactions,including a cavity-type solar receiver to receive solar energy and a rotary tube to react in.Andrewet al.[32]designed,modeled and optimized a 5 kWthscale solar thermochemical inclined granular-flow reactor,in which solar thermochemical energy was stored based on reduction/oxidation reactions of aluminum-doped calcium manganite particles.Simulation was done with different granular mass flow,radiative heat flow and inclination angle to evaluate the reactor performance,providing guidance for its realistic design and operation.

Heat storage for CSP is an emerging industry.Few studies have been done in this field,especially for the high-temperature heat storage system [33,34].Most of them focus on the materials or reactions[35].Also,some reactors have been designed,simulated,and experimentally tested[36].Anyway,investigation for reactors is still at the starting stage and lab-scale reactors are still lacking in current researches.The reactors mentioned above have their characteristics.The rotary reactor is a good solution due to uniform temperature and little particle decomposition,while the cost may be higher because of the large volume.Some of the reactors directly receive solar radiation but it also leads to non-uniform heating.And the reactors generally include many different parts,increasing structural complexity.To explore the possible reactor,this study focused on the spiral coil reactor,which is promising to be widely applicable to the thermochemical energy storage system.The spiral coil has many advantages like simple structure,no running internal components,temperature controllable,and highpressure resistance.Fluid in the coil is influenced by centrifugal and viscosity force so it moves towards the outer wall,forming a secondary flow and enhancing the turbulence.The coiled pipe structure increases the effective mixing area.Therefore,the performance of mixing,mass,and heat transfer is better than straight tubes with the same volume.Reactions can be performed at higher Reynolds numbers.When both of the gas and solid phases exist in the coil,due to the inertial and drag force from CO2,particles flowing in the coil show non-uniformity so that solid particles(CaCO3/CaO)cannot be fully contacted with the gas.For this reason,understanding the particle flow law in the two-phase flow in the reactor is significant for reactor design and optimization of the operating conditions.

2.Physical Model

The physical model used in this investigation is shown in Fig.1.Considering computational complexity,a three-ring spiral coil of radiusr=16 mm,curvature radiusR=150 mm and pitchD=48 mm is selected as the study object.CO2and CaCO3particles flow through the reactor from the bottom to the top.In the flowing process,CaCO3particles are heated and then decompose to CaO and CO2with thermal energy released.In the simulation,CaCO3particle diameter is 50 μm and the density is set as 2700 kg·m-3.Other parameters are presented in Table 1.To ensure the normal flowing of CaCO3particles in spiral coil,particle mass flow rate is set to 0.869 kg·s-1when the volume fraction of solid particles is 0.2 with different inlet gas flow rates of 2 m·s-1,3 m·s-1,and 4 m·s-1.In addition,the effects of volume fraction of solid particles(0.1,0.15,and 0.2) and wall temperature (1100 K,1200 K,and 1300 K) are also investigated in the manuscript.

Table 1Simulation parameters in the spiral pipe

3.Mathematical Model

Generally,the two-phase flow in the spiral coil reactor shows inhomogeneity because of centrifugal force and gravity,causing CaCO3/CaO particles to gather on the outer wall and bottom of the spiral coil.Otherwise,due to the effect of drag force on solidphase from CO2,local inhomogeneity occurs,which means local agglomeration and dispersion of particles and then the solid particles cannot fully contact with the gas.Thus investigating the flowing law of CaCO3/CaO particles is necessary.

For a two-phase flow system,structural inhomogeneity and state multivalue are the main characteristics.Energyminimization multi-scale model(EMMS)is proposed to solve these two problems [37].Structural inhomogeneity causes multi-scale interaction between particle fluids,which is related to system stability.For example,when the dilute phase and dense phase all exist in a system,the interaction mechanism between particles and fluid in the two areas is completely different.Therefore the traditional mass and momentum conservation analysis method is not enough to determine the state of the system.In the EMMS model,complex multiscale interaction is divided into micro-scale effects in dilute and dense phases and macro-scale effects in the interacting phase.This can simplify the calculation.Then energy minimization is combined with stability conditions and the state of two-phase flow can be determined.EMMS drag model combined with a two-fluid model (Eulerian model) is established in the simulation.The assumptions in the two-fluid model are as follows:

(1) The particle size is uniform.

(2) Particles are isothermal,inelastic,and sooth monodisperse balls.

(3) Small interaction forces such as lift,brown force and virtual mass force are ignored.

(4) Energy transfer due to pressure,stress and viscous separation is not considered.

3.1.Mass conservation

whereVis instantaneous velocity.It can be replaced by the average velocity of solid phaseus.

3.2.Momentum conservation equation

Based on Eulerian two-phase model,momentum conservation equations can be expressed as follows:

For gas phase

where βgsis gas solid-phase drag coefficient,usis particle average velocity.The fifth term on the right side of the equation represents the momentum transfer of the solid phase.

Fig.1.Spiral coil model.

3.3.Particles pseudo-temperature equation

For solid phase,a transport equation [39] describing randomly moving particles caused by particle collision is defined as:

where Θsis particles temperature:

In Eq.(6)represents fluctuating velocitys-us.

Because of particle impact,granular pressure includes kinetic energy and particle collision,expressed as:

Besides,in Eq.(5),ksis the energy diffusion coefficient of particles:

The definition of radial distribution functiong0and wave energy dispersion γ caused by inelastic collision is given by Eqs.(9) and (10):

Apart from the equations mentioned above,residual source terms are related to energy conversion between different phases.Drag force plays a significant role in the solid and gas phase.The most conventional model is the Gidaspow drag model [38].

When εg＜0.8,the Gunn equation is used to describe the dense gas-solid flow.The gas-solid drag coefficient is shown below:

When εg≥0.8,the drag coefficient can be provided by Wen-Yu model:

where the drag coefficient for a single particleCdonly depends onRe:

To accurately study the particle flow characteristics which cannot be observed inside the reactor in experiments,the EMMS model is adopted in the gas-solid phase flow.It proposed structure parameters based on the energy-minimization multi-scale method.Structure parameter is calculated by the average resistance coefficient and then gas-solid phase flow can be simulated combining with two-phase flow.EMMS has been proved more suitable with experimental results by many researches and it can be obtained by Eqs.(15) and (16):

3.4.Constitutive equation

Constitutive relations connect the control equations to make the equations closed.In this chapter constitutive equations are used as follows.

Stress tensor of gas phase and solid phase is shown in Eqs.(17)and (18):

Eq.(19) presents the diffusion coefficient of granular temperature (Syamlal-O’Brien):

and kinetic energy transfer is:

Shear viscosity of the solid phase is defined in Eq.(21):

where μs，col,μs，kin,μs，fris respectively collision viscosity of solid phase,dynamic viscosity (Syamlal-O’Brien),and friction viscosity of solid phase,which can be calculated by Eqs.(22),(23) and (24):

3.5.Model verification

As a proof of concept,a comparison is carried out for EMMS model verification between the EMMS model and paper published by Yanget al.[40].Fig.2 shows the porosity distribution along the radial at different bed heights.Slightly difference exists here because some detail factors are not given in their literature.However,the simulation results are identical with that from Yang,and thereby the EMMS model is valid in the manuscript.

3.6.Grid independence

In order to analyze the independence of the grid of the model,the simulation under different grid sizes is necessary.Fig.3 shows the transverse distribution of the volume fraction of solid particles along the cross section with the helix angel of 720°.The distribution trend of granular volume fraction under the three different grid sizes is consistent.The curves changes greatly in the middle,while the two ends close to the pipe wall tend to be stable.For the three different grid sizes,the results of the coarse grid are different from those of the other two grids.Therefore,to reduce the amount of calculation and satisfy the accuracy of the calculation,the grid number of 2,061,696 is selected in the simulation.The grid structure in the cross section is shown in Fig.4.The grids near the pipe wall are encrypted because of their importance for the coil structure.

4.Results and Discussions

4.1.Flow and distribution regularity of solid particles in the first ring

CaCO3particles are uniformly distributed at reactor inlet with a certain initial velocity.With CO2gas flowing through the pipe,there will be a settlement tendency of CaCO3solid particles under the effect of gravity.At the same time,particles are also affected by drag force from the high speed flow of CO2,and both of solid and gas phase is under the centrifugal force.These factors all increase uncertainty in particle flow and distribution,which is more obvious at the beginning of flowing.Therefore,this chapter mainly focuses on flow and distribution characteristics of CaCO3particles in the first ring of the pipe at 0.5 s.

4.1.1.Distribution regularity of flow along the section

Solid-phase particles enter the pipe with a certain velocity.As Fig.5 shows,they are affected by different forces.The first one is the drag force from CO2.It can be broken down into component forces along thez-axis andy-axis,leading to particles moving along the two directions.Besides,the centrifugal force and gravity of particles themselves also influence their behavior in the spiral coil.

Fig.2.Porosity distribution along the radial at different bed heights.

Fig.3.Transverse distribution of granular volume fraction along the cross section under different grid sizes.

In this simulation,inlet gas flow velocity is set to 2 m·s-1,3 m·s-1,and 4 m·s-1.Fig.6(a)shows the particle distribution contour on the section at 0.5 s with the helix angle ranging from 0°to 360°.On the inlet section(φ=0°)solid particles are uniform.When φ=45°,solid particles are influences by centrifugal force so that they start to move from the inner wall to the outer wall.As the flow proceeds,when φ=90°solid particles not only move outward but also settle on the bottom of the pipe.This change is not very clear here.However,when the helix angle is 135°-180°,settlement tendency becomes more obvious while the particle distribution near the outer wall does not change a lot.When φ=225°,solid particles are uniformly distributed on the upper right side of the tube wall and present a concave shape on the lower right side.The reason is that the solid particles on the lower left side of the coil want to move toward the right wall under the effect of centrifugal force,but due to the aggregation by gravity,these particles are resisted.Finally,they all gather on the bottom of the pipe.Distribution when φ=270°is the same with φ=225°except for more accumulation on the bottom wall.When the helix angle is equal to 315°,the concave shape nearly disappears because all the particles in the coil are affected by the centrifugal force and then they all move right.When φ=360°,with solid particles keeping gathering,the dilute phase is on the top of the pipe,leading to the drag force affecting solid particles get lager and then these particles accumulate on the top wall.In the whole flowing process,distribution changes are not obvious with flowing.It forms agglomeration causing lager the drag force.At this time the resultant force of drag and centrifugal force is bigger than gravity so that these particles do not fall to the bottom.Otherwise,it can be found that with flow proceeds,most of the particles are distributed in the lower right side of the spiral coil,and on the left wall of the coil there even no particle distribution.So it can be concluded initially that when the gas flow rate is 2 m·s-1and the flow time is 0.5 s,gravity is the most effective factor in the first ring.The second is centrifugal force and the drag force on solid particles has the least impact.At the same time,in some small areas,the resultant force of centrifugal and drag force can be larger than gravity.

Fig.4.Grid structure.

Fig.5.Force diagram of solid particles.

Fig.6.Solid particles distribution along the cross section at different gas initial velocity.

Changing the gas flow rate to 3 m·s-1,particle distribution contour is shown in Fig.6(b).Compared with the velocity of 2 m·s-1,the phenomenon of downward accumulation appears later.When the helix angle is φ=0°-135°,solid particles integrally tend to move right.It can be explained by the change of the inlet velocity of CO2gas.The drag force will get larger with the increase of gas rate so that solid particles move quickly in the tube,leading to an increase of the centrifugal force.With constant gravity,the tendency of solid particles to move to the right is greater than the tendency to settle down.However,with particles depositing to a certain amount,the growing resistance on CO2gas makes its velocity decrease,and the drag force on solid particles also reduces.As can be seen when φ=180°-360°,the gravity is larger than other forces at this time so that solid particles start to deposit.It can be summarized that when the flow rate is 3 m·s-1and the flow time is 0.5 s,centrifugal force and gravity alternately dominate the flow and particle distribution in the first ring of the spiral coil.Drag force has the least effect and in some small areas,the resultant force of centrifugal and drag force is larger than gravity.When the gas flow rate is set to 4 m·s-1,it can be found in Fig.6(c)that with the further increase of centrifugal force,the tendency of particles moving to the right is more and more obvious.Instead,the tendency of particles accumulating both to the bottom and the top is weakened.The area where is no particle distribution becomes larger.

To study the flow and distribution behavior at 0.5 s in the first ring,transverse and longitudinal volume fractions along the section are compared and analyzed with different gas flow rates.The helix angle is 90°-360°.The transverse direction is the central distribution from the inner wall to the outer wall and the longitudinal direction is the central distribution from the bottom to the top,which is shown in Fig.7.

The results are presented in Fig.8.When the gas flow rate is 2 m·s-1,for Fig.8(a),volume fraction increases from the left to the right and the average value is about 0.16.It is lower than at the entrance because of the accumulation caused by gravity.For Fig.8(b),curves do not change monotonously.The volume fraction decreases first and then increases near the top of the pipe.This variation trend is accord with the contour in Fig.6(b).When the gas flow rate rise to 3 m·s-1,in Fig.8(c)it can be found that curves still show increase change but for different helix angle(means different positions in the pipe),solid particle concentration on the left side of the coil decreases as the flow progresses and on the right side,it increases with the increase of φ.Vertically,in Fig.8(d) the curves show a concave shape.This appearance becomes more obvious with the growing helix angle.The average concentration is about 0.14.When φ is equal to 90°,the change from the bottom to the top in the pipe is not very large while when φ is 180-360°,solid particle volume fraction suddenly gets lager,reaching about 0.26.When the gas flow rate is 4 m·s-1,the average value of concentration decreases to about 0.12 in Fig.8(e).For Fig.8(f),it still keeps a concave shape.When the helix angle is 90°,the volume fraction on the top is even higher than is at the bottom.However,this phenomenon does not last long.When φ=270°-360°,the solid phase volume fraction near the top wall is far less than is near the bottom wall.Overall,with the gas initial flow rate increases,the concentration of solid particles rises from left to right and its average value decreases gradually.Besides,from the bottom to the top of the pipe,it shows a concave change and this trend becomes more obvious with the helix angle getting lager.

Fig.7.Distribution diagram along the cross section.

Fig.8.Solid particle distribution along the horizontal (left side) and vertical (right side) cross section at different initial gas velocity.

4.1.2.Regularity of flow along the section

Commonly,the flow of solid particles influences its distribution in the tube,so it’s necessary to study the particle flow rules in spiral coils.

When the initial velocity of the gas phase is set to 2 m·s-1and the flowing time is 0.5 s,the contour of solid particle distribution along the flow section is shown in Fig.9(a),where the helix angle varies from 0°to 360°.It can be found that the secondary flow appears when φ=90°.As the flow proceeds,this form of mobility is strengthened.The secondary flow overspreads to the whole pipe when φ=225°and is damaged when φ=270°.At the same time,there are fewer particles on the inner wall of the pipe because of the centrifugal force,so the flow rate becomes bigger here.Instead,the flow rate is smaller at the bottom and outer wall of the pipe due to particle agglomerating.When φ=360°,though the secondary flow is destroyed before,there forms a new and small secondary flow on the inner wall.Fig.9(b)shows the contour if particle distribution when the gas flow rate is 3 m·s-1,which is close to it is 2 m·s-1except for the velocity value.Moreover,the situation when the gas flow rate is 4 m·s-1is also studied.As Fig.9(c) shows the secondary flow on the inner wall is enhanced because of the greater gas flow rate.

Fig.9.Stream of solid particles along the cross section at different initial gas velocity.

Likewise,to better understand the flow characteristics in the first ring of the reactor,transverse and longitudinal Reynold numbers (Re) is compared and analyzed under different gas flow rate with 90°-360° helix angle.The results are presented in Fig.10.In Fig.10(a),the Reynold number of solid particles first increases and then decreases when φ is 90°.With the flow continuing,theRenearing the inner wall becomes greater.Also,Rereaches a maximum value and horizontally decreases when the helix angle is 360°.This phenomenon results from centrifugal force and drag force in the gas.In detail,solid particles are distributed uniformly in the reactor at the initial stage.However,after a few minutes,the particles are affected by the centrifugal and drag forces which lead to a decrease in particle concentration.Therefore,the largerReis obtained owing to less resistance on the inside of the reactor.Additionally,as shown in Fig.10(b),theReof solid particles is lower at the bottom of the reactor when the helix angle is 90°.In contrast,the particle velocity is higher on the top of the reactor.This phenomenon becomes more obvious at the higher helix angle.Similar to Fig.10(a),Redoes not change a lot at the initial stage which means the flow rate is lower at the bottom and the top of the reactor and is stable in the middle.However,particles slowly accumulate at the bottom with the effect of gravity later,resulting in largerReowing to less particle concentration at the top of the reactor.Moreover,Fig.8(c)and(d)shows the variation trends of transverse and longitudinalRewhen the flow rate is 3 m·s-1.It can be found that the results in Fig.8(c) and (d) are similar to those in Fig.8(a)and (b).In Fig.10(c),theRecurves with 270°-360° helix angle show as ‘‘S” shape and the largestReis located at the left side of the reactor.The same phenomenon is also found in Fig.10(e)when the flow rate is 4 m·s-1.In addition,Fig.10(f)shows the largestReis located in the middle of the reactor.In summary,the variation trend of transverse and longitudinalReis consistent.For transverse distribution,the maximumReappears near the inner wall of the pipe and for longitudinal distribution,it appears in the upper middle of the pipe.

4.2.Analysis of particle flow characteristics in the whole spiral coil

To study the flow state of CaCO3particles in the spiral coil,the particle distribution in the whole spiral coil within 3 s will be discussed in this chapter.

4.2.1.Particle distribution along the flow section

Fig.11(a) is the contour of solid particle distribution with the helix angle varying from 0° to 1080° and the gas initial flow rate is 2 m·s-1.It shows that the distribution in the first ring is similar to Fig.6(a).With the flow continuing,solid particles accumulate at the bottom and the outer wall.Besides,some solid particles also gather on the top of the pipe and this phenomenon gets obvious as φ gets lager.The distribution almost keeps unchanged after the helix angle is 900°.Changing the gas flow rate to 3 m·s-1,results are shown in Fig.11(b).Likewise,distribution in the first ring is similar to Fig.6(a).Because of the increase in gas flow rate,solid particles are accelerated so that the centrifugal force increases.Relatively,the gravity is constant so the aggregation on the lateral wall is more serious than it on the bottom of the pipe.Stable distribution appears after φ=900°.Fig.11(c) is the particle distribution contour when the gas flow rate is 4 m·s-1.Also in the first ring it does not change much.With a further increase of gas velocity,the centrifugal force affected on solid particles is strongly enhanced and most of particles gather on the lateral wall.Compared with centrifugal force,influence of gravity is less evident.It can be seen that after the helix angel reaching 720°,the distribution is almost constant and the difference between distribution on the top and the bottom gets smaller.It is almost symmetry when φ is 1080°.

Fig.10.Reynold numbers of solid particles along the horizontal (left side) and vertical (right side) cross section at different initial gas velocity.

To study the particle distribution clearly and accurately in the whole spiral coil when the flow time is 3 s,solid particle volume fraction in the section is compared and analyzed under different gas flow rates both horizontally and vertically,with helix angle changing from 90° to 1080°.The results are present in Fig.12.When the gas flow rate is 2 m·s-1,for Fig.12(a),the volume fraction of solid particles gradually increases from the inner wall to the outer wall of the coil.As the flow proceeds,particle concentration on the inner wall(R=-1.0)becomes lower and lower because of centrifugal force,so the difference between the two sides get larger and get the maximum value when φ=1080°,where solid phase particle concentration on the inner wall is zero and on the outer wall it is about 0.26.In the vertical direction,as Fig.12(b)shows,at the beginning of flow solid particle volume fraction decreases quickly near the bottom of the pipe wall.And at the bottom of the pipe wall the concentration always keeps a high level.All the curves present a concave shape.This distribution is consistent with the contour in Fig.11(a).When the gas flow rate rises to 3 m·s-1,solid particle distribution still increases monotonously in Fig.12(c).Longitudinally the concave gets larger in Fig.12(d) with the increase of helix angle.Finally,Fig.12(e) and (f) shows particle concentration when the gas flow rate is 4 m·s-1.Overall changes are similar to the previous.For Fig.12(f),the minimum value of volume fraction is the lowest in these three conditions.

Fig.11.Solid particles distribution along the cross section at different gas initial velocity.

4.2.2.Regularity of flow along the section in the whole coil

The contour of particle flow in the whole three rings spiral coil at the third second is shown in Fig.13(a).It shows that when φ is 90-180°,secondary flow is formed in the pipe and is strengthened in the next flow.Besides,when φ=360° a new miniature secondary flow appears close to the inner wall.Then this small secondary flow is also strengthened and tends to be steady after φ=900°.Fig.13(b)is the contour when the gas flow rate is 3 m·s-1.It is similar to Fig.13(a) except the value of velocity and stronger secondary flow.When the gas flow rate is set to 4 m·s-1,it can be found in Fig.13(c) that the secondary flow is enhanced again because of the velocity increases.At the same time due to the larger drag force and centrifugal force,a zone with a velocity of zero appears on the inside of the tube wall.That means there are no solid particles in this area.

Similarly,to better understand flow characteristics,theReis calculated and analyzed in both lateral and vertical direction with a helix angle from 90° to 1080° when the flow time is 3 s.The gas initial flow rate is still respectively set to 2 m·s-1,3 m·s-1,and 4 m·s-1.The results are shown in Fig.14.In Fig.14(a),theReincreases first and then decreases at the beginning stage.However,withRincreases,few particles are distributed near the inner wall which is called the dilute phase,and thereby a decrease inRe.In Fig.14(b),when φ=90°,Reat the bottom is lower and is higher than that at the top of the reactor.While when φ=360°,particles gather on the bottom wall under the effect of gravity,causing the resistance increase.Instead on the top of the pipe,particle concentration and the flow resistance is lower so thatRehere is higher.Afterward,solid particles change from the dilute phase to the dense phase.Thus,theRecurves show a downward trend in the upper area.With the gas flow rate growing,it can be seen thatRenear the inner wall gets larger in Fig.14(c) and (e).SomeRecurves show ‘‘S” shape and the change range becomes smaller.Compared with Fig.14(b),(d) and (f) don’t change a lot.The maximum values of differentRecurves are concentrated in the middle of the pipe.

4.3.Effect of different solid particle content and wall temperature

4.3.1.Distribution regularity of flow along the section under different particle content

To comprehensively show the flow characteristic of gas-solid phase flow in the spiral coil,the effect of inlet particle volume fraction is also investigated.Fig.15 shows the particle distribution when the volume fraction of solid particles is 0.1 and 0.15 at the inlet of the spiral coil.The inlet gas velocity is 2 m·s-1.

Particle distribution when its volume fraction is 0.1 at the inlet is presented in Fig.15(a).When the helix angle is 45°,solid particles start to move to the outside and lower wall under the influence of gravity and centrifugal force.Because of the reduction of solid particles,on the inside of the coil there is almost no particle distribution.This phenomenon is not very obvious at this moment.When φ=90°,the accumulation of particles on the lower right side of the pipe increases and the particle vacuum zone is conspicuous,where the volume fraction of solid particles is close to zero.With the flow continuing,the particle vacuum zone near the inner wall of the coil gradually expands.The particle accumulation gradually develops as well when the helix angle ranging from 135° to 225°.After the helix angle is 270°,it can be seen that particle distribution turns stable.In the whole flow process in the first ring of the spiral coil,the tendency which particles move to the top is not obvious so the concave shape which has appeared in Fig.6(a)doesn’t exit.The accumulation phenomenon mainly exists at the lower right side of the spiral coil.Gravity and centrifugal force play a decisive role in particle distribution.

Fig.12.Solid particle distribution along the horizontal (left side) and vertical (right side) cross section at different initial gas velocity.

Fig.15(b) is the particle distribution contour with the particle volume fraction of 0.15.Solid particles distribute uniformly when φ=45°,and the particle vacuum zone appears when φ=90°,which is later than Fig.15(a).Meanwhile,increasing particles make them easier to gather,resulting in an increase of the effect of drag force.It adds the particle accumulation on the outer and top wall.

Fig.13.Stream of solid particles along the cross section at different gas initial velocity.

Similarly,when the range of helix angle is 135°-225°,the particle vacuum zone becomes larger and the accumulation of solid particles increases.When φ=270°,the concave shape appears.The tendency that particles at the bottom of the coil move laterally is hindered by the accumulation.Therefore,they are deposited on the bottom.

4.3.2.Regularity of flow along the section under different particle content

Fig.16 shows the velocity contour of solid particles along the flow section.When the particle volume fraction is 0.1,it can be seen in Fig.16(a) that the particle velocity is relatively uniform with the helix angle ranging from 0° to 90°.The secondary flow appears when φ=135°and is immediately destroyed by a new secondary flow close to the inner wall,which develops when φ is 135°-270°.Solid particles near the inner wall moves faster due to their less quantity.Then they are influenced by the centrifugal force and begin to move horizontally.With the particle volume fraction increasing near the outer wall,flow resistance gets larger and the particle velocity becomes lower.When the helix angle is 270°-360°,the flow turns steady and the granular flow doesn’t change basically.Fig.16(b)shows the contour of granular velocity when the particle volume fraction is 0.15.Compared with Fig.16(a),the secondary flow appears earlier when the helix angle is 90°.However,the difference of granular velocity between the left and right side is not obvious until the new secondary flow forms when φ=180°.With the flow proceeds,the high granular velocity zone gets lager when φ=225°-360°.It is smaller than it in Fig.16(a),which can be explained by the reduction of the dilute phase area.

Overall,less volume fraction of solid particles resulting in a more uneven velocity distribution,compared with Fig.9(a).The increase of particle concentration lead to an increase of flow resistance,but if the content of solid particles is too low,as Fig.16(a)shows,a larger particle vacuum zone weakens the maximum value of particle velocity they can reach.

4.3.3.Distribution regularity of flow along the section under different wall temperature

Apart from different gas velocity and particle volume fraction,due to the high temperature environments where thermochemical energy storage operates,the effect of the wall temperature on flow characteristic is also investigated.The simulation results show that the effect of wall temperature is not obvious under different wall temperature of 1100 K,1200 K and 1300 K.It has been discussed above that the centrifugal force and gravity are the most decisive factors for the behavior of solid particles in the spiral coil.The variation of wall temperature doesn’t change these two factors.Besides,the properties of solid particles are relatively stable and hardly affected by different wall temperature.

5.Conclusions

This study simulates particle flow in the spiral coil reactor.This reactor is designed to supply a new solution for thermochemical energy storage reactors.To investigate the characteristics of gassolid phase flow,CaCO3particles are used as simulation material.Particle distribution and the flow rate are presented under different gas inlet velocity.The position inside the reactor is expressed in the helix angle,which varies from 0°to 1080°.The main conclusions are shown as follows:

As the flow proceeds,solid particles gradually accumulate at the bottom and outer wall of the spiral coil.When the initial gas velocity is 2 m·s-1,solid particles mainly accumulate at the bottom under the initial gas velocity of 2 m·s-1.With theReincreases,the effect of centrifugal force gets greater.Solid particles accumulate at the bottom and outer wall of the coil evenly when the initial gas velocity is 3 m·s-1.When it turns to 4 m·s-1,the accumulation mainly happens on the outer wall.The accumulation phenomenon becomes obvious with the increase of the helix angle and is stabilized when φ ＞720°.

Fig.14.Reynold numbers of solid particles along the horizontal (left side) and vertical (right side) the cross section at different initial gas velocity.

When the initial gas velocity is 2 m·s-1and 3 m·s-1,agglomerated solid particles also exist on the top wall of the coil.The accumulation is not serious but can be strengthened with the flow as well.When the initial gas velocity is 4 m·s-1this phenomenon disappears.

Centrifugal force moves solid particles from inside to outside so at the beginning of flowing,a secondary flow forms near the outer wall of the coil.With the flow continuing,this secondary flow is destroyed due to the changes in particle concentration.The new secondary flow will appear near the inner wall and become stronger.

Fig.15.Solid particles distribution along the cross section at different particle volume fraction.

When the volume fraction of solid particles is reduced from 0.2 and 0.1,agglomerated solid particles at the bottom decreases and almost disappear on the top of the coil.The unevenness of granular velocity distribution also increases.Particles have larger velocity in the flow process when the volume fraction is 0.15.

Fig.16.Stream of solid particles along the cross section at different particle volume fraction.

Overall,the results of the simulation show that due to the particular shape of the spiral coil,solid particles are strongly affected by centrifugal force in addition to their gravity and the drag force from the gas phase.It causes an accumulation phenomenon.Solid particles unevenly distribute in the coil.At the same time,this uniformity promotes the formation of secondary flow,enhancing turbulence.For the reactor itself,advantages like simple structure,small volume,and so on make it promising and applicable in the thermochemical energy storage system.However,this paper focus on the flow characteristics under different gas flow velocity,further studies like heat transfer,reaction,or experiments of this reactor are expected.

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

The authors acknowledge the financial support provided by Natural Science Foundation of Jiangsu Province (BK20180936)and the Initial Funding of Scientific Research for the Introduction of Talents (YJ2021-41).

Nomenclature

Cddrag coefficient for a single particle

Dpitch,mm

ddiameter,mm

eparticle collision elastic recovery coefficient

Fdrag force,N

Gsparticles mass flow rate,kg·s-1

gacceleration of gravity,m·s-2

g0radial distribution function

ksdiffusion coefficient

kΘstemperature diffusion coefficient

nnumber of coil turns

Pspressure of solid phase,Pa

Rcurvature radius,mm

ReReynolds number

rcoil radius,mm

tcalculation step,s

Δttime step,s

Uggas velocity,m·s-1

usparticle average velocity,m·s-1

u′sfluctuating velocity,m·s-1

Vinstantaneous velocity,m·s-1

Wvelocity along section,m·s-1

βgsgas solid phase drag coefficient

γ wave energy dispersion

ε volume fraction,%

Θsparticle temperature,K

μgviscosity of gas phase,kg·m-1·s-1

μsshear viscosity of solid phase,kg·m-1·s-1

ρ density,kg·m-3

τ stress tensor

Φgskinetic energy transfer

φ helix angle,(°)