Qiang Zheng,Jingxuan Yang,*,Wenhao Lian,Baoping Zhang,Xueer Pan,Zhonglin Zhang,Xiaogang Hao,*,Guoqing Guan*

1 School of Chemistry and Chemical Engineering,Taiyuan University of Technology,Taiyuan 030024,China

2 School of Chemical Engineering and Technology,North University of China,Taiyuan 030051,China

3 Laboratory of Energy Conversion Engineering,Institute of Regional Innovation (IRI),Hirosaki University,2-1-3 Matsubara,Aomori 030-0813,Japan

Keywords:CFD Multiphase flow Downer reactor Numerical simulation Heat transfer

ABSTRACT The performance of binary particles mixing and gas–solids contacting,which is considered qualitatively to have a significant influence on the heat transfer in internal heated circulating fluidized beds,is carefully investigated by means of a numerical approach in the newly developed high solids-flux downer lignite pyrolyzer(φ0.1 m×6.5 m).Since binary particles are used in this system,a reasonably validated 3D,transient,multi-fluid model,in which three heat transfer modes relating to the convection,conduction and radiation are considered,is adopted to simulate the flow behavior,temperature profiles as well as volatile contents.The simulation results showed that the solids stream impinges the left wall surface initially and turns towards the right wall in the further downward direction and then shrinks during this process resulting in that the solids concentrate a little more at the central region.In the further downward section of the downer,the particle flow disperses near the right wall and develops uniformly.Meanwhile,the coal phase is slowly heated in the downer and it is found that most of the heat absorbed by the coal is from the convection heat transfer mode.To explore the heat transfer mechanism more quantitatively,two indexes (mixing index and contacting index) are proposed,and it is found that the mixing index initially increased fast and later remained at a relatively flat state.For the contact index,it shows a trend with a first rising and then falling,finally rising continuously.Also,it is found that the convection heat transfer is closely correlated to the contacting status of gas–coal which indicates that the improving of the gas–coal contacting efficiency should be an effective way to strengthen the coal particle heating process.

1.Introduction

As a process to effectively utilize the low-rank coals for the concurrent production of power,fuels,and chemicals,integrated coal gasification combined cycle (IGCC) has been the focus of great attention in recent research activities worldwide[1–4].To improve the overall gasification efficiency more in the IGCC system,a highdensity triple-bed combined circulating fluidized bed(TBCFB)lowtemperature gasifier is proposed [5–9],in which a downer-type coal pyrolyzer,a bubbling-fluidized-bed-type char gasifier,and a riser-type combustor for the combustion of unreacted char are included,and the heat generated from the combustion of char is transferred for the pyrolysis/gasification by using solid heat carriers with a high solids flux circulated between the three reactors[10,11].One of main features of the TBCFB gasifier is the installation of the downer-type coal pyrolyzer,where the coal is pyrolyzed and further the produced char and volatile products such as tar and low-molecular weight gases can be effectively and rapidly separated in the latter cyclone separator.

In the downer-type coal pyrolyzer,the solid heat carriers,often particles such as sand,catalytic particles and ash,are mixed with the feeding coal particles and provide heat for coal pyrolysis reaction [12,13].Many researchers have conducted extensive researches and found that the catalytic particles,such as dolomite,olivine and char showed catalytic activity for tar upgrading in the pyrolysis process.In these particles,the char is more attractive owing to its low cost,natural production inside the gasifier (produced by pyrolysis reaction)and the good catalytic activity.Previous results have shown that the porous textural structure of char and large specific surface areas can provide abundant active surfaces for tar cracking and prolong the residence time of tar for promoting the interaction of tar with char[14–16].Also,recently,it is proposed that the char can serve as not only catalysts but also heat carrier in the pyrolysis process [14,17–19].Wanget al.[20] simulated TBCFB system with the char as the heat carrier by Aspen Plus,and found that the mass ratio of char to coal is 5.5,whereas the mass ratio of quartz sand and ash to coal are 11 and 12,respectively,to meet the requirements of heat transportation.It is noticed that the internal solids circulation could be decreased due to its lower density than quartz sand and ash.Thus,the TBCFB gasifier with the char as the heat carrier and catalysts for tar upgrading could have lower operation cost.However,only a few literatures on the numerical simulation of coal pyrolysis process in the downer with the char as the heat carrier can be found.

Additionally,there is a binary particles system involved coal and char particles in the downer reactor.In previous studies,the heat transfer characteristic was claimed to be controlled by the binary particles mixing state in such a binary particles system in other fluidized beds where the mixing and separation phenomenon is obvious[21,22].Based on this understanding,Fushimiet al.[23,24]carefully investigated the mixing index in the downer referred other fluidized beds.They evaluated the initial feeding structure on the performance,and found that the tangential arrangement of feeding nozzle gave better mixing than the normal arrangement.However,in their work,the mixing index employing as an evaluation method in the downer still remains debatable.In the downer with a feeding nozzle,the inhomogeneous gas–solid flow affects not only the mixing of binary particles but also the contacting of gas–solid.In particular,the gas–solid contact could greatly affect the hydrodynamics,heat transfer and pyrolysis reaction [25].Thus,it is necessary that the inhomogeneous gas–solid flow should be quantified by considering the mixing of binary particles and the contacting of gas–solids.Meanwhile,the regulation mechanism of gas–solid flow on the heat transfer characteristics is limited.It is important to explore the relationship between the hydrodynamics and heat transfer characteristics to improve the reactor performance.

In this work,the specially designed downer reactor equipped with an additional lateral nozzle for coal feeding (LN-Downer) is simulated.The multi-fluid Eulerian model is adopted here with reference to Shuet al.[26].Also,a devolatilization model for the char catalytic system is introduced to simulate the high-flux coal pyrolysis with the circulating char as the heat carrier and catalyst in the LN-Downer.The hydrodynamics and heat and mass transfer characteristics are predicted.In addition,to quantify the inhomogeneous gas–solid flow,the mixing index and contact index are proposed and the regulation mechanisms of gas–solid flow on heat transfer characteristics are explored.

2.Model Descriptions

2.1.Assumptions

In order to facilitate the model construction and ensure the good convergence and acceptable computational time,some basic simplification and assumptions are made as follows:

(1) The solid particle is assumed as a spherical particle and the size remains unchanged during the pyrolysis process [27].

(2) The pyrolysis products are divided into char and volatile,and volatile is made of CO,CO2,CH4,C2H6,H2,H2O and gaseous tar.

(3) The carrier gas and volatile are treated as one mixed phase.

(4) The external moisture in the coal particles is removed in the preheating stage.

(5) The mass and heat transfer resistances inside the particle are ignored,that is,the particles are at uniform temperature throughout and there is no internal diffusion [28,29].

(6) The walls are assumed to be at the adiabatic state.

2.2.Governing equations

The system is described by using a single gas phase and two granular phases representing coal and char respectively.Based on the concept of gas–solids two-phase flow,a multi-fluid Eulerian model (MFM) for multiple granular phases with different particle densities,sizes and even temperature has been extended,which treats both gas phase and solid phases as an interpenetrating continuum and each phase has its own governing equations and therefore it is suitable for the modeling of dense gas–solid reactors.In previous literature,the MFM approach with modified constitutive models has been efficiently applied to the two granular phases system (including silica sand–nylonshot [30],hot sand–cold sand [31] and coal mixture–ash [26]) with the downer pyrolyzer and a prediction results agreed well with the experimental data [30,31].Herein,since the used char showed a slightly change by the measurement of thermogravimetric [32],the char is assumed not involved into the mass transfer (just like sand or ash) and based on this assumption,the simulation of coal–char granular system is implemented using the MFM approach.The standard governing equations of Eulerian framework,including mass,momentum,energy and species transport equation are not reproduced here and can be found in Refs.[33,34].

2.3.Constitutive relations for hydrodynamics

The constitutive relations for the unclosed terms in the governing relations are given as follows.Herein,several modified models(i.e.interphase drag force,interphase heat transfer,etc.) are adopted,and the effects of these modified models have been evaluated in details by Shuet al.[31].

The kinetic theory of granular flow(KTGF)is used for modeling the constitutive laws of solids phase.The original KTGF model has been used extensively for the monodisperse system.To describe the polydisperse flow dynamics for the binary particle systems,a binary KTGF model derived by Chaoet al.[35]considering the fluid dynamic particle velocity differences and particle–particle fraction is applied,which are summarized in Table 1.The solid phases pressurepi,shear viscosity μi,granular conductivity κi,bulk viscosity λiand dissipation of kinetic energy due to the particle–particle collisions γiare derived from the KTGF model.

Table 1The kinetic theory of granular flow for two granular phases system [35]

The binary particle drag considering binary particle momentum coupling derived on the basis of such binary KTGF[36]is used and the momentum exchange coefficient βijis shown as follow.

A multi-scale gas–particle drag model of Penget al.[37] is adopted to consider the effect of the mesoscale cluster structure by using the effective cluster diameterdcl，ito replace particle diameterdpand the gas–particle interphase momentum exchange coefficient βgiis

2.4.Constitutive relations for heat transfer

The heat transfer in the fluidized beds has been an important part of many researches in the past.In the process of coal pyrolysis,the particles transmit heat fluxes are implementedviafour modes as follows:

(1) Heat convection between gas and both coal and char phases

As a circulating heat carrier,the char particles carry heat into the downer reactor,and the convective heat transfer occurs between gas phase and either char or coal phases owing to the temperature difference.The volumetric rate of convection heat transfer is

where the heat transfer coefficienthgiis expressed as

Notably,the heat transfer coefficienthgiis correlated withNusc.To characterize the effect of mesoscale structure on the heat convection,a correlation of theNuscproposed by Shuet al.[31]is evaluated using the modified Gunn model[31],which can be expressed as follows.

(2) Direct heat conduction during a collision between coal and char particles

Direct thermal conduction occurs through the contact area of the particles due to the elastic deformation when binary particles collide with each other.Herein,the existence of lateral nozzle will lead to a higher solid holdup as well as a higher collision frequency and enhance the direct heat conduction.The expression of the rate of collisional heat transfer was derived by Changet al.[38],which is based on the MFM model.By using the stochastic collision frequency and the heat conduction due to the elastic deformation during a single collision[39],the rate of direct thermal conductionQijcan be calculated by:

Correspondingly,the particle-to-particle heat exchange coefficienthijcan be obtained:

(3) Thermal radiation between coal and char particles

The particle thermal radiation in the high solid flux downer by the absorption or emission at the particle surface is extended by Shuet al.[26]from the individual particle radiation model by combining particle number density and individual particle radiation.Based the assumption that an individual coal particle is surrounded by many char particles,the temperature of char phase replaces the environment temperature in the expression.The rate of thermal radiation between coal phase and surrounding char phase is:

(4) Endothermic effect of pyrolysis process

The coal pyrolysis reaction is an endothermic process.To simplify the calculation in this model,the rate of heat transfer from pyrolysis reaction is expressed as follow,which is assumed to be proportional to the reaction conversion,regardless of the reaction conditions and coal species.

whereRcoalis the rate of mass loss of coal due to the pyrolysis reaction and ΔHreactis the pyrolysis reaction heat,and the value is–0.425 MJ·kg-1taken from Shuet al.[26] base on experimental measurements.

2.5.Devolatilization model

Pyrolysis of coal is a complicated decomposition process,which involves various products,including gaseous tar,volatile,char and ash.The details of devolatilization scheme have been reported in many literatures in the past and do not reproduced here.In coal–char binary particles system with the circulating char as the heat carrier and catalyst,a distinctive feature is that the released heavy tar from coal will contact with the porous structure of hot char and cracking into light tar,as shown in Fig.1,which has been proved by other researchers [15,16,40].

The aforementioned features make the devolatilization model complicated.To simplify the simulation,the global devolatilization model involving the effect of cracking reaction over the char particles is adopted and the reaction mechanism can be expressed in the following form:

Due to the complex composition of coal particles,there is no standard stoichiometric equation for description of the pyrolysis product generations.To date,the most common way is to determine the molecular coefficients of the products by the empirical formula or based on the proximate and ultimate analyses of the coal tested.Herein,the equivalent stoichiometric coefficientsa–hderived from the experiment results by Panet al.[32]are displayed in Table 2 and the rate of devolatilization will be allocated to each component in proportion to its stoichiometric coefficient.

Table 2Stoichiometric coefficients for devolatilization and tar cracking

Table 3Material properties and parameters of char and coal particles [26,42]

Table 4Proximate and ultimate analyses of the coal sample

Table 5The operating conditions and simulation parameter settings

Fig.1.Schematic diagram of coal devolatilization with char catalytic effect.

In the global devolatilization model,it is assumed that the rate of devolatilization is first-order governed by the amount of volatile remaining in the particle,which is formulated as

wheremvolis the sum of volatile content in a control volume,is the potential ultimate yield of the volatile.The kinetics parameters obtained from Mahalatkaret al.[41]are specified asA=1×105s-1andEvol=9.9774×104J·kmol-1which are independent of coal type and operating parameters but related to the particle temperature.Meanwhile,the rate of devolatilization can be allocated to each component in proportion to its stoichiometric coefficient.

Fig.2.Three-dimensional structure of (a) simulation geometry and (b) final numerical grid.

Based on the assumption (1) (see Section 2.1),the particle size remains constant,but the particle density changes with the devolatilization as

2.6.Numerical setting for the multi-fluid model

The MFM is performed using the commercial software FLUENT,and the governing equations are discretized by the finite control volume technique with the SIMPLE algorithm in the pressurebased solver used for pressure–velocity coupling.To obtain higher accuracy of the results,the second-order upwind scheme is added for discretizing momentum,granular temperature and energy equation.The QUICK integration scheme is adopted to solve the volume fraction equation.The user defined functions (UDFs) are used for implementing the modified the constitutive relations.

The experiment results of Fushimiet al.[23]are selected to validate the numerical models of hydrodynamics and heat transfer,and the schematic diagram of apparatus is mainly consisted of a co-current downer (100 mm i.d.and 6 m in height) with a coal feeding system and a solids distributor positioned at the top.The solids distributor is positioned 13 vertically brass tube to ensure a uniform char particles distribution.The details of multiphase flow behavior in the reactor can be describes as follows:the circulating char particles at high temperature from the riser as the heat carrier are re-distributed through the brass tube and then enter the downer,the carrier gas is introduced with a specified flow rate to carry the coal particles,and the coal phase preheated to a specific temperature is injected by the lateral nozzle into the downer reactor,and then mixed and heated by the char particles concurrently flowing downward.

For the simplification,the simulation of downer reactor is carried out without the char particles distributor,that is,the feeding of char particles is assumed as a uniform char flow at the top inlet to replace the solids distributor.Similarly,the feeding of coal particles is simplified as a lateral nozzle.Fig.2(a) and (b) shows the simulation geometry setting according to the experiment and mesh model of simulation domain,respectively.The simulation geometry is simplified as a downer with a lateral nozzle (25 mm i.d.) mounted at 0.1 m below the distributor outlet.This reactor is modeled with the structured mesh by the meshing tool ICEM.The grid independency is carried out with three grids numbers(39,697,66,801,152,809) as shown in Fig.3 and the mesh with about 66,000 elements is applied which has been proven to be independent.

Herein,the mixture of carrier gas and volatile is set as the primary phase.The first solid phase is the coal particles,which actually is a mixture composed of dry coal,produced char and ash.The second solid phase is the circulating char particles.

Fig.3.Grid sensitivity analysis.

The inlet boundary is set as a velocity inlet condition specified for both the top inlet and the lateral nozzle,and an atmospheric pressure outlet condition is applied at the outlet.Initially,the char phase velocity is set to 4.9 m·s-1calculated fromwith a feeding temperature of 1288 K.The inlet velocity for the carrier gas and coal phase is calculated from vg=ma/Ainρgwith a same temperature of 273 K.At the wall,a no-slip boundary condition is used for the gas phase,whereas the Johnson and Jackson slip wall boundary condition is used for the two solids phases.The particle–wall restitution coefficient is set at 0.2,and the specularity coefficient is 0.01 according to the study by Shuet al.[30,31].A time step of 10–4is chosen since it is suitable to reach the converge criteria.

According to the study of Shuet al.[26],the density,specific heat,thermal conductivity and viscosity of each gas species are calculated as a piecewise-polynomial or a piecewise-linear function of temperature.The material properties and parameters of char and coal particles are summarized in Table 3.Herein,the physical parameters of the gas and solids mixture obey the volume/massweighted-mixing law.

The proximate analysis and elemental analysis of the coal from the experiment of Panet al.[32] are shown in Table 4.

The detailed operating conditions and parameter settings in the simulations are listed in Table 5.

3.Validation

Fig.4.Comparison of non-dimensional temperature distribution between experimental data and simulation results.

Fig.5.Comparison of mixing index in experiment and simulation.

Fig.6.Instantaneous changes of the proportions of the components in the gas product with time at the outlet in 0–50 s.

In order to validate the model accuracy in the predicting of the flow and heat transfers in the downer,the experimental data from Fushimiet al.[23]are used.The boundary conditions implemented in the numerical simulation are the same as those in the experiment,in which the injected sand is mixed with the circulating sand with a different temperature,and the lower temperature is 298 K while the higher temperature is 323 K.Especially,the cold particles is guided by the solid distributor at the top,and the hot particles pass through the lateral nozzle.In order to compare the simulation results with the experimental data,the non-dimensional temperature as in the study of Fushimiet al.[23] is defined as

whereT′is the temperature of local mixture solids at the measured point defined by Shuet al.[31]

Fig.4 compares the experimental results and the calculated curves of non-dimensional temperature at the plane ofZ=0.1,1.8,3.8 m when the flow state becomes stabilized.It can be seen that the characteristics of the non-dimensional temperatures are well captured by the simulation.

In addition,Fig.5 shows the comparison of the mixing index between experiment and simulation.The calculation result of the model of this work are in positive agreement with the experimental data when compared with Fushimi’s work.The tendency of this work agrees with experiment data but the index atZ>1.8 m is underestimated.The simulation results of mixing index atZ=1.8 m in Fushimi’s work are closer to the experimental date but the tendency atZ>1.8 m is not well.

Thus,the aforementioned verification demonstrates that the present model should be reliable for the simulation of flow and heat transfers in the downer.

4.Results and Discussion

Fig.6 shows the instantaneous changes of the proportions of the components in the gas product with time at the outlet in 0–50 s.It can be seen that the proportions of product components reach a stable state when the simulation time is 8 s.Therefore,the results of flow time of 8 s are selected for analysis.

4.1.The transfer and reaction behaviors in downer with the lateral nozzle

4.1.1.Flow behavior analysis

Fig.7.(a) Axial profiles of the cross-sectional average solids holdup of char and coal phase.(b) Cross-sectional solids holdup contour at different vertical position.

The axial profiles of the cross-sectional average solids holdup of char and coal phase are shown in Fig.7(a).Herein,it should be noted that the mass-weighted average as follow is applied to compute the cross-sectional average holdup,since the most common form of area-weight average is hard to reflect flow development,especially in the non-uniformity flow structure.

As shown in Fig.7(a),the axial profile of char holdup is nonuniform in the upper part of vertical section and the double peaks exist atZ=0.6 and 2.2 m.With the flow developing along the downer,the char holdup decreases gradually,eventually approaching a constant of 0.06 until the exit of the downer.Additionally,the coal holdup decreases very rapidly to 0.02 within a short distance from the lateral nozzle and falls slowly to 0.007 at the down side of the column.

Fig.8.Temperature distribution of each phase along the downer pyrolyzer.

The radial location contours of solids holdup obtained from the simulation are shown in Fig.7(b)which provide more detailed particles distribution information.Six locations (Z=0.2,0.6,1.2,2.2,3.4,5.8 m)along the downer are selected since they are the feature points of the curve of average solids holdups.According the holdup contours atZ=0.2 m,it could infer how the feeding coal from the lateral nozzle and penetrates the char downstream to impinge the left wall surface caused by the intense interaction with high-speed carrier gas.A horseshoe-shaped structure of char holdup is formed due to the interaction of char downstream.This flow behavior is similar to those observed in the previous literature using the same single lateral nozzle under the same carrier gas velocity but with a lower solids flux[23].The char holdup reaches its one of peak values atZ=0.6 m since the char particles further move to the left wall,causing a higher char concentration.AtZ=1.2 m,the solids holdup contour seems to indicate that the solids flow,including both char and coal flows,turns towards the right wall and then shrinks in this process.The radial profile of solids holdup atZ=2.2 m indicates that the particles concentrates at the central region so that the other char holdup peak exists here.This is an important characteristic of solids flow development in the LNDowner,which will influence the contact behavior of gas–solids as indicated in the later section.AtZ=3.4 m,a clear dispersion of solids flow appears near the right wall where the particle flow impinges and deflects.As the particles further fall down,a solids concentration ring is formed in the central region atZ=5.8 m,leading a more homogeneous radial solids distribution with a lower local solids holdup.As described above,the axial solids holdup in the LN-Downer with a solid flux up to 400 kg·m-2·s-1varies significantly and the radial solids holdup distribution is less uniform mainly due to the intense disturbance of radial feeding jet to char downstream.

4.1.2.Distribution of temperature and volatile content

Fig.9.The proportion value of heat gained by the coal particles and the amount of heat transfer.

Fig.10.Content distribution of each volatile component in gas phase along the downer pyrolyzer.

Fig.8 shows the temperature evolution for each phase along the height of the downer.As mentioned above,the downer can be operated at a relatively high mixture ratio of char to coal,therefore a significant amount of char heat carriers supports the massive heat,that is far more than the requirement for the coal heating and thus the temperature of char decreases slightly from 1283 to 1198 K.Meanwhile,due to the lower specific heat capacity of gas,the gas phase temperature increases immediately from 473 K(as mentioned in the operating conditions)to the high temperature level approaching the char phase below the lateral nozzle,and later decreases continuously due to the heat exchange and the increasing of the specific heat capacity caused by the increasingly higher concentration of volatile products.Meanwhile,the temperature of coal particles increases rapidly from the initial 473 K at the upper section(Z<2 m)and after this section,the temperature further rises almost linearly to the final 1078.37 K.

As mentioned above,the coal particles in the downer absorb heatviafour modes.There are several inter-phase heat transfer mechanisms,including gas–coal convection heat transfer,char–coal conduction heat transfer and char particles thermal radiation,except the heat loss due to pyrolysis reaction.To study the heat transfer characteristics,the rate and proportion of conduction,convection,radiation heat transfer are quantified during coal heating process as shown in Fig.9.

In Fig.9,it can be seen that the rate of gas–coal convection heat transfer is far greater (remained above 60%) than those based on other mechanisms,implying that the gas–coal heat transfer is major heat transfer mechanism in the heating process of coal.Herein,the particle thermal radiation contributes a large proportion of heat transfer in the upper part of reactor and further in the down part owing to the decrease of ΔTbetween char and coal phase.The coal–char direct heat transfer mechanism has a negligible contribution although the larger solids flux leads to a higher particles number density and higher collision frequency.

The axial profiles of volatile content in gas phase at different heights are shown in Fig.10.Herein,the volatile composition is in the form of mass fraction of gas phase.The volatile products could be observed at the bed height of 2 m where the temperature of coal is higher than 800 K.Meanwhile,with the temperature of coal phase increasing along axial directions,the volatile products are gradually accumulated since higher coal temperature leads to higher reaction rate for the pyrolysis.Furthermore,a larger species content difference can be found in the volatile with the volatile content obtained in the order of H2O>Tar>CH4>CO2>H2>CO>C2H6.

4.2.Effect of binary particles mixing and gas–solids contacting on heat transfer characteristics

4.2.1.Mixing index and contact index distribution profiles

The mixing index,which has been widely studied,was applied to quantify the degree of mixing of binary particles.It can be calculated by different empirical correlations [43–47].Here,based on the variance indices,the mixing index is calculated by

whereXkpresents the mass ratio of binary particles.The expression of mass ratio developed from a DEM method[24]for suiting multifluid model can be obtained as

The mixing index can be used to calculate the dimensionless mixing index as

where σ0indicates the mixing index of the complete segregation and can be calculated by σ0=.The dimensionless mixing index can be also used to define two extreme mixing states,IM=0 as complete segregation andIM=1 as the binary particles completely mixed.

The state of gas–solids contact on the flow field is characterized using a contact index,IC,in which a value of 1 indicates the highest uniform solids holdup.Different definitions on the contact index have been presented in the literatures [25,48,49].Herein,the contact indexICis defined as

whereAis the facet area of the local grid,and,denoting the average solids holdup over the surface,is formulated as

The evolution of mixing index of binary particles and contact index of gas–coal are shown in Fig.11.Herein,considering the contact index along the reactor height,the flow development along the axial direction can be classified into three regions,i.e.,injection mixing region (Region Ⅰ),intermediate transition region (RegionⅡ),and developing region (Region III).

Fig.11.Vertical profiles of each solid phase mixing and contact index in the downer.

In the Region Ⅰ,the contact index increases due to the enlargement of the flow region but varies within a narrow range whereas the mixing index increases very rapidly to 0.7 due to the intense mixing of char and coal flow by the severe turbulence.In the regionⅡ,there is a obvious fluctuation of the contact index.The contact index profile elevates somewhat within 0.7 m

The non-uniform initial distribution of binary particles due to the coal feeding nozzle design always need much longer distance to achieve a fully contact state,but it is significant that the mixing of char–coal proceeds much fast within a short distance.Similar variation of mixing index has been observed by Fushimiet al.[23],in which they calculated it based on the non-dimensional temperature distributions.The study has examined the effects of coal feeding nozzle arrangement on the mixing index but did not examine the contact index.However,the variation of contact index would significantly affect the heat transfer behaviors,which would be further verified by the following analysis.

4.2.2.The effect of contact index on the convective heat transfer

To further understand the relationship between two indexes and heat transfer characteristics,convective heat transfer as the main heat transfer mechanism is carefully studied by combining with the mixing of binary particles and the contacting of gas–solids.The convection heat transfer coefficient is adopted to clearly show the relativity.Fig.12 shows the comparison of cross-section averaged convection heat transfer coefficient between gas and coal phases and contact index.The mixing index does not show a relevance,thus it is not reproduced here.As shown in the figure,an increase ofICleads same changes in the convection heat transfer coefficient and the coefficient is proportional to the contacting of gas–solids.

Fig.12.Vertical profile of cross-section averaged convection heat transfer coefficient and contact index.

In details,the heat transfer coefficient initially decreases with the increase of the contacting of gas–solids in the region Ⅰ.This may be explained by the two factors,i.e.,the gas turbulence and the contacting of gas–solids,which affects the heat transfer coefficient.In the region Ⅰ,under the intense interaction of high-speed feed jet with the char downstream,the gas turbulence seems to be the domination factor.Due to the decrease in the gas turbulence along the axial direction with the increase in the heat transfer coefficient,the contacting of gas–solids seems to be prevailed as the main factor in turn.

These results clearly reveal that the improving of the contacting of gas–solids is the most efficient way to strengthen the coal particle heating process in the downer by enhancing the convective heat transfer.It is also suggested that the coal feeding nozzle arrangement design is needed to be carefully considered to improve the contacting of gas–solids.

5.Conclusions

The multi-fluid model is applied for the simulation of high solids flux coal pyrolysis process with char as the heat carrier in the LN-Downer.The CFD models of hydrodynamics and heat transfer have been validated by using the experiment data.The flow behaviors of coal and char phases,and heat transfer and reaction characteristics in the LN-Downer are captured and the mixing of binary particles and the contacting of gas–coal are investigated.The following conclusions are obtained.

(1) For the LN-Downer,the solids stream behavior is observed.The solids stream impinges the left wall surface initially and turns towards the right wall in the further downward direction and then shrinks during this process leads to the solids concentrated a little more at the central region.In the further down section of the downer,the particle flow disperses near the right wall and develops uniformly.

(2) The coal phase is slowly heated in the downer and the temperature of both gas and char in the downer remains at a high-level,and the heat obtained by the coal is mainly contributed by the convection heat transfer mechanism.In addition,the volatile content profile is increased with the increase in the coal temperature which shows the volatile content obtained by the prediction in the order of H2O>Tar>CH4>CO2>H2>CO>C2H6.

(3) The mixing of binary particles and the contacting of gas–coal are characterized by the mixing index and the contact index,respectively.The mixing index profile is initially raised fast and later remains at a relatively flat state.The contact index firstly rises and then falls,finally increases continuously.

(4) The convection heat transfer is proved to closely correlate to the contacting of gas–coal and this finding suggests that the improving of the contacting of gas–solids should be more useful for the coal particle heating process.

As discussed,we have studied the heat transfer behavior and two indexes evolution in the downer with a lateral arrangement.Future studies need to focus on the tangential arrangement using the proposed two indexes since the distribution of its contact index is still clouded.More details of flow behavior are also needed for the application of coal feeding structure.

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 was supported by the National Natural Science Foundation of China (U1710101).The authors also thank Mr.Junwu Wang for his help in establishment of the multi-fluid Eulerian model.

Nomenclature

Afacet area of the local grid,m2

Cddrag coefficient

ddiameter of particle,m

Eaverage elastic modulus,GPa

Evolactivation energy for devolatilization,kJ·mol-1

erestitution coefficient

ecoalemissivity of coal

fvolume fraction of dense phase

Gssolid mass flux,kg·m-2·s-1

ggravity acceleration,m·s-2

g0radial distribution function

Henthalpy,J·kg-1·mol-1

hheat transfer coefficient,W·m-3·K-1

mmass of a particle,kg

NuNusselt number

nnumber concentration of particles,m-2

Ppressure,kPa

Qheat transfer between phases,W

Runiversal gas constant

Rcoalreaction rate for coal pyrolysis reaction,kg·m-3·s-1

ReReynolds number

rradius of particle,m

Xmass ratio of binary particles

Ttemperature,K

T′local mixture solids temperature,K

ttime,s

tithe non-dimensional temperature

Vcollision velocity,m·s-1

v velocity,m·s-1

vtterminal velocity,m·s-1

vslipslip velocity,m·s-1

Ymass fraction

Zaxial distance from downer inlet,m

β interphase momentum exchange coefficient,kg·m-3·s-1

γ collisional dissipation of energy,kg·m-1·s-3

ε volume fraction

Θ granular temperature,m2·s-2

κ thermal conductivity,W·m-1·K-1

λ the ratio of solids holdup to porosity

μ dynamic viscosity,Pa·s

ρ density,kg·m-3

σpmixing index

σ0mixing index of the complete segregation

σkBoltzmann constant,J·K-1

Superscripts

col collisional

fri frictional

kin kinetic

Subscripts

g gas phase

cl cluster

icoal phase

jchar phase

max maximum