Numerical simulation of flow field and residence time of nanoparticles in a 1000-ton industrial multi-jet combustion reactor

Jie Ju,Xianjian Duan,Bismark Sarkodie,Yanjie Hu,*,Hao Jiang,Chunzhong Li,*

1 Key Laboratory for Ultrafine Materials of Ministry of Education,School of Materials Science and Engineering,East China University of Science and Technology,Shanghai 200237,China

2 Guangzhou Huifu Research Institute Co.Ltd.,Guangzhou 510665,China

Keywords:Combustion reactor Residence time distribution Particle flow trajectory Back-mixing Numerical simulation

ABSTRACT In this work,by establishing a three-dimensional physical model of a 1000-ton industrial multi-jet combustion reactor,a hexahedral structured grid was used to discretize the model.Combined with realizable k-ε model,eddy-dissipation-concept,discrete-ordinate radiation model,hydrogen 19-step detailed reaction mechanism,air age user-defined-function,velocity field,temperature field,concentration field and gas arrival time in the reactor were numerically simulated.The Euler-Lagrange method combined with the discrete-phase-model was used to reveal the flow characteristics of particles in the reactor,and based on this,the effects of the reactor aspect ratios,central jet gas velocity and particle size on the flow field characteristics and particle back-mixing degree in the reactor were investigated.The results show that with the decrease of aspect ratio in the combustion reactors,the velocity and temperature attenuation in the reactor are intensified,the vortex phenomenon is aggravated,and the residence time distribution of nanoparticles is more dispersed.With the increase in the central jet gas velocities in reactors,the vortex lengthens along the axis,the turbulence intensity increases,and the residence time of particles decreases.The back-mixing degree and residence time of particles in the reactor also decrease with the increase in particle size.The simulation results can provide reference for the structural regulation of nanoparticles and the structural design of combustion reactor in the process of gas combustion synthesis.

1.Introduction

The gas-phase combustion method [1-7] is widely used in the industrial preparation of SiO2,TiO2,SnO2,Fe2O3and other functional nanomaterials due to its advantages such as its continuous process,easy scale,high chemical purity,good dispersibility and uniform particle size of the product nanoparticles.Combustion reactor [8] is the core equipment in the preparation of nanomaterials by gas phase combustion [9-12].The distribution of velocity field,temperature field [13],concentration field and other kinetic factors in the combustion reactor directly affect the nucleation and growth process of nanoparticles,and thus determine the properties of the products.Due to the complexity of the equipment structure and the instantaneous variability of the combustion process of industrial combustion reactor,it is difficult to observe the characteristics of the internal flow field and back-mixing [14,15]of the reactor in the experiment,which plays a decisive role in the properties of the product.Recently,with the development of numerical simulation technology [16-19],we can not only get the velocity field,temperature field,concentration field and other basic parameters in the combustion reactor quickly and accurately through numerical simulation[20-23],but also the residence time and flow trajectory of nanoparticles in the combustion reactor can be explored,thus providing reference for the study of the nucleation and growth process of nanoparticles [24-26].

In recent years,Grohnet al.[27] explored the impact of factors such as volume concentration on aerosol particles and its structure change in turbulent flame reactor formation rate using eddy dissipation concept of chemical reaction model.They simulated the two-dimensional flow field in the combustion reactor with the generation rate of particles and compared with the experimental values.Their results show that the method is consistent with the experimental value.They further asserted that the optimization of reactor structure could reduce the degree of particle backmixing and broaden the particle size distribution.Konget al.[28]investigated the influence of particle size distribution on the internal flow field in a fluidized bed combustion reactor,and obtained the influence of particle size distribution width on particle residence time and chemical reaction rate by using Euler-Lagrange method and coupling method of computational fluid dynamics and discrete element method (CFD-DEM).The results show that with the increase in particle size distribution width,the residence time of particles in the reactor is reduced,and the CO2yield and fuel conversion are improved.Liet al.[29]explored the key mechanism of the interaction between turbulence and chemical reaction,adopted the finite rate model,comprehensively compared various methods of chemical and mixed time scale evaluation,and proved the applicability of the finite rate combustion model in the stirrer reactor under the medium and low oxygen content.Shakleinet al.[30] explored the numerical results of polyoxymethylene burning behavior in a reactor were studied by using OpenFOAM software,component transport model,combustion model,radiation model.The effect of reactor geometry on polymer combustion was investigated in a two-dimensional model.Some suggestions for structural design optimization of combustion reactor are given.Due to the diversity of industrial combustion reactor structure and the complexity of combustion process,the current numerical simulation of industrial combustion reactor is mainly focused on two-dimensional or small-scale model [31-34],but there are few studies on the geometric structure of industrial combustion reactor and the variation of combustion condition and residence time of particles during the amplification process.

The organization of this article is as follows.Firstly,a threedimensional physical model of the thousand-ton multi-jet combustion reactor is established and the model is discretized by using a hexahedron structured grid.Following this,finite rate/eddy dissipation model (FR/ED),the eddy-dissipation-concept (EDC),discrete-ordinate radiation model(DO),hydrogen 19-step detailed reaction mechanism and discrete-phase-model (DPM) were used to numerically simulate the flow field characteristics and particle movement trajectory in the reactor.Finally,the effects of changing the ratio of length to diameter,central jet velocity and particle size on the flow field and particle back-mixing degree in the reactor were investigated.The simulation results can provide a theoretical basis for industrial design of combustion reactor geometry,and provide a reference for the study of the nucleation and growth process of nanoparticles.

2.Construction of Basic Model

2.1.Geometric model and basic data

The geometric model of the multi-jet combustion reactor is composed of four parts:nozzle,combustion furnace,straight barrel section and bottom section.The basic data are shown in Fig.1.Based on the known industrial kiloton multi-jet combustion reactor,the diameter of the straight cylinder section is 600 mm,the aspect ratio is 4.17,and the gas velocity of the premix gas incident on the Mix surface (yellow) of the central jet is 50 m·s-1.Through the changes of the aspect ratio as shown in Table 1 (Reactor-P)P400 indicates that the diameter of the straight cylinder section is changed to 400 mm,and the aspect ratio is 6.25,and so on,the gas velocity of the central jet shown in Table 1 (Reactor-V),V40 indicates that the air velocity of central jet Mix surface is 40 m·s-1,and so on.When the diameter of the straight cylinder section is 800 mm,SiO2particles with 10,20,40 nm were incident respectively,and their effect on the variation in temperature field,velocity field,concentration field,particle residence time distribution and flow trajectory in the multi-jet combustion reactor were explored.Main simulation process and model schematic diagram and specific parameters are shown in Fig.1(a)and(b),the gas distribution incidents in the combustion reactor are shown in Fig.1(c).

Table 1The changing parameters of combustion reactor under different conditions

Table 2Model selection table

Fig.1.(a)Schematic diagram of the parameters and combustion process of the combustion reactor;(b)physical structure diagram of the combustion reactor;(c)nozzle gas distribution incidents.

This model is divided into hexahedron structured grids.With the aim of ensuring better implementation of boundary fitting,boundary layer grids are divided at the junction of combustion reactor wall and gas flow,and the grid is refined and densified in the local area with large speed,temperature,density and chemical changes.After grid independence verification,the total number of grids was determined to be 2.86-3.25 million.The grid independence verification process is shown in Fig.2.Based on Fig.2(III),the global grid is scaled 0.8,0.9 and 1.1 times at the global grid scaling factor respectively,thus obtaining the numerical simulation results as shown in Fig.2(a) and (b).The grid shown in (II),(III)and(IV)in Fig.2 was adopted,the temperature variation trend of the axis is consistent,and the average velocity of the central axis is 32.17,32.39,32.69 m·s-1respectively.The average temperature of the central axis is 1352.59,1377.37,1384.75 K respectively,and the error range is within 3%.The rationality and credibility of grid scale modification are proved,and the numerical simulation results are independent of grid scale,which proved the rationality and credibility of the grid scale.Thus,the grid shown in Fig.2(III)was selected: the boundary layer grid was divided with 1 mm as the basis and 1.2 as the ratio,and the maximum grid scale was 12 mm.Commercial software Fluent [35-38] was used to carry out the numerical simulation.Standard wall function was adopted to conduct convective heat transfer between the wall of the combustion reactor and the outside world,and the convective heat transfer coefficient was 237.2 W·m-1·K-1.Velocity inlet and pressure outlet boundary conditions were used.The central jet inlet,is a mixture of hydrogen and oxygen,with a molar ratio of H2:O2=0.25:0.1575.The central jet gas velocity of the basic model is 40 m · s-1.The H2at the inlet is the annular shielding gas with an incident velocity of 8 m·s-1.The other inlet gas which is air had a gas velocity of 20 m · s-1.When the velocity field and temperature field of the combustion reactor stabilize,SiO2particles of different sizes are injected from the Mix surface,and the velocity changes according to the gas velocity of the central jet.

2.2.Mathematical model

In this paper,the temperature,velocity and concentration fields in the reactor are numerically simulated by component transport model,realizablek-ε model,FR/ED,EDC,DO radiation model and 19-step detailed reaction mechanism of hydrogen (Table 2).

Mass conservation equation:

whereSmis the mass added to the continuous phase from the dispersed secondary phase,ρ is density,tis time and uiis the component of velocity in the ‘X’ direction.

Fig.2.(I),(II),(III) and (IV) Nozzle grids of different scales;(a) and (b) reactor axis velocity and temperature.

Momentum conservation equation:

where ujis the velocity component in the‘Y’direction,pis the static pressure,τijis the stress tensor,giis the gravitational volume force in the ‘X’ direction,and Fiis the external volume force and the source term.

Fig.3.(a)Axial velocity field,(b)axis velocity and(c)axial plane velocity streamline of the central axis with different aspect ratios in reactors;(d)axial velocity field,(e)axis velocity and (f) axial plane velocity streamline of the central axis with different central jet gas velocity in reactors.

Realizablek-ε model turbulent kinetic energyk:

Realizablek-ε model dissipation rate ε:

among them,theC2=1.44，C1ε=1.9，σk=1.0，σε=1.2 as constants;Gkis the turbulent kinetic energy caused by laminar flow velocity gradient.Gbis turbulent kinetic energy caused by buoyancy;YMis the wave generated by diffusion;SkandSε are the source terms.

The Chemkin-CFD solver is selected in Fluent,which uses the sparse matrix solving algorithm to integrate the detailed chemical reaction mechanism into the turbulent reaction.The source term in the conservation equation for the mean speciesi,is modeled as:

The field equation of the DO radiation model is:

whereIis the incident radiation intensity;Tis optical depth;ais radiation attenuation coefficient;Sis scattering coefficient;Ris refraction coefficient.

The concept of air age [39] represents the time required for air to reach a certain place in space,and the expression of air age transport equation tensor is:

where τ is the age of air at a point in space;ρ is air density;uis the velocity vector;ΓAis air age diffusivity,ΓA=μ/Sc+μt/Sct;μ is aerodynamic viscosity;μtis the turbulent viscosity of air;ScandSctare Schmidt number and turbulent Schmidt number respectively.

The DPM was used to reveal the particle flow trajectory and residence time in the reactor.Equilibrium forces on particles:

where the first and second terms on the right are the drag force and gravity force of particles per unit mass,respectively,Frepresents other forces (e.g.,thermal forces,virtual mass forces,etc.).

The functional relationship between particle size and mass fraction is described by Rosin-Rammler method [40] in the equation below:

wheredmis mean diameter;nis the spread parameter;dis diameter;Ydis spread parameter.In this study,the particle size distribution is defined by fitting particle size distribution data into Rosin-Rammler equation using python language.

Steady-state and transient modes are used in the simulation process.Firstly,the velocity field,temperature field,concentration field and other internal flow field data were solved by steady-state model.Then,after the flow field in the combustion reactor is stabilized,the residence time and flow characteristics of particles were investigated by transient analysis using the stabilized flow field as the initial value.

Fig.4.(a)Axial surface temperature field,(c)temperature field of diameters at different positions and(e)central axis temperature with different aspect ratios in reactors;(b)axial surface temperature field,(d) temperature field of diameters at different positions and (f) central axis temperature with different central jet gas velocity in reactors.

Fig.4 (continued)

3.Results and Discussion

3.1.Velocity field

The velocity field in the combustion reactor determines the residence time of nanoparticles in the reactor,and the velocity streamline affects the movement trajectory of nanoparticles and the degree of back-mixing.The uniform velocity attenuation of a certain acceleration in the axial flow of the reactor is beneficial to the uniformity of the velocity field and the formation of uniform particle size nanoparticles.Premixed hydrogen and oxygen gas is shot into the combustion reactor in a circular speed and ignited in the reactant to start combustion.At the initial stage of the reaction,hydrogen and oxygen react violently,and the speed rises rapidly from the wall of the reactor.The shock wave generated by the combustion explosion of hydrogen and oxygen causes the airflow speed to fluctuate greatly.After stable combustion,the gas velocity is stable.After the combustion reaction,the gas velocity decreases rapidly.When entering the end of the furnace,the volume per unit length decreases due to the continuous shrinkage of the cylinder neck,and the gas velocity continues to rise until the outlet gas escapes.

Fig.5.Axial plane(a)O2,(b)OH and(c)H2O mass fraction with different aspect ratios in reactors;central axis(d)O2,(e)OH and(f)H2O mass fraction with different aspect ratios in reactors.

Fig.6.Axial plane (a) O2,(b) OH and (c) H2O mass fraction with different central jet gas velocities in reactors;central axis (d) O2,(e) OH and (f) H2O mass fraction with different central jet gas velocities in reactors.

It can be seen from Fig.3(a) and (b) that the decrease in the aspect ratios of the reactor leads to the acceleration of the velocity attenuation rate in the straight cylinder section of the reactor and the increase in gas velocity in the tail section of the furnace after the necking.It can be seen from Fig.3(c) that with the decrease in aspect ratios of the reactor,the eddy current in the reactor gradually increases from zero.

It can be seen from Fig.3(d)and(e)that the central hydrogenoxygen premixed gas is injected into the combustion reactor with a small diameter at a high speed,and the annulus auxiliary gas is injected into the reactor at a low gas velocity synchronously,resulting in a high gas velocity in the center of the reactor and a low gas velocity around the reactor.Under the action of fluid viscous shear force,eddy current is formed in the reactor.The increase in gas velocity of the central jet leads to the lengthening of the core area of the jet flow in the reactor and the rise in the overall velocity in the reactor.Fig.3(f) shows that the vortex in the reactor extends along the axis of the reactor as the gas velocity of the central jet increases.The airflow vortex leads to the wandering,collision and coagulation of nanoparticles in the growth process,which is not conducive to maintaining the uniformity of nanoparticles.

3.2.Temperature field

Combined with realizablek-ε model,EDC model and 19-step hydrogen combustion reaction mechanism,the temperature field in the combustion reactor was simulated and the reactor axis temperature was extracted as shown in Fig.4.In order to observe the morphological characteristics of flame in the reactor and the detailed temperature distribution in the reactor,as shown in Fig.4(c)and(d),the temperature fields on the axial surface of each reactor and the end face of the combustion reactor (500 mm),the end face of the straight cylinder (3000 mm) and the outlet of the reactor (6000 mm) were intercepted.

From the common characteristics of all reactors,the central hydrogen-oxygen premixed gas is injected into the combustion reactor in a circular speed,and the gas velocity at the center of the circular speed is lower than the combustion speed,resulting in a w-shaped flame at the reactor.After intense combustion of hydrogen and oxygen,the premixed gas burns stably and the temperature is stable.When the combustion reaction is over,the temperature of the central jet gas decreases rapidly until it reaches the average temperature at the end of the reactor.

Fig.7.(a) Axial turbulence intensity and (b) turbulence intensity of central axis with different aspect ratios in reactors;(c) axial turbulence intensity and (d) turbulence intensity of central axis with different central jet gas velocities in reactors.

The temperature field in the combustion reactor determines the temperature history of nanoparticles,and influences the nucleation,growth and sintering of nanoparticles.The length and width of the flame determine the scope of potential flow core area in the reactor,and thus affect the nucleation and growth time of nanoparticles.It can be seen from Fig.4(a),(b) and (c) that with the decrease in the aspect ratios of the reactor,the decreasing trend of temperature in the reactor becomes slow,the average temperature decreases,and the range of potential flow core area shrinks.Fig.4(d),(e),and (f) shows the influence of different central jet gas velocities on the temperature field in the reactor.With the increase in gas velocity of the central jet,the outlet temperature increases,and the overall temperature increases.The increasing gas velocity of central jet does not significantly change the length and width of the core region of the potential flow.However,the escape rate of nanoparticles increases and the residence time of nanoparticles in the potential flow core becomes shorter.The residence time of nanoparticles in the core region of the potential flow is shorter,resulting in the reduction of nucleation time and particle size.

3.3.Concentration field

The concentration field of each component in the combustion reactor affects the rate of chemical reaction,whiles the rate of reaction directly affects the rate of nucleation and growth of nanoparticles.An increase in the concentration of the product results in a probable increase in nucleation of nanoparticles collision of nanoparticles,and an increase in particle size.In Fig.5,the mass fraction of O2represents the composition of the reactants,the mass fraction of OH represents the composition of the intermediates,and the mass fraction of H2O represents the composition of the products.

In the combustion reactor,when the reactants are injected into the combustion reactor at high speed and react violently in the reactor,the mass fraction of the reactants drops rapidly to a lower concentration and is stable to ensure the reaction to proceed.At the same time,the mass fraction of the reaction intermediates and products increased rapidly and the reaction was stable.After the combustion reaction ends,the mass fraction of intermediate products rapidly becomes zero.The gas diffuses and the mass fraction of product H2O on the central axis decreases and maintains the average content at the end of the furnace.Under the action of gas diffusion,the unreacted O2content in the ring gap protective gas rises to the average value and remains stable at the central axis.

It can be seen in Fig.5 that as the aspect ratios of the combustion reactor decreases,the rising distance of the reactant mass fraction on the central axis of the reactor advances and the final mass fraction content decreases.The decrease rate of the mass fraction of the products and intermediates was accelerated,and the final mass fraction remained the same.All components change dramatically at 2 m and 2.3 m,indicating that the combustion process of hydrogen and oxygen flame ends at this position.

As can be seen from Fig.6,the mass fraction of reactants on the central axis of reactants decreases and the mass fraction of products increases as the gas velocity of central jet increases.The increase in mass fraction of the product leads to an increase in the concentration of the product in the region which increases the tendency of nanoparticles nucleation and increment in particle size of nanoparticles.

Fig.8.(a) Axial air ages and (b) the air age of the central axis with different aspect ratios in reactors;(c) axial air ages and (d) the air age of the central axis with different central jet gas velocities in reactors.

3.4.Turbulence intensity

In combustion reactor,the value of turbulence intensity can be used to characterize the degree of turbulence.The larger the airflow fluctuation,the more unstable the nucleation and growth process of local nanoparticles,and the agglomeration phenomenon of nanoparticles is significantly enhanced,which is not conducive to the formation of good morphology and uniform particle size nanoparticles.

In the combustion reactor,premixed gas is injected into the combustion reactor at a high speed and reacts violently at the reactor,resulting in violent fluctuations in the air flow at the reactor wall,significant increases in turbulence intensity,and decreases in turbulence pulsation after combustion stability.When the combustion reaction ends,the flow pulsation increases and the turbulence intensity increases rapidly.After the combustion reaction,the airflow becomes stable gradually,and the turbulence intensity decreases and tends to be stable.

It can be seen from Fig.7(a) and (b) that with the decrease in the aspect ratios of the combustion reactor,the overall turbulence intensity in the reactor decreases and airflow fluctuation decreases.It can be seen from Fig.7(c) and (d) that the increase of gas velocity of central jet leads to the improvement in turbulence intensity and turbulence amplitude in the reactor.The combustion at the flame core of a single combustion reactor becomes stable,the flow fluctuation amplitude at the flame outer flame increases,and the turbulence intensity increases.With the end of the combustion process,the turbulence intensity decreases gradually.

3.5.Air age

Air age is defined as the time it takes for air to reach a certain position in space from the entrance,which can reflect the freshness of air in a certain space.In the combustion reactor,the smaller the physical quantity,the shorter the time for the gas to reach there.The air age cloud chart can intuitively show the mixing of gases with different residence time.The air age value of the ideal horizontal plug flow reactor should increase with the increase in the distance from the inlet surface of the reactor,otherwise it indicates that there is partial gas backflow (gas reflux) in the structure design of the reactor.The back-mixing of nanoparticles can be directly caused by gas reflux,which is not conducive to the formation of good shape and uniform particle size nanoparticles.

The user-defined-function (UDF) is programmed in C language and Fluent is coupled to obtain the air age distribution in the combustion reactor.After the premixed gas enters the reactor,due to the difference of gas velocity between the central high-speed jet gas and the surrounding annulus protection gas,the flow vortex is formed under the action of fluid shear force,and the gas backflow generated by the vortex leads to the increase of gas arrival time in the reactor.It can be seen from Fig.8(a) and (b) that the value of air age in the reactor increases with the decrease in the aspect ratios of the reactor,while Fig.8(c)and(d)shows that with the increase in the central jet gas air velocity,the value of air age in the reactor decreases continuously.There is a certain dead zone in the combustion reactor where the air age is too large,resulting in the mixing of a many numbers of gases with different residence time.The structural design is not conducive to the horizontal push forward of the air flow in the reactor.It can be improved by reducing the diameter of the straight cylinder section of the combustion reactor or increasing the gas velocity of multiple jets.

3.6.Nanoparticles

The residence time and temperature history of nanoparticles in the combustion reactor greatly affect the morphology and size of nanoparticles.When the residence time is too long,the nucleation and growth of nanoparticles accelerate,and the particle size of nanoparticles will become larger.The temperature history will then affect the lattice type and aggregation degree of nanoparticles.The back-mixing of nanoparticles caused by the uneven distribution of gas velocity and circulation in the combustion reactor will greatly increase the residence time of some nanoparticles,which is not conducive to the formation of uniform particle size nanoparticles.

In this simulation,the particle size parameters of nanoparticles were fitted by Rosin-Rammler equationviaDPM.Within 0-0.02 s,94080 particles with uniform particle size of 10-40 nm were injected into the reactor through the Mix inlet to obtain the flow trajectory and residence time distribution of nanoparticles with different particle sizes in the reactor.It can be seen from Fig.9(a)and (b) that the residence time of nanoparticles in the reactor is prolonged and the back-mixing degree of nanoparticles increases with the decrease in the aspect ratios of the combustion reactor.It can be seen from Fig.9(c) and (d) that the residence time of nanoparticles in the reactor decreases with the increase in gas velocity in the center of the reactor.

It can be seen from Fig.10 that the residence time of 41%-46%nanoparticles in the reactor is between 0.2-0.3 s,and the increase of particle size leads to the increase in the quantity of nanoparticles escaping within 0.3 s from 42.03% to 65.61%.

The initial time ist0and the fraction of nanoparticles between timetandt+dtisE（t）dt,the average residence time of nanoparticles is，The variance,where variancecan quantitatively represent the ‘‘width” of the distribution curve and the degree of escape of nanoparticles at the same time.The larger the value of,the more concentrated the escape time of nanoparticles.

Fig.10.Residence time distribution table of (a) 10 nm,(b) 20 nm and (c) 40 nm particle size;(d) residence time distribution table of different particle sizes.

Fig.11.Variance chart of particle residence time.

It can be seen from Fig.11 that the reduction of the aspect ratios of the combustion reactor leads to the dispersion of the concentrated escape time of nanoparticles,while the increase of the gas velocity of the central jet has no obvious effect on the concentration of the escape time of nanoparticles.The escape time of nanoparticles become more concentrated with the increase of particle size.In this multi-jet combustion reactor,if the same batch of precursor materials want to obtain nanoparticles with relatively uniform particle size,a relatively large slenderness ratio structure should be adopted in the straight cylinder section of the reactor based on considering the flame width,and the slenderness ratio should be kept between 4-6.The gas velocity of the central jet affects the morphology and length of the flame.A lower gas velocity (≤40 m·s-1) will lead to poor uniformity among the particle sizes of nanoparticles.Therefore,a higher gas velocity(≥50 m·s-1)should be used in parameter design.

4.Conclusions

The physical model of the 1000-ton industrial multi-jet combustion reactor is established,using the realizablek-ε model,EDC,hydrogen 19-step detailed reaction mechanism,DPM,etc.The velocity field,temperature field,concentration field,flow path and residence time of nanoparticles in combustion reactor were simulated numerically.With the decrease in the aspect ratios of the combustion reactor,the central jet gas velocity attenuation is enhanced,the gas vortex phenomenon is intensified,the overall temperature in the reactor decreases,the turbulence intensity decreases,the air age increases,the residence time distribution of nanoparticles is more dispersed,and the back-mixing degree increases.With the increase in jet gas velocity at the center of the combustion reactor,the flow vortex lengthens along the axis,the overall reactor temperature rises,the turbulence intensity increases,the air age decreases,and the residence time of nanoparticles decreases.Furthermore,an increase in the particle size of incident nanoparticles in the combustion reactor results in more concentrated in the residence time distribution and a decrease in the degree of back-mixing.

CRediT Authorship Contribution Statement

Jie Ju:Conceptualization,Formal analysis,Software,Writing -original draft.Xianjian Duan:Resources,Validation.Bismark Sarkodie:Methodology,Writing -original draft.Yanjie Hu:Funding acquisition,Writing -review &editing.Hao Jiang:Supervision.Chunzhong Li:Funding acquisition,Writing -review &editing.

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(21978088,91534202,51673063),Shanghai Technology Research Leader(20XD1433600),the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutes of High Learning,the Basic Research Program of Shanghai(17JC1402300),the Shanghai City Board of education research and innovation project,and the Fundamental Research Funds for the Central Universities (222201718002).Additional support was provided by Feringa Nobel Prize Scientist Joint Research Center.

Nomenclature

aradiation attenuation coefficient

dmmean diameter,mm

Fforce,N

Fithe external volume force and the source term,N

Gbthe turbulent kinetic energy caused by buoyancy,J

Gkthe turbulent kinetic energy caused by laminar flow velocity gradient,J

githe gravitational volume force in the I direction,N

Ithe incident radiation intensity,J·cm-2

kturbulent kinetic energy,J

nthe spread parameter

ppressure,Pa

Rrefraction coefficient

Sscattering coefficient

Skthe source terms

Smquality of the incremental,kg

Sε the source terms

Scthe Schmidt number

Sctthe turbulent Schmidt number respectively

Toptical depth

ttime,s

uivelocity in the ‘X’ direction,m·s-1

ujvelocity in the ‘Y’ direction,m·s-1

YMthe wave generated by diffusion

ΓAair age diffusivity

ε dissipation rate,%

μ aerodynamic viscosity,Pa·s

μtthe turbulent viscosity of air,Pa·s

ρ density,kg·m-3

τ the age of air at a point in space,s

τijstress tensor,Pa