Thermophoresis effects on gas-particle phases flow behaviors in entrained flow c

Chao Dai,Fan Gu*

School of Energy and Environment,Southeast University,Nanjing 210096,China

1.Introduction

The Study on the pulverized coal gasification has attracted interests of researchers.Improvements of experimental studies have laid a firm foundation for coal gasification study.Ahnet al.[1]studied the effects of gasification temperature pressure on gasification kinetics of coalchar with CO2atelevated pressure with a pressurized drop tube furnace reactor.Kajitaniet al.[2,3]concluded the gasification rate of four different coal chars gasified with CO2using a PDT or TGA athigh temperature and pressure.

In addition,establishing a coal gasification simulation model is also important for the investigation of coal gasification.Irfanet al.[4]reviewed the kinetics and the reaction rate equations for char-CO2gasification both in the reaction kinetic control region(low temperature)and the diffusion control region(high temperature)and at both low and high pressures.Their work facilitates the further improvement of the coal gasification model.As is known,coal gasification system is one of gas-particle phases flow reaction systems.Both Lagrangian and Eulerian models have been applied to simulating gas-particle phase flow system.Compared to the Lagrangian model,the Eulerian model treats all different phases mathematically as continuous and fully inter penetrating and reducing number of governing equations.Vicenteet al.[5]developed a coal gasification simulation model in entrained flow coal gasifier using Eulerian methods,considering gravity and drag in the model.Their results show good agreement for both the main and minor species,and temperature with experimental data.In this paper,a new Eulerian model based their work was established,considering particle thermophoretic force besides gravity and drag.

The particles suspended in a gas with a temperature gradient are subject to a force called thermophoretic force,directed in the opposite direction to the temperature gradient.Todaet al.[6]examined the relation between the diameter of particles and thermophoretic effect accurately by getting rid of the particle movement induced by the effects of natural convection and gravity.They found that smaller particles receive more remarkably the thermophoretic effect than larger ones and the effects are sensitive with the diameter especially for particles of small diameter and/or low thermal conductivity.Epstein[7]proposed a theoretical model for calculating thermophoretic force for small Knudsen numbers but their results show poor agreement between the experimental results obtained by Schadt and Cadled[8].Brock[9]extended Epstein's analysis and obtained better agreement.Talbotet al.[10]studied velocity pro files of seed particles driven by thermophoretic force in the laminar boundary layer adjacent to a heated flat plate.They found that the theory of Brock,with an improved value for the thermal slip coefficient,gave the best agreement with experiment for low Knudsen numbers.

Char gasification could cause certain gas temperature gradients along both axial and radial two directions in the gasifier.So thermophoretic force may have some effects on migration of coal-char particles,especially sufficiently small ones.However,considering the effects of particle thermophoresis in coal gasification has not appeared in previous studies and this study is essential for coal gasification simulation.

This paper studied the temperature gradient and thermophoretic forces along both gasifier axial and radial two directions at wall temperatures of 1100 °C,1200 °C,1300 °C and 1400 °C.It also presented compared calculated results of particle volume fraction,velocity,and gasification reaction rate whether particle thermophoresis is considered in the gasification model.Talbot's theoretical model for particle thermophoresis is adopted in this paper,owing to its similar conditions with ours.

2.Char-CO2 Entrained Flow gasifier

The geometric model in this study is based on the experimental furnace adopted in Ref.[1]and its diameter is 52 mm.The geometry of the reactor is cylindrical.For a coal gasified in a gasifier,it is in a reducing environment and the temperature is not as high as that of fuel combustion.For these reasons,the following assumptions are adopted to simplify the physical problem.(1)The flow field is steady,axisymmetric,incompressible.(2)The wall temperature of the gasifier is uniform which has been adopted in other studies[11-13].(3)The inlet temperature is heated to the size of corresponding wall temperature.Because of the assumption of axisymmetric flow,the three dimensional gasifier can be reduced to a two-dimensional reactor in the simulation[14].The geometric model is shown as Fig.1 and the length is set as 500 mm

The mapped mesh method is adopted in this model which is helpful to reduce the calculating error.To validate the grid dependence,four grid sizes are adopted in this geometry to simulate a simply coupling problem of flow and heat transfer.The wall temperature is 1100°C and the inlet temperature 25 °C.The inlet velocity is 0.1 m·s-1and CO2as the flow medium.As Fig.2 shows,the grid size of 600×20 can meet the requirements of grid independence.

The conditions of char gasification are determined as Table 1.A mixture of reactant gas including CO2and N2gases is admitted into the gasifier at a flow rate of 0.5 m·s-1.So the flow in the gasifier is streamline and the problems of turbulent flow are not considered through the course of this study.The ultimate analysis of coal and coal char used in the simulation is summarized in Tables 2 and 3.This paper needs to assume that only char density changes in the gasification reaction and the volume will keep constant.The way of the change of char density is given:

Fig.1.The physical model of entrained flow coal gasifier.

Fig.2.The temperature distribution along the gasifier central axis with difference grid sizes.

whereRis the value of the reaction rate expressed by carbon mass concentration,kg·m-3·s-1.Moreover,the carbon conversion(X)in the gasification reaction is defined as Eq.(1):

whereAis the mass fraction of ash andCis the mass fraction of carbon in the coal char at any time.The subscripts of “o”and “x”are the un-reacted coal char and the reacted coal char,respectively.

Table 1Conditions of char-gasification[1]

Table 2Properties of Indonesian Rotor coal[1]

Table 3Ultimate analysis of Rotor coal char and chemical analysis of ash[1]

In addition,the gasifieris heated up by the fixed wall temperature.it is assumed that the initial and inlet gas temperatures remain consistent with wall temperature.At the entrance of the gasifier,the difference between gas and particle temperature has been ignored,too.

3.Numerical Method

A Eulerian model was establishing in this paper based on the experimental equipment adopted in Ref.[1].The particle thermophoresis model would be added to this model and the effects of particle thermophoresis on coal-char gasification was considered in the simulation in this study.The main governing equations include continuity equations,momentum equations along the gasifier axial and radial directions,and energy equations of gas and particle phases.gasification chemical kinetic of coal char and the Eq.(1)also need to be coupled to this model.The numerical model is solved using COMSOL Multiphysics 5.0.

3.1.Continuity equations

In Eulerian model,both the particle and gas phases are solved using an Eulerian approach and an additional equation is solved the volume fraction of the particle phase locally.The two Continuity equations can be simplified for the incompressible flow,as follows[15]:

3.2.Momentum equations

The momentum equations for the continuous and dispersed phases,using the non-conservative forms of Ishii are as follows:

For fluid-solid mixtures,Eq.(7)is modified in the manner of Enwald[16]:

For the low particulate concentration in this model,the solid pressure could be ignored in this model[16].So the Eq.(8)can be modified:

Fmis the drag term of drag force between two phases,where Fm,g=-Fm,p= βuslip,β is the drag force coefficient,where uslip=up-ug.Fi(i=g,p)is the momentum transfer term which only includes particle thermophoretic force in this paper.

The drag force coefficient β in this study can be modeled for dilute flows as follows:

In this model,the drag coefficientCdcan be computed from the Schiller-Neumann model,which is one of the most employed drag correlations in the last decades[17,18].

The viscous stress tensors are also needed to be defined in this paper.The dynamic viscosity of the respective phase can be expressed as a simple mixture viscosity,which is defined by Krieger[16]and given in Eq.(13).The Krieger type model can cover the entire range of particle concentrations and Φp,maxis 0.62 in Eq.(11).

In the end,Talbot's model[10]for particle thermophoresis is adopted for its similar conditions with that in this simulation.

whereKnis Knudsen number,Cs,CmandCtare all numerical factors of order unity which must be obtained from kinetic theory,Cs=1.147,Cm=1.146,Ct=2.20,cis the mean niolecular speed,Λ is the gasparticle thermal conductivity ratio,Λ = λg/λp[10,19,20].

3.3.Energy equations

There are convective,conductive and radiative heat transfers between the gases,particles and reactor walls in the gasifier.Two basic energy equations,for gas and particle phases are as follows.

In this model,the gas phase is assumed to be transparent and radiative heat transfer to particles assumed to be isotropic.P1 model is used to solve the radiative heat transfers to particles.The basic parameters of radiative heat transfers to particles are summarized in Table 4[11].

Table 4Parameters of radiative heat transfer[11]

3.4.Chemical reaction

In this paper,only one Reaction(16)is coupled to the Eulerian model.

Q,heat of the reaction,is defined by enthalpy of reactants and resultants.

whereRmolis the reaction rate,mol·m-3·s-1,His the reaction enthalpy,J·mol-1,andhco,hco2are formation enthalpies,J·mol-1.

The gasification reaction rate is obtained by fitting the experimental data[1].

whereA=174.1 s-1,E=71.5 kJ·mol-1[1],PCO2is the size of the partial pressure of CO2andPis the size of the total pressure in the gasifier,based on the unit for MPa.The sign “k”,reaction rate constant,is defined by Arrhenius formula.

4.Results and Discussions

4.1.Validation of gasification reaction rate

To validate the developed chemical reaction rate equation,the predicted results of Eq.(19)are compared with the experimental data of Ahn[1].As Fig.3 shows,the gasification reaction rate equation is able to predict coal char gasification process accurately at wall temperatures of 1100 °C,1200 °C,1300 °C and 1400 °C.

Fig.3.Comparisons of carbon conversion vs reaction time between numerical predictions and experimental measurements[1].

4.2.The particle thermophoresis

In this section,the gas temperature gradient and thermophoretic force are investigated.Firstly,the predicted isothermal contours in the entrained flow coal gasifier are shown in Fig.4(a)and the maximum and minimum temperatures are also marked in the isothermal contours.The temperature difference increases with wall temperature increasing,which is caused by the increase of reaction rate.Fig.4(b)demonstrates the conclusion by presenting the volume fraction contours of CO generated in the gasifier.The mass fraction of CO increases with wall temperature increasing and the maximum value is only 0.0284130,which has little effects on gas-particle phases flow behaviors.

Then,the characteristics in five cross sections are investigated to show the entire gasifier performance clearly.The five cross sections are built in the gasifier,0.1 m,0.2 m,0.3 m,0.4 m,and 0.5 m from the inlet.Figs.5 and 6 present the gas temperature gradients and particle thermophoretic forces along both radial and axial directions of the gasifier in the five cross sections.The particle thermophoretic force has significant correlation with the gas temperature gradient and has the same trend and the opposite direction with the gas temperature gradient has.They all increase with wall temperature increasing.As Fig.5 shows,the radial gas temperature gradient and particle thermophoretic force reach the maximum values near the wall surface of gasifier.Compared to the gas temperature gradient and particle thermophoretic force along the radial direction,those along axial direction are too small to be ignored.

Fig.4.Isothermal contours and CO mass fraction contours in the drop tube furnace.

Fig.5.Gradient of gas temperature and thermophoretic force along the radial direction.

Fig.6.Gradient of gas temperature and thermophoretic force along the axial direction.

4.3.Effects on particle distributions

This paper contrasts computational results of the particle volume fraction in five cross sections whether the particle thermophoresis is considered in this simulation model.The effects on the particle distributions can be reflected.These effects are obvious near the wall surface of gasifier at all wall temperatures,where gas temperature gradient has the maximum value.The computational result of particle volume fraction with thermophoresis effects is lower than that without the effects,shown in Fig.7.At 1400°C wall temperature,the changes of particle volume fraction are becoming remarkable,which may be caused by higher gasification reaction rate or other factors.

Fig.7.Comparisons of coal char volume fraction with thermophoresis or not.Talbot,None.

Fig.8.The trends of the difference and variance ratio of particle volume fraction on wall surface with increase of the wall temperature.

For estimating thermophoresis effects on the computational results of particle volume fraction,Fig.8 presents the trends of the difference and variance ratio of particle volume fraction on wall surface with the wall temperature increases whether the particle thermophoresis is considered in this simulation model.The value of the particle volume fraction increases the wall temperature increases in all five cross sections.These trends are consistent with those of the radial gas temperature gradients and the particle thermophoretic forces.The maximum variance ratio of particle volume fraction on wall surface reaches up to 1.38%whether the particle thermophoresis effects are considered in the simulation.

4.4.Effects on particle velocity

The changes of particle velocity are also need to be studied[6,10]because the thermophoresis will directly influence the particle velocity and the particle velocity change will affect the particle distance.The changes of axial velocity can be negligible in Fig.9,which are associated with the small axial gas temperature gradients and thermophoretic forces presented in Fig.5.However,the changes of radial velocity are observable,especially at wall temperature of 1400°C as Fig.10 shows,owing to the higher gas temperature gradients and thermophoretic forces along this direction presented in Fig.3.So effects of particle thermophoresis are reflected in the changes along radial direction in this paper.

4.5.Effects on gasification reaction rate

The reaction rate is one of main characteristics of coal char gasification,which will affect the temperature field in the gasifier.So in this section,it is investigated that the effects are on the calculation result of gasification reaction rate whether the particle thermophoresis is considered in the simulation model.

Fig.11 presents the compared results of gasification reaction rate in the five cross sections whether the particle thermophoresis is considered in the model.At wall temperatures of 1200°C and 1300 °C,the compared results are only observable near the wall surface of gasifier in five cross sections in Fig.11(2),(3),which has the same trend with that particle volume fraction has.As Fig.11(4)shows,the differences of the compared results become remarkable at 1400°C wall temperature,which is also consistent with the changes the particle distribution has.

5.Conclusions

In this study,a numerical model was developed to investigate particle thermophoresis effect on gas-particle phases flow behaviors in entrained flow coal gasifier based on Eulerian method.Four wall temperatures was considered,including 1100 °C,1200 °C,1300°C and 1400°C.The main findings of the present study can be summarized as follows:

(1)The gas temperature gradient and particle thermophoretic force along axial direction can be negligible in comparison to thosealong radial direction in the gasifier.Besides,the radial gas temperature gradient and particle thermophoretic force increase with the increase of wall temperature.

(2)Considering particle thermophoresis had some effects on the distribution of particle volume concentration in simulation model,especially at wall temperature of 1400°C.The effects were obvious near the wall surface of gasifier at all wall temperatures where the computational result of particle volume fraction with effects of particle thermophoresis is lower than that without the effects.Then the maximum particle volume fraction variance ratio reaches up to 1.38%on wall surface of the gasifier.

(3)For the calculation of particle velocity in the gasifier,the change of axial velocity is too small to be ignored and that of radial velocity is observable,especially at wall temperature of 1400°C.

(4)There are few effects on calculation result of gasification reaction rate caused by particle thermophoresis,only the effects are significantly at wall temperature of 1400°C.

With further decrease of particle size and further increase of reaction temperature the particle thermophoresis may have more effects on the investigation of gas-particle phases flow behaviors in entrained flow coal gasifier.So it is meaningful that more attention is paid to develop the gasification model in which particle thermophoresis is considered.

Nomenclature

Cmmomentum exchange coefficient

Cp,ggas specific heat capacity at constant pressure,J·kg-1·K-1

Cp,pparticle specific heat capacity at constant pressure,J·kg-1·K-1

Csthermal slip coefficient

Cttemperature jump coefficient

dpparticle diameter,m

FT,rthermophoretic force,rcomponent,N·m-3

FT,zthermophoretic force,zcomponent,N·m-3

KnKnudsen number,2 L·d-1

lmean free path of gas molecules,m

PrPrandtl number

RepReynolds number

Tgas temperature,K

Tpparticle temperature,K

up,zfalling velocity of coal char particle

Vpvolume of a coal char particle

Λ gas-particle thermal conductivity ratio,Λ = λg/λp

λggas thermal conductivity,W·m-1·K-1

λpparticle thermal conductivity,W·m-1·K-1

φpvolume fraction of particle

φgvolume fraction of gas

ρggas density,kg·m-3

ρpparticle density,kg·m-3

Subscripts

g gas

p particle

r radial direction

z axial direction

Fig.11.Comparisons of the gasification reaction rate with thermophoresis or not.Talbot

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