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Development of a Dense discrete phase model for 3D numerical simulation of coal combustion in an industrial

scale circulating fluidized bed boiler

Massoud Massoudi Farid, Hyo Jae Jeong, Jungho Hwang

2015.11.5

Department of Mechanical EngineeringYonsei University

Circulating Fluidized Beds in Korea

2

§ Korea South-East Power Co.- Co-firing (coal + biomass or waste), 10% - CFB boiler at Yeosu Power Plant

§ Korea Southern Power Co.- Co-firing (coal + biomass), 5%- Super Critical CFB boiler at Samcheok

Power Plant (under construction until 2015)

§ Korea East-West Power Co.- 100% Biomass, 30MW- CFB boiler at Donghae Power plant

Numerical methods for particle laden flows

Eulerian-Lagrangian

In Lagrangian frame

In Eulerian frame

It is suitable for Low volume fraction of solids since:

1) Solid Volume fraction was neglected.

2) particles interaction was neglected.

Eulerian-Eulerian

Discrete Phase Method(DPM)Multiphase Eulerian-Granular

Method(MEGM)

Disadvantages:1) It just shows general flow

behavior.2) It is not possible to model

particle surface reactions.3) We have to define lots of

phases to handle particle size distributions.

Eulerian-Lagrangian

In Eulerian frame

In Lagrangian frame

Dense Discrete Phase Method(DDPM)

Assumptions

1) Trajectory of a discrete phase particle is predicted by integrating the force balance equation of the particle on lagrangian reference of frame.

2) N.S equations are solved for fluid phases on Eulerian reference of frame. 3) For calculation of the particles interactions, first the position of the particles are mapped on the

Eulerian grid and the interactions are calculated on the Eulerian grid, then calculated interaction terms are mapped back on the particles positions.

Advantages:

1) It predicts more exact details of flow2) Size distribution is modeled in a

natural way in the Lagrangianformulation

4

v Zhang et al. analyzed cold flow at a 150MWe circulating fluidized bed (CFB) employing a3D unsteady Eulerian granular multiphase model. They presented the whole loop pressureprofile, solids volume fraction profiles and solids vertical velocity.

v Ref. : Zhang, et. al, “3D CFD simulation of hydrodynamics of a 150MWe circulating fluidized bed boiler”, ChemicalEngineering Journal, 2010, 162, 821–828.

5

Literature Review: Numerical simulation of CFB – 1

v Adamczyk et al. analyzed combustion at an industrial circulating fluidized bed (CFB) employing a 3D unsteady DDPM. They presented pressure drop, solids volume fraction profiles and temperature profile. However, no information about combustion products werepresented.

v Ref. : Adamczyk, et. al, “Modeling of particle transport and combustion phenomena in a large-scale circulatingfluidized bed boiler using a hybrid Euler–Lagrange approach”, Particuology, 2014.

6

Literature Review: Numerical simulation of CFB – 2

Boiler Geometry

Due to computational

barriersReal CFB

340 MWe CFB boiler located in Yeosu, Korea.

17 m

8m

1.16

m

1.05 m

Symmetry B.C

7

Simulated zone and mesh

Cal

cula

tion d

om

ain

UDF

Boundary condition and PSDBoundary and operating Conditions Size distribution (Rosin Rammler)

Coal

Min Diameter 1 mm

Max Diameter 16 mm

Mean Diameter 6.5 mm

Spread parameter 1.120114

Sand

Min Diameter 50 µm

Max Diameter 2000 µm

Mean Diameter 1000 µm

Spread parameter 1.98931

8

Hydrodynamic Boundary conditions

Primary air inlet 101 (kg/s)

Return leg inlet 0.361 (kg/s)

Secondary air inlet 54.2 (kg/s)

Outlet pressure -91.5 Pa

Wall B.CGas No Slip

Solid Reflect

Heat transfer Boundary Conditions

Primary air Temperature 482.15 K

Secondary air Temperature 498.15 K

Return Leg air Temperature 1073.15 K

Wall Temperature 632.15 K

Division wall Temperature 632.15 K

Wing wall tubesTemperature

1st Super heater 686.65 K

2nd Super heater 766.65 K

Gs(kg/s)Cyclone A Cyclone B

384 305

9

ResultsPressure drop and circulation rate:

10

ResultsSolid VOF:

H=1

H=3

H=6

H=10

H=15

H=20

H=35Walls X=0

11

ResultsGas Velocity:

H=1

H=3

H=6

H=10

H=15

H=20

H=35

X=0

H Averaged velocity0.4 6.18

3 5.4

6 5.21

10 5.11

20 5.1

35 4.71

12

Results

H=1

H=3

H=6

H=10

H=15

H=20

H=35

X=0

Temperature:

H Averaged Temperature0.4 1212.4453 1178.1976 1156.20510 1149.34320 1135.41135 1042.409

13

Results

H=1

H=3

H=6

H=10

H=15

H=20

H=35

X=0

O2 mole fraction:

HAveraged O2 mole fractio

n0.4 0.1168893 0.0791076 0.07750910 0.07147920 0.04450235 0.041857

14

Results

H=1

H=3

H=6

H=10

H=15

H=20

H=35

X=0

CO2 mole fraction:

HAveraged CO2 mole fr

actionz1=0.4 0.088602z2=3 0.110953z3=6 0.104716z4=10 0.110959z5=20 0.128557z6=35 0.130368

ResultsHeat Fluxes:

15

SH1

SH2

SH3

SH4

SH5

SH6

E1

SH7

SH8

SH9

SH10

SH11

E2

SH12

SH13

DW

2 Mega Watts

12.5 Mega Watts

6.3 Mega Watts

3.6 Mega Watts

5.7 Mega Watts

11 Mega Watts

35 Mega Watts

5.3 Mega Watts

17.8 Mega Watts

8.2 Mega Watts

9.9 Mega Watts

9.7 Mega Watts K

9.3 Mega Watts

12 Mega Watts

8.2 Mega Watts

10.7 Mega Watts

Furnace Walls 81 Mega Watts

Roof 9 Mega Watts

Total heat Fluxes:246 Mega WattsWhich is close to the measured value.

16

Conclusion

Numerical simulation of an industrial scale fluidized bed furnace was done using DDPM.

Pressure drop, Solid volume fraction contour, Temperature and species profiles and contours were displayed.

Details of heat fluxes were presented.

Pressure drop, temperature, O2 mole fraction, and heat fluxes were matched with measurements.

Thank you for your attention

Appendix

18

Discrete Phase Method(DPM)

Assumptions

1) Solid particles have low Volume fraction and they can not affect fluid motion. Hence Volume fraction is not considered in N.S equations.

2) There is no particles interaction.3) Trajectory of a discrete phase particle is predicted by

integrating the force balance equation of the particle.4) Coal particles interact directly only by gas phase via

drag force.5) Coal particles do not interact directly by sand phase.6) Coal particles transfer heat directly only to gas phase.

Eulerian-Lagrangian

In Lagrangian frame

In Eulerian frame

Particle forceBalance forSolid Phase

xp

ppD

p Fg

uuFt

u r+

-+-=

¶¶

rrr )(

)( 24Re18

2D

ppD

Cd

Fr

m=

Momentum of FluidPhase

)()()( otherDPM FFgpvvvt

rrrrrr++r+t×Ñ+-Ñ=r×Ñ+r

¶¶

Eulerian-Eulerian

In Eulerian frame

In Eulerian frame

Assumptions1) It is a multiphase flow method and N.S equations are solved for both phases.2) Solid and fluid phases are treated in the same way as interpenetrating continua.3) granular properties are added to solid phase by solving an additional equation for solids

fluctuating energy or granular temperature.4) There is no limitation for volume fraction. Hence effects of volume fraction should be

considered in N.S equations

Multiphase Eulerian-Granular Method(MEGM)


÷øö

çèæ =ra×Ñ+ra¶¶

r0)()(1

gggggrg

vt

r÷øö


r0)()(1

sssssrs

vt

r

)(

)()(

gssg

ggggggggggg

vvK

gpvvvt

rr

rrrr

-+

ra+t×Ñ+Ña-=ra×Ñ+ra¶¶

)(

)()(

sggs

ssssssssssss

vvK

gppvvvt

rr

rrrr

-+

ra+t×Ñ+Ñ-Ña-=ra×Ñ+ra¶¶

Gas Equations Solid Equations

Continuity:

Momentum:

Continuity:

Momentum:

sg

ggggg

gggggggg

Q

Sqvt

phvh

t+

+×Ñ-Ñt+¶¶

a=ra×Ñ+ra¶¶ rrr :)()(

gs

sssss

ssssssss

Q

Sqvt

phvht

+

+×Ñ-Ñt+¶¶

a=ra×Ñ+ra¶¶ rrr :)()(

Energy: Energy:

a

Volume fractions

rr

r

vr

Reference density

Density

Velocity

The subscripts g and s refer to gas and solid

gr

sggs KK =

t)( ssp Q

Interphase momentum exchange coefficient

Stress-strain tensor

Solid pressure.

Gravity accelerationp Pressure shared by all phases

h

Enthalpy

qr

sggs QQ -=

Heat flux,, and S Source term

Intensity of heat exchange between the two phases


Granular Temperature

Generation of energy by the solid stress tensor

Diffusion of energy or diffusive flux of granular energy

Unit tensor

Diffusion coefficient

Energy exchange between the two phasesCollisional dissipation of energy

gssssssssssss φkvIpvt ss

+g-QÑ×Ñ+Ñt+-=úûù

êëé Qra×Ñ+Qra¶¶

QQ )(:)()()(23 rr

The kinetic energy due to the random motion of particles is represented by the granular temperature

of the solid phase ( ). Utilizing the kinetic theory, the transport equation of the granular temperature takes the form:

sQ

sss vIp rÑt+- :)(

ssk QÑQ

I

skQ

sQg

sgsgs Kφ Q-= 3

Important features:

§ Coal and sand particles interact directly by gas phase via drag force.

§ Coal particles interact directly by sand phase via solid stress tensors of sand and coal, and ; respectively.

§ Coal and sand particles transfer heat directly by each other and gas phase.

§ In DDPM there is no restriction for the volume fraction of the discrete phase. so volume fraction of the discrete phase should be considered in the gas momentum equations. hence relation between volume fractions becomes .

coaltsandt

1=a+a+a coalsq

Interaction is calculated at grid level


23

÷øö


r0)()(1

gggggrg

vt

r

licitDDPMgDDPMDDPMggg

gggggggg

SvvKg

pvvvt

,exp)(

)()(

+-++×Ñ

+Ñ-=×Ñ+¶¶

rrr

rrr

rat

arara

Gas Equations Solid Equations

Continuity:

Momentum:

Particle forceBalance forSolid Phase

24Re18

2D

ppD

Cd

Fr

m=

interact

)()( FF

gvvF

tv

xp

ppD

p rr++

rr-r

+-=¶¶

s

sineractionF t

r×Ñ-=

1

a

Volume fractions

rr

r

vr

Reference density

Density

Velocity

The subscripts g and p refer to gas and particles

gr

DDPMK

t


Stress-strain tensor

Gravity acceleration

p Pressure Source term from particles

DDPMS

DF

Drag Force

m

viscosity

xF

External force

24


Ivvv ssssTsssss

rrr×Ñ-+Ñ+Ñ= )

32()( mlamat


Generation of energy by the solid stress tensor

Diffusion of energy or diffusive flux of granular energy

Unit tensor

Diffusion coefficientCollisional dissipation of energy

ss sssssssssss kvIpvt QQ g-QÑ×Ñ+Ñt+-=úû

ùêëé Qra×Ñ+Qra¶¶ )(:)()()(

23 rr

For calculation of particles interactions we need to calculate solid Stress-strain tensor on EulerianGrid. This tensor is a function of the kinetic energy due to the random motion of particles which is

represented by the granular temperature of the solid phase ( ). Utilizing the kinetic theory,the transport equation of the granular temperature takes the form:

sQ

sss vIp rÑt+- :)(

ssk QÑQ

I

skQ

sQg Dense Discrete Phase Method(DDPM)

25

kinscolss ,, mmm +=

ss

ssssssscols egd ap

ram2/1

,0, )1(54

÷øö

çèæ Q

+=

ANSYS FLUENT extension (UDFs)

Steam outlet

UDF

There is a limit for maximum VOF in a cell equal to

0.63 % of cell volume

If VOF is over limit Redistribution of VOF to neighbor cells

Mass LossIf all neighbor cells are fullaand the number of iteration

per time step is low

3) Calculation of pressure drop along furnace based on mass of particles in each section4) Calculation of circulation rate5) Calculation of PSD at furnace outlet6) Non uniform boundary condition at inlet. The air mass flow rate at the bottom of at different sections has different values.

26

12

3

456

Reactions

After 10 seconds no combustion occurred( it took around 10 days)

Gas Phase Reactions Ar Er (J/kmol) m a b c

CH2.84O0.761 → 0.239CH4 + 0.761CO + 0.942H24.26×106 [1/s] 1.08×108 0 1 1 0

CH2.84O0.761 + 1.33O2 → CO2 + 1.42H2O 2.12×1012 [1/K/s] 2.03×107 0 1 1 0

CO +0.5O2 → CO22.239×1012 [(m3/kmol)0.75/s] 1.674×108 0 1 0.25 0.5 [H2O]

H2 + 0.5O2 → H2O 6.8×1015 [(m3/kmol)0.75/K-1/s] 1.67×108 -1 0.25 1.5 0

CO + H2O → CO2 + H2275 [(m3/kmol)0.5/s] 8.374×107 0 1 1 0

H2 + CO2 → CO + H2O 0.0265 [(m3/kmol)0.5/s] 3960 0 1 1 0

CH4 + 0.5O2 → CO + 2H24.4×1011[(m3/kmol)0.75/s] 1.25×108 0 0.5 1.25 0

CH4 + H2O → CO+ 3H28.7×107[(m3/kmol)0.5/s] 2.51×108 0 0.5 1 0

Solid Phase reactions Ar [kg/m2/sec/Pa0.5] Er(J/kmol)

C(s) + 0.5O2 →CO 0.052 6.1 x 107

C(s) + CO2 →2CO 0.0732 1.125 x 108

C(s) + H2O→CO + H2 0.0782 1.15 x 108

Governing Equations:

å=

-=×Ñ+¶¶ n

pqppqqqqqq mmv

t 1)()()( &&

rrara

å=

=n

qq

11a

)())((

)()(

,,1

qvmqliftq

n

pqpqppqpqqppq

qqqqqqqqqqq

FFFvmvmvvK

gpvvvt

rrrr&

r&

rr

rrrr

+++-+-

++×Ñ+Ñ-=×Ñ+¶¶

å=

ratarara

Volume Fraction Equation

Continuity

Momentum of FluidPhase

lss

ssssssssss

ssk

vIpvt

fg

trara

+-QÑ×Ñ

+-Ñ+-=Q×Ñ+Q¶¶

QQ )(

:)()()( rr

GranularTemperature

)())((

)()(

,,1

svmslifts

N

lslsllslsslls

ssssssssssss

FFFvmvmvvK

gppvvvt

rrrr&

r&

rr

rrrr

+++-+-+

+×Ñ+Ñ-Ñ-=×Ñ+¶¶

å=

ratarara

Momentum of SolidPhase

Governing Equations:

aVolume Fraction r

Density vr

Velocity

m&

Mass transfer between Phases

p

Pressure

t

Phase Stress-Strain Tensor

gr

Gravitational accelerate

K


Fr

External Body Force

liftFr

Lift Force

vmFr

Virtual Mass Force

sQ


Lift Force:

•Due to velocity gradients

•Important for large particles

)()(5.0 qpqpplift vvvF rrrr´Ñ´--= ar

Virtual Mass Force:

fff)()()(

Ñ×+¶

= qq v

dtdtd r

•Due to Relative acceleration of Phase p to the primary Phase q

÷÷ø

öççè

æ-=

dtvd

dtvd

F ppqqqpvm

rrr

ra5.0

•Important when secondary phase density is much smaller than

primary phase

Fluid-Solid exchange coefficient

65.2

43 --

= ls

lsllsdsl d

vvCK a

raa rr

Gidaspow model

[ ]687.0)Re(15.01Re

24sl

sldC a

a+=

l

lssls

vvdm

r rr-

=Re

s

lssl

sl

llssl d

vvd

Krr

-+

-=

ara

maa 75.1)1(150 2

For

For

8.0>la

8.0£la

Solid Pressure

•Due to using Maxwellian velocity distribution, granular tempera

ture appears

sssssssssss gep Q++Q= ,02)1(2 arra

sse

Coefficient of restitution for particle collision (around 0.9)

ssg ,0

Radial distribution function

Kinetic Term Collision Term

Radial distribution function

1

31

max,0 1

-

úúú

û

ù

êêê

ë

é

÷÷ø

öççè

æ-=

s

sgaa

•Governs the transition from compressible condition to incompr

essible condition•Is a correction factor to modify the probability of collisions in

dense beds

For one solid phase:

max,sa

Max Packing Volume fraction

Solid Shear Stresses:

Ivvv ssssTsssss

rrr×Ñ-+Ñ+Ñ= )

32()( mlamat

Gidaspow model

Stress-strain tensor for solid phase:

Shear viscosity=sm kinscols ,, mm +=

ss

ssssssscols egd ap

ram2/1

,0, )1(54

÷øö

çèæ Q

+=

sssssssssss

ssskins eg

egd

aaa

rm

2

,0,0

, )1(541

)1(9610

úûù

êëé ++

+Q

=

2/1

,0 )1(34

÷øö

çèæ Q

+=p

ra ssssssss egd

Bulk viscosity

=sl

Accounts for the resistance of the granular particles to compression and expansion


The collisional dissipation of energy

The generation of energy by the solid stress tensor

lss

ssssssssss

ssk

vIpvt

fg

trara

+-QÑ×Ñ

+-Ñ+-=Q×Ñ+Q¶¶

QQ )(

:)()()( rr

sss vIp r-Ñ+- :)( t

ssk QÑQ

The diffusion of energy

sQg

lsf

The energy exchange between phases

=Qsk

Diffusion Coefficient (Gidaspow model)

par

apr

ssssssss

sssssssss

sss

egd

egeg

d

Q+

+úûù

êëé ++

+Q

=

)1(2

)1(561

)1(348)(150

,02

2

,0,0

2/32,02 )1(12

ssss

ssss

dge

sQ

-=Q ar

pl

slsls K Q-= 3f

Boundary Conditions

||,0max,

36 sss

s

ss Ug

rrQ-= r

aafpt

Granular Boundary condition:

Liquid Phase:

Wall: No slip

Inlet: Velocity inlet

Outlet: Atmosphere Pressure

Solid Phase:

Wall: Partial slip:

Outlet: Atmosphere Pressure

23

02

max,||,||,0

max,

)1(34

36 sssw

s

sssss

s

ss geUUgq Q--×Q= r

aapr

aafp rr

[ ] hj

ijjjjii

i SuJhxTk

xpeu

x+÷÷

ø

öççè

æ+-

¶¶

¶¶

=+¶¶ å

''')( tr

xu

xu

xu ,Fg

xxpuu

x l

l

i

j

j

iijii

i

ij

iji

i ¶¶

-¶

¶+

¶¶

=++¶

¶+

¶¶

-=¶¶ mmtr

tr

32)]([)(

0)()( =¶¶

+¶¶ v

yu

xrrGoverning Equations-Gas phase

=×Ñ )( iYurr iit

tmi RY

ScD +Ñ+×Ñ ))(( ,

mrConservation of Fluid Mass

Conservation of momentum

Conservation of energy

Conservation of species

conduction

Diffusion –thermal(Dufour effect)

Viscous dissipation

Heatsource/Sink

Reaction termThe diffusive mass flux in turbulent

Body force (중력 제외)Shear force

40

Governing Equations-Gas phaseTurbulence model (Realizable k-ε) for SCGP

kMbkjk

t

ji

i

SYGGxk

xku

x+--++

úúû

ù

êêë

é

¶¶

÷÷ø

öççè

æ+

¶¶

=¶¶ re

smmr )(

eeeee

ene

erresmmre SGC

kC

kCSC

xxu

x bj

t

ji

i

+++

-+úúû

ù

êêë

é

¶¶

÷÷ø

öççè

æ+

¶¶

=¶¶

31

2

21)(

Turbulence model (Standard k-ε) for E-Gas

kMbkjk

t

ji

i

SYGGxk

xku

x+--++

úúû

ù

êêë

é

¶¶

÷÷ø

öççè

æ+

¶¶

=¶¶ re

smmr )(

eeeee

ereesmmre S

kCGCG

kC

xxu

x bkj

t

ji

i

+-++úúû

ù

êêë

é

¶¶

÷÷ø

öççè

æ+

¶¶

=¶¶ 2

231 )()(

Gk: represents the generation of turbulence kinetic energy due to the mean velocity gradientsGb: generation of turbulence kinetic energy due to buoyancyYM: contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate σk and σε: turbulent Prandtl numbers for k and ε, respectively. Sk and Sε: user-defined source terms

• 유동의 와류, 회전, 곡률에 대해 높은 정확도를 가짐 (Manual, ANSYS FLUENT).→ 가스화기 축을 중심으로 와류 유동이 많은

SCGP의 해석에 유리

• 석탄 가스화기에 다양한 난류모델을 적용 후 결과비교를 통해 Standard k-ε 모델이 타당성과 해석시간 측면에서 가장 적절하다고 함1). (Silaenand Wang, International Journal of Heat andMass transfer 2010;53:2074-2091.).

• 과거문헌에 의하면 E-Gas에 Standard k-ε모델 적용결과 실제 운전결과와 유사한 결과를 얻음2),3).

Ref. :[2] Ma and Zitney. Computational Fluid Dynamic Modeling of Entrained-Flow Gasifiers with Improved Physical andChemical Submodels, Energy & Fuels, 2012;26;7195–7219.[3] Luan et al. Numerical analysis of gasification performance via finite-rate model in a cross-type two-stage gasifier,International Journal of Heat and Mass Transfer, 2013;57;558-566. 41

42

Governing Equations-Particle phase

xp

pxpD

p Fg

uuFdt

du+

-+-=

rrr )(

)(

24Re18

2D

ppD

Cd

Fr

m=

Particle motion equation

Drag force

Turbulent (stochastic) tracking model)(' tuuu +=

• 입자의 궤적에 순간적인 가스의 난류 변동 (u’ )을 포함.• 석탄 및 가스화게 주입과 연소로 인한 가스의 난류(선회)가 입자 거동에 주는 영향을 해석하기에 적합.

)θ(σε)( 44pRppfg

ppp

ppp TAh

dtdm

TThAdt

dTcm -++-= ¥

Conservation of energy for particle

hfg: latent heat of coal (J/kg)εp: particle emissivityσ: Stefan-Boltzmann constant (5.669×10-8 W/m2-K4)θR : radiation temperature (K).

43

Governing Equations-Radiation sub modelDiscrete Ordinates (DO) radiation model

ò ×++=+++×Ñp

WFp

sp

ss4

0

42 ')'()',(

4),()()( dsssrIETansrIaasI P

PPPrrrrrrr

s : path length (m) a : absorption coefficient of gas phaseap: equivalent absorption coefficient due to the presence of particulates n: refractive index σ: Stefan-Boltzmann constant (5.669×10-8 W/m2-K4)

σp: equivalent particle scattering factor I: radiation intensity (W/sr) EP: equivalent emissionT: local temperature (K) Φ: phase functionΩ': solid angle

)1)((0

,ps

I

ii

ieTa kee -

=

-= å

ε : emissivity of gas phaseaε,i : emissivity weighting factor for the ith fictitious gray gas the bracketed quantity is the ith fictitious gray gas emissivityκi: absorption coefficient of the ith gray gas (1/m) p: sum of the partial pressures of all absorbing gases (Pa)

Weighted Sum of Gray Gases Model (WSGGM)

sa )1ln( e-

-=

a: absorption coefficient of gas phase

Radiation heat source is included in the source term in the energy equation.

44

Coal Reaction sub modelEvaporation

)1ln( mcpp BkA

dtdm

+-= ¥r

mp: water droplet mass(kg)kc: mass transfer coefficient (m/s)

Devolatilization

dtdtRRRRmmf

tm tt

apow

v ))(exp()()1(

)(20 1220 11

0,,òò +-+=

--aa

Homogeneous reaction

[ ]),,,(,min PRmixrxn xxkRRR e= cbaRTEmrrxn CCCeTAR r

321)/(-=

Ap: droplet surface area (m2)ρ∞: density of bulk gas (kg/m3)

R1 and R2: competing rates that control the devolatilization over different temperature ranges.mv(t): volatilized mass at time t (kg)mp,0: initial coal particle mass (kg)

ma: ash content of coal (kg)fw,0: mass fraction of evaporating/boiling material

Rrxn: chemical reaction rate calculated by reaction kinetics Rmix: turbulence mixing rate k: function of turbulence kinetic energyε: dissipation rate of turbulence kinetic energyxR and xP : mole fractions of reactant xR and product xP

Ar: pre-exponential factor m: exponent of temperature Er: activation energy (J/kmol) R: universal gas constant (8314 J/kmol-K) C1 and C2 : molar concentrations of the first and second reactantsa and b: corresponding reaction orders with respect to the two reactants C3: concentration of a third speciesc: corresponding reaction order.

45

Coal Reaction sub model

Heterogeneous reaction (Volume Reaction Model)

)1ln(1)1(/ xxePAdtdx RTEn

irrr ---= - yh

rkinr

rrkinnrp

p

RDDR

pAdt

dm

,,0

,0,

+-= h

x: carbon conversion of char particle ηr: effectiveness factor Ar: pre-exponential factor Ei: activation energy (J/kmol)

R: universal gas constant (8314 J/kmol-K) Pr: partial pressure of species i (Pa) Ψ: pore structure parametern: apparent reaction order.

Heterogeneous reaction (Random Pore Model)

ηr: effectiveness factor pn: bulk partial pressure of the gas phase (Pa)

D0,r: diffusion rate coefficient for reaction r (kg/m2/sec/Pa0.5)Rkin,r: kinetic rate of reaction r ( kg/m2/sec/Pa0.5)

development of a dense discrete phase model for 3d ... · pdf fileansys fluent extension...

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