a comparison of various models in predicting ignition

Paper # 070CO-0042 Topic: Coal and Biomass Combustion and Gasification8th US National Combustion Meeting

Organized by the Western States Section of the Combustion Instituteand hosted by the University of Utah

May 19-22, 2013.

A Comparison of Various Models in Predicting Ignition Delay inSingle-Particle Coal Combustion

Babak Goshayeshi1 James C. Sutherland2

1 Graduate Research Assistant,2 Associate Professor

Department of Chemical EngineeringUniversity of Utah, Salt Lake City, UT 84112

In this paper, individual coal particle combustion under laminar conditions was simulated using variouslevels of complexity in the particle and gas phase chemical kinetics. In the gas phase, detailed gas-phasechemical kinetics based on GRI3.0 and flame-sheet (infinitely-fast chemistry) are considered and com-pared. On the particle side, models for vaporization, devolatilization and char oxidation/gasification areconsidered. For devolatilization, the Kobayashi-Sarofim model and Chemical Percolation Devolatiliza-tion (CPD) models are compared. The mass, momentum and energy governing equations are fullycoupled between the particle and the gas phase. Ignition delay as a metric is considered to comparethe simulation prediction with experimental data. The effects of particle size, coal type and gas-phasetemperature on the ignition delay are studied and compared with experimental data.

1 Introduction

Coal combustion/gasification is a complex process with many coupled sub-processes occurringsimultaneously [1]. Furthermore, most practical coal combustion systems are turbulent, furthercomplicating the modeling challenge because of the nonlinear coupling occurring across a multi-tude of length and time scales. Even with modern day computers, resolving the entire physics ofthe problem remains prohibitively expensive. Coal combustion/gasification models must addressparticle dynamics in turbulent flow, gas-phase thermochemistry, heterogeneous reactions betweenthe coal and gas, devolatilization/pyrolysis, vaporization, radiative heat transfer, etc.The modeling challenge for coal combustion is further complicated by the varying properties andchemical structure of different coal types [2,3], and by the fact that the coal properties change sig-nificantly throughout a coal particle’s lifetime in a combustor [4–6]. The combustion process in thiswork is divided into three processes: vaporization, devolatilization and char oxidation/gasification.Models for devolatilization vary widely in complexity, with the most sophisticated models account-ing for the chemical structure of the coal and its effect on the devolatilization process [1]. In 1971a constant value proposed for the combustion rate of each coal type [7]. Arrhenius form modelssuch as the single-rate [8] and Kobayashi [9] models describe devolatilization with a kinetic rate.In 1976, the Distributed Activation Energy (DAE) model [10] proposed using a gaussian distribu-tion for the activation energy. Determining the parameters for the gaussian distribution were thechallenges of this model [11]. Representing coal as a collection of 14 functional group includingaromatic rings, aliphatic chains and bridges and oxygen-carrying groups was a significant step in

1

8th US Combustion Meeting – Paper # 070CO-0042 Topic: Coal and Biomass Combustion and Gasification

devolatilization modeling [12, 13]. The Chemical Percolation Devolatilization (CPD) model ac-counts for the thermal decomposition of the macromolecular network and accounts for structuralvariation among various coal types [1,14,15], and can accurately describe light-gas evolution fromcoal devolatilization [16].Char oxidation and gasification are heterogenous reactions, and are significantly slower than thevaporization and devolatilization processes [1, 17]. There are many factors influence the char oxi-dation, such as coal structure, coal type, the gas-phase environment (e.g., oxygen partial pressure)and temperature [18, 19]. The products of char oxidation are mainly carbon dioxide and monox-ide [20, 21].The One-Dimensional Turbulence (ODT) model, first proposed by Kerstein [22], has been suc-cessfully applied to a variety of turbulent flows, including particle-laden flows [23] as well asstrong turbulence-chemistry interaction including extinction and reignition [24]. Several assump-tions in ODT are made a priori. Most notably among these is the assumption that the flow fieldis statistically one-dimensional (implications of this assumption are discussed in [24, 25]). Thepresent study is intended to form the foundation for development of coal combustion and gasifica-tion models within ODT, and focuses on single-particle dynamics in a laminar environment. Thisallows consideration of the particle and gas phase combustion models separate from concerns ofparticle-particle interaction, turbulence, etc.

2 Governing Equations

The governing equations for gas and particle phase are provided here. The details of governingequations can be found in [25]. A one-dimensional domain aligned with the y-coordinate andevolving in time was considered in this work.

2.1 Gas Phase

The overall mass conservation equation is given by [25, 26]

∂ρ

∂t= −

∂v∂y

+

np∑j=1

S pjm, (1)

where S p jm is the particle source term and np is the total number of particles. Individual speciesconservation equations are given as

∂ρYi

∂t= −

∂ρYiv∂y−∂Ji

∂y+ ωi +

np∑j=1

S pjYi (2)

where ωi is the reaction source source term of species i and S p jYi is the release rate of species ifrom particle j into the gas phase.Momentum equations are typically evolved for component of momentum aligned with the ODT

2


line (y-direction) and at least one orthogonal component,

∂ρv∂t

= −∂ρvv∂y−∂τyy

∂y−∂P∂y

+

np∑j=1

S pjv, (3)

∂ρu∂t

= −∂ρvu∂y−∂τyx

∂y+

np∑j=1

S pju. (4)

where v and u refer to lateral and streamwise velocities, respectively. Finally, the energy equationis

∂ρe0

∂t= −

∂ρe0v∂y

−∂pv∂y−∂τyyv∂y−∂q∂y

+

np∑j=1

S pje0 . (5)

Closure of this system is achieved by the ideal gas equation of state, p = ρRT/M and constitutiverelationships for the diffusive fluxes [26]

τyy = −43µ∂v∂y, (6)

τyx = −µ∂u∂y, (7)

q = −λ∂T∂y

+

ns∑i=1

hiJi, (8)

Ji = −ρYi

XiDmix

i∂Xi

∂y. (9)

The source terms S pm, S pv, S pu, S pe0 and S pYi which account for interphase heat, mass and momen-tum transfer, will be defined in §2.3. Corresponding exchange terms are included in the particlephase governing equations.In ODT, additional models are incorporated to model the effects of turbulent mixing [22, 26]. Forthe purposes of this paper, only laminar flow is considered to isolate the effects of the thermochem-ical models from the turbulence models.

2.2 Particle Phase

The motion of a single particle in gas-solid flows can be described by using Newton’s second law

mpdui,p

dt= mpgi + Fc + S p j,v (10)

where i denotes the ith direction, mp, ui,p, gi, S p j,v, and Fc are mass of single particle, particlevelocity, gravity acceleration, force generated by fluid-particle interaction, and force generated byparticle-particle interaction. For this study, particle-particle interaction is neglected (Fc = 0) and

3


the drag force is described by Stokes’ law so that the particle momentum equations become

dupj

dt=

gi

(ρp − ρg

)ρp

+ S p j,u, (11)

dvpj

dt=

gi

(ρp − ρg

)ρp

+ S p j,v, (12)

Particle source terms for v (S pj,v) and u (S pj,u) are given by (16) and (17), respectively.Given the evolution of the particle velocity according to (11) and (12), the particle position evolvesas

dxi,p

dt= ui,p, (13)

where xi,p is particle location in ith direction.The particle energy evolution is given by

dTp

dt=−Ap

mpCp

[hc

(Tp − T

)+ εσ

(T 4

p − T 4w

)]+ S r, (14)

where Tp, Tw and T are the particle, wall, and gas temperatures respectively. Cp, mp, Ap and ε arethe particle heat capacity, mass, surface area and emissivity respectively, σ is the Stefan-Boltzmannconstant, hc = Nuλ/dp is the convective heat transfer coefficient with Nu = 2.0 + 0.6Re1/2

p Pr1/3 [27],and S r is the temperature source term due to vaporization and heterogeneous reactions defined by(20)The overall mass balance on coal particle (mp) is divided into three phenomenological categoriesdescribing the evolution of moisture (mH2O), volatiles (mv), and char (mc),

dmp

dt=

dmH2O

dt+

dmv

dt+

dmc

dt. (15)

2.3 Source Terms

The momentum exchange terms which appear in the gas and particle momentum balances are

S pv = −mp fd

τpVpg

(v − vp

), (16)

S pu = −mp fd

τpVpg

(u − up

)(17)

where τp =d2

p

18νgis the particle relaxation time [28], fd is the drag force coefficient and Vpg is a

scaling term representing the volume of the cell, respectively. The model employed for fd is

fd =

1 Rep < 11 + 0.15Re0.687

p 1 < Rep < 10000.0183Rep Rep > 1000

,

4


where

Rep =dp

∣∣∣up − ug

∣∣∣νg

(18)

is the particle Reynolds number dp is the particle diameter, and νg is the gas kinematic viscosity.Subscripts p and g indicate particle and gas phase properties, respectively.Most of the particle mass (except ash) are released to the gas phase during the combustion process.Furthermore, char oxidation and gasification requires additional species from the gas phase such asoxygen and carbon monoxide. The mass source term for single particle for species i can be writtenas

S pYi =

(dmi

dt

)Evap

+

(dvi

dt

)Dev

+

(dmi

dt

)Oxid

+

(dmi

dt

)Gasif

. (19)

The models for evaporation, devolatilization, and char oxidation/gasification in 19 will be dis-cussed in §3.2.The energy source term for the gas phase energy conservation equation, (5), is given as

S pe0 = α(S p,CO∆HCO + S p,CO2∆HCO2

)Oxid

+ α

(dmc

dt

)H2O

∆HGaifH2O

+ α

(dmdt

)CO2

∆HGasifCO2

, (20)

where α is heat fraction that released to the gas and 1 − α is the heat fraction absorbed by theparticle [29]. This source term includes the heat of char oxidation (exothermic) also CO2 and H2Ogasification (endothermic).Finally, the source term appearing in the particle energy balance, (14), is written as

S r =1 − αmpCp

(S p,CO∆HCO + S p,CO2∆HCO2

)Oxid

+1 − αmpCp

(dmc

dt

)Gasif

H2O∆HGasif

H2O

+1 − αmpCp

(dmc

dt

)Gasif

CO2

∆HGasifCO2

+1

mpCp

(S p,H2O

)EvapλEvap, (21)

where Cp is particle heat capacity and ∆H is the enthalpy of reactions.

3 Chemical Reaction Models

3.1 Gas Phase

We consider two models for the gas-phase chemistry: detailed kinetics (§3.1.1) and infinitely fast(flame-sheet) chemistry (§(3.1.2)).

5


3.1.1 Full Chemistry

The detailed chemistry calculation is applied to obtain the gas phase properties. A reduced GRImechanism, consisting of 24 species and 86 reaction is utilized [30].

3.1.2 Flame-Sheet

The flame-sheet model assumes infinitely fast reaction according to

ri → πi (22)

where ri and πi are the moles of ith species (except O2) in reactants and flame-sheet product, re-spectively. It is assumed that the products of reaction are CO2, H2O and N2. The required oxygento burn each species is defined as

ξi = (σiC + σiH/4 − σiO/2) i ≡ species, except O2 (23)

where ξi represents stoichiometric oxygen to burn the one mole of species i and σi j is the numberof element j in the species i. The stoichiometric oxygen requirement can be calculated as

θ =∑

i

riξi i ≡ species, except O2 (24)

The equivalence ratio, Φ =rO2θ, is used to determine the products of reaction. In rich conditions

(Φ ≥ 1),

πi =

Erc i = CO2

ErH/2 i = H2O

ErN/2 i = N2

rO2 − θ i = O2

0 otherwise

(25)

where Erj is the amount of element j provided by the reactants,

Erj =

∑riσi j i , O2. (26)

Likewise, for rich conditions (Φ < 1),

πi =

rCO2 + EπC i = CO2

rH2O + EπH/2 i = H2O

rN2 + EπN/2 i = N2

0 i = O2

ri(1 − Φξ j∑j ξ j

) otherwise

(27)

where Eπ is the amount of produced element by reaction (22) that in rich situation can be calculatedby

Eπj = Φ

∑i

riσi jξi∑k ξk

. (28)

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3.2 Particle Phase

In the proposed model, a coal particle consists of moisture, volatile, char and ash. Figure 1 de-picts the coal’s constituents and the models that describes mass exchange. For example, evap-oration only adds moisture into the gas phase; however, char oxidation produces CO2 and COand consumes O2. The models that describe the consumption of coal constituents are outlined in§3.2.1-§3.2.3

moisture

volatile ash

char

Char Oxidation &Gasification

Devolatilization

Evaporation

Thursday, February 28, 2013Figure 1: Coal Constituents

3.2.1 Evaporation

The moisture content evolution is given by

dmH2O

dt= −

(S p,H2O

)Evap= kv

(PH2O,sat

RT−

PH2O

RTg

)ApMw,H2O, (29)

where kv is the mass transfer coefficient of steam into air [29,31], PH2O,sat is the saturation pressureof water at particle temperature, PH2O is partial pressure of water in gas. For purposes of energycoupling, the latent heat of vaporization for water is calculated from the Watson relation [32].

3.2.2 Devolatilization

Two devolatilization models with different complexity and computational cost were applied in thiswork.

Kobayashi Model: Devolatilization rate described in this model has two weighted first order Ar-rhenius reaction rates [9],

dmv

dt= −

[α1A1e(−E1/RTp) + α2A2e(−E2/RTp)

]mv, (30)

7


where α1 and α2 are weight of each rate [9]. Different reactions have been proposed for theKobayashi devolatilization model [33], there is no an universally accepted form. In this work,we assume

CHaOb → bCO +a + b − 1

2H2 +

1 − b2

C2H2, (31)

where a and b are calculated from coal’s ultimate and proximate analysis. There is general agree-ment on CO and H2 as the products for Kobayashi model, but accounting for tar in the gas phaseis less established. In this work, C2H2 will represent tar in the gas phase.

Chemical Percolation Devolatilization (CPD) Model: CPD is one of the most accurate (and com-plex) models available to predicts the production rates of the species during the devolatilization.It requires simultaneous solution of 34 ODEs per particle. The volatile composition produced byCPD changes through the time.Details of the CPD model are discussed in [16].

3.2.3 Char Oxidation/Gasification

Char oxidation and gasification represent heterogeneous reactions at the particle surface. Themass-exchange terms are accounted in the mass balance, (2). Char oxidation is a complex phe-nomenon which depends on many factors such as temperature and oxygen concentration. The rateof consumption of char by oxidation is described by [18](

dmc

dt

)Oxid

=rcwc

νpπd2

p, (32)

where ν = 2/(1+ψ) designates the stoichiometric ratio of carbon consumption, wc is the molecularweight of carbon and rc is the the reaction rate of char.There are several models and equations that explain char oxidation reaction rate, the Langmuir-Hinshelwood is a kinetic expression that frequently used. This approach describes competingadsorption (O2) and desorption (CO) on char surface that makes it more attractive. There aremultiple forms for Langmuir-Hinshelwood, but it was shown by [18] that

rc =k2k1 pnr

o2,s

k1 pnro2,s + k2

(33)

yields better results, where k1 and k2 are Arrhenius rate constants that their parameters are given inTable 1, nr = 0.3 and po2 s is the partial pressure of oxygen at particle surface [18].

Table 1: Arrhenius parameters for k1 and k2 in Eq.(33) as suggested by [18].

A (mol/s·m2·atmn) E (kJ/mol)k1 93.0 0.1k2 26.2 109.9

8


Char oxidation and gasification are heterogeneous reactions that consume char. The presence ofcarbon dioxide and water vapor around the coal particle can increases the likelihood of gasificationreactions at high temperatures through

C(s) + CO2 −→ 2CO, (34)C(s) + H2O −→ CO + H2. (35)

The differential equation that describes char gasification is(dmc

dt

)Gasif

i= −kimc; i ≡ CO2,H2O (36)

where ki is given by [34]ki = Ai p

ng

i exp(−Ei/RTp

)(37)

and pi represents the partial pressure of CO2 and H2O around the particle for reactions (34) and(35), respectively. The remaining parameters in (37) are given in Table 2.

Table 2: Arrhenius parameters for use in (37), as suggested by [34, 35].

CO2 H2OT < 1473 T ≥ 1473 T < 1533 T ≥ 1533

E (J/kmol) 2.71 × 108 1.63×108 2.52×108 1.40×108

A(kg.s−1.pa−ng

)3.34 × 108 6.78 × 104 2.89 × 108 8.55 × 108

ng 0.54 0.73 0.64 0.84

4 Result & Discussion

Simulations were performed to investigate the effect of furnace temperature, particles size and coaltype on ignition delay of coal particle. Furthermore, for particle and gas phase calculation, twomethods with different levels of complexity and computation cost are utilized. To validate thesimulation predictions, ignition delay as a metric is identified to compare the simulation resultswith experimental data.

4.1 Ignition delay

In experiments, the most widely used methods to identify ignition delay are based on visual obser-vation by measuring the intensity of visible light emission [36, 37]. In the experiment results usedin this work [37], CH∗ emission is considered as an indicator of the high-temperature flame front.The ignition point characterized as the half of the CH∗ maximum signal interrogated by a CCDcamera equipped with a 431 nm imaging filter. However, this signal was contaminated by CO2

∗

and thermal radiation from hot soot and char particle [37].Computationally, it is not obvious how to determine the ignition point. For example, thresholdvalues of temperature or species mass fractions, or the inflection point in the particle temperature-time history (as suggested by [36]). Physically, the inflection point in the particle temperature

9


history represents the location where the asymptotic heating of the particle by its surroundings isovertaken by the heat transfer due to chemical reaction nearby the particle.Figure 2a shows the simulation prediction for ignition delay based on several plausible criteria.For the species criteria, ignition is defined as the time at which the species mass fraction is 50%of its maximum value. CO is chosen to be representative of the products of devolatilization andchar oxidation, OH was chosen as a reasonable gas-phase flame indicator, and CHx is the sum ofthe CH2 and CH3 mass fraction, and is meant to be a surrogate representation of CH∗ which is thebasis of the experimental measurements of ignition delay. The error-bars in Figure 2a represent25% and 75% of the maximum mass fraction in the profiles of species as they marked in Figure 2b.The time-evolution of these species and the particle temperature at the particle position are shownin Figure 2b.

1200 1300 1400 1500 1600 1700 18000

0.01

0.02

0.03

0.04

0.05

Furnace Temperature (K)

Ignitio

n D

ela

y (

sec)

CHxCOOH(

∂Tp

∂t

)min(

∂Tg

∂t

)max

Exp

(a) Ignition delay for various criteria. Speciescriteria are based on the time at which thespecies mass fraction reaches half of its maxi-mum.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04500

1000

1500

2000

time (sec)

Temp

erat

ure

(K)

ParticleGas

∂T p

∂ tmi n

∂T g

∂ tma x

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.5

1

1.5

2

time (sec)

mass

frac

tion

CHx× 104

CO× 102

OH× 103

CO2

(b) Species (bottom) and particle temperature (top) his-tories. Crosses indicate 25% and 75% of the maximumspecies mass fraction and squares show the particle tem-perature inflection point ( ∂Tp/∂t|min) and the maximum gas-phase temperature increase rate ( ∂Tg/∂t|max).

Figure 2: Ignition delay identified with half of maximum in species profile. Pittsburgh coal particlewith size of 92.4 µm (75-105µm) injected into 20 vol% O2 with N2 diluent.

Since the ignition delay criteria based on CHx provides reasonable agreement between the simu-lation and experimental data, it is used to identify the ignition delay in the rest of the paper wherereduced mechanism utilized in the gas phase.The CHx criteria is unavailable in flame-sheet method (see §3.1.2) because intermediate speciesare not available. Therefore, we use CO and the particle temperature history inflection point asmeasures of ignition delay. As shown in Figure 2, these are not expected to be highly accurateindicators of ignition delay, but provide a reasonable approximation. If it is assumed that thetrue prediction of flame-sheet method lays between the CO and particle inflection point, a faircompression between detailed kinetics and flame-sheet can be made.

4.2 Effect of Furnace Temperature

Using the ignition delay criteria established in §4.1, the effect of furnace temperature on igni-tion delay for Pittsburgh and Black Thunder coals is investigated. Tables 3 and 4 summarize the

10


simulation parameters and coal composition, respectively.

Table 3: Simulation parametersGas Composition (mass fraction) ParticleO2 CO2 H2O N2 size cut mass mean size density (kg/m3)0.2 0.3 0.12 0.38 75µm-105µm 92.4µm 1200

Table 4: Proximate and ultimate analysis, as reported in [37].Proximate(wt.% as received) Ultimate (wt.% daf)

Moisture Ash Volatiles Fixed C C H O N SPittsburgh 1.4 6.9 35.4 56.3 82.9 5.6 7.7 1.6 2.2

Black Thunder 10.8 5.4 40.4 43.8 64.1 2.2 29.1 0.9 0.5

4.2.1 Detailed Chemistry

Figure 3a shows the ignition delay as a function of furnace temperature for Pittsburgh (Figure 3a)and black thunder (Figure 3b) coals, respectively. Results for the CPD and Kobayashi models, bothwith detailed chemistry in the gas-phase, are compared with experimental data. Due to speciationand production various species by CDP, this model is more successful in predicting the ignitiondelay than Kobayashi model - particularly at higher furnace temperatures.

1200 1300 1400 1500 1600 1700 18000

0.01

0.02

0.03

0.04

0.05


Ign

itio

n D

ela

y (

se

c)

CPD

Kob

Exp

(a) Pittsburgh

1200 1300 1400 1500 1600 1700 18000

0.01

0.02

0.03

0.04

0.05


Ign

itio

n D

ela

y (

se

c)

CPDKobExp

(b) BlackThunder

Figure 3: Ignition delay vs initial furnace temperature. ’CPD’, ’Kob’ and ’Exp’ represent the CPDmodel, Kobayashi model and experimental data, respectively. The reduced mechanism in the gasphase was used.

The volatile consumption fractions at the ignition point for both models are reported in Figure 5.The CPD model shows a much more pronounced effect of the furnace temperature on the volatileconsumption fraction at ignition. As a consequence of producing highly reactive species such asH and CH4, the consumption fraction of CPD model at high temperature is lower than Kobayashi

11


model. While both models account for differences in coal types, the CPD model appears to moreaccurately capture the variation in ignition delay across the two coal types considered here.Figure 4 shows the particle temperature at ignition using the inflection point and CHx criteria withthe CPD model and detailed chemistry in the gas phase. This figure indicates that the particletemperature at the location where ignition occurs can vary dramatically, and that the inflectionpoint criterion results in significantly different particle temperatures at ignition. Furthermore, theuncertainty in particle temperature at ignition point is quite high at low furnace temperatures.

1200 1300 1400 1500 1600 1700 1800700

800

900

1000

1100

1200

1300

1400

1500


Pa

rtic

le T

em

pe

ratu

re (

K)

Ignition

Inflection

Figure 4: Pittsburgh coal particle temperature at ignition and inflection point. Ignition is character-ized by half of CHx maximum. Error bars show 25% and 75% of maximum. Reduced mechanismand CPD model are utilized.

1100 1200 1300 1400 1500 1600 1700 18000

0.2

0.4

0.6

0.8

1


Co

nsu

mp

tio

n F

ractio

n

CPDKob

(a) Pittsburgh

1100 1200 1300 1400 1500 1600 1700 18000

0.2

0.4

0.6

0.8

1


Consum

ption F

raction

CPDKob

(b) BlackThunder

Figure 5: Volatile consumption fraction versus initial furnace temperature. ’CPD’ and ’Kob” arerepresenting CPD model, Kobayashi model, respectively. These results produces by employingreduced mechanism in the gas phase.

4.2.2 Flame-Sheet Model

We now consider the flame-sheet model for the gas-phase chemistry treatment. As a very inex-pensive model, this is attractive for use in large-scale simulations, provided that it is sufficientlyaccurate. Figure 6 shows the ignition delay as a function of furnace temperature, analogous to theresults shown in Figure 3 for detailed gas-phase chemistry. As discussed in §4.1, the CO profile

12


at particle position and inflection point in particle temperature history are used to identify the igni-tion point. Consistent with the analysis in §4.1 surrounding Figure (2a), the experimental data arenearly bracketed by the CO and inflection point criteria, except at low furnace temperatures. How-ever, the flame-sheet model does not perform as well as the CPD model with the detailed chemistrytreatment, and fails to capture the nonlinear trend of ignition delay versus furnace temperature thatthe data shows. However, some of this discrepancy can be attributed to the lack of a suitable metricfor ignition delay with the flame-sheet model, as discussed in §4.1.

1200 1300 1400 1500 1600 1700 18000

0.01

0.02

0.03

0.04

0.05


Ign

itio

n D

ela

y (

se

c)

CPD-COKob-COCPD −

(∂Tp

∂t

)min

Kob −(

∂Tp

∂t

)min

Exp

(a) Pittsburgh

1200 1300 1400 1500 1600 1700 18000

0.01

0.02

0.03

0.04

0.05


Ign

itio

n D

ela

y (

se

c)

CPD-COKob-COCPD −

(∂Tp

∂t

)min

Kob −(

∂Tp

∂t

)min

Exp

(b) BlackThunder

Figure 6: Ignition delay vs initial furnace temperature. ’CPD’, ’Kob’ and ’Exp’ are representingCPD model, Kobayashi model and experimental data, respectively. These results produced byemploying flame-sheet calculation in the gas phase.

4.3 Particle Size Effects

The experimental data were conducted on cuts of particle sizes [37], yielding some uncertainty asto the effect of particle size variation within the cut on the resulting ignition delay. The effect ofparticle size on ignition delay illustrated in Figure 7. The triangles connected by dash-dot linesindicate ignition delay for the particle sizes cuts used in the experiments at the three different sizeranges [37].Figure 7a compares experimental data to results for the CPD and Kobayashi models with detailedgas-phase chemistry. It appears that the models are too sensitive to the particle size in their pre-diction of ignition delay. Nevertheless, the CPD model with detailed gas-phase chemistry doescompare more favorably with the experimental data than the Kobayashi model.In Figure 7a ignition delay prediction versus particle size are illustrated and compared with exper-imental data. The prediction obtained by using CPD and Kobayashi-Sarofim model are reported.At constant temperature CPD model is initially more active than Kobayashi-Sarofim model. Dueto this fact, CPD model produces more volatile which leads to faster ignition. The simulation re-sults suggests that at small particle size cut(55µm-74µm), the ignition onsets by ignition of biggerparticle in the cut, however, at the big particle size cut (105µm-74µm) it is smaller particle in thecut that initiates the ignition.Ignition delay trends using the flame-sheet model are shown in Figure 7b.

13


40 60 80 100 1200

0.01

0.02

0.03

0.04

0.05

0.06

Particle Size (µm)

Ign

itio

n D

ela

y (

se

c)

CPDKobExp

(a) Reaction

40 60 80 100 1200

0.01

0.02

0.03

0.04

0.05

0.06

Particle Size (µm)

Ign

itio

n D

ela

y (

se

c)

CPD-COKob-COCPD −

(∂Tp

∂t

)min

Kob −(

∂Tp

∂t

)min

Exp

(b) flame-sheet

Figure 7: Ignition delay vs particle size. Pittsburgh coal particle injected into 12% vol O2 in N2at1320

4.4 Computation Cost

The performed simulation consists of carrier (gas) and dispersed (particle) phases. In each phasetwo methods were utilized and results were compared. A schematic of utilized methods and num-ber of Ordinary Differential Equation (ODE) used by each method is illustrated in Figure 8.Using flame-sheet instead of detailed calculation can reduces the gas phase computation costby 55%-65%, regarding the devolatilization model. Furthermore, in particle phase, employingKobayashi-Sarofim model is approximately 35% cheaper than CPD model.

Full Chemistry‣ 24 Species 23 ODEs‣ 86 Reaction

CPD‣ 34 ODEs‣ 37 Expr

Flame-sheet‣ 7-11 Species 6-10 ODEs‣ ~1 Reaction

K-S‣ 1 ODEs‣ 5 Expr

~ 35%

~ 55-65%

Computation Cost Reduction in Each Phase

Figure 8: Computation cost reduction in each phase. Blue and red boxes are representing gas andparticle phases.

5 Conclusions

This paper considered several models for coal particle ignition and compared these to experimentalmeasurements available in the literature for two coal types at various furnace temperatures and forseveral particle sizes. We considered two models for devolatilization (CPD and the Kobayashi-Sarofim model) and two for the gas phase chemistry treatment (detailed kinetics and a flame-sheetmodel). These models essentially trade complexity for cost.

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To the authors’ knowledge, this is the first simulation performed using detailed kinetics in thegas phase and the high-fidelity CPD model for devolatilization of coal particles. The CPD modelattempts to predict the light-gas evolution for the coal particles.The results indicate that simpler Kobayashi-Sarofim and flame-sheet models capture general trendspresent in the experimental data, but fail to provide quantitative agreement. On the other hand,the CPD model paired with detailed gas-phase chemistry provides reasonable agreement with theexperimental observations over all reported conditions.One significant challenge in comparing to experimental data is determining how to define ignitionin the simulation. This is particularly challenging for the flame-sheet model where intermediatespecies are unavailable for comparison against the emission measurements of CH∗ in the experi-ment. Sensitivity of the model predictions, which can be tied to a resulting uncertainty, are alsopresented.

Acknowledgment

This material is based upon work supported by the Department of Energy under Award NumberDE-NT0005015. The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.

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a comparison of various models in predicting ignition

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