progress variable model for NO prediction in pulverized coal flames

Accepted Manuscript A priori study of an extended flamelet/progress variable model for NO prediction in pulverized coal flames

Kun Luo, Chunguang Zhao, Xu Wen, Zhengwei Gao, Yun Bai, Jiangkuan Xing, Jianren Fan PII:

S0360-5442(19)30512-2

DOI:

10.1016/j.energy.2019.03.110

Reference:

EGY 14946

To appear in:

Energy

Received Date:

15 August 2018

Accepted Date:

19 March 2019

Please cite this article as: Kun Luo, Chunguang Zhao, Xu Wen, Zhengwei Gao, Yun Bai, Jiangkuan Xing, Jianren Fan, A priori study of an extended flamelet/progress variable model for NO prediction in pulverized coal flames, Energy (2019), doi: 10.1016/j.energy.2019.03.110

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ACCEPTED MANUSCRIPT

A priori study of an extended flamelet/progress variable model for NO prediction in pulverized coal flames By Kun Luo, Chunguang Zhao, Xu Wen, Zhengwei Gao, Yun Bai, Jiangkuan Xing, Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China

Submitted to

Energy

____________ * Corresponding author. E-mail address: [email protected] (J. Fan). 1 / 36

ACCEPTED MANUSCRIPT

ABSTRACT An extended flamelet/progress variable (FPV) model is developed in this work to predict the NO formation in pulverized coal flames with a newly defined progress variable. The validity of the model is assessed through an a priori analysis, in which the thermo-chemical values predicted with the extended FPV model are compared with the corresponding reference results. It is found that the NO mass fraction in the pulverized coal flames can be well predicted with the extended model, which is sensitive to the progress variable. The prediction accuracy can be further improved by optimizing the definition of progress variable. The effects of strain rate and initial temperature on the performance of the extended FPV model are also investigated. The overall good agreements between the developed model predictions and the detailed chemistry solutions demonstrate that the extended FPV model has a better performance for NO prediction than the conventional one in pulverized coal flames. Compared with the conventional model, the deviations of maximum NO mass fraction predicted with the extended FPV model are decreased by 92.97%, 86.80% and 95.14% for three different strain rate cases as well as 86.80%, 82.81% and 87.45% for three different initial temperature cases, respectively. Keywords： Pulverized coal flame; NO formation; Flamelet/progress variable; A priori analysis.

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ACCEPTED MANUSCRIPT

Nomenclatures Variables

Ac

pre-exponential factor in the char-oxidation model

Av

pre-exponential factor in the devolatilization model

C

progress variable

CD

drag coefficient

C pg

specific heat capacity of gas

C pp

specific heat capacity of particle

C p fuel

specific heat capacity of fuel

C pox

specific heat capacity of oxidizer

Dk

mass diffusivity of species k

DH e

gaseous thermal diffusivity

DZ

diffusivity of coal particle mixture fraction

DC

diffusivity of progress variable

dp

coal particle diameter

Ec

activation energy in the char-oxidation model

Ev

activation energy in the devolatilization model

 Fvol

initial mass fraction of volatiles

Fvol0

mass fraction of volatiles given through proximate analysis

gi

the i th direction gravity acceleration

He

total enthalpy

H evol ,k

enthalpy of specie k in the volatiles

3 / 36

ACCEPTED MANUSCRIPT H eCO (T )

enthalpy of CO at the gas temperature

H eO2 (T )

enthalpy of O2 at the gas temperature

H ef

enthalpy of fuel stream at adiabatic condition

H eox

enthalpy of oxidizer stream at adiabatic condition

K DIFF

diffusion rate term

K KIN

kinetic rate term

Le

Lewis number

mp

instantaneous mass of coal particle

m 0p

initial mass of coal particle

mchar

instantaneous mass of char

mvol

instantaneous mass of volatiles

mvol ,k

instantaneous mass of specie k in the volatiles

M ox

mass of gas originating from the oxidizer

M pro

mass of gas originating from the char oxidation products

M vol

mass of gas originating from the volatiles

Nu

Nusselt number

n

total particle number in local cell

P

static pressure

Pcg

parameter used to describe char-oxidation stage

pO2

partial pressure of O2

Pr

Prandtl number

R

universal gas constant

4 / 36

ACCEPTED MANUSCRIPT Re p

particle Reynolds number

Q

factor used to consider the high particle heating rate

Qchar

heat release in the char conversion process

QC

reaction heat per unit mass of char oxidation products

Qvol ,k

latent heat of specie k in the volatiles

S x

interphase coupling source term

Sr

energy transfer during the process of devolatilization and char-oxidation

T

gas temperature

Tp

particle temperature

T0ox

initial temperature of oxidizer

T0 fuel

initial temperature of fuel

ui

the i th direction velocity of gas

u pi

the i th direction velocity of particle

urel

relative velocity between gas phase and solid phase

V

volume of grid cell

W

mean molecular weight of the mixture

Wk

molecular weight of species k

Yk

mass fraction of species k

Yvol ,k

mass fraction of species k in the volatiles

Ychar ,k

mass fraction of species k in the char-oxidation products

Y fuel ,k

species boundary condition of the fuel side in flamelet equation

Z

mixture fraction of coal particle

5 / 36

ACCEPTED MANUSCRIPT Greek symbols



NO factor in the progress variable



the ratio of N 2 to O2 for the air



gas phase density

p

coal particle density

g

dynamic viscosity

 ij

Kronecker delta function



heat conductivity

 k

reaction rate of species k

d

particle relaxation time

 st

mass stoichiometric coefficient of oxygen required for char-oxidation



a small positive quantity

H e

enthalpy defect

H echar

change of enthalpy in the gas phase due to char-oxidation

Tchar

temperature variation due to char oxidation

T fuel

temperature variation of fuel stream due to heat losses

Tox

temperature variation of oxidizer stream due to heat losses



scalar dissipation rate



flamelet solutions including all thermo-chemical states



the ratio of the heat release absorbed by the environment

Abbreviations CFD

computational fluid dynamics

6 / 36

ACCEPTED MANUSCRIPT CPD

chemical percolation devolatilization

DC

detailed chemistry

FGM

flamelet generated manifolds

FPV

flamelet/progress variable

IFRF

international flame research foundation

LES

large eddy simulation

PCC

pulverized coal combustion

PDF

probability density function

PSIC

Particle-Source-In-Cell

S-CO2

supercritical carbon dioxide

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ACCEPTED MANUSCRIPT

1. Introduction In recent years, supercritical carbon dioxide (S-CO2) cycle, considered as a promising technology, has caught extensive interests due to its high cycle efficiency, low cost and system compactness, and thus has great potential to be applied in coal-fired power plant [1-7]. It is well known that pulverized coal combustion (PCC) is an important way of energy conversion in coal-fired power plant. However, large quantities of pollutants are released during the process of PCC, which inevitably increases the environment burden and causes health problems. Nowadays, the standards of pollutants emission are more and more stringent in all coal-fired power systems [8]. Therefore, it is necessary to conduct a fundamental research on pollutants formation in PCC to provide guidance for the design of S-CO2 boiler. Due to minor fraction and extremely high temperature in the PCC field, pollutants are difficult to be accurately measured. As an alternative, computational combustion is considered as an effective tool to obtain instantaneous distributions of gas temperature and chemical species in detail [9-14], which is particularly useful for investigating the pollutants formation. To describe pollutants formation, resolving transport equations of all species with detailed chemistry reaction kinetics is desired. However, it is unrealistic due to extremely high computational cost when applied to a large scale simulation. As a result, numerical investigations of pollutants formation in PCC with simplified chemistry have been conducted in the recent years. It is found that the NOx formation in the coal-fired boilers is strongly influenced by the coal type, particle size, combustion technology and operation conditions [8], which makes the prediction of NOx formation very challenging. Since the NOx emitted from PCC consists mostly of NO, much attention has been paid to the NO prediction. Kurose et al. [15] utilized a two-step global chemical reaction mechanism to predict the gaseous volatiles 8 / 36

ACCEPTED MANUSCRIPT combustion in PCC field which was generated by a real low-NOx burner. The NO formation and reduction models were applied in a post-processing way. Muto et al. [16] applied a global chemical mechanism to simulate a laboratory-scale pulverized coal flame produced with a triple stream burner in the context of large eddy simulation (LES). The existing NO formation and reduction models were incorporated to investigate the NO concentration in different oxy-fuel conditions, and it was found that O2 concentration and equivalence ratio had a great impact on the variation of NO concentration. Hashimoto et al. [17] assessed the ability of three fuel NO formation models by predicting NO formation in the configuration of a 760 kW test furnace, in which a global chemical mechanism was used for the volatiles combustion. Du et al. [18] numerically evaluated a modified air staging technology to reduce NO formation in a 600 MW wall-fired boiler with a 4-step reaction mechanism for the volatiles combustion. In these studies, gas phase reaction between volatiles and oxidizer was mostly described by global reaction mechanism to reduce computational cost, and the prediction of NO formation was conducted by the additional NO formation and reduction models. However, the NO formation and reduction models were all formulated as functions of the major species. As only simplified chemical reaction mechanism was used, the prediction accuracy of major species was not guaranteed. What is more, some minor species in the NO models could not be obtained in the PCC field, which were approximated with the quasi-steady-state assumption. Unavoidably, the prediction error was also caused by this treatment [15, 17]. Therefore, more advanced combustion models with detailed chemistry reaction mechanism are required to accurately predict NO formation. Flamelet model is such an advanced model which considers detailed chemistry reaction mechanism by only solving transport equations of several representative trajectory variables. 9 / 36

ACCEPTED MANUSCRIPT To date, flamelet model has been successfully applied to gaseous combustion and spray combustion [19-23]. In the recent years, it has also been extended to predict the process of PCC [12, 13, 24-28]. Vascellari et al. [12] developed an extended flamelet/progress variable (FPV) model to study the process of single coal particle ignition, and the flame structure could be accurately reproduced. Watanabe et al. [24] applied an extended FPV model [20] to the process of PCC, in which both devolatilization and char combustion were considered simultaneously. Good agreements of gas temperature and major species mass fractions between the extended FPV model results and detailed chemistry simulation results proved the validity of the extended FPV model. The variation of moisture was further considered [25], and the unsteady processes in PCC were selected to evaluate the model. Overall agreements between the model results and the experimental data were obtained. Rieth et al. [26] proposed a flamelet model with two mixture fractions especially for PCC in the framework of LES, in which the mixing between the volatiles and oxidizer was treated separately from the mixing between the char off gases and oxidizer. The performance of the model was evaluated on a semi-industrial international flame research foundation (IFRF) coal furnace, and the predicted values were in overall good agreement with the experiment data. In our previous work, we have developed an extended FPV model with LES to investigate the process of PCC, in which devolatilization, char oxidation as well as radiation were all considered [13]. A pulverized coal jet flame of laboratory scale was used to validate the model, and the experimental data were well predicted. It should be noted that all abovementioned flamelet model studies on coal combustion have been focused on the predictions of temperature, velocity, major species mass fractions and combustion process, while the investigation of major pollutant species NO is not taken into account. 10 / 36

ACCEPTED MANUSCRIPT The conventional flamelet model based on fast chemistry assumption (Damköhler number is larger than 1 [29]) has been proven to be able to capture major species evolution with short chemical time scale. Nevertheless, the chemical time scale of NO formation is so long that the NO evolution is still in progress when major species have reached equilibrium states. To account for the long chemical time scale for NO prediction, some efforts have been made to improve the conventional flamelet model in gaseous combustion. van Oijen et al. [30] proposed a novel progress variable definition to predict the NO formation based on flamelet generated manifolds (FGM) method. Ketelheun et al. [31] introduced an additional transport equation of NO in the FGM approach, in which the NO source term was extracted from the flamelet library. Ihme et al. [32] also solved an additional NO transport equation in the FPV context. The source term of NO was divided into the production and consumption terms, in which the consumption term was modeled with the local NO mass fraction. Boucher et al. [33] proposed a new method for flamelet table generation to account for the mixing state of long chemical time scale, in which a plug flow calculation and the premixed flamelet calculation were performed separately. Although remarkable progress has been made for NO prediction in gaseous combustion, there is rare study on investigation of NO formation in the process of PCC with flamelet model. Following the work of van Oijen et al. [30] in the gaseous combustion, the objective of this work is to extend our previous study [13] to predict the NO formation in pulverized coal flame by means of redefining the progress variable as a first attempt. The performance of the extended FPV model is evaluated through an a priori analysis, which has been widely used in previous studies [12, 28, 34, 35]. In the a priori analysis, detailed chemistry simulations are conducted to provide reference solutions. The trajectory variables are then 11 / 36

ACCEPTED MANUSCRIPT obtained from the above reference solutions with detailed chemistry and are used to access a pre-computed flamelet library. Finally, the thermo-chemical values extracted from the flamelet library are compared with the corresponding values in reference solutions. In addition, the effects of operating conditions (i.e., strain rate and initial temperature) on the performance of the flamelet model are investigated to further validate the developed model.

2. Mathematical description In the detailed chemistry simulations, the two-phase reactive flow is considered to be operated in the variable density low-Mach number regime. The governing equations for gas phase are introduced first. The governing equations for solid phase and the sub-models for coal combustion are presented subsequently. The interphase coupling source terms are provided in the end of this section.

2.1. Governing equations for gas phase For gas phase, the instantaneous conservation equations of mass, momentum, total enthalpy as well as chemical species can be formulated as [35]     u j     Sm , t x j

(1)

   ui     ui u j  u  P    ui u j  2  g      ij k   Sui ,   g    t x j xi x j   x j xi  3 xk 

(2)

   H e     u j H e  P     t x j t x j

(3)

  Yk     u jYk     t x j x j

 H e     DH e   S  H e ,  x j  

 Y    Dk k    k  S k , x j  

(4)

where  denotes the gas phase density which can be obtained from the ideal gas state equation written as P  

R T . Here P is the static pressure, R is the universal gas W

constant, W represents the mean molecular weight of the mixture and T denotes the gas 12 / 36

ACCEPTED MANUSCRIPT temperature. ui represents the i th direction velocity of gas, H e denotes the total enthalpy,

Yk is the mass fraction of species k ,  g is the dynamic viscosity,  ij denotes the Kronecker delta function, DH e

denotes the gaseous thermal diffusivity calculated with

DH e   /  C pg , where  is the heat conductivity and C pg

denotes the specific heat

capacity of gas. Dk represents the mass diffusivity of species k and is equal to DH e with the assumption of Le  1 [25, 34].  k denotes the reaction rate of species k , which can be determined from the detailed reaction mechanism GRI-Mech 3.0 [36]. S m , Sui , S H e and

S k represent the interphase coupling source terms, which will be described in Section 2.3.

2.2. Governing equations for solid phase In the present work, the pulverized coal particle consists of ash, volatiles and fixed carbon, among which ash is considered to be inert. Moisture in coal is added to ash due to its little amount. Coal devolatilization and char-oxidation are considered in the process of PCC. 2.2.1 Conservation equations The governing equations of mass, momentum as well as energy for each coal particle are formulated as dm p



dt

m p du pi dt

dmchar dmvol ,  dt dt



3CD   ui  u pi  m purel  m p gi , 4d p  p

m p C p p dTp dt

where

mp

(5)



m p C pg Nu  T  Tp  3Pr   d

(6)

    Sr , 

(7)

represents the instantaneous mass of coal particle,

mchar

represents the

instantaneous mass of char, and mvol represents the instantaneous mass of volatiles. CD denotes the drag coefficient calculated by Wen-Yu’s formulation [37] and d p represents the 13 / 36

ACCEPTED MANUSCRIPT coal particle diameter. u pi is the i th direction velocity of particle,  p denotes the coal particle density, and urel denotes the relative velocity between gas phase and solid phase. C p p denotes the specific heat capacity of particle. gi denotes the i th direction gravity

acceleration. T represents the gas temperature, and Tp is the particle temperature. Nu represents

the

Nusselt

number

obtained

from

Ranz-Marshall

model

with

1/3 Nu  2  0.552 Re1/2 [38]. Re p represents the particle Reynolds number. Pr denotes p Pr

the Prandtl number.  d is the particle relaxation time written as  d   p d p2 / (18 g ) . Sr is the energy transfer during the process of devolatilization and char-oxidation, which can be dm dm written as Sr   ( vol ,k Qvol ,k )  1    ( char Qchar ) . mvol ,k is the instantaneous mass of dt dt k

specie k in the volatiles, Qvol ,k represents the latent heat of specie k in the volatiles and is neglected in the present work, and Qchar represents the heat release in the char conversion process.  denotes the ratio of the heat release absorbed by the environment. The radiation heat transfer is extremely complicated in the pulverized coal flames and it is difficult to characterize the radiation effect appropriately. At a first step, the radiation heat transfer is neglected in the present work. 2.2.2 Devolatilization model The classical single-step devolatilization model [39] is employed to describe devolatilization of the coal particles, which is written as dmvol *  K vol 1  Fvol  m0p  m p  , dt

(8)

 E K vol  Av exp   v  RT p 

(9)

  , 

 where m0p denotes the initial mass of coal particle. Fvol denotes the initial mass fraction of  volatiles, which is calculated as Fvol  Fvol0  Q . Here the mass fraction of volatiles Fvol0 is

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ACCEPTED MANUSCRIPT given through the proximate analysis, and the factor Q is used to consider the volatiles increase due to high particle heating rate with a value of 1.52 [35]. The pre-exponential factor

Av and the activation energy Ev are determined by the chemical percolation devolatilization (CPD) model [40] using the same type of coal. The final values of Av and Ev are set as Av  4.474 103 s 1 and Ev  1.9188 104 J /mol respectively. These parameters have been

extensively evaluated in our previous studies [13, 34, 41]. The gas phase reaction of volatile matter is quite crucial in PCC, but the exact components of volatiles are still open issues. Based on our previous studies [13, 34, 41], the volatiles are postulated as gas mixture consisting of CH4, C2H2 and CO for the identical coal type. Here Yvol ,k

is introduced to represent the mass fraction of species k

calculation of

Yvol ,k

in the volatiles. The

needs to satisfy the mass conservation and low heating value

conservation according to the proximate and ultimate analyses of the coal [42]. 2.2.3. Char-oxidation model The classical kinetic/diffusion surface reaction model developed by Baum and Street [43] is used to describe the char-oxidation. The char-oxidation process is formulated as C S   0.5  O 2   N 2   CO +0.5 N 2 .

(10)

To ensure mass conservation, N2 is included and  is set to 3.76 for the air. Then, the mass variation of char-oxidation can be obtained from

dmchar K DIFF K KIN   d p2 pO2 , dt K DIFF  K KIN K DIFF

5.06 1012  Tp  T     dp  2 

 E K KIN  Ac exp   c  RT p 

(11)

0.75

,

(12)

  , 

(13)

15 / 36

ACCEPTED MANUSCRIPT where pO2 denotes the partial pressure of O2, K DIFF represents the diffusion rate term, and

K KIN represents the kinetic rate term. The pre-exponential factor Ac is set to 1.1102 s 1 and the activation energy Ec is set to 5.0 104 J/mol [42].

2.3. Source terms The two-way coupling source terms between two phases are described through the Particle-Source-In-Cell (PSIC) technique [44]. The source terms of Eqs. (1)-(4) are written as n

dm p ,i



1 Sui   V

 d  m p u pi   j  dt  ,  j

i

dt



1 V

n

1 S m   V

 dmvol   dmchar      ,  dt i  dt i 

  i

(14)

n

(15)

1 n  m p C pg Nu T  Tp    H evol ,k dmvol ,k   H echar dmchar      S  He        ,   k V i  3Pr d dt dt  i   i i  

S k

 1 n  dmvol  for k  volatiles  V   dt   i  i  .   1 n  dmchar   for k  char     V dt i i   for k  others 0

(16)

(17)

Here n denotes the total particle number in a local cell, V represents the volume of the grid cell, and the summation index i loops over each particle within the local cell. H evol ,k is the enthalpy of specie k in the volatiles, and H echar denotes the change of enthalpy in the gas phase

due

to

char-oxidation,

which

is

formulated

as

H echar    st  1 H eCO (T )   st H eO2 (T )   Qchar . Here  st represents the mass stoichiometric coefficient of oxygen required for char-oxidation (  st  1.33 ).

H eCO (T ) and H eO2 (T )

represent the enthalpies of CO and O 2 at the gas temperature T, respectively. It is assumed that the temperature of char-off gas CO is equal to the temperature of gas surrounding the coal particle. 16 / 36

ACCEPTED MANUSCRIPT

3. FPV model for NO prediction in PCC In this section, the FPV model for PCC [13] is further extended to predict the NO mass fraction. The definitions of mixture fraction and progress variable are described first. Then the species and temperature boundary conditions for solving the one-dimensional flamelet equations are presented. Furthermore, the parameterization process of flamelet library is introduced. The procedure of the a priori analysis is described. The governing equations of the extended flamelet model are described in the end. 3.1. Definitions of mixture fraction and progress variable Following previous studies [13, 45], the mixture fraction of coal particle is defined as: Z=

M vol  M pro M vol  M pro  M ox

,

(18)

where M vol represents the mass of gas originating from the volatiles, M pro represents the mass of gas originating from the char oxidation products, and M ox represents the mass of gas originating from the oxidizer. The transport equation of mixture fraction of coal particle can be written as

   Z    u j Z     t x j x j

 Z     DZ   SZ , x j  

(19)

where DZ represents the diffusivity of coal particle mixture fraction, which can be obtained using the Le=1 assumption [13, 24, 25]. S Z denotes the interphase coupling source term, given by

WO  WN2 dm  1 n  dm S Z =    vol  char 1  0.5 2 V i  dt dt  WC

  . i

(20)

Here WO2 denotes the molecular weight of O 2 , WN2 represents the molecular weight of

N 2 , and WC represents the molecular weight of C . 17 / 36

ACCEPTED MANUSCRIPT The FPV model has been demonstrated to be efficient to predict the evolution of major species in the process of PCC [12, 13, 24, 25, 34, 41, 45]. In the conventional FPV model, the progress variable typically consists of a linear combination of major reaction products to reflect the evolution of combustion process from the non-reacting state to equilibrium state. For example, one of the conventional progress variables for PCC is defined as [13, 34, 45], C =YCO2  YH2O  YH2 .

(21)

However, the minor species such as NO in slow chemical reaction process cannot be correctly predicted as they are not incorporated in the conventional progress variable. To overcome this issue, the NO mass fraction is also included to define the progress variable to represent the slow chemical reaction process following the work of van Oijen et al. [30] in gaseous combustion. As a result, the new progress variable is defined as C =YCO2  YH2O  YH2   YNO .

(22)

Considering that the NO mass fraction is relatively small compared with the amount of major species, the NO mass fraction is thus multiplied by a large coefficient  in Eq. (22) so that the contribution of NO in progress variable is comparable to other major species [30, 46]. To examine the effect of the weight of NO mass fraction on prediction accuracy, four different values of 

are investigated, corresponding to 0, 50, 100 and 150, respectively. For

simplicity, the extended FPV models with different definitions of progress variable are referred to as model 1-4 in the following sections. 3.2. Boundary conditions for flamelet equations Since the char-oxidation products (i.e. CO and N2) are used to define the mixture fraction of coal particle according to Eq. (18), the mass fraction of species k in the char-oxidation products can thus be written as [13, 24, 25, 41, 45] 18 / 36

ACCEPTED MANUSCRIPT

Ychar ,k

WCO  W  0.5 W N2  CO    0.5 WN2 W  0.5 W N2  CO  0 

for k  CO

,

for k  N 2

(23)

for k  others

where WCO represents the molecular weight of CO. The species boundary conditions on the fuel side for the flamelet equations are given by

Y fuel ,k 

M volYvol ,k  M proYchar ,k M vol  M pro



Yvol ,k  Pcg Ychar ,k 1  Pcg

.

(24)

Here the new parameter Pcg [13, 41, 45] is defined as Pcg  M pro / ( M vol   ) ,

(25)

where the parameter  is defined as a small positive quantity to guarantee that Pcg is well defined during the whole process of PCC. The newly introduced parameter Pcg can roughly represent the coal burning stage and reduce the dimension of the flamelet library [13, 41, 45]. It remains zero at the whole devolatilization stage, while becomes positive with the beginning of char oxidation. The parameter Pcg is solved instantaneously based on Eq. (25) in the detailed chemistry simulation. To consider the char oxidation effect, temperature boundary condition on the fuel side of the flamelet equations is adjusted by [13, 41, 45]

Tchar  where QC

 QC M pro

C p fuel  M vol  M pro 



 QC Pcg

C p fuel 1  Pcg 

,

(26)

denotes reaction heat per unit mass of char oxidation products, and C p fuel

represents the specific heat capacity of fuel. An additional manifold (i.e., enthalpy defect

H e ) [47] is introduced to consider the heat loss in the combustion system, which is written as

19 / 36

ACCEPTED MANUSCRIPT H e  H e   H eox  Z  H ef  H eox   ,

(27)

where H ef and H eox are referred to as the enthalpy of fuel stream and oxidizer stream at adiabatic condition, respectively. To consider the enthalpy defect in flamelet library, the temperature boundary conditions in the flamelet equations are adjusted by [48, 49]

T fuel  H e / C p fuel , Tox  H e / C pox ,

(28)

where C pox represents the specific heat capacity of oxidizer. Thus, the temperature boundary conditions on both fuel stream side and oxidizer stream side in the flamelet equations can be written as [13, 41, 45] H e  T0ox  C pox  T   T  H e   QC Pcg  0 fuel C p fuel C p 1  Pcg  fuel 

for Z=0

,

(29)

for Z=1

where T0ox represents the initial temperature of oxidizer, and T0 fuel represents the initial temperature of fuel. 3.3. Flamelet solutions and FPV library Based on the above boundary conditions, the flamelet solutions can be achieved by solving the steady one-dimensional diffusion flamelet equations considering various values of Pcg , enthalpy defects H e as well as scalar dissipation rates  . In the present work, the

solutions of flamelet equations are calculated using the FlameMaster code [50], and the GRI-Mech 3.0 mechanism [36] is applied for chemical reaction. Fig. 1 presents the flamelet solutions of NO mass fraction at various conditions. With the evolution of char surface reaction indicated by Pcg , the mass fraction of NO increases with a peak at a little higher mixture fraction. For a larger enthalpy defect, the mass fraction of NO decreases, as shown in Fig. 1(a). Fig. 1(b) shows the flamelet solutions of NO mass fraction at Pcg =0 and H e =0 20 / 36

ACCEPTED MANUSCRIPT 1 for various values of  ranging from 0.001 s to the extinction limit. It is found that the

NO mass fraction decreases with the increasing of the scalar dissipation rate, which can be attributed to the stretch of reaction zone. It is noted that the scalar dissipation rate is replaced by the progress variable during creating the flamelet library in the FPV approach. This is followed in the present work.

(a) (b) Fig. 1. (a) Flamelet solutions of NO mass fraction against mixture fraction Z at  =1 s 1 considering various values of Pcg and H e (b) Flamelet solutions of NO mass fraction against mixture fraction Z at Pcg=0 and H e =0 considering various values of  .

Therefore, the flamelet solutions  which include all thermo-chemical states can be represented by the following trajectory variables Pcg , H e , Z and C using the FPV method [20], and a flamelet library can be formulated as

 =  Pcg , H e , Z , C  .

(30)

The validity of this extended FPV model is evaluated through the a priori analysis. The procedures of the a priori analysis are summarized as follows. First, reference solutions are obtained by detailed chemistry simulation, where the transport equations of mass, momentum, all species, total enthalpy as well as coal particle mixture fraction are directly calculated with detailed reaction mechanism. Then, the trajectory variables are obtained from the reference solutions. The trajectory variables are subsequently used to access the thermo-chemical data in a pre-computed flamelet library. In the end, the thermo-chemical data extracted from the 21 / 36

ACCEPTED MANUSCRIPT flamelet library are compared with the corresponding values obtained in the reference solutions. The a priori analysis can assess the suitability between the trajectory variables and the pre-computed flamelet library, which is crucial to correctly describe the thermo-chemical state. Although a priori analysis is the focus of the present work, here we outline the extended FPV model for practical applications in the sense of a posteriori analysis. For practical applications, the governing equations of trajectory variables are directly solved in the flow field. The governing equation of coal particle mixture fraction is the same as Eq. (19), which describes the mixing state of fuel stream and oxidizer stream. The governing equation of progress variable is solved to describe the chemical reaction process, written as

  C    u jC     t x j x j

 C     DC   S C , x j  

(31)

where DC represents the diffusivity of progress variable, obtained based on the Le=1 assumption. SC denotes the source term of progress variable, which can be obtained from the flamelet library. In addition, the governing equation of total enthalpy is solved to describe the heat transfer between the gas phase and solid phase, which has the same formulation as Eq. (3) in the detailed chemistry simulation. The enthalpy defect H e is then calculated by Eq. (27). The new parameter Pcg is solved instantaneously and formulated as Eq. (25), which reflects the burning stage of the coal particle. The trajectory variables calculated with the governing equations mentioned above are then used to access the flamelet library to obtain the thermo-chemical quantities. The flamelet equation boundary conditions and the flamelet library formulation are identical with those introduced in the above sections. The presumed probability density function (PDF) method [13] can be applied to account for the 22 / 36

ACCEPTED MANUSCRIPT turbulence-chemistry interaction in PCC. Note that the assessment of the extended flamelet model for practical applications is beyond the scope of the present work, which will be investigated in future study.

4. Computational configuration and numerical schemes The validity of the extended FPV model is assessed in the classic configuration of a laminar counterflow pulverized coal flame [34] . The symmetric configuration consists of two opposed injection ports, and the length of each injection port is 0.02 m, which is identical to the distance between the two ports. A square domain is thus formed as schematically presented in Fig. 2. The coal particles transported by the air stream enter from the upper port, while the pure air stream enters from the lower port. The initial velocity of coal particle is the

Fig. 2. Schematic diagram of the computational configuration.

same as that of the transport air, and each coal particle diameter is uniformly set as 40  m . The Newland bituminous type coal [51] is used and the data of proximate and ultimate analyses are listed in Table 1. The devolatilization temperature of coal particle is set to be 600 K according to Ref. [43]. Different operating conditions (i.e., strain rate and initial temperature) discussed in the following study are summarized in Table 2. As a comparison, a pure gas flame of volatiles (i.e. Case a) using the same operating conditions as Case c is also simulated. In the pure volatiles flame, the gas mixture with the same compositions (i.e., CH4, 23 / 36

ACCEPTED MANUSCRIPT CO and C2H2) as the volatiles enters from the upper port, while pure air enters from the lower port. Table 1. Properties of the Newland bituminous type coal Proximate analysis (wt. %) mattera

Volatile Fixed carbona Asha Moistureb Low heating valuea High heating valuea

26.9 57.9 15.2 2.6 28.1MJ/kg 29.1MJ/kg

Ultimate analysis (wt. %) Carbona Hydrogena Oxygena Nitrogena Total sulfura Combustible sulfura

71.90 4.40 6.53 1.50 0.44 0.39

aDry bAs

basis received Table 2. Operating conditions of the different cases. Case

a (pure gas flame of volatiles) b c d e f

Strain rate (s-1) 100 50 100 150 100 100

Initial temperature (K) 600 600 600 600 1000 1400

In the present study, both the detailed chemistry simulations and the a priori tests are conducted using the solvers based on the open source computational fluid dynamics (CFD) toolbox OpenFOAM 2.3.0 [52]. The validity of the solvers has been widely evaluated in our previous works [13, 41, 45]. The PIMPLE algorithm [52] is employed to achieve the coupling between the pressure field and velocity field. A second-order implicit scheme is employed to the time integration terms, and a second-order central differencing scheme is applied to the spatial integration terms. The computational domain is discretized with 300  300 uniform structured grid points for all cases. To check the grid resolution, Case c is also conducted with a fine mesh resolution of 350  350 , and the results are compared with those from the coarse mesh, as presented in Fig. 3. It shows that the numerical results with the current coarse grid

24 / 36

ACCEPTED MANUSCRIPT points are almost identical to those with a fine mesh resolution, which ensures the grid-independency of detailed chemical simulation results in the present work.

Fig. 3. The instantaneous profiles of CH4 mass fraction, CO mass fraction, NO mass fraction, H2O mass fraction and gas temperature along the central axis for Case c obtained with the coarse and fine mesh resolutions.

5. Results and discussions 5.1. Temperature and NO characteristics of the counterflow flames Before evaluating the performance of the extended FPV model, the instantaneous contours of gas temperature and NO mass fraction in laminar counterflow pulverized coal flame (i.e., Case c) are briefly described. As a comparison, the pure gas flame of volatiles (i.e., Case a) is also presented, as shown in Fig. 4. The instantaneous distributions of coal particles colored by volatiles fraction are also included. It is found that the peak gas temperature of central axis is 2110 K at y  10 mm in the pure gas flame of volatiles. While the peak gas temperature of central axis is 2013 K at y  5 mm in the pulverized coal flame, which is almost 100 K lower than the former. This might be attributed to the “particle cooling effect” [53]. The pure volatiles combustion is occurred in the middle of the computational domain, while the region of pulverized coal flame is closer to the oxidizer stream inlet due to the coal particle inertia. In addition, a large amount of NO is produced in the high temperature region, which shows that gas temperature plays an important role in the process of NO formation. 25 / 36

ACCEPTED MANUSCRIPT Compared to the pure gas flame of volatiles, the high temperature region and high NO mass fraction region in the pulverized coal flame are more narrowed. The maximum of NO mass fraction in the pulverized coal flame is also lower than that in the pure gas flame of volatiles, which can be attributed to the difference of gas temperature between the two flames.

Fig. 4. The instantaneous contours of gas temperature and NO mass fraction for Case a (the top row) and Case c (the bottom row). The instantaneous distributions of coal particles colored by the fraction of volatiles for Case c.

5.2. A priori analysis The validity of the extended FPV model for NO prediction in pulverized coal flame is investigated through the a priori analysis in this subsection. The instantaneous values of CH4 mass fraction, CO mass fraction, H2O mass fraction as well as gas temperature along the central axis are compared between the reference solutions and the a priori results, which are presented in Fig. 5. The left panel of Fig. 5 corresponds to the pure volatiles flame, while the right panel corresponds to the pulverized coal flame. The CH4 mass fraction is selected since 26 / 36

ACCEPTED MANUSCRIPT

(a)

(b)

(c)

(d) Fig. 5. Comparisons of the instantaneous profiles between the reference solutions obtained from the detailed chemistry (DC) simulations and the a priori results predicted with different models (model 1-4) along the central axis for Case a (left) and Case c (right): (a) CH4 mass fraction; (b) CO mass fraction; (c) H2O mass fraction; (d) gas temperature.

it is one of the postulated species of volatiles, and the CO mass fraction is an important intermediate species during the process of PCC. The H2O mass fraction is a major final reaction product in the PCC field. The gas temperature is also a key quantity related to NO formation. It can be observed that the a priori results obtained with the four models agree well with the reference values in both the pure gas flame of volatiles and pulverized coal 27 / 36

ACCEPTED MANUSCRIPT flame. The addition of different proportions of NO mass fraction to progress variable has little impact on the prediction. Fig. 6 illustrates the comparisons of NO mass fraction between the a priori results predicted with the four models and the detailed chemistry solutions along the central axis. It is found that NO mass fractions in both the pure volatiles flame and pulverized coal flame are significantly over-predicted by model 1, where the NO mass fraction is not incorporated in the progress variable. Specifically, for the pure volatiles flame, the maximum 3 value of NO mass fraction predicted by model 1 is 1.45 10 at the location y  9.20 mm ,

which deviates considerably from the reference result ( 2.85 10

4

at the location

y  9.93 mm ). For the pulverized coal flame, a significant difference between the predicted value ( 7.7110

4

4 at the location y  4.60 mm ) and the reference result ( 1.80 10 at the

location y  4.93 mm ) is also observed. While the variation trend of NO mass fraction can be overall correctly predicted by model 2, in which the NO mass fraction (  =50) is included. For the pure volatiles flame, the position of peak value of NO mass fraction ( y  9.93 mm ) is identical with the reference solution ( y  9.93 mm ). Compared to that predicted by model 1 3 4 ( 1.45 10 ), the maximum value of NO mass fraction ( 3.64 10 ) is closer to the reference 4

value ( 2.85 10 ). For the pulverized coal flame, compared to that predicted by model 1 ( 7.7110

4

4 at the location y  4.60 mm ), a considerable improvement ( 2.87 10 at the

location y  5.07 mm ) can be obtained by model 2. As the value of  is increased to 100 in model 3, the predicted values of NO mass fraction are more accurate compared with those predicted by model 2 for both pure volatiles flame and pulverized coal flame. As the value of

 is set to 150 in model 4, the predicted values are even better. This is related to the fact that in the conventional FPV model, the gradient of NO mass fraction against progress variable is extremely high in the flamelet table. Thus, large interpolation error is produced during the 28 / 36

ACCEPTED MANUSCRIPT table extraction process, which may result in the incorrect prediction of NO mass fraction. As the addition of NO mass fraction to the progress variable increases, the gradient of NO mass fraction is reduced, so that the mapping becomes smoother and the reduced interpolation error is expected. As a result, the prediction accuracy of NO mass fraction is improved.

Fig. 6. Comparisons of the instantaneous profiles of NO mass fraction between the reference solutions obtained from detailed chemistry (DC) simulation and the a priori results predicted with different models (model 1-4) along the central axis for Case a (left) and Case c (right).

Based on the above results, it can be concluded that for both the pure gas flame of volatiles and pulverized coal flame, the extended FPV model with the addition of a certain proportion of NO mass fraction to progress variable not only has the ability to predict the gas temperature and major species (i.e., CH4, CO and H2O) but also has a significant improvement in capturing the variation trend of NO mass fraction and the position of peak value. As the proportion of NO mass fraction increases, the predicted values of major species and gas temperature are almost identical with the reference values, and the predicted values of NO mass fraction are closer to the reference values. These results demonstrate that redefining the progress variable is really an effective method for NO prediction in flamelet modeling. It is meaningful to extend the FPV model for pulverized coal combustion to predict NO formation.

5.3. The effects of strain rate and initial temperature 29 / 36

ACCEPTED MANUSCRIPT The performance of the extended FPV model for NO prediction at various strain rates is investigated in this subsection at first. The strain rates for three cases (i.e. Case b, c and d) studied below are set as 50 s-1, 100 s-1 and 150 s-1, respectively, and other settings keep the same. Similar to Section 5.2, the a priori results of NO mass fraction predicted with the extended FPV model are compared to the corresponding values of the reference solutions along the central axis for the three cases, as shown in Fig. 7. For simplicity, here only model 3 is evaluated as a representative of the extended FPV model. For comparison, the a priori results predicted with the conventional FPV model (i.e., model 1) are also included. It is clear that the a priori results of NO mass fraction from model 3 are in generally good agreement with the reference solutions in the whole region for all three cases, while the discrepancy between the a priori results from model 1 and the reference values is significant. The variation trend of NO mass fraction can also be predicted by model 3, although slight deviations can be observed. Specifically, for Case b, the maximum of NO mass fraction 4

4

predicted with model 3 ( 3.07 10 ) is closer to the reference value ( 2.38 10 ), while model 3 1 gives an obvious overestimation ( 1.22 10 ). The position of peak value obtained with

model 3 ( y  3.67 mm ) is identical with the reference result ( y  3.67 mm ) which is more accurate than that obtained with model 1 ( y  2.87 mm ). Similar conclusions can be made from Case c and Case d. Compared with the conventional FPV model predictions, the deviations of maximum NO mass fraction predicted with the extended FPV model are decreased by 92.97%, 86.80% and 95.14% for the three different strain rate cases. The overall good agreement proves that the extended FPV model can significantly improve the prediction accuracy of NO mass fraction in pulverized coal flame under various strain rate conditions. The performance of the extended FPV model at various initial temperatures is then 30 / 36

ACCEPTED MANUSCRIPT investigated. The initial temperatures of air and coal particles for three cases (i.e., Case c, e and f) studied below are set as 600 K, 1000 K and 1400 K, respectively, and other settings

(a)

(b)

(c) Fig. 7. Comparisons of the instantaneous profiles of NO mass fraction between the reference solutions obtained from detailed chemistry (DC) simulations and the a priori results predicted with model 1 and model 3 along the central axis for three cases (i.e., (a) Case b, (b) Case c, (c) Case d) at different strain rates.

keep the same. As shown in Fig. 8, the instantaneous values of NO mass fraction predicted with the extended FPV model are compared to the reference solutions in the detailed chemistry simulations along the central axis for the three cases. Similarly, model 3 is evaluated as a representative of the extended FPV model. It is obvious that the a priori results of NO mass fraction obtained with model 3 are more accurate than those obtained with model 1 for all cases. Model 3 can capture both the variation trend of NO mass fraction and the position of maximum NO mass fraction, although a slight discrepancy still exists. For Case c, both the peak value and the corresponding value position predicted with model 3 ( 2.58 10 31 / 36

4

ACCEPTED MANUSCRIPT 4 at the location y  4.87 mm ) are much closer to the reference results ( 1.80 10 at the 4 location y  4.93 mm ) compared to those predicted with model 1 ( 7.7110 at the location

y  4.60 mm ). This is also true for other cases. Compared with the conventional FPV model

(a)

(b)

(c) Fig. 8. Comparisons of the instantaneous profiles of NO mass fraction between the reference solutions obtained from detailed chemistry (DC) simulations and the a priori results predicted with model 1 and model 3 along the central axis for three cases (i.e., (a) Case c, (b) Case e, (c) Case f) at different initial temperatures.

predictions, the deviations of maximum NO mass fraction predicted with the extended FPV model are decreased by 86.80%, 82.81% and 87.45% for the three different initial temperature cases. The overall good agreement between the a priori results predicted with model 3 and the reference results shows that the extended FPV model has the ability to improve the prediction accuracy of NO in pulverized coal flame under various initial temperature conditions.

6. Conclusions An extended flamelet/progress variable model for NO prediction in pulverized coal 32 / 36

ACCEPTED MANUSCRIPT flame is developed by redefining the progress variable in this work. The validity of the model is evaluated by means of the a priori analysis, and the sensitivity of progress variable definition on the prediction accuracy is examined. The effects of operating conditions (i.e., strain rate and initial temperature) on the performance of the extended FPV model are also investigated. The results of the a priori analysis indicate that the developed FPV model has good capability in predicting NO mass fraction in pulverized coal flames. Compared with the conventional FPV model, the extended FPV model shows better prediction accuracy with optimizing the definition of progress variable. This is also true for cases under various strain rates and initial temperatures.

Acknowledgements The study was supported by the National Key Research and Development Program of China (2017YFB0601805) and the National Natural Science Foundation of China (51390493).

References [1] Xu J, Sun E, Li M, Liu H, Zhu B. Key issues and solution strategies for supercritical carbon dioxide coal fired power plant. Energy 2018;157:227-46. [2] Sun E, Xu J, Li M, Liu G, Zhu B. Connected-top-bottom-cycle to cascade utilize flue gas heat for supercritical carbon dioxide coal fired power plant. Energy Conversion and Management 2018;172:138-54. [3] Le Moullec Y. Conceptual study of a high efficiency coal-fired power plant with CO2 capture using a supercritical CO2 Brayton cycle. Energy 2013;49:32-46. [4] Mecheri M, Le Moullec Y. Supercritical CO2 Brayton cycles for coal-fired power plants. Energy 2016;103:758-71. [5] Bai Z, Zhang G, Li Y, Xu G, Yang Y. A supercritical CO 2 Brayton cycle with a bleeding anabranch used in coal-fired power plants. Energy 2018;142:731-8. [6] Hanak DP, Manovic V. Calcium looping with supercritical CO2 cycle for decarbonisation of coal-fired power plant. Energy 2016;102:343-53. [7] Pioro I. Handbook of Generation IV Nuclear Reactors. Woodhead Publishing Series in Energy 2016. [8] Chang S, Zhuo J, Meng S, Qin S, Yao Q. Clean coal technologies in China: current status and future perspectives. Engineering 2016;2(4):447-59. [9] Franchetti BM, Cavallo Marincola F, Navarro-Martinez S, Kempf AM. Large Eddy simulation of a 33 / 36

ACCEPTED MANUSCRIPT [10]

[11] [12] [13] [14]

[15] [16] [17]

[18]

[19] [20] [21] [22] [23] [24] [25] [26] [27]

[28] [29]

pulverised coal jet flame. Proceedings of the Combustion Institute 2013;34(2):2419-26. Stein OT, Olenik G, Kronenburg A, Cavallo Marincola F, Franchetti BM, Kempf AM, et al. Towards Comprehensive Coal Combustion Modelling for LES. Flow, Turbulence and Combustion 2012;90(4):859-84. Olenik G, Stein OT, Kronenburg A. LES of swirl-stabilised pulverised coal combustion in IFRF furnace No. 1. Proceedings of the Combustion Institute 2015;35(3):2819-28. Vascellari M, Tufano GL, Stein OT, Kronenburg A, Kempf AM, Scholtissek A, et al. A flamelet/progress variable approach for modeling coal particle ignition. Fuel 2017;201:29-38. Wen X, Luo K, Jin H, Fan J. Large eddy simulation of piloted pulverised coal combustion using extended flamelet/progress variable model. Combustion Theory and Modelling 2017;21(5):925-53. Tufano GL, Stein OT, Kronenburg A, Frassoldati A, Faravelli T, Deng L, et al. Resolved flow simulation of pulverized coal particle devolatilization and ignition in air- and O 2 /CO 2 -atmospheres. Fuel 2016;186:285-92. Kurose R, Makino H, Suzuki A. Numerical analysis of pulverized coal combustion characteristics using advanced low-NOx burner. Fuel 2004;83(6):693-703. Muto M, Watanabe H, Kurose R, Komori S, Balusamy S, Hochgreb S. Large-eddy simulation of pulverized coal jet flame – Effect of oxygen concentration on NOx formation. Fuel 2015;142:152-63. Hashimoto N, Watanabe H, Kurose R, Shirai H. Effect of different fuel NO models on the prediction of NO formation/reduction characteristics in a pulverized coal combustion field. Energy 2017;118:47-59. Du Y, Wang Ca, Lv Q, Li D, Liu H, Che D. CFD investigation on combustion and NOx emission characteristics in a 600 MW wall-fired boiler under high temperature and strong reducing atmosphere. Applied Thermal Engineering 2017;126:407-18. Pitsch H, Peters. N. A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combustion and Flame 1998;114(1-2):26-40. Pierce CD, Moin P. Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. Journal of Fluid Mechanics 2004;504:73-97. Watanabe H, Kurose R, Hwang S, Akamatsu F. Characteristics of flamelets in spray flames formed in a laminar counterflow. Combustion and Flame 2007;148(4):234-48. Franzelli B, Fiorina B, Darabiha N. A tabulated chemistry method for spray combustion. Proceedings of the Combustion Institute 2013;34(1):1659-66. Olguin H, Gutheil E. Influence of evaporation on spray flamelet structures. Combustion and Flame 2014;161(4):987-96. Watanabe J, Yamamoto K. Flamelet model for pulverized coal combustion. Proceedings of the Combustion Institute 2015;35(2):2315-22. Watanabe J, Okazaki T, Yamamoto K, Kuramashi K, Baba A. Large-eddy simulation of pulverized coal combustion using flamelet model. Proceedings of the Combustion Institute 2017;36(2):2155-63. Rieth M, Proch F, Clements AG, Rabaçal M, Kempf AM. Highly resolved flamelet LES of a semi-industrial scale coal furnace. Proceedings of the Combustion Institute 2017;36(3):3371-9. Rieth M, Clements AG, Rabaçal M, Proch F, Stein OT, Kempf AM. Flamelet LES modeling of coal combustion with detailed devolatilization by directly coupled CPD. Proceedings of the Combustion Institute 2017;36(2):2181-9. Messig D, Vascellari M, Hasse C. Flame structure analysis and flamelet progress variable modelling of strained coal flames. Combustion Theory and Modelling 2017;21(4):700-21. Peters N. Laminar diffusion flamelet models in non-premixed turbulent combustion. Progress in 34 / 36

ACCEPTED MANUSCRIPT [30] [31] [32] [33]

[34] [35] [36] [37] [38] [39] [40]

[41] [42]

[43] [44] [45]

[46]

[47] [48] [49]

energy and combustion science 1984;10(3):319-39. Van Oijen J, De Goey L. Predicting no formation with flamelet generated manifolds. Proceedings of the 4th European Combustion Meeting. Vienna, Austria; 2009. Ketelheun A, Olbricht C, Hahn F, Janicka J. NO prediction in turbulent flames using LES/FGM with additional transport equations. Proceedings of the Combustion Institute 2011;33(2):2975-82. Ihme M, Pitsch H. Modeling of radiation and nitric oxide formation in turbulent nonpremixed flames using a flamelet/progress variable formulation. Physics of Fluids 2008;20:055110. Boucher A, Bertier N. A method to extend flamelet manifolds for prediction of NOx and long time scale species with tabulated chemistry. International Journal of Sustainable Aviation 2014;1(2):181-202. Wen X, Wang H, Luo Y, Luo K, Fan J. Evaluation of flamelet/progress variable model for laminar pulverized coal combustion. Physics of Fluids 2017;29(8):083607. Wen X, Luo K, Wang H, Luo Y, Fan J. Analysis of pulverized coal flame stabilized in a 3D laminar counterflow. Combustion and Flame 2018;189:106-25. Smith G, Golden D, Frenklach M, Moriarty N, Eiteneer B, Goldenberg M, et al. GRI-Mech version 3.0. 1999. Wen CY. Mechanics of fluidization. (Vol. 62, pp. 100-111). In Chem Eng Prog Symp Ser 1966;62:100-11. Ranz WE, Marshall WR. Evaporation from drops. Chem Eng Prog 1952;48(3):141-6. Badzioch S, Hawksley PG. Kinetics of thermal decomposition of pulverized coal particles. Industrial & Engineering Chemistry Process Design and Development 1970;9(4):521-30. Fletcher TH, Kerstein AR, Pugmire RJ, Solum MS, & Grant DM. Chemical percolation model for devolatilization. 3. Direct use of carbon-13 NMR data to predict effects of coal type. Energy & Fuels 1992;6(4):414-31. Wen X, Luo Y, Luo K, Jin H, Fan J. LES of pulverized coal combustion with a multi-regime flamelet model. Fuel 2017;188:661-71. Hashimoto N, Kurose R, Hwang S-M, Tsuji H, Shirai H. A numerical simulation of pulverized coal combustion employing a tabulated-devolatilization-process model (TDP model). Combustion and Flame 2012;159(1):353-66. Baum MM, Street PJ. Predicting the Combustion Behaviour of Coal Particles. Combustion Science and Technology 1971;3(5):231-43. Crowe CT, Sharma MP, Stock DE. The particle-source-in cell (PSI-CELL) model for gas-droplet flows. Journal of fluids engineering 1977;99(2):325-32. Wen X, Luo K, Luo Y, Kassem HI, Jin H, Fan J. Large eddy simulation of a semi-industrial scale coal furnace using non-adiabatic three-stream flamelet/progress variable model. Applied Energy 2016;183:1086-97. van Oijen JA, Donini A, Bastiaans RJM, ten Thije Boonkkamp JHM, de Goey LPH. State-of-the-art in premixed combustion modeling using flamelet generated manifolds. Progress in Energy and Combustion Science 2016;57:30-74. Hossain M, Jones JC, Malalasekera W. Modelling of a bluff-body nonpremixed flame using a coupled radiation/flamelet combustion model. Flow, turbulence and combustion 2001;67(3):217-34. Baba Y, Kurose R. Analysis and flamelet modelling for spray combustion. Journal of Fluid Mechanics 2008;612. Fujita A, Watanabe H, Kurose R, Komori S. Two-dimensional direct numerical simulation of spray flames - Part 1: Effects of equivalence ratio, fuel droplet size and radiation, and validity of flamelet 35 / 36

ACCEPTED MANUSCRIPT [50] [51] [52] [53]

model. Fuel 2013;104:515-25. Pitsch H. FlameMaster: A C++ computer program for 0D combustion and 1D laminar flame calculations. 1998. Hwang SM, Kurose R, Akamatsu F, Tsuji H, Makino H, Katsuki M. Application of optical diagnostics techniques to a laboratory-scale turbulent pulverized coal flame. Energy & fuels 2005;19(2):382-92. Weller HG, Tabor G, Jasak H, Fureby C. A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in Physics 1998;12(6):620. Nakamura M, Akamatsu F, Kurose R, Katsuki M. Combustion mechanism of liquid fuel spray in a gaseous flame. Physics of Fluids 2005;17(12):123301.

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Highlights 

An extended flamelet/progress variable model for NO prediction in pulverized coal flames is developed.

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The validity of the flamelet model is evaluated through an a priori analysis.

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The model is sensitive to the progress variable definition.

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The effects of strain rate and initial temperature are investigated.