Flamelet modeling of laminar pulverized coal combustion with different particle sizes

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Original Research Paper

Flamelet modeling of laminar pulverized coal combustion with different particle sizes Xu Wen a,b,⇑, Jianren Fan b a b

Institute for Simulation of reactive Thermo-Fluid Systems, TU Darmstadt, Darmstadt 64287, Germany State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China

a r t i c l e

i n f o

Article history: Received 18 April 2019 Received in revised form 3 July 2019 Accepted 3 September 2019 Available online xxxx Keywords: Pulverized coal combustion Flamelet tabulation method A priori analysis Particle size

a b s t r a c t In this work, flamelet modeling of pulverized coal flame stabilized in a laminar counterflow is conducted. Particularly, the effects of particle size on the flamelet model performance are investigated. The a priori tabulated thermo-chemical quantities are compared with the corresponding values in the detailed chemistry solutions, which are obtained by solving the transport equations for all species mass fractions existing in the employed detailed chemical reaction mechanism. The detailed chemistry solutions show that the pulverized coal flame structure can be changed significantly by varying the particle size. While pulverized coal flame structure with small particles is similar to the pure gas flame, it becomes much more complex when the particle Stokes number is larger than unity. Large coal particles can directly cross the flame front to the opposite side and disperse over a large region, resulting a significantly wrinkled flame front and a considerably broadened reaction zone. Comparisons between the tabulated thermo-chemical quantities and the detailed chemistry solutions show that the CH4, O2 and H2O species mass fractions and their RMS (root mean square) values for all cases can be well predicted by the classical flamelet model without any modification, while the peak values of OH mass fraction, gas temperature and heat release rate for the large particle case cannot be correctly captured. For all cases, the mass fractions of combustion-mode-sensitive species cannot be correctly predicted in the premixed flame reaction zone by the employed diffusion-flame-based flamelet model. Such discrepancies are even more pronounced at large particle conditions since the premixed flame reaction zone tends to be broadened. Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

1. Introduction In the long run, use of coal is bound to continue to be significant, especially for countries such as China, Germany and United States because of their large electricity demand and the size of their large reserves [1]. However, coal is known as a ‘‘dirty” fuel and large amounts of pollutants and greenhouse-gases are released from pulverized coal-fired power plants every year. Efforts are therefore required to make the use of coal more efficient and environmentally acceptable. Pulverized coal combustion is an extremely complex phenomenon, which experiences several interaction processes: particle heating up, devolatilization, volatiles combustion, and char surface reactions. There are also complex interactions between the flow, particle transport, combustion and heat transfer in pulverized coal combustion, ⇑ Corresponding author at: Institute for Simulation of reactive Thermo-Fluid Systems, TU Darmstadt, Darmstadt 64287, Germany. E-mail address: [email protected] (X. Wen).

which are not well understood yet. Both experiments and numerical simulations are useful to improve our understanding of pulverized coal combustion. However, experiments are difficult to be applied to such complicated multiphase combustion systems. Numerical simulation has become an increasingly important tool to describe the pulverized coal combustion behaviors as large-scale computational resources are widely available [2–10]. Great progresses have been made in recent years to develop advanced numerical models for pulverized coal combustion, such as the gaseous combustion models with finite rate chemistry [11–15,9,10,8,3,4], high-fidelity devolatilization model [7], etc. The flamelet model [16] is one of the most promising gaseous combustion models since it can take detailed chemical reaction mechanisms into account with a reasonable computational cost. In the flamelet model, a chemtable (i.e. chemistry table or flamelet library), storing the quantities of interest, is pre-calculated by solving prototype one-dimensional (1D) laminar flames. The flamelet chemtable will then be accessed by several trajectory variables (also called controlling variable), which are directly transported

https://doi.org/10.1016/j.apt.2019.09.004 0921-8831/Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

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in the flow solver. The flamelet model has been widely used in simulations of gaseous and spray combustion [17,18]. The flamelet model for pulverized coal combustion is still under development [19,12,8,10,11,20]. The first attempt was made by Vascellari et al. [19] who employed the flamelet concept to model coal particle ignition during the devolatilization process. Recently, the coal particle ignition process was further studied by Vascellari et al. [20] with an extended flamelet model, in which the scalar dissipation rate was reformulated to adapt to the particle boundary layer. Knappstein et al. [21] applied a so-called ‘‘flamelet-generated manifold (FGM) model [20]” to evaluate the uncertainties of coal particle devolatilization model on prediction of coal particle ignition. Watanabe and Yamamoto [9,10] proposed a flamelet approach for pulverized coal combustion, in which both the devolatilization and char surface reactions were considered. Rieth et al. [8] developed a steady laminar flamelet (SLF) model [16] for pulverized coal combustion based on two mixture fractions. In Ref. [12], we proposed an extended flamelet/progress variable (FPV) approach [22] for pulverized coal combustion, in which the devolatilization, char surface reactions and radiation were all considered. The newly proposed flamelet model was validated against experimental data and good agreements were achieved. Recently, the extended FPV model for pulverized coal combustion was reformulated to reduce the possible interpolation error during the table extraction process [23]. The performance of the reformulated flamelet model was extensively evaluated by comparisons with the detailed chemistry (DC) solutions, including various intermediate species mass fractions. In previous studies [11–15,9,10,8], the flamelet models for pulverized coal combustion were developed based on the assumption that the gas fuels (e.g. volatiles, char off-gases) have been released from the particles completely before reaching the flame front. The conventional gaseous flamelet model is then justified for pulverized coal combustion. However, this assumption is only valid for very small coal particles (i.e. Stokes number St is much less than 1). For large coal particles, they can cross the stagnation plane (S.P.) with a large fraction of gas fuels inside [14]. These two different combustion scenarios are schematically illustrated in Fig. 1. In this

figure, the vertical red lines indicate the locations of the stagnation plane. For small coal particles, the flame front is stabilized around the stagnation plane, while for large coal particles, the location of the reaction zone is determined by the particle trajectory. As shown in Fig. 1b, large particles can cross the stagnation plane from the fuel side to oxidizer side or from the oxidizer side to fuel side. Thus, it is important to understand how well the gaseous flamelet model can approximate the pulverized coal combustion characteristics with large particles. In previous studies [12,8,21], the flamelet models were generally applied to the simulations of pulverized coal combustion directly in an a posteriori sense, without the evaluation of the suitability of the chemtable and trajectory variables specifically for pulverized coal combustion. By neglecting the char-oxidation and radiative heat transfer, Messig et al. [11] and Vascellari et al. [20] evaluated the suitability of the flamelet chemtable on onedimensional counterflow flames and single coal particle ignition, respectively. Incorporating both char-oxidation and radiative heat transfer, the suitability of both the flamelet chemtable and trajectory variables was evaluated in Ref. [23] on two-dimensional counterflow flames. In that work [23], various operating conditions (including strain rate, coal particle loading rate and radiation) were investigated to challenge the gaseous flamelet model. The main findings are that the operating conditions influence the performance of the flamelet model. For specific operating conditions, the flamelet model performs well. However, for other operating conditions (e.g. high strain rate), discrepancies exist between the tabulated chemical quantities and the reference results of detailed chemistry solutions. However, in all these studies [11,20,23], the coal particles were monodispersed (dp ¼ 100 lm in Refs. [11,20], and dp ¼ 5 lm in Ref. [23], and the effect of particle size on the performance of the flamelet model is still unclear. In the aforementioned context, this work aims to investigate the effect of particle size on the performance of flamelet model. To this end, pulverized coal flame with different particle sizes stabilized in a laminar counterflow is simulated with detailed chemistry. The suitability of the flamelet model is evaluated through a priori analyses. In the a priori approach, the trajectory variables

Fig. 1. Schematic diagram of coal flamelet stabilized in a counterflow for different particle sizes. The coal particles are injected from the left side while the oxidizer is injected from the right side. The vertical red lines indicate the locations of the stagnation plane (S.P.). In (b), the points represent the coal particle positions, the arrows indicate the velocity vectors, the numbers indicate different particles, while the colors indicate the fraction of gas fuels remaining in the coal particles (black: low; blue: high). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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that are used to access the flamelet chemtable are calculated directly from the DC solutions, in which the transport equations for species mass fractions and energy are directly solved. The tabulated thermo-chemical quantities are compared to the corresponding values in the DC solutions. Various thermo-chemical quantities, including the gas temperature, stable species mass fractions, intermediate species mass fractions, the RMS (root mean square) values of the interested thermo-chemical variables, reaction source terms, and heat release rate, are compared. In addition, the effect of particle size on the gas phase combustion mode (i.e. premixed or non-premixed) is investigated, which is meaningful for the selection of different flamelet models for different operating conditions. To the authors’ best knowledge, this is the first study to investigate the particle size effect on the performance of flamelet model, with various thermo-chemical quantities being compared. 2. Numerical models 2.1. Governing equations for the gas and solid phases The gas phase is solved in an Eulerian manner. In the detailed chemistry simulations, the governing equations for the mass, momentum, total enthalpy and species mass fractions are solved without filtering or averaging [23],


 @ q @ quj ¼ S_ C;m þ @xj @t

ð1Þ


     @ ðqui Þ @ qui uj @p @ @u @u 2l @u þ ¼ þ l i þ j  dij k þ S_ C;ui @t @xi @xj @xj @xi 3 @xk @xj ð2Þ

respectively. DZv ol and DZpro are the diffusion coefficients, which are

calculated under the assumption of unity Lewis number. S_ C;Zv ol and S_ C;Z are the two-way coupling source terms, which will be given pro

in Section 2.2. The mixture fractions obtained from Eqs. (5) and (6) are employed to access the flamelet library. The flamelet tabulation method for pulverized coal combustion will be described in Section 2.4. The Newlands bituminous type of coal fired in the CRIEPI burner [26] is used and its properties are given in Table 1. Due to the simplified configuration of the CRIEPI burner and the welldocumented experimental data, the Newlands bituminous type of coal was extensively studied by many researchers [12,3,5,27,8]. Thus, the model parameters for this type of coal have been well established. Neglecting the little portion of H2 O in the coal particle (and the corresponding evaporation process), each particle is only composed of volatile matter, char and ash. For simplicity, the ash is assumed as an inert substance and the char is assumed to be only composed of carbon (i.e. Cs ) [5–7,12,8]. The single coal particles are tracked in a Lagrangian manner. The coal particle motion is described using Newton’s second law. As the coal particle density is much larger than that of the gas phase, only the drag and gravity forces are of importance. Neglecting the Stefan flow effect [12,6,28], the energy exchange between the coal particle phase and gas phase consists of the convection, radiation, and chemical enthalpy associated with the devolatilization and char-oxidation. Based on the above assumptions, the mass conservation equation for a single coal particle can be written as,

dmp dmv ol dmchar ¼ þ dt dt dt

ð7Þ

the coal particle velocity in the ith direction up;i can be calculated as,


   @ ðqHe Þ @ quj He @p @ @H þ þ ¼ qa e þ S_ C;He @t @t @xj @xj @xj

ð3Þ

 ! ! dup;i 3C D q
ui  up;i j u  up j þ g i ¼ dt 4dp qp


   @ ðqY k Þ @ quj Y k @ @Y þ ¼ qDk k þ x_ k þ S_ C;m;k @t @xj @xj @xj

ð4Þ

and the evolution of coal particle temperature T p can be calculated as,

where q is the gas phase density, t is the Eulerian time, uj is the gas phase velocity in the jth direction, xj is the Cartesian coordinate in the j direction, p is the static pressure, l is the dynamic viscosity, dij is the Kronecker delta function, He is the specific total enthalpy, a is the thermal diffusion coefficient, Y k is the mass fraction of species k; Dk is the mass diffusivity of species k, which is calculated _ k is the reaction rate under the assumption of unity Lewis number. x of species k, which is calculated by directly solving the Arrhenius formulation with the GRI-Mech 3.0 mechanism [24]. S_ C;i describes the interactions between the coal particle phase and gas phase. The formulations of S_ C;i will be provided in Section 2.2. For pulverized coal combustion, it is a common assumption that devolatilization and char surface reactions take place separately [9,10,12,25,23,15]. Based on this assumption, two mixture fractions are introduced to describe the local mixing state of volatiles and char off-gases,


   @ ðqZ v ol Þ @ quj Z v ol @ @Z þ ¼ qDZv ol v ol þ S_ C;Zv ol @xj @t @xj @xj

ð5Þ



   @ qZ pro @ quj Z pro @ @Z ¼ qDZpro pro þ S_ C;Zpro þ @xj @xj @t @xj

ð6Þ

where Z v ol and Z pro are mixture fractions for volatiles and char offgases, which are related to the mass of gas originating from the volatile matter nv ol , char off-gases npro and oxidizer stream noxi as,

 Z v ol ¼ nv ol = nv ol þ npro þ noxi , and Z pro ¼ npro = nv ol þ npro þ noxi ,

ð8Þ




mp C p;p dT p pldp C p;g Nu T  T p 2 ¼ þ ep pdp 0:25hGi  rT 4p þ S_ r dt Pr

ð9Þ where mp ; mv ol and mchar are the instantaneous mass of a single coal particle, volatile matter and char, respectively. C D is the drag coefficient, which is calculated according to the model proposed by Wen and Yu [29]. The drag force coefficient proposed by Wen and Yu [29] is a semi-empirical relation, which was obtained by conducting a series of fluidization experiments. It has been widely used in pulverized coal combustion simulations [30,15,3] due to its simple formulations, although more advanced models exist in the literature [31,32]. dp is the particle diameter, which is assumed to be constant during the pulverized coal combustion process [5,13,3]. Previous works [5,33] reported that changes in coal particle diameter due to swelling and shrinkage during devolatilization and char combustion processes do not affect the thermo-chemical quantities

Table 1 Properties of the Newlands bituminous coal [26] (aAs received. bDry basis.) Proximate analysis ½wt%

Ultimate analysis ½wt%

Fixed carbona Volatile mattera Asha Moistureb High heating valuea

57.9 26.9 15.2 2.6 1

Carbona Hydrogena Nitrogena Oxygena Total sulfura

71.90 4.40 1.50 6.53 0.44

Low heating valuea

28.1 MJ  kg

1

Combustable sulfura

0.39

29.1 MJ  kg

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distributions significantly. Thus, these effects are neglected in the current work. qp is the particle density, which is calculated as,

qp ¼ 6mp = pd3p . g i is the gravity acceleration in the ith direction. C p;p is the specific heat of coal particle, T is the gas temperature, Nu denotes the Nusselt number calculated by the Ranz-Marshall model [34], and Pr is the Prandtl number, set to be 0.6 [6]. ep is the particle emissivity, set to be 0.85 [35], hGi is the cell-averaged incident radiation between the radiating particles and gray gases, which is calculated with the P1 model developed by Cheng [36]. The conservation equation for hGi can be referred to [23]. S_ r is the temperature source term due to devolatilization and charoxidation. The formulation of S_ r is referred to our previous work [23]. 2.2. Two-way coupling terms The two-way coupling terms are calculated with the ParticleSource-In Cell (PSI-Cell) model [37]. The source terms in the continuity, momentum, energy and species mass fraction governing equations are calculated as [23],

1 S_ C;m ¼  V

 N  X dmp dt

n

¼ n

    X N  K 1X dmv ol dmchar ¼ þ S_ C;m;k V n dt n dt n k ð10Þ

1 S_ C;ui ¼  V 1 S_ C;He ¼  V


 N  X d mp up;i dt

n

ð11Þ

n


 N  X mp C p;g Nu T  T p

3Pr sd n D

þ ag hGi  4r Ti4

 þ S_ T;g

n

n

ð12Þ

where V denotes the volume of the grid cell in which the particle resides, N is the number of particles presenting in the local cell volume, and the summation index n loops over all coal particles that exist within the local cell. K is the number of species in the volatile matter and char-oxidation reactions, and k is the summation index. S_ T;g is the interphase heat transfer due to devolatilization and charoxidation [35]. In this work, the latent heat of the devolatilization is not considered. ag is the absorption coefficient of the gray gas. In this work, ag is set to be 0.075 following the previous works [35,6,12] where the same type coal was used and the simulation results were compared to the experimental data. r is the StefanBoltzmann constant. In this work, we assume char is totally converted to CO, and its conversion rate is described with a coal combustion sub-model, as will be described in the next subsection. Based on this assumption and the definitions for volatiles and char off-gases mixture fractions, the source terms of S_ C;Z and S_ C;Z in v ol

pro

Eqs. (5) and (6) can be calculated as [23],

1 S_ C;Zv ol ¼  V S_ C;Zv ol

 N  X dmv ol n

dt

ð13Þ n

  N  M O2 þ cM N2 1X dmpro ¼ 1þ V n dt 2M C n

ð14Þ

where MO2 ; MN2 and MC are the molecular weights of species O2 ; N2 and C, respectively. c is the ratio of N2 to O2 in the oxidizer stream. 2.3. Coal combustion sub-models The coal combustion sub-models presented in this section are the same as those in Refs. [12,23], which have been extensively

validated against well-documented experimental data. The devolatilization rate is described with the model by Badzioch and Hawksley [38]. The model parameters are set according to the recommended values in Ref. [39]. The devolatilization rate strongly depends on the particle heating rate. To consider the overall high heating rate effect (above 104 K  s1 ), a Q-factor is introduced in the devolatilization model for all simulations. In the current work, the volatile matter is treated as the postulated chemical species composed of CH4, C2H2 and CO [12]. The mass fraction of species k in volatile matter, Y v ol;k , is calculated from the coal’s proximate and ultimate analysis to meet both the mass balance and the lower heating value balance according to Ref. [7]. For the studied Newlands bituminous type coal [26], the fractions of CH4 ; C2 H2 and CO are calculated to be 55%; 11% and 34%, respectively [12,40]. Note that the summation of the lower heating value of the volatile matter and char in the numerical simulation should be similar to the experimental data. The lower heating values of the postulated species in volatile matter, i.e., CH4 ; C2 H2 and CO, are 50, 48.2 and 1

10.1 MJ  kg , respectively. The lower heating value of char oxida1

tion is around 32.0 MJ  kg . According to the fractions of the species compositions in volatile matter, the lower heating value of the 1

coal particle in the simulation can be calculated as 28.3 MJ  kg

1

[12], which is close to the experimental data of 28.1 MJ  kg [41]. For the same type coal, the evaluation of the suitability of the postulated volatile matter compositions was conducted in our previous work [40]. The char conversion rate is characterized with the model by Baum and Street [42]. In the current work, the char-oxidation product is assumed to be CO [12,8]. To ensure overall conservation of elemental mass during char reaction with air, the species released from char surface does not only include intermediate fuels of CO but also N2 that goes along with the consumed O2 [12,23,10,8],

Cs þ 0:5ðO2 þ cN2 Þ ! CO þ 0:5cN2 Based on these assumptions, the fraction of species k in char offgases, Y pro;k , can be calculated as [23,10],

Y pro;CO ¼

M CO ; M CO þ 0:5cMN2

Y pro;N2 ¼

0:5cM N2 M CO þ 0:5cMN2

ð15Þ

2.4. Flamelet model for pulverized coal combustion For flamelet modeling of pulverized coal combustion, it is essential to describe the interphase mass and heat transfer. As described in Section 2.1, the interphase mass transfer is described by the introduced two mixture fractions, Z v ol and Z pro . We note that the space of (Z v ol ; Z pro ) is a unit triangle, which may lead to various numerical problems during the table extraction process [43]. Following the work by Hasse and Peters [43], Z v ol and Z pro are transformed into their sum and the ratio of Z pro to their sum, viz.,

Z ¼ Z v ol þ Z pro ;

X¼

Z pro Z v ol þ Z pro þ 

ð16Þ

Here a small positive number  is introduced to avoid dividing by zero in cells where the amount of fuel gases is negligible. By this means, the thermo-chemical states are evolved in a unit square space (Z; X). The newly introduced parameter Z can be regarded as the coal particle mixture fraction, while X is referred to as the mixing parameter [43]. The mass transfers between the coal particle phase and gas phase are strongly coupled with the heat transfer. For example, the coal particles are first heated up by radiative heat transfer to release the volatiles and in turn, combustion products of volatiles heat the coal particles further to initiate the char-oxidation

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process. In the flamelet model for pulverized coal combustion, the solid particles are treated as the gas fuels in the flamelet chemtable, such that the conventional gaseous flamelet equations can be used. It is clear that the interphase heat transfer, such as the heat transfer between the coal particle phase and gas phase through radiation and convection in real combustion system cannot be represented by the gaseous flamelet chemtable. In previous studies [12,8,10,11], the interphase heat transfer in the gaseous flamelet chemtable was considered by varying the temperature boundary conditions for the gaseous flamelet equations. For example, in Refs. [12,8,10], the flamelet equations are solved by setting various fuel temperatures. The fuel temperatures are finally related to the total enthalpy, which is used to access the flamelet chemtable. In this work, this method is retained to approximate the interphase heat transfer. In previous works of flamelet modeling for pulverized coal combustion, the gas fuels (i.e. volatiles and char off-gases) are assumed to be released from the coal particle completely before reaching the flame front [12,8,10,11]. Based on this assumption, the pulverized coal flame can be approximated with the gaseous flamelet model. The mass and heat transfers between the coal particle phase and gas phase are then considered by adjusting the boundary conditions for the gaseous flamelet equations. As reported in Ref. [14] and schematically shown in Fig. 1, such treatment may be sufficient for small coal particles, but for large particles, this assumption needs to be justified since the flamelet boundary conditions can be disturbed by large particles. Considering that the diffusion combustion mode is dominant in the counterflow pulverized coal flame [15], the diffusion-flamebased FPV approach [22] is adopted in this work. In the FPV

5

approach, the flamelet element is assumed to be a 1D counterflow flame. Thus, the species mass fractions and temperature boundary conditions on the fuel and oxidizer sides of the counterflow need to be specified. The mass fraction of species k on the fuel side of the flamelet, Y fuel;k , can be determined by weighting the mass of volatile matter and char off-gases [23],

Y fuel;k ¼

nv ol Y v ol;k þ npro Y pro;k ¼ ð1  X ÞY v ol;k þ XY pro;k nv ol þ npro

ð17Þ

The second relation is obtained according to the definition of X, see Eq. (16). It is clear that Y fuel;k is a linear function of X, which is attracting in the flamelet model since the interpolation error can be largely reduced without high mesh resolution. For the diffusion flamelet model, the atmospheric air is used as the oxidizer, thus, the species compositions on the oxidizer side of the flamelet Y oxi;k correspond to, Y oxi;O2 ¼ 0:23 and Y oxi;N2 ¼ 0:77. In summary, the non-premixed flamelet equations are solved for various values of mixing parameter X and fuel temperature T f to represent the interphase mass and heat transfers. To characterize the strain rate on the pulverized coal flame, the scalar dissipation rate v in the flamelet equations is also varied from the equilibrium limit to the extinction limit. The flamelet equations are solved using the FlameMaster package [44]. To keep consistency with the detailed chemistry simulations, the flamelet equations are solved based on the assumption of unity Lewis number for the GRI-Mech 3.0 mechanism [24]. In Fig. 2, the gas temperature is plotted against mixture fraction at v ¼ 1 s1 for various values of fuel temperature T f . Flamelets shown in Fig. 2a are generated at the condition of X ¼ 0 while

Fig. 2. Flamelet data of gas temperature T against mixture fraction Z at v ¼ 1 s1 (a) X ¼ 0, and (b) X ¼ 0:9 for various values of fuel temperature T f . Flamelet data of (c) gas temperature T, and (d) reaction progress variable Y PV against mixture fraction Z at T f ¼ 600 K and X ¼ 0 for various values of scalar dissipation rate v. In (a), the blue sample points are extracted from the detailed chemistry simulation for the D100 case. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 2b presents the flamelets at the condition of X ¼ 0:9. The gas temperature obtained from the detailed chemistry simulation for the D100 case is superimposed in Fig. 2a. It can be observed that for a specific value of Z, the gas temperature increases with increasing the value of T f . Note that the coal particles can be either heated up or cooled down at different operating conditions. To establish the whole combustion regime, both higher and lower values of T f are specified, compared to the initial coal particle temperature (600 K). As shown in Fig. 2a and b, the pink zones between T f ¼ 300 K and T f ¼ 600 K indicate the heat loss effects. The zones above the pink zone represent the heat gain effects. Comparing the gas temperature in the flamelet table and the detailed chemistry solutions, it can be observed that although the upper limit of the gas temperature can be covered by the flamelet table, some sample points with low temperature cannot be represented. In these regions, an extrapolation method [45] is adopted. In our previous work [46], the adopted extrapolation method was validated in a turbulent pulverized coal flame. Comparing the gas temperature at different values of X shown in Fig. 2a and b, it is observed that the location of peak temperature moves toward the larger mixture fraction as the value of X increases. On the other hand, the flamelets at the condition of T f ¼ 600 K and X ¼ 0 for various values of v are shown in Fig. 2c. It is seen that the peak temperature decreases with increasing v. At extremely high v (e.g., v ¼ 1000 s1 in Fig. 2c), flame quenching happens. At this condition, pure air and pure fuel mix with each other without reaction (i.e., the pure mixing condition), and the corresponding value of reaction progress variable Y PV is zero, as shown in Fig. 2d. The definition of Y PV will be given shortly. Note that the chemical states in the transition region between the flamelet with the highest v and the extinguished flamelet are not available. In the FPV approach [22], v is replaced by Y PV , which can partially represent the states in the transition region (see Fig. 3 in Ref. [22]). For the uncovered transition region, the chemical states are obtained as follows. The gas temperature is obtained with a linear interpolation method, while the species mass fractions are obtained by collapsing to the last burning flamelet. This flamelet table extension method is generally adopted for both gaseous combustion [22] and pulverized coal combustion [23,11]. Particularly, Messig et al. [11] reported that the thermo-chemical quantities in the pulverized coal flame can be well predicted with the extended flamelet library. To illustrate the effect of X on the thermo-chemical quantities further, the total enthalpy He is plotted in the mixture fraction space for various values of X and T f at v ¼ 1 s1, as shown in Fig. 3. The total enthalpy obtained from the detailed chemistry simulation for the D100 case is superimposed to check if the whole

range of enthalpy defect can be covered. From the enthalpy distribution in the flamelet table, it can be observed that for a specific value of Z, the total enthalpy increases with increasing the value of X. According to the definition of X, it is easily calculated that X stays at zero during the devolatilization process (npro ¼ 0), when char-oxidation begins, the value of X increases to be positive (npro > 0). Thus, the value of X indicates the coal particle burning stage. The flamelet solutions shown in Fig. 3 indicate that the total enthalpy increases with progressing the coal particle burning stage. Comparing the enthalpy in the flamelet table and that in the detailed chemistry solutions, it can be observed that the enthalpy in the detailed chemistry simulation can be quite low, which cannot be fully covered by the present flamelet library. As described before, the extrapolation method proposed by Ketelheun et al. [45] is adopted to extend the lower limit of the total enthalpy. The flamelet solutions need to be parameterized as a function of the trajectory variables so that the flamelet chemtable can be accessed. The flamelet solutions can be first parameterized using
 the FPV approach as, U ¼ U X; T f ; Z; Y PV , where the reaction progress variable Y PV is defined as,

Y PV ¼ Y H2 O þ Y CO2 þ Y H2

ð18Þ

This definition of reaction progress variable has been validated in our previous works [47,12,23,48] by comparing the flamelet predictions against the experimental and DNS data. Unlike the conventional reaction progress variable for gas combustion [49], CO is not included in the progress variable. For the studied Newlands bituminous type coal, the species compositions in volatile matter contain CO, and the char-oxidation products also include CO. Thus, the progress variable cannot describe the ‘‘progress” of reactions if CO is included as a part of the progress variable. In the a priori analysis, Y PV is calculated from the DC solutions, where all species mass fractions are available. Different from the a posteriori analysis where the trajectory variables are calculated with the corresponding transport equations, in the a priori analysis the trajectory variables are calculated from the detailed chemistry solutions. The a priori analysis is particularly useful to evaluate the suitability of the flamelet table since the flow behaviors are the same in the flamelet predictions and the detailed chemistry simulations. In the a posteriori analysis, the suitability of the flamelet table is hard to be evaluated independently due to the direct interactions between the flow filed and the chemistry. In fact, a small discrepancy in the flamelet table can accumulate during the simulation and result in final large discrepancies of the flamelet predictions [50,11]. Note that the transport equation for T f is difficult to be formulated in the flow solver since it only characterizes the boundary value of the flamelet. In this work, T f is finally related to the normalized total enthalpy Hnorm by conducting a coordinate transformation. The normalization procedure of the total enthalpy can be referred to Ref. [23]. Finally, the thermo-chemical quantities in the flamelet chemtable are parameterized as,

U ¼ Uð X; Hnorm ; Z; Y PV Þ

ð19Þ

In the present work, the flamelet chemtable is generated with 10  51  51  61 points for X  Hnorm  Z  Y PV , respectively. The total memory requirement for this table is approximately 1.5 GB, which contains all of the species mass fractions, gas temperature, and source term of reaction progress variable. 3. Numerical configuration Fig. 3. Flamelet data of total enthalpy He against mixture fraction Z at v ¼ 1 s1 for various values of mixing parameter X and fuel temperature boundary T f . The blue sample points are extracted from the detailed chemistry simulation for the D100 case. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.1. Computational setup To avoid the configuration related complexity, the pulverized coal flames stabilized in a laminar counterflow are simulated.

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The computational setup is schematically illustrated in Fig. 4. The computational domain is a 2D square field and the side length is 20 mm. The coal particles transported by the air stream are injected from the upper port. The coal particles are uniformly distributed at the inlet. The particle temperature is equal to that of the transport air of 600 K, which corresponds to the devolatilization temperature T dev [38]. The initial coal particle velocity is the same as the local fluid velocity, being set to be 1 m/s. From the lower port, the atmospheric air is injected into the computational domain, with the velocity magnitude and temperature being the same as those from the upper port. The Reynolds number based on the inlet flow velocity and the side length is 398. The details of the computational setup can be referred to our previous work [23]. 3.2. Computational details The computational domain is discretized into 300  300 grid points. The meshes are uniform and Cartesian. It has been checked in Ref. [40] that further refinement of grid does not significantly affect the numerical results. The gas phase governing equations are solved with a finite volume method (FVM) using the SIMPLE algorithm. The detailed chemistry simulations are performed with a solver called pccFRFoam [15] while the table extraction process is conducted with a solver called pccFPVFoam [12]. Note that in the a priori analysis, the flamelet chemtable extraction process is conducted by executing the flow solver only one time step. Thus, there are no cumulative interactions between the gas phase and particle phase. Both solvers are developed based on the open-source finitevolume CFD code OpenFOAM-v2.3.1 [51]. A second-order central differencing scheme is used to calculate the convection terms while the limitedLinear scheme, which limits towards upwind in regions of rapidly changing gradient [51], is applied for scalar equations. The diffusion terms are evaluated with a second-order central difference scheme while the Euler-implicit scheme is applied for time integration. Both solvers have been extensively validated in Refs. [13,12] by comparisons with the welldocumented experimental data. To investigate the effect of coal particle size on the performance of flamelet model, four computations are performed for different particle sizes. Specifically, in different simulations, the particle diameters are set to be uniform and equal to dp ¼ 5, 60 and 100 lm, referred to as D005, D060 and D100, respectively. The cor-

Fig. 4. Schematic of computational setup of the counterflow pulverized coal flame.

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responding Stokes numbers with respect to the global strain rate a (i.e., a ¼ 2u=Lp , where Lp is the distance between the upper and lower port) are St ¼ asd ¼ 6:9  103 ; 1; 2:76, respectively, where sd is the particle relaxation time. To represent the practical pulverized coal combustion, an additional simulation with polydisperse particles is conducted, referred to as Dvar. In this case, the coal particle sizes are subjected to the normal distribution. The mean value is set to be 50 lm while the standard variance is 16 lm. The expected minimum and maximum particle sizes of this distribution are set to be 5 and 100 lm, respectively. The same mass flow

rate of coal particles (1:6  105 kgs1) and strain rate (100 s1) are used for all cases. According to the employed mass flow rate, the number of particles are calculated to be 240000000, 28935, 30000 and 240000 for the cases D005, D060, D100 and Dvar, respectively. Note that the numerical error could be introduced for the D100 case where the particle size is comparable to the grid size [52]. In this study, we only focus on resolving the flame structure with sufficient mesh resolution while the numerical error introduced by large particles is neglected.

4. Results and discussion 4.1. Pulverized coal combustion characteristics for different particle sizes In Ref. [14], the effect of particle size on the coal flamelet behaviors was analyzed by neglecting the radiative heat transfer. In this work, the radiative heat transfer is considered, and the effects of particle size on the pulverized coal combustion characteristics are analyzed in this section. In Fig. 5, the contour plots of gas temperature calculated with different coal particle sizes are presented. The streamlines colored with the fluid velocity magnitude, and the coal particle velocity vectors colored with the fraction of volatile matter Y v ol are superimposed. For clarity, only 150 sample particles are displayed in these figures. The reaction progress variable _ Y PV is introduced to identify the reaction zone, which source term x _ YH O þ x _ Y CO þ x _ Y H . The pink bold line _ Y PV ¼ x is defined as, x 2 2 2 _ Y PV ¼ 104 kg  m3  s1 , which shown in Fig. 5 is the isoline of x indicates the location of coal particle ignition. Note that Y PV is defined based on the reaction products, thus, a small positive value of the Y PV source term indicates the beginning of coal combustion. _ Y PV is set equal to 104 kg  m3  s1 to ensure conIn this work, x sistency with our previous work [15], where the detailed coal combustion characteristics were analyzed. A first observation is that the pulverized coal flame structure can be changed significantly by varying the particle size. For the case D005, the coal particles follow the streamlines closely, and they cannot penetrate into the peak temperature region. The reaction zone is not perturbed by the particles. The pulverized coal flame structure is similar to that of the pure gas flame [14]. It is expected that the gaseous flamelet model is justified for this condition. For the case D060, the flame structure becomes more complex. Although the overall structure is similar to that of D005, the flame front is wrinkled by the dispersed coal particles. It is observed that although the coal particles follow the streamlines near the upper port, some coal particles are lifted up by the opposed oxidizer stream after they penetrate into the reaction zone, i.e., the particles reversal. The peak temperature of D060 is lower than that of D005. This is explained as follows. In the case D060, there are many coal particles penetrated into the peak temperature region. The hot gases in the peak temperature region tend to be cooled down by the local cold particles. Different from the small particle case, most of the large particles (expect the reversal ones) cannot achieve the thermal equilibrium with the local gas phase, as shown in Fig. 6. This

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Fig. 5. Instantaneous distributions of gas temperature (left side in each subfigure) and streamlines (right side in each subfigure) in various cases. The streamlines are colored with the fluid velocity magnitude. The particles and particle velocity vectors are colored with the fraction of volatiles in the coal particle Y v ol . The pink bold line is the isoline _ Y PV ¼ 104 kg  m3  s1 . Note that only 150 sample particles are superimposed in these figures to make the other distributions clear. (For interpretation of the references of x to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Comparison of coal particle temperature and gas temperature for the small particle case D005 and the large particle case D060. The particle temperature is extracted from the region j x j< 1 mm, while the gas temperature is extracted along the central axis of the counterflow. The reversal particles in the D060 case are indicated..

phenomenon is similar to the cooling effect found in the spray combustion [53]. For the case D100, the coal particle paths do not follow the streamlines. The coal particles can cross the peak temperature region with high fraction of volatiles. As a result, the flame structure is considerably different from the cases D005 and D060. Specifically, it is seen that the flame front is significantly wrinkled, and the reaction zone is considerably thickened. The flame structure relies on the trajectory of the particles. For the case Dvar, the coal particle sizes are varied between 5 lm and 100 lm with a mean diameter of 50 lm. It is observed that although a few of large coal particles can cross the high temperature region, the

overall flame structure is similar to that of D060. It is thus interesting to investigate whether the performance of the gaseous flamelet model is similar for D060 and Dvar. From these observations, it can be concluded that the ‘‘trajectory” of gas temperature depends on the particle diameter. In flamelet modeling for pulverized coal combustion, the characterization of the char surface reactions is very important due to the complicated interactions between different fuel streams. Thus, it is essential to investigate the extents of char surface reactions in different cases. In Fig. 7, the instantaneous distribution of char off-gases mixture fraction Z pro is displayed. The coal particles

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Fig. 7. Instantaneous distribution of char off-gases mixture fraction. The particles and particle velocity vectors colored with the fraction of fixed carbon Y C s in various cases are superimposed. Note that only half of the computational domain (10 mm < x < 0) is shown and only 75 sample particles are superimposed.

colored with the fraction of fixed carbon Y C s are superimposed. From the distribution of Z pro , it can be observed that in the small coal particle case D005, the char off-gases prevail around the stagnation plane, while those are negligible in the large coal particle
 case D100, i.e., max Z pro  0. This is a consistent result since the small coal particles are easily burnt out with the surrounding hot gases. Compared to the case D005, the high Z pro is distributed in isolated regions in the cases D060 and Dvar. This is related to the particle reversal in cases D060 and Dvar (see the particle velocity vector), which allows a long residence time for char surface reactions. The distribution of Y C s in coal particle corresponds to that of Y v ol shown in Fig. 5. As the volatiles released from the coal particle, the fraction of fixed carbon in coal particle becomes higher and higher, till the maximum value 0.8 is reached. Fig. 8 shows the mean reaction zone thickness of different cases, which is defined as the width between the isoline of x_ Y PV ¼ 104 kg  m3  s1 . It can be observed that the thickness of mean reaction zone increases from 3.2 mm for D005 to 8 mm for D100. The wider reaction zone in the case D100 is due to large inertia of large coal particles, which can penetrate the flame front and disperse in a wider region. For gaseous flamelet, the reaction zone thickness can be uniquely determined by the parameter of scalar dissipation rate [16]. However, it is shown here that for pulverized coal flame, the reaction zone thickness is also dependent on the

Fig. 8. Mean reaction zone thickness of different cases.

particle diameter. Thus, it is desirable to investigate how much can the gaseous flamelet model approximate the pulverized coal flame calculated with different particle sizes, which is the focus of Section 4.2. In Fig. 9, the scatter plots of gas temperature colored by the OH mass fraction are plotted in the mixture fraction space for the D005 case and D100 case. The flamelet data of gas temperature at the condition of X ¼ 0 and T f ¼ 600 K for various values of v are also superimposed, as indicated by the purple solid lines. The instantaneous data are extracted from the entire computational domain. Comparing the results from D005 and D100, it is seen that the gas temperature in the large particle case D100 spreads over a larger region than that in the small particle case D005. The profile of gas temperature for the case D005 is similar to the gaseous flamelet. For the case D100, some low temperature scatters can be observed around Z ¼ 0:09, which indicates that the localextinction may happen in large particle cases. These nonequilibrium states are not included in the flamelet chemtable generated with steady flamelet equations (see Fig. 2). At these nonequilibrium conditions, the chemical states are obtained by linearly interpolating the states between the coldest flamelet and the mixing line. In both cases, the position of peak temperature of the counterflow flame simulation moves towards the smaller mixture fraction than that of flamelet calculations. This is associated with the different transport processes in the flamelet calculation and the counterflow flame simulation. The flamelet calculations are conducted by solving the one-dimensional nonpremixed flamelet equations, in which only the diffusion along the normal direction of the flamelet is considered. However, in the studied counterflow flame, the thermo-chemical quantities are transported in both the normal and tangential directions of the flame front through both convection and diffusion. From the distribution of the OH mass fraction, it can be observed that the high OH mass fraction locates around the peak temperature region. However, for both cases the positions of peak OH mass fraction slightly move towards the smaller mixture fraction than that of peak gas temperature. Note that only the flamelet data at the condition of X ¼ 0 and T f ¼ 600 K is shown in Fig. 9. The upper limits of the temperature in the detailed chemistry solutions can be covered by the flamelet data by increasing the temperature boundary conditions (see Fig. 2a).

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Fig. 9. Scatter plots of gas temperature colored by the OH mass fraction shown in the mixture fraction space for the D005 case (left) and D100 case (right). The branches corresponding to the pure mixing and two-phase reactions are denoted. The flamelets at the condition of X ¼ 0 and T f ¼ 600 K for various values of v are superimposed (i.e. the purple solid lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

4.2. Quantitative comparisons In this section, the performance of gaseous flamelet model for pulverized coal combustion is evaluated by comparing the tabulated thermo-chemical quantities to the reference results of DC solutions in an a priori sense. In the a priori tests, the trajectory variables that are used to access the flamelet chemtable are calculated from the DC solutions. The accessed thermo-chemical quantities are then compared to the corresponding values in the DC solutions. Fig. 10 compares the gas temperature T between the reference results obtained from numerical simulations with detailed chemistry and the a priori profiles for the gaseous flamelet model along the central axis (x ¼ 0). Note that the field varies in the x direction, particularly for the large particles, as shown in Fig. 5. To describe the variances of T along the x direction, the RMS values of gas temperature T rms are calculated as a function of y, which are displayed

in Fig. 10. For the case D005, the tabulated values of T agree with the reference results very well, and the variance of T is minor. However, for other cases, although the overall profiles are predicted, the peak values of gas temperature are over-predicted. Particularly, the case D100 shows the largest discrepancies among these cases over the region between y ¼ 3:5 mm and y ¼ 8 mm. The over-prediction of gas temperature for the large coal particle cases might attribute to the occurrence of local-extinction. This is because at these conditions the steady flamelets with higher gas temperature tend to be accessed [54]. From these observations, it is concluded that the trajectory of gas temperature depends on the particle size. Similarly, Neophytou and Mastorakos [55] reported that the performance of the gaseous flamelet model for spray combustion also depends on the droplet size. In that work [55], they suggested to add droplet diameter as one of the trajectory variables in the flamelet chemtable to consider the particle size effect. This method may also be useful for pulverized coal

Fig. 10. Comparisons of gas temperature, T, and RMS of gas temperature, T rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

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combustion due to the similar transportation mechanism between coal particle and droplet. From the distributions of T rms , it can be observed that the variance of T increases with increasing particle size. Comparing the cases between D060 and Dvar, it is seen that the polydisperse particles tend to generate larger variance values than the monodisperse particles. The mass fractions of major product species of CO2 and H2O are compared in Figs. 11 and 12, respectively. The RMS values of Y CO2 and Y H2 O are also shown in these figures. It is seen that both Y CO2 and Y H2 O are overall correctly predicted by the gaseous flamelet model for all cases, which suggests that the major reaction products are not very sensitive to the particle size effect. However, with a closer observation, it is seen that for Y CO2 and Y H2 O , small discrepancies can be observed at around y ¼ 5 mm for the case D100. It

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can also be observed that for uniform particles, the larger the coal particles, the larger the RMS values. Similar to the findings for gas temperature, compared to the monodisperse particles, the polydisperse particles tend to generate large variances of Y CO2 and Y H2 O . In Figs. 13 and 14, the reactant species mass fractions of Y CH4 and Y O2 , together with their variance values are compared between the DC solutions and the tabulated quantities. It can be observed that the Y CH4 is well predicted for all cases. Although small discrepancies can be observed for Y O2 at around y ¼ 5 mm, the overall profiles of Y O2 are also well predicted by the gaseous flamelet model for all cases. It is suggested that the particle size has negligible effect on the distributions of reactant species mass fractions if the flow field is correctly predicted (i.e. the a priori analysis). For small coal particles of D005, only small variances of Y CH4 and Y O2

Fig. 11. Comparisons of CO2 mass fraction, Y CO2 , and RMS of CO2 mass fraction, Y CO2 ;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

Fig. 12. Comparisons of H2O mass fraction, Y H2 O , and RMS of H2O mass fraction, Y H2 O;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

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Fig. 13. Comparisons of CH4 mass fraction, Y CH4 , and RMS of CH4 mass fraction, Y CH4 ;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

Fig. 14. Comparisons of O2 mass fraction, Y O2 , and RMS of O2 mass fraction, Y O2 ;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

can be observed around the flame front (y  5 mm). For large coal particles, the variances of Y CH4 and Y O2 spread over a large region. For all cases, Y O2 ;rms shows a peak value around the flame front. Figs. 15 and 16 compare the intermediate species mass fractions of Y CO and Y H2 between the reference results and the a priori profiles for the gaseous flamelet model. The RMS values of Y CO;rms and Y H2 ;rms are also presented. It can be observed that even for small coal particles of D005, the Y CO and Y H2 show discrepancies between the reference results and flamelet predictions in a certain region between y ¼ 5 mm and y ¼ 6 mm. Previous works [56,57] reported that the flamelet predictions of these intermediate species are sensitive to the prototype flamelets (i.e. 1D counterflow diffusion flame or 1D freely propagating premixed flame). To clar-

ify this, the Takeno’s flame index [58] is introduced to investigate the gas phase combustion mode,



FI ¼

rY F  rY O2  jrY F  rY O2 j þ x_ Y

ð20Þ PV

>0

where Y F and Y O2 are the mass fractions of the fuel and oxygen, respectively. FI ¼ 1 indicates the non-premixed combustion regime while the premixed combustion regime is identified by _ Y PV > 0 FI ¼ 1. Note that the calculation of FI is conditioned on x to exclude the rapid devolatilization region where FI is calculated to be 1 [14]. Following the work by Hara et al. [27], the fuel mass fraction is defined as, Y F ¼ Y CH4 þ Y CO þ Y C2 H2 . The value of FI is indi-

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Fig. 15. Comparisons of CO mass fraction, Y CO , and RMS of CO mass fraction, Y CO;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

Fig. 16. Comparisons of H2 mass fraction, Y H2 , and RMS of H2 mass fraction, Y H2 ;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

cated by the background color of Figs. 15 and 16. It is observed that the region with evident discrepancies between the DC solutions and tabulated results mainly locates in the premixed combustion zone, which is consistent with the findings reported in previous works [56,57] that Y CO and Y H2 cannot be correctly predicted in the premixed combustion region using the diffusion-flame-based flamelet model. To remedy the weakness of single-mode-based flamelet model, new flamelet tabulation methods that incorporate multicombustion modes for partially premixed combustion are needed [59,60], which will be explored in the future work. From the distributions of FI shown in Figs. 15 and 16, it is seen that larger coal particles tend to generate a wider premixed combustion region. As a result, the discrepancies between the reference results and the flamelet predictions exist in a larger region. Thus, for pulverized coal combustion systems with large particles, a generalized flamelet

model should be developed, e.g., by incorporating the partially premixed flamelet as the archetypal flamelet element [57,60]. Comparing the cases between D060 and Dvar, it is seen that the presence of a small number of large particles does not have significant effects on the performance of the gaseous flamelet model on prediction of Y CO and Y H2 . Similar to the findings reported above, the larger the coal particles, the larger the variances of Y CO and Y H2 . In addition, it is seen that compared to Y H2 and Y H2 ;rms ; Y CO and Y CO;rms are better predicted by the gaseous flamelet model. The minor species mass fraction of Y OH , which is often used as an indicator of the flame front, is compared in Fig. 17 between the DC solutions and flamelet predictions. It is seen that the peak value of Y OH can only be correctly predicted for small coal particles of D005, while for larger coal particles, the peak value of Y OH is generally over-predicted by the gaseous flamelet model. In addition, it

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Fig. 17. Comparisons of OH mass fraction, Y OH , and RMS of OH mass fraction, Y OH;rms , between the reference results of detailed chemistry and the a priori profiles for the gaseous flamelet model along y.

is seen that the reference profiles of Y OH;rms are overall captured by the gaseous flamelet model for all cases. In a posteriori tests, the governing equations for the reaction progress variable and total enthalpy are directly solved in the flow solver. Thus, it is important to investigate whether the reaction _T _ Y PV and the heat release rate x progress variable source term x can be correctly predicted in the a priori analysis. The comparisons _ T between the reference results and the flamelet pre_ Y PV and x of x dictions are shown in Fig. 18. It can be observed that the profiles of x_ Y PV and x_ T are overall captured by the gaseous flamelet model, although the discrepancies do exist. For example, the peak values _ Y PV are not correctly predicted for all cases. The reason for this of x _ Y PV between the difference may be related to the interpolation of x quenched and the first burning solution in the non-premixed flamelet chemtable [11]. This issue could be addressed by extending

the flamelet equations to the unsteady formations [54]. The effect _ T is obvious. It is seen that for of particle size on prediction of x _ T is incorrectly predicted near the cases D060, D100 and Dvar, x _T lower port (y  3 mm), while for the case D005, the profile of x is reproduced by the gaseous flamelet model. The agreement of the heat release rate in the D005 case confirms the suitability of the flamelet model for small particles, i.e., the basic assumption that the gas fuels have been released from the coal particles before they reach the flame front is applicable. Thus, the discrepancies in the large particle cases can only result from their different combustion characteristics from those in the small particle case. Particularly, it can be related to the fact that the basic assumption used to formulate the flamelet model for pulverized coal combustion is no longer strictly valid. Comparing with the gas temperature shown in Fig. 10, it is seen that the over-prediction of gas temper-

_ Y PV , and heat release rate, x _ T , between the reference results obtained from numerical simulations with detailed Fig. 18. Comparisons of progress variable source term, x chemistry and the a priori profiles for the gaseous flamelet model along y.

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ature results in the under-prediction of heat release in the large particles cases. This is explained as follows. On one hand, these two variables are obtained with different methods in the transition zone, as described in Section 2.4. In the large coal particle case, the chemical states in the transition zone prevail due to the local strong interphase heat transfer (see Fig. 9b). On the other hand, the high sensitivity of the non-linear chemical reaction rates may result in the incorrect prediction of the heat release rate. This is particularly true when the FPV model is applied to the transition zone, as reported by Messig et al. (see Fig. 5 in Ref. [11]) and Rieth et al. (see Fig. 2 in Ref. [50]). 5. Conclusions In this work, the effects of particle size on the performance of flamelet model is investigated. Pulverized coal flame stabilized in a laminar counterflow is simulated with detailed chemistry for different particle sizes. The results show that the pulverized coal flame structure can be changed considerably by varying the particle size. While the pulverized coal flame structure with small coal particles is similar to that of the pure gas flame, the flame structure with large coal particles becomes much more complex. For large coal particles, they can cross the flame front and disperse over a large region. As a result, the flame front is significantly wrinkled, and the reaction zone thickness is broadened. The quantitative comparisons between the detailed chemistry solutions and the flamelet predictions show that the species mass fractions of Y CH4 ; Y O2 and Y H2 O are well predicted by the classical flamelet model without _ T of large any modification, while the peak values of Y OH ; T and x particles cannot be captured. For all cases, the combustionmode-sensitive species of CO and H2 in the premixed combustion region cannot be correctly predicted by the present diffusionflame-based FPV model. Such discrepancies are even more pronounced for large particles since they tend to broaden the premixed combustion region. The RMS values of the thermochemical quantities can be overall correctly predicted by the employed flamelet model. The larger the particles, the larger the RMS values. The findings reported in this work are also useful for further flamelet model development. On the one hand, for pulverized coal combustion systems with large particles, the performance of the flamelet model can be improved by reformulating the flamelet equations, e.g., by introducing the particle size as an additional manifold. On the other hand, to characterize the whole combustion regime in pulverized coal combustion system, a generalized flamelet model that considers both premixed and diffusion combustion modes should be developed, e.g., by incorporating the partially premixed flamelet as the archetypal flamelet element. Acknowledgement The authors gratefully acknowledge the financial support of Natural Science Fund of China (Grant No: 51390490). Xu Wen is also grateful to the financial support by the Alexander von Humboldt Foundation, Bonn, Germany. In addition, we are grateful to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially. References [1] C.R. Shaddix, Coal combustion, gasification, and beyond: developing new technologies for a changing world, Combust. Flame 159 (2012) 3003–3006. [2] M. Muto, K. Yuasa, R. Kurose, Numerical simulation of soot formation in pulverized coal combustion with detailed chemical reaction mechanism, Adv. Powder Technol. 29 (2018) 1119–1127. [3] X.-Y. Zhao, D.C. Haworth, Transported PDF modeling of pulverized coal jet flames, Combust. Flame 161 (2014) 1866–1882.

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[4] M. Stöllinger, B. Naud, D. Roekaerts, N. Beishuizen, S. Heinz, PDF modeling and simulations of pulverized coal combustion–Part 2: application, Combust. Flame 160 (2013) 396–410. [5] O. Stein, G. Olenik, A. Kronenburg, F.C. Marincola, B. Franchetti, A. Kempf, M. Ghiani, M. Vascellari, C. Hasse, Towards comprehensive coal combustion modelling for LES, Flow, Turbul. Combust. 90 (2013) 859–884. [6] B. Franchetti, F.C. Marincola, S. Navarro-Martinez, A. Kempf, Large eddy simulation of a pulverised coal jet flame, Proc. Combust. Inst. 34 (2013) 2419– 2426. [7] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, A numerical simulation of pulverized coal combustion employing a tabulateddevolatilization-process model (TDP model), Combust. Flame 159 (2012) 353–366. [8] M. Rieth, A. Clements, M. Rabaçal, F. Proch, O. Stein, A. Kempf, Flamelet LES modeling of coal combustion with detailed devolatilization by directly coupled CPD, Proc. Combust. Inst. 36 (2017) 2181–2189. [9] J. Watanabe, K. Yamamoto, Flamelet model for pulverized coal combustion, Proc. Combust. Inst. 35 (2015) 2315–2322. [10] J. Watanabe, T. Okazaki, K. Yamamoto, K. Kuramashi, A. Baba, Large-eddy simulation of pulverized coal combustion using flamelet model, Proc. Combust. Inst. 36 (2017) 2155–2163. [11] D. Messig, M. Vascellari, C. Hasse, Flame structure analysis and flamelet progress variable modelling of strained coal flames, Combust. Theor. Model. 21 (2017) 700–721. [12] X. Wen, K. Luo, H. Jin, J. Fan, Large eddy simulation of piloted pulverised coal combustion using extended flamelet/progress variable model, Combust. Theor. Model. 21 (2017) 925–953. [13] X. Wen, H. Jin, O.T. Stein, J. Fan, K. Luo, Large eddy simulation of piloted pulverized coal combustion using the velocity-scalar joint filtered density function model, Fuel 158 (2015) 494–502. [14] X. Wen, K. Luo, H. Jin, J. Fan, Numerical investigation of coal flamelet characteristics in a laminar counterflow with detailed chemistry, Fuel 195 (2017) 232–242. [15] X. Wen, K. Luo, H. Wang, Y. Luo, J. Fan, Analysis of pulverized coal flame stabilized in a 3D laminar counterflow, Combust. Flame 189 (2018) 106–125. [16] N. Peters, Turbulent Combustion, Cambridge University Press, 2000. [17] H. Pitsch, Large-eddy simulation of turbulent combustion, Annu. Rev. Fluid Mech. 38 (2006) 453–482. [18] J. van Oijen, A. Donini, R. Bastiaans, J. ten Thije Boonkkamp, L. de Goey, Stateof-the-art in premixed combustion modeling using flamelet generated manifolds, Prog. Energy Combust. Sci. 57 (2016) 30–74. [19] M. Vascellari, H. Xu, C. Hasse, Flamelet modeling of coal particle ignition, Proc. Combust. Inst. 34 (2013) 2445–2452. [20] M. Vascellari, G. Tufano, O. Stein, A. Kronenburg, A. Kempf, A. Scholtissek, C. Hasse, A flamelet/progress variable approach for modeling coal particle ignition, Fuel 201 (2017) 29–38. [21] R. Knappstein, G. Kuenne, A. Ketelheun, J. Köser, L. Becker, S. Heuer, M. Schiemann, V. Scherer, A. Dreizler, A. Sadiki, Devolatilization and volatiles reaction of individual coal particles in the context of FGM tabulated chemistry, Combust. Flame 169 (2016) 72–84. [22] C.D. Pierce, P. Moin, Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion, J. Fluid Mech. 504 (2004) 73–97. [23] X. Wen, H. Wang, Y. Luo, K. Luo, J. Fan, Evaluation of flamelet/progress variable model for laminar pulverized coal combustion, Phys. Fluids 29 (2017) 083607. [24] G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W. Gardiner Jr, GRI-Mech 3.0, 1999, , 2011. [25] X. Wen, Y. Luo, K. Luo, H. Jin, J. Fan, LES of pulverized coal combustion with a multi-regime flamelet model, Fuel 188 (2017) 661–671. [26] S.M. Hwang, R. Kurose, F. Akamatsu, H. Tsuji, H. Makino, M. Katsuki, Application of optical diagnostics techniques to a laboratory-scale turbulent pulverized coal flame, Energy Fuels 19 (2005) 382–392. [27] T. Hara, M. Muto, T. Kitano, R. Kurose, S. Komori, Direct numerical simulation of a pulverized coal jet flame employing a global volatile matter reaction scheme based on detailed reaction mechanism, Combust. Flame 162 (2015) 4391–4407. [28] M. Rabaal, B.M. Franchetti, F.C. Marincola, F. Proch, M. Costa, C. Hasse, A.M. Kempf, Large eddy simulation of coal combustion in a large-scale laboratory furnace, Proc. Combust. Inst. 35 (2014) 3609–3617. [29] C.Y. Wen, Mechanics of fluidization, in: Chem. Eng. Prog., Symp. Ser., volume 62, pp. 100–111. [30] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, A numerical simulation of pulverized coal combustion employing a tabulateddevolatilization-process model (TDP model), Combust. Flame 159 (2012) 353–366. [31] J. Xie, W. Zhong, A. Yu, Mp-pic modeling of cfb risers with homogeneous and heterogeneous drag models, Adv. Powder Technol. 29 (2018) 2859–2871. [32] A.A. Zaidi, T. Tsuji, T. Tanaka, A new relation of drag force for high stokes number monodisperse spheres by direct numerical simulation, Adv. Powder Technol. 25 (2014) 1860–1871. [33] M. Muto, K. Tanno, R. Kurose, A DNS study on effect of coal particle swelling due to devolatilization on pulverized coal jet flame, Fuel 184 (2016) 749–752. [34] W. Ranz, W. Marshall, Evaporation from drops, Chem. Eng. Prog. 48 (1952) 141446.

Please cite this article as: X. Wen and J. Fan, Flamelet modeling of laminar pulverized coal combustion with different particle sizes, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.09.004

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X. Wen, J. Fan / Advanced Powder Technology xxx (xxxx) xxx

[35] R. Kurose, H. Makino, A. Suzuki, Numerical analysis of pulverized coal combustion characteristics using advanced low-NOx burner, Fuel 83 (2004) 693–703. [36] P. Cheng, Two-dimensional radiating gas flow by a moment method, AIAA J. 2 (1964) 1662–1664. [37] C.T. Crowe, M.P. Sharma, D.E. Stock, The particle-source-in cell (PSI-CELL) model for gas-droplet flows, J. Fluids Eng. 99 (1977) 325–332. [38] S. Badzioch, P.G. Hawksley, Kinetics of thermal decomposition of pulverized coal particles, Indust. Eng. Chem. Process Des. Develop. 9 (1970) 521–530. [39] CBC workshop, , 2017 (Accessed: 2017-04-02). [40] X. Wen, H. Wang, Y. Luo, K. Luo, J. Fan, Numerical investigation of the effects of volatile matter composition and chemical reaction mechanism on pulverized coal combustion characteristics, Fuel 210 (2017) 695–704. [41] S.-M. Hwang, Observation of spray flame stabilized in a laminar counterflow field, in: Proc. thirty-eighth Japanese Combust. Symp., 2000. [42] M. Baum, P. Street, Predicting the combustion behaviour of coal particles, Combust. Sci. Technol. 3 (1971) 231–243. [43] C. Hasse, N. Peters, A two mixture fraction flamelet model applied to split injections in a di diesel engine, Proc. Combust. Inst. 30 (2005) 2755–2762. [44] H. Pitsch, Flamemaster: A C++ computer program for 0D combustion and 1D laminar flame calculations, Cited in (1998) 81. [45] A. Ketelheun, G. Kuenne, J. Janicka, Heat transfer modeling in the context of large eddy simulation of premixed combustion with tabulated chemistry, Flow, Turbul. Combust. 91 (2013) 867–893. [46] X. Wen, M. Rieth, A. Scholtissek, O.T. Stein, H. Wang, K. Luo, A.M. Kempf, A. Kronenburg, J. Fan, C. Hasse, A comprehensive study of flamelet tabulation methods for pulverized coal combustion in a turbulent mixing layer–Part I: a priori and budget analyses, Combust. Flame (2019). [47] X. Wen, K. Luo, Y. Luo, H.I. Kassem, H. Jin, J. Fan, Large eddy simulation of a semi-industrial scale coal furnace using non-adiabatic three-stream flamelet/ progress variable model, Appl. Energy 183 (2016) 1086–1097. [48] X. Wen, K. Luo, Y. Luo, H. Wang, J. Fan, Large-eddy simulation of multiphase combustion jet in cross-flow using flamelet model, Int. J. Multiph. Flow 108 (2018) 211–225.

[49] M. Ihme, L. Shunn, J. Zhang, Regularization of reaction progress variable for application to flamelet-based combustion models, J. Comput. Phys. 231 (2012) 7715–7721. [50] M. Rieth, A.M. Kempf, O.T. Stein, A. Kronenburg, C. Hasse, M. Vascellari, Evaluation of a flamelet/progress variable approach for pulverized coal combustion in a turbulent mixing layer, Proc. Combust. Inst. 37 (2019) 2927–2934. [51] H.G. Weller, G. Tabor, H. Jasak, C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys. 12 (1998) 620–631. [52] K. Luo, H. Pitsch, M. Pai, O. Desjardins, Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor, Proc. Combust. Inst. 33 (2011) 2143–2152. [53] M. Nakamura, F. Akamatsu, R. Kurose, M. Katsuki, Combustion mechanism of liquid fuel spray in a gaseous flame, Phys. Fluids (1994–present) 17 (2005) 123301. [54] M. Ihme, Y.C. See, Prediction of autoignition in a lifted methane/air flame using an unsteady flamelet/progress variable model, Combust. Flame 157 (2010) 1850–1862. [55] A. Neophytou, E. Mastorakos, Simulations of laminar flame propagation in droplet mists, Combust. Flame 156 (2009) 1627–1640. [56] H. Wu, Y.C. See, Q. Wang, M. Ihme, A pareto-efficient combustion framework with submodel assignment for predicting complex flame configurations, Combust. Flame 162 (2015) 4208–4230. [57] B. Franzelli, B. Fiorina, N. Darabiha, A tabulated chemistry method for spray combustion, Proc. Combust. Inst. 34 (2013) 1659–1666. [58] H. Yamashita, M. Shimada, T. Takeno, A numerical study on flame stability at the transition point of jet diffusion flames, in: Symposium (International) on Combustion, volume 26, Elsevier, pp. 27–34. [59] P.D. Nguyen, L. Vervisch, V. Subramanian, P. Domingo, Multidimensional flamelet-generated manifolds for partially premixed combustion, Combust. Flame 157 (2010) 43–61. [60] X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, J. Fan, A generalized flamelet tabulation method for partially premixed combustion, Combust. Flame 198 (2018) 54–68.

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