Evaluation of coal particle volatiles reaction by using detailed kinetics and FGM tabulated chemistry

Fuel xxx (2016) xxx–xxx

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Evaluation of coal particle volatiles reaction by using detailed kinetics and FGM tabulated chemistry R. Knappstein ⇑, G. Kuenne, T. Meier, A. Sadiki, J. Janicka Institute of Energy and Power Plant Technology, Darmstadt University of Technology, Jovanka-Bontschits-Straße 2, 64287 Darmstadt, Germany

a r t i c l e

i n f o

Article history: Received 30 May 2016 Received in revised form 2 September 2016 Accepted 4 October 2016 Available online xxxx Keywords: Coal combustion Devolatilization FGM Tabulated chemistry Detailed chemistry simulation

a b s t r a c t The method of Flamelet Generated Manifolds (FGM) coupled with a coal devolatilization model is investigated with regards to its capability to accurately predict the volatiles combustion process of a single coal particle which is exposed to hot product gases. In this approach the gas phase chemistry is mapped onto a three-dimensional manifold controlled by the mixture fraction, a reaction progress variable and the enthalpy. Comparisons to results obtained by a detailed gas phase chemistry simulation which serves as a reference solution are made. Thereby the same numerical setup (i.e., code and mesh) is applied in order to judge on the chemistry treatment by FGM. In the analysis emphasis is put on the chemical states and their description in the context of tabulated chemistry. Also, the influence of common simplifying assumptions regarding the volatiles composition onto the combustion process is investigated. The analysis includes both the overall volatiles conversion as well as the gas phase chemistry around the particle in detail. As the applied configuration setup has a strong non-stationary character, the limitations of the FGM approach based on stationary premixed flamelets are demonstrated. Conclusions regarding the validity of FGM modeling assumptions in single coal particle simulations are drawn. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Pulverized coal combustion contributes to a significant degree to the worldwide primary energy consumption [1]. In order to reduce its environmental impact by an effective usage, a comprehensive understanding of coal and its conversion is required, which is obtained by both experiments and numerical simulation techniques. In the early stages of the coal conversion process the coal particles are subject of rapid heating. Volatiles release, ignition and volatiles reaction are the main processes during this phase. Fundamental knowledge is required in order to design reliable models for an appropriate description of these phenomena. Experimental research on single particles is conducted to obtain this understanding and to evaluate the validity of models. For instance, data of particle ignition measurements in a hot laminar coflow by Shaddix and Molina [2,3] are widely used as reference. Levendis et al. [4] focus on a phenomenological description of the partly strong differences in the combustion behavior of coals of different rank. Köser et al. [5] applied planar OH-LIF – measurements for the characterization of single particle combustion. Further examples of experimental investigations can be found in the literature ⇑ Corresponding author.

(e.g., [6–8]). Research on single coal particle ignition and volatiles combustion is also conducted numerically. For instance, a detailed study of coal particle ignition was carried out by Vascellari et al. [9]. In their work, the authors compared detailed chemistry simulations with non-premixed flamelet model results with overall good agreement both between the detailed chemistry and the flamelet simulation and with regards to experimental findings. Goshayeshi and Sutherland [10] evaluated the predictive capability of less elaborated models by comparing them to a detailed gas phase reaction mechanism coupled with a detailed coal kinetics model. It could be observed that the simplistic models are capable of reproducing trends but show less quantitative agreement with the detailed chemistry treatment. In their study, the authors also took the ignition delay as a decisive metric to judge on the agreement with experimental data. It was found, that the detailed models are well-suited to predict the ignition delay correctly. In our previous work [11] we simulated the ignition and volatiles reaction of single coal particles in a premixed flat flame configuration using a Flamelet Generated Manifold (FGM) approach. In the applied setup, particles cross a closed flame front and hence, are subject of rapid heat up due to the exposure to hot product gases. In our study, it was one of the aims to numerically reproduce the experimentally found particle ignition heights. Good agreement could be found regarding the global behavior. However, a

E-mail address: [email protected] (R. Knappstein). http://dx.doi.org/10.1016/j.fuel.2016.10.033 0016-2361/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Knappstein R et al. Evaluation of coal particle volatiles reaction by using detailed kinetics and FGM tabulated chemistry. Fuel (2016), http://dx.doi.org/10.1016/j.fuel.2016.10.033

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quantification of the accuracy of the combustion process around the particle and the justification of modeling assumptions remained an open question. In particular the accurate description of the non-premixed combustion regime around the particle with a stationary and premixed flamelet base as well as the substitution of the complex volatiles by the simple surrogate methane were the issues. In order to evaluate the former and to approximate the flat flame burner situation as good as possible, the same premixed flamelet-database was chosen in the present study. The aim of this work is threefold: Firstly, the accuracy in the description of the transient volatiles combustion process within the FGM context gets evaluated against a simulation that adopts a detailed gas phase reaction mechanism, which serves as a reference solution. Therefore, the same numerical setup (i.e., code and mesh) is applied. Conclusions regarding the validity of the FGM approach in strong non-stationary single coal particle combustion simulations are drawn. Differently to the work of Vascellari et al. [9], a premixed flamelet tabulation method under consideration of heat losses is used. Secondly, an analysis of the volatiles reaction process of single coal particles is given. Emphasis is put on the chemical states present during the volatiles combustion process and their description in the context of tabulated chemistry. Thirdly, the impact of different volatiles compositions on ignition and volatiles reaction gets examined. The outline of this work is as follows: In Section 2, numerical methods within the applied CFD-code are briefly exposed. Furthermore, the FGM modeling strategy and the mathematical description of the detailed chemistry approach are provided. Section 3 outlines the numerical configuration. Results are presented in Section 4 which is split into a description of the physical processes during the volatiles conversion process, an analysis of the impact of different assumed volatiles compositions and a comparison between FGM and detailed gas phase chemistry simulation results. At the end a summary is given.

2. Modeling and numerical methods 2.1. CFD-code FASTEST The academic block-structured CFD-code FASTEST is based upon the 3D finite volume method and solves the incompressible, variable density Navier-Stokes equations

@ q @ðquj Þ ¼ Sprt;m ; þ @xj @t

ð1Þ

@ qui @ðqui uj Þ @ @p ¼ sij  þ qg i þ Sprt;ui : þ @xj @xj @xi @t

ð2Þ

Herein, mass transfer between the phases is considered by particle source terms Sprt , which get detailed in Section 2.4. The coal particles are modeled by a Lagrangian approach. Hence, they are treated as spatially non-resolved discrete elements, which interact with the gas phase (2-way coupling). The temporal evolution of each particle is computed by an adaptive, explicit Runge-Kutta scheme of fourth order [12], whereas the time integration of the gas phase is performed by using an explicit, three-stage Runge-Kutta scheme of second order. Multi-dimensional Taylor-series expansion with second order accuracy [13] is used for the spatial discretization of the velocity. To ensure boundedness of scalar quantities the TVDlimiter suggested by Zhou et al. [14] is applied. Continuity is satisfied by solving a pressure correction equation within each RungeKutta stage.

2.2. FGM tabulated chemistry The FGM approach belongs to the group of flamelet models, which means that a turbulent flame is assumed to be an ensemble of laminar 1D-flames [15]. Initial formulations for premixed laminar flames within the flamelet context go back to de Goey and Thije Boonkkamp [16]. The development of the FGM approach originates from the work of van Oijen [17], van Oijen and de Goey [18] and van Oijen et al. [19]. The parallel development of the similar Flame-Prolongation of Intrinsic Low-Dimensional Manifolds (FPI) approach was conducted by Gicquel et al. [20]. Within the framework of FGM, detailed kinetics are considered for the gas phase reaction by computing laminar one-dimensional flames under premixed conditions prior to the actual CFD simulation. These flamelets then get tabulated on the basis of only a few control variables, which in turn have to be transported by the LES solver. In the present work, these are the mixture fraction f, the enthalpy h and a reaction progress variable Y CO2 .


 @ qf @ðquj f Þ @ @f þ Sprt;f þ ¼ qD @t @xj @xj @xj

ð3Þ


 @ qh @ðquj hÞ @ k @h þ Sprt;h þ ¼ @xj @t @xj cp @xj

ð4Þ


 @Y @ @ @ ðquj Y CO2 Þ ¼ qD CO2 þ x_ CO2 ðqY CO2 Þ þ @t @xj @xj @xj

ð5Þ

In this work, the flamelet computation is done by using the 1D detailed chemistry flame code CHEM1D [21,22] adopting the GRI 3.0 reaction mechanism [23]. Air and methane are oxidizer and fuel, respectively. Especially the simplifying choice of methane as fuel is of interest here, since it determines the volatiles composition. In our previous work [11] methane was also taken since coal combustion was assisted by a methane flame. In such gas assisted coal flames a further table dimension would be required for realistic volatiles compositions, which did not correspond with the model development state. Furthermore, the real volatiles composition was unknown. In this work this simple fuel gets validated against realistic volatiles compositions (Section 4.2) in order to judge on the impact of such simplifications. The mixture fraction f is defined as the sum of the elemental mass fractions of carbon and hydrogen ðf ¼ Z C þ Z H Þ. The enthalpy h consists of the sensible and the standard formation enthalpy and is therefore a conservative quantity. As the corresponding transport equation does not include a source term, no resolution requirements for the latter have to be met in LES computations, which makes this enthalpy form more advantageous for the treatment within the tabulated chemistry approach. As it is detailed in [24], the CO2 mass fraction is chosen as the reaction progress variable as a compromise between thermo-chemical accuracy and resolution requirements. Since carbon dioxide is not part of the assumed volatile composition, the transport equation of the progress variable (Eq. (5)) does not include a particle source term. For the tabulation, the flamelet computation is repeated for different equivalence ratios within the flammability range and also for varying enthalpy levels to account for heat transfer effects between the phases and towards walls. For an in depth description of the tabulation technique particularly with regards to the inclusion of enthalpy, the reader is referred to Ketelheun et al. [25]. A Lewis number of unity is assumed both for the flamelet computation and within the detailed chemistry CFD simulation, which is described in the following section. The manifold was extended to the full mixture fraction range by adopting an extrapolation technique given by Ketelheun et al. [26] to account for mixing processes. Within the approach, a

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non-reactive mixture is assumed outside the flammability limits. As volatiles enter the gas phase at different temperature levels depending on the particle state, preheated fuel is considered in the table. The final table is parameterized by the mixture fraction, the reaction progress variable and the enthalpy and mapped onto an equidistant grid consisting of 501  101  186 points (mixture fraction, reaction progress and enthalpy dimension) for a fast non-searching table access. In summary, the flamelet computation and tabulation underlies the following restrictions, which could contribute to deviations to the detailed chemistry solution: First, flamelets have a premixed structure. Second, flamelets are computed adopting a steady state chemistry assumption. Third, the influence of diffusive fluxes in mixture fraction as well as enthalpy direction are neglected during the flamelet generation process. This negligence arises since flamelets of different mixture fraction and enthalpy level are computed independently of each other and stringed together within the subsequent tabulation procedure. These restrictions should be kept in mind, when comparing FGM results with detailed chemistry.

As for the computations of flamelets, the GRI 3.0 reaction mechanism [23] is also used within the DC simulation in FASTEST. Hence, transport equations are solved for N s ¼ 53 species Y k ,


 @ @ @ @Y ðqY k Þ þ ðquj Y k Þ ¼ qD k þ x_ k þ Sprt;Y k ; @t @xj @xj @xj

ð6Þ

where the chemical source terms follow from the N r ¼ 325 elementary reactions according to

x_ k ¼ Mk

m00k;j  m0k;j



kf;j

j¼1

Ns Y

m0k;j

ck  kb;j

k¼1

Ns Y

m00k;j

ck

!

:

ð7Þ

of the forward reactions (kf;j ) follow from Arrhenius approaches, whereas the backward reaction constants (kb;j ) are obtained from the forward rates through the equilibrium constants. Mk and ck are the molar mass and the molar concentration of species k, respectively. Laminar viscosity and heat conductivity follow from the empirical temperature dependent equations [27]

cp

8

¼ 1:67  10




T 298 K




k T ¼ 2:58  105 cp 298 K

dT prt 3a  ðT  T prt Þ: ¼ D dt cp;prt qprt 2prt

are set to typical values of 1260 J=ðkg KÞ and 1200 kg=m3 , respectively. Devolatilization is described by the Single First Order Reaction (SFOR) model proposed by Badzioch and Hawksley [32]. It describes the volatiles release rate via

Sprt;m ¼


 1 X dY  mprt;0 V cell prt dt

ð13Þ

Sprt;ui ¼


 1 X dY  mprt;0 ui;prt V cell prt dt

ð14Þ

Sprt;f ¼


 1 X dY  mprt;0 f prt V cell prt dt

ð15Þ

Sprt;h ¼


 1 X dY dT prt dY  mprt;0 hprt   mprt;0 hpyr cp;prt mprt  V cell prt dt dt dt ð16Þ

ð8Þ

0:69 :

Sprt;Y k ¼


 1 X dY  mprt;0 Y k;vol V cell prt dt

Sprt;hs ¼


 1 X dY dT prt dY  mprt;0 hprt;s   mprt;0 hpyr cp;prt mprt  V cell prt dt dt dt

ð9Þ

Due to the stiffness of the species transport equations the chemical source terms get separately integrated within each Runge-Kutta stage by using the Livermore solver LSODE [28]. Differently to FGM the sensible enthalpy is transported in DC _ T follows computations where the corresponding source term x from the elementary reactions (e.g., [29]).


 X Ns @ qhs @ðquj hs Þ @ k @hs 0 _ k þ Sprt;hs  k¼1 Dhf;k x ¼ þ @xj @xj cp @xj |fflfflfflfflfflfflfflfflfflfflfflffl @t ffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð10Þ

x_ T

Within DC this enthalpy form is preferred [29]. Contrary to FGM _ T in Eq. (10) is not the proper resolution of the heat release source x an issue, as high spatial resolution requirements already have to be met for the accurate solution of all species transport equations including radicals.

ð12Þ

Herein, Y and Y 0 are the current and final volatile yield, respectively. The Arrhenius parameters as well as Y 0 follow from pyrolysis kinetics investigations of the applied coal [33] and were set as specified in Table 1. For details regarding the experimental technique the reader is referred to [33,34]. The particle source terms (in Eqs. (1)–(4), (6) and (10)) are formulated according to

0:51 ;

ð11Þ

Herein, a is the heat transfer coefficient based on a Nusselt number calculated according to the correlation of Ranz and Marshall [30,31]. T denotes the gas phase temperature at the particle position. The particle heat capacity cp;prt and the particle density qprt

k¼1

The stoichiometric coefficients on the educt and product side are indicated by m0k;j and m00k;j , respectively. The reaction constants

l

In the investigated generic configuration, which is depicted in Section 3, the rapid heating of a coal particle in burnt gases gets reproduced. Since the purpose of the present study is an evaluation of the accuracy and validity of FGM simulation results, the impact of radiation is not of interest and therefore not considered here. Hence, changes in the particle temperature evolve according to


 dY E : ¼ ðY 0  YÞAT bprt exp dt RT prt

2.3. Detailed chemistry (DC)

Nr  X

2.4. Interaction of gaseous and discrete phase

ð17Þ

ð18Þ Herein, V cell denotes the volume of the cell which the source terms get projected onto. Thereby the non-resolved particle is treated as a point (Particle Source In Cell method (PSIC)) [35]. The index 0 denotes the particle’s initial state. The quantities f prt ; hprt and hprt;s describe the state of the gaseous volatiles entering the Eulerian phase from the particle. Since volatiles are assumed to be pure methane within the FGM context, f prt equals unity. In FGM computations the volatiles enthalpy hprt is taken from the chemistry table and is a function of the table control variables, whereas it gets calculated depending on volatiles composition and temperature in case of DC (hprt;s ). Heat of pyrolysis is calculated from energy balance considerations of the applied coal. Its term, hpyr , depends on

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Table 1 Devolatilization kinetic parameters for Eq. (12). Y0

A

b

E

0:5494

29; 058 1=s

0

42; 879 J=mol

the assumed volatiles composition as it is detailed later. Y k;vol is the mass fraction of the k-th species in the volatiles. The present work investigates the volatiles gas phase reaction. Therefore the heterogeneous char conversion is not taken into account. 3. Configuration The setup detailed in this section approximates the situation in which a coal particle is exposed to rapid heat up after it has crossed a premixed flame front as it was the case in [11]. All simulations are carried out using the generic rectangular domain depicted in Fig. 1. Herein, the particle is artificially kept at a constant position (x ¼ 2 mm) on the center axis, which is numerically realized by neglecting its drag (see Eq. (14)). As detailed in Meier et al. [36], a spatial resolution of 50 lm is the maximum allowable cell size for a correct reproduction of flame speed and structure when the GRI 3.0 mechanism is used. In order to ensure a sufficient degree of accuracy a grid size of Dx ¼ 40 lm is taken, which results in a total of 312,500 cells. The Eulerian field is initialized with the chemical equilibrium state of product gases resulting from methane-air combustion with U ¼ 0:6555. A constant mass flux with u ¼ 0:4 m=s of the same chemical state is imposed at the inlet to provide the volatiles reaction with oxygen. A fresh particle (T prt ¼ 300 K) is initiated in this hot environment at the beginning of the simulation. The particle Reynolds number Reprt is much smaller than one and hence, the flow is laminar. A physical time of 10:5 ms was simulated with a time step size of Dt ¼ 1:5  107 s until volatiles conversion ended. A particle size of 20 lm was chosen, which is smaller than typical particles in pulverized coal combustion. However, it is considered meaningful because of three reasons. Firstly, the focus of the present work lies on a comparison between DC and FGM simulations as well as on the evaluation of modeling assumptions of the latter. A larger particle would only affect the total fuel amount, the particle heat up rate and hence, the volatiles release rate, but not the observable qualitative phenomenology of the conversion process. Thus, the chemistry of the combustion process of volatiles should not be influenced by the particle size in the context of numerical simulations. Secondly, a short volatiles conversion process (which corresponds with a small particle size) is desirable as DC simulations are computationally expensive and the simulated physical time is a critical factor. Thirdly, a particle smaller than the cell conforms to modeling restrictions of the EulerianLagrangian approach in which the particle itself is not resolved. 4. Results 4.1. Physical processes in volatiles reaction A detailed gas phase chemistry simulation was performed in order to evaluate the physical processes during volatiles reaction of a single coal particle. As depicted in Fig. 2 data are analyzed alongside the center line of the configuration. In this simulation the volatiles are solely composed of CH4 . The hot product gases surrounding the particle transfer heat to the particle, which in turn increases its temperature. Hereupon volatiles enter the gas phase, which is depicted in the left column of Fig. 2. Before any reaction occurs, the species mass fractions are affected by the mixing of volatiles gases. Once a flammable

Fig. 1. Schematic of the computational domain. The blue and red colored surfaces indicate inlet and outlet, respectively. Symmetry boundaries are gray-colored. The particle is depicted at its position on the center axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

mixture and a sufficient amount of activation energy is provided, this mixture initially starts to react at the particle position. In the following (mid column in Fig. 2) a mixture close to stoichiometry diffuses in radial direction and forms a sphere shaped reaction zone around the particle, which can particularly be seen in the _ CO2 ; Y OH and the temperature. A slight asymmetry in shape of x the reaction strength can be observed which is due to the flow approaching the particle from the left. When the volatiles release is almost over, the reaction decreases again and chemistry approaches its equilibrium state (right column in Fig. 2). It should be kept in mind that the particle and correspondingly the boundary layer around it are not resolved. Hence, due to spatial resolution limitations a mixing state composed of released volatiles and surrounding gases forms in the particle containing cell. The processes occurring in a physical particle boundary layer in the very early phase right after the onset of ignition cannot correctly be described in the context of the unresolved particle modeling approach. So, until a sufficient amount of volatiles diffuses in radial direction and thereby shifts the reaction to a properly resolvable radius, the particle containing cell represents a spatially integrated mean of the diffusion flame which would form close around the particle in the very early phase of volatiles reaction.

4.2. Impact of volatiles composition Substitution of complex volatiles by simpler surrogates is a usual modeling aspect in the context of numerical simulations. In our previous work [11] it was assumed that volatiles are solely composed of methane within the modeling context. By adopting detailed gas phase chemistry simulations this assumption can be verified against a realistic volatiles composition, which was unknown in our previous study and got recently determined experimentally [34]. Thereby, it can be quantified to which extent a complex fuel such as volatiles can be substituted by a simple surrogate such as methane. The experimentally determined composition is given in Table 2. The properties of the coal are summarized in Table 3. As the GRI 3.0 reaction mechanism is adopted for the gas phase chemistry, species which are not part of the mechanism have to get assigned to other volatiles species. Namely, benzene, toluene and C3 H6 , which constitute a total mass fraction of 26.9% are replaced by C3 H8 . Although the aromatic hydrocarbons have a different reactivity, this is considered to be the least impacting substitution since the mentioned species have comparable heating values [37].

Please cite this article in press as: Knappstein R et al. Evaluation of coal particle volatiles reaction by using detailed kinetics and FGM tabulated chemistry. Fuel (2016), http://dx.doi.org/10.1016/j.fuel.2016.10.033

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Fig. 2. Species mass fractions, chemical source term of CO2 and gas phase temperature along the configuration center line following from the DC simulation for different instances after particle initialization.

Table 2 Experimentally determined volatiles composition of high-volatiles Columbian coal Norte [34]. Species mass fraction Y CO2 Y CO Y CH4 Y C2 H6 Y C2 H4 Y C2 H2 Y C3 H8 Y C3 H6 Y NH3 Y HCN Y Benzene Y Toluene

Value 0:1431 0:2812 0:1220 0:0272 0:1108 0:0085 0:0305 0:0162 0:0019 0:0058 0:1697 0:0831

Table 3 Coal properties of Columbian Norte. Proximate analysisa Moisture Ash Volatile matter Fixed carbon Ultimate analysisb Carbon Hydrogen Oxygen Nitrogen Sulfur a b

As received. Dry and ash free basis.

wt.% 2.89 8.45 35.80 52.86 wt.% 78.14 5.22 13.55 1.96 1.13

As it can be observed in Fig. 2, the reaction zone is almost symmetric around the particle. Making use of this only values downstream of the particle are plotted for an improved recognizability in the following. In Fig. 3 it is depicted how a different complexity in volatiles composition affects the conversion process. Regarding the impact of the volatiles composition it can be observed, that an oxygen deficit forms at the particle position and becomes larger until the maximum extent of the chemical reaction process is reached. This deficit is less distinct when O-containing species are part of the volatiles composition. Also, it can be observed that radicals such as OH show only slight sensitivities both regarding their spatial distribution and their temporal evolution. Differences occur for carbon dioxide. This species is part of the realistic composition and hence, it occurs in the particle vicinity not only because of chemical reactions but also through mixing of volatiles with the surrounding gas phase. Both, shape and temporal evolution deviate. When using only methane as volatiles a sphere-shaped reaction zone with a correspondingly shaped CO2 distribution is yielded. Mass release of complex volatiles causes a peak of CO2 at the particle position. If one looks at other major product gases such as H2 O, one can see that results of both compositions quantitatively differ from each other but are in agreement regarding their shape. However, also the production of water is affected by the volatiles composition. This is plausible as O-containing molecules are part of the realistic volatiles composition and hence, a larger amount of O-containing product gases forms. As mentioned in Section 2.4, heat of pyrolysis is taken into account for the energy balance. For the realistic volatiles composition, hpyr amounts to 85:5 kJ=kg, which corresponds to physically correct behavior. If pure methane is assumed as the volatiles composition, an artificial physical situation is introduced. In that case one has to use the corresponding and significantly larger heating value for the determination of hpyr to maintain a correct energy balance. Owing to this modeling assumption the situation is artifi-

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Fig. 3. Species mass fractions, chemical source term of CO2 and H2 O as well as gas phase temperature along the configuration center line for different instances after particle initialization. Solid lines: volatiles consisting solely of CH4 . Dotted lines: experimentally determined volatiles composition.

cial as such amounts of heat would not be released in a physical volatiles conversion process. Accordingly, hpyr ensues to 23:4 MJ=kg in case of pure methane. In the left of Fig. 4 particle heat up curves are depicted. The particle heat up when neglecting pyrolysis heat is included for comparison. As it can be seen at about 0:5 ms where mass release sets on, large amounts of enthalpy are extracted from the gas phase and lead to a decreased particle heat up rate in the methane case. The correspondingly lower gas phase temperature is depicted in the left column of Fig. 3. As the chemical reaction close to the particle sets on and quickly becomes stronger, the heat release (mid column of Fig. 3) enhances particle heating and devolatilization again. As a consequence devolatilization (shown in the right of Fig. 4) is shifted by approximately 0:3 ms. In summary, the investigated volatiles compositions cause plausible differences in the chemistry around the particle, which can be assigned to composition properties. Gas phase temperature level and major species concentrations are affected to a significant degree. The introduction of an artificial volatiles composition

(i.e., pure methane) and the corresponding consistent energy treatment results in a somewhat unphysical, however explainable behavior of the particle properties which arises from the large contribution of the pyrolysis term. Local differences in the gas phase chemistry as well as a shift in particle devolatilization originating from an affected particle heat up could be observed. However, if one regards duration and phenomenology of the overall volatiles conversion process, deviations remain within reasonable bounds. Hence, in simulations of individual particles (such as flat flame configurations) realistic complex volatiles compositions can be substituted by methane with an acceptable error following from local deviations in the chemistry and a consistent but artificial energy treatment. However, the influence of the observed differences onto the overall combustion process in real coal furnaces with millions of coal particles remains to be investigated. It can be expected, that configurations, in which the major heat release comes from methane pilot flames and only to a minor degree from the volatiles reaction are probably less affected by the substitution of volatiles with simple surrogates.

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Fig. 4. Comparison of particle properties during heat up and devolatilization.

4.3. Comparison between FGM and DC In the context of FGM certain inherent modeling assumptions are made. As outlined in Section 2.2 these are steady state flamelet chemistry, premixed flamelet structure and negligence of fluxes in mixture fraction as well as in enthalpy dimension during flamelet computation. It is the aim of the present work to quantify to which extent this approach is capable of reproducing the transient, partially premixed regime of the volatiles reaction process as computed in a DC simulation which serves as the reference solution. In the work of Franzelli et al. [38] a partially premixed spray combustion flame comparable to the one of the present work is investigated. Herein premixed and non-premixed flamelet data bases are compared to a multi-regime tabulation technique. A detailed chemistry reference solution for the one-dimensional axisymmetric counterflow jet was taken. One of the conclusions drawn was that only the multi-regime flamelet tabulation overcomes the deficiencies of both, the premixed and the non-premixed tabulations. The present work aims first, to evaluate the suitability of the approach under consideration of heat losses between the phases which is considered of particular importance in the context of coal particle combustion. This is accounted for by the inclusion of enthalpy as the third table control variable. Second, the present work assesses the impact of transient effects in a threedimensional configuration. For the comparison between FGM and DC (Section 4.3) volatiles are assumed to be solely composed of methane. Heat of pyrolysis is neglected in equal measure for both DC and FGM in Section 4.3. This is done in order to avoid the impact of the artificially high pyrolysis heat contribution and the consequential temporal separation of methane generation inside the particle expressed by the latent heat extraction from the fluid and its combustion (see Fig. 4). 4.3.1. Physical space Fig. 5 depicts a comparison between FGM and DC simulation results for the volatiles combustion process. The mixture fraction as a passive scalar is in good agreement for all stages of the conversion process. Differences occur for educts such as methane and oxygen but also for intermediate species like OH. Comparing the results, the FGM approach seems to reveal a more advancing reaction than the DC. This can be deduced from the significantly lower CH4 -peak and the more distinct O2 -deficit in the FGM as well as from the temporal development of the radical pool, for which OH is taken as an example. After a certain period of time the amount of OH increases and follows the FGM solution. As will be detailed below, this characteristics are most probably a consequence of transient conditions in chemical kinetics, which are not captured

within the stationary flamelet approach. The simulations reveal slight quantitative differences for CO2 but good agreement regarding its distribution and temporal development. If one evaluates the chemical source of the latter, it can be observed that FGM shows a much higher conversion rate and accordingly, an increased temperature level. Here, it is likely that in addition to the above mentioned non-stationarity aspect the chosen premixed flamelet combustion regime affects the reproducibility of zones dominated by diffusion. Amongst other things Franzelli et al. [38] investigated the applicability of premixed flamelet databases to regimes which are very similar to the one in the present work. In [38] deviations of comparable size were observed for the chemical source term of the progress variable, which could clearly be attributed to the regime the flamelets are based on. Hence, the observed differences are not surprising. However, their source must be identified, which is done in the following. 4.3.2. Composition space In order to judge on the differences between FGM and DC simulation results, certain stages of the volatiles conversion process are depicted in composition space in Fig. 6. All cell values on the configuration center axis from particle position (x ¼ 2 mm) downstream till the outlet (x ¼ 5 mm) are evaluated. States are projected onto the mixture fraction – gas phase temperature plane. In that scatter plot each circle denotes the state of a cell obtained by the FGM simulation, whereas the squares indicate results obtained by DC. The colors of the symbols thereby signify the reaction progress normalized with the corresponding manifold equilibrium value (in dependence of mixing state and enthalpy level). Right after particle initialization (t ¼ 0:20 ms) the states are determined by a drop in gas phase temperature which is due to heat transfer to the particle. Devolatilization has not yet started. Hence, mixing does not play a role at that instant. Both, FGM and DC chemical states are very close to chemical equilibrium and almost identical. As the devolatilization process sets on (t ¼ 0:59 ms), volatile gases and the surrounding product gases mix with each other which can be seen in the occurrence of richer mixture fraction states. Here, the normalized reaction progress decreases until 0.7. Effects of finite rate chemistry become apparent, which are principally captured by the FGM. However, FGM and DC differ significantly from each other in that instant. This is due to a lag in the temporal development of reactivity of the DC as will be detailed further below. Mixing with volatile gases induces a chemical state within the reactive region of the manifold in cells close to the particle. Hence, chemical reaction and further mixing (due to the ongoing devolatiliztion process) overlap.

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Fig. 5. Species mass fractions, mixture fraction, chemical source term of CO2 as well as gas phase temperature and enthalpy along the configuration center line for different instances after particle initialization. Solid lines: DC simulation. Dashed lines: FGM simulation.

As the volatiles conversion further proceeds, the above mentioned concurrence of mixing and chemical reaction leads to values outside the manifold (t ¼ 0:98 ms). These values correspond to the particle containing cell. Here, the FGM result is further away from chemical equilibrium as determined by the manifold than the DC. As the table bases on independent computations of premixed onedimensional flamelets, which differently to non-premixed flamelets do not take fluxes in mixture fraction direction into account during the flamelet generation, it is hence subject of an underlying regime assumption that affects the shape of the manifold. Because of these regime assumptions in the tabulation process such deviations can occur in situations of strong mixing with volatiles. Since the detailed chemistry is not subject of such assumptions, it is capable of reproducing the diffusion-like regime dominant at this particular position. However, the occurrence of such states outside the manifold is limited to the particle containing cell. As it can further be seen in Fig. 6, FGM and DC converge against an equilibrium state through reactive and diffusive processes. Here, deviations between the concepts also exist. Their origin is investigated more deeply in Section 4.3.3.

In Fig. 7 it is schematically depicted how chemical states outside the manifold can occur. The undisturbed chemical state of the surrounding gases is indicated by 1. As outlined above, cooling by the particle and mixing by devolatilization leads to chemical states within the reactive region, which is denoted by 2 in Fig. 7. The path from 2 to 3 indicates the chemical reaction of the volatiles. Concurrently, further volatiles having state 4 (pure fuel) enter the gas phase and mix with the burnt volatiles. This mixing process resulting in state 5 is represented by the dashed black line. The ways the DC and FGM methodologies treat states outside the manifold are different. Using detailed kinetics, chemical equilibrium is reached after a sufficient amount of time. Hence, if further mixing could be switched off, the chemical equilibrium would be reached in the context of the reaction mechanism, which is indicated by the green1 arrow in Fig. 7. Using FGM instead, a negative reaction progress is not intended by the methodology. Hence, the chemical equilibrium state cannot be reached by chemical kinetics, if one starts

1 For interpretation of color in Fig. 7, the reader is referred to the web version of this article.

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Fig. 6. Chemical states alongside center axis at different stages of volatiles conversion process for different instances after particle initialization. Circles denote FGM results. Squared symbols indicate DC results. The color bar signifies the reaction progress normalized with the corresponding manifold equilibrium value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

from a super-equilibrium state. Dissolving this situation happens through diffusive and convective fluxes. As the manifold does not provide any super-equilibrium states, the chemical equilibrium value at the corresponding mixture fraction and enthalpy level is extracted from the table as this is the closest chemical state the table can provide. However, differences between the super-equilibrium state and the equilibrium value taken from the table are small as both states are burnt and density, viscosity and temperature differ only slightly. Furthermore, the occurrence of states outside the manifold is a spatially very limited event (i.e., only one cell is affected). An illustration of the three-dimensional chemistry table and the reactive region in particular is given in Fig. 8. Herein, it is exemplarily depicted how the chemical states around the particle are exposed to the latter. As shape and strength of the reactive region depend on the enthalpy level and chemical states during the volatiles mixing process are exposed to this sensitive region, the consideration of enthalpy as a table control parameter can be of relevance for the proper description of the conversion process. In order to classify typical chemical states as discussed above within the three-dimensional manifold, states along the center line downstream of the particle at around 1 ms are illustrated in Fig. 8

exemplarily. In the left the shape of the manifold spanned by the mixture fraction, the reaction progress variable and the enthalpy is depicted. Here, the contour indicates the normalized reaction progress. In the right the same instant is shown within the translucent manifold revealing the reactive region. Each cell value alongside the center line is depicted by one green sphere, whereas the blue arrow indicates an increasing distance to the particle. Only the particle containing cell state (denoted by 1) is outside the manifold. With increasing particle distance the states cross the reactive region (2) until an equilibrium state right at the border of the manifold (3) is reached. 4.3.3. Analysis of transient effects Detailed chemistry and FGM differ in the way their chemical states are reached. Whereas for FGM it is only a matter of traversing a manifold, in case of DC it is subject to the detailed reaction kinetics. This section is explicitly dedicated to the impact of transient effects. Particle properties of both simulations, FGM and DC, are illustrated in Fig. 9. As the figure reveals, the particle is subject of drastic heat up in the order of 600,000 K/s, which shows the strong

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Fig. 7. Schematic illustration of the mechanism that leads to chemical states outside the manifold exemplary shown at a constant enthalpy level. State 1: chemical equilibrium of surrounding gases. From 2 to 3: chemical reaction of volatiles. Overlapping to this reaction mixing of fresh volatiles (4) with burnt volatiles (3) yields a chemical state, which is outside the manifold (5).

Fig. 8. Section of the three-dimensional chemistry table. PV represents the normalized reaction progress variable. In the right the reactive region is revealed by the translucent manifold. Green spheres indicate chemical states of individual cells on the center line. The state denoted by 1 corresponds with the particle containing cell. 2 marks the region, in which significant chemical reaction takes place. At 3 chemical equilibrium is reached. The blue arrow denotes an increasing distance to the particle. The illustration exemplary shows chemical states at around 1 ms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

non-stationary character of the setup. As long as the chemical reaction around the particle has not set on both approaches are close to each other. From that point (T prt  900 K) deviations in the particle temperature induce slight differences in the particle volatiles mass fractions. Overall, especially changes in the particle temperature appear rather uneven for the FGM particle, which suggests that in FGM computations the gas phase temperature field varies stronger. An evaluation of the chemical source term of CO2 integrated over the complete domain as a measure for overall volatiles conversion yields very good agreement between DC and FGM (Fig. 10). It can be observed that the DC has a time lag of

approximately 0.2 ms within the first 2 ms. Since a radical pool has to form following the reaction kinetics of the mechanism in the DC simulation, this lag is very small if one considers that the setup is characterized by a strong non-stationarity. Even the fact that the flamelets used for the FGM tabulation are stationary does not impose a significant constraint for the investigated transient volatiles conversion processes. However, differences in composition space were observed. These could be due to the above mentioned time lag in the DC simulation. In order to better judge on the differences a source term evaluation as schematically depicted in Fig. 11 was conducted.

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Fig. 9. Comparison of particle properties.

Fig. 11. Illustration of the conditioned comparison in between DC and tabulated values.

Fig. 10. Chemical source term of CO2 integrated over the complete domain.

The DC simulation cell values downstream of the particle alongside the center axis were extracted. Each one has a chemical source for CO2 obtained within the detailed chemistry simulation, which _ CO2 ;DC . Also values for mixture fraction, progress is denoted by x variable and enthalpy can be attributed to the extracted DC simulation results. With these table control parameters originating from the DC the chemistry table used in FGM computations is _ CO2 ;Table is accessed and a corresponding source term denoted by x extracted. Finally the difference between both source terms _ CO2 ¼ x _ CO2 ;Table  x _ CO2 ;DC ) gets computed. It quantifies the dif(Dx ference between realistic chemistry kinetics and the corresponding chemical reaction as indicated by the FGM with its inherent modeling assumptions and thereby provides a measure for the tempo_ CO2 is ral lag in the evolution of the chemical reaction. If Dx positive, the chemistry table indicates a larger value for the chemical source of CO2 than computed by the DC. Accordingly, a negative value signifies a stronger DC reaction. A direct comparison of local values of the source term resulting from the FGM computa_ CO2 ;DC is not meaningful, since the former already foltion with x lows from its history which differs to the DC development as demonstrated above. Namely, a more progressive reaction in the FGM context yields higher gas phase temperatures around the particle which lead to an intensified particle heat up. This in turn releases more volatiles that again impact the flame structure. Hence, a direct comparison of conversion rates along local center

line positions would imply inseparable effects resulting from the previous reaction progress. _ CO2 and x _ CO2 ;DC are In Fig. 12 the temporal courses of Dx depicted at different axial distances to the particle. Due to the different axes of ordinate the illustration is split into two ranges; the left depicts the close vicinity to the particle, the right one covers further distances. For the close vicinity of the particle (left of Fig. 12) a partially strong temporal delay of the DC can be observed. However, at dax ¼ 40 lm the DC source term becomes as strong as the reaction which would have taken place within the tabulated chemistry context for a short range of time (at about 1.5 ms). For slightly larger distances (dax ¼ 80 lm and dax ¼ 120 lm) the FGM table continuously suggests a stronger reaction. However, since the volatiles reaction can be well approximated as sphere-shaped, the contribution of such small distances to the overall volatiles conversion is small as it scales with the radius (distance to particle) to the power of two. The more intense reaction in the close vicinity of the particle within the tabulation context also explains the higher heating rate that could be observed in Fig. 9 between t  0:5 ms and t  1:2 ms. The subsequent decline in particle heating rate corre_ CO2 in the region of t  1:5 ms. lates with the negative values for Dx Regarding the distances within the range dax ¼ 200 lm to 440 lm it can be clearly observed that after a more progressive advance of the tabulated chemistry reaction the detailed reaction kinetics follow with a delay and become stronger with growing radius. At these particle distances, the magnitude of the temporal lag is much smaller than closer to the particle. However, due to the quadratic influence of the particle distance the reaction in this range contributes strongly to the good agreement shown in Fig. 10. In summary it can be said that the detailed chemistry reaction is slightly shifted towards larger radii compared to tabulated chemistry equivalents and that the former compensates a more

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_ CO2 ;DC according to Fig. 11 for different axial distances to the particle. _ CO2 as well as x Fig. 12. Dx

progressive advance of the tabulated reaction with a delay in time. The impact of fluxes neglected in the applied FGM approach could not completely be separated from non-stationary chemistry effects. Therefore, an estimation concerning the influence of the former is given in Appendix A. 5. Conclusion In the present work the FGM method coupled with a simple devolatilization model was investigated with respect to its capability to accurately reproduce the gas phase chemistry of the volatiles reaction. For this purpose a detailed chemistry simulation adopting the GRI 3.0 reaction mechanism was taken as a reference solution. Different modeling assumptions concerning flamelet regime, steady state flamelet chemistry and choice of volatiles composition were assessed. The former could not completely be separated from non-stationary chemistry effects. Regarding different volatiles compositions, a realistic one obtained in experiments was compared to methane as a simple surrogate. It was shown that the conversion process is not affected in a global sense whereas minor but explainable differences occur in species mass fractions and in the gas phase temperature. If the focus lies on the overall coal conversion and particle characteristics, realistic volatiles (if approximately describable with GRI 3.0 species) can be substituted by methane in individual coal particle simulations with acceptable deviations in the gas phase chemistry with limited local extent. Regarding the comparison between FGM and DC deviations both in physical and in composition space were observed. Their significant occurrence was however limited to only a few cells around the particle and could be attributed to the choice of a premixed flamelet regime and a delay in the temporal development of detailed chemistry

kinetics. The distinction of this time lag depends on the distance to the coal particle. For the cumulated volatiles conversion process very good agreement between FGM and DC could be observed. In summary it was one of the aims of this work to demonstrate the potential but also limitations of a premixed FGM modeling approach in the context of coal volatiles combustion. At this we considered a single particle, which on one hand allows a very detailed assessment but on the other hand represents a different situation to the particle group combustion dominant in real furnaces. Accordingly the findings and corresponding conclusions represent a necessary, however not sufficient piece of knowledge with regard to these applications. With the observed differences between FGM and reference solution in mind the applied approach seems to be suited for further development towards the inclusion of char conversion and hence, towards the consideration of multimixture fraction regimes, where complex volatiles compositions could be taken into account. Acknowledgements The authors kindly acknowledge financial support through Deutsche Forschungsgemeinschaft (DFG) through SFB/TRR 129. Computations were performed on the Lichtenberg High Performance Computer in Darmstadt. Appendix A A.1. Estimation of neglected fluxes in the applied FGM approach In order to judge on the impact of diffusion in mixture fraction and enthalpy direction, the order of magnitude of mixing and

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chemical source terms gets estimated. The significance of these fluxes can be obtained by considering the species transport equation when transformed into composition space (see e.g., [39] for the derivation). In this transformed form,

q

@Y k 1 @2Y k 1 @2Y k _ k þ qvf þ qvY CO ; /x 2 2 @Y 2 2 2 @t @f CO2

ð19Þ

the scalar dissipation rates v/ representing this fluxes out of which only the one towards the progress variable direction is accounted for in the table generation process. Accordingly, if the other terms like the scalar dissipation rate towards the mixture fraction direction

vf


 @f @f ¼ 2D @xi @xi

ð20Þ

provide a contribution comparable to the other terms of the transport equation, errors are introduced. In the following an order of magnitude estimation is provided to identify the impact of the different terms on the right hand side of Eq. (19). In Fig. 13 the scalar dissipation rate vf is exemplarily depicted for t ¼ 1:87 ms. It can be seen that vf is significantly present close around the particle. This confirms that mixing is a fundamental process. However, its impact is bounded to a region around the particle narrower than the reaction zone. Since vY CO 2

is considerably smaller than vf , it is therefore not further evaluated. Different terms of Eq. (19) are given in Table 4. As only a limited amount of species and radial positions is evaluated, the given data serve only as an estimation of the terms’ order of magnitude. Values are given at particle distances of 80 lm as well as 180 lm. It can be seen that mixing contributes to a relevant but not dominant amount to the temporal change in species mass fraction, which can be concluded from the order of magnitude of the

Fig. 13. Chemical source term of CO2 and scalar dissipation rate at t ¼ 1:87 ms.

Table 4 Contributing terms in Eq. (19) at different distances to particle.

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_ k . Furthermore, the influcorresponding chemical source term x ence of mixing decreases more drastically with growing radius than the chemical reaction strength. Judging from the given exemplary data, the terms neglected in the table generation can have a certain contribution in the close vicinity to the particle as they are of comparable order as the source term. Analogous conclusions can be drawn for diffusive fluxes in enthalpy direction as mixture fraction and enthalpy are strongly correlated.

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