- Email: [email protected]

Proceedings

ScienceDirect

of the

Combustion Institute

Proceedings of the Combustion Institute xxx (2014) xxx–xxx

www.elsevier.com/locate/proci

Flamelet model for pulverized coal combustion Junya Watanabe ⇑, Kenji Yamamoto Research & Development Center, Mitsubishi Hitachi Power Systems, Ltd., Japan

Abstract A new ﬂamelet model applicable to the simulation of pulverized coal combustion has been developed. First, a modeling approach that considers the coupling with both devolatilization and char combustion was adopted. We changed the fuel composition of the ﬂamelet equation relative to the states of devolatilization and char combustion. In order to determine the fuel composition coming through the char combustion, all the gasiﬁed char was assumed to be converted into CO by the oxidation reaction. The validity of the developed ﬂamelet model was examined in a simple two-dimensional pulverized coal jet ﬁeld ignited by burnt co-ﬂows. The accuracy of the model was evaluated by comparing its instantaneous distributions of temperature, CO2 mass fraction, and OH mass fraction with those of a detailed chemistry model. Good agreement was obtained in terms of the overall features of turbulent structures and combustion state, although the ﬂamelet model showed slightly quicker ignition due to the transitional state in the ignition process being insuﬃciently reproducible. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Pulverized coal combustion; Flamelet; Detailed chemistry; Turbulent jet ﬂame; Ignition

1. Introduction Pulverized coal combustion technologies must be advanced to achieve stable ignition, attain highly-eﬃcient combustion, and reduce NOx and CO2 emissions in coal-ﬁred thermal power plants. The ﬂow and combustion state inside a coal-ﬁred boiler must be understood in detail to improve performance and develop new combustion technologies. Numerical analysis is a powerful tool for this purpose. Therefore, many simulations of pulverized coal combustion have been extensively conducted. Recently, large-eddy simulation (LES) ⇑ Corresponding author. Address: 832-2 Horiguchi, Hitachinaka-shi, Ibaraki-ken 312-0034, Japan. E-mail address: [email protected] (J. Watanabe).

of pulverized coal combustion has been applied to laboratory-scale burners [1–5]. In our group, LES is also applied to a large-scale boiler furnace with a coal feed rate of 3000 kg/h [6]. The selection of a turbulent combustion model strongly aﬀects the accuracy of predicting the combustion state. In previous simulations of pulverized coal combustion (including the aforementioned work), the eddy-breakup model and eddy dissipation model [7] have often been used because of their extensive range of application. However, the concept of these models is intuitive as both unreasonably replace the chemical time scale with a turbulent time scale [8]. These models also do not consider the ﬂame structure that interacts with turbulence. Thus, these models cannot correctly reﬂect the inﬂuence of chemical kinetics and turbulence-chemistry interactions. In order to reproduce

http://dx.doi.org/10.1016/j.proci.2014.07.065 1540-7489/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

2

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

such non-equilibrium behavior as ignition and extinction, more sophisticated models that consider the ﬁnite rate chemistry with detailed reaction mechanism are preferred. However, the high computational cost of such models for practical use is not aﬀordable. The ﬂamelet model is one of the most promising because it can take detailed chemical kinetics into account at a reasonable computational cost. Various ﬂamelet models have been developed and applied to simulations of gaseous combustion [9–13] and spray combustion [14–16]. However, as far as we know, no ﬂamelet model has been coupled with a coal combustion model that takes both devolatilization and char surface reaction into account, although a ﬂamelet model applied to gasiﬁed coal volatile combustion has been reported [17,18]. The purpose of this study is to develop a ﬂamelet model applicable to the simulation of pulverized coal combustion. The accuracy of the model is investigated by comparing it with a ﬁnite rate chemistry model with a detailed reaction mechanism. 2. Numerical methods In this study, the simulations of pulverized coal combustion using the ﬂamelet model (ﬂamelet simulation) and using the ﬁnite rate chemistry model with a detailed reaction mechanism (detailed chemistry simulation) are compared. In both simulations, the gas phase and coal particles are solved in an Eulerian manner and a Lagrangian manner, respectively. The main focus of this study is how well ﬂamelet simulation reproduces detailed chemistry simulation with the same calculation models. To save on the computational cost of detailed chemistry simulation, we use some simpliﬁed models, such as a relatively simple reaction mechanism that considers hydrocarbons of low molecular weight. Moreover, the radiation and the soot formation are neglected. The following sections ﬁrst describe details of the ﬂamelet simulation, and then brieﬂy mention the numerical models used for the detailed chemistry simulation.

@qh @qui h Dp @ @h þ S C;h ; þ ¼ þ qa @t @xi Dt @xi @xi

ð3Þ

qRT ; ð4Þ M where q is the gas density, ui is the gas velocity, p is the pressure, sij is the viscous stress tensor, h is the enthalpy, a is the thermal diﬀusivity, R is the universal gas constant, T is the gas temperature, and M is the mean molecular weight of gas. Note that SC,m, SC,mom,i and SC,h are the source terms due to coal combustion, as calculated by the particle-source-in cell model [19]. The numerical methods for dispersed phase are described next. One coal particle is assumed to be composed of volatile matter, char, and ash. The changes in mass, momentum, and temperature of a particle are calculated as follows: p¼

dmp dmchar dmvol ¼ þ ; dt dt dt

ð5Þ

dmp U i 3C D q ¼ ðui U i ÞU rel mp þ gi mp ; 4d p qp dt

ð6Þ

dmp C p T p Nuk ¼ S ext ðT T p Þ þ Qc ; dt dp

ð7Þ

The non-ﬁltered and non-averaged conservation equations for mass, momentum, enthalpy, and the state equation for ideal gas are solved in the gas phase as follows:

where mp is the total mass of a particle, mchar is the mass of char, mvol is the mass of volatile matter, Ui is the particle velocity, dp is the particle diameter, qp is the particle density, Urel is the relative velocity between gas and the particle, CD is the drag coeﬃcient, Cp is the speciﬁc heat, Tp is the particle temperature, k is the thermal conductivity of gas, Sext is the surface area of the particle, and Qc is the energy transfer due to char combustion and devolatilization. The Nusselt number Nu is calculated by using the Ranz–Marshall model [20]. This model does not take Stefan ﬂow into account during pyrolysis. We have estimated the inﬂuence by using a stagnant-ﬁlm model [21]. In the case simulated in this study, the diﬀerence in the heat transfer coeﬃcient is less than 7%. The devolatilization and char combustion models used are the same as those used in our previous work [3,6]. A modiﬁed single reaction rate model called FoDeF model was used for the devolatilization model; a kinetic/diﬀusion surface model that considers char oxidation and gasiﬁcation reactions was used for the char combustion model. Our previous work describes these models in detail and demonstrates their validity. A new ﬂamelet model (described in the next section) is used for the turbulent combustion model in the gas phase.

@q @qui þ ¼ S C;m ; @xi @t

ð1Þ

2.2. Flamelet modeling for coal combustion

@qui @qui uj @p @ þ ¼ þ sij þ S C;mom;i ; @xi @xj @t @xj

ð2Þ

In this study, we propose a ﬂamelet model coupled with a coal combustion model. In the ﬂam-

2.1. Governing equations and numerical models for ﬂamelet simulation

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

elet approach, the conservation equation of the mixture fraction is solved in physical space, and the mixture fraction is used as a parameter to obtain the gas composition from a ﬂamelet database. The ﬂamelet database is generated beforehand by solving the ﬂamelet equations. For coal combustion, devolatilization and char combustion are supposed to progress separately in diﬀerent processes. Thus, the production rate and composition of fuel gas emanating from the volatile matter diﬀer from those of fuel gas emanating through char combustion. In the present modeling, we separately solve the conservation equations of mixture fractions of these fuel gases as @qZ vol @qui Z vol @ @Z vol þ ¼ qa @xi @t @xi @xi 1 X dmvol ; ð8Þ V cell particle dt @qZ char @qui Z char þ @t @xi

@ @Z char ¼ qa @xi @xi X 1 dmchar ; V cell particle dt

ð9Þ

where Vcell denotes the volume of a mesh cell. The particle-in-cell model is used to calculate the last terms in Eqs. (8) and (9). The unity Lewis number is assumed. Here, Zvol and Zchar are deﬁned as Z vol ¼

m0vol

Z char ¼

m0vol ; þ m0char þ m0ox

m0vol

m0char ; þ m0char þ m0ox

tively simple reaction mechanism that considers hydrocarbons of low molecular weight. The fractions of these species (represented by Yvol,k) are set to meet the mass balance of the ultimate analysis. How to determine the fuel gas composition coming through char combustion (represented by Ychar,k) is a key issue for an appropriate modeling of coal combustion. Some parts of the gas species are consumed along with some products being produced through char surface reactions, thus causing a complicated change in gas composition. This change in gas composition coupled with char combustion must be correctly modeled. In the present modeling, it is assumed that all solid carbon corresponding to m0char is converted into CO by the char oxidation reaction that consumes oxygen in the oxidant as follows: C þ 0:5ðO2 þ aN2 Þ ! CO þ 0:5aN2 :

ð13Þ

For the air oxidant, a = 3.76 is used. Based on this assumption, Ychar,k is obtained as follows: 8 M CO for k ¼ CO > > < M CO þ0:5aM N2 0:5aM N2 Y char;k ¼ ð14Þ for k ¼ N2 ; M CO þ0:5aM N2 > > : 0 for k ¼ others where MCO and M N2 denote the molecular weights of CO and N2, respectively. Note that the oxidant is consumed for the conversion of char into CO. The mass of the consumed oxidant is calculated as M O2 þ aM N2 0 mchar ; MC

ð10Þ

m0ox;conv ¼ 0:5

ð11Þ

where M O2 and MC denote the molecular weights of O2 and C, respectively. The fuel composition Yfuel,k is thus determined as

where m0vol is the mass of gas originating from the volatile matter, m0char is the mass of gas originating from the char and m0ox is the mass of gas originating from the oxidant. When two mixture fractions are considered, two-dimensional ﬂamelet equations [22–24] are, in a precise sense, solved to obtain the ﬂamelet database. However, dealing with two-dimensional ﬂamelet equations is complicated. In the present modeling, we introduce two new variables of Z and A as follows: Z ¼ Z vol þ Z char ;

3

Y fuel;k ¼

¼

1 þ A þ 0:5

M O2 þaM N2 MC

:

A

The upper bound of Z where the fuel composition is imposed is calculated as

ð12Þ Ordinary one-dimensional ﬂamelet equations with a single scalar dissipation rate v are solved in Z space at diﬀerent values of A. Depending on the value of A, the fuel composition of the ﬂamelet equation changes relative to the states of devolatilization and char combustion. The fuel gas coming from the volatile matter is assumed to be composed of CO, CH4, and C2H2 in this study. We use this assumption to apply a rela-

m0vol Y vol;k þ ðm0char þ m0ox;conv ÞY char;k m0vol þ m0char þ m0ox;conv M þaM Y vol;k þ A þ 0:5 O2 M C N2 A Y char;k

ð16Þ

Z max ¼

A ¼ Z char =Z vol ¼ m0char =m0vol :

ð15Þ

¼

m0vol

m0vol þ m0char þ m0char þ m0ox;conv 1þA

1 þ A þ 0:5

M O2 þaM N2 MC

: A

ð17Þ

Table 1 lists the coal properties used in this study. The assumed composition of gasiﬁed volatile matter Yvol,k is also listed. In this study, dry coal is simulated for a simple case. Fig 1 shows the fuel compositions Yfuel,k at some values of A, which are imposed as boundary conditions on the fuel side of the ﬂamelet equations. In this study, the

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

4

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

Table 1 Coal properties.

0.3 (a)

scalar dissipation rate χ = 4.5 s-1 A 0.000 0.061 0.123 0.246 0.369 0.614 1.230

Proximate analysis (dry basis wt%) Volatile matter 38.9 Char 47.8 Ash 13.3 Fuel composition originating from the volatile matter, Yvol,k 100 (wt%) CO 34.8 41.3 CH4 23.9 C2H2

CO2 mass fraction

0.25 0.2 0.15 0.1 0.05 0 2500 (b)

2300 2100

2000 T, K

Mass fraction of fuel, Yfuel,k

0.7 N2

0.6

1900 1700

1500

0.1

0.2

1000

0.5 0.4

CO

500

0.3 0

0.2 CH4

0.1 0

C2H2 0

0.2

0.4

0.6

0.8

1

1.2

1.4

A

0

0.2

0.4

Z

0.6

0.8

1

Fig. 2. Flamelet data of (a) CO2 mass fraction and (b) gas temperature at v = 4.5 s1 for each A value. The inset shows a zoom of temperature proﬁles around the peak.

Fig. 1. Fuel compositions for ﬂamelet equations at each A value.

steady one-dimensional ﬂamelet equations are solved at p = 0.1 MPa without considering radiation by using the FlameMaster code [25]. GRI-Mech 2.11 [26] is used as the reaction mechanism. Fig. 2 shows an example of ﬂamelet data (CO2 mass fraction and gas temperature distributions) obtained at v = 4.5 s1 for various A values. Note that Zmax becomes less than unity for A > 0 as calculated in Eq. (17). For example, in the case of A = 1.23, the oxidant corresponding to Z = 0.24 is needed to convert the gasiﬁed char into CO. Also, the temperature assigned for fuel gas in the ﬂamelet equations becomes higher as the value of A increases (see Fig. 2b). This is because the temperature increase due to the heat of reaction associated with the char oxidation reaction is taken into account. The temperature increase can be estimated as follows: DT ¼ ¼

Qox m0char C p;fuel m0vol þ m0char þ m0ox;conv Qox A ; C p;fuel 1 þ A þ 0:5 M O2 þaM N2 A MC

The proposed ﬂamelet model is based on the ﬂamelet/progress variable (FPV) approach [10]. The progress variable Cpv is introduced and used as a parameter referring to the ﬂamelet database. The following conservation equation of Cpv is solved in physical space. @qC pv @qui C pv @ @C pv þ S Cpv þ ¼ qa ð19Þ @xi @t @xi @xi where SCpv is the source term of Cpv. In this study, we used the CO2 mass fraction as the progress variable (C pv ¼ Y CO2 ). The CO mass fraction is not included in Cpv because CO is produced in different processes from combustion in the gas phase, such as devolatilization and char surface reactions. The enthalpy h solved in Eq. (3) is also used as a parameter referring to the ﬂamelet database. Consequently, the gas phase composition is determined from the ﬂamelet data using the parameters of Z, A, Cpv, and h. 2.3. Detailed chemistry simulation

ð18Þ

where Qox is the heat of reaction for the char oxidation reaction shown in Eq. (13), and Cp,fuel is the speciﬁc heat of the fuel gas. As the value of A increases, the peak CO2 mass fraction and gas temperature become higher.

In addition to Eqs. (1)–(4), the conservation equations of gas species are also solved in the gas phase for the detailed chemistry simulation as follows: @qY k @qui Y k @ @Y k þ xk þ S C;m;k þ ¼ qa @xi @t @xi @xi ð20Þ

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

Here, Yk is the mass fraction of species k, and xk is the reaction rate of species k, which is calculated by the ﬁnite rate chemistry model with GRI-Mech 2.11 [26]. Also, SC,m,k is the source term due to coal combustion. The unity Lewis number assumption is used for all species. The particle model and coal combustion model are the same as those used for the ﬂamelet simulation.

Slip wall B.C.

Co-flow conditions

100 mm

U = 3 m/s T = 1862 K YN2 = 0.711, YO2 = 0.084 YCO2 = 0.158, YH2O = 0.043

y O

x

Jet (coal + air) conditions

SR = 0.21 U = 20 m/s (with periodic fluct.) T = 350 K

200 mm Slip wall B.C.

Outflow B.C. Non-reflective B.C. for p

Fig. 3. Numerical mesh and conditions.

5

3. Numerical conditions 3.1. Flow conﬁguration and mesh Figure 3 illustrates the computational mesh and ﬂow conditions simulated in this study. To reduce the computational cost, the simulations are conducted two-dimensionally. The domain is 200 mm long and 100 mm high. The mesh has 39,000 cells. There is a coal/air mixture jet inlet with a 1-mm-wide slit at the center of the left boundary. The mean velocity of the jet is 20 m/ s, with periodic velocity ﬂuctuation at an amplitude of 4 m/s and a Strouhal number of 0.4 being imposed to enhance the turbulent transition. The stoichiometric ratio of the coal/air mixture is SR = 0.21. In this study, only small coal particles less than 5 lm in diameter are considered, as ignition can be achieved in a short distance. High temperature co-ﬂows with a burnt gas composition exist next to the jet in order to ignite the coal particles. Figure 3 also shows the other boundary conditions. At the outlet boundary, the nonreﬂective boundary condition is imposed for pres-

Flamelet

Detailed chemistry

B

A

Fluctuation range of ignition position 0.05 0.22 (a) CO2 mass fraction

Fluctuation range of ignition position

Detailed chemistry

Flamelet

350 2200 K (b) Particle temperature Detailed chemistry

C

Flamelet

D

0 0.0035 (c) OH mass fraction Fig. 4. Comparisons of instantaneous distributions of (a) CO2 mass fraction, (b) particle temperature, and (c) OH mass fraction.

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

6

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

sure, with free outﬂow conditions being imposed for the other variables.

4. Results and discussion The result of detailed chemistry simulation is used as a reference to evaluate the accuracy of the developed ﬂamelet model for coal combustion.

3.2. Numerical schemes The same schemes are used for both ﬂamelet and detailed chemistry simulations. For the convection terms, a fourth-order central diﬀerence scheme is used. A limiter function is applied for the scalar equations. For the diﬀusion terms, a second-order central diﬀerence scheme is used. Time integration is performed by using the fourth-order Runge–Kutta method for the convection terms, and by the second-order CrankNicolson method for the diﬀusion terms. The time step is determined so that the maximum Courant number is less than 0.1 for the ﬂamelet simulation and less than 0.02 for the detailed chemistry simulation, in order to guarantee time accuracy.

4.1. Comparison of instantaneous distributions Figure 4 compares the instantaneous distributions of CO2 mass fraction, particle temperature, and OH mass fraction between the ﬂamelet simulation and detailed chemistry simulation. The ﬂamelet simulation can reproduce a turbulent ﬁeld and combustion state qualitatively similar to those of the detailed chemistry simulation. As shown in Fig. 4a, ignition occurs in the mixing layer between the coal jet and co-ﬂow, where CO2 is generated (regions A and B). The development of the jet width is almost the same between both simula-

Detailed chemistry

A

Flamelet

(a) Gas temperature

Detailed chemistry

B

Flamelet

(b) CO2 mass fraction Detailed chemistry

Flamelet

C

(c) OH mass fraction Fig. 5. Comparisons of scatter plots of (a) gas temperature, (b) CO2 mass fraction, and (c) OH mass fraction.

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

tions. The turbulent structure can be clearly observed from the particle distributions (Fig. 4b). In both simulations, a characteristic coherent structure consisting of large-scale eddies is formed due to Kelvin–Helmholtz instability in the shear layer, and the eddies develop downstream. The pulverized coal particles are transported by these eddies and heated at the contact surfaces with the high-temperature co-ﬂows. The combustion reactions progress along these eddies where OH production is obvious (see Fig. 4c). OH production inside the jet core is somewhat overestimated in the ﬂamelet simulation (regions C and D). Ignition position is compared next. The ignition position is deﬁned as the upstream edge where the CO2 mass fraction becomes larger than 0.18 (15% greater than the value of co-ﬂow). The ignition position changes at each time, causing the ignition position to ﬂuctuate unsteadily. The range of ignition position is shown in Fig. 4a. The ignition distance from the inlet is from 9.7 mm to 11.3 mm for the detailed chemistry simulation and from 5.9 mm to 7.4 mm for the ﬂamelet simulation. The ﬂamelet simulation underestimates the ignition distance by roughly 35% upstream of the detailed chemistry simulation. 4.2. Comparison of scatter plots Figure 5 compares the scatter plots of instantaneous gas temperature, CO2 mass fraction, and OH mass fraction against Z. The instantaneous data is obtained from the entire domain. Overall, the ﬂamelet simulation reproduces the data distribution observed in the detailed chemistry simulation. As shown in Fig. 5a, the maximum temperature appears at around Z = 0.08 for both simulations and is 2200 K for the detailed chemistry simulation and 2116 K for the ﬂamelet simulation. That is, there is error of about 4% for maximum temperature. Even larger error (about 20%) exists for the maximum OH mass fraction (see Fig. 5c). In contrast to the ﬂamelet simulation, many super-equilibrium OH concentrations [8] exist for the detailed chemistry simulation. Also, there are no data points in some intermediate regions (shown as regions A, B, and C in Fig. 5) for the ﬂamelet simulation. These data points correspond to transitional states in the ignition process. Therefore, the present ﬂamelet model does not suﬃciently resolve the ignition process. One possible reason for this drawback is the inappropriate choice of the progress variable. The present model uses CO2 mass fraction as the progress variable. However, CO2 is just a ﬁnal product and does not play an important role in the initial process of combustion. The eﬀect of the choice of Cpv will be investigated in the future. Another possible reason is that the present ﬂamelet database is generated based on the steady ﬂamelet equations. Ihme and See [27] reported

7

that the ﬂame state predicted by the FPV model based on steady ﬂamelet equations was primarily conﬁned to the upper stable branch of the Sshaped curve, which explained the short ignition distance. The FPV approach based on unsteady ﬂamelet equations may be required in order to predict the ignition process more accurately. 5. Conclusions This paper proposed a ﬂamelet model for simulating pulverized coal combustion. The developed model was based on the ﬂamelet/progress variable approach, and coupled with both devolatilization and char combustion. The prediction accuracy of our model was investigated by comparing it with a detailed chemistry model in a simpliﬁed pulverized coal jet conﬁguration. The simulation using the present ﬂamelet model well reproduced a characteristic combustion state appeared in simulation results obtained by using the detailed chemistry model. The maximum temperature in the ﬂame can be captured with error of roughly 4%. The proposed ﬂamelet model estimated ignition faster than the detailed chemistry model, but underestimated the ignition distance deﬁned from the CO2 mass fraction increase by about 35%. The present ﬂamelet model tends to have diﬃculty reproducing the transitional state in the ignition process. To improve ignition prediction capability, a more appropriate choice of progress variable or the formation of a database using unsteady ﬂamelet equations may be required.

References [1] R. Kurose, H. Makino, Combust. Flame 135 (2003) 1–16. [2] R. Kurose, H. Watanabe, H. Makino, KONA Power Particle J. 27 (2009) 144–156. [3] K. Yamamoto, T. Murota, T. Okazaki, M. Taniguchi, Proc. Combust. Inst. 33 (2011) 1771–1778. [4] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, Combust. Flame 159 (2012) 353–366. [5] O.T. Stein, G. Olenik, A. Kronenburg, et al., Flow Turbul. Combust. 90 (2013) 859–884. [6] K. Yamamoto, D. Kina, T. Okazaki, M. Taniguchi, H. Okazaki, K. Ochi, Proc. ASME 2011 Power, POWER2011-55367, 2011. [7] B.F. Magnussen, B.H. Hjertager, Proc. Combust. Inst. 16 (1977) 719–729. [8] N. Peters, Turbulent Combustion, Cambridge University Press, UK, 2000. [9] N. Peters, Proc. Combust. Inst. 21 (1986) 1231– 1250. [10] C.D. Pierce, P. Moin, J. Fluid Mech. 504 (2004) 73– 97. [11] H. Pitsch, M. Ihme, An unsteady/ﬂamelet progress variable method for LES of nonpremixed turbulent combustion, AIAA Paper 2005–557, 2005.

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

8

J. Watanabe, K. Yamamoto / Proceedings of the Combustion Institute xxx (2014) xxx–xxx

[12] M. Ihme, C.M. Cha, H. Pitsch, Proc. Combust. Inst. 30 (2005) 793–800. [13] K. Yunoki, T. Murota, K. Miura, T. Okazaki, Proc. ASME 2013 Power, POWER2013-98143, 2013. [14] Y. Baba, R. Kurose, J. Fluid Mech. 612 (2008) 45– 79. [15] H.-W. Ge, E. Gutheil, Combust. Flame 153 (2008) 173–185. [16] Y. Itoh, N. Oshima, J. Therm. Sci. Technol. 4 (1) (2009) 122–130. [17] A. Williams, M. Pourkashanian, J.M. Jones, Prog. Energy Combust. Sci. 27 (2001) 587–610. [18] M. Vascellari, H. Xu, C. Hasse, Proc. Combust. Inst. 34 (2013) 2445–2452. [19] C.T. Crowe, M.P. Sharma, D.E. Stock, Trans. ASME J. Fluid Eng. 99 (1977) 325–332. [20] W.E. Ranz, W.R. Marshall, Chem. Eng. Prog. 48 (1952) 141–146.

[21] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed., John Wiley & Sons Inc, NY, 2002, pp. 704–706. [22] C. Hasse, N. Peters, Proc. Combust. Inst. 30 (2005) 2755–2762. [23] C. Felsch, M. Gauding, C. Hasse, S. Vogel, N. Peters, Proc. Combust. Inst. 32 (2009) 2775–2783. [24] E. Doran, H. Pitsch, A multi-dimensional ﬂamelet model for ignition in multi-feed combustion system, Report No. TF-121, Stanford University, 2011. [25] H. Pitsch, available at http://www.stanford.edu/ group/pitsch/FlameMaster.htm. [26] C.T. Bowman, R.K. Hanson, D.F. Davidson, W.C. Gardiner, Jr., V. Lissianski, G.P. Smith, D.M. Golden, M. Frenklach, M. Goldenberg, GRI-Mech 2.11, 1997, available at http://www.me.berkeley.edu/gri-mech/. [27] M. Ihme, Y.C. See, Combust. Flame 157 (2010) 1850–1862.

Please cite this article in press as: J. Watanabe, K. Yamamoto, Proc. Combust. Inst. (2014), http:// dx.doi.org/10.1016/j.proci.2014.07.065

Copyright © 2023 C.COEK.INFO. All rights reserved.