Large eddy simulation of a syngas jet flame: Effects of preferential

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Combustion

Large eddy simulation of a syngas jet flame: Effects of preferential diffusion and turbulence-chemistry interaction Kazui Fukumoto, Changjian Wang, and Jennifer Wen Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b00130 • Publication Date (Web): 12 Apr 2019 Downloaded from http://pubs.acs.org on April 13, 2019

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Large eddy simulation of a syngas jet flame: Effects of preferential diffusion and turbulence-chemistry interaction K. Fukumoto1,2*, C.J. Wang1,3*, and J. X. Wen2. 1

School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China,

2

Warwick FIRE, University of Warwick, Coventry, CV4 7AL, United Kingdom

3

Anhui International Joint Research Center on Hydrogen Safety, Hefei, 230009, China,

KEYWORDS Non-premixed flame, Turbulence, Lewis number, Thermal diffusion, Tabulated chemistry, Eddy dissipation concept

ABSTRACT A simulation of the syngas jet flame of Sandia ETH/Zurich B is conducted using an in-house version of FireFOAM. Combustion is modelled using (i) the newly extended eddy dissipation concept (EDC) for the large eddy simulation (LES) published by the authors’ group and (ii) the 74-step CO-H2-O2 mechanism. The effects of the non-unity Lewis number and thermal diffusion (= Soret diffusion) are considered in the mass fraction and enthalpy equations. Systematic validation and model sensitivity studies have been conducted against published

1 ACS Paragon Plus Environment

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experiments from TNF workshops. The predictions were in very good agreement with the relevant experimental data. The axial position of peak H2O moved toward the nozzle direction owing to the different diffusion coefficient of H2. In the radial direction, the effect of preferential diffusion was observed at x/d < 20. After considering the effects of the non-unity Lewis number and thermal diffusion, as well as the detailed reaction mechanisms, the results were slightly better than those obtained under previous numerical conditions.

1.

INTRODUCTION Synthesis gas (Syngas) is a fuel mixture gas consisting of carbon monoxide and hydrogen

(sometimes containing carbon dioxide), which is produced during the gasification process of certain materials. Syngas is used as an intermediate gas to produce synthetic natural gas, aroma and methanol.1 It is important in the chemical industry, as well as in the development of fuel cells, diesel engines, spark ignition engines and power generation.2,3 When syngas is used as fuel in a diesel engine, the emissions of CO2 are generally reduced. It may also be a potential substitute fuel for internal combustion engines, although further studies are required to improve efficiency.3 The flame characteristics of syngas vary according to the ratio of H2, owing to high its diffusivity and reactivity. Barlow et al.4 measured scalar and velocity data of a syngas jet flame of 40% CO, 30% H2 and 30% N2 by volume, with the fuel injected using two different nozzle diameters. The axial profiles of the data for the two flames were in good agreement when the distance from the nozzle was normalised by the nozzle diameter. However, measured OH and NO were higher in the flame with the larger nozzle diameter owing to the lower scalar


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dissipation rate and longer residence time. These data are available in a TNF workshop report5 and are useful for validating computational code and combustion models. Correa and Gulati6 experimentally and numerically investigated a syngas jet flame of 27.5% CO, 32.3% H2 and 40.2% N2 by volume. The predicted mixture fraction and its variance, temperature and concentrations were in agreement with the experimental data, whereas the predicted jet decayed too fast owing to use of the standard k- model. More recently, Hwang et al.7 experimentally investigated the stability characteristics of H2 and syngas jet flames along with coaxial air, reporting a decrease in the flame stability limit with an increase in the amount of CO. Also, local extinction appeared slightly downstream from the nozzle at a high injection velocity, whereas it was observed near the nozzle at a low injection velocity. Dinesh et al.8 performed simulations of hydrogen-enriched jet flames. They revealed that inclusion of H2 significantly influenced the flame temperature and formation of combustion products in the jet flames owing to the high diffusivity and reactivity of H2. Zhao et al.9 simulated a syngas jet flame by the transported composition probability function (PDF) method; they also investigated the sensitivity of sub-models such as the turbulence model parameters, radiation treatments, chemical reaction mechanisms and mixing models for the PDF method. They suggested that the selection of sub-models and these parameters gave better agreement with the experimental data. Wang et al.10 simulated H2 and H2/CH4 jet flames to investigate their radiative characteristics, finding that the predicted radiative fraction was in good agreement with the experimental data. Further, the effect of ground surface reflectance on surface emissivity power was not significant for the H2 jet flames. Although many numerical studies on turbulent syngas jet flames have been conducted, relatively few numerical investigations based on large eddy simulation (LES) of a turbulent jet


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flame have considered the effect of preferential diffusion.11,12 Therefore, it is often believed that the effects of preferential diffusion do not play an important role at sufficiently high Reynolds numbers.8 Conversely, some previous studies have noted the influence of non-unity Lewis numbers. Giacomazzi et al.11,12 simulated a turbulent syngas jet flame considering non-unity Lewis numbers and reported that preferential mass diffusion of H2 controlled flame stabilisation near the nozzle. Meier et al.13 also suggested that preferential mass diffusion played an important role, especially near the nozzle. Takagi et al.14 pointed out that the flame near the nozzle was locally laminar owing to the high viscosity caused by the increase in temperature. In this study, the effects of non-unity Lewis numbers and thermal diffusion are considered. Combustion is modelled using the newly extended eddy dissipation concept (EDC) for the LES, as published by the authors’ group,15,16 and is further improved to consider the finite reaction rate, which uses the 74-step CO-H2-O2 mechanism of Maas et al.17 Several EDC models for the LES have been proposed18,19–21 but only Maule et al.21 considered the finite reaction rate in the EDC model. The formulation of Maule et al. was built by coupling the partial stirred reactor concept22 with the EDC model. The widely used laminar flamelet model23,24 can take into account the detailed reaction mechanism in the turbulent flame simulation at a low computation cost. This is because the look-up table (flamelet library) is built before the simulation. On the other hand, the effects of thermal diffusion and laminar-turbulence transition have yet to be taken into account in the laminar flamelet model, although laminar-turbulence transition can be considered in the recently proposed EDC model.25 The present study reported a sensitivity test of numerical models to reveal the underlying physics in the turbulent syngas jet flame; in particular, the effect of preferential mass diffusion


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on the numerical results is discussed. Further, an extended EDC model with a finite reaction rate is newly presented and validated with experimental data.

2.

NUMERICAL SOLVER FireFOAM,26 which is an LES-based fire simulation solver within the OpenFOAM®

toolbox,27 is used as a basic numerical framework for the present study. The code has been previously used to simulate pool fires,15,16,28,29 wall fires,30 jet flames31 and flame spread on solid surfaces.25 For the present study, an in-house version of FireFOAM, which contains recent developments by the authors’ group,15,16,25,31 is used. The dynamic Smagorinsky model suggested by Gernamo et al.32 and Lily33 is also implemented, following references.29,34 The effects of preferential diffusion, as well as the detailed reaction mechanisms, are newly considered in this study.

2.1. Governing equations The governing equations solved by the in-house version of FireFOAM are expressed as follows. Continuity equation   u j  0 t x j

(1)

Momentum equation

 ui  ui u j    x j x j t

  u u j 2 uk   prgh    ij     g j xj    SGS   i   xi   x j xi 3 xk   xi

(2) (3)

prgh  p   g j x j


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Mass fraction equation of gas species J

  YJ  uiYJ   SGS YJ   jiJ )   J  ( t xi xi  Sct xi 

(4)

Sensible enthalpy equation

 SGS h  h  ui h Dp    ,    )   jiJ (hJ )   q    qrad (   t xi Prt x j J Dt xi  

(5)

where the effect of preferential diffusion in Equations (4) and (5) is newly implemented in Eqs. (4) and (5); ˉ and ˜ above the variables are the time average and density-weighted average, respectively; prgh is pressure excluding the gravity effect; SGS is obtained by the dynamic Smagorinsky model32,33 and  is calculated based on Sutherland’s law,27 given as



AsT 0.5 1  Ts / T

(6)

kg/m/s,

where As = 1.67212  10−6 (kg/m/s/K0.5) and Ts = 170.672 (K).  is obtained by m2/s,

   / (Cp  )

(7)

where λ is obtained by the modified Eucken correction as35

   Cv (1.32 

1.77 R ) Cv

W/m/K,

(8)

where Cp is calculated based on the seven coefficients polynomials.36 The mass diffusion flux jiJ in Eqs. (4) and (5) is given as jiJ    DJ

YJ DJT T  xi T

kg/m2/s,

(9)

where DJ = α/LeJ, and DJT is obtained by the empirical expression, given as38 T J

7

D  2.59 10 T

0.659

 M J0.511 X J    J M J0.511 X J   YJ     0.511 0.489   J M J X J    J M J X J 

kg/m/s

(10)


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2.2. Turbulence modelling In this study, the dynamic Smagorinsky model is programmed in the FireFOAM solver, with implementation following reference:34

 SGS    CS  filter  S 2

1  u u j  Sij   i   2  x j xi 

kg/m/s and s−1,

(11)

(12)

where Sij is the symmetrical component of the velocity gradient tensor, with its magnitude given as S  2Sij Sij





0.5

, and  filter is the filter size (m). Cs is the Smagorinsky constant, which is

dynamically determined following Gernamo et al.32and Lilly33as

Cs2 

1 Lij M ij , 2 M kl M kl

(13)

denotes the average value computed by the local faces values. Lij is called the Germo

where

identity and Lij and Mkl are given as

 iu j  u i u j Lij  u





m2/s2 and

(14)

 2     S   (15) m2/s2, M kl   filter S S  4 S  kl kl    where is the value of the test filter for the dynamic Smagorinsky model, with the width of the 

test filter given as  filter = 2 filter . For numerical stability, Cs is clipped at zero or 0.23 following implementation in Ansys FLUENT.38 kSGS is also dynamically given as27,34 2 2 kSGS  CI  filter S

m2/s2,

(16)


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where CI is dynamically determined as CI 

KN N2

,

(17)

where K and N are given as

K

1   ui u j  uiu j 2





m2/s2 and

(18)

m2/s2,

(19)

  2 2  N   2filter  4 S  S   

2.3. Combustion modelling 2.3.1. Infinitely fast chemistry Infinitely fast chemistry for the syngas jet flame is considered as

1 H 2  O2  H 2O , 2

(20)

1 CO  O2  CO2 . 2

(21)

The EDC model was first suggested by Magnussen.39,40 Magnussen focused on strong dissipation intermittency in high Reynolds number turbulence and assumed that the area is divided into (i) ‘fine structures’ within the turbulence and (ii) ‘surrounding fluids’. Owing to strong dissipation in the fine structures, viscous dissipation and molecular stirring occur therein and the fine structures are considered a homogeneous constant pressure reactor. Conversely, the surrounding fluids are assumed to be inhomogeneous, with negligible viscous dissipation and molecular stirring. According to Moule et al.,21 EDC closure can be interchangeable with the PDF model using two Dirac delta functions. Thus, the primary function of the EDC model is estimation of the


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parameters, e.g. the mass fraction of the fine structures γ and the mass transfer rate m * s−1 between the fine structures and surrounding fluids. More discussion of the EDC formulation can be found in reference.21 Furthermore, the original EDC models39,40 were strongly dependent on grid resolutions for the application of LES, which is thought to be caused by the direct replacement of turbulent kinetic energy k with the sub-grid scale (SGS) kinetic energy kSGS.15 Magnussen’s model was built for the Reynolds averaged Navier–Stokes (RANS) equations; hence, Chen et al.15,16 attempted to estimate k and  (termed total k and  ) from kSGS based on the energy cascade concept.41 The model parameters were theoretically derived on the assumption that the characteristic length and velocity scale of the fine structures were equal to the Kolmogorov length and its velocity scale, respectively. The detailed derivation of the extended EDC model for the LES can be found in references.15,16 Fukumoto et al.25 further modified Chen et al.’s formulation to capture the laminar-turbulent transition in flame spread on PMMA walls. Since k becomes low in the laminar region, it provides the nonphysical small reaction rate via the EDC model. Therefore, the reaction time scale was determined by comparing the time scale computed by the expressions of Vervisch and Poinsot42 and Chen et al.’s extended EDC model,15,16 taking the minimum. The time averaged reaction rate of chemical species J is given as

 J   (YJ  YJ* ) / min ( EDC , diff )

kg/s/m3,

(22)

where  EDC is the reaction time scale based on turbulent diffusion, as computed by the EDC model and  diff is the reaction time scale based on viscous diffusion. For infinitely fast chemistry with more than two chemical reactions, the stoichiometric O2-tofuel mass ratio must be considered in relation to the global fuel amount, such as YH  YCO 2


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(referred to as ‘multi component fuel’). Wang et al.31 suggested the expression of infinitely fast chemistry for multi component fuel; relatively simpler expressions are used in this study:

 Y* YO*2 Y fu* ,new  Y fu* ,n  fu ,nWfu min  fu ,n ,   fu ,nW fu  O ,nWO  2 2

  

 Y* YO*2 YO*2 ,new  YO*2  O 2 ,nWO2 min  fu ,n ,   fu ,nW fu  O ,nWO  2 2

 and  

 Y* YO*2  Ypr* ,new  Ypr*  pr ,nWpr min  fu ,n ,    fu ,nW fu  O ,nWO   2  2

fu = H2 or CO

pr = CO2 or H2O,

(23)

(24)

(25) (26)

* YJ*  Ynew

where YJ*,n is the mass fraction of chemical species J of the nth reaction equation in the fine structures, and initial YJ* is given as YJ*  YJ . Equations (23)–(26) repeat the H2 reaction in Eq. (20) and the CO reaction in Eq. (21). The difference between the standard formulations and those above is that YJ* is replaced at each reaction number and the reaction equation of H2 is set to n = 1 because of its high reactivity. The obtained YJ* is substituted into YJ* in Eq. (22).

 EDC in Eq. (22) is calculated based on Chen et al.’s EDC model for the LES; it is given as  EDC 

 (YJ  YJ* ) 1      J ,EDC m 

s,

(27)

where  J ,EDC is the reaction rate (kg/s/m3) computed by the EDC model,  is the mass fraction of the fine structures,  , is the reaction fraction of the fine structure and m * is the mass transfer rate (1/s) between the fine structures and surrounding fluids. The detailed derivation of the extended EDC model was described in previous studies.15,16,25 In Chen et al.’s EDC model, L must be defined as an input parameter and is newly tested based on Wang et al’s study43 for jet flames:


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L  0.223 out m and

(28)

 out  0.13( x / d nozzle ) m,

(29)

where x is the distance from the nozzle outlet,  out is the outer scale and dnozzle is the diameter of the nozzle. As mentioned above, k becomes low in the laminar region and yields a nonphysical small reaction rate via the EDC model. Therefore, the reaction rate in the laminar region should be evaluated by a different expression, such as one based on the Arrhenius equation. However, the reaction time scale of a laminar flame is generally small compared with the time step size Δt and can cause numerical instability; this is often referred to as the stiffness problem.46 Generally, the controlling time scale for a laminar flame is the diffusion time scale at which the diffusion flux enters each computational cell. In the vicinity of the stoichiometric surface, the reaction rate for the mass fraction equation reactant species J is obtained following Vervisch and Thierry:42

 d 2YJ ( Z )  2    dZ

J    D ( 2 YJ )    D Z  2

kg/s/m3,

(30)

2 where D Z is called the scalar dissipation rate44 and  D( 2 YJ ) is the same as the diffusion

term of the mass fraction equation of chemical species J, i.e. the diffusion rate of chemical species J when flow is laminar.25 The reaction time scale  diff based on molecular diffusion in Eq. (22) was estimated based on Eq. (30). On the fuel-lean side (Zst > Z ), the amount of fuel is less than that of oxygen; fuel diffusion is hence the controlling time scale. Similarly, oxygen diffusion is the controlling time scale in the stoichiometric condition on the fuel-rich side (Zst ≤ Z ). Further, preferential diffusion and multi component fuel are newly considered in this study.

The time scale is given as


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 diff 

 diff 

where

  Y  J

J

fu

  J ( DJTT )fu      Y         J  J  T  LeJ   fu   YO2 / s     DOT2 T    YO2       T  LeO     2



J

DJT



fu

T  DHT 2 and  DCO

s

  

  Y  J

fu

  

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s

Z st  Z ,

Z st  Z ,

 YCO  YH2 .

2.3.2. Finite reaction rate In this study, laminar-turbulence transition is taken into account in the combustion simulation. Following a previous study,25  diff and  EDC are used as the criteria. When  diff >  EDC , turbulent mixing is stronger than molecular diffusion; this is considered turbulent combustion. For turbulent combustion, the finite reaction rate is considered using the extended EDC model. The model assumed that the region in the computational cell is divided into fine structures and surrounding regions, with combustion occurring only in the fine structures of turbulence. The fine structures are considered a perfectly stirred reactor and the steady state of the following equation is solved under the initial conditions obtained from the current mass fractions, density and temperature in each computational cell:45

dYJ* J*  m * (YJ0  YJ* ) ,  dt 

(33)

where  J* is the reaction rate of chemical species J in the fine structures computed by the Arrhenius equation and Y J0 is the mass fraction of chemical species J in the surrounding fluids. When m * is large, the solution of Eq. (33) becomes different from that of laminar combustion;


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therefore, m * corresponds to the mixing rate. As the turbulent mixing rate increases, the solution departs from equilibrium.46 This feature cannot be expressed by the infinitely fast chemistry assumption. Infinitely fast chemistry assumes that the first term on the right-hand side of Eq. (33) is sufficiently large compared with the second term. Y J0 is obtained by the following correlation: YJ   YJ  (1.0   )YJ0 ,

(34)

For laminar combustion (  diff   EDC ), the ordinary differential equations (ODEs) are given as

dYJ J  ,  dt

(35)

where Eqs. (33) and (35) are stiff ODEs due to  J* and J . These equations are solved by a relatively simple look-up table approach, as described in Section 2.4. The reaction rate is given as

J   m 

J 

 (YJ*  YJ ) 1  

 (YJ ,t t  YJ ) t

kg/s/m3

kg/s/m3

 diff   EDC

 diff   EDC

(36)

(37)

where YJ* and YJ ,t  t are the solutions of Eqs. (33) and (35), respectively. 2.4. Look-up table approach Solving Eqs. (33) and (35) by direct integration (DI) requires a very high computation time. The combustion models solving the mass fraction equation require that the stiff ODEs, such as the EDC model and probability density function (PDF) model, be solved9,47 but the computation cost of this is generally very high. Fukumoto and Ogami showed that computation cost was decreased by < 1%,56 which means that the cost of DI is more than 100 times that of using lookup tables. Therefore, many researchers have tried to reduce the computation cost of the reaction


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calculation using reduced mechanisms,11,12,48 in-situ adaptive tabulation (ISAT),49,50 combustion models that use look-up table,8,23,24 artificial neural networks (ANNs)51–53 and flamelet generated manifolds.54,55 These approaches may reduce the prediction accuracy but the combination of the LES or direct numerical simulation with DI for a detailed mechanism is not still feasible. Fukumoto and Ogami56,57 developed a relatively simple look-up table approach that was applied to the EDC model based on the Reynolds averaged Navier–Stokes (RANS) equations; the obtained results were in very good agreement with those obtained without using the look-up table. This technique is termed the in-situ look-up table approach. The obtained values are stored in the look-up table using key index variables such as the mixture fraction, progress variable and time scale, which is similar to the laminar flamelet model. Therefore, it is thought to be an intermediate approach between the ISAT and the flamelet model. This previous study showed that the results obtained by three key index variables provide better concentrations than those obtained with the key index variables, i.e. mixture fraction and progress variable. Further, a lookup table divided into 200 × 200 × 200 cells gave the best agreement with the results obtained by DI. Therefore, a look-up table divided into 200 × 200 × 200 cells is used in this study. For application to the LES and the treatment of laminar-turbulence transition, the look-up table approach is slightly updated in this study. Figure 1 shows a schematic image of the convergence of the data (a), construction of the lookup table (b) and normalised distance (%) vs number of sampled data (c). For simplicity, only a two-dimensional look-up table, which has two key index variables, is illustrated in Fig. 1. The point P is a sampled point obtained from the flow field, and Qn,m, Qn+1,m, Qn,m+1 and Qn+1,m+1 are stored points in the look-up table. The data can be stored only at the stored points; therefore, the data at point P must be converted into data at the stored points. As shown in Fig 1 (a), the


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Energy & Fuels

averaged data become gradually closer to the data at the stored point Qn,m as data collection advances. If the data are available at the stored points, the reaction rate P can be obtained from the stored points (Qn,m, Qn+1,m, Qn,m+1 and Qn+1,m+1) by linear interpolation. If not, Eqs. (33) and (35) are solved by DI rather than linear interpolation, and P is given as  Yt* reac  Yt    P   reac  1   reac  m *

 Yt  reac  Yt    P  reac    t  reac

s 1

 diff   EDC , and

(38)

s

s 1

 diff   EDC ,

(39)

s

where  reac is the reaction time scale. P is weighted and is dependent on the normalised distance r between the sampled point P and stored points, as shown in Fig. 1 (b). The stored reaction rate  Q in the look-up table is given as

Q 

 f  f l

l

l

P ,l

kg / s / m 3 ,

(40)

l

where  Q is saved at the neighbouring stored points (Qn,m, Qn+1,m, Qn,m+1 and Qn+1,m+1) in Fig. 1 (b), fl is the lth weight function,  P ,l is the lth sampled reaction rate at the point P and  Q is used for interpolation at l > 3. The averaging procedure of P can be improved using the weight function, as shown in Fig. 1 (c). In previous studies,56,57  Q was l > 5 but the improvement of

 Q between l = 3–5 is very small, as shown in Fig. 1 (c). The weighting function is computed as


Energy & Fuels

r   fl  exp     0.2 N 

l  1, and

fl  1

l  1,

where r ranges from 0 to

(41) (42)

N and N is the number of key indexes, i.e. N = 3 in this paper.

However, if data are missing at the stored points, fl is set to 1, It should be noted that fl = 1 corresponds to the standard averaging procedure.

50 Normalize distance (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 59

40

using weight function no weight function (fl = 1)

30 20 10 0 0

5 10 15 Number of sampled data (c)

20

Fig. 1 Schematic image of the convergence of the data (a); construction of the look-up table (b), taken from reference;56 and normalised distance (%) vs number of sampled data (c). Distance


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Energy & Fuels

from the stored point is normalised by the maximum distance from the neighbouring stored points. A value of 0% indicates that the averaged data (reaction rate) Q is equal to that at the stored point Qn,m as shown in Fig.1 (a). The stored data are randomly updated, with the probability of update set to 1/1000 (following previous studies).56,57 For example, when the simulation is started with the initial values prepared by infinitely fast chemistry, as described in Section 2.3.1, the reaction rates related to the minor species are given using the initial values. There would be many time steps required to obtain the correct concentrations, with incorrect concentrations saved in the look-up table. Therefore, the data in the look-up table need to be updated to reach the final solution. In an unsteady simulation, the accumulated interpolation error could not be neglected. The interpolation error err is evaluated as err   J Ylookup, J  1 ,

(43)

where Ylookup,J is the mass fraction estimated from the interpolated reaction rate. When err > 1.0  10−1, DI is performed as the interpolation error is very large. It is assumed that most of err occurs from the reaction rates of species used as the progress variables (= H2O and CO2). To avoid reaction progress due to the interpolation error, which causes an accumulated interpolation error, the mass fraction of H2O and CO2 are modified as

YH2O,new  YH2O,lookup  err

P,H O,lookup , P,H O,lookup  P,CO ,lookup

(44)

P,CO ,lookup , P,H O,lookup  P,CO ,lookup

(45)

2

2

YCO2 ,new  YCO2 ,lookup  err

2

2

2

2


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

P,H O,new  2

P,CO

2 ,new



YH 2 O,new  YH 2 O

 reac YCO2 ,new  YCO2

 reac

Page 18 of 59

s 1 , and

文字列を

s 1 ,

文字列を

2.5. Radiation model and estimation of mean beam length FireFOAM solves the radiative transfer equation for non-scattering media using the finite volume discrete ordinates method. The weighted sum of grey gas model (WSGGM) of Smith et al.58 is used to estimate emissivity εrad. The total absorption coefficient including the soot contribution is calculated by arad  

ln(1   rad ) Lbeam

1/m,

(48)

where arad is the gas absorption coefficient and Lbeam is the mean beam length. In this study, the jet flame shape is approximated as a ‘cone’, where the base of the cone is located in the downstream region and the tip of the cone is set at the nozzle outlet. Lbeam is given as Lbeam 

3.6Vf 3.6Vf ,  Sf  rf (rf  Larc,f )

(49)

where Vf is the flame volume, Sf is the surface area of the flame, rf is the radius of the cone and Larc,f is the arc length of the cone. Vf is computed following Yang et al.’s study,59 who used the following criterion to determine the flame border, given as

Ro 

1 , 1  s( J YJ )fu / YO2

(50)

Yang et al. 59 suggested the criterion 0 ≤ Ro ≤ 0.99; however, the tip of the flame volume and flame height were different for this flame. Therefore, a slightly changed criterion of 0 ≤ Ro ≤ 0.8 is used to fit the predicted flame height xf, where the definition of flame height is the maximum


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Energy & Fuels

coordinate in the axial direction with Z = Zst.16 The term rf in Eq. (49) is given as 0.5

rf  3Vf / ( xf  ) 

Larc,f   xf2  rf2 

and Larc,f is given as

0.5

(51)

,

where xf = 47d. 5 2.6. Inlet velocity condition In this study, the following equation for the velocity condition, which is similar to that in references,60,61 is applied at the inlet (= nozzle outlet in Fig. 3). 60

 i ( y, z ) sin  2 nf 0t  ( y, z, nf 0 ) , ui ( y, z, t )  umean,i   au uRMS,

(52)

n 1

 where au = 0.229, which is determined to give the same RMS of the velocity fluctuation uRMS,i

when the second term on the right-hand side is averaged by time, and umean ,i is the mean velocity  profile at the nozzle outlet. umean ,i and uRMS,i are obtained from the experimental data.4,5

2.7. Outlet velocity condition The convective boundary condition is used for the outflow boundary condition.  ui  ucu j   0, x j t

(53)

where uc is the convective velocity computed as the average of the maximum and minimum velocities at the outlet. 2.8. Correlation of Lewis number and molecular weight Smoke62 suggested a simplified transport approach to estimate viscosity, diffusion coefficient and thermal conductivity for combustion systems. In this approach, LeJ is used to estimate the


Energy & Fuels

diffusion coefficient of chemical species J. If LeJ is not available from previous studies, it must be prepared by a preliminary simulation using kinetic theory.46

4

2 Other species

Species including C and H or N 3

2

Le

Le

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 59

Giacomazzi et al. [63] Neophytou et al. [64] Hawkes et al. [65] Smoke [62] 0.23737M 0.53012 0.40692+0.038592M -0.00013816M 2

1

0 0

1

20

40

60

Giacomazzi et al. [12] Giacomazzi et al. [63] Hawkes et al. [65] Smoke [62] 0.26130+0.026172M

80 100 120 140 160 M

0 0

10

20

30

40

50

M

Fig. 2 Predicted and previous studies’ Lewis numbers. Left figure shows Le of species including C and H or N (such as CH4 and HCN) and right figure shows Le of other species.

Figure 2 shows Le values from previous studies.12,63–65 Le increases with an increase in molecular weight. The Le values of chemical species including C and H or N (such as CH4 and HCN) in the previous studies can be expressed as LeJ  0.23737 M J0.53012

(54)

or the alternative expression LeJ  0.40692  0.038592 M  0.00013816 M 2

M  146

(55)

For other species (such as H2, CO, H2O, CO2, H OH, NO and N2) , LeJ is given as (56)

LeJ  0.26130  0.026172M J


Page 21 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

where Eqs. (54) and (56) are a function of MJ; therefore, LeH estimated by Eq. (56) is slightly different from previous values owing to a small MJ.

2.9. CO-H2-O2 reaction mechanism In this study, the detailed reaction mechanism of CO-H2-O2 suggested by Maas et al.17 is used, which consists of 74 irreversible reaction equations including H2, O2, H2O, CO, CO2, N2, H, O, OH, HO2, H2O2, CH, CH2O and HCO. At the first cell on the burner rim, infinitely fast chemistry is applied to H2, CO, H2O, CO2 and O2 in order to sustain the flame; other species are obtained by detailed reaction mechanisms. The radical species (O, OH and H) facilitate ignition and the high temperature is not sufficient to sustain the flame. This ignition problem is often called ‘flame stabilisation’ and was previously reported by Giacomazzi et al.12 and Zhao et al.9 for the Sandia ETH/Zurich Flame. Giacomazzi et al.12 simulated the flame stabilisation mechanism near the nozzle using a very fine grid size (  10−5 m) and the obtained reaction rate of H was coupled with the simulation of the whole domain. Also, Zhao et al.9 sustained the flame using a local equilibrium calculation for the ignition zone.

3.

RESULTS Sandia ETH/Zurich Flame B of Barlow et al.4,5 was simulated in this study. The computational

domain is presented in Fig. 3. Dinesh et al.8 who performed a simulation of the same scenario, reported that the flame was fully developed at t = 0.27 s; therefore, the data were taken at 0.28 s < t. Prt and Sct are set to 0.4 following Dinesh et al.’s simulation.8 The Lewis numbers of chemical species are set to LeCO = 1.06, LeH2 = 0.29, LeO2 = 1.09, LeH 2O = 0.77, LeCO2 = 1.35,


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 59

LeN2 = 0.97, LeHCO = 1.27, LeHO2 = 1.10, LeH2O2 = 1.12 and LeCH 2 O = 1.28 following Giacomazzi

et al.12 whereas LeCH = 0.89 is obtained by Eq. (55). These numbers change DJ in Eq. (9). In this study, a second order accurate central linear scheme for the momentum equations (the linear scheme limited by total variation diminishing to the governing equations of the mass fraction of chemical species and the energy equation) as well as the second order backward differential scheme for time marching are used. The Courant number is set to 0.7 and the time step size is about 1.0 × 10−6–3.0 × 10−6 s. The velocity profiles at the inlet are set based on Eq. (52) and the mean velocity is 45 m/s; Re = 16,700, where umean , x = 45 m/s, d = 7.72 mm and = 2.08 × 10−5 m2/s. Fuel composition at the inlet is 40% CO, 30% H2 and 30% N2 by volume. The co-flow air velocity is set to 0.7 m/s and the co-flow and inlet temperatures are set to 290 and 292 K, respectively. Six cases were tested with different numerical treatments, as listed in Table. 1.

Table. 1 Numerical conditions. The thermal diffusion effect is denoted as ‘Soret effect’. jiJ

Le

Soret effect

Chemistry

Le  1

Unapplied

Infinitely fast

Unapplied

Le  1

Unapplied

Infinitely fast

EDC/Laminar model

Applied

Le  1

Unapplied

Infinitely fast

D

EDC/Laminar model

Applied

Le  1

Unapplied

Infinitely fast

E

EDC/Laminar model

Applied

Le  1

Applied

Infinitely fast

F

EDC/Laminar model

Applied

Le  1

Applied

Finite rate

Case

Combustion model

A

EDC

Unapplied

B

EDC/Laminar model

C


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Energy & Fuels

Fig. 3 Computational domain of the syngas jet flame

3.1. Computational grid and grid dependency test In order to investigate computational grid dependency, two computational grids are prepared. A total of 3,356,000 cells for a fine grid and 1,728,000 cells for a coarse grid are set. Table 1 shows the numerical conditions for Case E for both computational grids. Dinesh et al.8 used a computational domain with approximately 3.4 million cells for the same scenarios and Lysenko et al.20 performed a jet flame simulation with a similar Reynolds number using approximately 1.3 million cells. For the finer grid, x is set to 0.8 mm and 5.6 mm at the first and last cell, respectively, and y and z are each set to 0.16 mm at the centre of the nozzle. For the coarse grid, x is set to

1.0 mm and 18.9 mm at the first and last cells, respectively, and y and z are each set to 0.2 mm at the centre of the nozzle. Figure 4 shows the axial predicted means ux , T and Z vs the experimental data at different grid resolutions. Z is defined based on Bilger’s definition as66


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Z 

2YC / M C  0.5YH / M H  (YO,  YO ) / M O 2YC,inlet / M C  0.5YH,inlet / M H  (YO,   YO,inlet ) / M O

Zst 

Z O , / M O 2YC,inlet / M C  0.5YH,inlet / M H  (YO,  YO,inlet ) / M O

Page 24 of 59

, and

,

(57)

(58)

where subscripts C, H and O are atomic species and YO, is the mass fraction of O in the ambient air. Generally, the numerical simulations capture the experimental data, as shown in Fig. 4, although slight grid dependency is observed from the temperature and mass fraction of CO2 at x/d = 20. It can be seen from Fig. 4 that the grid resolution effect is small at x/d = 5 and 10; therefore, molecular diffusion is considered to be accurately captured by both the coarse and fine grids. The improvement of the predictions is marginal compared with the computation cost. Hence, a total of 1,728,000 cells is used in the subsequent sections.

3.2. Validation and model sensitivity tests The numerical treatment becomes detailed in Cases A–F. Case A is the standard condition and its difference from Chen et al.’s model15,16 is L  in Eq. (28) and Eqs. (23)–(26). In Cases B–F, the laminar combustion model is applied. Equation (9) is applied to jiJ in Eq. (5) in Cases C–F. Le ≠ 1 is considered in Cases D–F. The effect of thermal diffusion is further considered in Cases E–F. The 74-step detailed reaction mechanism is taken into account in Case F. Although several assumptions are taken into account in the simulations, a numerical condition is changed step by step in Cases A–F. Therefore, the effect of an assumption can be quantified by comparing neighbouring cases. However it should be noted that consideration of finite reaction is coupled


Page 25 of 59

with the look-up table approach, indicating an inclusion of two assumptions in Case F. A total of 1,728,000 cells is used in all cases.

0.4 20

2000

0.15

0.6 40

2500 CO 2 ~ T

0.18

0.12

1500 H2O

0.09

1000

0.06

0.2 0.03

0 0

15

30

45

60

0 75

500

0 0

15

30

0.25

2500

1500

0.1 1000 H2 O 500 2290

1 r/d

0.25

1

0.25

500 3290

2

~ T [K]

1000

2000

~ T

0.2

CO 2

x/d = 40 1500

0.15

CO 2

0.1 H2O

1000

0.05

H2O 1

1000 H 2O

x/d = 20

0.15

0 0

1500 CO 2

0.1

r/d

1500

0.1

0.15

0 0

2000

~ T

0.2

2000

~ T [K]

0 0

x/d = 10

~ T

0.05

Mass fraction

0.05

290

~ T [K]

CO 2

75

2500

0.2 Mass fraction

2000 ~ T [K]

Mass fraction

0.15

60

0.25

x/d = 5

~ T

0.2

45 x/d

x/d

0.05

~ T [K]

~ ux

0.21

~ Z

~ ux [m/s]

60

1 Exp [5] 1,728,000 cells 0.8 3,356,000 cells

~ Z

Mass fraction

80

Mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

500 2

3

4

5290

500 0 0

2

r/d

4

6

8

10290

r/d

Fig. 4 Predicted means u x , T , Z and mass fractions of H2O and CO2 vs the experimental data at different grid resolutions.

Figure 5 (left) shows an overview of the predicted flame, as visualised by the flame volume defined by Ro = 0.8 in Eq. (50) for Case F. The concave–convex shape increases with distance from the nozzle outlet (x = 0 m). Takagi et al.14 reported that a laminar flame was observed near


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 59

the nozzle owing to the increase in viscosity caused by the high temperature, even at a high Reynolds number (= 18,000). This phenomenon was termed ‘local laminarisation’ and was not seen in a cold jet flow. Thus, treatment of laminar-turbulence transition is considered in the present study. In terms of turbulence models such as the dynamic Smagorinsky model, SGS approaches 0 when flow is laminar. However, laminar-turbulence transition is generally not taken into account in combustion models.6,8–10

Fig. 5 Overview of the predicted flame defined by the flame volume with Ro = 0.8 in Case F (left) and iso-surface of the stoichiometric mixture fraction (0.295) coloured by (  diff −  EDC ) in Case F (right). Ro is defined in Eq. (50).

Figure 5 (right) shows the predicted iso-surface of the stoichiometric mixture fraction, coloured on the basis of (  diff −  EDC );  EDC is shown as the red region and  diff is shown as the blue region (Eq. (22)). At x < 0.02 m,  diff is applied intermittently, with only  EDC dominating thereafter. Thus, the laminar region is observed near the nozzle at x < 0.02 m, whereas it is not seen in the downstream region at x > 0.02 m. This laminar-turbulent transition is consistent with that of previous experimental studies.13,14 Figure 6 shows the temperature contours in Cases A–F. The major difference between cases is the maximum value of T, which is due to differences in the combustion model and Le. A high


Page 27 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

maximum T is observed in Cases D and E near the nozzle owing to jiJ in Eq. (5) and Le ≠ 1. Therefore, it is considered that the effect of Le is very strong near the nozzle. In Cases D and E, infinitely fast chemistry is used and H2 is preferentially supplied to the flame sheet (as compared with CO) owing to Le ≠ 1. Conversely, the maximum temperature is decreased in Case F because the finite reaction rates are used.

Fig. 6 Temperature distribution in Cases A–F. The maximum temperature at each upper figure is set to 2400 K for comparison. Figure 7 shows the axial profiles of the velocity, mixture fraction, temperature and mass fractions. The predictions of H2 in Cases D–F are in reasonable agreement with the experimental data, with Cases A–C agreeing less well; therefore, consideration of Le ≠ 1 improves the prediction of H2. The axial profiles of the mass fraction of H2O in Cases D–F slightly shift to the upstream region compared with those in Cases A–C. This is because the Lewis number of H2 is much lower (= 0.29 in Cases D–F) than unity and so H2 diffuses more rapidly. The mass fractions of CO and CO2 in Cases A–E are similar; therefore, the Lewis number effect is less important for the predictions of CO and CO2 than for those of H2 and H2O. Further, the mass


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 59

fraction of OH predicted using the detailed reaction mechanism is in reasonable agreement with the experimental data, although this is a minor species. The predicted axial velocities are slightly underestimated at 30 > x/d. The mixture fractions are overestimated, especially at 45 < x/d. Therefore, the predicted temperatures and mass fractions of H2O and CO2 are higher at 45 < x/d. Also, the predicted mass fractions of O2 are significantly lower than the experimental data at 45 < x/d, which is outside of the flame (flame height = 47d).5 The predicted mixture fraction is different from the measurements, indicating that mass transfer prediction is problematic at 45 < x/d. Since the axial velocities are in good agreement, the grid resolution is thought to be sufficient. A possible explanation for this is that Sct and Prt are not dynamically determined on the assumption that turbulent thermal and mass diffusivities are linearly correlated with μSGS. In the simulations, Sct = 0.4 and Prt = 0.4 are used but these values might decrease in the downstream region. The mixture fraction is overestimated, indicating that the mixing of fuel gas and air is underestimated. Therefore, the concentration of O2 is very low at 45 < x/d. Zhao et al.9 studied the same scenario using 2-D RANS with the PDF model and the standard k-ε model. The prediction accuracy in the downstream region was improved if the parameters of the k-ε model were adjusted. However, in the context of applicability, such changes are thought to be undesirable and discrepancy will likely occur at a different position. Although several researchers have performed simulations of the same scenario,8,9,11,12 none of these predictions achieved good agreement with the measurements in the downstream region. Such a difference in the downstream region was not observed in previous simulations of various experiments.48,67,68 When the definition of flame height is the axial coordinate of Z = Zst, the predicted flame height is 49.5d in Case E, where Zst = 0.295.4


Page 29 of 59

0.04 0.03 ~ Y H2

Exp [5] Le=1 EDC (Case A) Le=1 EDC/Lam (Case B) Le=1 EDC/Lam jiJ (Case C) Le≠1 EDC/Lam jiJ (Case D) Le≠1 EDC/Lam jiJ Soret (Case E) Le≠1 EDC/Lam jiJ Soret Finite rate (Case F)

0.02 0.01

60

0 0.1

50

0.08

40 ~ YH2O

u~x [m/s]

47 (Case C)

30

0.06 0.04

43.8 (Case D)

20 0.02

10 0 1

0 0.6

0.8

0.5 0.4

~ Z

~ YCO

0.6 0.4

Z=0.295

0.3 0.2

0.2

0.1

0 2500

0 0.25

2000

0.2 ~ YCO2

~ T [K]

52.7 (Case F)

1500

0.15 0.1

54.3 (Cases A-E)

1000 0.05 500 290

0

0.25

0.003

0.2 0.002 0.15

~ YOH

~ Y O2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.1

0.001

0.05 0 0

15

30

45

60

75

0 0

15

30

45

60

75

x/d

x/d

Fig. 7 Axial profiles of velocity, mixture fraction, temperature and mass fractions.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 59

Fig. 8 Distribution of DSGS (left) and D (right) in Case F Figure 8 shows the distribution of DSGS (left) and D (right) in Case F. As confirmed by the predicted concentrations of H2 and H2O, the Lewis number affected the positions and values. It is considered that molecular diffusion is not important in turbulent jet flames. DSGS along the centreline is close to zero and increases in the downstream region. Further, D , near the position of peak temperature, is very large. Thus, Le influences the axial profiles of the mass fractions and T, as well as their radial profiles near the nozzle. Figure 9 shows the radial profiles of velocity, mixture fraction, temperature and mass fractions at x/d = 0.5. The predicted values in Cases D–F are more diffusive than those in Cases A–C owing to the effect of Le ≠ 1, which can be deduced by the radial profile of the mixture fraction. Owing to the difference in the mixture fraction between Le ≠ 1 and Le = 1, the laminar flamelet model should not be applied near the nozzle. The peak temperatures and mass fractions of H2O and CO2 with Le = 1 in Cases A–C are different from those with Le ≠ 1 in Cases D and E owing to the strong effect of Le. However, such a strong feature is inhibited when using the detailed reaction mechanism, as shown in Case F. The mass fractions of H2O and CO2 in Cases D and E are slightly different from each other owing to thermal diffusion. Thermal diffusion moves


Page 31 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

lighter species such as H2O and H2 from a location at low temperature to one at high temperature. Similarly, heavier species such as CO2, CO and O2 are transferred from a location at high temperature to one at low temperature. However, the effect of thermal diffusion is not prominent, except for H2O and CO2. Unfortunately, there are no experimental data at x/d = 0.5 in Fig. 9 and so the effect of preferential diffusion cannot be validated. However, the effects of Le and thermal diffusion are still observed at x/d = 20 and the tendencies at x/d = 0.5 and 20 are similar. Figure 10 shows the radial profiles of velocity, mixture fraction, temperature and mass fractions at x/d = 20. The simulation data of Dinesh et al.8 are also shown for reference. The computational conditions were: laminar flamelet model, dynamic Smagorinsky model, total of approximately 3.4 million cells and Sct = 0.4. The value of ux is somewhat different from that of the experimental data. The predictions obtained in this study are better than those of Dinesh et al.8 In general, the trends in the predicted values in the present study are similar to the experimental data, except for ux. The peak temperatures and mass fraction of H2O in Cases A–C are different from those in Cases D and E owing to the strong effect of Le, and the predictions in Cases A–C are better than those in Cases D and E. As confirmed in Fig. 5, a very high instantaneous T was observed in Cases D and E, causing a discrepancy in the mean temperature. This is slightly improved by considering the detailed reaction mechanism in Case F. Thus, the effects of Le and thermal diffusion should be considered with the finite reaction rate. Figure 11 shows the temperature and mass fraction of H2O and CO2 with the finer grid. Figure 11 is depicted because the grid dependency was observed at x/d = 20 in Fig. 4. The tendencies of temperature and mass fractions in Cases A and E are similar to those with the coarser grid. Moreover, the predictions in Case E are in


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 59

reasonably good agreement with the experimental data, which indicates that the discrepancy at x/d = 20 is due to a lack of grid resolution. Figure 12 shows the radial profiles of velocity, mixture fraction, temperature and mass fractions at x/d = 40, which is close to the position of peak T. The general trend of the predicted values in each case is similar to the experimental data. The differences among cases are not clear when compared with that at x/d = 0.05–20. Figure 13 shows the radial profiles of velocity, mixture fraction, temperature, and mass fractions at x/d = 60. The large errors are found close to the centre (r/d = 0) except for the velocity, whereas the predictions is in reasonably good agreement with the experimental data at 3 < r/d. Figure 14 shows the radial profiles of the mixture fraction and mass fractions of H2O and CO2 at x/d = 2–10. A difference in the mass fractions of H2O and CO2 owing to the effect of thermal diffusion is found in Cases D and E. Also, the mixture fraction with Le = 1 (Case C) is different from that with Le ≠ 1 (Case D). Hence, the mixture fraction based on Eq. (57) is different from that computed by the transport equation of the mixture fraction that is often used with the laminar flamelet model. When Le = 1, the mixture fraction computed by the transport equation is the same as that estimated by Eq. (57). The mixture fraction in the flow field should be consistent with that in the look-up table or flamelet library.


Page 33 of 59

0.04

0.02 0.01

60

0 0.12

50

0.1

40

0.08 ~ YH2O

~ ux [m/s]

~ YH2

0.03 Le=1 EDC (Case A) Le=1 EDC/Lam (Case B) Le=1 EDC/Lam jiJ (Case C) Le≠1 EDC/Lam jiJ (Case D) Le≠1 EDC/Lam jiJ Soret (Case E) Le≠1 EDC/Lam jiJ Soret Finite rate (Case F)

30

0.06

20

0.04

10

0.02

0 1

0 0.6 0.5

0.8

0.4

~ Z

~ YCO

0.6 0.4

0.2 0.1

0 2500

0 0.25 0.2 ~ YCO2

2000 ~ T [K]

0.3

0.2

1500

0.15 0.1

1000 0.05 500 290 0.6

0 0.005

0.5

0.004 ~ YOH

0.4 ~ YO2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.3

0.002

0.2

0.001

0.1 0 0

0.003

0.2

0.4

0.6

0.8

1

0 0

0.2

0.4

0.6

0.8

1

r/d

r/d

Fig. 9 Radial profiles of velocity, mixture fraction, temperature and mass fractions at x/d = 0.5


Energy & Fuels

0.04 0.03 ~ YH2

Exp [5] Laminar Flamelet [8] Le=1 EDC (Case A) Le=1 EDC/Lam (Case B) Le=1 EDC/Lam jiJ (Case C) Le≠1 EDC/Lam jiJ (Case D) Le≠1 EDC/Lam jiJ Soret (Case E) Le≠1 EDC/Lam jiJ Soret Finite rate (Case F)

0.02 0.01 0 0.1

60

0.08

40 ~ YH2O

~ ux [m/s]

50

30

0.06 0.04

20 10

0.02

0 1

0 0.6 0.5

0.8

0.4

~ Z

~ YCO

0.6 0.4

0.3 0.2

0.2

0.1

0 2500

0 0.25 0.2 ~ YCO2

~ T [K]

2000 1500

0.15 0.1

1000 0.05 500 290 0.6

0 0.003

0.5 0.002 ~ YOH

0.4 ~ Y O2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 59

0.3 0.2

0.001

0.1 0 0

1

2 r/d

3

4

5

0 0

1

2

3

4

5

r/d

Fig. 10 Radial profiles of velocity, mixture fraction, temperature and mass fractions at x/d = 20.


Page 35 of 59

2000 Exp [5] 3,356,000 cells Case A 1500 Case E

T 0.2 0.15 CO2

0.1 0.05 0 0

1000

H2 O 1

T [K]

0.25

Mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

500 2

3

4

5

r/d

Fig. 11 Radial profiles of temperature and mass fractions of H2O and CO2 at x/d = 20 with the fine grid.


Energy & Fuels

0.04 0.03 ~ YH2


0.01

60

0 0.1

50

0.08 ~ YH2O

40

~ ux [m/s]

0.02

30

0.06 0.04

20 0.02

10

0 0.6

0 1

0.5

0.8

0.4

~ Z

~ YCO

0.6 0.4

0.2 0.1

0 2500

0 0.25 0.2 ~ YCO2

2000 ~ T [K]

0.3

0.2

1500

0.15 0.1

1000 0.05 500 290 0.6

0 0.003

0.5 0.002 ~ YOH

0.4 ~ YO2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 59

0.3 0.2

0.001

0.1 0 0

2

4

6

8

10

0 0

2

4

6

8

10

r/d

r/d



Page 37 of 59

0.04

0.02 0.01

60

0 0.1

50

0.08

40

0.06

YH2O

ux [m/s]


YH2

0.03

30

0.04

20 0.02

10

0 0.6

0 1

0.5

0.8

0.4

Z

YCO

0.6 0.4

0.3 0.2

0.2

0.1

0 2500

0 0.25 0.2

2000 YCO2

T [K]

0.15

1500

0.1

1000 0.05 500 290 0.6

0 0.003

0.5 0.002 YOH

0.4 YO2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.3 0.2

0.001

0.1 0 0

2

4

6

8

10

0 0

2

4

6

8

10

r/d

r/d



Energy & Fuels

1 0.8

x/d = 2

x/d = 5

x/d = 10

x/d = 2

x/d = 5

x/d = 10

x/d = 2

x/d = 5

x/d = 10

x/d = 5

x/d = 10

~ Z

0.6 0.4 0.2 0 2400

~ T [K]

1800 1200 600 293 0.1 0.08 ~ YH2O

0.06 0.04 0.02

0 0.25 x/d = 2

0.2 0.15

~ YCO2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 59

0.1 0.05 0 0

0.5

1 r/d

Le=1 EDC (Case A) Le=1 EDC/Lam (Case B)

1.5

2 0

0.5

Le=1 EDC/Lam jiJ (Case C) Le≠1 EDC/Lam jiJ (Case D)

1 1.5 2 0 1 r/d r/d Le≠1 EDC/Lam jiJ Soret (Case E) Le≠1 EDC/Lam jiJ Soret Finite rate (Case F)

2

3

Fig. 14 Radial profiles of the mixture fraction and mass fractions of CO2 and H2O at x/d = 2–10.


Page 39 of 59

0.1


~ YH2O

0.08 0.06 0.04 0.02

2500

0.6

2000

0.5 0.4

1500

~ YCO

~ T [K]

0

1000

0.1 0

0.25

0.25

0.2

0.2

0.15

0.15

~ YCO2

~ Y O2

0.3 0.2

500 290

0.1

0.1

0.05

0.05

0 0 0.04

0 0.003

0.03 ~ YOH

0.002 ~ YH2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.02

0.001 0.01 0 0

0.2

0.4

~ Z

0.6

0.8

1

0 0

0.2

0.4

~ Z

0.6

0.8

1

Fig. 15 Temperature and mass fractions vs mixture fraction in the axial direction. Figures 9–13 compare the predicted data with the experimental data and a discrepancy is observed in the downstream region. Thus, the mixture fraction space is better for evaluating the turbulence-chemistry interaction. Figure 15 shows the predicted and measured temperature and


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 59

mass fractions vs mixture fraction. The mixture state is defined as the fuel-rich state Zst < Z , the near-stoichiometric state Z ≈ Zst or the fuel-lean state Z < Zst. The predicted mass fractions of H2O in Cases A–C and F are slightly different on the fuel-rich side, indicating that reaction rate of H2 is underestimated compared with the experimental data. The predicted data in Cases D and E are in good agreement with the experimental data. In this study, the reaction rate of H2 is first evaluated, followed by CO (Eqs. (23)–(26)). The mass fraction of CO2 becomes small owing to consumption of O2 when the mass fraction of H2O is large, such as in Cases D and E. Owing to the artificial priority concept for the reaction rate, the predicted data are in reasonably good agreement with the experimental data without considering the finite reaction rate. Generally, the oxidation rate of CO is slower than that of H2 and it should not be evaluated by infinitely fast chemistry. Barlow et al. suggested that the ratio of the chemical reaction time scale of CO to the flow time scale is approximately unity.4 As described above, infinitely fast chemistry assumes that the first term on the right-hand side in Eq. (33) is sufficiently large compared with the second term. The reaction rate of CO should be evaluated by an Arrhenius type expression, such as the detailed reaction mechanism used in this study. Nevertheless, the predicted values using Eqs. (23)–(26) in Cases D and E better capture the experimental data than those using the detailed reaction mechanism in Case F, indicating that Maas et al.’s mechanism evaluates the reaction rate of H2 as being relatively slow under the fuelrich condition. Hence, the detailed reaction mechanism should be modified in order to obtain better predictions than those obtained for Cases D and E.


Page 41 of 59

As shown in Fig. 15, based on the mass fractions of H2O in Cases C and D, the effect of Le ≠ 1 is important on the fuel-rich side. Moreover, the turbulence-chemistry interaction is significant at the fuel-rich side, which can be deduced from the mass fractions of H2O in Cases E and F. 0.12 0.1 0.08 ~ Y H2 O

Le=1 EDC (Case A) Le=1 EDC/Lam (Case B) Le=1 EDC/Lam jiJ (Case C) Le≠1 EDC/Lam jiJ (Case D) Le≠1 EDC/Lam jiJ Soret (Case E) Le≠1 EDC/Lam jiJ Soret Finite rate (Case F)

0.02 0 0.6 0.5

2000

0.4 ~ YCO

~ T [K]

0.06 0.04

2500

1500

0.1

500 290

0

0.6

0.25

0.5

0.2 ~ YCO2

0.4 ~ YO2

0.3 0.2

1000

0.3 0.2

0.15 0.1

0.1

0.05

0

0

0.04

0.005

0.03

0.004 ~ YOH

~ Y H2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.02

0.003 0.002

0.01 0 0

0.001 0.2

0.4

0.6

0.8

1

0 0

0.2

0.4

~ Z

0.6

0.8

1

~ Z

Fig. 16 Radial temperature and mass fractions vs mixture fraction at x/d = 0.5.


Energy & Fuels

In Fig. 16, the influence of the laminar combustion model on the temperature and mass fraction of CO2 in Cases A and B is observed. Le ≠ 1 and a difference in chemistry affect the temperature and mass fractions of H2O and CO2 in the entire mixture fraction space, whereas a thermal diffusion influence is seen near the stoichiometric to fuel-rich condition. 0.1 0.08 ~ Y H2 O


0.06 0.04 0.02 0 0.6

2500

0.5

2000 ~ T [K]

0.4 ~ YCO

1500

0.1

500 290

0

0.6

0.25

0.5

0.2 ~ YCO2

0.4 ~ YO2

0.3 0.2

1000

0.3

0.15 0.1

0.2 0.05

0.1 0

0

0.04

0.003

0.03 ~ YOH

0.002 ~ YH2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 59

0.02

0.001 0.01 0 0

0.2

0.4

~ Z

0.6

0.8

1

0 0

0.2

0.4

0.6

0.8

1

~ Z

Fig. 17 Radial temperature and mass fractions vs mixture fraction at x/d = 20.


Page 43 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

As shown in Fig. 17, the radial peak temperature and mass fractions of H2O and CO2 in Cases D and E are slightly higher than the experimental data at x/d = 20. It should be noted that these are slightly overestimated owing to a lack of grid resolution, as confirmed in Fig. 4. Further, the temperature and mass fractions of H2O and CO2 are in good agreement with the experimental data at the fuel-rich and -lean sides. Conversely, the mass fractions of H2O and CO2 deviate at the fuel-rich side. The effect of Le ≠ 1 is observed in the temperature and mass fractions of H2O and CO2 in Cases C and D. Thermal diffusion influences the mass fraction of H2O near the stoichiometric condition, as can be seen for Cases D and E. The differences in the temperature and mass fractions of H2O and CO2 in Cases E and F are caused by consideration of the detailed reaction mechanism near the stoichiometric to fuel-rich condition.


Energy & Fuels

0.1 0.08 ~ YH2O


0.06 0.04 0.02 0

2500

0.6 0.5 0.4

1500

~ YCO

~ T [K]

2000

0.3 0.2

1000

0.1

500 290

0

0.6

0.25

0.5

0.2 ~ YCO2

~ YO2

0.4 0.3 0.2

0.15 0.1

0.1

0.05

0

0

0.04

0.003

0.03 ~ YOH

0.002 ~ Y H2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 59

0.02

0.001 0.01 0 0

0.1

0.2

0.3

0.4

0.5

0 0

0.1

0.2

0.3

0.4

0.5

~ Z

~ Z

Fig. 18 Radial temperature and mass fractions vs mixture fraction at x/d = 40. Figure 18 shows temperature and mass fraction vs mixture fraction at x/d = 40 and 60. The difference in Cases A–F is somewhat smaller than that at x/d = 20. The influences of Le ≠ 1 (Cases C and D) and chemistry (Cases E and F) are confirmed from the mass fractions of H2O.


Page 45 of 59

0.1 0.08 0.06

Y H2 O


0.04 0.02 0 0.6

2500

0.5

2000 YCO

T [K]

0.4

1500

0.1

500 290

0

0.6

0.25

0.5

0.2

0.4

0.15

YCO2

YO2

0.3 0.2

1000

0.3 0.2

0.1

0.05

0.1 0

0

0.04

0.003

0.03 YOH

0.002 YH2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.02

0.001 0.01 0 0

0.1 ~ Z

0.2

0 0

0.1 ~ Z

0.2

Fig. 19 Radial temperature and mass fractions vs mixture fraction at x/d = 60. As can be seen from Fig. 19, none of the effects is not observed at x/d = 60, which indicates that turbulent mixture controls the combustion reactions. Table 2 summarises the influence of laminar flame, species diffusion, Le, thermal diffusion and chemistry vs the mixture fraction.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 59

Table. 2. Summary of the mixture fraction space, which has the influence of the physical assumptions. ‘Minor’ means the influence is minor, ‘fuel rich’ is Zst < Z , ‘st’ is Z ≈ Zst and ‘fuel lean’ is Z < Zst. Laminar

jiJ

Le

Soret effect

Chemistry

minor

fuel rich

centreline minor

minor

fuel rich

x/d = 0.5

st

minor

fuel lean–st–fuel rich st–fuel rich

fuel lean–st–fuel rich

x/d = 20

minor

minor

st–fuel rich

st

st–fuel rich

x/d = 40

minor

minor

st

minor

st

x/d = 60

minor

minor

minor

minor

minor

In summary, even in Cases A–C, the predictions capture well the experimental data; it is difficult to see substantial advantages in Cases D–F. This is because the artificial priority concept for the reaction rate using Eqs. (23)–(26) may calculate the difference in reaction rate between H2 and CO. However, the reaction rate should be taken into account theoretically, using an Arrhenius type expression. From the axial and radial mass fractions of H2O and CO2 in Cases D and E, consideration of preferential diffusion slightly improves the prediction accuracy under the fuel-rich condition, although the peak temperature and mass fraction of H2O tend to be overestimated, especially near the nozzle, as shown in Figs 6, 9 and 16. Therefore, the detailed reaction mechanism should be taken into account for the predictions near the nozzle; however, this causes a slight deviation under the fuel-rich condition, as shown in Fig. 17. In addition, certain minor species such as OH or NOx require the reaction mechanism. For further improvement, the detailed reaction mechanism should be refined to better predict the mass fractions under the fuel-rich condition.


Page 47 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

4.

CONCLUSIONS A simulation of the syngas jet flame of Sandia ETH/Zurich B was conducted using an in-house

version of FireFOAM. Combustion was modelled using (i) a newly extended EDC for the LES published by the authors’ group and (ii) a 74-step CO-H2-O2 mechanism. The radiation properties of the gases were evaluated using the established WSGGM. The effect of non-unity Lewis numbers was taken into account in the mass fraction and enthalpy equations. Systematic validation and model sensitivity studies were conducted against published experimental data from TNF workshops, which included the velocity, temperature and concentrations of chemical species. A laminar flame was observed near the nozzle at x < 0.02 m, whereas it was not seen in the downstream region at x > 0.02 m. Further, a very high temperature was observed near the nozzle when infinitely fast chemistry and Le ≠ 1 were applied. The effect of Le was very strong near the nozzle. Along the axial direction, the mass fractions of H2 and position of H2O were improved when considering Le ≠ 1. Conversely, the Lewis number effect was less important for the predictions of CO and CO2 than for those of H2 and H2O. The prediction of OH was in reasonable agreement with the experimental data. At x/d = 0.5, which is near the nozzle, the strong effect of Le was confirmed based on differences in the mixture fractions. Thermal diffusion increased the peak mass fraction of H2O but decreased that of CO2. At x/d = 20, the influences of Le and thermal diffusion were still found; moreover, the predictions were slightly improved by considering the finite reaction rate. At x/d = 40, which is the position of peak temperature, the predictions were close to the


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 59

experimental data. The effects of thermal diffusion and the Lewis number, as well as a difference in the mixture fraction due to non-unity Lewis number, were observed at x/d = 2–10. The laminar flame combustion model affected the results only very close to the nozzle. Species diffusion could be ignored when Le ≠ 1 and thermal diffusion were not considered. The effects of Le, thermal diffusion and chemistry were strong under the fuel-rich condition and stoichiometric condition; less so for the fuel-lean condition. These gradually decreased with increasing distance from the nozzle outlet. Beyond the flame height (= 47d), none of the effects were not observed owing to the strong turbulent mixture. The predictions involving preferential diffusion slightly facilitated accuracy under the fuel-rich condition. However, the peak temperature and mass fraction of H2O tended to be overestimated, especially near the nozzle. Therefore, the detailed reaction mechanism should be taken into account for predictions near the nozzle, although it caused a slight deviation under the fuel-rich condition. The detailed reaction mechanism affected the prediction accuracy and should be modified for further improvement of prediction accuracy under the fuel-rich condition. The present results indicate a significant role of preferential diffusion in syngas jet flames owing to the very different diffusion coefficient of H2. Results taking into account the effects of Le and thermal diffusion, as well as the detailed reaction mechanism, were slightly improved compared with predictions lacking these new treatments.

AUTHOR INFORMATION Corresponding Authors Changjian Wang E-mail: [email protected] Fax: 86-551-62905590 Kazui Fukumoto E-mail: [email protected]


Page 49 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

ACKNOWLEDGEMENT The in-house version of FireFOAM used in this study firstly developed in the project funded by the National key research and development programme special for inter-governmental cooperation (No. 2016YFE0113400) and the European Commission FP7-PEOPLE-2012-IIF (Grant number 328784). The authors acknowledge helpful support validating the look-up table approach with Prof. Ogami, Mr. Hongo and Mr. Morimori from Ritsumeikan University.

NOMENCLATURE Cp = heat capacity at constant pressure [J/kg/K] Cv = heat capacity at constant volume [J/kg/K] d = diameter [m] D = effective diffusion coefficient [m2/s] g = gravitational acceleration [m/s2] h = sensible enthalpy [J/kg] k = turbulent kinetic energy [m2/s2]

L = characteristic length of flame Le = Lewis number M = molecular weight


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u = velocity or velocity scale [m/s] p = pressure [N/m2] Prt = turbulent Prandtl number q = heat release rate per volume [W/m3]

 = radiative heat flux [W/m2] qrad r = radius [m] R = gas constant [J/kg/mol] Sct = turbulent Schmidt number t = time [s] T = temperature [K] xj = coordinate in j direction X = mole fraction Y = mass fraction Z = mixture fraction Greek

= thermal diffusivity [m2/s] ε = turbulent dissipation rate [m2/s3] λ= thermal conductivity [W/m/K]


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Energy & Fuels

= density [kg/m3]

 = viscosity [kg/m/s]  = kinematic viscosity [m2/s]  = time scale [s]

 = reaction rate [kg/s/m3] subscripts diff = diffusion EDC = EDC model f = flame fu = fuel gas = gas i, j, k,l = coordinate index inlet = inlet J = chemical specie RMS =root mean square SGS = sub-grid scale

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Large eddy simulation of a syngas jet flame: Effects of preferential

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