Journal of Thermal Science Vol.20, No.6 (2011) 548555

Received: March 2011 Yunardi: Senior Lecturer Supported by Ministry of National Education, Republic of Indonesia No. 433/SP2H/PP/DP2M/VI/2010

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DOI: 10.1007/s11630-011-0509-y Article ID: 1003-2169(2011)06-0548-08

Investigation of Detailed Kinetic Scheme Performance on Modelling of Turbu-lent Non-Premixed Sooting Flames

Y. Yunardi1, D. Darmadi1, H. Hisbullah1 and M. Fairweather2

1. Department of Chemical Engineering, Syiah Kuala University, Banda Aceh, Indonesia

2. Energy and Resources Research Institute, SPEME, University of Leeds, Leeds, United Kingdom

© Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2010

This paper presents the results of an application of a first-order conditional moment closure (CMC) approach

coupled with a semi-empirical soot model to investigate the effect of various detailed combustion chemistry

schemes on soot formation and destruction in turbulent non-premixed flames. A two-equation soot model repre-

senting soot particle nucleation, growth, coagulation and oxidation, was incorporated into the CMC model. The

turbulent flow-field of both flames is described using the Favre-averaged fluid-flow equations, applying a stan-

dard k-ε turbulence model. A number of five reaction kinetic mechanisms having 50 – 100 species and 200 –

1000 elementary reactions called ABF, Miller-Bowman, GRI-Mech3.0, Warnatz, and Qin were employed to study

the effect of combustion chemistry schemes on soot predictions. The results showed that of various kinetic

schemes being studied, each yields similar accuracy in temperature prediction when compared with experimental

data. With respect to soot prediction, the kinetic scheme containing benzene elementary reactions tends to result

in a better prediction on soot concentrations in comparison to those contain no benzene elementary reactions.

Among five kinetic mechanisms being studied, the Qin combustion scheme mechanism turned to yield the best

prediction on both flame temperature and soot levels.

Keywords: soot; conditional moment closure; combustion; kinetic scheme; non-premixed; turbulent flame

Introduction

Today, the production of solid particles within a flame, known as soot, represents an important field in combus-tion research. Investigations in recent years have focused on the development of combustion systems having high combustion efficiency, low fuel consumption and low pollutant emissions. Emission of soot from a practical combustion device reflects poor combustion conditions and loss of efficiency. Soot generation usually results from an incomplete combustion and typically occurs at fuel-rich regions of the flame. Although some of the par-

ticles are oxidized in the flame, soot that escapes from oxidation is considered a serious environmental pollutant. Soot is also associated with health risks since both poly-cyclic aromatic hydrocarbons (PAHs) that are precursors of soot and soot-associated organics have been identified to be carcinogenic. On the other hand, in cases where soot oxidation is completed within a flame, higher pro-duction of intermediate soot is desirable for increasing the radiant heat transfer from the flame. Thus, the emis-sion of soot from a flame is determined by the competi-tion between soot formation and oxidation.

Soot formation has been recognized as one of the most

Y. Yunardi et al. Investigation of Kinetic Scheme Performance on Modelling of Turbulent Non-Premixed Sooting Flames 549

Nomenclatures Other symbols

d diameter ensemble averaging

k reaction rate constant D diffusion coefficient

u axial velocity M molar mass

Q transported scalar N number or particle number density

A surface area or pre-exponential factor Y mass fraction

C constant density

Greek symbols w production rate

scalar dissipation * integration over cross section limited by |r|<R

mixture fraction conditional expectation of at some value

sample space variable

Superscripts

+ scalar of equal diffusivity

complicated phenomena involving many chemical and physical processes. It is remarkable that within only a few milliseconds since the start of combustion, hydro-carbon fuel molecules containing only a few carbon at-oms transform into soot particles having 106 – 1012 car-bon atoms. Despite the lack of a unique chemical or physical structure, it is commonly accepted among scien-tists involved in soot research that the basic physical and chemical processes taking place in soot formation such as nucleation, surface growth, coagulation and oxidation are the same, regardless of fuel or type of flame. Even though many efforts have been made to give better un-derstanding on the essential features of the chemistry and physics of soot formation and oxidation, they are still incomplete and too many unknowns [1-3].

Gas-Phase Combustion Chemistry

Detailed combustion kinetic schemes developed from hundreds of elementary radical reactions have been in-creasingly used to modelling the combustion process. Among the various hydrocarbon fuels, the methane combustion chemistry is the most frequently investigated and developed, and a large number of detailed as well as reduced mechanisms have been reported. Table 1 lists five detailed kinetic schemes employed in the present investigation, of which the first four mechanisms were developed for the combustion of C1 and C2 hydrocar- bons [4-7], whereas the Qin mechanism was optimized for propane combustion [8]. Each scheme is briefly described in the next paragraphs.

Appel et al [4] developed a kinetic scheme, known as ABF mechanism, for the combustion of C2 hydrocarbons with the aim at accurately predicting the soot formation in ethane, ethylene and acetylene flames. Their starting mechanism is that of Wang and Frenklach [9] which was modified by improving the small-molecule gas-phase

reactions, revising the PAH gas-phase part, and supple-menting elementary reactions for soot particle coagula-tion, soot particle aggregation, and soot surface growth. Since the mechanism was prepared for prediction of soot level in a hydrocarbon flame where the PAHs are consid-ered dominant in the inception step, benzene reactions have been included in the scheme.

Table 1 Kinetic schemes used in this study

No Chemical kinetic schemes No. species No. reactions

1 ABF [4] 101 1034

2 Miller-Bowman [5] 46 224

3 GRI-Mech3.0 [6] 53 325

4 Warnatz [7] 52 299

5 Qin [8] 70 463

The resulted scheme consisting of 101 species and

1034 elementary reactions that has been tested against experimental data of ethane, ethylene and acetylene laminar premixed flames in terms of major and minor chemical species, aromatics, soot volume fractions, and soot particle diameters.

The second full kinetic mechanism tested under this study is the scheme published by Miller and Bowman [5]. The scheme consisting 46 species and 224 elementary reactions represents the oxidation mechanisms for C1 and C2 hydrocarbons, HCN and NH3, accompanied by a sub-set describing the interaction between hydrocarbon spe-cies and nitrogen chemistry. The nitrogen chemistry comprehensively covers the universally recognised paths to NO production and destruction, including the thermal mechanism, prompt mechanism, fuel- nitrogen paths ( including the oxidation of HCN and NH3, and the NO→HCN→N2 mechanism), thermal de-NOx and RAPRENO mechanisms, nitrogen dioxide mechanism, and the nitrous-oxide mechanism. Since the scheme is

550 J. Therm. Sci., Vol.20, No.6, 2011

optimized for C1 and C2 hydrocarbon combustion, ele-mentary reactions for further than C2 combustion are not considered at all.

The GRI-Mech3.0 constitutes the latest version of the GRI-series’ kinetic schemes developed through research sponsored by the Gas Research Institute [6]. The focus of the research was to develop an optimized detailed chemical reaction mechanism capable of the best repre-sentation of natural gas flames and ignition in a wide range of systems and conditions. The scheme comprises of 53 species and 325 reaction steps which are important for describing natural gas ignition and propagation, in-cluding NO formation and reduction. The GRI-Mech3.0 scheme, being the final development in the project, built upon GRI-Mech2.11 by the analysis of new detailed data sets including shock- tube observations. Although the scheme includes up to C3 hydrocarbon reactions, the mechanism itself is optimized for methane, and not for propane combustion.

Warnatz mechanism [7] is one of the early hydrocarbon mechanisms developed through a number of experimen-tal and theoretical studies spanning several papers and years. The reference provided in this publication is not a single authoritative source, but describes the develop-ment of the C1 to C4 mechanism and applies this to the calculation of sooting flames of propane and butane. The detailed chemical kinetic scheme consists of 299 reversible reactions and 52 species. The combination of the hydrocarbon and nitrogen chemistries provides a very comprehensive reaction scheme encompassing the oxida-tion of the C1 to C4 hydrocarbons, the mechanism of formation and consumption of soot precursors, and the thermal, prompt, fuel, and nitrous oxide routes of NOx

chemistry. Although the mechanism includes reactions for soot precursor, benzene has not yet considered in the scheme as an important species in soot formation.

The kinetics for C1 and C2 components of the Qin et al. [8] mechanism was created by removing the nitrogen and propane chemistry parts of the GRI-Mech3.0 scheme [6]. A number of 258 additional reactions representing pro-pane chemistry were then introduced into the mechanism to construct a scheme with 70 species and 463 chemical reactions. Although the mechanism focuses on propane combustion, its predictive ability with regards to laminar flame speed and shock tube ignition delay has been tested for different fuels, in particular CH4, C2H4, C2H6, C3H4 and C3H6. Despite neglecting NO chemistry, the mechanism used here integrates reactions which lead to the formation of the cyclic polyaromatic hydrocarbons of benzene and phenyl. The reactions with acetylene, the soot precursor, mainly responsible for the growth of PAH and soot were also included in the mechanism. Poten-tially important benzene formation paths through reac-tions of C2H2, C3H3, n-C4H3 and n-C4H5 are also consid-

ered, giving the mechanism excellent potential for the calculation of sooting flames.

Mathematical Formulation and Calculation

Conditional Moment Closure (CMC) – Semi Empiri-cal Soot Model

A general first-order, parabolic CMC equation can be developed by averaging the instantaneous equation gov-erning species mass fraction, Yi in statistically stationary, turbulent reacting flow, on the condition that the instan-taneous mixture fraction equals an arbitrary value . In the case the conserved scalar and reactive scalar have different diffusion coefficients, that is Di ≠ D, an un-closed form of the CMC equation can be written as pre-sented in Eq. 1.

2

2

*

,

1

2

1

i i i

i i

i y i

Q D Qu

x D

D QD

D x x

w e

(1)

For the derivation of the conditional gas-phase species mass fraction equation, both reactive and conserved sca-lars are assumed to diffuse equally, which implies Di = D. On the basis of this assumption, the second and last terms on the right hand-side of Eq. 1, representing the source terms that generate differential and spatial diffusion, re-spectively, are cancelled. The scalar dissipation was modelled using the approach of Girimaji [10], while the remaining non-linear chemical source term i was

modelled as for simple first-order closure. Mean values were obtained using the CHEMKIN package [11], by varying the chemical kinetic schemes in accordance to those shown in Table 1.

In addition to the CMC species transport equation, the soot model employed in the present study requires the solution of two additional transport equations for the soot mass fraction sY and the soot particle number density Ns

[12-13]. In the case of differential diffusion being neglected,

the transport equations for sY and sN are obtained in

a similar way as for the gas-phase species, setting

s sY ND D D for ,s si Y N in Eq. 1, to give:

2

2

1

2s s

s

Y YY

Q Qu

x

(2)

2

2

1

2s s

s

N NN

Q Qu

x

(3)

where the superscript + refers to a scalar of equal dif-fusivity. When the differential diffusion of soot particles

Y. Yunardi et al. Investigation of Kinetic Scheme Performance on Modelling of Turbulent Non-Premixed Sooting Flames 551

is taken into account, fixing the molecular coefficients of soot particles and nuclei equal to zero, i.e. DYs = DNs = 0 for i=Ys, Ns, Eq. 1 can be simplified by neglecting the dissipation term, this being the first term on the right hand side. However, the ey,i, spatial diffusion terms seen in Eq. 1, now becomes significant. The transport equa-tions considering the effects of differential diffusion are modelled as Eqs. 4 and 5.

*

0.4( )

s s

s

s s

Y YY

Y Y

K

Q Qu D

x x x

Q Q

(4)

*

0.4( )

s s

s

s s

N NN

N N

K

Q Qu D

x x x

Q Q

(5)

The source terms sY in Eqs. 2 and 4 account for

the effects of soot nucleation, surface growth and oxida-tion. Acetylene and benzene were selected as the incipi-ent species responsible for soot nucleation[14]. However, the former species was considered as the only chemical contributor to the increase in soot mass via surface growth. The soot nucleation proceeds via C2H2 ↔ 2Cs + H2 and C6H6 ↔ 6 Cs + 3H2. It is assumed that surface growth continues via an acetylene reaction similar to the one in soot nucleation. Soot oxidation is assumed to pro-ceed through Cs + 0.5 O2→ CO and Cs + OH → CO + H. Now, the source term for the soot mass fraction equation can be written as Eq. 6.

2 22 2

6 66 6

2 22 2

22

1 C HC H

2 C HC H

3 C HC H

4 OO

5 OHOH

2 ( )

6 ( )

2 ( )

( )

( )

s

sY T

sT

sT s

sT s

sT s

Mk Q Q M

Mk Q Q M

Mk Q A Q M

Mk Q A Q M

Mk Q A Q M

(6)

The source terms sN in Eqs. 3 and 5 represent

the production and reduction of soot particle number density due to nucleation and agglomeration, respectively, expressed as Eq. 7.

2 2 6 61 C H 2 C Hmin

1/6 1/ 22

2 ( ) 6 ( )

662

s

s

s

s

AN T T

Y B Ta N

N s

Nk Q Q k Q Q

C

Q QC Q

Q

(7)

Reaction rate constants for nucleation, surface growth and oxidation that appear in Eqs. 6 and 7 are presented in Table 2.

Table 2 Reaction rate constants for soot formation and oxida-tion, in the form of the Arrhenius expression kj = ATb exp (Ta/T) (units K, kmol, m, s).

ki A b Ta

k1 1.0×104 0.0 21,000

k2 0.75×105 0.0 21,000

k3 0.75×103 0.0 12,100

k4 7.15×102 0.5 19,680

k5 3.60×101 0.5 0

Experimental Conditions of Target Flames

The non-premixed atmospheric pressure methane flame considered in the present study has been experi-mentally reported by Brookes and Moss [15]. The impor-tant characteristics of the flame are presented in Table 3. The flame was confined within a cylindrical pressure vessel with a length of 980 mm and internal diameter of 155 mm. A pure methane fuel jet was issued from a cy-lindrical nozzle of 4.07 mm in diameter with an exit ve-locity of 20.3 m s1. The jet flame was rim stabilized by an annular premixed pilot flame, and a co-flowing air stream occupied the remainder of the inlet contained within the cylindrical liner. Temperature measurements were performed using fine-wire thermocouples and mean mixture fraction was measured by microprobe sampling and mass spectrometric analysis. The mean soot volume fraction was measured using laser extinction tomography and results were reported at heights of 300, 350, and 425 mm above the nozzle. Table 3 Operating conditions for the atmospheric methane flame

Flame operating pressure /atm 1

Fuel mass flow/g min1 10.3

Air mass flow/g min1 708

Fuel temperature/K 290

Air temperature/K 290

Fuel jet velocity/m s1 20.3

Exit Reynolds number 5000

Flow-field Calculation and Solution of the CMC Equations

The calculation of flow and mixing fields was achieved by solving the Favre-averaged forms of the par-tial differential equations which describe conservation of mass, momentum and the transport of mixture fraction and its variance. A standard kε turbulence model was

552 J. Therm. Sci., Vol.20, No.6, 2011

used to close the above equation set. A modified version of the GENMIX code [16] was implemented in the solu-tion of the two-dimensional, axisymmetric forms of the transport equations.

Flow and mixing field information from the turbulent flow calculations employing a reacting-flow density were passed to the CMC model, where the set of species mass fractions, soot mass fraction, particle number density and enthalpy equations were solved in mixture fraction space. The flow and mixing field are related to the reactive sca-lar field through the mean density, and comparison be-tween densities obtained from the CMC solution and prescribed equilibrium values showed little variation at the locations examined in the flames considered. Cou-pling of the flow field and CMC calculations was there-fore deemed unnecessary for the calculations reported. Solution of the CMC equations in real space was achieved using a fractional step method, implemented using the stiff ODE solver VODE [17] which applies a backward differentiation formula approach to the solu-tion of the non-linear equation set. Second-order differ-ential sample space terms were determined using a cen-tral differencing approximation. The computational grids consisted of 68 radial nodes in mixture fraction space and 38 nodes in physical space.

Results and Discussion

Mixture Fraction and Temperature Predictions

Fig 1 presented predicted averaged mixture fraction and temperature in axial profile compared to the experi-mental data. It should be noted that the predicted mixture fractions are originated from the flow field calculation based on adiabatic equilibrium calculation derived from Qin et al [8] mechanism. In the previous study [18] using similar calculation, the results showed that the predicted flow fields were found to be insensitive to the particular kinetic scheme employed. Therefore, predicted flow fields produced by each kinetic scheme in this study were not compared. The symbol and lines in Fig. 1 represent the experimental data and predicted values, respectively. It is well known that the use of Cε2=1.92 in the standard k-ε turbulence model over-predicts the spreading rate of a round jet. However as seen in Fig.1, the predicted mix-ture fraction follows the experimental data quite well, which was achieved by adjusting Cε2 from 1.92 to 1.84.

Fig. 1 also illustrated the predicted temperature by the CMC- based soot model approach at the centreline of the flame, based on different chemical kinetic mechanisms. Apart from the temperature prediction by ABF [4], Miller- Bowman [5] and Qin et al [8] mechanisms, the temperature prediction by other chemical mechanisms predicted well the peak temperature at the axial position of 350 mm in the flame. Up to this position, all kinetic mechanisms

yielded similar prediction. However, above this position, the temperature prediction by the former three mecha-nisms tended to be constant following the experimental trend in the range of 1650-1690 K. In the meantime, pre-dicted temperatures by the other two kinetic mechanisms suddenly declined after peaking at a position of 350 mm above the nozzle. In general, it is evident that the axial temperature evolution predicted by ABF [4], Miller- Bowman [5] and Qin et al [8] is qualitatively and quantita-tively in better agreement with experimental data than that produced by other remaining two kinetic mecha-nisms.

Fig.1 Axial profiles of mixture fraction and temperature (symbol-measurement; — ABF; ----- Miller-Bowman, ······· GRI Mech3.0, −·−·− Warnatz, −··−··− Qin et al)

Fig.2 depicted the calculated mixture fraction and ra-

dial temperature profile at axial height of 150, 200, 250, 300, 350, and 425 mm above the nozzle. Compatible with the axial profile, the predicted radial mixture frac-tion profile is in excellent agreement with the experi-mental data at all heights. Inspection of the radial profile of the temperature predictions by five kinetic mecha-nisms, the trend of predictions is consistent with the one obtained in the axial profile where the combustion chem-istries of ABF [4], Miller-Bowman [5] and Qin et al [8] gave similar best result, as clearly evidence from the evolution of predicted temperatures they produced in each radial profile at each axial location in the flame. The predicted temperature yielded by these mechanisms was able to catch the radial off-centre peak temperature superior than that of GRI Mech3.0[6] and Warnatz [7]. Although the lat-ter two mechanisms were able to precisely predict the location of the radial peak temperatures, their predicted peak temperature values were lower than that of the ex-perimental data. In contrast, all radial peak temperatures were accurately predicted by the former three mecha-nisms both in terms of position and value. However, temperature predictions in the fuel-lean region were fal-ling below measured values, particularly for the flame above 250 mm. Weakness in the k–ε turbulence model and negligence of conditional turbulence fluctuations are believed to be mainly responsible for this poor perform-

Y. Yunardi et al. Investigation of Kinetic Scheme Performance on Modelling of Turbulent Non-Premixed Sooting Flames 553

ance in the calculations. Nonetheless, it is important to note that all mechanisms failed to reproduce the meas-ured values of temperature in fuel-lean regions in the flame above 250 mm from the nozzle. In general, the results from Fig. 1 and Fig. 2 suggested that the predic-tion of axial and radial temperatures in the flame is not significantly influenced by the use of particular kinetic scheme tested in this study.

Soot Level Predictions

In contrast with the temperature prediction, significant differences among the kinetic mechanisms employed were evident in the prediction of the soot volume fraction in the atmospheric methane flame, as presented in Fig. 3. The graph on the upper left of Fig. 3 described a com-parison between the predicted axial soot volume fraction generated by different kinetic mechanisms and the ex-perimental data. With the exception to the prediction by Qin et al. mechanism [8], predicted results by all other mechanisms were significantly lower than that of ex-perimental measurements. There are at least two reasons to explain why Qin et al mechanism [8] produced soot

volume fraction predictions in better agreement with the experimental data than those of other mechanisms. First, this mechanism was able to accurately reproduce tem-perature prediction in both axial and radial profiles. The source terms which account for soot, as shown in Eq. 6 and Eq. 7, strongly depend on temperature. Therefore, if the temperature prediction is correct, it is highly likely that soot volume fraction prediction will also be correct. Second, the nucleation step in the soot model considers acetylene and benzene as the precursors for soot and Qin et al mechanism[8] contains elementary reactions repre-senting the formation and destruction of benzene which do not exist in other mechanisms of Miller – Bowman [5], GRI Mech3.0 [6] and Warnatz [7]. Since the ABF mecha-nism [4]) also includes elementary reactions of benzene, the calculated soot volume fraction by this mechanism is also far better than those of produced by mechanisms of Miller – Bowman [5], GRI Mech3.0 [6] and Warnatz [7], indicating that benzene plays a crucial role in the nuclea-tion step. As a consequence, those mechanisms which do not contain elementary reactions of benzene, such as Miller – Bowman [5], GRI Mech3.0 [6] and Warnatz [7] are

Fig.2 Radial profiles of mixture fraction and temperature (symbol-measurement; — ABF; ----- Miller-Bowman, ······· GRI Mech3.0,

−·−·− Warnatz, −··−··− Qin et al)

554 J. Therm. Sci., Vol.20, No.6, 2011

Fig.3 Axial and radial profiles of soot volume fractions (symbol-measurement; — ABF; ------Miller-Bowman, ······· GRI Mech3.0, −·−·− Warnatz, −··−··− Qin et al)

not able to reproduce predictions of better agreement with the experimental data. It is noticeably understand-able because the latter three mechanisms were prepared for methane combustion which does not require includ-ing elementary reactions of benzene.

Similar findings were also obtained in the prediction of soot volume fraction in the radial profile, as presented in the last three graphs of Fig. 2. At the axial height of 300 mm above the nozzle, the soot level in the fuel-rich region calculated by Qin et al [8] mechanism was far be-yond the experimental data. However, better predictions were later obtained for the flame heights of 350 mm and 425 mm. Meanwhile, soot level predictions by other mechanisms, with the exception to ABF mechanism [4], are far below the experimental data in all axial positions concerned. The above finding suggests that in addition to acetylene, introduction of benzene as one of the soot precursors in the nucleation step improves the soot level prediction. Consequently, kinetics mechanisms which contained elementary reactions of benzene formation and destruction generated far better soot level prediction, in closer agreement with experimental data, compared to those which do not include the benzene elementary reac-tions.

Concluding Remarks

On the basis of the results from investigating the ap-plication of five detailed combustion kinetic schemes on soot level prediction in the turbulent non-premixed flame being studied, a number of conclusions can be with-drawn:

The temperature predictions in both axial and radial profiles are not significantly influenced by particular combustion kinetic scheme employed.

The assumption that benzene as another soot precursor in the nucleation step, in addition to acetylene, improved the soot level prediction in the methane turbulent non- premixed flame.

Among five detailed combustion kinetic schemes tested in this study, the Qin et al mechanism [8] gave su-perior predictions for both temperature and soot level in the flame.

Combustion kinetic mechanisms containing elemen-tary reactions of benzene formation and destruction gen-erated better prediction in terms of soot level in the flame than those of without containing benzene elementary reactions.

Results obtained from the calculation of soot level in the flame using the CMC based soot model are heavily reliant upon the kinetic scheme used in its application, and therefore the selection of appropriate scheme plays an important role for accurate soot level prediction in a flame.

Acknowledgment

The authors wish to express their gratitude to the Di-rectorate General of Higher Education (DGHE), Ministry of National Education, Republic of Indonesia for their financial support for the work described through Over-seas and International Publication Research Scheme, Contract No: 433/SP2H/PP/DP2M/VI/2010 dated June

Y. Yunardi et al. Investigation of Kinetic Scheme Performance on Modelling of Turbulent Non-Premixed Sooting Flames 555

11, 2010.

References

[1] Ross, A.B., Junyapoon, S., Jones, J.M., Williams, A. and

Bartle, K.D., A study of different soots using pyrolysis–

GC–MS and comparison with solvent extractable mate-

rial. J. Anal. Appl. Pyrolysis. Vol. 74 (2005), pp. 494–

501.

[2] Santamaria, A., Yang, N., Eddings, E., and Mondragon, F.,

Chemical and morphological characterization of soot and

soot precursors generated in an inverse diffusion flame

with aromatic and aliphatic fuels. Combust. Flame. Vol.

157 (2010), pp. 33–42.

[3] De Iuliis, S., Chaumeix, N., Idir, M., and Paillard, C.-E.,

Scattering/extinction measurements of soot formation in

a shock tube. Exp Therm Fluid Sci.. Vol. 32 (2008), pp.

1354–136.

[4] Appel, J., Bockhorn, H. and Frenklach, M., Kinetic Mod-

eling of Soot Formation with Detailed Chemistry and

Physics: Laminar Premixed Flames of C2 Hydrocarbons.

Combust. Flame. Vol. 121 (2000), pp. 122–136.

[5] Miller, J.A. and Bowman, C.T., Mechanism and model-

ling of nitrogen chemistry in combustion. Prog Energy

Combust Sci. Vol. 15 (1989), pp. 287-338.

[6] Smith, G.P., Golden, D.M., Frenklach, M., Moriarty, N.W.,

Eiteneer, B., Goldenberg, M., Bowman, C.T., Hanson,

R.K., Song, S., Gardiner, W.C., Lissianski, V.V. and Qin,

Z., http://www.me.berkeley.edu/gri_mech/, accessed 27th

July 2010.

[7] Warnatz, J., The Mechanism of High Temperature Com-

bustion of Propane and Butane, Combust Sci Technol.

Vol. 34 (1983), pp. 177–200.

[8] Qin, Z., Lissianski, V.V.,Yang, H., Gardiner, W. C., Davis,

S. G. and Wang, H., Combustion chemistry of propane: A

case study of detailed reaction mechanism optimization.

Proc Combust Inst. Vol. 28 (2000), pp. 16631669.

[9] Wang, H., and Frenklach, M., A Detailed Kinetic Model-

ing Study of Aromatics Formation, Growth and Oxidation

in Laminar Premixed Ethylene and Acetylene. Combust.

Flame. Vol. 110 (1997), pp.173221.

[10] Girimaji, S.S., On the Modeling of Scalar Diffusion in

Isotropic Turbulence. Phys Fluids A. Vol. 4 (1992), pp.

25292537.

[11] Kee, R.J., Rupley, F.M., and Miller, J.A., CHEMKIN II:

A FORTRAN Chemical Kinetics Package for the Analy-

sis of Gas-Phase Chemical Kinetics. (1996) Sandia Na-

tional Laboratories, New Mexico, Report No. SAND89-

8009B.

[12] Leung, K.M., Lindstedt, R.P., and Jones, W.P., A simpli-

fied reaction mechanism for soot formation in non-

premixed flames. Combust. Flame. Vol. 87 (1991), pp.

289–305.

[13] Lindstedt, R.P. in: H. Bockhorn (Ed.), Soot Formation in

Combustion. (1994), p. 417. Springer-Verlag, Berlin.

[14] Yunardi, Woolley, R.M., and Fairweather, M., Condi-

tional Moment Closure Prediction of Soot Formation in

Turbulent, Non-Premixed Ethylene Flames, Combust.

Flame. Vol. 152 (2008), pp. 360–376.

[15] Brookes, S.J. and Moss, J.B., Predictions of soot and

thermal radiation properties in confined turbulent jet dif-

fusion flames. Combust. Flame. Vol. 116 (1999), pp.

486503.

[16] Spalding, D.B., GENMIX: A general computer program

for two-dimensional parabolic phenomena. (1977), Per-

gamon Press, Oxford, England.

[17] Brown, P.N., Byrne, G.D.and Hindmarsh, A.C., VODE: A

Variable-Coefficient ODE. Solver. SIAM J. Sci. Stat.

Comput. Vol. 10 (1989), pp. 10381051.

[18] Fairweather, M., Woolley, R.M. and Yunardi,. Analysis of

kinetic mechanism performance in conditional moment

closure modelling of turbulent, non-premixed methane

flames. Combust Theor. Model. Vol. 10 (2006), pp.

413438.