Fuel 153 (2015) 154–165

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Fuel

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Experimental and numerical studies of biodiesel combustionmechanisms using a laminar counterflow spray premixed flame

http://dx.doi.org/10.1016/j.fuel.2015.02.0790016-2361/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: dalviso@ing.una.py (D. Alviso).

D. Alviso a,⇑, J.C. Rolon a, P. Scouflaire b,c, N. Darabiha b,c

a Laboratorio de Mecánica y Energía, Facultad de Ingeniería, Universidad Nacional de Asunción, Campus Universitario, San Lorenzo, Paraguayb CNRS, UPR 288, Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion (EM2C), Grande Voie des Vignes, 92290 Châtenay-Malabry, Francec Ecole Centrale Paris, Grande Voie des Vignes, F-92290 Châtenay-Malabry, France

h i g h l i g h t s

�We have done experimental and numerical studies of biodiesel and methyl decanoate (MD) spray premixed flames.� OH PLIF as well as emission spectroscopy and visualization of CH� and OH� are employed experimentally.� Numerically, a new biodiesel kinetic scheme was developed by combining two existing kinetic schemes.� CH� and OH� submechanisms were added to both biodiesel and MD kinetic schemes.� The schemes were validated, as well as CH� and OH� submechanisms for both biodiesel and MD.

a r t i c l e i n f o

Article history:Received 30 July 2014Received in revised form 10 October 2014Accepted 19 February 2015Available online 10 March 2015

Keywords:BiodieselMethyl decanoateEmission spectroscopyOH PLIFKinetic modeling

a b s t r a c t

Biodiesel is a mixture of long chain fatty acids such as methyl esters and is mainly used in diesel engines.Its fundamental properties and combustion pathways still need to be analyzed and validated. The presentstudy concerns the creation and development of new data for the combustion of rapeseed methyl esterbiodiesel (RME) and methyl decanoate as a surrogate fuel (MD). Experimental and numerical studies areconducted on a laminar counterflow premixed flame configuration where spray biodiesel/air (or MD/air)is injected against methane/air mixture at atmospheric pressure for different strain rates and equivalenceratio conditions. As chemical schemes for methane/air reactions are enough well known, this configura-tion is suitable to perform validations of chemical schemes for biodiesel/air (or MD/air) combustion, bytaking methane/air flame as a reference. Planar Laser-Induced Fluorescence (PLIF) of OH as well as visibleand UV chemiluminescence measurements of the excited radicals CH�ðA2DÞ and OH�ðA2RþÞ areemployed to experimentally analyze the biodiesel and MD flame structure. The counterflow spray MDflame is simulated by choosing a skeletal reaction mechanism to which we add CH� and OH� reactions.In the case of biodiesel flame simulations, a new surrogate kinetics is developed by combining two exist-ing skeletal kinetics schemes. The new scheme guarantees not only a good prediction of measured radi-cals but also a good methane/air flame speed which is necessary to well predict the flame front position inthe counterflow configuration. CH� and OH� sub-mechanisms are also added to this kinetic scheme. Thenumerical predictions of the CH� concentration are very close to the experimental profiles along the cen-tral axis, for both biodiesel and MD kinetic schemes. However the numerical and experimental resultsshow differences in the OH� production routes between MD and methane flames.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Biodiesel is a complex mixtures of several methyl esters withdifferent chain lengths and degrees of unsaturation. Due to theirlong chain composition, the number of possible reaction pathways

in a chemical reaction scheme increases drastically. The develop-ment of such schemes is therefore very challenging and thesimulation of biodiesel combustion becomes extremely time-consuming as it requires enormous computing resources even insimple configurations such as homogenous reactors. In practice,analysis are done on surrogates or synthetic fuels with shorterchain lengths. These surrogates are structurally very similar toactual biodiesel methyl esters. Thanks to the development ofcomputer resources over last decade, the studied surrogate chain

Fig. 1. Schematic of the counterflow burner.

D. Alviso et al. / Fuel 153 (2015) 154–165 155

length and the degree of unsaturation have been increasedcontinuously.

In this sense, Seshadri et al. [1] have used the directed relationgraph (DRG) method developed by Lu and Law [2,3] to reducedetailed combustion mechanism of methyl decanate (MD)C11H22O2 [4] to a skeletal mechanism including 125 species and713 elementary reactions. The model has been validated withexperiments studying the limits of ignition and extinction of acounterflow MD/air diffusion flame.

More recently, Luo et al. [5] have developed a skeletal mechan-ism including 115 species and 460 elementary reactions to study atri-component surrogate consisting of methyl decanoate C11H22O2

(MD), methyl 9-decanoate (MD9D) C11H20O2 and n-heptane C7H16.Validations have been performed against 0-D simulations using thedetailed mechanism and experimental data for spatially homoge-neous systems, 1-D flames and 3-D turbulent combustion.

Most of biodiesel surrogate chemical schemes have beenvalidated employing either homogeneous reactors or diffusionflames [1–3]. Although spray counterflow flames have been stud-ied [6–8], to our knowledge no spray biodiesel surrogate combus-tion has yet been conducted. The main objectives of the presentwork are first to develop a counterflow flame of spray biodiesel/air (or MD/air) against methane/air mixture in order to carryexperiments, and then to use experimental results to validate bio-diesel chemical schemes by performing detailed numerical simula-tions. We have chosen this configuration in order to have anadditional requirement on the performances of the chemicalschemes studied. This latter should be able to correctly predictboth biodiesel and methane flame front structures simultaneously.This constraint is particularly interesting because it makes possibleto validate relative radical peaks in both flame fronts. In fact, che-mical schemes for methane/air reactions are enough well known.Therefore we first measure experimentally the relative profiles ofthe radicals in the biodiesel front with respect to those of themethane flame front. These relative experimental values are thenused to validate the relative radical profiles obtained numerically.

A convenient way to experimentally study the flame behavior isto analyze space and time-resolved emissions of CH� and OH�.Indeed, these two radicals are naturally present in the reactionzone and permit to determine important macroscopic propertiessuch as flame location, flame speed, and heat release rate evolu-tion. However, these radicals are generally considered as tracersbecause they have no significant effect on combustion reactionmechanisms. For this reason, CH� and OH� are very often not takeninto account in reduced chemical schemes, and comparison withexperimental data are consequently not done [9,10].

In this work we perform measurements of CH� and OH� naturalemissions as well as planar laser induced fluorescence (PLIF) of OH.We have also measured temperature profiles. Experiments havebeen conducted for several spray biodiesel and MD flames in thecounterflow configuration for different values of equivalence ratioand strain rate. By these measurements we seek to obtain data tovalidate simulated flame structures and also the production andconsumption reactions of CH� and OH� for both biodiesel and MDflames.

Simulations are performed using a one-dimensional axi-sym-metric formulation as developed by Franzelli et al. [8]. MD/methane opposed configuration is simulated employing the skele-tal kinetic scheme proposed by Seshadri et al. [1]. To carry biodie-sel flames simulations this latter scheme could not be used becauseit does not contain all the chemical components structures con-tained in the rapeseed biodiesel. We therefore employed thescheme proposed by Luo et al. [5]. Although this scheme containsall pathways for all components of the biodiesel, it could not givea good methane/air flame speed. The consequence of this was that

the flame front locations and the stagnation point were not wellpredicted. We therefore have developed and validated a new che-mical scheme by carefully combining the schemes proposed bySeshadri et al. [1] and Luo et al. [5]. We have also completed allmechanisms with CH� and OH� formation, chemiluminescenceand quenching sub mechanisms. The available literature data wererecently summarized by Panoutsos et al. [11]. Most CH� and OH�

reactions and rate constants found in literature [9,11–14] arevalidated with experiments involving light hydrocarbon flamessuch as methane, but no validation has yet been made for biodieselsurrogate. Therefore another objective of this work is to validatethese sub-mechanisms.

2. Experimental setup

2.1. Counterflow burner device

The experiments were carried out using a counterflow burner(Fig. 1). The setup will be briefly described below, further informa-tion can be found in [15,16]. The burner consists of two opposedaxisymmetric convergent nozzles of 20 mm inner diameter. Thedistance between the two nozzle exits is kept constant to 40 mmin all experiments. A premixed gaseous flow of methane and airis injected at ambient pressure and temperature through the lowerside of the burner, while a spray flow of methyl decanoate (MD) orrapeseed methyl ester (RME) conveyed by air is injected at 400 Kfrom the upper side. Each nozzle is surrounded by a coaxial nozzlewhich is fed by nitrogen in order to protect the reaction zones fromambient perturbations that could disturb the measurements.

The fuel spray is obtained by a classical liquid atomizer same asthe one used in [16] by injecting an air flow above a vertical pipeplunged in the reservoir with the liquid. The liquid is pushed updue to pressure difference and is pulverized by air. The advantageof this system is that the size distribution of the spray is particular-ly narrow [17]. The inconvenience is that we were restricted towork with small air flow rates and consequently with lean biodie-sel and MD flames.

An electrically heated pipe is used to maintain the spray flowheated between the atomizer and the burner. The upper burneras well as surrounding nitrogen are heated electrically at the sametemperature as the spray fuel flow. The whole line and the wholeupper burner are kept at 400 K. The two opposed flows form a

Fig. 2. Structures of the main components of rapeseed-derived biodiesel.

Table 2MD mass flow rates (g/h) corresponding to the nine cases studied (I–IX). Air mass flowrates _mair are given in (g/h), MD/air mixture injection velocities V in (cm/s), and strainrates � in s�1.

_mair ¼ 307 _mair ¼ 359 _mair ¼ 437V ¼ 29:5 V ¼ 34:4 V ¼ 42:2� ¼ 42:5 � ¼ 45:1 � ¼ 49:2

U ¼ 0:20 – – 8.2 (VII)U ¼ 0:22 – – 8.7 (VIII)U ¼ 0:26 7.0 (I) 8.2 (IV) 9.7 (IX)U ¼ 0:28 7.5 (II) 8.7 (V) –U ¼ 0:31 8.3 (III) 9.7 (VI) –

156 D. Alviso et al. / Fuel 153 (2015) 154–165

stagnation plane and two laminar flame fronts appear on each sideof it. The premixed methane/air flame front is formed at few mil-limeters from the lower injector exit. The hot burnt gases fromthe methane/air combustion are located between the flame frontand the stagnation plane and ensure additional heating on the bio-diesel or MD/air flame.

This counterflow of biodiesel/air (or MD/air) against methane/air is chosen in order to have an additional constraint whenvalidating chemical schemes:

� Methane/air mixture is easy to be stabilized experimentally andhas been studied extensively and for which validated kineticschemes can be found in the literature. Its flame front willtherefore serve as a reference to analyze the experimental andnumerical results.� Another advantage is that, as the biodiesel flash point is

relatively high, the methane/air opposed flame (easier toignite), through hot burnt gases, ensures additional heating onthe reactive zone. Therefore, experimentally there is no needto vaporize the liquid fuel by injecting the fluid at a hightemperature.

2.2. Biodiesel chromatography/mass spectrometry

Before starting flame studies, biodiesel fuel composition wasanalyzed with liquid chromatography and mass spectrometry(LC–MS) technique. The objective of this measurement was toobtain the chemical composition of studied biodiesel fuel. Thisinformation is needed as input to carry the simulations and to cor-rectly estimate the equivalence ratio of the biodiesel flame.

The estimation of rapeseed-derived biodiesel concentrationsand mole fractions is presented in Table 1. In comparison to the lit-erature values [4], it corresponds to the classical composition ofbiodiesel obtained from this oil. From this table, rapeseed-derivedbiodiesel formula is estimated: C18:9H33:3O2. In order to estimatethe measurement precision, the analysis was realized severaltimes. The repeatability observed in the measures for each methylester was about 98%.

The chemical structure of each methyl ester is presented inFig. 2. The structures of these components show considerable simi-larities in these chemical species, each with a methyl esterattached to a large hydrocarbon chain. Main differences are:

� the length of the hydrocarbon chain; 15 atoms of carbon formethyl palmitate and 17 for the other methyl esters,� the number of double bonds in the hydrocarbon chain; no dou-

ble bond for methyl palmitate and methyl stearate, one doublebond for methyl oleate, two for methyl linoleate and three formethyl linolenate.

2.3. MD flames conditions

We have performed experimental and numerical studies of ninedifferent combinations (A–I) of equivalence ratio (/) and strainrate (e) gathered in Table 2. The strain rates are estimated using

Table 1Composition of rapeseed-derived biodiesel.

Rapeseed biodiesel composition

Methyl ester CC (ppm) Mole fraction

Palmitate 417 4.73Stearate 157 1.78Oleate 5660 64.21Linoleate 1866 21.16Linolenate 715 8.11

the definition given by [18]. The methane flame was kept constantthroughout the study (injection temperature = 300 K, / = 0.62,methane/air flow velocity = 50 cm s�1), in all experiments.

2.4. Biodiesel flame conditions

The biodiesel flame equivalence ratio is / = 0.28. The biodiesel/air flow velocity at the injector face is 29:5 cm s�1 and the massflow rate per unit area (mass flux) is 0:029 g cm�2 s�1. The biodie-sel and air mass flow rates at the upper burner are 6.9 and 307 g/h,respectively. The injection temperature at the upper burner is400 K. The methane/air mixture (/ = 0.62) is injected at tem-perature 300 K, and velocity = 50 cm s�1.

2.5. Flow rate measurements formal errors

All gaseous mass flow rates are controlled by the mass flowmeters with an accuracy of �1:5% and a repeatability of �0:5%

of the full scale (Bronkhorst mass flowmeters). The biodiesel andMD liquid mass flows were measured with an accuracy of �10%.The overall uncertainty of strain rate, methane and biodiesel andMD flames equivalence ratios can therefore be estimated at�2:5%;�1:5% and �12%, respectively.

3. Diagnostic techniques

Several diagnostic techniques are employed to analyze theflame structure:

3.1. Emission spectroscopy

The visible and UV chemiluminescence of the excited radicals

CHðA2DÞ, denoted CH�, and OHðA2RþÞ, denoted OH�, were

Fig. 4. Axial CH� emission profiles of the averaged and Abel inverted datanormalized with the peak values, from MD Flame VII.

D. Alviso et al. / Fuel 153 (2015) 154–165 157

measured by Optical Emission Spectroscopy (OES). The objective ofthese measurements is to determine the relative CH� and OH�

emissions of biodiesel and MD flames with respect to those ofthe methane flame.

Two UV lenses with focal lengths of 500 mm were used to focusthe global light emitted by the flame into the entrance slit of aspectrometer (Acton Research, Model SpectraPro 2750).Measurements were conducted using spheric mirrors with focallength of 750 mm and with a diffraction grating of 1200 grating/mm. The emission spectra along the burner axis was recorded bya 1024� 256 pixels Intensified CCD camera (Roper Scientific,Inc.). A subtraction of the ambient background and CO2 was done.

As the biodiesel and MD flames are very lean, the emission isvery low, then a compensation on the slit opening was made,always taking care of having a reasonable spectral resolution.Therefore, for CH� and OH�, slit widths of respectively 500 lmand 750 lm were chosen, giving respectively a spectral resolutionof 0.27 and 0.3 nm. The exposure time was kept constant to100 ms. The CH� population was obtained by making an integra-tion between 420 and 440 nm wavelengths, while the OH� popula-tion was acquired between 300 and 320 nm wavelengths.

For the CH� and OH� population in both flames, an average over50 images was made. The uncertainty of the measurement wasestimated from the CH� and OH� maximum population in the 50images, in comparison to the average values. For the methaneflame it was �20% and for biodiesel and MD flames it was �25%.

3.2. Direct visualization

Direct view images of CH� and OH� emission have been record-ed using a 512� 512 pixels ICCD camera (Princeton Instruments)equipped with UV-lens (Nikkor 105 mm focal length). Narrow-band interference filters were interposed along the optical pathfor capturing the CH� and OH� emission. The filter used for CH�

has 60% transmission and a 10-nm wide bandpass centered around430 nm. The OH� filter is centered at 313 nm, 10-nm bandpass and68% transmission in the maximum. As these results are comple-mentary to the spectroscopy measurements, the exposure timewas fixed to 100 ms and an average over 50 images was made.

Fig. 3A presents a typical MD flame front obtained from CH�

visualization. This figure shows that the flame front is slightlyconvex. The line of sight creates an integrated signal along its tra-jectory and increases the measured emission. As the flame front isaxi-symmetrical, Abel inversion is used to eliminate the effects ofthe integration and get the trace of the flame front in the symmetryplane of the burner as done in [9,10] (Figs. 3B, 4). It should be notedthat the Abel inversion has shifted slightly the location of the max-imum CH� emission intensity.

Fig. 3. Averaged (A) and Abel inverted (B) image of CH� emission from MD FlameVII.

The resolution of the CCD camera and the depth of field (aboutthe flame length) limit the accuracy of the vertical positioningalong the flame axis to �0:2 mm. Then, due to the slight flamesoscillation, the flame position was estimated with an accuracy of�0:5 mm.

3.3. OH PLIF

Fig. 5 presents the experimental optical setup used to realizeOH PLIF measurements. The laser sheet dimension was about30� 0:5 mm2, and it was transported directly to the jet axis andwas positioned in the flame zone. The OH radical is excited witha dye laser CONTINUUM ðRhodamine 590Þ pumped by a Nd:YAGlaser CONTINUUM doubled ð800 mJ @ 532 nmÞ. The Q 1ð6Þ OH

transition of the Q 00 ¼ 0; Q 0 ¼ 1 band of the ðA2R;X2PÞ systemwas excited at 283.043 nm with an energy of about 18 mJ.

The fluorescence images were collected on the same cameraused for the direct visualization (512� 512 pixels ICCD). In thiscase, the camera gate was kept constant to 20 ns. This allows theCCD to drastically reduce the chemiluminescence signals.Furthermore, the same filter used for the OH� visualization waschosen to collect the OH fluorescence signal.

Measurements have been performed in linear regime of fluores-cence. For this reason, an estimation of the laser sheet energywas carried out by directing the laser beam to a quartz cell, filledwith dodecane, and then visualizing the fluorescence signal withthe same ICCD camera. The images were then divided by the

Fig. 5. PLIF optical setup.

Fig. 6. Counterflow premixed flames configuration.

158 D. Alviso et al. / Fuel 153 (2015) 154–165

recorded laser intensity profiles to compensate for the laser profilefluctuations.

The OH profiles were corrected with the laser sheet energy pro-file on a single shot basis. An average over 100 OH PLIF images wasdone, taking into account the slight flames oscillation. As the LIFimages were not corrected for quenching, the thermal distributionamong energy levels, and saturation effects, the color scale in theresulting images represents pure fluorescence intensity, and doesnot directly correspond to OH mole fraction. Nevertheless, it wasshown that quenching effects on the OH PLIF signals are constantalong a counterflow flame [19]. For this reason, it may be consid-ered that the OH LIF signals in our experiments are within acalibration constant linearly proportional to the OH radicalpopulation.

The spatial resolution obtained by the optical arrangementswas 120 lm. In order to extract the OH axial profiles along thejet axis, at each axial position the OH intensity values are summedup over the central part of each horizontal line (100 pixels or12 mm). Results will be represented as a function of the axialposition.

3.4. Temperature measurements

We have determined the temperature along the jet axis with acommercial thermocouple Pt–30%Rh/Pt–6%Rh type B of 200 lm ofwire diameter (Omega P30R-008) for MD Flames VII, VIII, and IXonly. This thermocouple temperature range is 600–2100 K.

The temperature profiles were obtained by taking intoaccount the perturbations produced by the thermocouple.Indeed, the flame attachment to the thermocouple can be mini-mized by carefully introducing the thermocouple in the flame.However, there was an attachment of the methane flame frontdue to flame stabilization much like that on a bunsen flame.Therefore this part of the profiles is not very accurate, howeverthe rest is still comparable with the numerical results. The mea-sured temperatures were corrected for radiative heat losses[20].

The measured temperature signal fluctuates and the maximumoscillation amplitude is �5 K in fresh gases, and �60 K close to thecombustion zones. We have made the temperature profile mea-surements in the burner axial direction, using steps of 100 lm inthe flame front.

Fig. 7. Structures of biodiesel surrogates.

4. Numerical approach

4.1. Governing equations

We consider an axisymmetric counterflow configuration shownin Fig. 6. A methane–air mixture is injected from the right sidewhereas mono-disperse spray biodiesel or MD fuel conveyed byair is injected from the left side. We model our system by consid-ering detailed chemistry and mixture-averaged transport model,same as the one developed by Kee et al. [21]. Thermodynamicand transport data used for calculations are those provided alongwith the kinetic schemes [1,5]. To solve balance equations, weemploy similarity approach by searching for similar solutions ofboth gaseous and spray flow equations in the vicinity of the centralaxis [6]. These similar solutions have the form: gas densityqg ¼ qgðzÞ, gas radial velocity ug ¼ r UgðzÞ, gas axial velocityvg ¼ vgðzÞ, gas temperature Tg ¼ TgðzÞ, species mass fractionsYk ¼ YkðzÞ; k ¼ 1; . . . ;Nsp (Nsp is the number of species), dropletradius Rl ¼ RlðzÞ, droplet number density nl ¼ nlðzÞ, spray radialvelocity ul ¼ r UlðzÞ, spray axial velocity v l ¼ v lðzÞ, and droplettemperature Tl ¼ TlðzÞ, where the superscript g represents gaseousphase and the superscript l the liquid phase. For more details on

governing equations one may refer to the recent work ofFranzelli et al. [8].

4.2. Biodiesel kinetic modeling

As it can be seen in Section 2.2, biodiesel is a complex mixtureof methyl esters with different chain lengths and degrees ofunsaturation. In order to avoid these difficulties, simplified syn-thetic fuels, called ‘‘surrogate fuels’’, with shorter chain lengthsare chosen to carry numerical combustion studies.

In this sense, Seshadri et al. [1] used the directed relation graph(DRG) method proposed by Lu and Law [2,3] to reduce methyldecanoate C11H22O2 (MD) detailed mechanism due to Herbinetet al. [4] to a skeletal mechanism consisting of 125 species and713 elementary reactions. The chemical structure of methyl decan-oate MD is presented in Fig. 7A.

More recently, Luo et al. [5] developed a skeletal mechanismwith 115 species and 460 reactions for a tri-component biodieselsurrogate, which consists of methyl decanoate (MD), methyl 9-de-cenoate C11H20O2 (MD9D) and n-heptane C7H16 (chemical struc-tures presented in Fig. 7). Methyl-9-decenoate was chosenbecause the double bond is at the same position as the one inmethyl oleate and at the same location as the first double bondin methyl linoleate and in methyl linolenate (Fig. 2).

In the present work, the simultaneous presence of two differentfuels (biodiesel and methane) is an additional requirement so thatthe chemical scheme should be able to predict both flame frontschemical structures. In fact the chemical scheme should be ableto predict the radical profiles and the position of the flame front.In a counterflow configuration, the flame front is positioned at a

Fig. 8. Methane/air laminar flame speed simulated by different chemical schemes. Fig. 9. MD/air laminar flame speed simulated by different chemical schemes.

D. Alviso et al. / Fuel 153 (2015) 154–165 159

point where the flame speed is equal to the local flow speed.Therefore, we have first used the skeletal kinetic schemes proposedby Seshadri et al. [1] and Luo et al. [5] to simulate 1-D freely-propagating premixed methane/air flames using REGATH package[22]. The corresponding flame structures and flame speeds arecompared to those obtained using the GRI 3.0 methane/air kineticscheme [23] and the experimental results due to Dirrenberger et al.[24] and Vagelopoulos et al. [25]. The comparison (Fig. 8) showedthat results obtained by the skeletal kinetic scheme due to [1] arevery close to those obtained by using the GRI 3.0 scheme andexperiments. But the methane/air flame speed obtained using thescheme due to [5] is far from experiments and the one obtainedby using the GRI 3.0 scheme.

The skeletal mechanism due to [5] includes methyl9-decenoate, a biodiesel surrogate with one double bond. And asrapeseed-derived biodiesel studied in this work is mainly com-posed of unsaturated methyl esters (Table 1), i.e methyl esters withone or more double bonds. In order to obtain the good methane/airflame speed we combined the skeletal kinetic schemes due to [1,5].Therefore, the resulting kinetic model proposed here is designedfrom the original oxidation framework of methyl decanoate pro-posed by [1]. This latter chemical scheme is used as a starting basemodel. Then additional species found in kinetic scheme of [5] andthe corresponding reactions are added. This guarantees reproduc-ing the principal features of the methyl decenoate/air combustioncharacteristics. Thus, the new combined scheme, with 185 speciesand 911 elementary reactions, has the advantages of both schemes.As it can be seen on Fig. 8, the new scheme predicts correctly themethane/air flame speed as does the scheme due to [1]. It alsoallows to carry simulations of the unsaturated methyl ester:methyl 9-decenoate. We have also performed 1-D freely-propagat-ing premixed methyl decanoate/air flames using both the newscheme and that of Luo et al. [5]. The flame speeds have been com-pared to the experimental and simulation results available inWang et al. [26]. As we can see in Fig. 9, the results obtained usingthe new model are very close to the experimental results forequivalence ratios lower than 0.9. However they are very close tothose obtained by model VI [1] for all equivalence ratios. On theother hand, we can see that the agreement of the results obtainedusing the scheme due to Luo et al. [5] is poor for lean MD/air flamesbut very good for rich MD/air flames.

Finally, methyl palmitate and stearate (without double bonds)will be represented by MD. And methyl oleate, linoleate and linole-nate (with one or more double bonds) will be represented byMD9D. As the studied rapeseed-derived biodiesel formula is

C18:9H33:3O2 (Section 2.2), and the developed model consists of spe-cies MD ðC11H22O2Þ and MD9D ðC11H20O2Þ, in order to keep con-stant the number of carbon atoms, a factor of 18.9/11 was takeninto account.

4.3. CH� and OH� chemical reactions

The literature data for different kinetics of formation, quenchingand chemiluminescence of CH� and OH� in flames were recentlysummarized by Panoutsos et al. [11], where the authors have given6 sub-mechanisms that account for the formation and destructionof the species CH� and OH�. We have included these sub-mechan-isms in the chosen fuel/air combustion mechanisms. The thermo-chemical data for CH� and OH� are added as well. The transportcoefficients for the excited species are the same as those of theground state species. We have evaluated corresponding resultsby comparing them against our experimental data. The 6 sub-mechanisms give the same order of magnitude in the concentra-tion of these species, and the ones with the best agreement forCH� and OH� were selected. These points will be developed indetails in Section 5.6 and 5.9.

It should be noted that, as expected, due to the low mole frac-tions of the excited species, no significant differences in the flamefronts positions were found with the addition of these sub-mechanisms.

4.4. Simulation conditions

The simulations for the counterflow spray flame were per-formed using the Spray–Counterflow code of the REGATH packagewith detailed thermochemical and transport properties developedat EM2C laboratory [22]. To carry methyl decanoate simulations,the skeletal mechanism due to [1] including 125 species and 713reactions was chosen. The upper stream (spray/air) is kept at aninitial temperature of 400 K and the lower stream (methane/air)is at 300 K. The droplet velocity matches the gas velocity at theinjector exit. The initial droplet diameter is D0

l = 30 lm and thedroplet number density is nl = 820 droplets per cm3. The liquidmethyl decanoate properties used for the simulations are: specificmass qq ¼ 871 kg=m3, latent heat of evaporation L ¼ 289:9 kJ=kg,boiling temperature Tboil ¼ 497 K and the constant pressure heatcapacity cpl ¼ 2:05 kJ=ðkg KÞ [27,28]. The pressure is equal to oneatmosphere.

To carry biodiesel flames simulations, the kinetic scheme devel-oped in this work and detailed in Section 4.2, with 185 species and

160 D. Alviso et al. / Fuel 153 (2015) 154–165

911 elementary reactions, was used. As it will be shown inSection 5.2, the preheated two-phase flow of spray fuel and aircompletely vaporizes before reaching the flame front, and conse-quently studied spray flames can be considered as entirely gas-eous. Therefore, for biodiesel flames simulation, only gaseousequations are taken into account, and all liquid equations andsource terms are neglected.

5. Results and discussions

5.1. Typical flame structure

Fig. 10 presents a typical spray MD flame structure. The bound-ary conditions correspond to the flame I (see Table 2). In this figurez ¼ 0 corresponds to the upper burner edge and z ¼ 40 to the lowerburner edge. The premixed methane/air flame front is located atabout z ¼ 20:2 mm. At this point, the gas temperature increasesvery rapidly from 300 K to 1600 K within 1 mm. The CH� mole frac-tion profile at this point has a local maximum of 1.5E�12 (seeFig. 15 for the scale) and its width at half maximum is 0.2 mm.The stagnation point (axial velocity V ¼ 0) is located atz ¼ 12:3 mm.

The initial droplet diameter is 30 lm. The droplets are conveyedby a gaseous MD/air mixture. The global equivalence ratio of theliquid/gaseous MD/air mixture is 0.26. In Fig. 10 (left) we can seethat the droplet diameter decreases progressively between z ¼ 0and z ¼ 7 mm and then vanishes very rapidly at z ¼ 8 mm.

Fig. 10. Spray MD Flame I: Drop

Fig. 11. Spray MD Flame I: Drop

Consequently in Fig. 10 (right) the MD mass fraction increasesfrom its initial value 1.03E�02 to a maximum of 2.13E�02 dueto droplet evaporation and then diminishes very rapidly atz ¼ 11 mm due to thermal dissociation. The droplet number densi-ty increases progressively from 8.2E+08 to 8.5E+08 droplets per m3

due to the decrease of the flow velocity and then diminishes veryrapidly at z ¼ 8 mm. The MD flame front is located at z ¼ 11:8 mm.

Due to the small value of equivalence ratio of the MD/air flame,the corresponding flame speed is too small (about 5 cm s�1), that iswhy the MD flame front is very close to the stagnation point. Thetemperature variation at the MD side is essentially due to heat dif-fusion across the stagnation point. The heat released by the MDflame front has small influence at this region. The CH� mole frac-tion profile at this point has a local maximum of 2.53E�13 andits width at half maximum is 0.5 mm (see also Fig. 15 (left)).

The ratio between the maximum CH� mole fraction (respective-ly OH�) at the MD flame front to the maximum CH� mole fraction(respectively OH�) at the methane flame front will be called RCH�

(respectively ROH� ). These ratios will be used to analyze the CH�

and OH� sub-mechanisms in Section 5.6. The ratio RCH� for MDflame I is 0.17.

5.2. Influence of droplet diameter

For the solution with a 10 lm diameter (Fig. 11), we can seethat MD droplets are evaporated almost immediately right afterthe upper injector. The diameter decreases from 10 to 0 lm in only

lets diameter D0l ¼ 30 lm.

lets diameter D0l ¼ 10 lm.

Fig. 13. Comparison between the experimental and numerical OH profile of MDFlame I.

D. Alviso et al. / Fuel 153 (2015) 154–165 161

1 mm. The MD mass fraction increases in this zone from its initialvalue 1.03E�02 and it rapidly reaches the maximum plateau value2.13E�02. It finally decomposes when the gas temperatureincreases in the reaction zone at 11.8 mm from the upper edgeburner.

For the solution with a 30 lm droplet diameter (Fig. 10 left), theevaporation front is located at about 8 mm from the upper injectorand it is about 4 mm from the MD flame front. The solution with a30 lm diameter takes more time to completely evaporate the dro-plets, the gas temperature decreases slightly in this zone because apart of energy is transferred from the gas to the droplets. The MDmass fraction has the same evolution as the 10 lm solution and thereaction zone is also at 11.8 mm from the edge burner. Therefore,in both cases the droplets do not reach the high temperature reac-tion zone. As it has been shown, for this type of atomizer, the dro-plet diameter is less than 30 lm [16], then studied spray MDflames can be considered as entirely gaseous even for diameterup to 30 lm.

5.3. Gaseous and two-phase simulations comparison

Fig. 12 gives a comparison between a gaseous and a two-phase(30 lm droplets diameter) simulation for MD Flame I. The MDmass fraction in the gaseous simulation has a constant value of2.13E�02 up to 9 mm far from the upper injector, while asexplained before in the two-phase simulation, it increases from1.03E�02 to 2.13E�02 due to droplet evaporation. It reaches a pla-teau, and then, they both decrease very rapidly at 11 mm from theupper injector, about 0.8 mm before the MD flame front. It can alsobe noted that there is a very small difference between the tem-perature profiles. In fact in the two-phase simulation, in the zonebetween the upper burner and the MD Flame front, the tem-perature slightly decreases due to the heat transfer to the droplets.This small difference does not introduce any significant differencein the location of high temperature gradient.

5.4. Experimental and numerical profiles of OH radical

Fig. 13 gives a comparison between numerical and experimen-tal profiles of the OH radical obtained by PLIF the MD Flame I. TheOH measurements are only qualitative, therefore the experimentalprofiles were normalized by the maximum values of this radical,corresponding to the methane/air flame.

The position of the increase in the OH mole fraction due to theMD and methane flames are well predicted by the simulation.Furthermore, the relative OH mole fraction of the MD/air flameROH, compared to that of methane/air flame is well predicted by

Fig. 12. Gas and two-phase simulation of MD Flame I.

the simulation. However, OH is underestimated by the simulationin the hot zone between the two flame fronts.

5.5. Experimental and numerical profiles of temperature

Fig. 14 gives a comparison between experimental and numeri-cal profiles of the temperature for the MD Flame VII. The predictionof the temperature profile is very close to the one measuredexperimentally. A difference of about 60 K is observed for the max-imum temperature which is in the range of the precision of themeasurements. At the right hand side of the methane/air flamefront there is a large discrepancy between the results due tomethane/aire flame stabilization on the thermocouple as explainedin Section 3.4. We should note that following the thermocouplemanufacturer, due to low precision of type B thermocouple, thetemperatures lower than 600 K are not valid and are not reported.

In order to estimate the temperature near both nozzle exits atype K thermocouple was used. The temperature measured withthis thermocouple near the upper burner was 450 K (50 K increasedue to heating effects), and near the lower burner 290 K. These arethe temperature values used during simulations.

5.6. Experimental and numerical profiles of CH� and OH� radicals

Fig. 15 gives a comparison between experimental and numeri-cal mole fraction profiles of CH� (left) and OH� (right) radicals for

Fig. 14. Comparison between the experimental and numerical temperature profilesof MD Flame VII.

Fig. 15. Comparison between experimental and numerical profiles of CH� (left) and OH� (right) radicals for MD Flame I. The experimental profiles are normalized.

162 D. Alviso et al. / Fuel 153 (2015) 154–165

the MD Flame I. As the measurements do not give absolute values,in order to make comparisons with the numerical results, theexperimental profiles of CH� and OH� emissions were normalizedby their maximum values corresponding to the methane/air flamefront. Also we present the curves of OH� in logarithmic scale,because the maximum peak mole fraction of MD/air flames is con-siderably lower than that of the methane/air flame. As we can seein this figure, the numerical predictions of CH� and OH� mole frac-tions are very similar to the experimental profiles along the axis.The positions of the peaks match almost perfectly. The experimen-tal profiles are slightly thicker than the simulated ones, howeverthis can be explained by the poorer spatial resolution in theexperiments.

We have studied the 6 sub-mechanisms discussed in [11]describing the production, quenching and chemiluminescence ofCH� and OH� (Section 4.3). The results obtained conducted us tofirst focus on the sub-mechanisms proposed by Elsamra et al.[12], and Smith et al. [13] (see Appendix A). We should note that,concerning quenching and chemiluminescence of CH� and OH�,both sub-mechanisms have the same elementary reactions andcorresponding rate constants. The main difference between thetwo sub-mechanisms concerns the formation reactions of CH�

(R2) and OH� (R4) (see Table 3).Elsamra et al. [12] have studied the temperature dependence of

reaction (R2) using pulsed laser photolysis techniques. Their sub-mechanism gives the best prediction of RCH� ratio, which is equalto 0.17 in the case of the MD Flame I compared to the experimentalvalue Rexp

CH� ¼ 0:14. But the value of ROH� obtained by this sub-mechanism is equal to 0.0007, which is too small compared tothe experimental value Rexp

OH� ¼ 0:01.Smith et al. [13] proposed a rate constant for OH� formation by

measuring absolute concentrations of OH� in a flat premixed low-

Table 3CH� and OH� formation reactions.

# Reactions Elsamra et al. [12]

A n

R1 C2Hþ O() COþ CH� 6:02� 1012 0

R2 C2Hþ O2 ) CO2 þ CH� 6:02� 10�04 4.4

R3 CHþ O2 () COþ OH� 6:0� 1010 0

R4 Oþ HþM() OH� þM – –

Reaction rate coefficients given in the form k ¼ ATnexpð�E=RTÞ. Units are mol cm cal s.

pressure methane–air flame. By employing this sub-mechanismwe obtained RCH� ¼ 0:25 which is far from Rexp

CH� ¼ 0:14, butROH� ¼ 0:0022 is closer to Rexp

OH� ¼ 0:01.We therefore have used the sub-mechanism of Elsamra et al.

[12] by replacing rate constants of the OH� reactions (R3) and(R4) by those of Smith et al. [13]. In this case, the maximum CH�

mole fractions at MD and methane flame fronts are doubled, how-ever the ratio remains unchanged, RCH� ¼ 0:17. Considering thevery small mole fractions of the measured species (2.53E�13 and1.5E�12 for MD and methane flames, respectively) and the uncer-tainties in the chemical excitation modeling, the predictions qual-ity with the skeletal MD kinetic model is very good. Also, themaximum OH� mole fraction at the methane flame front remainsunchanged, 9.52E�12, but the ratio ROH� is decreased to 0.0014.This decrease of ROH� is in fact due to a competition between CH�

and OH� formation reactions.The agreement is notable when comparing RCH� and Rexp

CH� , con-sidering that the production of CH� is inherently sensitive to thepredicted mole fraction of species C2H through reactions (R1)and (R2) (see Table 2), which are responsible for about 5% and95% respectively of the CH� formation in MD flames. Therefore,reaction (R2) clearly dominates reaction (R1) under these condi-tions of equivalence ratio and strain rate. Then, as it was men-tioned before, it must be noted that there is a competitionbetween CH� and OH� formation reactions which gives still moreuncertainty to the CH� chemical excitation modeling.

In reaction (R3) it is shown that the formation of OH� is inher-ently sensitive to the predicted mole fraction of species CH.Therefore, the relative CH mole fraction at MD flame front withrespect to that of methane flame front is only 0.1%, which is dueto the very small production of the precursors of CH in MD flames.This might be the reason of the underestimation of the OH� mole

Smith et al. [13]

E A n E

457 6:2� 1012 0 0

�2285 4:1� 1013 0 4500

0 6:0� 1010 0 0

– 3:63� 1013 0 0

D. Alviso et al. / Fuel 153 (2015) 154–165 163

fraction. By contrast, in the combustion of n-alkane fuels, the CHprecursors are produced in large quantities. This reaction accountshowever for about 33% of the OH� formation in MD Flame I.

Another chemical reaction leading to the formation of OH� radi-cal is the one presented in reaction (R4), which accounts for about57% of the OH� formation in MD Flame I. The remainder 10% comesfrom reverse quenching Reaction OH� þM�OHþM, where OH�

radical is formed by thermal excitation within the flame.However, there might be other reactions that could be very impor-tant in the OH� formation path in MD Flames, and that would be inpart responsible for the considerable difference between thenumerical and experimental results (even if the absolute valuesare very small).

5.7. Influence of strain rate e

Experimental and numerical CH� mole fraction profiles of MDflames I, IV and IX (constant /) are presented in Fig. 15 left,Fig. 16 left, and Fig. 16 right respectively. Strain Rate e increasesby increasing the MD/air mixture injection velocity whilemethane/air velocity remains constant (see Table 1). The MD flamefront in all cases is very close to the stagnation plane, because ofthe very low flame velocity due to its very low equivalence ratio.The numerical positions of the flame fronts are coherent with theexperimental results. In this situation by increasing e the methane

Fig. 16. Comparison of the CH� experimental and numerical profiles for different straiexperimental profiles are normalized.

Fig. 17. Comparison of the CH� experimental and numerical profiles for different equivaleexperimental profiles are normalized.

flame front is slightly displaced towards the lower burner and thedistance between simulation peak and experimental peak slightlyincreases. But as the MD flame front is very close to the stagnationpoint, species maximum values are slightly modified by strain rate.The ratio RCH� is well predicted in all cases.

5.8. Influence of equivalence ratio /

Experimental and numerical CH� mole fraction profiles of MDflames IV, V and VI (constant e) are presented in Fig. 16 left,Fig. 17 left, and Fig. 17 right, respectively. The MD and methaneflames position are very well predicted for all cases. As the MDequivalence ratio does not vary much, the MD flames position doesnot either. The ratio RCH� is well predicted in all cases.

5.9. Biodiesel flame: Experimental and numerical profiles of CH� andOH� radicals

Fig. 18 gives a comparison between experimental and numeri-cal mole fraction profiles of CH� (left) and OH� (right) radicals forbiodiesel/air flame. The experimental values of Rexp

CH� and RexpOH� are

0.1091 and 0.0076, respectively. Simulations are performed usingthe new skeletal kinetic model presented in Section 4.2. Amongthe 6 studied sub-mechanisms [11], the one suggested by Smithet al. [13] gives the best prediction of RCH� and ROH� ratios, which

n rates: MD Flame IV (/ ¼ 0:26; e ¼ 45:1 s�1) and IX (/ ¼ 0:26; e ¼ 49:2 s�1). The

nce ratios: MD Flame V (/ ¼ 0:28; e ¼ 45:1 s�1) and VI (/ ¼ 0:31; e ¼ 45:1 s�1). The

Fig. 18. Comparison between experimental and numerical profiles of CH� (left) and OH� (right) radicals for biodiesel flame.

Table 4OH� and CH� formation, chemiluminescence and quenching reactions of Smith et al.Reaction rate coefficients given in the form k ¼ ATnexpð�E=RTÞ. Units are mol cm cal s.

# Reactions A n E

R1 CHþ O2 () COþ OH� 6:0� 1010 0 0

R2 OþHþM() OH� þM 3:63� 1013 0 0

R3 OH� ) OHþ hm 1:45� 106 0 0

R4 OH� þN2 () OHþ N2 1:08� 1011 0.5 �1238

R5 OH� þ O2 () OHþ O2 2:10� 1012 0.5 �482

R6 OH� þH2O() OHþ H2O 5:92� 1012 0.5 �861

R7 OH� þH2 () OHþ H2 2:95� 1012 0.5 �444

R8 OH� þ CO2 () OHþ CO2 2:75� 1012 0.5 �968

R9 OH� þ CO() OHþ CO 3:23� 1012 0.5 �787

R10 OH� þ CH4 () OHþ CH4 3:36� 1012 0.5 �635

R11 C2 þ OH() COþ CH� 1:11� 1013 0 0

R12 C2Hþ O() COþ CH� 6:20� 1012 0 457

R13 C2Hþ O2 ) CO2 þ CH� 4:10� 1013 0 4500

R14 CþHþM() CH� þM 3:63� 1013 0 0

R15 CH� ) CHþ hm 1:85� 106 0 0

R16 CH� þ N2 () CHþ N2 3:03� 102 3.4 �381

R17 CH� þ O2 () CHþ O2 2:48� 106 2.14 �1720

R18 CH� þ H2O() CHþH2O 5:3� 1013 0 0

R19 CH� þ H2 () CHþH2 1:47� 1014 0 1361

R20 CH� þ CO2 () CHþ CO2 0.241 4.3 �1694R21 CH� þ CO() CHþ CO 2:44� 1012 0.5 0

R22 CH� þ CH4 () CHþ CH4 1:73� 1013 0 167

R23 C2 þH2 () C2HþH 4� 105 2.4 1000

R24 CHþ CH() C2 þH2 5� 1012 0 0

R25 Cþ CþM() C2 þ M 3� 1014 0 �1000

R26 Cþ CH() C2 þ H 5� 1013 0 0

R27 Oþ C2 () Cþ CO 5� 1013 0 0

R28 C2 þ O2 () COþ CO 9� 1012 0 980

Table 5OH� and CH� formation, chemiluminescence and quenching reactions of Elsamra et al.Reaction rate coefficients given in the form k ¼ ATnexpð�E=RTÞ. Units aremol cm cal s.

# Reactions A n E

R1 CHþ O2 () COþ OH� 4:82� 1010 0 167

R2 OH� ) OHþ hm 1:45� 106 0 0

R3 OH� þ N2 () OHþN2 1:08� 1011 0.5 �1238

R4 OH� þ O2 () OHþ O2 2:10� 1012 0.5 �482

R5 OH� þ H2O() OHþH2O 5:92� 1012 0.5 �861

R6 OH� þ H2 () OHþH2 2:95� 1012 0.5 �444

R7 OH� þ CO2 () OHþ CO2 2:75� 1012 0.5 �968

R8 OH� þ CO() OHþ CO 3:23� 1012 0.5 �787

R9 OH� þ CH4 () OHþ CH4 3:36� 1012 0.5 �635

R10 C2Hþ O() COþ CH� 6:02� 1012 0 457

R11 C2Hþ O2 ) CO2 þ CH� 6:02� 10�04 4.4 �2285

R12 CH� ) CHþ hm 1:85� 106 0 0

R13 CH� þ N2 () CHþ N2 3:03� 102 3.4 �381

R14 CH� þ O2 () CHþ O2 2:48� 106 2.14 �1720

R15 CH� þ H2O() CHþ H2O 5:3� 1013 0 0

R16 CH� þ H2 () CHþ H2 1:47� 1014 0 1361

R17 CH� þ CO2 () CHþ CO2 0.241 4.3 �1694R18 CH� þ CO() CHþ CO 2:44� 1012 0.5 0

R19 CH� þ CH4 () CHþ CH4 1:73� 1013 0 167

164 D. Alviso et al. / Fuel 153 (2015) 154–165

are equal to 0.1987 and 0.0062, respectively, to be compared to theexperimental values Rexp

CH� ¼ 0:1091 and RexpOH� ¼ 0:0076.

As we can see in Fig. 18, the numerical predictions of CH� andOH� mole fractions are very close to the experimental profilesalong the axis. The positions of the biodiesel and methane flamepeaks match almost perfectly. The experimental profiles are slight-ly thicker than the simulated ones, however this can be explainedby the poorer spatial resolution in the experiments. Consideringthe very small mole fractions of the measured species (1.23E�13and 1.40E�13 for biodiesel CH� and OH� mole fraction,

respectively) and the uncertainties in the chemical excitation mod-eling, the predictions quality with the skeletal biodiesel surrogatekinetic model is very good. The agreement is good when compar-ing RCH� and Rexp

CH� as well as ROH� and RexpOH� . The production of CH�

is inherently sensitive to the predicted mole fraction of speciesC2H;C and H through reactions (R1) and (R2) (see Table 3). Theproduction of OH� is inherently sensitive to the predicted molefraction of species CH, O and H through reactions (R3) and (R4).

6. Conclusions

This work presents experimental and numerical studies ofmethyl decanoate and biodiesel combustion. We have studiedCH� and OH� emission profiles, as well as temperature and OH spe-cies profiles. The first step of this work was to design a setup thatpermits to study the behavior of such flames. For that purpose, acounterflow configuration was chosen where a lean premixedmethane/air mixture is injected from the lower part of the burner

D. Alviso et al. / Fuel 153 (2015) 154–165 165

and a spray biodiesel/air (or MD/air) mixture is injected from theupper burner. Measurements of CH� and OH� emissions, OH PLIFand temperature profiles have been performed for several biodie-sel and MD equivalence ratio and strain rate conditions.

A convenient way to experimentally study the flame behavior isto analyze space and time resolved emission of CH� and OH�. Thechemical scheme should be able to correctly represent these spe-cies but also their peak position at the flame. This latter is con-trolled by the flame speed because the flame front is located at apoint where its speed is equal to that of the flow. In this work, tocarry MD flame simulations, MD kinetic scheme consisting of125 species and 713 elementary reactions due to [1] was chosen.To carry biodiesel and MD flame simulations reproducing goodflame speeds, a new biodiesel surrogate model was developed bycombining the skeletal kinetic schemes due [1,5]. The kinetic mod-el proposed here is designed from the original oxidation frame-work of methyl decanoate proposed by [1]. This chemical schemewas used as a template, and then additional species found in [5]kinetic scheme and the corresponding reactions were added. Thecombined scheme predicts correctly the methane/air combustionand flame speed and also it allows to carry simulations of aunsaturated methyl ester: methyl 9-decenoate. The developedkinetic model consists of 185 species and 911 reactions. As CH�

and OH� are not taken into account in the original schemes, severalsub-mechanisms from [11] were added to the developed biodieseland chosen MD kinetic schemes.

By comparing experimental and numerical OH and temperatureprofiles, we have validated the global flame structure simulatedwith the chosen mechanism. For MD flames, concerning the CH�

profile comparison, the predictions quality with the skeletal MDkinetic model is very good. In particular, the relative value of thelocal maximum CH� mole fraction at the MD flame front withrespect to that of methane flame front (RCH� ) is very well predicted.

Considering the OH� profile comparison, the relative maximumOH� mole fraction (ROH� ) is not very well predicted. A competitionexists between OH� and CH� formation reactions for these MDflames conditions of strain rate and equivalence ratio. Reaction(R3) shows that the formation of OH� is inherently sensitive tothe predicted mole fraction of species CH. Therefore, the relativeCH mole fraction at MD flame front with respect to that of methaneflame front is only 0.1%, which is due to the very little productionof the precursors of CH in MD flames. This might be the reason ofthe underestimation of the OH� mole fraction. By contrast, in thecombustion of n-alkane fuels, the CH precursors are produced inlarge quantities. Reaction (R4) is also important in the OH� forma-tion in MD flames, while the remainder percentage comes fromreverse quenching Reaction OH� þM�OHþM. However, theremight be other reactions that could be very important in the OH�

formation path in MD flames, and that would be in part responsiblefor the considerable difference between the numerical andexperimental results.

For biodiesel, concerning the CH� and OH� experimental andnumerical results comparison, the predictions quality with theproposed skeletal biodiesel kinetic model is very good. In par-ticular, the relative values of the local maximum CH� and OH� con-centrations at the biodiesel flame front with respect to that ofmethane flame front (RCH� and ROH� ) are very well predicted.

Acknowledgement

This research was supported by Itaipu Binacional (Paraguay),Laboratorio de Mecánica y Energía – Facultad de Ingeniería,

Universidad Nacional de Asunción and EM2C laboratory, UPRCNRS 288, Ecole Centrale Paris (France).

Appendix A

Tables 4 and 5.

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