* Corresponding Author: alexander.konnov@forbrf.lth.se

Proceedings of the European Combustion Meeting 2015

The Temperature and Pressure Dependences of the Laminar Burning Velocity:

Experiments and Modelling

Alexander A. Konnov *

Division of Combustion Physics, Lund University, Lund, Sweden

Abstract

The laminar burning velocity at standard conditions, i.e. atmospheric pressure and initial temperature of 298 K is

invaluable for characterization of combustion properties of the given fuel, for understanding of the underlying

chemistry, validation of kinetic models, calibration of turbulent flame models, etc. However, in general

applications, from domestic appliances to engines and gas turbines, pressure and initial temperature of the mixture

are often higher than standard ones. Elucidation of the temperature and pressure dependences is therefore important

both from practical and fundamental points of view: many engineering and CFD codes implement empirical power

law equations to evaluate burning velocity at elevated conditions often not covered in laboratory experiments;

comparison of the power exponents α (for temperature dependence) and β (for pressure dependence) obtained from

experiments and derived from different kinetic mechanisms provides an independent tool for model validation and

analysis; finally, interpreting measurements obtained at different temperatures and/or pressures using these relations

helps to check that the data are not biased by some systematic or random errors.

1. Introduction

The adiabatic laminar burning velocity is a

fundamental parameter of any combustible mixture,

which depends on the stoichiometric ratio, pressure and

temperature. It is remarkable that different expressions

for this concept are still used in textbooks on

combustion and in many research papers. For instance

Lewis and von Elbe [1, 2], and Tanford and Pease [3]

used the term “burning velocity”, while Coward and

Hartwell [4, 5] and others used the term “fundamental

speed of flame propagation” or “fundamental flame

speed”. Coward and Payman [6] discussed the

appropriateness of this term, which originates from the

expression “la vitesse normale” introduced by Mallard

and Le Chatelier [7], and suggested it as preferable.

Nowadays, however, the words “flame speed” are often

used instead of the term “fundamental flame speed”, the

replacement which can be misleading. Indeed, the

flame speed of the burner stabilized flames is zero,

while at other conditions it can be affected by stretch,

heat losses and bulk flow movement. Therefore, the use

of the words “flame speed” without adjective

“fundamental” should be discouraged.

By definition, the laminar burning velocity, SL, is the

velocity of a steady one-dimensional adiabatic free flame

propagating in the doubly infinite domain. Other

definitions specific for a particular method of

measurements were discussed as well, yet it was

concluded that “it seems impossible to give a precise

definition for burning velocity which will be equally

applicable to plane and spherical flames” [8]. It is,

however, unfeasible to perform experiments with plane

flames in the doubly infinite domain both from obvious

practical and from fundamental points of view; indeed,

planar flames are intrinsically unstable in open domains

due to thermal expansion across the flame front. This

Landau-Darrieus instability leads to wrinkling and

flame surface growth producing flame acceleration.

The laminar burning velocity is, therefore, not a

measurable quantity; it is derived from other observables

using different assumptions or theoretical models. The

ultimate uncertainty of the experimentally obtained

burning velocity is thus defined both by the uncertainty

(accuracy) of the measurements and by the accuracy

(validity) of the underlying models.

The laminar burning velocity at standard conditions,

that is, atmospheric pressure and initial temperature of

298 K is invaluable for characterization of combustion

properties of the given fuel, for understanding of the

primary chemistry and for validation of kinetic models.

Although comparison of the laminar burning velocities

with 1-D modelling is often used for validation of

detailed reaction mechanisms, one should remember

that the majority of the measurements performed prior

to 1980’s possess significant spread and could deviate

from the “real” values by as much as a factor of 2, e.g.

[9]. A greater part of the methods for measuring

laminar burning velocities involves curved (Bunsen

type), stretched (counter-flow) or spherical time-varying

flames. Wu and Law [10] demonstrated experimentally

that flame stretch due to flame front curvature and/or

flow divergence must be taken into account in the data

processing. Experimental difficulties generating

uncertainties in measuring burning velocities could be

common or different for different methods. They are

analyzed in the present overview to demonstrate a range

of remaining problems and challenges in the

measurements.

2. Temperature and pressure dependences

In general applications, from domestic appliances to

engines and gas turbines, pressure and initial

temperature of the mixture are often higher than

standard ones. Certain applications like industrial gas

turbines require pressures as high as 30 atm and operate

at temperatures close to minimum ignition temperature.

It is therefore important to quantify the effects of

pressure and initial temperature on the adiabatic laminar

burning velocity of many practical fuels. These effects

were often interpreted using empirical correlations as

2

outlined below. Moreover, in determining turbulent

burning velocities or other flame properties, an accurate

correlation of the laminar burning velocity is essential

[11, 12]. It is thus not surprising that investigations of

the laminar burning velocity at different initial

temperatures and pressures are numerous and have quite

long history.

2.1. Correlations for temperature dependence

Different empirical correlations describing variation

of the laminar burning velocity, SL, with initial

temperature have been developed. For example,

experiments performed in 1950’s and 1960’s [13, 14]

were often approximated by equations in the form

SL = A + BTα (1),

where T is initial temperature of the mixture. The most

popular correlation describing the effect of initial

temperature on the laminar burning velocity

SL = SL0 (T/T0)α (2),

where T0 is the reference temperature and SL0 is the

burning velocity at this temperature, was used in this or

equivalent form also since 1950’s, e.g. [15, 16].

Variations of the mixture composition and pressure in

other measurements indicated that power exponent

coefficient, α, varies with pressure and equivalence

ratio. Therefore complex equation in the form

SL = CTα P

-D+ET (3)

was proposed by Babkin and Kozachenko [17].

Coefficients C, α, D and E in Equation (3) were found

different for different equivalence ratios and pressure

ranges. Pressure dependence of the power exponent

coefficient, α, in Eq. (2) was sometimes neglected or

averaged, e.g. [18], yet its variation with equivalence

ratio was studied both in lean and rich flames, as it will

be discussed in the following.

2.2. Correlations for pressure dependence

The first experiments demonstrating the effect of

pressure on the burning velocity have been performed

by Ubbelohde and Koelliker [19], who covered the

range from 1 to 4 bars. Since then the measurements

were often interpreted using empirical power-law

pressure dependence

SL = SL0 (P/P0)β

1 , (4),

where SL0 is the burning velocity at reference conditions

(usually at 1 atm), and P0 is the reference pressure. This

power-law Eq. (4) has its rationale in early theories of

flame propagation. The very first (on the priority see

Manson [20]) thermal theory of Mallard and Le

Chatelier [7] considered only heat and mass balance and

indicated inverse dependence of SL with pressure.

Jouguet [21], Crussard [22], Nusselt [23], and Daniell

[24] developed this theory explicitly introducing an

overall reaction rate W. Zeldovich and Frank-

Kamenetsky [25] further advanced this theoretical

approach showing that the mass burning rate m = ρ SL

is proportional to the square root of the overall reaction

rate W. Since W is proportional to Pn exp(-Ea/RT),

where n is the overall reaction order, the mass burning

rate shows a power exponent dependence of n/2. The

power exponent β is therefore

β = n/2 -1 (5),

which is 0 for bimolecular reactions and -0.5 for the

first order reactions. This consideration is still in use for

explaining changes of the overall reaction order with

pressure, e.g. [26, 27].

Another type of the pressure dependence correlation,

SL = SL0 (1 + β2 log(P/P0)) , (6)

was first proposed by Agnew and Graiff [28]. Sharma

et al. [18] and Bose et al. [29] interpreted their

measurements using Eq. (6) and presented discrete

coefficients β2 for several equivalence ratios. Iijima and

Takeno [30] derived a similar correlation with the

parameter β2 linearly dependent on the stoichiometry.

Equations (4) and (6) are in fact related through series

expansion as was noticed by Dahoe and de Goey [31],

although the values of β1 and β2 are not equal.

An entirely different correlation

SL = SL0 exp (b(1 - (P/P0)x) , (7)

was proposed by Smith and Agnew [32]. Since the

parameters b and x were found to be dependent on the

composition of the oxidizer and the burning velocity at

reference conditions, respectively, it was not attempted

by others, except by Konnov et al. [33] for sub-

atmospheric methane + hydrogen + air flames.

Other empirical correlations describing pressure and

temperature dependence of the burning velocity were

suggested as well, since, as it is mentioned above, the

power exponent β is different at different pressures,

initial temperatures and varies with mixture

composition. Babkin and Kozachenko [17] performed

extensive studies of methane + air flames covering a

wide range of equivalence ratios, initial temperatures

and pressures. They demonstrated that the power

exponent β decreases with the increase of pressure

within the range from 1 to 8 atm, while in the range

from 8 to 70 atm the exponent is almost constant. It has

its maximum value in near-stoichiometric mixtures

decreasing towards lean and rich mixtures. Even after

this seminal study of Babkin and Kozachenko [17],

correlations in the form of equation (4) or (6) are often

used, knowing that the power exponent β1 or coefficient

β2 does not have a constant value.

2.3. Data consistency – role of α and β

Typical presentation of the laminar burning velocity

measurements is in coordinates SL vs. equivalence ratio,

ϕ. Figure 1 shows such an example for methane + air

flames at selected pressures up to 5 atm [34].

Experiments denoted as “present work” were performed

from P = 1.5 to 5 atm and for 0.8 < ϕ < 1.4 using the

heat flux method. For comparison, experimental data

from the literature [27, 35, 36, 37, 38, 39] have been

included together with predictions of GRImech 3.0 and

USC Mech II. For this type of graphs further discussion

can be focused on agreement/disagreement of different

sets of measurements and on agreement/disagreement

between experiments and model predictions. It is,

however, difficult to assess if the data obtained at

different pressures, even from the same set, are

3

consistent or not. It will be shown in the following that

analysis of the pressure (or temperature) dependence

provides a powerful tool for this assessment. Indeed,

since the laminar burning velocity of the given fuel

depends on the stoichiometric ratio, pressure and

temperature only, SL = f(ϕ, P, T), interpretation of

experimental and modeling results using correlations

outlined above provides additional dimensions which

allow for elucidation of possible outliers or

inconsistency.

Fig. 1. Comparison of the burning velocities of methane + air flames from experimental (symbols) and

simulation (lines) results for 2, 3, 4 and 5 atm as functions of equivalence ratio [34].

2.3.1. Pressure dependence of methane flames

The pressure dependence of methane flames has

been extensively studied. Andrews and Bradley [14]

reviewed available experimental data before 1972 and

proposed the correlation SL = 43 P-0.5

cm/s for

stoichiometric mixtures at pressures above 5 atm.

Dahoe and de Goey [31] reviewed and interpreted

available experimental data using Equation (4) or (6).

Goswami et al. [34] extended this analysis using their

own data shown in Fig. 1 and comparing with the

literature as summarized below.

In the log-log coordinates, the most frequently used

power-law pressure dependence (Eq. (4)) should

become a straight line. This was indeed observed for all

equivalence ratios with minor deviations at ɸ = 0.8 and

1.4 and pressure of 1.5 atm. Calculations performed

using GRImech 3.0 [39] and USC Mech II [40] have

also been processed to derive power exponents β1 (Eq.

(4)). Although the modeling results plotted in a log-log

scale look quite linear, careful analysis shows that they

do not exactly follow Eq. (4). This is in line with earlier

observations [17, 26, 27], which demonstrated that the

overall reaction order decreases with the pressure

increase from 1 to 5 atm.

The power exponents β1 (Eq. (4)) derived from the

experiments of Goswami et al. [34] are compared with

the selected literature data in Fig. 2. In this graph the

older measured values for which no stretch correction

was implemented are not shown. Uncertainties in the

power exponents were evaluated using the least-squares

method taking the typical uncertainty of the measured

burning velocity of 0.8 cm/s into account. Most

recently Dirrenberger et al. [41] obtained close values of

the power exponent β1 in lean flames of methane using

the same heat flux method. Also shown are values of

4

the power exponents derived from the modeling using

both GRImech 3.0 and USC Mech II.

Fig. 2. Variation of the power exponent β1 (Eq. (4))

with equivalence ratio at elevated pressures. Open

squares: [36], open triangles: [42], solid triangle: [43],

star: [44], solid line: [45], dash-dot line: [31], dashed

line: [46], circles: [34], green stars: [41]. Red line: GRI-

mech., blue line: USC Mech II.

What can be concluded and learned from the

comparison shown in Fig. 2?

Both the power exponents obtained

experimentally and derived using two kinetic models

show parabola-like variation with equivalence ratio

from lean to moderately rich mixtures in qualitative

agreement with the literature [17, 36, 42, 45, 46].

Linear variation of the power exponent β1 suggested by

Dahoe and de Goey [31] is therefore not supported by

these results.

Power exponents β1 obtained by Halter et al.

[42] are obvious outliers, or they possess rather high

uncertainty.

The difference between calculations using

GRImech 3.0 and USC Mech II is minor in rich flames,

increasing toward lean flames. This observation is

consistent with Fig. 1, where burning velocities

calculated using these two models remain close in rich

flames with increasing divergence in lean flames with

the pressure increase. GRImech 3.0 has been efficient

in capturing the pressure behavior of SL especially in

lean mixtures.

USC Mech II uses certain reaction rate

constants from GRImech 3.0 and still shows significant

divergence especially in lean mixtures. Simple

comparison of the model predictions with experimental

data shown in Fig. 1 cannot be conclusive for the model

screening since the difference between two mechanisms

is close to the scattering of the SL measurements.

Analysis of the pressure dependence as shown in Fig. 2

thus provides an additional tool for kinetic model

validation.

2.3.2. Pressure dependence for other hydrocarbons

Combustion of methane as the main constituent in

natural gas has been a key field of research for many

years. Methane (or natural gas) is burnt, premixed or

non-premixed, in a large variety of conditions: at room

and elevated initial temperatures, at atmospheric and

high pressures. Much less experiments have been

performed with other hydrocarbons also present in

natural gas.

Goswami [47] has recently measured burning

velocities of ethane + air and propane + air flames at

pressures up to 5 atm using the heat flux method.

Figures 3 and 4 taken from Goswami [47] compare

available stretch-corrected data for these mixtures at

atmospheric pressure. Significant spread of the data

even at 1 atm is obvious, yet it is well established that

burning velocities of hydrocarbon flames decrease with

the pressure rise very similar to methane flames, e.g.

[48, 49]. In other words, the pressure dependence of the

burning velocity in the form of Eq. (4) satisfactorily

describes existing measurements [50].

Detailed analysis of the burning velocities for many

hydrocarbons aimed at the evaluation of their

consistency is yet to be done, therefore Figure 5 [47]

presents only power exponents β1 (Eq. (4)) derived from

the experiments performed using the heat flux method.

In lean mixtures ethane and propane flames possess

close values of the power exponents, while in rich

mixtures those for ethane are higher than for other fuels

studied. One may note that Metghalchi and Keck [50]

found significantly different values of the power

exponent for propane in the range of equivalence ratios

0.8 – 1.2.

Fig. 3. Comparison of the burning velocities of

ethane + air flames at 1 atm as a function of equivalence

ratio. Available stretch-corrected data: [49, 51, 52, 53,

54], present work denotes Goswami [47].

0.6 0.8 1.0 1.2 1.4

Equivalence ratio

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

Po

wer

exp

one

nt

5

Fig. 4. Comparison of the burning velocities of

propane + air flames at 1 atm as a function of

equivalence ratio. Available stretch-corrected data: [49,

51, 52, 53] , present work denotes Goswami [47].

Fig. 5. Variation of the power exponent β1 (Eq. (4))

with equivalence ratio at elevated pressures for

methane, ethane, and propane flames, taken from

Goswami [47].

Interestingly, in the recent study of Dirrenberger et

al. [41] devoted to the pressure dependence of n-pentane

flames, the power exponents determined in the range 0.7

< ɸ < 0.9 are found increasing from -0.37 to -0.33 in

good agreement with those shown in Fig. 5 for ethane

and propane. It could be speculated that the pressure

dependence of the burning velocities of lean flames for

normal alkanes has close similarity, yet further analysis

and more experiments should be performed.

2.3.3. Different behavior for H2 pressure dependence

Hydrogen + air flames behave largely different as

compared to the flames of hydrocarbons. It was early

realized that burning velocity of hydrogen flames may

increase with the pressure rise, e.g. [30]. Moreover, the

overall reaction order, n, (see Equation (5)) varies non-

monotonically with pressure and is considerably

different for different equivalence ratios [55]. At

certain combinations of equivalence ratio and pressure,

the effective reaction order of hydrogen flames can

assume negative values.

Unstretched laminar burning velocities of hydrogen

flames at high pressures are available mostly from

constant volume bombs [56, 57, 58, 59, 60, 61]. The

systematic measurements in hydrogen + air mixtures

[56] are shown in Fig. 6 and compared with the Konnov

[62] hydrogen model predictions. It is interesting that

the calculated burning velocities converge with the

experiments as the pressure increases. Good agreement

of these experiments with the calculations could not be

expected in rich mixtures at atmospheric and moderate

pressures because the measurements of [56, 63] were

found consistently lower than other data from the

literature [62]. This was recently confirmed by Dayma

et al. [61] who covered pressure range from 0.2 till 3

atm. Non-monotonic behavior in this study was

substantiated and supported by the modeling using

kinetic schemes of Burke et al. [64] and of Keromnes et

al. [65].

Fig. 6. Unstretched laminar burning velocities for

hydrogen + air flames at standard temperature as a

function of initial pressure [62]. Measurements:

symbols; calculations: lines with corresponding small

symbols. Equivalence ratios: crosses: 0.75; diamonds:

1.05; squares: 1.8; [56]; solid circles: 3 [56]; open

circles: 3 [12].

Measurements of the laminar burning velocities

were also conducted using different technique based on

particle tracking velocimetry and image processing for

burner-stabilized flames in a high-pressure chamber

[12]. These results for equivalence ratio = 3 are shown

in Fig. 6 to illustrate significant disagreement of the

available experimental data at elevated pressures, which

is much higher than expected experimental uncertainty.

Negative pressure dependence of the mass burning

rates was experimentally proved and analyzed in the

0 1 2 3 4 5

Pressure, atm

100

150

200

250

300

350

Bu

rnin

g v

elo

city, cm

/s

6

mixtures H2 + O2 + diluent (He, Ar or CO2) also studied

in spherical flames by Burke et al. [66]. It was

demonstrated that many contemporary hydrogen kinetic

schemes fail to predict these observations and require

further improvement.

Fig. 7. Laminar burning velocity of 85:15 % H2 +

N2 with 1:7 O2:He oxidizer at ɸ = 0.6 and 298 K.

Symbols: Goswami et al. [67]; lines: predictions of

different models.

The only measurements of the burning velocities in

non-stretched flat flames of hydrogen at high pressure

have been recently performed by Goswami et al. [67].

They were compared with several kinetic models as

well, as shown in Fig. 7. Again, all tested mechanisms

except GRImech 3.0 overpredict these results with

increasing relative divergence at higher pressures

approaching 10 atm.

The composition of the mixtures studied in flat non-

stretched [67] and spherical [61, 66] flames was

different. However, analysis of the comparison between

different experimental data and essentially the same

collection of hydrogen kinetic schemes indicate that the

measurements, especially in lean flames, are probably

inconsistent and call for further investigation.

Experimental difficulties generating uncertainties in

measuring burning velocities from spherical flames

have recently been discussed in several publications,

e.g. by Wu et al. [68] and Varea et al., [69]. This

inconsistency is also manifested in the analysis of the

temperature dependence of hydrogen flames outlined in

the following Section 2.3.5.

2.3.4. Temperature dependence of methane flames

Temperature dependence of the laminar burning

velocity provides another dimension for the analysis of

the data consistency. Andrews and Bradley [14]

reviewed experiments with methane flames prior to

1972 and noted considerable scatter in both the

magnitude of the burning velocity and its rate of

increase with temperature. For stoichiometric flames

they derived correlation SL = 10 + 0.000371T2. Since

then it was generally accepted that the power exponent

α for methane flames is 2, while for other hydrocarbon

+ air mixtures it ranges between 1.5 and 2 [70].

Metghalchi and Keck [50, 71] investigated the effect of

temperature on the burning velocities of several fuels

using Equation (2) and proposed linear function of the

power exponent α with equivalence ratio independent of

the fuel type: α = 2.18 - 0.8(ɸ-1) in the range of

equivalence ratios 0.8 – 1.2. Dahoe and de Goey [31]

processed essentially the same experimental data as did

Andrews and Bradley [14] using both Equations (1) and

(2). They concluded that mean value of α in Equation

(2) for stoichiometric methane + air flames is 1.89 with

apparent scattering from 1.5 to 2.2.

Konnov [72] further analyzed the temperature

dependence of methane flames focusing on comparison

of the power exponents α obtained experimentally and

derived from predictions of two kinetic schemes: the

Konnov mechanism and the GRI-mech. 3.0 in the range

of equivalence ratios from 0.5 to 2. This comparison

together with recent updates is shown in Fig. 8. Both

models are in good agreement with the measurements in

methane + air flames in the range of ɸ from 0.8 to 1.2

[18, 44, 73, 74]. Furthermore, they qualitatively

reproduce rapid increase of α from stoichiometric to

very lean methane mixtures.

Fig. 8. Power exponent coefficient, α, in Eq. (2) for

methane + air flames. Crosses: [74], open diamonds:

[44], solid diamonds: [73], open circles: [29], solid

circle: [75], open squares: [36], solid triangles: [17],

open triangles: [18], long-dash line: [30], dash-dot line:

[76], dash- double dot line: [45], dash-triple dot line:

[77], red solid line: [78], blue stars: [41]. Solid line:

modeling using the Konnov mech., short-dash line:

modeling using the GRI-mech. 3.0.

Unexpected non-monotonic behavior of α was found

in rich methane + air flames [72]. Both calculated

dependences peak at ɸ = 1.4, at higher equivalence

ratios they level off approaching α = 2. In the dedicated

experiments of Yan et al. [79] notable decrease of the

0.4 0.8 1.2 1.6 2.0

Equivalence ratio

1

2

3

Tem

pe

ratu

re p

ow

er

expo

ne

nt,

7

power exponent was confirmed from ϕ = 1.3 towards ϕ

= 1.45. Most recently Dirrenberger et al. [41] extended

determination of the power exponent α up to ϕ = 1.7

essentially confirming predictions of the two models.

This variation of the power exponents α clearly

indicates significant changes in the combustion

chemistry that is modification of the relative role of the

elementary reactions, as discussed by Konnov [72] and

Yan et al. [79]. Moreover, Goswami et al. [34] pointed

out on the resemblance and relation of the anomalous

behavior of the power exponent β1 (Fig. 2) and power

exponent α suggesting a general coupling of the flame

response on the pressure and temperature variation.

What can be concluded and learned from the

comparison shown in Fig. 8?

The temperature power exponent α obtained

experimentally and derived using two kinetic models

shows parabola-like variation from lean to moderately

rich mixtures. Linear variation expressions of α with

equivalence ratio suggested by Metghalchi and Keck

[50, 71], Iijima and Takeno [30], Stone et al. [76], and

Takizawa et al. [77] should not be used.

The powers exponents derived from earlier

experiments of Babkin and Kozachenko [17] and Lauer

and Leukel [73] may possess rather high uncertainty due

to inaccuracies in the measurements of the laminar

burning velocity itself caused by the lack of stretch

correction.

The results of Bose et al. [29] are obvious

outliers.

Two essentially different kinetic schemes: the

Konnov mechanism and the GRI-mech. 3.0 predict very

close power exponents for methane flames. This

unexpected insensitivity was observed for other fuels as

well and will be discussed in the following.

2.3.5. Temperature dependence of hydrogen flames

Measurements of the laminar burning velocity of

hydrogen flames are as numerous as those of methane.

However, available data on the effect of temperature on

the burning velocities of H2 + air flames interpreted

using correlation SL = SL0 (T/T0)α are rather scarce.

Heimel [16] and Milton and Keck [80] determined

discrete values of the power exponent α, while Liu and

MacFarlane [81] proposed linear correlations below and

above the maximum of the burning velocity as a

function of equivalence ratio with the junction value of

α = 1.571. Iijima and Takeno [30] covered practically

the same range of equivalence ratios (0.5 < ϕ < 4) and

observed modest increase of α without a minimum.

These measurements were analyzed by Konnov [72],

who calculated laminar burning velocities of hydrogen

+ air flames in the range of equivalence ratios from 0.35

to 8.5. From the calculations the power exponents α

were derived as shown in Fig. 9. Modeling results

confirmed small variation of α in the range of ϕ from 1

to 3. In the very lean and very rich mixtures, however,

the temperature power exponent increases dramatically.

Sensitivity analysis revealed the reason of this behavior

[72].

Apart from the studies mentioned above, where the

power exponent α was derived directly, a number of

works [82, 83, 84, 85, 86, 87] presented burning

velocities of H2 + air flames at room and elevated

temperatures without evaluation of the power exponent

in the form of Eq. (2). For these studies, the power

exponent α was extracted with a least-square fit

procedure by Alekseev et al. [88]. All available and

extracted values of α from the experimental data are

shown in Figure 9.

Fig. 9. Power exponent α for H2 + air flames at

standard conditions. Solid symbols and thick lines:

experiments [16, 30, 80, 81, 89], open symbols: fit to

experimental data [82, 83, 84, 85, 86, 87], made by

Alekseev et al. [88]; thin lines: modeling.

A new mechanism was employed to investigate the

temperature dependence of the laminar burning velocity

of H2 flames by Alekseev et al. [88]. The conditions of

Figure 9, i.e. the standard conditions of p = 1 atm and T0

= 298K, where the majority of available literature data

were obtained, were further analyzed. For the modeling

with the new mechanism indicated as “current

mechanism” in Fig. 9, the power exponent α was

derived from a least-square fit to the simulated data in

the range of temperatures 250-500K. It was found that

the value of α does depend on the fitted temperature

range, which also means that the power law in the form

of Eq. (2) with constant α is not valid for a wide

temperature intervals. However, for 250-500 K such

correlation is still reasonably accurate, and it

corresponds to the range of the majority of the H2 + air

burning velocity measurements. Also shown for

8

comparison in Figure 9 is the performance of the most

recent H2 model of Keromnes et al. [65] at the same

conditions.

The two models, as well as the previous version of

the mechanism [62], were found to give almost identical

results. Comparing the calculations to the experimental

data, it can be observed that they are in a reasonable

agreement with the most recent measurements of Krejci

et al. [86]. The data of Krejci et al. [86] also possess

less scattering for the α(ϕ) dependence than the

measurements of Hu et al. [82]. However, in the very

lean mixtures (ϕ<0.5), a solid conclusion cannot be

drawn due to the large discrepancies in the experimental

data. Notably, at ϕ = 0.3 there are three measurements

available, from Verhelst et al. [89], Bradley et al. [84]

and Das et al. [85], which differ by about a factor of 5.

Also, all modeling studies shown in Figure 9 predict a

trend of rapid rise of α in lean mixtures, which is

supported by the data of Krejci et al. [86] and Das et al.

[85]. The latter is the only study, which indicates a very

high α in a very lean mixture. However, it should be

noted that in this case α is based on just two temperature

points in a narrow interval of 25K (298K and 323K),

though the rise of the burning velocity was

considerable. Nevertheless, the results extracted from

Das et al. [85] are valuable as a possible evidence for a

trend found in the modeling, yet should not be seen as

an attempt to determine exact value of α at ϕ = 0.3.

It should be also noted that Das et al. [85] employed

the counterflow technique. In the other studies of very

lean H2 + air flames, Bradley et al. [84] and Verhelst et

al. [89], a spherical bomb method was used. For these

last two cases, the flame configuration was unstable due

to a high Lewis number at ϕ = 0.3. This could be seen as

one of the possible reasons for the remaining

discrepancy.

What can be concluded and learned from the

comparison shown in Fig. 9?

The contemporary kinetic models for hydrogen

combustion are capable to reproduce the experimental

data in a wide range of conditions.

It was shown that the temperature exponent

cannot be treated as a constant for hydrogen flames,

even to a first approximation. For a given fuel-oxidizer

mixture, it strongly depends on equivalence ratio,

diluent content and correlation temperature interval.

A rapid increase of α in very lean mixtures was

observed.

New experimental measurements in the very

lean H2+air mixtures are required to confirm the quality

of the model prediction for these conditions.

2.3.6. Peculiarities of the temperature dependence

Nowadays it is a common practice to compare new

measurements of the burning velocity with the

modelling using several kinetic schemes, if available, to

validate them and to recommend the most suitable one

for the given fuel. When measurements are performed

at different initial gas temperatures, the temperature

dependence in the form of empirical Equation (2) can

also be analysed. As was exemplified by Konnov [72],

the power exponent, α, can be derived from the

modelling and compared with experimental data. Such

analyses are illustrated for methane and hydrogen

flames in the previous sections. They clearly indicate

outliers and help to reveal inconsistency in the

measurements.

On the other hand, close examination of the models’

behaviour demonstrates that the mechanisms showing

large difference in prediction of the burning velocities

can be very close with respect to the prediction of the

power exponents α. This has been earlier observed for

methane [72], ethanol [90], hydrogen [88] and other

fuels. To elucidate the underlying reasons of this

observation, a dedicated study for methyl formate, MF,

flames was performed by Christensen et al. [91] as

summarized in the following.

Laminar burning velocities of methyl formate and

air flames were determined at atmospheric pressure and

initial gas temperatures of 298, 318, 338 and 348 K.

Measurements were performed in non-stretched flames,

stabilized on a perforated plate burner at adiabatic

conditions, generated using the heat flux method. The

measurements at 338 K shown in Fig. 10 are compared

to modelling using the mechanisms of Glaude et al. [92]

and Dievart et al. [93]. The Dievart mechanism is in

better agreement with the present experiments in lean

and slightly rich flames, while the Glaude mechanism is

systematically over predicting the experimental results.

Included in the figure as well are the data of Wang et al.

[94] obtained at 333 K with good agreement.

Fig. 10. Laminar burning velocities of MF+air as a

function of ϕ at 338 K. Symbols: experimental data and

lines: modelling. Squares and circles: Christensen et al.

[91]; diamonds: Wang et al. [94] at 333 K. Solid line:

Dievart et al. [93] and dotted line: Glaude et al. [92].

The power exponents α derived from the new

experimental data are shown in Fig. 11. Presented in

the figure as well are the power exponents derived from

the modelling results using the mechanisms of Glaude et

9

al. [92] and Dievart et al. [93]. The calculated values are

in relatively good agreement although there is an

increasing discrepancy between the experimental and

calculated coefficients α towards richer flames, as the

experimental coefficients are larger. Both mechanisms

show a minimum located at equivalence ratio 1.2.

Fig. 11. Power exponent, α, as a function of ϕ.

Symbols: experiments [91] and lines: modelling.

Dashed line: Glaude et al. [92], solid line: Dievart et al.

[93].

Despite over predicting the experimental results of

SL, the Glaude et al. [92] mechanism is good at

predicting the temperature dependence of the laminar

burning velocity. To investigate the deviations seen at

rich conditions as well as the kinetics behind the

temperature dependence, a separate sensitivity analyses

were performed for the laminar burning velocity and for

the power exponents α. To identify the chemistry

responsible for this discrepancy, a sensitivity analysis

was performed with the Glaude et al. and the Dievart et

al. mechanisms at 298 K. The normalized sensitivity of

the laminar burning velocity with respect to the rate

constant, k, is commonly defined as

𝑆𝑒𝑛𝑠(𝑆𝐿, 𝑘) =𝜕𝑆𝐿

𝜕𝑘

𝑘

𝑆𝐿 (8)

The 20 most sensitive reactions for SL of

stoichiometric mixture are presented in Fig. 12. The

results indicate that the laminar burning velocity is

sensitive to reactions from the H2 - O2 subset as well as

to C1 chemistry. The sensitivity spectra for both

mechanisms are essentially very close.

The sensitivity analysis of the laminar burning

velocity as above is commonly used to reveal key

reactions responsible for the differences between model

and experiment or between models. Intriguing was,

however, that two mechanism largely different in

predicting the burning velocities (Fig. 10) show close

performance with respect to the temperature dependence

prediction, Fig. 11.

Fig. 12. Normalized sensitivity coefficients for the

laminar burning velocity of MF+air flames at ϕ = 1.0

To gain further insight into the relation of the

temperature dependence and the key reactions, a

sensitivity analysis of the power exponent α has been

performed for the first time [91]. As mentioned above,

the normalized sensitivity of the laminar burning

velocity can be described by Eq. (8). In a similar

manner the normalized sensitivity of the power

exponent with respect to the rate constant, k, can be

defined as

𝑆𝑒𝑛𝑠(𝑎, 𝑘) =𝜕𝑎

𝜕𝑘

𝑘

𝑎 (9)

By utilizing that the sensitivity of the power

exponent and the laminar burning velocity both are

functions of k, and that the temperature dependence is

described by Eq. (2), the partial derivatives with respect

to k can be calculated using the product rule. It can then

be shown that the normalized sensitivity of the power

exponent with respect to k can be obtained as

𝑆𝑒𝑛𝑠(𝑎, 𝑘) =𝑆𝑒𝑛𝑠(𝑆𝐿,𝑘)−𝑆𝑒𝑛𝑠(𝑆𝐿0,𝑘)

𝑙𝑛(𝑇

𝑇0) 𝛼

(10)

In this equation T0 refers to the reference

temperature of 298 K and T to the arbitrary elevated

temperature (398 K in the study of Christensen et al.

[91]).

Figure 13 shows normalized sensitivity coefficients

of the power exponent for stoichiometric mixture.

When comparing the sensitivity of SL, Fig. 12, and the

sensitivity of α, Fig. 13, one can see some important

differences. Most noticeable is that the sensitivity

coefficients of the power exponent are roughly 1 order

of magnitude smaller than the sensitivity coefficients of

SL. There are also several reactions in the sensitivity of

SL that are displayed with opposite sign in the

sensitivity spectra of α. This indicates that as the

temperature is increased from 298 to 398 K, several

chain promoting reactions become less important and

10

these reactions are now displayed with negative

sensitivity. The same is true for several chain inhibiting

reactions that display positive sensitivities in Fig. 13.

One last observation is that while the two mechanisms

displayed similar results for the sensitivities of the

laminar burning velocity in shape and reaction ranking,

the sensitivity coefficients of α are more scattered.

Fig.13. Normalized sensitivity coefficients for the

power exponent α of MF+air flames at ϕ = 1.0.

This analysis explains why the mechanisms showing

large difference in prediction of the burning velocities

can be very close with respect to the prediction of the

power exponents α. In fact, the normalized sensitivity

coefficients for the power exponent are roughly one

order of magnitude smaller than commonly used

normalized sensitivity coefficients for the burning

velocity. This means that if the differences in reaction

rate constants of two models are manifested in, say,

20% difference in the burning velocity, one may expect

only 2% difference in the power exponent α.

It also implies that comparison of the experimental

alpha coefficients and those derived from the modelling,

as shown in Fig. 11, cannot be used for kinetic model

validation, as has been suggested in other studies, unless

the model is significantly incapable in the burning

velocity prediction. On the other hand, this comparison

can serve for analysis of experimental data consistency.

Indeed, since the models are more “robust” in

calculation of the alpha coefficients, substantial

deviation between experiments and modelling most

probably indicates potential problems in the

measurements. This analysis of experimental data

consistency has recently been demonstrated for

hydrogen + air mixtures [88], where contradiction of

several datasets and modelling was evidenced in lean

flames.

3. Experimental uncertainties

Quite often measurements of the laminar burning

velocities are reported with a stated accuracy of 1-2 %.

These evaluations are usually based on the accuracy of

equipment used. In practice, however, scattering of

available data at the same conditions of temperature,

pressure and equivalence ratio often exceeds 5 and even

10% as illustrated in Figs. 1, 3, 4, and 6 above. There

are several reasons for this inconsistency.

Firstly, technical details important in data

processing are most often not reported in archival

publications. Thus each attempt of measurements in a

new laboratory and even re-visiting the same

experiment after some time has passed at the same place

is unique since operating experiment and data

processing involves the effect of operator.

Second, both equipment and theory behind

each of the methods mentioned above are in a constant

development.

Moreover, there are no protocols in place to

renounce older data even if the author himself or herself

realized that the published results were incorrect or

highly uncertain. This leads to an accumulation of

results hardly suitable for model validation due to large

degree of scatter.

Several reviews devoted to comparison of the

experimental approaches and of the results obtained

deserve to be mentioned. In 1953 Linnett [8] described

the following methods: (1) Egerton-Powling flat flame

method; (2) Soap bubble method; (3) Closed spherical

vessel method; (4) Cylindrical tube method; (5) Bunsen

burner method. In the seminal review of Andrews and

Bradley [95] in 1972 essentially the same methods were

further scrutinized and the maximum burning velocity

of methane + air flame at 1 atm and 298 K of 45 ±2

cm/s was recommended. Enlightening Fig. 14

composed by Law [96] is basically an extension of the

similar figure compiled by Andrews and Bradley [95].

Law [96] has emphasized that after the work of Wu and

Law [10], which demonstrated the importance of the

stretch correction in the data processing, the uncertainty

of the burning velocity measurements was reduced to

less than ±8 cm/s (the scattering in Andrews and

Bradley [95] plot was of the order of ±25 cm/s), while

contemporary measurements together with non-linear

stretch correction are indeed consistent within ±2 cm/s.

Although the stretch correction is extremely

important, other experimental difficulties generating

uncertainties in measuring burning velocities were

realized and reviewed. These difficulties could be

common or different for different methods; some

methods for measuring burning velocity are now

considered obsolete. Ranzi et al. [97] and Nilsson and

Konnov [98] limit their discussion to four methods:

Bunsen burner, spherical flames, counter-flow flames

and flat flames stabilized using the heat flux method. In

the recent review of Egolfopoulos et al. [99] only the

last three were carefully analyzed and compared. This

review summarizes the state of the art in the data quality

and demonstrates a range of remaining problems and

11

challenges in the measurements. Many exciting

developments in the field presented and analyzed by

Egolfopoulos et al. [99] open new prospects in the

improvement of the theoretical and experimental

approaches.

Fig. 14. Variation of measured maximum laminar

burning velocities of CH4 +air mixtures at standard

conditions as a function of year of publication, taken

from Law [96].

Concluding remarks

In most practical situations combustion is

accompanied by flames. With a few exceptions like

detonations or explosions, flames of different natures

and appearances propagate in engines, in domestic

appliances, in gas-turbine combustion chambers, etc. It

is therefore natural that laboratory studies of flames

provide valuable information on combustion

characteristics important both for solution of

engineering problems and for development and

validation of combustion models.

The laminar burning velocity and its temperature

and pressure dependences is important both from

practical and fundamental points of view: many

engineering and CFD codes implement empirical power

law equations to evaluate burning velocity at elevated

conditions often not covered in laboratory experiments.

Moreover, comparison of the power exponents α (for

temperature dependence) and β (for pressure

dependence) obtained from experiments and derived

from different kinetic mechanisms provides an

independent tool for model validation and analysis. The

power exponents α are not very sensitive to the rate

constants implemented in the modeling; therefore they

are more suitable for analysis of consistency of the

measurements and helps to check that the data are not

biased by some systematic or random errors.

Acknowledgements

The author is grateful to all his co-authors who

contributed to the present analyses of the pressure and

temperature dependences, especially to Mayuri

Goswami, Vladimir A. Alekseev, Moah Christensen,

Jenny D. Nauclér, and Elna J.K. Nilsson.

References

[1] B. Lewis, G. Von Elbe, Proc. Combust. Inst. 1-2

(1948) 183-188.

[2] B. Lewis, G. Von Elbe, Combustion, flames and

explosions of gases, Cambridge, Univ Press, 1961.

[3] C. Tanford, R.N. Pease, J. Chem. Phys. 15 (1947)

861-865.

[4] H.F. Coward, F.J. Hartwell, J. Chem. Soc. (1932)

1996-2004.

[5] H.F. Coward, F.J. Hartwell, J. Chem. Soc. (1932)

2676-2684.

[6] H.F. Coward, W. Payman, Chem. Rev. 21 (1937)

359-366.

[7] E. Mallard, H.L. Le Chatelier, “Recherches

expérimentales et théoriques sur la combustion des

mélanges gazeux explosifs,” Ann. des Mines, Ser. 8,

IV (1883): Memoir I, “Température d’inflammation

des mélanges gazeux” (pp. 274-295); Memoir II,

“Sur la vitesse de propagation de la flamme” (pp.

296-395); Memoir III, “Sur la température de

combustion et les chaleurs spécifiques des gaz” (pp.

396-561).

[8] J.W. Linnett, Proc. Combust. Inst. 4 (1953) 20-35.

[9] M.J. Brown, D.B. Smith, Proc. Comb. Inst. 25

(1994) 1011-1018.

[10] C.K. Wu, C.K. Law, Proc. Combust. Inst. 20

(1984) 1941-1949.

[11] H. Kobayashi, T. Tamura, K. Maruta, T. Niioka,

Proc. Combust. Inst. 26 (1996) 389-396.

[12] X. Qin, H. Kobayashi, T. Niioka, Exp. Therm.

Fluid Sci. 21 (2000) 58-63.

[13] G.L. Dugger, Effect of initial mixture temperature

on flame speed of methane-air, propane-air, and

ethylene-air mixtures. NACA Report 1061, Lewis

Flight Propulsion Lab., 1952.

[14] G.E. Andrews, D. Bradley, Combust. Flame, 19

(1972) 275-288.

[15] G.L. Dugger, D.D. Graab, Proc. Combust. Inst. 4

(1953) 302-310.

[16] S. Heimel, Effect of initial mixture-temperature on

burning velocity of hydrogen-air mixtures with

preheating and simulated preburning, NACA

Technical Note 4156, Lewis Flight Propulsion

Laboratory, 1957.

[17] V.S. Babkin, L.S. Kozachenko, Combust. Expl.

Shock Waves, 2 (1966) 46-52.

[18] S.P. Sharma, D.D. Agrawal, C.P. Gupta, Proc.

Combust. Inst. 18 (1981) 493-501.

[19] L. Ubbelohde, E. Koelliker, Journal fur

Gasbeluchtung und Wasserversorgung, 59 (1916)

49-57.

[20] N. Manson, Combust. Flame, 71 (1988) 179-187.

[21] E. Jouguet, Sur la propagation des déflagrations

dans les mélanges gazeux. Compt. Rend. Acad. Sci.,

Paris, 156 (1913) 872-875.

[22] L. Crussard, Les déflagrations en régime

permanent dans les milieux conducteurs. Compt.

12

Rend. Acad. Sci., Paris, 158 (1914) 125-128.

[23] W. Nusselt, Die Zundgeschwindigkeit brennbarer

gasgemische, Z. Ver. Deut. Ing. 59 (1915) 872-878.

[24] P.J. Daniell, Proc. Roy. Soc., A, 126 (1930) 393-

405

[25] Ya.B. Zeldovich, D.A. Frank-Kamenetsky, Compt.

Rend. Acad. Sci. USSR, 19 (1938) 693.

[26] F.N. Egolfopoulos, C.K. Law, Combust. Flame, 80

(1990) 7-16.

[27] C. Rozenchan, D.L. Zhu, C.K. Law, S.D. Tse,Proc.

Combust. Inst. 29 (2002) 1461-1469.

[28] J.T. Agnew, L.B. Graiff, Combust. Flame, 5 (1961)

209-219.

[29] P.K. Bose, S.P. Sharma, S. Mitra, Laminar Burning

Velocity of Methane-Air Mixture in the Presence of

a Diluent. Proc. of The 6th

Int. Symp. on Transport

Phenomena in Thermal Engineering, May 9-13,

1993, Seoul, Korea, pp. 648-653, Begell House Inc.

[30] T. Iijima, T. Takeno, Combust. Flame 65 (1986)

35-43.

[31] A.E. Dahoe, L.P.H. de Goey, J. Loss Prevention

Proc. Indust. 16 (2003) 457-478.

[32] D. Smith J.T. Agnew Proc. Combust. Inst. 6 (1957)

83-88

[33] A.A. Konnov, R. Riemeijer, L.P.H. de Goey, Fuel

89 (2010) 1392-1396.

[34] M. Goswami, S. Derks, K. Coumans, W.J. Slikker,

M.H. de Andrade Oliveira, R.J.M. Bastiaans,

C.C.M. Luijten, L.P.H. de Goey, A.A. Konnov,

Combust. Flame 160 (2013) 1627-1635.

[35] H. Kobayashi, T. Nakashima, T. Tamura, K.

Maruta, T. Niioka, Combust. Flame, 108 (1997)

104-117.

[36] X.J. Gu, M.Z. Haq, M. Lawes, R. Woolley,

Combust. Flame, 121 (2000) 41-58.

[37] O. Park, P.S. Veloo, N. Liu, F.N. Egolfopoulos,

Proc. Combust. Inst. 33 (2011) 887-894.

[38] M.I. Hassan, K.T. Aung, G.M. Faeth, Combust.

Flame 115 (1998) 539-550.

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

Moriarty, B. Eiteneer, M. Goldenberg, C.T.

Bowman, R.K. Hanson, S. Song, W.C. Gardiner, Jr,

V.V. Lissianski, Z. Qin,

http://www.me.berkeley.edu/gri_mech/ 1999.

[40] H. Wang, X. You, A. Joshi, S.G. Davis , A. Laskin,

F.N. Egolfopoulos, C.K. Law,USC Mech Version II.

High-Temperature Combustion Reaction Model of

H2 / CO / C1-C4 Compounds.

http://ignis.usc.edu/USC_Mech_ II.htm .2007.

[41] P. Dirrenberger, H. Le Gall, R. Bounaceur, P.A.

Glaude, F. Battin-Leclerc, Energy Fuels, 29 (2015)

398-404.

[42] F. Halter, C. Chauveau, N. Djebaili-Chaumeix, , I.

Gokalp, Proc. Combust. Inst. 30 (2005) 201-208.

[43] M. Elia, M. Ulinski, M. Metghalchi, Trans. ASME,

123 (2001) 190-196.

[44] P. Han, M.D. Checkel, B.A. Fleck, N.L. Nowicki,

Fuel 86 (2007) 585-596.

[45] S.Y. Liao, D.M. Jiang, Q. Cheng, Fuel, 83 (2004)

1247-1250.

[46] P. Ouimette, P. Seers, Fuel, 88 (2009) 528-533.

[47] M. Goswami, Laminar burning velocities at

elevated pressures using the Heat Flux method, PhD

thesis, Technische Universiteit Eindhoven, The

Netherlands, 2014.

[48] M.I. Hassan, K.T. Aung, O.C. Kwon, GM. Faeth, J.

Propuls. Power, 14 (1998) 479-488.

[49] G. Jomaas, X.L. Zheng, D.L. Zhu, C.K. Law, Proc.

Combust. Inst. 30 (2005) 193-200.

[50] M. Metghalchi, J.C. Keck, Combust. Flame, 38

(1980) 143–154.

[51] C.M. Vagelopoulos, F.N. Egolfopoulos, Proc.

Comb. Inst. 27 (1998) 513-519.

[52] K.J. Bosschaart, L.P.H. de Goey, Combust. Flame

136 (2004) 261-269.

[53] W. Lowry, J. de Vries, M. Krejci, E. Peterson, Z.

Serinyel, W. Metcalfe, H. Curran, G. Bourque, J.

Eng. Gas Turbines Power, 133 (2011) 091501-1-9.

[54] O. Park, P.S. Veloo, F.N. Egolfopoulos, Proc.

Combust. Inst. 34 (2013) 711-718.

[55] C.K. Law, Combust. Sci. Technol. 178 (2006) 335-

360.

[56] K.T. Aung, M.I. Hassan, G.M. Faeth, Combust.

Flame 112 (1998) 1-15.

[57] O.C. Kwon, G.M. Faeth, Combust. Flame 124

(2001) 590-610.

[58] S.D. Tse, D.L. Zhu, C.K. Law, Proc. Combust.

Inst. 28 (2000) 1793-1800.

[59] F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst.

23 (1990) 333-340.

[60] S. Kwon, L.-K. Tseng, G.M. Faeth, Combust.

Flame 90 (1992) 230-246.

[61] G. Dayma, F. Halter, P. Dagaut, Combust. Flame,

161 (2014) 2235-2241.

[62] A.A. Konnov, Combust. Flame 152 (2008) 507-

528.

[63] K.T. Aung, M.I. Hassan, G.M. Faeth, Combust.

Flame 109 (1997) 1-24.

[64] M.P. Burke, M. Chaos, Y. Ju, F.L. Dryer, S.J.

Klippenstein, Int. J. Chem. Kinet., 44 (2012) 444-

474.

[65] A. Keromnes, W.K. Metcalfe, K.A. Heufer, N.

Donohoe, A.K. Das, C.J. Sung, J. Herzler, C.

Naumann, P. Griebel, O. Mathieu, M.C. Krejci, E.L.

Petersen, W.J. Pitz, H.J. Curran, Combust. Flame

160 (2013) 995-1011.

[66] M.P. Burke, M. Chaos, F.L. Dryer, Y. Ju, Combust.

Flame, 157 (2010) 618-631.

[67] M. Goswami, J.G.H. van Griensven, R.J.M.

Bastiaans, A.A. Konnov, L.P.H. de Goey, Proc.

Combust. Inst. 35 (2015) 655-662.

[68] F. Wu, W. Liang, Z. Chen, Y. Ju, C.K. Law, Proc.

Combust. Inst. 35 (2015) 663–670.

[69] E. Varea, J. Beeckmann, H. Pitsch, Z. Chen, B.

Renou, Proc. Combust. Inst. 35 (2015) 711–719.

[70] Ö.L. Gülder, Correlations of laminar combustion

data for alternative S.I. engine fuels. SAE Tech. Pap.

Ser. SAE 841000; 1984.

[71] M. Metghalchi, J.C. Keck, Combust Flame 48

(1982) 191-210.

13

[72] A.A. Konnov, Fuel, 89 (2010) 2211-2216.

[73] G. Lauer, W. Leuckel, Archiv. Combust. 15 (1995)

7-23.

[74] R.T.E. Hermanns, A.A. Konnov, R.J.M. Bastiaans,

L.P.H. de Goey, K. Lucka, H. Kohne, Fuel, 89

(2010) 114-121.

[75] A.M. Garforth, C.J. Rallis, Combust. Flame, 31

(1978) 53-68.

[76] R. Stone A. Clarke P. Beckwith, Combust. Flame,

114 (1998) 546-555.

[77] K. Takizawa, A. Takahashi, K. Tokuhashi, S.

Kondo, A. Sekiya, Combust. Flame, 141 (2005)

298-307.

[78] M. Akram, P. Saxena, S. Kumar, Energy Fuels, 27

(2013) 3460-3466.

[79] B. Yan, Y. Wu, C. Liu, J.F. Yu, B. Li, Z.S. Li, G.

Chen, X.S. Bai, M. Alden, A.A. Konnov, Int. J.

Hydrogen Energy, 36 (2011) 3769-3777.

[80] B.E. Milton, J.C. Keck, Combust. Flame 58 (1984)

13-22.

[81] D.D.S. Liu, R. MacFarlane, Combust. Flame 49

(1983) 59-71.

[82] E. Hu, Z. Huang, J. He, H. Miao, Int. J. Hydrogen

Energy 34 (2009) 8741-8755.

[83] G.W. Koroll, R.K. Kumar, E.M. Bowles, Combust.

Flame 94 (1993) 330-340.

[84] D. Bradley, M. Lawes, K. Liu, S. Verhelst, R.

Woolley, Combust. Flame 149 (2007) 162-172.

[85] A.K. Das, K. Kumar, C.J. Sung, Combust. Flame

158 (2011) 345-353.

[86] M.C. Krejci, O. Mathieu, A.J. Vissotski, S. Ravi,

T.G. Sikes, E.L. Petersen, A. Keromnes, W.

Metcalfe, H.J. Curran, J. Eng. Gas Turbines Power

135 (2013), Paper 021503.

[87] A.A. Desoky, Y.A. Abdel-Ghafar, R.M. El-

Badrawy, Int. J. Hydrogen Energy 15 (1990) 895-

905.

[88] V.A. Alekseev, M. Christensen, A.A. Konnov, The

effect of temperature on the adiabatic burning

velocities of diluted hydrogen flames: a kinetic study

using an updated mechanism. Combust. Flame, doi:

10.1016/j.combustflame.2014.12.009

[89] S. Verhelst, R. Woolley, M. Lawes, R. Sierens,

Proc. Combust. Inst. 30 (2005) 209-216.

[90] A.A. Konnov, R.J. Meuwissen, L.P.H. de Goey,

Proc. Combust. Inst. 33 (2011) 1011-1019.

[91] M. Christensen, E.J.K. Nilsson, Konnov, A.A.. The

Temperature Dependence of the Laminar Burning

Velocities of Methyl Formate + Air Flames. Fuel,

submitted.

[92] P.A. Glaude, W.J. Pitz, M.J. Thomson, Proc.

Combust. Inst. 30 (2005) 1111-1118.

[93] P. Diévart, S.H. Won, J. Gong, S. Dooley, Y. Ju,

Proc. Combust Inst. 34 (2013) 821-829.

[94] Y.L. Wang, D.J. Lee, C.K. Westbrook, F.N.

Egolfopoulos, T.T. Tsotsis, Combust. Flame. 161

(2014) 810-817.

[95] G.E. Andrews, D. Bradley, Combust. Flame, 18

(1972) 133-153.

[96] C.K. Law, AIAA J, 50 (2012) 19–36.

[97] E. Ranzi, A. Frassoldati, R. Grana et al. Prog.

Energy Combust. Sci. 38 (2012) 468-501.

[98] E.J.K. Nilsson, A.A. Konnov, Flame studies of

oxygenates. Book chapter in: Development of

detailed chemical kinetic models for cleaner

combustion, Editors: F. Battin-Leclerc, J. M.

Simmie, E. Blurock, ISBN: 978-1-4471-5306-1

(Print) 978-1-4471-5307-8 (Online), Springer, 2013,

pp. 231-280.

[99] F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-

Höinghaus, C.K. Law, F. Qi, Prog. Energy Combust.

Sci. 43 (2014) 36 – 67.