i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7

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Numerical study on laminar burning velocity and NOformation of premixed methane–hydrogen–air flames

Erjiang Hu, Zuohua Huang*, Jianjun Zheng, Qianqian Li, Jiajia He

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

a r t i c l e i n f o

Article history:

Received 12 April 2009

Received in revised form

15 May 2009

Accepted 16 May 2009

Available online 23 June 2009

Keywords:

Methane

Hydrogen

Laminar burning velocity

NO formation

* Corresponding author. Tel.: þ86 29 8266507E-mail address: zhhuang@mail.xjtu.edu.c

0360-3199/$ – see front matter ª 2009 Interndoi:10.1016/j.ijhydene.2009.05.080

a b s t r a c t

Numerical study on laminar burning velocity and NO formation of the premixed methane–

hydrogen–air flames was conducted at room temperature and atmospheric pressure. The

unstretched laminar burning velocity, adiabatic flame temperature, and radical mole

fractions of H, OH and NO are obtained at various equivalence ratios and hydrogen frac-

tions. The results show that the unstretched laminar burning velocity is increased with the

increase of hydrogen fraction. Methane-dominated combustion is presented when

hydrogen fraction is less than 40%, where laminar burning velocity is slightly increased

with the increase of hydrogen addition. When hydrogen fraction is larger than 40%,

laminar burning velocity is exponentially increased with the increase of hydrogen fraction.

A strong correlation exists between burning velocity and maximum radical concentration

of HþOH radicals in the reaction zone of premixed flames. High burning velocity corre-

sponds to high radical concentration in the reaction zone. With the increase of hydrogen

fraction, the overall activation energy of methane–hydrogen mixture is decreased, and the

inner layer temperature and Zeldovich number are also decreased. All these factors

contribute to the enhancement of combustion as hydrogen is added. The curve of NO

versus equivalence ratio shows two peaks, where they occur at the stoichiometric mixture

due to Zeldovich thermal-NO mechanism and at the rich mixture with equivalence ratio of

1.3 due to the Fenimore prompt-NO mechanism. In the stoichiometric flames, hydrogen

addition has little influence on NO formation, while in rich flames, NO concentration is

significantly decreased. Different NO formation responses to stretched and unstretched

flames by hydrogen addition are discussed.

ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction realized in the spark-ignition engines. However, due to the

With increasing concern about energy shortage and stringent

emission regulation, the development of alternative fuel

engines has attracted more and more attention in engine

community. Natural gas is a clean fuel in which methane is its

major component, is considered to be one of the favorable

fuels for engines. The naturalgasfuelled engines have been

5; fax: þ86 29 82668789.n (Z. Huang).ational Association for H

slow burning velocity of natural gas and its poor lean-burn

capability, the natural gas spark-ignition engine still remains

its disadvantages like low thermal efficiency, large cycle-by-

cycle variation, and poor lean-burn capability, and these will

decrease the engine power output and increase the fuel

consumption [1,2]. One of the effective methods to solve the

problem is to mix the natural gas with a fuel that possesses

ydrogen Energy. Published by Elsevier Ltd. All rights reserved.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 76546

high burning velocity. Hydrogen is regarded as the best

gaseous candidate for natural gas due to its very high burning

velocity, and the combination of natural gas with hydrogen is

expected to improve the lean-burn characteristics and

decrease the engine emissions (mainly HC and CO), but NOx

emissions will be increased [3–6]. Thus, the investigation on

combustion mechanism of hydrogen addition into methane

and decreasing NOx has become one of the most important

topics in combustion.

Flame propagation is strongly related to the improvement

of combustion in spark ignition (SI) engines. In conventional SI

engine, combustion initiates from the spark plug where the

flame front will develop and propagate to the combustion

chamber volume [7]. By the time when 5–10% of fuel/air

mixture is burned, the combustion process in SI engines is

well established and the flame front moves quickly in the

engine cylinder [8]. The burning velocity directly affects the

flame propagation speed and hence, the operation of the SI

engine. Faster burning in SI engines leads to a more robust and

repeatable combustion and permits engine operation with

substantially larger amount of exhaust gas recirculation (EGR),

bringing the reduction in NOx emission. Fast burning results

in the decreased combustion duration and the compact

combustion process will improve engine thermal efficiency

and decrease fuel consumption [5–7].

Laminar burning velocity is the fundamental parameter in

combustion and it is base for determining turbulent burning

velocity. Laminar burning velocity can be used to validate the

chemical reaction mechanisms [9,10] and is of practical

importance in the design and optimization of internal

combustion engines and power plant burners [11]. Experi-

mental and numerical studies of methane–hydrogen fuel

blends have been conducted on laminar burning velocity

measurement, intermediate species measurement and

chemical kinetics simulation. Yu et al. [12] investigated the

laminar burning velocity of methane–hydrogen mixtures and

showed that the laminar burning velocities of methane–

hydrogen mixtures increased linearly with the increase of

hydrogen fraction in the fuel blends. Law and Kwon [13]

studied the hydrogen flame doped with small fraction of

hydrocarbon fuel and revealed the inhibition of hydrocarbon

fuel in addition to the hydrogen combustion. The results

showed that the laminar burning velocity and flame temper-

ature decreased remarkably by adding a small fraction of

hydrocarbon fuel. Halter et al. [14] investigated the effect of

initial pressure and hydrogen fraction on laminar burning

velocity of methane–hydrogen flame and their results showed

that laminar burning velocity was increased with the increase

of hydrogen fraction in fuel blends and was decreased with

the increase of initial pressure. Naha et al. [15] conducted the

numerical study of hydrocarbon–hydrogen flames and

revealed the influence of hydrogen addition on emissions by

analyzing the mole fraction profiles of NO, C2H2 and CO. Using

isotope shift/planar laser induced fluorescence spectroscopy,

Katoh et al. [16] detected two types of OH radicals in the

methane–hydrogen–air flame. These two OH radicals are

detected separately from the methane–air flame and the

hydrogen–air flame.

In the numerical study, most of simulations were con-

ducted with the CHEMKIN [17] and/or the COSILAB [18]

laminar premixed flame codes where detailed kinetic

schemes can be implemented [19,20]. However, these simu-

lation and chemical kinetics analysis mostly focused on

methane-rich flames [21–27] or hydrogen-rich flames [13,28],

and few literatures reported on the combustion mechanism in

the case of hydrogen addition over wide range of hydrogen

fractions. Previous studies in engines and flame showed that

NOx concentration of methane combustion was increased as

hydrogen was added especially at large hydrogen fraction

[29–32]. This is regarded as the increase of combustion

temperature when hydrogen is added. However, the chemical

mechanism of hydrogen addition on NOx formation in pre-

mixed methane–air flames has not well been understood.

The objectives of this study will focus on the chemical

kinetic mechanisms of hydrogen addition on burning velocity

and NO formation in the methane–air flames. Flames with

various hydrogen fractions and equivalence ratios at room

temperature and atmospheric pressure are included. The

study will broaden the understanding of methane–hydrogen–

air mixture flames and provide new guidance to low emission

combustion.

2. Computational methods and chemicalmechanism validation

A freely propagating adiabatic, premixed, unstretched planar

flame was simulated by using PREMIX [17], a steady laminar

one-dimensional flame code. PREMIX uses a hybrid time-

integrating/Newton iteration technique to solve the steady-

state mass, species and energy conservation equations and

can simulate the propagating flame. Equations were solved by

using the TWOPNT, a boundary value problem solver in the

CHEMKIN package [33]. Also built in the CHEMKIN package are

a transport property processor and a gas-phase interpreter

which provide the species transport properties and process

the chemical reaction mechanism.

One of the critical elements for simulation is the proper

reaction mechanism that can describe the essential funda-

mental reaction paths followed by the overall reaction. GRI-

Mech is an optimized detailed chemical reaction mechanism

for the calculation of natural gas chemical reaction process

and the latest version is GRI 3.0 [19]. GRI 3.0 consists of 325

elementary chemical reactions with associated rate coeffi-

cient expressions and thermochemical parameters for 53

species. It includes the detailed combustion reaction mecha-

nism for hydrogen. The ranges of GRI 3.0 are 1000–2500 K in

temperature, 10 Torr to 10 atm in pressure and 0.1–5.0 in

equivalence ratio.

To simulate and interpret the effect of hydrogen addition

on methane–air chemical reactions, the chemical kinetics

mechanism used in the calculation must be capable of the

calculation of pure methane and methane–hydrogen fuel

blends. Prior to the calculation, the GRI 3.0 mechanism needs

to be validated by the experimental results. Ren et al. [21,22]

implemented the GRI-Mech in the PREMIX code and validated

this kinetic mechanism for hydrogen–methane blends by

comparing the computed laminar burning velocities with

those from experiments at low equivalence ratios (0.63–0.73)

and hydrogen mole fractions in the fuel less than 8%. In this

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7 6547

study, the validation of reaction mechanism was attempted

for the stoichiometric and rich methane–air mixture as well as

for methane–hydrogen–air mixture with high hydrogen

fraction.

Fig. 1 shows the comparison between the computed

laminar burning velocities by using GRI-Mech 3.0 and experi-

mental results from literature [34]. Good agreement is found

except at high hydrogen fraction, and this is probably related

to the used kinetic scheme. Maximum deviation of 16% is

presented in the stoichiometric hydrogen flame. However,

this deviation will not affect the results and conclusions of the

analysis. The results show that GRI 3.0 can well reproduce the

laminar burning velocity of methane–hydrogen–air mixtures

at stoichiometric mixture flame and rich mixture flame as

well as methane–hydrogen–air flame. GRI 3.0 was also vali-

dated in the calculation of laminar flame speed [21–23,35] and

ignition delay time [36,37] for methane–hydrogen–air flames

in the previous literatures.

In this study, at the upstream boundary, the initial

temperature and initial pressure are set at 303 K and 0.1 MPa,

respectively. Mole fraction of hydrogen in the fuel blends (XH2 )

is defined as,

XH2¼ nH2

nCH4þ nH2

(1)

where nCH4 and nH2are the mole fraction of methane and

hydrogen in the fuel blends, respectively. Hydrogen fractions

in the fuel are varied from 0% to 100% with interval of 10%. The

composition of air is 21% of oxygen and 79% of nitrogen in

volumetrically.

Fig. 2 – Unstretched laminar burning velocity versus

equivalence ratio for methane–air and hydrogen–air

mixtures.

3. Results and discussions

3.1. Unstretched laminar burning velocity

Unstretched laminar burning velocity (ul) is plotted as a func-

tion of equivalence ratio for methane–air and hydrogen–air

mixtures as shown in Fig. 2. In the case of methane–air flame,

Fig. 1 – Comparison between computed burning velocities

with GRI-Mech 3.0 and those from experiment for

methane–hydrogen–air mixtures.

the unstretched laminar burning velocity of fuel-lean

mixtures is increased with the increase of equivalence ratio

and it decreases as the mixtures become fuel-rich. Peak value

of unstretched laminar burning velocity of methane–air

mixture is presented at the equivalence ratio of 1.1 and that of

hydrogen–air mixture is presented at equivalence ratio of 1.8.

The unstretched laminar burning velocities from other liter-

atures obtained by Yu [12], Law [13], Hu [34] and Tanoue [38]

for methane–air mixture and Hu [39], Takahashi [40], Sun [41]

and Dowdy [42] for hydrogen–air mixture are also plotted in

Fig. 1. The results show that the data of the present study

show good agreement with those of literatures.

Unstretched laminar burning velocity versus hydrogen

fraction at three equivalence ratios (f ¼ 0:8, 1.0 and 1.2) are

plotted in Fig. 3. The figure clearly shows that the values of

unstretched laminar burning velocity are below the averaged

values estimated by molar proportions. This reveals the

strong non-linear influence from hydrogen addition on

chemical kinetics. When hydrogen fraction is less than 40%, it

is the regime of methane-dominated combustion. Here

laminar burning velocity is slightly almost linearly increased

with the increase of hydrogen addition. When hydrogen

fraction is larger than 40%, laminar burning velocity shows an

Fig. 3 – Unstretched laminar burning velocity versus

hydrogen fraction at different equivalence ratios.

Table 1 – Summary of variables (0.1 MPa, 303 K).

f A B C D t

0.8 0.28462 0.00229 0.37426 0.00200 15.41042

1.0 0.39836 0.00367 0.49842 0.00812 18.28432

1.2 0.34798 0.00467 0.44489 0.01452 19.47500

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 76548

exponential increase with the increase of hydrogen fraction.

This is consistent with the phenomenon that engines fuelled

with methane–hydrogen mixtures appear backfire and

knocking due to the rapid increasing burning velocity when

the hydrogen fraction becomes high, especially above 50–60%

[43].

On the basis of the numerical results, the following corre-

lation is proposed:

ul ðm=sÞ ¼ Aþ B� XH2;�0 � XH2

� 40%�; (2)

ulðm=sÞ ¼ Cþ D� exp�XH2

=t�;�40 < XH2

� 100%�: (3)

The values of A, B, C, D and t are tabulated in Table 1.

3.2. Flame structure

As demonstrated in Fig. 1, the measured and calculated

unstretched laminar burning velocities were in reasonably

good agreement. Therefore, the calculation can gain better

understanding of the effect of hydrogen addition on laminar

burning velocity. The approach involved numerical simula-

tions of methane–air flames with various fractions of

hydrogen addition.

Typical predicted structures of plane unstretched

methane–hydrogen–air flames at the stoichiometric condi-

tions are illustrated in Fig. 4. Results in Fig. 4a and b provide

the base line flame structure without hydrogen addition.

Fig. 4b–h shows a similar pattern of flame structure for

mixtures with hydrogen fractions of 40%, 80% and 100%. In

each pair of figures, the left graph gives the temperature

distribution and stable concentrations of reactants and

products (CH4, H2, O2, H2O, CO, CO2), whereas the right graph

shows the concentration profiles of radical species (H, O, OH,

CH3), as function of distance through the flame. Maximum

mole concentrations of H, O and OH radicals are also plotted in

the figure.

In these figures, the consumption of CH4, the formation of

intermediate species CO, and the oxidation of CO to CO2 can

be clearly observed. CO concentration gives its peak value

almost at the same position where CH4 concentration falls to

zero, while CO2 concentration postpones to CO and will

increase as CO is oxidized. Fuel is completely consumed at

1 mm or slight less than 1 mm and main temperature rising

(approximately 70%) will be achieved at this position, and then

gradually reaches the equilibrium condition after this posi-

tion. Actually, complete equilibrium will not reach even at

4 mm. The slow approaching to equilibrium is primarily

a consequence of the dominance of three-body recombination

reactions in this region [44].

In the stoichiometric methane–air flame, the radical OH has

the largest peak concentration in the flame, with H has roughly

10–30% lower than that of OH in peak concentration.

Concentration of O is less than half of H concentration and CH3

gives the lowest concentration. In hydrogen–air flame, the

largest concentration is H radical. In methane–hydrogen–air

flame, the mole fractions of H, O and OH are increased when

hydrogen is added and this will promote the combustion of

methane–air flame. As reported by Kwon and Faeth [45], the

increase of peak concentration of H would lead a correspond-

ing increase of flame laminar burning velocity. For pure

Fig. 4 – Predicted flame structure of premixed stoichiometric methane–hydrogen–air flame.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7 6549

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 76550

hydrogen–air flame and methane–hydrogen–air flame with

hydrogen fraction of 80%, the increase of O2 concentration

near the cold boundary of the flame prior to O2 decreasing

approaches the reaction zone of the flame. This reflects the

dominate effect from the preferential diffusion of fast-

diffusing reactant, H2, compared to the slow-diffusing reac-

tants, CH4 and O2 [46], resulting in a rapid reduction in H2

concentration as mixture approaches the active reaction zone.

3.3. H and OH radical behaviors

The flame structure in Fig. 4 indicates that H and OH radicals

have the highest concentrations among all radicals in the

premixed methane–hydrogen–air flames. This behavior is due

to the strong correlation between laminar burning velocity

and peak concentration of H in the reaction zone of premixed

flames as observed by Padley [47] and Butler [48]. Based on

flame structure analysis, this correlation is also to be observed

in the premixed flames of this study.

Fig. 5 gives laminar burning velocity and maximum mole

fraction of H, OH and HþOH in the reaction zone for the

methane–air flames. The results show that, comparing with

the maximum H and OH concentrations, the most robust

Fig. 5 – Laminar burning velocities and peak H, OH and

H D OH mole fraction in the reaction zone of methane–air

flames.

correlation between laminar burning velocities and radical

concentrations for laminar premixed methane–air flames is

demonstrated when using maximum mole fraction of HþOH

in the flames. The scattering degree for the correlation of

laminar burning velocity as a function of maximum mole

fraction of HþOH is small in this study. Therefore, these

results demonstrate an existing best-fitting correlation

between laminar burning velocity and maximum mole frac-

tion of HþOH for methane–air flames as following,

ulðm=sÞ ¼ 0:07929þ 22:92321ðXH þ XOHÞmax (4)

where XH and XOH are mole fractions of H and OH in the

reaction zone, respectively.

Fig. 6 shows laminar burning velocity and peak mole

fraction of HþOH at different hydrogen fractions at three

equivalence ratios. Enhancement of chemical reaction with

hydrogen addition is resulted from the increase of H, O and OH

mole fractions as hydrogen is added. Good linear-fit correla-

tion is existed between laminar burning velocity and peak

HþOH mole fraction. Laminar burning velocity is increased

with the increase of peak HþOH mole fraction. The formulas

are as follows,

Fig. 6 – Laminar burning velocity and peak H D OH mole

fraction for different hydrogen fractions at three

equivalence ratios.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7 6551

ulðm=sÞ ¼ �0:16786þ 53:65323ðXH þ XOHÞmax for f ¼ 0:8 (5)

ulðm=sÞ ¼ �0:26365þ 48:21428ðXH þ XOHÞmax for f ¼ 1:0 (6)

ulðm=sÞ ¼ �0:24373þ 44:85874ðXH þ XOHÞmax for f ¼ 1:2 (7)

3.4. Adiabatic flame temperature and Zeldvoich number

Hydrogen addition will increase the laminar burning velocity.

One reason is the increase of H radical concentration as

hydrogen is added, and another is the increase of adiabatic

flame temperature Tad as hydrogen is added. Adiabatic flame

temperature through Arrhenius kinetics exerts an influence

on laminar burning velocity. The clear evidence of such strong

dependence is the close correlation between ul and Tad as

shown in Fig. 7 for methane–air and hydrogen–air flames. In

methane–air mixture, the two factors not only give the same

pattern but they give their peak on the rich side with close

equivalence ratios. At the same Tad, laminar burning velocity

of fuel-lean mixtures and fuel-rich mixtures almost give the

same value except at high rich conditions. However, in

hydrogen–air mixture, this correspondence is offset in which

Tad shows its peak at f ¼ 1:1 while ul gives peaks at f ¼ 1:8, as

shown in Fig. 7b. This sufficiently off-stoichiometric peak of ul

at rich side is a consequence of the highly diffusive nature of

hydrogen. Specially, since ulwffiffiffiffiffiLep

and the freestream Le in

Fig. 7 – Unstretched laminar burning velocity and adiabatic

flame temperature of methane–air and hydrogen–air

mixtures.

sufficiently lean and rich hydrogen–air mixtures are 0.33 and

2.3 respectively. The effect of Le is to reduce ul on the fuel-lean

side but to increase ul on the fuel-rich side, leading to the peak

value of ul toward the rich side. The gradient of ul on the fuel-

lean side shows larger decreasing compared with that on the

fuel-rich side [49].

The temperature profiles of the stoichiometric methane–

hydrogen–air flames are given in Fig. 8a. The figure shows that

at small hydrogen fraction, hydrogen addition has a little

influence on the temperature. The equilibrium adiabatic

flame temperature will increase only 15 K from methane–air

flame to methane–hydrogen–air flame with 40% hydrogen

fraction but another 120 K increase in temperature will reach

when hydrogen fraction is increased from 40% to pure

hydrogen–air flame. The curves of ul and Tad versus hydrogen

fraction also give the same trend as shown in Fig. 8b.

Asymptotic analyses of Zeldovich and co-workers [50]

expressed laminar burning velocity in terms of the square root

of Arrhenius expression in adiabatic flame temperature Tad

with overall activation energy, Ea. Peters and Williams [51]

have derived an asymptotic structure of the flame that intro-

duced the inner layer temperature T0 in fuel consumption.

The inner layer temperature characterizes the balance

between chain-branching reactions and chain-breaking effect

of the fuel consumption and recombination reactions, and is

interpreted as the critical temperature ‘‘at and above which

chemical reactions take place’’ [52]. Peters and Williams [51]

Fig. 8 – Temperature profiles and comparison of ul and Tad

at different hydrogen fractions.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 76552

expressed the activation temperature Ea=R in terms of mass

flux(ruul) and adiabatic flame temperature(Tad) as following,

Ea

R¼ �d2½lnðruulÞ�

dð1=TadÞ(8)

where R denotes universal gas constant, and ru, ul are the

unburned gas density and the unstretched laminar burning

velocity, respectively. The differential is evaluated by calcu-

lating ruul at given hydrogen fraction and equivalence ratio,

and by slightly varying its value through the substitution of

a small quantity of nitrogen by inert argon [53].

Integration of Eq. (8) gives the Eq. (9),

2lnðruulÞ ¼ �Ea

R1

Tadþ C (9)

where C is the integration constant.

Therefore, ul can be expressed as,

ul ¼expð0:5CÞ

ru

exp

�� Ea

2R1

Tad

�(10)

The activation temperature Ea=R can be derived from the

linear plot of 2lnðruulÞ against 1=Tad. Fig. 9 gives the variation

of 2ln(ruul) with 1=Tad at different hydrogen fractions for the

stoichiometric flame. The value of Ea=R is decreased with the

increase of hydrogen fraction. C is also the function of

hydrogen fraction. Values of Ea=R and C are tabulated in

Table 2.

As mentioned above, is the inner layer temperature which

represents the crossover temperature between chain-

branching and chain-termination reactions. Within the

temperature profile of a premixed flame, it demonstrates

a transition position from inert preheat zone to reaction zone,

and this is also the position where the second derivative

vanishes and the gradient gives the maximum value. Fig. 10

gives the temperature profiles, the first derivative of temper-

ature and the second derivative of temperature at various

hydrogen fractions. The results show that T0 is decreased with

the increase of hydrogen fraction and this is consistent with

the tendency of overall activation energy (Ea). Based on

Fig. 9 – Variation of 2lnðruulÞ with 1/Tad at different

hydrogen fractions.

fundamental combustion theory [54], the easier occurrence of

combustion reaction of H2–air mixture than that of CH4–air

mixture is due to low activation energy of hydrogen compared

with that of methane. With the increase of hydrogen fraction,

the activation energy of methane–hydrogen mixture is

decreased because the critical temperature or transition

temperature (T0) is decreased. The values of Ea and T0 at

different hydrogen fractions are also tabulated in Table 2.

From the value of Ea=R, the Zeldovich number, Ze can be

calculated [53,55,56] by,

Ze ¼ Ea

RTad � Tu

T2ad

(11)

Zeldovich number (Ze) is a dimensionless form of overall

activation energy. It represents the sensitivity of chemical

reactions to the variation of maximum flame temperature,

and the inverse of it physically denotes an effective dimen-

sionless width of the reaction zone [57]. Fig. 11 gives the

variation of Zeldovich number against hydrogen fraction for

the stoichiometric mixtures. The figure shows that Ze is

largely influenced by hydrogen addition. The increase of

hydrogen fraction results in the decreasing of Ze because of

the decrease of inner flame temperature (T0). This behavior

reflects the controlling influence of the flame temperature

which increases with the increase of XH2. This facilitates the

temperature-sensitive two-body branching reactions relative

to the temperature-insensitive three-body termination reac-

tions [53], leading to overall faster reactions and reducing

overall activation energy with the increase of XH2.

3.5. Effect of hydrogen addition on NO formation

In the combustion of fuels that contain no nitrogen, nitric

oxide (NO) is formed by three chemical mechanisms or routes

that involve nitrogen from the air. They are thermal or Zel-

dovich mechanism, prompt or Fenimore mechanism, and

N2O-intermediate mechanism [54]. Thermal mechanism

dominates in high-temperature combustion over a wide range

of equivalence ratios, while prompt mechanism is particularly

important in fuel-rich combustion. It appears that the N2O-

intermediate mechanism plays an important role in the

production of NO in the high lean and low-temperature

combustion process.

Fig. 12 gives NO mole fraction profiles as a function of

distance at different equivalence ratios. The figure demon-

strates that near the stoichiometric mixture (f ¼ 0:9 and

f ¼ 1:0), formation of nitric oxide is almost completed at the

distance greater than 8 cm from the flame front. Because of

the high flame temperature near the stoichiometric mixtures,

the NO formation is resulted from the Thermal NO mecha-

nism. While in fuel-rich flames (f ¼ 1:2 and f ¼ 1:3), there are

a lot of CH radicals in the flame front and the flame temper-

ature is lower, so NO formation is resulted from the Fenimore

prompt-NO mechanism which occurs within the flame front.

At fuel-lean premixed combustion (f ¼ 0:6 andf ¼ 0:7), NO

formation is also almost completed at the distance of 8 cm

from the flame front. NO is generated via N2O mechanism,

which is analogous to the thermal mechanism in that O-atom

attacks molecular nitrogen. This reaction has been often over-

estimated since it is usually an insignificant contributor to the

Table 2 – Summary of calculation conditions (0.1 MPa, 303 K, f[1:0).

XH2 /% Tad/K T0/K ul/m/s Ea/R/K C Ea/kJ/mol Ze

0 2230 1332 0.406 35,183 14.191 292.46 13.63

20 2236 1308 0.463 34,491 14.034 286.71 13.34

40 2245 1245 0.555 34,255 14.144 284.74 13.20

60 2259 1188 0.725 33,404 14.131 277.67 12.80

80 2289 1130 1.147 31,300 13.734 260.18 11.86

100 2365 764 2.432 22,846 11.009 189.90 8.42

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7 6553

total NO. However, fuel-lean conditions can suppress the

formation of CH, and hence lead to less Fenimore NO while

low temperatures can suppress the Zeldovich NO. What

remains is NO generated via N2O. All of these circumstances

lead to the N2O route to be the major source of NO in fuel-lean

premixed combustion [58].

Fig. 13 shows the prediction of NO concentrations at 10 cm

downstream from flame front as a function of equivalence

ratio for methane–air flames. The dependence of NO

concentration as a function of equivalence ratio gives two

peak values, in the stoichiometric mixtures due to the Zel-

dovich thermal-NO mechanism and in fuel-rich mixture at

equivalence ratio around 1.3 due to the Fenimore prompt-NO

mechanism, and this is consistent with the results in the

literatures [59,60].

Fig. 14 gives NO mole fraction profiles of methane–

hydrogen–air mixtures at the stoichiometric and rich flames.

In the case of f ¼ 1:0, formation of NO is almost completed at

the distance of 8 cm from the flame front due to the Zeldovich

thermal-NO mechanism. While in the rich flames, the most of

NO is formed within the flame front due to the Fenimore

prompt-NO mechanism. NO is not increased with hydrogen

Fig. 10 – Temperature profiles at different hydrogen

fractions.

addition in both the stoichiometric flames or the rich flames

seem to be some counterintuitive. Usually, one may easily

think that with the addition of hydrogen which itself has high

adiabatic flame temperature, mixtures of methane and

hydrogen will burn at higher temperature than pure methane,

and lead to increasing in NO.

Fig. 15 presents NO mole fraction at 10 cm downstream

from flame front in methane–hydrogen–air flames with

different hydrogen fractions. The figure shows little variance

of NO concentration in the stoichiometric flames with

different hydrogen fractions. As discussed above, the adia-

batic temperature at 10 cm downstream from flame front

gives little variation with the increase of hydrogen fraction.

The same behavior of small temperature variation with

hydrogen addition was found by Gauducheau et al. [26] in

their study of premixed flames.

It is obviously seen that the behavior of premixed but

stretched flames of methane–hydrogen–air mixtures differs

significantly from that of unstretched flames studied in this

study. It was observed experimentally and confirmed

computationally that if the equivalence ratio is kept constant,

the addition of hydrogen to the methane–air flames in a stag-

nation flow, or on the cylinder burner, would increase flame

temperatures significantly [21,32,61]. This leads eventually to

the increase of the NO emissions in stretched flames [32]. This

difference between stretched flame and unstretched flames

can be explained from the preferential diffusion of atomic and

molecular hydrogen, as being analyzed in the literatures [61]

and [62].

Fig. 11 – Zeldovich number versus hydrogen fraction.

Fig. 12 – NO mole fraction of methane–air flame versus

distance at different equivalence ratios.

Fig. 14 – NO mole fraction of methane–hydrogen–air

flames.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 76554

In fuel-rich mixtures (f ¼ 1:3), NO concentration at 10 cm

downstream from flame front is notably decreased with

hydrogen addition. This decrease is apparently due to the

reduced availability of hydrocarbon radicals, which are major

precursors of the Fenimore prompt-NO mechanism.

Considering different responses of stretched and

unstretched flames of both the stoichiometric and rich

mixtures with respect to enrichment by hydrogen, it can be

assumed that, in the real burners, an overall change of NO

emissions is defined not only by mixing mode (premixed or

diffusion flames) but also by turbulent intensity. When the

structure of the real flame approaches the quasi-laminar case,

Fig. 13 – NO mole fraction of methane–air flame at 10 cm

downstream of flame front versus equivalence ratio.

little change or decrease of NO formation with enrichment by

hydrogen is presented. This behavior is supported by the

experimental study of hydrogen addition to methane in

different burners [63–65].

Fig. 15 – NO mole fraction at 10 cm downstream from flame

front versus hydrogen fraction.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 6 5 4 5 – 6 5 5 7 6555

4. Conclusions

Numerical study on laminar premixed methane–hydrogen–air

flames was conducted at room temperature and atmospheric

pressure. The unstretched laminar burning velocity, adiabatic

flame temperature, and radical mole fraction of H, OH and NO

are obtained at various hydrogen fractions and equivalence

ratios. The main conclusions are summarized as follows.

Laminar burning velocity is increased with the increase of

hydrogen fraction. In the case of hydrogen fraction less than

40%, it is the regime of methane-dominated combustion. Here

laminar burning velocity is slightly increased with the

increase of hydrogen addition. When hydrogen fraction is

larger than 40%, laminar burning velocity is exponentially

increased with the increase of hydrogen fraction.

Enhancement of chemical reaction with hydrogen addition

is due to the increase of H, O and OH concentrations in the

flame as hydrogen is added. A strong correlation exists

between burning velocity and peak radical concentrations of

HþOH radicals in the reaction zone of premixed flames. High

burning velocity corresponds to high radical concentration in

the reaction zone.

With the increase of hydrogen fraction, the adiabatic flame

temperature is increased. The overall activation energy of

methane–hydrogen mixture is decreased, and the inner layer

temperature and Zeldovich number are also decreased. This

behavior reflects the controlling influence of the flame

temperature which is increased with the increase of XH2 . This

facilitates the temperature-sensitive two-body branching

reactions relative to the temperature-insensitive three-body

termination reactions.

The curve of NO versus equivalence ratio shows two peaks,

presenting at the stoichiometric mixtures due to the Zeldo-

vich thermal-NO mechanism and at fuel-rich mixtures due to

the Fenimore prompt-NO mechanism. In the stoichiometric

flame, hydrogen addition has little effect on NO, while in the

fuel-rich flames, NO concentration decreased significantly.

The behavior of premixed but unstretched flames of

methane–hydrogen–air mixtures differs significantly from

that of stretched flames.

Acknowledgments

This study is supported by National Basic Research Program of

China (Grant No. 2007CB210006) and National Natural Science

Foundation of China (Grant Nos. 50636040 and 50821604).

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