A study of NOx formation in hydrogen flames

International Journal of Hydrogen Energy 32 (2007) 3572 – 3585 www.elsevier.com/locate/ijhydene

A study of NOx formation in hydrogen flames Martin Skottene1 , Kjell Erik Rian ∗ Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 23 December 2006; received in revised form 27 February 2007; accepted 27 February 2007 Available online 18 April 2007

Abstract The aim of this work is to improve the knowledge of modeling NOx formation in hydrogen flames. Four different detailed reaction mechanisms have been tested for eight laminar flames, and two of these mechanisms have been tested for a turbulent jet flame. The numerical results have been compared with experimental data from the literature. Sensitivity and integral reaction flow analyses are applied to identify important reaction steps. Formation of NO through NNH radicals was found to be important in the hydrogen-air flames investigated. This work suggests that the H2 /O2 mechanism of Li et al. for pure hydrogen combustion may be combined with the N/H/O subset from Glarborg et al. for prediction of NOx in hydrogen-air flames. However, the pressure-dependency of the reaction N2 O + M   N2 + O + M should be further investigated and accounted for. For the turbulent hydrogen jet flame, the agreement between the predicted and measured NO levels was better with the mechanism of Glarborg et al. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Hydrogen combustion; NO formation; Modeling; Detailed mechanism

1. Introduction In the past few years, hydrogen has obtained a lot of attention as a future energy carrier. Combustion of hydrogen is relevant in fuel-cell afterburners, in power production with CO2 capture, and in utilization of biomass and waste. However, the use of hydrogen in conventional combustion equipment is not straightforward since hydrogen has some characteristics that strongly deviate from the main components of conventional fuels such as methane. Hydrogen has a high molecular diffusivity, a wide flammability range, a high laminar flame speed, and requires low ignition energy. Hydrogen combustion may give high temperatures, causing high levels of NOx when air is the oxidizer. The NOx formation can be reduced by using lean combustion or partly premixed combustion. However, this may lead to stability problems and possibility for flashback. One major technological challenge is to maintain both a high hydrogen content of the fuel and acceptable levels of NOx emissions. This requires new or modified existing combustion equipment for hydrogen ∗ Corresponding author. Tel.: +47 73593094; fax: +47 73593580.

E-mail address: [email protected] (K.E. Rian). 1 Present address: Det Norske Veritas, N-1322 HZvik, Norway.

combustion. Today, computational fluid dynamics (CFD) is an established tool in the development of combustion technology. This tool requires reliable models, e.g. for the chemistry of hydrogen combustion and its interaction with turbulent flow. A detailed model of the chemical kinetics is necessary to obtain accurate numerical predictions of the NOx emissions from a hydrogen combustor. The objective of this study is to improve the knowledge of modeling NOx formation in hydrogen flames. The H2 /O2 kinetics is important for accurate prediction of NOx formation. Recently, kinetic mechanisms made for hydrogen combustion have been tested against experiments by Ströhle and Myhrvold [1]. They found that the mechanism of Li et al. [2] was best suited for the prediction of H2 /O2 chemistry over a large range of conditions, and particularly for gas turbine conditions. The present work explores quantitatively the combination of the H2 /O2 mechanism by Li et al. with two different N/H/O subsets. First, a review of the important reaction steps for NOx formation in hydrogen flames is given. This is followed by a brief description of the selected kinetic mechanisms. Then, results from numerical simulations of eight laminar hydrogen flames and a turbulent hydrogen jet flame are compared with existing

0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.02.038

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

experimental data. Four different detailed reaction mechanisms were tested for each of the laminar flames, and numerical results from two different reaction mechanisms are compared with experimental data for the turbulent flame. In addition, results from sensitivity analyses of one of the laminar flames and results from integral reaction flow analyses of three of the laminar flames are presented and discussed. 2. NOx mechanisms in hydrogen flames A large number of elementary reactions contribute to the formation of nitrogen oxides (NO and NO2 ) in combustion, see e.g. [3]. The primary nitrogen oxide formed in combustion systems is NO, although significant amounts of NO2 can be produced due to conversion from NO in low-temperature mixing regions of nonpremixed systems [4, p. 269]. Three routes have been found important for NO formation in hydrogen flames [5]. These are the thermal route, the N2 O route, and the NNH route. The thermal NO or Zeldovich NO sub-mechanism consists of three elementary reactions [6,7], O + N2   NO + N,

(1)

N + O2   NO + O,

(2)

N + OH   NO + H.

(3)

Reaction (1) is both initiating and rate limiting. It is strongly dependent on temperature because of a high activation energy. Thermal NO is therefore important at high temperatures in flames. The essential reactions of the N2 O route are [7,8] N2 + O + M   N2 O + M,

(4)

N2 O + O   NO + NO,

(5)

N2 O + H   NO + NH.

(6)

For this route, the formation of NO is promoted at high pressures due to the presence of a third body, M, in reaction (4). At the same time, three-body reactions have typically a low activation energy. The effect is that low temperatures do not affect the formation rate of NO as much as in the thermal NO route. The N2 O route is also promoted at lean combustion. A few years ago, Bozzelli and Dean [9] proposed a new route for NO formation through NNH radicals. The essential reactions of the NNH route are N2 + H   NNH,

(7)

NNH + O   NO + NH.

(8)

The NNH route and the N2 O route are linked by the reaction [9] NNH + O   N2 O + H.

(9)

The NNH pathway appears to be important at flame fronts and other areas where relatively high concentrations of H and O radicals are present. Although Haworth et al. [10] state that reaction (8) represents a minor route to NO in most combustion

3573

systems, work by other researchers suggest that the NNH route can be especially important in hydrogen flames. Experimental evidence for the NNH mechanism has been found by Harrington et al. [11] in low-temperature (∼ 1200 K), low-pressure, premixed rich flames of hydrogen and air. Further experimental support for the NNH mechanism has been found in rich flames of H2 /O2 /N2 and CH4 /O2 /N2 at 1 atm [12], for lean combustion of hydrogen and air in a stirred reactor [13], and in H2 /CO flames diluted by CO2 [14]. A study by Charlston-Goch et al. [15] shows that NO formation through NNH may be important in premixed flames of CO/H2 /CH4 (synthesized coal-gas) and air at high pressures. Moreover, evaluations of the NNH route for hydrogen flames by Konnov and co-workers [5,13,16,17] show that this pathway is important at all temperatures at short residence times. At temperatures of 2100 K and higher, the thermal NO route becomes dominant after 1 ms. Recently, Konnov et al. [5,16,18] have suggested a new possible route for NO formation via N2 H3 radicals in hydrogen flames. From kinetic modeling of hydrogen combustion in stirred reactors, they found that this mechanism can be of importance in rich mixtures at relatively low temperatures (below 1500 K) when other routes of NO formation are suppressed. Molecular nitrogen is here believed to transform and eventually oxidize through the path: N2 → NNH → N2 H2 → N2 H3 → NH3 (NH2 ) → NH → N → NO. However, experimental evidence of the N2 H3 route has not been found in the literature. This route has not been included in the present analysis. 3. Selected reaction mechanisms for hydrogen combustion Historically, the H2 /O2 system was the first combustion mechanism to be developed for a practical fuel. In the combustion literature, most kinetic mechanisms are reported for hydrocarbon fuels. These mechanisms contain sub-mechanisms for H2 /O2 and NOx chemistry which can be used for hydrogen combustion modeling. Such H2 /O2 subsets can also be further optimized for pure hydrogen combustion. Here it is important to emphasize that the accuracy of the H2 /O2 kinetics will have a strong effect on the accuracy of the NOx predictions due to its effect on the flame temperature and the concentrations of H and O radicals. Updated detailed mechanisms for H2 /O2 combustion can be found in the literature, see for example [2,5,7,19]. Based on the findings from a recent evaluation of H2 /O2 mechanisms [1], the mechanism of Li et al. [2] has been selected here for further studies. However, this kinetic mechanism lacks NOx chemistry. It is therefore suggested to combine the H2 /O2 mechanism of Li et al. (later denoted as the “Li” mechanism for short) with an N/H/O subset from another kinetic mechanism. Since reactions producing NOx normally are consuming minimal amounts of radicals like H and O in the H2 /O2 chemistry, it is reasonable to assume that the NOx chemistry will not alter the H2 /O2 chemistry significantly. Another aspect of combining kinetic mechanisms from different sources is the consistency of the thermodynamic data for the combined kinetic mechanism. A reaction mechanism is usually given as a set of reversible reactions, and the reaction constants are normally presented only for the forward

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reactions. Thermodynamic data are used to calculate the reaction rate coefficients for the reverse reactions. Therefore, the same thermodynamic data should be used for calculating the reverse reactions in both the H2 /O2 chemistry and the NOx chemistry. Two mechanisms made for combustion of hydrocarbons, including NOx formation, are the kinetic mechanism of Glarborg et al. [20] and the kinetic mechanism from the University of California at San Diego [21]. When reactions with carbon are omitted, these mechanisms model pure hydrogen combustion. The kinetic mechanism of Glarborg et al. [20], without reactions with carbon, is denoted here as the “G” mechanism for short, and the kinetic mechanism from the University of California at San Diego [21], without reactions with carbon, is similarly denoted here as the “SD” mechanism for short. Two new mechanisms are then suggested here by replacing the H2 /O2 subsets of the G mechanism [20, reactions (1)–(22)] and the SD mechanism [21, reactions (1f)–(19f)] with the H2 /O2 chemistry of the Li mechanism [2, reactions (1)–(19)]. The new mechanisms are denoted as “LiG” and “LiSD”, respectively. In this work, thermodynamic data from Li et al. [2] are used for the H2 /O2 chemistry in both of the combined mechanisms. Differences in thermodynamic data for the H2 /O2 chemistry between the Li mechanism, the G mechanism, and the SD mechanism were only found for OH and HO2 . The thermodynamic data for the H2 /O2 chemistry were otherwise the same for all four mechanisms. The effect of the selection of thermodynamic data for OH and HO2 has been investigated for a counterflow, laminar hydrogen-air diffusion flame. The investigation showed that the present selection of thermodynamic data for OH and HO2 did not have a significant effect on the NO prediction for the tested flame [22]. Transport data from the G mechanism [20] are used for the LiG mechanism, and transport data from the SD mechanism [21] are used for the LiSD mechanism. No difference was found between transport data for common species of the Li, G, and SD mechanism and for common species of the G and SD mechanism. 4. Numerical simulations of laminar flames Numerical simulations of various one-dimensional, laminar hydrogen flames have been carried out to test the four selected reaction mechanisms. The simulations have been performed with the software system CHEMKIN 4.0.1 [23], and effects of multicomponent transport and thermal diffusion (the Soret effect) were included in the computations. The results are compared with measurements found in the literature. 4.1. Opposed-flow hydrogen-air diffusion flames Five different opposed-flow hydrogen-air diffusion flames have been simulated numerically, and the results are compared with experimental data obtained from RZrtveit et al. [24]. The counterflow burner simulated in this work had two coaxial ducts placed one above the other. The inside diameter of both ducts were 20 mm, and the distance between the ducts was

Table 1 Selected opposed-flow diffusion flames Fuel stream (%) H2 30.0 35.0 40.0 45.0 30.0

Flow (cm/s)

Eqv. ratio

O2

N2

Vfuel

Vair



premix

5.5

70.0 65.0 60.0 55.0 64.5

38.038 39.311 40.744 42.335 37.815

31.735 31.735 31.735 31.735 31.735

0.9 1.0 1.2 1.4 0.9

2.7

12.7 mm. The flames were laminar, and the flow in the ducts had a Reynolds number of ∼ 400. Fuel and air met in a stagnation plane at atmospheric pressure. In four of the flames, the fuel was a mixture of hydrogen and nitrogen. The fifth flame was a partially premixed flame where the fuel was a mixture of hydrogen, nitrogen and oxygen. In the simulations, an inlet temperature of 300 K was used for the fuel and the air. Relevant data of the simulated flames are given in Table 1, and further details of the experiments can be found in [24]. The opposed-flow flame reactor model in Chemkin 4.0.1. [23] was applied, and an adaptive grid was automatically generated by the code. The grid was refined until grid-independent solutions were achieved. Numerical results are compared with experimental data for the opposed-flow flames in Fig. 1 where the temperature and the mole fraction of NO are given as a function of the distance from the fuel outlet. The temperature profiles in Fig. 1 show that the G mechanism underpredicts the maximum temperature for these flames. The maximum temperatures calculated with the G mechanism are about 90 K below the maximum temperatures calculated with the other mechanisms. Since a lower flame temperature should lead to less thermal NO, it is somewhat unexpected that the G mechanism produces too much NO, as seen in Figs. 1(b), (d), (f), (h), and (j). This indicates that also other routes than the thermal NO route are contributing significantly to the NO formation predicted by the G mechanism. The temperature profiles calculated with the LiG, LiSD, and SD mechanisms are coinciding almost completely for the laminar diffusion flames in Figs. 1(a), (c), (e), and (g). This could be expected for the LiG and LiSD mechanisms since these mechanisms use exactly the same H2 /O2 subset. For the partly premixed flame, the width of the flame zone shows some variation for the different chemical mechanisms, see Fig. 1(i). However, the temperature profiles calculated with the LiG, LiSD, and SD mechanisms are also here coinciding almost completely in the high-temperature zone of the flame. Although the calculated temperature profiles seem to be a little narrower than the measured temperature profiles, the agreement between the temperature profiles calculated with the LiG, LiSD, and SD mechanisms and the measured temperatures is relatively good for all the tested fuel compositions. The mole fraction profiles of NO given in Figs. 1(b), (d), (f), (h), and (j) show that the LiG mechanism is in better agreement with the measurements than the G mechanism is. The predicted mole fractions of NO are still overpredicted compared to the

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

measurements in the high-temperature zone of the flames. However, NO measurements in flames are not trivial, and experimental errors should also be addressed. Due to removal of NO by chemical reactions on the quartz probe walls during sampling, the actual NO concentrations are believed to be a little higher than measured [24]. This may indicate that the LiG mechanism is the best suited mechanism among the tested mechanisms for the present laminar diffusion flames. The LiSD mechanism and the SD mechanism seem to underpredict the NO levels, especially for the most diluted hydrogen diffusion flame. A sensitivity analysis has been performed for each of the mechanisms to find rate-limiting reaction steps for the NO

G LiG LiSD SD exp

12 XNO (ppm)

T (K)

1500

formation. The relative sensitivities of the NO concentration to the reaction rate coefficients were calculated for the laminar diffusion flame which had a fuel composition of 60% N2 and 40% H2 (on a molar basis). The sensitivities were calculated at x = 0.69 cm, i.e. the location in the flame where both the temperature and the NO concentration are the highest. The H2 /O2 and N/H/O reactions to which the NO concentration is most sensitive are listed in Table 2. The corresponding relative sensitivities are presented in Fig. 2. The rate laws of reaction (II), (III), (IV), (VI), (XIV), and (XV) in Table 2 are modeled differently in the investigated mechanisms. Furthermore, the Arrhenius parameters are given

14

G LiG LiSD SD exp

2000

1000

10 8 6 4 2

500

0 0.4

0.6

0.8

1

1.2

0.4

0.6

x (cm)

20

1

1.2

G LiG LiSD SD exp

15 XNO (ppm)

1500

0.8 x (cm)

G LiG LiSD SD exp

2000

T (K)

3575

1000

10 5

500 0 0.4

0.6

0.8 x (cm)

1.2

0.6

0.8 x (cm)

1000

1

1.2

G LiG LiSD SD exp

25 XNO (ppm)

1500

0.4

30

G LiG LiSD SD exp

2000

T (K)

1

20 15 10 5

500

0 0.4

0.6

0.8 x (cm)

1

1.2

0.4

0.6

0.8

1

1.2

x (cm)

Fig. 1. Laminar, opposed-flow flames. Numerical results (lines) from four different chemical mechanisms compared with experimental data (symbols). (a) Fuel: 70% N2 , 30% H2 ; (b) fuel: 70% N2 , 30% H2 ; (c) fuel: 65% N2 , 35% H2 ; (d) fuel: 65% N2 , 35% H2 ; (e) fuel: 60% N2 , 40% H2 ; (f) fuel: 60% N2 , 40% H2 ; (g) fuel: 55% N2 , 45% H2 ; (h) fuel: 55% N2 , 45% H2 ; (i) fuel: 64.5% N2 , 30% H2 , 5.5% O2 ; (j) fuel: 64.5% N2 , 30% H2 , 5.5% O2 .

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

1500

T (K)

40

G LiG LiSD SD exp

2000

G LiG LiSD SD exp

35 30

XNO (ppm)

3576

1000

25 20 15 10

500

5 0.4

0.6

0.8 x (cm)

0.4

0.6

0.8 x (cm)

12

1000

1

1.2

G LiG LiSD SD exp

10

XNO (ppm)

1500

0

1.2

G LiG LiSD SD exp

2000

T (K)

1

8 6 4 2

500

0 0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6

0.4

x (cm)

0.6

0.8 x (cm)

1

1.2

Fig. 1. (continued).

Table 2 Reactions to which the NO concentration is sensitive No.

Reaction

I II III IV V VI VII VIII IX X XI XII XIII XIV XV

 O + OH H + O2  H+H+M  H2 + M H + OH + M   H2 O + M H + O2 + M   HO2 + M NH2 + NO   NNH + OH NH + NO   N2 O + H N + NO   N2 + O NNH   N2 + H NNH + H   N2 + H2 NNH + O   N2 O + H NNH + O   NH + NO NNH + O2   N2 + HO2 NNH + O2   N2 + O2 + H N2 O + M   N2 + O + M N2 O + H   N2 + OH

for the backward reaction step for reaction (I) in the G mechanism, for reaction (II) in the LiG and LiSD mechanisms, and for reaction (VII) in the SD and LiSD mechanisms. The reaction rate coefficient for reaction (IV) is modeled as pressure dependent, except from in the G mechanism. Similarly, the reaction rate coefficient for reaction (XIV) is modeled as pressure dependent, except from in the G and LiG mechanisms. It should also be noticed that the reactions (XI), (XII), and (XIII) are not included in the SD and LiSD mechanisms. The results of the sensitivity analysis for the NO concentration show that the highest relative sensitivity is obtained for reaction (VII) for the LiG, SD, and LiSD mechanisms. The backward reaction step of reaction (VII) is the well-known initiating

reaction step for thermal NO, cf. Eq. (1). For the G mechanism, it is observed that the rate-limiting steps are reactions (VI) and (XI). These reactions are representatives of the N2 O route and the NNH route, respectively. Although the G mechanism and the LiG mechanism contain the same N/H/O reactions, the relative sensitivity for reaction (VII) is considerably higher for the LiG mechanism than for the G mechanism. This is reasonable since the LiG mechanism predicts a higher flame temperature than the G mechanism. The sensitivity analyses show that sensitive reactions can be found from the thermal route, the N2 O route, and the NNH route for this hydrogen diffusion flame. Seven reversible reactions with NNH are listed in Table 2 as sensitive reactions with regard to NO formation. Well-modeled rate coefficients are required for these reactions for reliable NO predictions. NO is formed directly from NNH through reaction (XI), and the reaction is important as it is the most sensitive of the NNH reactions in the G and LiG mechanisms in this case. However, reaction (XI) is not included in the SD and LiSD mechanisms. The other reaction that provides a direct link between NO and NNH is reaction (V), and this reaction is included in all four mechanisms. From Fig. 2 it is observed that the NO concentration is more sensitive to reaction (V) in the SD and LiSD mechanisms than to the same reaction in the G and LiG mechanisms. Since reaction (V) is the only direct path from NNH to NO in the SD and LiSD mechanism, the NO concentration is expected to be more sensitive to this reaction. A similar effect may be expected for reaction (X). Reaction (X) links the NNH route to the N2 O route. When reaction (XI) is omitted, the NO concentration becomes more sensitive to reaction (X).

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

0.7

G LiG LiSD SD

0.6 0.5 Relative sensitivity

3577

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

XIII XIV

XV

Fig. 2. Sensitivity analysis for the NO concentration of the laminar, opposed-flow hydrogen-air diffusion flame with fuel composition of 60% N2 and 40% H2 . Relative sensitivities for the G, LiG, LiSD, and SD mechanisms.

For the present flame, the NO concentration is sensitive to reactions (VI), (XIV), and (XV) from the N2 O mechanism. Reaction (XIV) is the pressure-dependent reaction from the N2 O route. The reaction rate coefficient is modeled as pressure dependent in the SD and LiSD mechanisms, but not in the G and LiG mechanisms. This should be taken into consideration if NO formation in high-pressure hydrogen combustion is studied. To identify the reaction paths that produce the most NO in the opposed-flow diffusion flame with the fuel composition of 60% N2 and 40% H2 , integral reaction flow analyses were performed for the G, LiG, and LiSD mechanisms. Since the SD and the LiSD mechanism gave almost similar results, an integral reaction flow analysis will not be presented here for the SD mechanism. The results from the integral reaction flow analyses are presented by the reaction flow diagrams in Figs. 3–5. The thickness of the arrows in these figures is scaled corresponding to the formation rates given in 10−9 mol/s, where white arrows illustrate a 10 times greater formation rate than black arrows of the same thickness. Only reaction paths from N2 to NO are presented in the reaction flow diagrams in Figs. 3–5. When comparing these reaction flow diagrams, one should be aware of that there is a recirculation of NO, through the path NO → HNO → H2 NO → NH2 → NH, that contributes to the rate of formation of NH for the G and LiG mechanisms. It is observed that more N and NO are produced from NH for the G and LiG mechanisms than for the LiSD mechanism, cf. Figs. 3–5. Since the G mechanism and the LiG mechanism have the same NOx chemistry, but not the same H2 /O2 chemistry, a comparison of Figs. 3 and 4 shows the effect of the H2 /O2 chemistry applied. It is interesting to observe that the NNH and N2 O routes together produce more NO than the thermal route for both the G and LiG mechanism in this case. It is also observed that the LiG mechanism gives 80% more thermal NO than the G mechanism. This can be explained by the higher maximum flame temperature which is predicted by the LiG mechanism.

On the other hand, the G mechanism produces 118% more NO directly from NNH compared to the LiG mechanism. In addition, the NO formation through N2 O is 35.7% higher for the G mechanism compared to the LiG mechanism. Here the NNH route is the dominating path of NO formation for the G mechanism, and this seems to be the main reason why the G mechanism gives the highest level of NO. The formation of NO from NNH is an important mechanism in flame regimes where the concentration of H and O radicals is high, such as in flame fronts [9]. The results from the local sensitivity analysis, see Table 2 and Fig. 2, show that the NO formation is sensitive to NNH reactions where these radicals are essential. Predicted mole fraction profiles of H and O radicals from the G and LiG mechanisms for the present flame are given in Fig. 6. Here the G mechanism predicts about 40–50% more O and H than the LiG mechanism, which provides good conditions for the NNH route. The LiG mechanism has a H2 /O2 chemistry made for hydrogen flames, so this mechanism should probably give the most realistic concentrations of H and O. From the results of the present calculations the predicted temperatures and NO concentrations were also found to be in better agreement with experimental data for this mechanism. A comparison of Figs. 4 and 5 shows the effect of the different N/H/O subsets applied, since the H2 /O2 chemistry is the same for the LiG and LiSD mechanisms. The most important difference between the two mechanisms is that the LiSD mechanism lacks the direct reaction path from NNH to NO, see reaction (8). This appears to be the main reason why the SD and LiSD mechanisms give less NO than the G and LiG mechanisms. Since this reaction path is a significant path to NO in many hydrogen flames [5], the omission of it will be a disadvantage with the SD and LiSD mechanisms. From Figs. 4 and 5, it is observed that the NO formation from thermal NO is quite similar. This is because the predicted temperature is almost the same. The LiSD mechanism produces much more N2 O from NNH compared to the LiG mechanism,

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4.6

+H, +OH

NH 1.9

5.6

N

+O

+OH, +O2 NO

1.0 +O

163.9

+H, +O2+H NNH

N2

157.9

2.4

+O

+H, +O, +OH, +O2 4.4 +O

13.2

+O+M

15.1

1.9

+H

+H

N2O

Fig. 3. Reaction flow diagram for the G mechanism for the laminar, opposed-flow hydrogen-air diffusion flame with fuel composition of 60% N2 and 40% H2 . The formation rates are given in 10−9 mol/s.

2.6

+H, +OH

NH 0.9

4.3

N

+O

+OH, +O2

NO 1.8 +O

90.3

+H, +O2+H NNH

N2

87.2

1.1

+O

+H, +O, +OH, +O2 1.9 +O

9.5 +O+M 9.6 +H

N2O

1.4

+H

Fig. 4. Reaction flow diagram for the LiG mechanism for the laminar, opposed-flow hydrogen-air diffusion flame with fuel composition of 60% N2 and 40% H2 . The formation rates are given in 10−9 mol/s.

1.5

+H, +OH

NH 0.4

3.0

N

+O

+OH, +O2

NO 1.9 +O

44.1

+H NNH

N2

39.6

+H, +OH 4.4 +O

1.2 +O+M 0.7 4.8 +H, +OH

+H

N2O

Fig. 5. Reaction flow diagram for the LiSD mechanism for the laminar, opposed-flow hydrogen-air diffusion flame with fuel composition of 60% N2 and 40% H2 . The formation rates are given in 10−9 mol/s.

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

10000

4000 G LiG

8000

G LiG

3500 3000

6000

XO (ppm)

XH (ppm)

3579

4000

2500 2000 1500 1000

2000

500 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

1

x (cm)

x (cm)

Fig. 6. Mole fraction profiles of H and O radicals predicted by the G and LiG mechanisms for the laminar, opposed-flow hydrogen-air diffusion flame with fuel composition of 60% N2 and 40% H2 .

1.2

0.8 0.6 0.4 0.2 0

G LiG LiSD SD exp

1 XNO (ppm)

1 XNO (ppm)

1.2

G LiG LiSD SD exp

0.8 0.6 0.4 0.2

0

0.5

1

1.5

x (cm)

2

0

0

0.5

1

1.5

2

x (cm)

Fig. 7. Mole fraction profiles of NO for the premixed hydrogen-air flames at 0.05 bar (38 torr) and 0.1 bar (78 torr). Numerical results (lines) from four different chemical mechanisms compared with experimental data (symbols). (a) 0.1 bar; (b) 0.05 bar.

but it produces less NO from N2 O. The LiG mechanism produces twice as much NO directly from N2 O as the LiSD mechanism does. The reason for this can be the different reaction constants used for chemical reactions with N2 O, cf. [20,21]. For the N2 O route, reaction (5) was not as important as reaction (6) for the NO formation in the present case. 4.2. Low-pressure, premixed hydrogen-air flames Harrington et al. [11] have published experimental data for two laminar, premixed hydrogen-air flames at pressures of 0.05 bar (38 torr) and 0.1 bar (78 torr). The total flow rate in the experiments was 6 l/min of hydrogen and air at an equivalence ratio of  = 1.5, and a 6-cm-diameter McKenna burner was applied. The design of these experiments minimized the amount of NO produced through the thermal route and the N2 O route, and this gives an opportunity to study NO formation from the NNH mechanism. Since the NNH reactions represent a major difference between the N/H/O subsets applied in the present work, it would be of interest to compare numerical predictions with experimental data from these experiments.

The one-dimensional, premixed, laminar flame model in Chemkin 4.0.1 [23] was applied for the present numerical predictions. A measured temperature profile [11] was used in the simulations, and the energy equation was therefore not solved. Numerical simulations with up to 8000 grid nodes were performed to check the grid independency of the solutions. A grid resolution of 600 nodes was found sufficient to give grid-independent solutions for the present purposes. The predicted mole fraction of NO, as a function of the distance from the burner outlet, is compared with experimental data in Fig. 7. Compared to the experimental data, the SD and LiSD mechanisms predict negligible amounts of NO at both 0.05 and 0.1 bar. This is expected because these mechanisms lack the important reaction NNH + O   NH + NO. For the G and LiG mechanisms, the predicted peak mole fractions and profiles of NO agree reasonably well with the measurements at 0.1 bar. It is observed that the LiG mechanism underpredicts the NO level to some extent compared to the measured NO profile at this pressure. At 0.05 bar a significant discrepancy is found between the measured NO profiles and the predicted NO profiles. The predicted NO profiles with the G and

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2.4

+H

NH 2.4

N

0.1

+OH, +O2

+O

NO 777.8

+H, +O2+H NNH

N2

771.4

2.1

+O

+H, +O, +OH, +O2 4.2 +O

0.2

+O+M

4.2

0.1

N2O

+H

+H

Fig. 8. Reaction flow diagram for the G mechanism for the laminar, premixed hydrogen-air flame at 0.1 bar. The formation rates are given in 10−11 mol/s.

1.7

+H 1.7

N

NH 0.1 +O

+OH, +O2

NO 622.2

+H, +O2+H NNH

N2

617.4

1.6

+O

+H, +O, +OH, +O2 3.1 +O

0.1

+O+M

3.2

+H

0.1 +H

N2O

Fig. 9. Reaction flow diagram for the LiG mechanism for the laminar, premixed hydrogen-air flame at 0.1 bar. The formation rates are given in 10−11 mol/s.

LiG mechanisms continue to increase in the burned gases past where the measured NO profile levels off. Similar discrepancies between measurements and numerical computations have also been found by Harrington et al. [11] and by Konnov et al. [16]. However, relatively good agreement with the 0.05 bar experiment was obtained by Konnov et al. after an adjustment of the reaction rate coefficient for the reaction NNH + O   NH + NO and by employing a comprehensive detailed kinetic scheme for hydrogen combustion consisting of 238 reversible reactions and 31 species, including a novel N2 H3 route for NO formation [18]. Integral reaction flow analyses were also performed for the G, LiG, and LiSD mechanisms for the premixed hydrogen-air flame at 0.1 bar. Since the SD and the LiSD mechanism gave similar results, an integral reaction flow analysis will not be presented for the SD mechanism. Major reaction paths are presented in the reaction flow diagrams for the premixed hydrogenair flame in Figs. 8–10. Recirculation mechanisms for NO that contribute to the rate of formation of NH in the G and LiG

335.1

+H NNH

N2

332.5

+H, +OH 2.5 +O

2.4

+H

N2O

Fig. 10. Reaction flow diagram for the LiSD mechanism for the laminar, premixed hydrogen-air flame at 0.1 bar. The formation rates are given in 10−11 mol/s.

mechanisms, have been purposely left out from the diagrams to focus the attention on the reactions paths from N2 to NO. The thickness of the arrows in these figures is scaled corresponding to the formation rates given in 10−11 mol/s, where white arrows illustrate a 150 times greater formation rate than black arrows of the same thickness.

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

The results from the reaction flow analyses show that the NNH mechanism dominates the NO formation for this flame. The contribution from thermal NO is negligible, and the contribution from N2 O is small compared to the contribution from NNH. A comparison of Figs. 8 and 9 shows that the G mechanism leads to a larger rate of formation of NO than the LiG mechanism. Since the N/H/O chemistry and the temperature profile is the same for both of these mechanisms, the reason for this must be the different H2 /O2 chemistry. For this flame, more NO is produced via NNH for the G mechanism because this mechanism predicts higher concentrations of H and O radicals. A comparison of Figs. 9 and 10 shows how different N/H/O chemistry can affect the NO formation. The main reason for the difference in NO formation between the LiG and the LiSD mechanism is that the LiSD mechanism lacks the direct connection between NNH and NO through the important reaction NNH + O   NH + NO. 4.3. Low-pressure, premixed H2 /N2 O/Ar flame The detailed structure of a laminar, low-pressure, stoichiometric H2 /N2 O/Ar flame has been computed and compared with experimental data from Sausa et al. [25]. The flame was supported on a McKenna flat burner having a 6-cm stainlesssteel fritted plug. The plug was encircled by another sintered metal frit through which argon was flowed, thus forming a protective shroud that minimized mixing of any recirculating burned gases in the low-pressure chamber. The flame was stabilized on the burner at a pressure of 0.027 bar (20 torr). The gas flow rates were 1.6 and 1.4 l/min for the reactant gases and diluent, respectively, corresponding to a mass flow rate of 3.41 × 10−2 kg/m2 /s. The one-dimensional, premixed, laminar flame model in Chemkin 4.0.1 [23] was applied for the computation of the experimental flame. Since a measured temperature profile [25] was used in the simulations, the energy equation was not solved. Numerical simulations with up to 8000 grid nodes were performed to check the grid independency of the solutions. A grid resolution of 600 nodes was found sufficient to give grid-independent solutions for the present purposes. Calculated species concentrations with the LiG and LiSD mechanisms, as a function of the distance from the burner outlet, are presented and compared with experimental data in Figs. 11 and 12. The G and SD mechanisms are omitted since these mechanisms gave practically the same results as the LiG and the LiSD mechanism, respectively. Since N2 O is the oxidizer in this flame, the present differences in the H2 /O2 reactions will not be as important as if O2 was the oxidizer. The predicted NO level is in reasonable agreement with the experiments for both the LiG and the LiSD mechanism in Fig. 11(e). However, the LiSD mechanism seems to be in better agreement with the measurements than the LiG mechanism for this flame. With the LiG mechanism, the reactants seem to react too fast near the burner, resulting in too high concentrations of combustion products near the flame onset. The differ-

3581

ence between the two mechanisms is most obvious in Fig. 12 where radical concentration profiles are plotted. The predicted concentration profile of H radicals from the LiG mechanism is in significant disagreement with the experimental data near the burner. The reason for this discrepancy might be improperly modeled hydrogen atom transport. The concentration levels of O and OH radicals are also too high for the LiG mechanism, and the mechanism predicts a lower peak concentration of NH radicals compared to the measurements. To understand more of the differences between the results from the LiG and the LiSD mechanism for this flame, integral reaction flow analyses were applied. The major reaction paths from the integral reaction flow analyses are presented in Figs. 13 and 14. The attention has been focused on the nitrogen chemistry in the stoichiometric H2 /N2 O/Ar flame. The thickness of the arrows in these figures is scaled corresponding to the formation rates given in 10−7 mol/s, where white arrows illustrate a 10 times greater formation rate than black arrows of the same thickness. The dominant nitrogen reaction is N2 O+H  N2 +OH. This is the most important reaction for the direct conversion of N2 O to N2 . Other interesting reactions for the direct conversion of N2 O to N2 are the reactions N2 O + M   N2 + O + M and N2 O + OH   N2 + HO2 . In the LiG mechanism the reaction step N2 O + M → N2 + O + M predicts a rate of formation of O radicals which is three times larger than the equivalent value obtained from the LiSD mechanism. This appears to be the main reason for the high level of O radicals in the numerical results from the LiG mechanism. The reaction N2 O + M → N2 + O + M represents a key radical producing step promoting the combustion in the present flame. In the LiSD mechanism the reaction rate coefficient for this reaction step is modeled as pressure-dependent, but not in the LiG mechanism. In addition, the third-body efficiencies are modeled differently. For numerical simulations of high-pressure gas-turbine combustion, the pressure-dependency should be further investigated. Moreover, the rate of consumption of N2 O and OH due to the reaction N2 O + OH   N2 + HO2 is almost 40 times higher for the LiSD mechanism compared to the LiG mechanism. This may explain the overprediction of the OH level by the LiG mechanism in Fig. 12(c). A relatively small fraction of the N2 O is converted to NO. Here, the reaction N2 O + H   NH + NO is the major source of NO for both the mechanisms. Reactions involving NH and HNO radicals and N atoms are also contributing to the NO formation, but in a lesser degree. For the LiG mechanism, most of the NH radicals formed by the reaction N2 O+H   NH+NO are converted to N atoms by reactions with H or OH. Then most of the N atoms react with NO to form N2 . Some N atoms react with OH to form NO. Other pathways to NO formation via NH go through reactions with O radicals or via formation of HNO. For the LiSD mechanism most of the NH radicals formed by the reaction N2 O + H   NH + NO are converted to HNO radicals followed by a conversion to NO. This is probably due to the fact that the reaction rate coefficient for the reaction NH + OH   HNO+H has the double value of the same rate coefficient in the LiG mechanism. The additional pathways to NO formation are

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M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

14

20

12 10

12

[H2]

[N2O]

16 LiG LiSD exp

8

LiG LiSD exp

6 4

4 0

8

2 0

0.5

1

1.5

2

2.5

3

0

3.5

0

0.5

1

1.5

6

6

5

5

4

4

3

LiG LiSD exp

2

3

2.5

3

3.5

3

3.5

LiG LiSD exp

2

1 0

2

x (cm)

[H2O]

[N2]

x (cm)

1 0

0.5

1

1.5

2

2.5

3

0

3.5

0

0.5

1

1.5

x (cm)

2

2.5

x (cm)

0.5

[NO]

0.4 0.3 LiG LiSD exp

0.2 0.1 0

0

0.5

1

1.5

2

2.5

3

3.5

x (cm) Fig. 11. Concentration profiles of reactants and major products for the laminar, premixed, low-pressure H2 /N2 O/Ar flame. Numerical results (lines) from two different chemical mechanisms compared with experimental data (symbols). The concentrations are given in 10−8 mol/cm3 .

otherwise the same as for the LiG mechanism. An interesting observation is that the reversible reaction NNH + O   NH + NO, which is included in the LiG mechanism and not in the LiSD mechanism, represents a consumption of NO to form NNH in the present flame. However, the reaction seems to be of minor importance in this case. Different reaction constants in the kinetic mechanisms appear to be the main reason for the different results for the H2 /N2 O/Ar flame. 5. Numerical simulations of a turbulent hydrogen jet flame The G and LiG mechanisms have been tested by comparison of numerical simulation results with measurements for a turbulent, nonpremixed hydrogen jet flame. Experimental data for

this flame, which is also denoted as the H3 flame, can be found in the flame database for turbulent, nonpremixed flames at the Darmstadt University of Technology in Germany [26]. The fuel was a mixture of 50% hydrogen and 50% nitrogen flowing upwards out of a vertical tube with a diameter of 8 mm. An upward flow of air was supported around the fuel jet. The bulk velocities of the fuel and the air stream were 34.8 and 0.2 m/s, respectively. The reactants were supplied at a temperature of 300 K and a pressure of 1 bar. The numerical simulations were performed with an in-house CFD code called SPIDER [27,28]. This is a general-purpose CFD code which is based on the finite-volume method using curvilinear non-orthogonal coordinates for two- and threedimensional complex geometries. In the present simulations,

0.16

0.016

0.12

0.012 [O]

[H]

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

0.08 LiG LiSD exp

0.04

3583

LiG LiSD exp

0.008 0.004

0

0 0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

x (cm)

1.5

2

2.5

3

3.5

3

3.5

x (cm)

0.14 0.008

0.12

0.006

0.08

[NH]

[OH]

0.1 0.06 LiG LiSD exp

0.04 0.02 0

0

0.5

1

1.5

2

2.5

LiG LiSD exp

0.004 0.002

3

0

3.5

0

0.5

1

1.5

x (cm)

2

2.5

x (cm)

Fig. 12. Concentration profiles of radicals for the laminar, premixed, low-pressure H2 /N2 O/Ar flame. Numerical results (lines) from two different chemical mechanisms compared with experimental data (symbols). The concentrations are given in 10−8 mol/cm3 .

368.5

+H, +M, +O, + OH N2

16.3

12.5

4.9 N

NNH 14.4

16.7

1.9 +O

N2O

6.9

NH 36.7

4.0

+OH

+H

+OH

+H, +OH

HNO 7.2

+H 4.3

+H, +M, +OH

+O NO

Fig. 13. Reaction flow diagram for the LiG mechanism for the laminar, premixed H2 /N2 O/Ar flame at 0.027 bar. The formation rates are given in 10−7 mol/s.

a two-dimensional, axisymmetric, regular grid with 70 × 95 computational nodes was used. A modified k–ε turbulence model was applied (Cε2 = 1.83) [22], and Magnussen’s Eddy dissipation concept [29] for turbulent combustion with detailed chemistry [28,30] was used for the combustion modeling. Thermal radiation was accounted for by employing a radia-

tion model for optical thin flames [31]. Further details and discussions on the computational setup are found in [22]. Predicted mole fractions of OH and NO are compared with experimental data in Fig. 15. It is observed that the predicted NO level from the G mechanism is in better agreement with experimental data than the predicted NO level from the LiG

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373.5

+H, +M, +OH 6.9

N2

14.8

7.7 NNH

N

1.2 +OH

13.9 +H 8.2 +H, +OH

N2O

12.7 +OH

NH

HNO 13.1 +H, +M, +OH

32.7

2.4 +O

+H

NO Fig. 14. Reaction flow diagram for the LiSD mechanism for the laminar, premixed H2 /N2 O/Ar flame at 0.027 bar. The formation rates are given in 10−7 mol/s.

20

10 5 0

exp G LiG

4000 XOH (ppm)

15 XNO (ppm)

5000

exp G LiG

3000 2000 1000

0

10

20

30

40

50

60

70

0

0

10

20

x/d

30

40

50

60

70

x/d

Fig. 15. Favre-averaged mole fraction profiles. Numerical results (lines) from the G and LiG mechanisms compared with experimental data (symbols) along the nondimensional axis of the turbulent hydrogen jet flame.

mechanism. By studying the predicted mole fractions of H and O radicals (not presented here), it was found that the G mechanism gives about 75% higher levels of H and O radicals. This seems to be the main reason for the differences in the predicted NO levels. The temperature of this flame was also observed to be significantly lower than in an opposed-flow, laminar diffusion flame, which indicates that thermal NO should be less important. The path through NNH will be important for the NO formation in the present flame. This is also supported by the fact that the G mechanism gave a higher NO level than the LiG mechanism even though a slightly lower temperature was predicted. Both the tested mechanisms predict mole fractions of OH which are about twice as large as the measured values found in the experiments. Since the difference between the predicted levels and the measured level is much larger than the difference between the mechanisms, the deviation cannot be due to the kinetic model alone. The high OH levels are probably a result of inaccuracies in the turbulence model or the turbulent combustion model. From these results it is difficult to decide

which mechanism is the best. Accurate models for turbulence and combustion is essential for reliable predictions of NO concentrations in turbulent hydrogen flames. Further investigations on the turbulence modeling and the turbulent combustion modeling for hydrogen combustion is recommended to improve the numerical prediction capability. 6. Conclusions The theoretical modeling of NOx formation in hydrogen combustion has been studied. Four different detailed reaction mechanisms have been tested for eight laminar flames, and two of these mechanisms have been tested for a turbulent jet flame. The numerical results have been compared with experimental data from the literature. Sensitivity analyses and integral reaction flow analyses have been performed to throw light on important reaction steps and paths. For hydrogen-air flames, the numerical results from the present flame simulations seem to be in better agreement with experimental data when the H2 /O2 subset in the reaction

M. Skottene, K.E. Rian / International Journal of Hydrogen Energy 32 (2007) 3572 – 3585

mechanism from Glarborg et al. [20] is replaced with the H2 /O2 mechanism from Li et al. [2]. Formation of NO through NNH radicals is found to be important in the hydrogen-air flames investigated [11,24]. The reaction mechanism of Glarborg et al. predicts more NO from NNH radicals than the other mechanisms because the predicted level of H and O radicals becomes higher with this mechanism. The consequence is a considerably higher NO level than found in the experiments. As the mechanism of Glarborg et al. originally was made for hydrocarbon combustion, it has not been optimized for pure hydrogen combustion. The accuracy of the H2 /O2 chemistry is therefore seen to have a strong influence on the NOx predictions due to its effect on the flame temperature and the radical production. The results from numerical simulations of a premixed, lowpressure H2 /N2 O/Ar flame [25] indicate that the mechanism of Glarborg et al. gives a too high reaction rate for the reaction step N2 O + M → N2 + O + M. The H2 /N2 O/Ar flame is different from the other flames investigated since N2 O is used as the oxidizer. The consequence is that the H2 /O2 reactions will not be as dominant as when air is the oxidizer. A disadvantage of the San Diego mechanism [21] is the omission of the important reaction NNH + O   NO + NH, which is a representative reaction for the NNH route with respect to NO formation. For the turbulent hydrogen jet flame [26], the mechanism of Glarborg et al. showed better agreement between predicted and measured NO levels than the combined mechanism of Li et al. and Glarborg et al. Acknowledgments The authors would like to thank Mrs. Mona Skottene Twiss for her assistance on drawing the reaction flow diagrams and Dr. Tore Myhrvold, Dr. ]yvind Skreiberg, and Professor Ivar S. Ertesv˚ag for support and helpful discussions. References [1] Ströhle J, Myhrvold T. An evaluation of detailed reaction mechanisms for hydrogen combustion under gas turbine conditions. Int J Hydrogen Energy 2007;32:125–35. [2] Li J, Zhao Z, Kazakov A, Dryer FL. An updated comprehensive kinetic model of hydrogen combustion. Int J Chem Kinet 2004;36:566–75. [3] Miller JA, Bowman CT. Mechanism and modeling of nitrogen chemistry in combustion. Prog Energy Combust Sci 1989;15:287–338. [4] Kuo KK. Principles of combustion. New Jersey: Wiley; 2005. [5] Konnov AA, Colson G, De Ruyck J. NO formation rates for hydrogen combustion in stirred reactors. Fuel 2001;80:49–65. [6] Zeldovich YB. The oxidation of nitrogen in combustion and explosions. Acta Physicochim. USSR 1946;21:577. [7] Warnatz J, Maas U, Dibble RW. Combustion. Berlin: Springer; 2001. [8] Wolfrum J. Bildung von Stickstoffoxiden bei der Verbrennung. Chem Ing-Tech 1972;44:656.

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[9] Bozzelli JW, Dean AM. O + NNH: a possible new route for NOx formation in flames. Int J Chem Kinet 1995;27:1097–109. [10] Haworth NL, Mackie JC, Bacskay GB. An ab initio quantum chemical and kinetic study of the NNH + O reaction potential energy surface: how important is this route to NO in combustion?. J Phys Chem A 2003;107:6792–803. [11] Harrington JE, Smith GP, Berg PA, Noble AR, Jeffries JB, Crosley DR. Evidence for a new NO production mechanism in flames. Proc Combust Inst 1996;26:2133–8. [12] Hayhurst AN, Hutchinson EM. Evidence for a new way of producing NO via NNH in fuel-rich flames at atmospheric pressure. Combust Flame 1998;114:274–9. [13] Konnov AA, Colson G, De Ruyck J. The new route forming NO via NNH. Combust Flame 2000;121:548–50. [14] Konnov AA, Dyakov IV, De Ruyck J. Nitric oxide formation in premixed flames of H2 + CO + CO2 and air. Proc Combust Inst 2002;29:2171–7. [15] Charlston-Goch D, Chadwick BL, Morrison RJS, Campisi A, Thomsen DD, Laurendeau NM. Laser-induced fluorescence measurements and modeling of nitric oxide in premixed flames of CO+H2 +CH4 and air at high pressures. I. Nitrogen fixation. Combust Flame 2001;125:729–43. [16] Konnov AA, De Ruyck J. Temperature-dependent rate constant for the reaction NNH + O → NH + NO. Combust Flame 2001;125:1258–64. [17] Konnov AA. On the relative importance of different routes forming NO in hydrogen flames. Combust Flame 2003;134:421–4. [18] Konnov AA, De Ruyck J. A possible new route for NO formation via N2 H3 . Combust Sci Technol 2001;168:1–46. [19] Conaire MÓ, Curran HJ, Simmie JM, Pitz WJ, Westbrook CK. A comprehensive modeling study of hydrogen oxidation. Int J Chem Kinet 2004;36:603–22. [20] Glarborg P, Alzueta MU, Dam-Johansen K, Miller JA. Kinetic modeling of hydrocarbon/nitric oxide interactions in a flow reactor. Combust Flame 1998;115:1–27. [21] The San Diego mechanism, http://maeweb.ucsd.edu/combustion/ cermech/; 30 August, 2003. [22] Skottene M. Numerisk modellering av hydrogenforbrenning med fokus p˚a dannelse av NOx . Master’s thesis. Norwegian University of Science and Technology, Trondheim, Norway; 2005. [23] Kee RJ, Rupley FM, Miller JA, Coltrin ME, Grcar JF, Meeks E, et al. Theory manual, CHEMKIN Release 4.0.1. Reaction Design, Inc.; 2004. [24] RZrtveit GJ. NOx emissions from combustion of hydrogen mixtures. PhD thesis, Norwegian University of Science and Technology, Trondheim, Norway; 2002. [25] Sausa RC, Anderson WR, Dayton DC, Faust CM, Howard SL. Detailed structure study of a low-pressure, stoichiometric H2 /N2 O/Ar flame. Combust Flame 1993;94:407–25. [26] Flame data base for turbulent nonpremixed flames, http://www. tudarmstadt.de/fb/mb/ekt/flamebase/H3flame/; June, 2005. [27] Melaaen MC. Analysis of curvilinear non-orthogonal coordinates for numerical calculation of fluid flow in complex geometries. PhD thesis, Norwegian Institute of Technology, Trondheim, Norway;1990. [28] Gran IR. Mathematical modeling and numerical simulation of chemical kinetics in turbulent combustion. PhD thesis, Norwegian Institute of Technology, Trondheim, Norway; 1994. [29] Magnussen BF. Modeling of NOx and soot formation by the eddy dissipation concept. International Flame Research Foundation, 1st Topic Oriented Technical Meeting, Amsterdam, Holland, 17–19 October, 1989. [30] Ertesv˚ag IS. Turbulent strZyming og forbrenning: fr˚a turbulensteori til ingeniZrverkty. Tapir akademisk forlag: Trondheim, Norway; 2000. [31] International workshop on measurement and computation of turbulent nonpremixed flames, http://www.ca.sandia.gov/TNF/abstract.html, June, 2005.