Microscale Hydrogen Diffusion Flames

V.R. Lecoustre, P.B. SunderlandDept. of Fire Protection Engineering,

University of Maryland,College Park, MD 20742, USA

B.H. ChaoDept. of Mechanical Engineering,

University of Hawaii,Honolulu, HI 96822, USA

R.L. AxelbaumDept. of Energy, Environmental and Chemical Engineering,

Washington University,St. Louis, MO 63130, USA

Submitted to: 33rd Combustion Symposium (Beijing)

Submission Date: January 10, 2010

Corresponding Author:Peter B. SunderlandDept. of Fire Protection EngineeringUniversity of Maryland3104 J.M. Patterson BuildingCollege Park MD 20742 USAtel (301) 405-3095fax (301) 405-9383pbs@umd.edu

Colloquium: Laminar Flames

Alternate Colloquium: Reaction Kinetics

Total length: Using method 1

Word equivalent: 5327 (Total); limit 5800Main text: 3277References: 297Table 1: 46Table 2: 129Figures: 1581, as follows. Figure 1: 291; Figure 2: 320; Figure 3: 173; Figure 4: 314; Figure 5: 314; Figure 6: 169.

Affirmation to pay color reproduction charges if applicable: affirmed.

1

Abstract

Microscale hydrogen diffusion flames were studied experimentally and numerically. The

experiments involved laminar jet diffusion flames with hydrogen discharging downward from

stainless steel micro-tube burners with inside diameters of 0.15 mm. At their quenching limits

these flames had heat release rates of 0.46 and 0.25 W (hydrogen flow rates of 3.9 and 2.1 g/s)

in air and oxygen, respectively. These are apparently the weakest flames ever observed. Because

the flames were primarily diffusion controlled and hemispherical, they were modeled

numerically as spherical diffusion flames with detailed chemistry and transport. The modeling

results confirmed the measured quenching limits, identified these as being due to kinetic

extinction, and revealed high rates of reactant leakage near extinction. Different combustion

regimes were investigated by varying the hydrogen flow rate and spherical burner size, and the

main reactions contributing to the heat release rate were identified. The numerical study exhibits

the existence of a premixed flame regime as predicted by Liñán’s analysis of counterflow

diffusion flames.

Keywords: Kinetic extinction; laminar diffusion flames; oxygen-enhanced combustion;

quenching limits.

1. Introduction

This study is motivated by an a concern of fire hazards associated with small leaks in hydrogen

systems and the use of microcombustors for power generation. Butler et al. [1] examined the fire

hazards of small hydrogen leaks. They observed quenching limits of diffusion flames on small

tube burners and found the quenching mass flow rates for hydrogen to be about an order of

magnitude lower than those for methane and propane. At the quenching limits the flame height

was comparable to the quenching distance for premixed hydrogen flames, in agreement with

2

other studies [2,3]. Significantly smaller quenching limits for hydrogen were observed for

leaking compression fittings as well [1]. These hazards are now acknowledged in an SAE

recommended practice [4], which requires that hydrogen vehicles not have localized leaks in

excess of the measured quenching limits of Ref. [1].

Quenching limits are caused by kinetic extinction, which occurs at high scalar dissipation

rates (low Damköhler numbers) and may occur without external losses (i.e., losses other than

chemical enthalpy loss). Kinetic extinction phenomena affect the anchoring and stability of

practical flames and have been the subject of many studies, e.g., Refs. [5-7]. This is contrary to

radiative extinction [8], which occurs at high Damköhler numbers because of excessive radiative

heat loss and to date has only been conclusively observed in microgravity. Note that an increase

in flow rate decreases scalar dissipation rates in spherical diffusion flames but increases them in

spherical diffusion flames.

Microcombustors have potential advantages over batteries in terms of power generation

per unit volume and energy storage per unit mass [9]. Recent developments in micro-electro-

mechanical systems (MEMS) have enabled microcombustors with dimensions on the order of

1 mm [9]. The ability to burn weak but stable flames is important in the design of

microcombustors and it also may allow flames to serve as permanent pilots, thereby replacing

electric ignitors.

Several studies have examined flames that are among the weakest ever observed. Ronney

et al. [10] observed the burning of microgravity premixed flame balls during the STS-83 Space

Shuttle mission, with heat release rates as low as 0.5 – 1 W. Weak propane flames anchored on a

0.1 mm tube were found to have heat release rates as low as 1 W [2]. Nakamura et al. [3]

numerically predicted the existence of methane diffusion flames as weak as 0.5 W. The weakest

3

flame to date was reported by Butler et al. [1], which was a gas jet flame fueled by hydrogen

flowing downward into air from a micro-tube with inside diameter of 0.15 mm. This flame had a

heat release rate of 0.49 W and is further considered below.

Thus motivated, the objectives of this work are to experimentally observe microscale

hydrogen flames at their quenching limits in air and in oxygen, and to numerically investigate the

flame structure of spherical microflames to understand the mechanism of extinction in these

flames. The numerical code developed is a one-dimensional spherical code with detailed

chemistry and transport.

2. Experimental Methods and Results

The experiments involved two hydrogen diffusion flames, one burning in quiescent air and the

other in nearly quiescent oxygen. The burner was a stainless steel hypodermic tube with an

inside diameter of 0.15 mm and an outside diameter of 0.30 mm. Tests with platinum tubes of

similar dimensions had nearly identical quenching limits, ruling out significant effects of surface

reactions. The hydrogen jets issued downward. Horizontal and upward-flowing orientations also

were studied and quenching limits were only slightly higher [1]. Hydrogen flow rates were

measured with a rotameter. A pure oxygen ambient was obtained by placing the burner tip

40 mm above a 100 mm diameter supply of O2 flowing upward at 20 mm/s through a plenum

and a ceramic honeycomb flow straightener. There was no measurable change in the quenching

limit with changes in oxygen velocity.

The flames were not visible and hence were detected with a thermocouple 1 cm above the

burner tip. After ignition, the hydrogen flow rate was reduced slowly until each flame was

extinguished at its quenching limit. The images were recorded with a Nikon D100 camera at

4

ISO 200, f/1.4, and a shutter time of 30 s with room lights off. Additional experimental details

can be found in Butler et al. [1].

Color images of the two hydrogen flames at their quenching limits are shown in Fig. 1.

The test conditions for these flames are given in Table 1. The word “WE” on a U.S. dime is

included at flame scale to show that the flames are smaller than the smallest letters on U.S. coins.

The flames are hazy, suggesting distributed reaction zones rather than thin flame sheets.

The heat release rates associated with the mass flow rates are provided in Table 1. These

were obtained by assuming complete combustion of hydrogen and a lower heating value of

LHV = 120 kJ/g. Also included in Table 1 are the Reynolds, Froude, and Peclet numbers:

Re = u d / ; Fr = u2 / g d ; and Pe = ReD (lD / d) Sc , (1)

where u is the mean hydrogen velocity in the burner, d is the burner inside diameter, is

kinematic viscosity, g is the acceleration of gravity, lD is a characteristic diffusion length scale,

and Sc is the Schmidt number. Here lD is taken as 1 mm, and Sc is taken as 0.204 and 0.22 for

H2/air and H2/O2 flames, respectively [11]. The viscosity in Eq. (1) pertains to hydrogen at

laboratory pressure and temperature.

3. Numerical Methods

Although the flames are gas jets, their images (Fig. 1) suggest spherical symmetry near the

burner axis. The relatively high Froude numbers in Table 1 indicate that momentum dominates

over buoyancy in these two flames, while the low Peclet numbers indicate that diffusion

dominates over momentum. Nakamura et al. [3] numerically studied methane gas jet diffusion

flames on burners with diameters less than 1 mm and found the flames to be nearly

hemispherical for Pe < 5. Han et al. [12] observed and predicted the shapes of small hydrocarbon

jet flames, which they found to be only slightly affected by buoyancy and nearly hemispherical

5

owing to the comparable importance of streamwise diffusion and convection. Matta et al. [2]

reached similar conclusions for small propane flames. Cheng et al. [13] found that microjet

hydrogen diffusion flames with hydrogen issuing from tubes of 0.2 and 0.48 mm were

hemispherical near extinction.

The goal of the numerical effort is to understand the underlying mechanism for extinction

in micro-diffusion flames. Owing to this and the near spherical nature of the flames in Fig. 1, the

numerical modeling here is for spherically symmetric systems. The solver employed was

modified from the PREMIX [14] code. It solves conservation of mass, species, and energy at

steady state. The flow is assumed to be isobaric and laminar. Conventional finite difference

techniques with non-uniform mesh spacing were adopted to discretize the conservation

equations. The equations were then solved using Sandia TWOPNT [15], which adopts a

modified damped Newton’s method to solve boundary value problems. The diffusive and

convective terms were expressed by central and upwind difference formulas, respectively.

Chemical reaction rates, thermodynamic properties, and transport properties were evaluated by

CHEMKIN and the TRANSPORT library [16,17]. The hydrogen/oxygen/nitrogen chemistry was

extracted from GRI-Mech 3.0 [18], and included 67 reactions and 18 species. The key reactions

considered are listed in Table 2.

The boundary conditions were those of an adiabatic porous spherical burner [8,19]. The

inner boundary was assumed adiabatic in that a heat balance there equates conductive heating

from the gas with an increase in sensible enthalpy of hydrogen that was initially at 300 K. At the

burner surface, for each species mass diffusion is balanced with convective transport and, for H2,

with inflow. The outer boundary had a radius of 150 cm, a temperature of 300 K, and a

composition of either air or O2. For most of the flames considered here this simulated an infinite

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boundary. Adaptive mesh point addition was used to ensure that the solution was grid

independent. Radiative heat losses were neglected because effects of radiation are small for

hydrogen flames, particularly extremely small ones [20].

Quenching limits were defined as the extinction states of the steady state flames. Each

flaming solution obtained from a specified hydrogen flow rate was used as the starting condition

for a new simulation with a decreased mass flow rate. Extinction was identified when a solution

showed no significant rise of temperature.

The local scalar dissipation rate was obtained from

χ = 2 α (dZ / dr)2 , (2)

where r is radius and α and Z are the local thermal diffusivity and mixture fraction. The mixture

fraction is defined as

, (3)

where Y is the local mass fraction, M is atomic weight, and each subscript denotes the element

considered. Local equivalence ratio was evaluated from

= (1 / Zst – 1) / (1 / Z – 1) , (4)

where the stoichiometric mixture fraction Zst is 0.029 for H2/air and 0.13 for H2/O2. The peak

temperature, Tf, with its radius, rf, and scalar dissipation rate χf, are used to denote flame

properties, although the present flames have broadened reaction zones. The local chemical heat

release rate, Qc, was determined by summing over all reactions, and was integrated over the

entire domain to obtain the total chemical heat release rate.

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4. Numerical Results

Numerical investigations of quenching limits were performed for comparison with the

experimental results. These used a burner radius of 75 μm to match the radius of the

experimental burner. Numerical quenching limits were found to have hydrogen flow rates of

3.65 and 2.67 μg/s (i.e., heat release rates of 0.44 W and 0.32 W based on the lower heating

value of H2) for the H2/air and H2/O2 flames, respectively. The total heat release rates obtained by

numerical integration of Qc were about 3% lower than these values. The numerical quenching

limits are in reasonable agreement with the measurements of Table 1.

Details of the predicted H2/air flame just above the quenching limit are shown in Fig. 2 in

solid curves. This flame has a peak temperature of 1290 K, is located within 1.2 μm of the

burner, and has significant penetration of O2 to the burner surface. Conditions are fuel lean

across the entire domain, in agreement with Ref. [13], and  = 0.05 at the peak temperature. The

main reaction contributing to the heat release rate is R84 (H2+OH→H+H2O). The next largest

contributors are R35, R46, and R45 (see Table 2), which involve H radical consumption and HO2

chemistry. There is also one significant endothermic reaction, the chain branching reaction R38,

which is the most important chain branching reaction for hydrogen combustion [23].

The possibility that the extensive leakage of oxygen in this flame arises from interference

from the burner was investigated by considering (in dashed curves in Fig. 2) the quenching limit

of a flame stabilized by a burner with radius of 1 μm. This yields YH2 = 1 and T = 300 K at the

burner surface because the high flow velocities prevent O2 from reaching the burner.

Nevertheless, extensive O2 penetration into the reaction region occurs. Comparing the two flames

reveals that the larger burner truncates the flame below a radius of 75 μm, but has little effect

elsewhere. Values of Tf, rf, and χf are similar for both flames. The small flames induce high Qc,

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whose peaks increase from 3800 to 8000 W/cm3, when the burner is reduced from 75 μm to

1 μm. Reactions R46 and R35 have the highest peaks, but they occur at such small radii that R84

remains the dominant contributor to overall heat release. These high peaks involve the

consumption of H radical close to the burner, which are produced at greater radii, indicating the

importance of backward diffusion for H.

The impact of the H2 flow rate and burner radius were studied for many H2/air flames

near and above their quenching limits. Their effects on peak temperature and its location are

summarized in Fig. 3. At the highest hydrogen flow rates Tf and rf are independent of burner

diameter for all the burners considered. For the three larger burners, as flow rate decreases the

burner’s presence increases rf and reduces Tf and quenching occurs when rf approaches the

burner such that the reaction region attaches to the burner. For the smallest burner the burner

diameter has no effect on rf or Tf even at its quenching limit. Extinction is observed at a peak

temperature of about 1300 K regardless of burner diameter. Except near the quenching limits,

Fig. 3 shows that flame radius scales with 1.1, where is the mass flow rate.

Figure 3 suggests different behavior at high and low hydrogen flow rates. Typical flame

behavior at high flows is considered in Fig. 4, where the highest flow rate (10 mg/s) and the

largest burner (rb = 3.175 mm) in Fig. 3 is examined. This is a canonical diffusion flame with its

reaction region detached from the burner. Although there is some penetration of H2 and O2 across

the flame, the amount is small and at the burner surface YO2 = 0. The equivalence ratio at the

peak temperature is 0.65. The flame temperature is 2370 K, which is very close to the adiabatic

H2/air flame temperature. The scalar dissipation rate at the flame location is very low, χf =

5.210–6 s-1. This results in a broad mixing layer, as observed in Fig. 4.

9

Figure 4 shows two peaks in Qc, as opposed to one for the quenching limit flame of

Fig. 2. The larger peak corresponds to the location of H2O formation, with reaction R43 being

the major contributor. The smaller peak of Qc arises primarily from reactions R40 and R41. At

this location H radicals (which are mainly produced near rf) combine into H2. The main

endothermic reaction in this flame is again R38. Hydroxyl radical is produced primarily on the

oxidizer side of the flame and consumed on the fuel side.

When the hydrogen flow rate of Fig. 4 is decreased to 0.1 mg/s, the flame of Fig. 5

results. This corresponds to the knee bend in temperature in Fig. 3, where a further decrease of

flow rate does not change the flame size but drastically reduces Tf. For this flame, χf = 0.016 s-1,

which is four orders of magnitude larger than in Fig. 4. This flame is very close to the burner,

causing an increase of burner surface temperature to 2000 K. At the burner surface YO2 = 0.03.

The equivalence ratio at the peak temperature is 0.1. There exists only one peak on the Qc curve,

located near the burner, which is associated with R84 (OH+H2→H+H2O).

As flow rate decreases, rf and Tf generally decrease, as shown in Fig. 3, while χf increases.

Mills and Matalon [21] considered adiabatic spherical diffusion flames and found that Da ~ 2,

where Da is the reduced Damköhler number, defined as transport time divided by chemical time.

In spherical flames, decreasing the mass flow rate decreases the transport time until it is

comparable to the chemical time. A further decrease then causes kinetic extinction [22]. A

representation of transport time is χf – 1, such that

Da ~ χf – 1 exp ( –Ea / Ru Tf ) , (5)

where Ea is the activation energy and Ru the universal gas constant. Comparing Eq. (5) with that

of Ref. [21] yields χf ~ –2 , which explains the predicted χf near extinction for the flames of Figs.

2 and 4.

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Further insight into the quenching limits is available from Fig. 6, which considers again

the conditions of Fig. 3. The upper branch of this curve begins at low χf (i.e., high ) where the

peak temperature is independent of χf and is close to the adiabatic flame temperature of

hydrogen, 2370 K. A decrease of leads to an increase in dissipation rate. This in turn yields a

reduction in Tf owing to leakage of hydrogen through the flame.

Further increases in χf then lead to the interference of the burner with the flame for the

three larger burners. Although each of the curves looks like the upper and middle branches of an

S-shaped ignition-extinction curve, each is actually the upper branch combined with burner

interference. For the smallest burners, quenching occurs at the turning point of the S-curve,

indicating the kinetic extinction of a typical diffusion flame. Figure 6 shows that the quenching

limit is slightly lower for the 1 m burner than for the 75 m burner.

It is interesting to note that Fig. 2 exhibits the existence of a premixed flame regime in a

diffusion flame, as identified by Liñán [22]. This regime occurs when significant fuel or oxidizer

is present in the reaction region and leaks through the flame. The reaction rate becomes

controlled by the deficient reactant and the flame behaves like a propagating premixed flame.

While theoretically possible, a diffusion flame burning in the premixed flame regime had not

been observed before because it is in the physically unrealistic middle branch of the S curve. By

reducing the hydrogen flow rate from the flame shown in Fig. 4, the flame radius decreases and

eventually the reaction region reaches the burner as in Fig. 5. A further reduction in the hydrogen

flow rate then leads to abundant oxygen in the reaction region and excess oxygen at the burner

surface. The flame becomes leaner and cooler, but maintains the same location. The deviation

from typical diffusion flames shown in Figs. 3 and 6 indicates the transition to the premixed

flame regime instead of extinction. Extinction occurs when the flame temperature falls below

11

about 1300 K. The spherical flame of Fig. 2 demonstrates that the Liñán premixed flame regime

can indeed exist in a diffusion flame.

5. Conclusions

Quenching limits of hydrogen microflames were observed in air and oxygen. The flames were

simulated using a steady-state spherical flame code with detailed chemistry and transport and

without radiative losses. In the model hydrogen is supplied in a configuration that resembles an

adiabatic porous sphere burner. The main conclusions are as follows:

1. The measured quenching limits involve hydrogen jets flowing at 3.9 μg/s for the

H2/air flames and 2.1 μg/s for the H2/O2 flames, corresponding to heat release rates of

0.46 and 0.25 W, respectively. The H2/O2 flames are believed to be the weakest flames

ever observed. Numerical predictions of the quenching limits are in reasonable agreement

with the experiments.

2. Near quenching, high rates of O2 penetration to the fuel side are predicted, with

equivalence ratios at the peak temperature of 0.05 – 0.1.

3. The numerical results yield the upper branch of S curves, confirming that the

quenching limits are kinetic extinction events. These flames extinguish when χf reaches 1

s-1 (H2/air) and 2 s-1 (H2/O2), which is six orders of magnitude higher than in flames far

from the quenching limit. For burners with radii greater than 0.3 mm, quenching is

promoted when the burner prevents the flame from moving inward.

4. Large flames have low dissipation rates and a double peak in local heat release rate.

Flames with high scalar dissipation rate have a single peak in local heat release rate.

Hydroperoxy radical (HO2) chemistry is important in these flames.

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5. Through the interference of the burner, the premixed flame regime of a diffusion

flame, introduced by Liñán, can physically exist.

Acknowledgments

This work was co-funded by NASA (D.P. Stocker, grant monitor) and by NIST (J. Yang, grant

monitor). The authors thank C.W. Moran and M.S. Butler for their assistance with the

experiments.

References

[1] M.S. Butler, C.W. Moran, P.B. Sunderland, R.L. Axelbaum, Int. J. Hydrogen Energy 34 (2009) 5174-5182.

[2] L.M. Matta, Y. Neumeier, B. Lemon, B.T. Zinn, Proc. Combust. Inst. 29 (2002) 933-939.

[3] Y. Nakamura, H Yamashita, K Saito, Combust. Theo. Model. 10 (2006) 927-938.

[4] SAEJ2579, Recommended practice for general fuel cell vehicle safety, a surface vehicle recommended practice. Detroit, MI: SAE International; January, 2009.

[5] R. Chen, R.L. Axelbaum, Combust. Flame 142 (2005) 62-71.

[6] H.Y. Wang, W.H. Chen, C.K. Law, Combust. Flame 148 (2007) 100-116.

[7] F.A. Williams, Fire Safety J. 3 (1981) 163-175.

[8] K.J. Santa, B.H. Chao, P.B. Sunderland, D.L. Urban, D.P. Stocker, R.L. Axelbaum, Combust. Flame 151 (2007) 665–675.

[9] A.C. Fernandez-Pello, Proc. Combust. Inst. 29 (2002) 883-899.

[10] P.D. Ronney, M.S. Wu, H.G Pearlman, K.J. Weiland, AIAA J. 36 (1998) 1361-1368.

[11] B.J. Lee, S.H. Chung, Combust. Flame 109 (1997) 163-172.

[12] H. Han, S. Venkatesh, K. Saito, J. Heat Transfer 116 (1994) 954-959.

[13] T.S. Cheng, Y.C. Chao, C.Y. Wu, Y.H. Li, Y. Nakamura, K.Y. Lee, T. Yuan, T.S. Leu, Proc. Combust. Inst. 30 (2005) 2489-2497.

[14] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, E. Meeks, Premix: A FORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Report No. SAND85-8240, Sandia National Laboratories, 1987.

13

[15] J.F. Grcar, The Twopnt program for boundary value problems, Report No. SAND91-8230, Sandia National Laboratories, 1991.

[16] R.J. Kee, F.M. Rupley, E. Meeks, J.A. Miller, Chemkin-III: a Fortran chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics, Report No. SAND96-8216, Sandia National Laboratories, 1996.

[17] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, H.K. Moffat, A Fortran Computer Code Package for the Evaluation of Gas-Phase Multicomponent Transport Properties, Report No. SAND86-8246, Sandia National Laboratories, 1988.

[18] 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, V. Lissianski, Z. Qin, available at http://www.me.berkeley.edu/gri_mech/.

[19] K.J. Santa, Z. Sun, B.H. Chao, P.B. Sunderland, R.L. Axelbaum, D.L. Urban, D.P. Stocker, Combust. Theory Model. 11 (2007) 639-652.

[20] T.S. Cheng, C.Y. Wu, C.P. Chen, Y.H. Li, Y.C. Chao, T. Yuan, T.S. Leu, Combust. Flame 146 (2006) 268-282.

[21] K. Mills, M. Matalon, Combust. Sci. Tech. 129 (1997) 295-319.

[22] A. Liñán, Acta Astronaut. 1 (1974) 1007–1039.

[23] H.-Y. Shih, Int. J. Hydrogen Energy 34 (2009) 4005-4013.

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Table 1Experimental quenching limits

OxidizerH2

μg/sH2 . LHV

Wu

m/s

Re Fr Pe

Air 3.9 0.46 2.5 3.96 65 5.3O2 2.1 0.25 1.4 2.13 36 3.0

Table 2Selected H2-O2 reactions included in the simulations, from GRI Mech. 3.0 [18]

No. Reaction No. ReactionR1 2O+M → O2+M R43 H+OH+M→ H2O+MR2 O+H+M → OH+M R44 H+HO2 → O+H2OR3 O+H2 → H+OH R45 H+HO2 → O2+H2

R4 O+HO2 → OH+O2 R46 H+HO2 → 2OHR5 O+H2O2 → OH+HO2 R47 H+H2O2 → HO2+H2

R33 H+O2+M → HO2+M R48 H+H2O2 → OH+H2OR34 H+2O2 → HO2+O2 R84 OH+H2 → H+H2OR35 H+O2+H2O →

HO2+H2OR85R86

2OH+M → H2O2+M2OH → O+H2O

R36 H+O2+N2 → HO2+N2 R87 OH+HO2 → O2+H2OR38 H+O2 → O+OH R88 OH+H2O2 → HO2+H2OR39 2H+M → H2+M R89 OH+H2O2 → HO2+H2OR40 2H+H2 → 2H2 R115 2HO2 → O2+H2O2

R41 2H+H2O → H2+H2O R116 2HO2 → O2+H2O2

15

0.5 mm

WE

Fig. 1. Images of hydrogen flames at their quenching limits burning in air (left) and O2 (right). The tube inside and outside diameters are 0.15 and 0.30 mm. Camera exposures are ISO 200, f/1.4, 30 s. The word WE from a U.S. dime is shown at the same scale as the flames. Original in color.

16

Fig. 2. Species mass fractions (top) and temperature and local heat release rates (bottom) for H2/air flames near their quenching limits. Burner radii, H2, and χf are 75 μm, 3.65 μg/s, and 0.98 s-1 (solid curves) and 1 μm, 3.49 μg/s, and 1.18 s-1 (dashed curves).

mH2 (mg/s)

T f(K)

r f(cm)

10-3 10-2 10-1 100 1011000

1500

2000

2500

10-2

10-1

100

101

102

3.175 mm

75 m1 m

300 m1 m

75 m

3.175 mm

300 m

T

r

.

Fig. 3. Predicted H2/air peak temperature and its radius versus hydrogen flow rate for four burner radii.

17

r (m)

T(K)

Q(W/cm3 )

0 100 200 300 4000

500

1000

1500

0

2000

4000

T

QCR35

R84

R38 R3

R46

R45

rb = 75 m

R36

R35R46

1500 4000Yi

10-6

10-5

10-4

10-3

10-2

10-1

100

H2

O2

O

H2O

OH

HO2

H

H2O2

rb=75 m

10-6

Fig. 4. Species mass fractions (top) and temperature and local heat release rates (bottom) for a large H2/air flame. Burner radii, H2 , and χf are 3.175 mm, 10 mg/s, and 5.2x10–6 s-1.

18

Yi

10-6

10-5

10-4

10-3

10-2

10-1

100

H2 O2

O

H2O

OH

H

10-6

r (cm)

T(K)

Q(W/cm3 )

0 10 20 30 40 500

500

1000

1500

2000

2500

-0.005

0

0.005

0.01

0.015

0.02T

QC

R85R84

R38

R87

R43

R86

R89R41R35

2500 0.02

Fig. 5. Species mass fractions (top) and temperature and local heat release rates (bottom) for an H2/air flame near its quenching limit. Burner radii, H2 , and χf are 3.175 mm, 0.1 mg/s, and 0.016 s-1.

f (s-1)

T f(K)

10-6 10-5 10-4 10-3 10-2 10-1 100 1011000

1500

2000

2500

3.175 mm

75 m

1 m

300 m

Fig. 6. Predicted H2/air peak temperature versus scalar dissipation rate for four burner radii.

19

Yi

10-6

10-5

10-4

10-3

10-2

10-1

100

H2

O2

O

H2O

OH

HO2

H

Burnersurface

10-6

r (m)

T(K)

Q(W/cm3 )

3000 3500 4000 45000

500

1000

1500

2000

2500

-50

0

50

100

150

200

T

QC

R35

R84

R38

R3R86

R43

Burnersurface

2500 200

Figure Captions

Fig. 1. Images of hydrogen flames at their quenching limits burning in air (left) and O2 (right). The tube inside and outside diameters are 0.15 and 0.30 mm. Camera exposures are ISO 200, f/1.4, 30 s. The word WE from a U.S. dime is shown at the same scale as the flames. Original in color.

Fig. 2. Species mass fractions (top) and temperature and local heat release rates (bottom) for H2/air flames near their quenching limits. Burner radii, H2, and χf are 75 μm, 3.65 μg/s, and 0.98 s-1 (solid curves) and 1 μm, 3.49 μg/s, and 1.18 s-1 (dashed curves).

Fig. 3. Predicted H2/air peak temperature and its radius versus hydrogen flow rate for four burner radii.

Fig. 4. Species mass fractions (top) and temperature and local heat release rates (bottom) for a large H2/air flame. Burner radii, H2 , and χf are 3.175 mm, 10 mg/s, and 5.2x10–6 s-1.

Fig. 5. Species mass fractions (top) and temperature and local heat release rates (bottom) for an H2/air flame near its quenching limit. Burner radii, H2 , and χf are 3.175 mm, 0.1 mg/s, and 0.016 s-1.

Fig. 6. Predicted H2/air peak temperature versus scalar dissipation rate for four burner radii.

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