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International Journal of Hydrogen Energy 32 (2007) 2081 2093www.elsevier.com/locate/ijhydene

Characterization of high-pressure, underexpanded hydrogen-jet flames

R.W. Schefera,, W.G. Houfa, T.C. Williamsa, B. Bourne b, J. Colton b

aCombustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USAbSRI International, 333 Ravenwood Ave., Menlo Park, CA 94025, USA

Received 30 June 2006; accepted 2 August 2006

Available online 9 October 2006

Abstract

Measurements were performed to characterize the dimensional and radiative properties of large-scale, vertical hydrogen-jet flames. This data

is relevant to the safety scenario of a sudden leak in a high-pressure hydrogen containment vessel and will provide a technological basis for

determining hazardous length scales associated with unintended hydrogen releases at storage and distribution centers. Jet flames originating from

high-pressure sources up to 413 bar (6000 psi) were studied to verify the application of correlations and scaling laws based on lower-pressure

subsonic and choked-flow jet flames. These higher pressures are expected to be typical of the pressure ranges in future hydrogen storage

vessels. At these pressures the flows exiting the jet nozzle are categorized as underexpanded jets in which the flow is choked at the jet exit.

Additionally, the gas behavior departs from that of an ideal-gas and alternate formulations for non-ideal gas must be introduced. Visible flame

emission was recorded on video to evaluate flame length and structure. Radiometer measurements allowed determination of the radiant heat flux

characteristics. The flame length results show that lower-pressure engineering correlations, based on the Froude number and a non-dimensional

flame length, also apply to releases up to 413 bar (6000 psi). Similarly, radiative heat flux characteristics of these high-pressure jet flames obey

scaling laws developed for low-pressure, smaller-scale flames and a wide variety of fuels. The results verify that such correlations can be used to

a priori predict dimensional characteristics and radiative heat flux from a wide variety of hydrogen-jet flames resulting from accidental releases.Published by Elsevier Ltd on behalf of the International Association for Hydrogen Energy.

Keywords: Hydrogen; Turbulent jet; Combustion; Hydrogen flames

1. Introduction

The development of an infrastructure for hydrogen utilization

will require new safety codes and standards that establish guide-

lines for building the components of this infrastructure. Based

on a recent workshop on unintended hydrogen releases, one ofthe most common release scenarios involves leaks from pres-

surized hydrogen-handling equipment [1]. These leaks range

from small-diameter, slow-release leaks originating from holes

in delivery pipes to larger, high-volume releases resulting from

accidental breaks in high-pressure storage tanks. In all cases,

the resulting hydrogen fuel jet represents a potential fire haz-

ard, and the buildup of a combustible cloud poses a hazard if

ignited downstream of the leak.

Corresponding author. Tel.: +1 925294 2681; fax: +1 924294 2595.

E-mail address: [email protected](R.W. Schefer).

0360-3199/$- see front matter Published by Elsevier Ltd on behalf of the International Association for Hydrogen Energy.

doi:10.1016/j.ijhydene.2006.08.037

A scenario in which a high-pressure leak of hydrogen is

ignited at the source is best described as a classic turbulent-jet

flame [2]. While laboratory-scale, subsonic-jet flames burn-

ing hydrocarbon fuels have been studied extensively, data for

larger-scale, subsonic and, in particular, sonic (choked) jet

flames is less available. In a previous study by the present au-thors[3], measurements were performed in large-scale, vertical

flames to characterize the dimensional, thermal, and radia-

tive properties of ignited hydrogen jets. Jet flames originating

from a high-pressure source up to about 172 bar (2500psi)

were studied. The results showed that measured flame lengths,

for a wide range of operating conditions, collapsed onto the

same curve when plotted as a function of Froude number,

which measures the relative importance of jet momentum and

buoyancy. Furthermore, the good comparison with hydrocar-

bon jet flame lengths demonstrated that the non-dimensional

correlations are valid for a variety of fuel types. The radia-

tive heat flux measurements for hydrogen flames also showed

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good agreement with non-dimensional correlations and scal-

ing laws developed for a range of fuels and flame conditions.

A well-behaved linear dependence of radiative fraction on the

log of the flame residence time were found, in agreement with

non-sooting hydrocarbon flame data, but the radiative fractionfor the H2 flames at a fixed residence time is nearly a fac-

tor of two lower. The results verified that such correlations

can be used to predict radiative heat flux from a wide vari-

ety of hydrogen flames and established a basis for predicting

a priori the characteristics of flames resulting from accidental

releases.

The objective of the present investigation is to extend these

previous measurements toward the higher-pressure ranges ex-

pected in future hydrogen storage vessels. Thus, measurements

were obtained at storage pressures up to 413 bar (6000 psi) in

this study. This pressure range is also of interest because depar-

tures from ideal-gas behavior become important. In the follow-

ing section, the results of previous studies for relevant flame

characteristics will be summarized. In particular, correlations

for flame length and radiative heat flux from jet flames will be

presented, the concept of underexpanded jets will be briefly in-

troduced, and equations based on a simplified model of these

flows will be described.

2. Theory

2.1. Flame length

Studies in the literature have defined a flame length based

on the visible flame length, which is determined using either

visual observation[4]or photographs of the visible flame emis-

sion[5]. Alternative definitions of flame length can be based

on infrared flame emission or ultraviolet flame emission [3],

which give flame lengths that are 12% longer and 22% shorter,

respectively, than the visible flame length. Since most corre-

lations presented in the literature are based on visible flame

length, we will confine the present results to a flame length

based on visible emission.

Becker and Liang[4]obtained extensive experimental data

comparing flame lengths of hydrogen, carbon monoxide,methane, ethane, ethylene and propane. These data, combined

with results in the literature, were found to correlate well over

a range of operating conditions extending from the forced-

to natural-convection limits when using the appropriate non-

dimensional parameters. Kalghatgi [5] studied jet flames of

hydrogen, methane, propane and ethylene. In these studies,

the flame length data was extended from subsonic jet flows

to underexpanded sonic jets. Using the non-dimensional pa-

rameters of Becker and Liang, the data were found to collapse

onto a single curve. However, in the forced convective limit,

fitting constants determined by Kalghatgi differed from those

of Becker and Liang.

A correlation for flame length developed by Delichatsios[6]is based on a non-dimensional Froude number that measures

the ratio of buoyancy-to-momentum forces in jet flames. The

Froude number is defined as

Frf=uef

3/2s

(e/)1/4[(Tf/T)gdj]

1/2, (1)

whereueis the jet exit velocity,fsis the mass fraction of fuel at

stoichiometric conditions, (e/)is the ratio of jet gas density

to ambient gas density, dj is the jet exit diameter, and Tf is

the peak flame temperature rise due to combustion heat release.

Small values ofFrfcorrespond to buoyancy-dominated flames

while large values ofFrfcorrespond to momentum-dominated

flames. Further, a non-dimensional flame length, L, can be

defined as

L =Lffs

dj(e/)1/2

=Lffs

d , (2)

whereLfis the visible flame length and d is the jet momen-

tum diameter (=dj (e/)1/2). In the buoyancy-dominatedregime,L is correlated by the expression

L =13.5Fr

2/5f

(1 + 0.07Fr2f)1/5

for Frf< 5 (3a)

and in the momentum-dominated regime by the expression

L = 23 for Fr> 5. (3b)

It has been found that turbulent flame lengths are well-

correlated over a large range of flow conditions using these

non-dimensional parameters. Recent results by Schefer et al.

[3]showed that this correlation works well for vertical turbu-lent hydrogen jets, both subsonic and choked, originating from

sources at pressures up to 172 bar (2500 psi).

2.2. Flame radiation

The characterization of radiative heat flux is integral to the

development of safety codes and standards. In fuel-rich hydro-

carbon flames where significant amounts of sooty particles are

formed, radiation from soot dominates the radiative heat flux.

In hydrogen flames, gaseous emission accounts for nearly all

the radiative heat flux, with excited-state H2O* molecules be-

ing the only significant source of radiative emission. A usefulquantity to characterize the radiative heat flux from flames is

the radiant fraction,Xrad, which is defined as the fraction of the

total chemical heat release that is radiated to the surroundings:

Xrad =Srad

mfuelHc, (4)

whereSrad is the total radiative power emitted from the flame,

mfuel is the total fuel mass flow rate, Hc is the heat of com-

bustion and mfuelHc is the total heat released due to chemi-

cal reaction. For turbulent-jet flames, the radiative power can

be expressed in terms of a non-dimensional radiant power,C,

given by the general expression

C(x/L, r/L)=4R2qrad(x/Lf,r/Lf)

Srad, (5)

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where R is the radial distance from the flame centerline to the

location at which the radiant flux is measured and qrad(x,r)

is the radiant heat flux measured at a particular axial location,

x, and radial location, r. Experimental data further show that

C

may be expressed in non-dimensional form as a functionof burner diameter, flow rate and fuel type and, for turbulent-

jet flames, is dependent only on the normalized axial distance.

Under these conditions Eq. (5) reduces to

C(x/L)=4R2qrad(x/Lf)

Srad=

4R2qrad(x/Lf)

XradmfuelHc. (6)

The form of Eq. (6) was verified by Sivathanu and Gore[7] in

laboratory-scale turbulent-jet flames over a range of conditions.

Previous measurements by Schefer et al.[3] verified the valid-

ity of these heat flux scaling relations in larger-scale choked

hydrogen-jet flames at pressures up to 172 bar (2500 psi).

Turns and Myhr[8] showed that the flame radiative fractioncorrelated well with the flame residence time for a wide variety

of fuels. These fuels included methane, ethylene, propane and a

57% CO/43% H2mixture. The flame residence time as defined

by Turns and Myhr is given by the expression

f=fW

2fLffs

3fd2fuf

, (7)

where f, Wf, andLfare the flame density, width and length,

respectively. This definition of residence time takes into account

the actual flame density and models the flame as a cone. For

turbulent-jet flames, Wf is approximately equal to 0.17 Lf in

hydrocarbon[8] and hydrogen-jet flames[3]. Verification thatthe high-pressure, high-velocity jet flames studied here obey

these scaling laws would enable us to a priori quantify the heat-

flux characteristics of large-scale jet flames.

2.3. Underexpanded jets

For subsonic jets issuing into ambient air, the exit velocity

corresponds to a Mach number less than unity and the pressure

at the exit plane is just equal to atmospheric. For jets involving

a high-pressure storage device, the pressure drop across the jet

is often sufficient to result in an underexpanded jet in which the

flow is choked at the jet exit and the exit pressure is considerablygreater than atmospheric. The flow will then rapidly expand to

atmospheric pressure through a series of expansion shocks. A

convenient simplification of this expansion process involves the

concept of a notional, or fictional, nozzle. Kalghatgi [5]

used the notional nozzle concept to extend flame-length corre-

lations developed for subsonic jet flames to underexpanded jet

flames. Birch et al. [9,10] further developed this concept into

a pseudo-diameter, or an effective source diameter, that was

used to explain the concentration and velocity field decays in

non-reacting, high-pressure jet flows.

The concept of a notional nozzle as it relates to a high-

pressure release through a jet is illustrated in Fig. 1. Level 1

corresponds to the high-pressure source, Level 2 is the jet exitand Level 3 corresponds to the exit conditions after expansion

through the notional nozzle. This situation is equivalent to re-

P3, T3

V2

V3

d2

P2, T2

Level 3

Level 2

Level 1

deff

P1, T1

Notional NozzleExpansion Region

High-pressureReservoir

Fig. 1. Notional nozzle concept. (Birch et al. [10].)

placing the expansion process that occurs as the gas, which is

choked at the jet exit, expands to ambient conditions. The di-

ameter of the notional nozzle, deff, is larger than the jet exit

diameter, d2(=dj). Assuming no viscous forces and a uniform

velocity profile across the notional nozzle cross section, the

conservation of mass and momentum are written as follows:

2A2u2 = 3A3u3 Conservation of Mass (8)

and

2A2u22 3A3u

23 = A2(P3 P2)

Conservation of Momentum, (9)

whereA is the cross-sectional area. Solving Eq. (8) for 3A3,

substituting into Eq. (9) and rearranging gives

u3 = u2 (P3 P2)

2u2. (10)

Also, from Eq. (8), the notional nozzle diameter is given by

deff= d2

2u2

3u3= dj

2u2

3u3. (11)

This approach is entirely analogous to that of Birch et al. [10]

in which both the conservation of mass and momentum wereused to develop an expression for the notional nozzle diameter.

Conditions at Level 1, the high-pressure source, are typically

known quantities (in the present experiments they are mea-

sured). Following the approach of Birch and coworkers, condi-

tions at the jet exit, where the flow is sonic, can be determined

from Level 1 conditions using isentropic flow relations [11].

Since expansion to ambient conditions occurs through the no-

tional nozzle, the pressure P3 is equal to the ambient pressure.

The velocity u3 can then be calculated from Eq. (10) and the

notional nozzle diameter, deff, is given by Eq. (11). The no-

tional nozzle diameter and flow properties at the notional noz-

zle exit are then used in the correlations for the flame length

(Eqs. (1)(3)) and the flame residence time (Eq. (7)).The remainder of this paper highlights the experimental sys-

tem, measurement techniques, and presents results for flame

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tests using a 5.08-mm-diameter hydrogen (H2) jet at pressures

up to 413bar (6000 psi). Comparisons are made to measure-

ments obtained in laboratory-scale hydrogen flames and to jet

flames for a variety of fuels found in the literature. These com-

parisons will highlight the applicability of jet scaling laws andsimilarity variables to the present H2 jets and identify any dif-

ferences between hydrocarbon and hydrogen-fuel jets.

3. Experimental methods

3.1. Flow system

The tests were carried out at the SRI International Corral

Hollow test facility in Tracy, CA. A schematic of the flow de-

livery system is shown in Fig. 2. The hydrogen was provided

by a storage tube trailer supplied by Air Products. The trailer

consisted of eight high-pressure hydrogen storage tubes. The

volume of each tube was 617l (21.8 ft3) at a nominal pres-

sure of 431 bar (6258 psig) (actual initial pressures for the three

tests conducted were 431 (6253 psi), 425 (6173 psi) and 438 bar

(6349psi)). These pressures are considerably higher than the

previous release tests where the initial storage pressure was

about 172 bar (2500 psi) [3]. In previous tests, the hydrogen

was provided by a six-pack of conventional gas cylinders,

each with a volume of 49 l. Typically only two cylinders were

used during each blowdown test, which limited the test dura-

tion to about 100 s. The higher-pressure storage tubes in the

current tests are more representative of expected future hydro-

gen storage pressures. Two storage tubes were used for eachof three flame tests, with the remaining six tubes closed to the

manifold. During a typical tank blowdown test, the pressure

decreased from its initial value to near atmospheric pressure at

an exponential decay rate over a period of approximately 500 s.

0.5 cm ID

1.75 cm IDx 8.2 m length 15.2 cm ID

29.2 cm

StagnagtionChamber

Jet

0.79 cm ID

413 bar (6000 PSI) Test Setup

H2 storage tubes: 2 Banks of 4 tubesconnected to 0.5 cm ID tubing .Volume of each tube is 21.8 cubic feet.

dj= 0.508 cm ID

0.79 cm ID

Jet Nozzle

Details

1.9 cm IDx 3 m length

0.508 cm

4.44 cm

Fig. 2. Schematic of experimental flow delivery system for 413bar (6000 psi) tests.

It should be noted that the conventional hardware in the

commercially available tube trailer was modified to remove

several flow restrictions that would have limited the flow

throughput. Thus, the piping transporting the hydrogen out of

the trailer was maintained at a minimum inner diameter (ID) of5.08 mm. The hydrogen was delivered to a stagnation chamber

by two lengths of 1.9 and 1.75 cm ID stainless steel tubing.

The stagnation chamber, located just prior to the jet exit, was

29.2 cm in length by 15.2 cm inside diameter and was sized

to maintain a low flow Mach number (less than 1 103). At

this Mach number, the measured pressure and temperature in

the stagnation chamber were in excellent agreement with the

true stagnation conditions. Both the stagnation chamber pres-

sure and temperature histories were measured for the duration

of each test. The temperature was measured with a type-K

thermocouple, while the pressure was measured using a

piezoresistive pressure transducer. Both voltage outputs were

digitized at a 500Hz rate and stored on a Nicklet-digitized

storage scope for post-processing. The jet exit conditions

could then be calculated assuming isentropic expansion (see

Section 3.4) between the stagnation chamber and the verti-

cally orientated, 5.08-mm diameter jet exit. The stagnation

chamber was designed into the present experimental setup to

provide a more controlled, well-defined flow into the jet. In

the previous 172bar (2500 psi) tests, no stagnation chamber

was used and the jet exit conditions were calculated using

the Sandia Topaz network flow model [1214] to predict the

flow through the piping leading up to the jet exit. Also note

that the jet diameter in the present experiments was 5.08 mm,

which is smaller than the 7.94-mm jet diameter of the previoustests. This smaller diameter was selected so that the 5.08-mm

diameter pipe leading out of the trailer could supply sufficient

hydrogen flow to maintain a high pressure in the stagnation

chamber.

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Table 1

Flame conditions

Flame dJ (mm) uJ (m/s) Q (slm) m (g/s) mh1c

a (kW)

Lab flame: H2 1.91 87.7 15 0.021 2.641.91 116.3 20 0.028 3.34

1.91 174.5 30 0.042 5.01

1.91 261.6 45 0.062 7.52

1.91 349.0 60 0.083 10.0

Lab flame: CH4 1.91 58.2 10 0.110 5.54

1.91 87.3 15 0.166 8.32

1.91 98.9 17 0.188 9.42

1.91 116.6 20 0.222 11.08

SRI flame: H2 5.08

t= 10 s 5.08 1140 2.57 105 359.3 43 105

t= 50 s 5.08 1079 1.63 105 228.6 27 419

t= 100 s 5.08 1056 1.02 105 142.6 17 112

t= 200 s 5.08 1052 4.59 104 64.2 7705

t= 300 s 5.08 1059 2.02 104 28.2 3385t= 400 s 5.08 1067 8.02 103 11.2 1344

ahc = 118830kJ/kg for hydrogen heat of combustion; 50 016kJ/kg for methane.

Results of the present 5.08-mm-diameter jet flame tests were

compared with measurements obtained in a laboratory-scale,

1.91-mm-diameter H2 jet flame in which measurements were

obtained as part of the present study. In addition to a H 2 jet,

methane was also used as a fuel in the laboratory flame to ver-

ify the measured difference in radiative heat flux from CH 4and H2 flames. These measurements removed the effect of

any differences in jet geometry and radiometer calibration onthe measurements and facilitated a more direct comparison of

the radiative properties of the two fuels. Shown inTable 1are

the flow conditions associated with each of these flames. The

times shown in the table for the 5.08-mm-diameter flame cor-

respond to different times in the cylinder blowdown tests.

3.2. Flame length measurements

Digital video images of the flame were obtained to charac-

terize the flame structure and length. The visible flame images

were recorded using two Sony Model DCR TRV27 video cam-

eras. The cameras here were located approximately 14 m fromthe jet centerline and located vertically so that the two cam-

eras covered a field of view extending from the jet exit (x = 0)

to 15 m in the vertical direction. The fields of view were over-

lapped to provide a continuous view of the entire flame length.

The images were stored at a standard 30 fps video frame rate,

which is not of sufficient temporal resolution to follow the

flame movement. In addition, the individual frame exposure

time of 33 ms is insufficient to capture the instantaneous flame

structure, which is averaged over this exposure time. Multi-

ple images were averaged together at selected times to provide

information on the time-averaged flame properties and pro-

vide quantitative data on the relevant flame length scales. Be-

cause of the relatively weak flame luminescence, all tests wererun at night to eliminate background light and improve flame

visibility.

3.3. Radiative flux measurements

Similar to previous tests [3] heat flux measurements were

obtained using Medtherm Model 64P-1-22 SchmidtBoelter

thermopile detectors with a 150 view angle. A zinc selenide

(ZnSe) window on the face of the radiometer has 70% trans-

mission between 0.7 and 17 m. Three separate tests were per-

formed to maximize the amount of data obtained. In the firsttwo tests our procedure followed the method of Sivathanu and

Gore[7], in which a thermopile detector was placed at a radial

distance,R, of half the visible flame length,Lf/2, at a selected

time during the test. Using a previously developed model for

flame length variation during the tank blowdown[15], the flame

length was estimated to be 9.1m at a time of about 20 s after

the initiation of a test. Thus, radiometers were placed at a radial

distance,R, of 4.57 m from the jet centerline and at axial incre-

ments of 1.52 m along the flame length. The radiometer loca-

tions for tests 1 and 2 are indicated to the left side of the flame

shown schematically inFig. 3. These measurements enabled us

to verify whether the scaling laws for radiative heat flux pro-

files along the flame length at the higher tank pressures of the

present investigation matched results measured at lower pres-

sures. Four additional radiometers were also placed in the jet

exit plane at 0.3 m increments in the radial direction and aimed

in the direction of the jet flow to record the radial component

of the heat flux. Two tests were performed with this radiometer

orientation to verify the reproducibility of the data sets.

Once these scaling relationships were verified for the current

tests and the flame length history was established, a third test

was performed in which the six radiometers were placed along

an approximately 45 line from the jet centerline and originat-

ing from the jet exit. These radiometer placements are shown

on the right side of the flame in Fig. 3. Since the flame lengthvaried with time during each tank blowdown, these radiome-

ter locations resulted in six times during blowdown where the

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Luminousflame zone

FlameTip

H2

AmbientStill Air

x

r

x=1.52 m

x=3.04 m,

x=4.57 m

x=6.09 m

x=7.62 m

x=9.14 m

r=4.57 m

x=r=1.52 m

x=r=3.04 m

x=r=4.57 m

x=r=0.76 m

RadiometerLocations forTests 1 & 2

RadiometerLocations forTest 3

r=0.3 m

Fig. 3. Experimental setup and coordinate system for turbulent-jet flame.

radial and axial location of one radiometer are both equal to half

the visible flame length. Thus, the measured value of the radia-

tive heat flux at those locations, qrad(x/Lf= 0.5,r/Lf= 0.5),

and the known value ofC(x/Lf= 0.5,r/Lf= 0.5) could be

used to determine the total radiative power emitted from the

flame,Srad, from Eq. (5), The radiant fraction,Xrad, could thenbe determined from the known value of the heat release due

to chemical reaction,mfuelHc using Eq. (4). This approach is

similar to that used by Turns and Myhr [8].

3.4. Jet exit conditions

Stagnation chamber temperature and pressure were measured

directly during tank blowdown. The non-dimensional flame

length,L, and Froude number, Fr, used to correlate the flame

length (Eqs. (1)(3)) and the flame residence time (Eq. (7)) re-

quire conditions at the jet exit (Level 2 in Fig. 1) if the flow is

subsonic, and at the notional nozzle exit (Level 3) if the flowis choked and the jet is underexpanded. In the case of subsonic

flow, isentropic relations can be used to relate the known con-

Table 2

Compressibility factors for hydrogen at 300K

P (bar) P (psi) Z

68 1000 1.04

172 2500 1.10

344 5000 1.23

689 10 000 1.43

1034 15 000 1.65

ditions at Level 1 with those at the jet exit, Level 2. In the

underexpanded jet case, the isentropic relations are again used

to relate the conditions at Level 2 to Level 1. In addition, Eqs.

(10) and (11) for underexpanded jets are used to calculate con-

ditions at the notional nozzle exit.

The application of isentropic flow relations to tank blowdown

is straightforward at lower pressures where ideal-gas behavioris valid. In fact, at pressures up to about 172 bar (2500 psi), the

gas can be treated to a good approximation as ideal. However, at

higher pressures the gas behavior increasingly departs from that

of an ideal-gas and the relations must be modified to account

for gas compressibility. Equations of state such as the two-

constant van der Waals equation and the BeattieBridgeman

equation with five constants have been used to describe real-gas

behavior[16]. It has also been shown that real-gas behavior of

hydrogen in the present context of a sudden gas expansion from

a high-pressure reservoir can be adequately described through

an AbelNobel equation of state of the form

P=RH2T(1 b)

= ZRH2T, (12)

where Z = 1/(1 b) is the compressibility factor, b is the

co-volume constant, and RH2 is the gas constant for (RH2 =

4.1 2 N m/gm K). The value ofZfor an ideal-gas is unity (b=0

for an ideal-gas) and values different from unity indicate depar-

tures from ideal-gas behavior. Shown inTable 2are values ofZ

for hydrogen at a temperature of 300 K and various pressures.

The pressure range shown is indicative of expected future hy-

drogen storage pressures. It can be seen that departures from

ideal-gas behavior do indeed become significant at pressures

above 172 bar (2500 psi).

Rearranging the AbelNobel equation of state, Eq. (12), thegas density at the stagnation temperature and pressure, T0 and

P0, is given by

0 =P0

P0b + RH2T0, (13)

where b is 7.691 103 m3/kg for hydrogen. It can further

be shown for the isentropic flow of an AbelNoble gas from a

high-pressure stagnation state to the jet exit that gas density in

the stagnation reservoir and at the jet exit are related by

0

1 b0

=

j1 bj

1 +

1

2(1 bj)2

M2j

/(1),

(14)

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where M is the Mach number, is the specific heat ratio

and the subscripts 0 and jrefer to stagnation conditions and

conditions at the jet exit, respectively. Assuming choked (sonic)

flow at the jet exit, then Mj = 1 and Eq. (14) reduces to

0

1b0

=

j

1bj

1+

1

2(1bj)2

/(1). (15)

The left-hand side is known from the measured stagnation tank

conditions through Eq. (13) so that Eq. (15) can be solved to

obtain the jet exit density, j. Further, for isentropic flow of an

AbelNoble gas the ratio of the temperature in the stagnation

tank to the jet exit temperature is given by

T0

Tj= 1 +

1

2(1 bj)2

M2j (16)

which for choked flow at the jet exit becomes

Tj =T0

1 +( 1)/2(1 bj)

2 . (17)

Thus, knowing the measured stagnation tank temperature and

the jet exit density from Eq. (15), Eq. (17) can be used to

calculate the jet exit temperature. Now, from the AbleNoble

equation of state the pressure at the jet exit can be obtained

from

Pj =jRTj

1 bj. (18)

Finally, the sonic velocity, a, of an AbleNoble gas at the jet

exit can be determined from the known jet exit temperature,

the jet exit density, and the equation

uj = a =1

(1 bj)

RTj. (19)

4. Experimental results

4.1. Tank blowdown history

Fig. 4shows the measured stagnation chamber pressure andtemperature during the tank blowdown. FromFig. 4a it can be

seen that the initial storage tube pressure of 431 bar (6258 psi)

decreases to near atmospheric pressure at the end of the test.

The double exponential equation given in the figure provides a

best fit to the data. The total blowdown time for each test was

approximately 500600 s (for a two-tube blowdown). The stag-

nation temperature decreased rapidly to a minimum of about

45 C at about 140 s into the test before increasing due to heat

transfer from the surroundings. A best fit to the temperature

data is also given in the figure.

An interesting aspect of the stagnation chamber data is seen

during early times in the blowdown. Shown in Fig. 4b is an

expanded view of the temperature and pressure profiles corre-sponding to the first 10 s after the test was initiated. The stag-

nation pressure undergoes a rapid decrease over the first 0.5 s,

followed by a more gradual rate of decrease for times greater

than about 1 s. The stagnation temperature shows a similar ini-

tially rapid decrease during the first 0.5s, passes through a

minimum between 0.5 and 1 s into the release, followed by a

broader maximum at about 3 s. A gradual decrease then occursuntil 140 s into the release (seeFig. 4) where a second mini-

mum is located.

The cause for the more complex behavior at short release

times is unclear, but it can be speculated that the initially rapid

pressure decrease might be due to the longer time constant

associated with flow entering the stagnation chamber than that

associated with flow exiting the chamber through the relatively

short pipe leading to the jet exit. This scenario is based on the

sequence of operations that occurs before actual testing. Prior

to the initiation of a test, solenoid valves located at the exit

of the tube trailer and immediately upstream of the jet exit

are closed and residual gas in all lines is evacuated to assure

that the test is started with pure hydrogen in the system. Next

the solenoid valve at the exit of the tube trailer is remotely

opened to allow hydrogen to enter the system. Since the valve

between the stagnation chamber and the jet exit is closed, the

pressure equalizes with pure hydrogen throughout the system.

Thus, a constant initial pressure is attained in the hydrogen

storage tubes, all piping and in the stagnation chamber. To

initiate a test, the solenoid valve downstream of the stagnation

chamber is remotely opened and the pressurized hydrogen is

released through the jet exit. Due to the small volume of piping

after the stagnation chamber, it is speculated that the initial

flow of hydrogen from the stagnation chamber occurs rapidly,

while the large volume of piping between the storage tubesand the stagnation chamber requires a longer time to provide

an equal amount of hydrogen to the stagnation chamber. This

imbalance results in an initially rapid decrease in stagnation

chamber pressure before the hydrogen can be replenished at a

rate equal to that being released.

Shown in Fig. 5 is a comparison of measured stagnation

chamber pressure and temperature and the predicted behav-

ior using the Topaz network flow model. Several heat trans-

fer boundary conditions were tried in the model. In the initial

calculations, an adiabatic system was assumed in which zero

heat transfer to the high-pressure reservoir (H2 storage tubes),

the stagnation chamber and the piping occurred. The results(curve labeled adiabatic) showed a more rapid decrease in stag-

nation chamber pressure than measured and a stagnation cham-

ber temperature significantly below the experimental value.

Subsequent calculations assuming heat transfer to a constant

temperature wall showed that heat transfer to the reservoir dom-

inated the predicted temperature history and that the calculation

was insensitive to whether adiabatic or non-zero heat transfer

was imposed on the stagnation chamber and piping. Thus, pre-

dicted histories are shown inFig. 5assuming full heat transfer

to the reservoir, stagnation chamber and piping at a constant

wall temperatures of 289 and 267 K. The predicted pressure

and temperature histories show good agreement with measured

results for both values of wall temperature. The agreementis not exact because the actual wall temperature likely varies

in time and is dependent on the thermal mass of the walls.

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0

1000

2000

3000

4000

5000

6000

-50

-40

-30

-20

-10

0

10

20

0 100 200 300 400 500

Pstag(psig)

P_fit (psig)

Tstag(C)

T_fit (C)

Pstag

(psig)

Tstag

(C)

Time (s)

P=-45.2173+3141.95*exp(-0.0076595*t) +1635.99*exp(-0.0379651*t)

T=-51.375+0.035753*t+34.713*exp(-0.022375*t) +23.426*exp(-0.023006*t)

3500

4000

4500

5000

5500

6000

6500

-15

-10

-5

0

5

10

15

20

0 4 8 10

Pstag

(psig)

Tstag

(C)

Time (sec)

2 6

(a) (b)

Fig. 4. (a) Stagnation chamber pressure and temperature tank blowdown history for initial tube pressure of 431bar (6258 psig). (b) Stagnation chamber pressure

and temperature tank blowdown history during initial 10 s of blowdown. Initial tube pressure of 431bar (6258 psig).

0

1000

2000

3000

4000

5000

6000

0

50

100

150

200

250

300

0 100 200 300 400 500

MeasuredFull Heat Transfer, Tw=289 KFull Heat Transfer, Tw=267 KAdiabatic

Pstag

(psig)

Tstag

(K)

Time (s)

Twall = 289 K

Twall = 267 K

Adiabatic

Fig. 5. Comparison of experimentally measured and Topaz predicted stagnation chamber pressure and temperature during tank blowdown for initial tubepressure of 431bar (6258 psig).

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0

1000

2000

3000

4000

5000

6000

7000

0 50 100 150 200 250 300

PstagPjetPjetPstagPstorePjet

Pressure(psi)

Time (sec)

Topaz Storage Tube

Topaz Stagnation Chamber

Isentropic Ideal GasJet Exit

Measured Stagnation Chamber

Isentropic Abel-Noble Jet Exit

Topaz Jet Exit

Fig. 6. Comparison of experimentally measured pressure history and Topaz

predictions during tank blowdown. Initial tank pressure 431 bar (6258 psig).

In contrast, the Topaz network flow calculation assumes a con-

stant wall temperature during the entire tank blowdown.

Fig. 6 shows the pressure-history curves in the hydrogen

storage tube, the stagnation chamber and at the jet exit. The

measured stagnation pressure history is shown, while Topaz

predicted curves for the storage tube, stagnation chamber andjet exit are shown for comparison. The curves labeled isentropic

ideal gas jet exit and AbelNoble jet exit were calculated using

the measured values of stagnation chamber pressure and the

isentropic expansion of either an ideal-gas or a non-ideal gas

that obeys the AbelNoble equation of state. Note that the Topaz

model accounts for frictional losses and heat transfer in the

piping during expansion and thus does not assume an isentropic

expansion.

A comparison of the measured and predicted stagnation

chamber pressures shows that the measured pressure initially

decreases more rapidly than indicated by the model. Thus,

the initially rapid measured pressure drop over the first 0.5 sseen in Fig. 4b is underpredicted by the model, which does

not appear to predict the initial transient blowdown behavior.

However, for times greater than about 35 s the model predicts

only a slightly lower stagnation pressure.

Also shown inFig. 6is the predicted storage tube pressure.

It can be seen that the pressure in the tube is generally about

5% higher than the predicted stagnation chamber pressure at

the same time. This difference is due to losses in the pipes

connecting the storage tubes to the stagnation chamber, which

were minimized so that the highest stagnation chamber pressure

could be realized.

A comparison of jet exit pressures assuming isentropic flow

between the stagnation chamber and the jet exit shows thatthe ideal-gas assumption predicts up to 8% higher pressures

than an AbelNoble gas early in the tank blowdown where the

gas pressure is highest. For times greater than about 40 s the

two assumptions show good agreement and indicate ideal-gas

behavior is a good approximation. The predicted jet exit

pressure using the Topaz model is generally lower than the

isentropic expansion curves, reflecting the lower stagnationchamber pressures predicted by the model relative to the ex-

perimentally measured values. However, Topaz predictions

assuming an non-isentropic expansion between the stagnation

chamber and jet exit show good agreement with isentropic ex-

pansion results, indicating the isentropic expansion assumption

used to reduce the data is a good approximation.

Fig. 7shows a comparison of calculated jet exit conditions

based on isentropic expansion laws assuming an ideal-gas and

a gas that obeys the AbelNoble equation of state. As expected,

the maximum differences occur at the shortest blowdown times

where the pressures are highest. For example, at a time of

2 s into blowdown the stagnation chamber pressure is 312 bar

(4534 psi). The corresponding calculated jet exit properties for

an ideal gas and an AbelNoble gas are given in Table 3at a

time of 2 s. The differences at greater times become increasingly

small as the pressure drops.

4.2. Flame length

Fig. 8 shows typical single-frame video images of the vis-

ible flame at various times into the blowdown test. The field-

of-view in the images, which have been cropped in Fig. 8, is

about 11.3 m in the vertical direction, and about 5.0m in the

horizontal direction. In each image, the flame is vertically ori-

ented with jet flow from bottom to top, and the jet exit is lo-cated near the bottom center of the image. Fig. 8a corresponds

to a time very close to the initial flame ignition. Also seen in

the frame are two glowing wires extending horizontally across

the flame. These are the electrically heated nichrome wires

that are used as the ignition sources. They are located at dis-

tances ofx=1.9 and 2.6 m downstream of the jet exit and pass

through the jet centerline. Typically ignition occurs at the sec-

ond downstream wire where the flow velocity is sufficiently low

and the hydrogen/air mixture is within the flammability limits.

Figs. 8b and c, which are images taken at slightly later times,

show that from the initial ignition point the flame propagates

both upstream toward the jet exit where it stabilizes as a liftedflame (Fig. 8b) and downstream into the flammable mixture

created by the hydrogen and ambient air entrained into the jet.

The final image, Fig. 8d, corresponds to a time of 5s where

the flame has reached steady state. From this time until the end

of the test, the flame length slowly decreases over a period of

about 500s as the pressure in the hydrogen storage tube de-

creases. With the exception of changes in the total flame length,

the flame appearance remains constant during the test.

Flame lengths based on the visible flame video images were

used to determine the time-average flame length. The average

flame length, indicated by the data points in Fig. 9, was de-

termined from the flame length averaged over five successive

frames around the indicated time for each point. The flamelength decreases with time due to the decrease in mass flow

rate as tank pressure is reduced. Results are shown for all three

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Fig. 7. Comparison of calculated jet exit conditions using ideal-gas assumption and AbelNoble equation of state.

Table 3

Jet exit properties at a blowdown time of 2 s

Exit property Ideal gas AbelNoble gas % Difference

Pe (bar) 1.65 1.53 7.3

Te (K) 228 223 1.7

e (kg/m3) 17.6 14.8 16.0

ue (m/s) 1151 1284 1.2

m (kg/s) 0.41 0.385 6.1

blowdown tests to quantify the reproducibility of the flamelength data. Based on the three tests, the estimated uncertainty

in the time-averaged flame length is +/ 5%.

Shown inFig. 10is the non-dimensional flame length, L, as

a function of Froude number, Frf. The non-dimensional flame

length and the Froude number are given by Eqs. (1) and (2),

respectively. Included in Fig. 10 are flame length data from

Kalghatgi [5] for a range of fuels (H2, C3H8 and CH4) and

inlet flow conditions. Also shown is the flame length data of

Schefer et al. [3] for momentum-dominated jets at a lower

initial storage tube pressure of 2500 psi, which was found to

be in good agreement with the momentum-dominated value of

L = 23 forFr> 5. It can be seen that turbulent flame lengthsare well-correlated over a large range of flow conditions using

these non-dimensional parameters.

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Fig. 8. Photographs of visible flame luminosity at different times during

blowdown. Ignition wires are visible in first three times. Jet diameter is

5.08mm.

Values of Fr and L for the present data were calculated

using the time-averaged flame lengths in Fig. 9. Since the

present flow is choked at the jet exit, the concept of a no-

tional nozzle expansion and the effective source diameter

(as described in Section 2.3) was used in Eqs. (1) and (2)to reduce the hydrogen flame data and calculate the Froude

number. The present data are shown as solid red symbols in

Lvis(m)

0 100 200 300 400 500 600

Time (sec)

0

2

12

10

8

6

4

Fig. 9. Flame length history using visible flame emission.

1.0

10

102

0.1 1.0 10.0 100.0

H2choked (d=7.94 mm)

H2unchoked (d=7.94 mm)

CH4 (d=1.91 mm)H2(d=1.91 mm)

CH4(Kalghatgi)C3H8(Kalghatgi)

H2(Kalghatgi)

Present data (d=5.08 mm)

L*

Fr

L*=23L*=13.5Fr2/5/(1+0.07Fr2)1/5

Fig. 10. Variation of visible flame length with Froude number. Data is for

vertical jet orientation. Solid lines indicate correlations for buoyancy- and

momentum-dominated regimes as described by Eqs. (2) and (3).

Fig. 10over the range of 10

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0.0

0.20

0.40

0.60

0.80

1.0

1.2

0.0 0.50 1.0 1.5 2.0 2.5 3.0

C2H4 11.2

C2H4 20.2

CH4 12.5

CH4 6.4

C2H2 18.1C2H2 56.5

Fit to data of Ref. [7]H2data:

d=7.94mm / 2500psit=5 sec

t=10 sec

t=20 secd=5.08mm / 6000psi

t=20 sec

"

C*

x/Lvis

Fuel S (kW)

Fig. 11. Profiles of normalized radiative heat flux in a turbulent, hydrogen-jet

flame. Jet diameter is 5.08 mm. Jet orientation is vertical.

4.3. Radiative flux

The radiative heat flux measurements were integrated to

obtain the total heat radiated, Srad, which allowed the non-

dimensional radiant power, C , to be calculated from Eq. (6).

The distribution ofC for the present 5.08-mm-diameter H2-

jet flame is shown inFig. 11for a tank blowdown time of 20 s.

Data are shown for tests 1 and 2 in which the radiometers are

located along the length of the flame at a constant radial dis-tanceR (see configuration on left ofFig. 3). The blowdown time

of 20 s corresponds to a visible flame length that is twice the

radial distance R, in accord with the method of Sivathanu and

Gore[7]. It can be seen that the present data collapse onto a sin-

gle curve and show excellent agreement with the previous data

for lower-pressure hydrocarbon and hydrogen-jet flames. Thus,

the functional dependence for radiative heat flux expressed by

Eq. (6) applies to the present 413 bar (6000 psi) hydrogen-jet

flames.

The radiative heat flux data was also used to calculate the

radiant fraction,Xrad, using Eq. (4). In this case the data from

tests 1 and 2, as well as the data for the maximum radiativeheat flux obtained from the radiometers placed along a 45 line

to the flame centerline were used (configuration on right of

Fig. 3). The variation of radiant fraction with flame residence

time, given by Eq. (7), is shown in Fig. 12. Also shown is the

data of Turns and Myhr [8] for turbulent-jet flames using four

fuels with a wide variety of sooting tendencies. These fuels

included methane, ethylene, propane and a 57% CO/43% H2mixture. Also shown are previous results obtained in 1.91 mm,

subsonic hydrogen and methane jet flames at various flow rates

and in the 7.94-mm diameter hydrogen-jet flame during the

blowdown of a 172bar (2500 psi) source [3]. Note that the

data for non-sooting flames (CO/H2 and hydrocarbon flames

at shorter residence times) show a well-behaved, nearly lineardependence on log of the residence time. In contrast, at longer

residence times, the radiant fraction for fuels that have a high

0

0.05

0.1

0.15

0.2

0.25

0.3

1 10 100 1000

CO/H2(Turns&Myhr, 1991)CH4"C3H8"C2H4"

CH4(d=1.91 mm)H2(d=1.91 mm)

H2(d=7.94 mm)H2

"

Present data

RadiantFra

ction

Flame residence Time (ms)

Fig. 12. Radiant fraction as a function of flame residence time.

sooting tendency (propane and ethylene) becomes strongly de-pendent on residence time and behaves in a non-linear fashion.

The present data show excellent agreement with the previous

hydrogen-jet data and again indicate that, for a fixed flame res-

idence time, the radiant fraction of hydrogen jets is about a

factor of two lower than non-sooting hydrocarbon flames.

5. Summary and conclusions

Measurements were performed to characterize the dimen-

sional and radiative properties of large-scale, vertical hydrogen-

jet flames. High-pressure jets up to 413 bar (6000 psi) were

studied to verify the application of correlations and scaling lawsbased on lower-pressure subsonic and choked-flow jet flames.

At these pressures, the flows exiting the jet nozzle are cate-

gorized as underexpanded and the flow is choked at the jet

exit. Additionally, the gas behavior departs from that of an

ideal-gas and alternate formulations for non-ideal gas must be

introduced. The flame length results show that lower-pressure

engineering correlations based on the Froude number and a non-

dimensional flame length also apply to releases from storage

vessels at pressures up to 413 bar (6000 psi). Similarly, radiative

heat flux characteristics of these high-pressure jet flames obey

scaling laws developed for low-pressure, smaller-scale flames

and a wide variety of fuels. The results verify that such corre-

lations can be used to a priori predict dimensional characteris-tics and radiative heat flux from a wide variety of hydrogen-jet

flames.

Acknowledgments

This research was supported by the US Department of

Energy, Office of Energy Efficiency and Renewable Energy,

Hydrogen, Fuel Cells and Infrastructure Technologies Pro-

gram. The large-scale hydrogen-jet experiments were con-

ducted at the SRI International Corral Hollow Experimental

Site. Laboratory-scale flame experiments were conducted at

the Sandia Combustion Research Facility in laboratories sup-ported by the US Department of Energy, Office of Basic

Energy Sciences, Chemical Sciences.

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[3] Schefer RW, Houf WG, Bourne B, Colton J. Spatial and radiative

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[10] Birch AD, Huges DJ, Swaffield F. Combust Sci Technol 1987;52:

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[11]John JEA. Gas dynamics. Boston: Allyn and Bacon, Inc.; 1969.

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[13]Winters WS. TOPAZthe transient one-dimensional pipe flow analyzer:users manual. SAND85-8215, Sandia National Laboratories, Livermore,

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[14]Winters WS. TOPAZthe transient one-dimensional pipe flow analyzer:

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Documents

Schefer 2007