international journal of hydrogen energy xxx (xxxx) xxx
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: www.elsevier.com/locate/he
Development and application of hydrogen flare
radiation model for assessing hazard distance
Yongchen He a, Liang Pu a,b, Ruofan Sun a, Tongtong Yan a,
Hongbo Tan a,*, Zhao Zhang b
a
b
School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing, 100028, China
highlights
A appropriate flare hazard distance can effectively prevent potential thermal hazards.
A new model for predicting the hazard distance of hydrogen flares is developed.
Simulations and the new model improved prediction accuracy of hydrogen flare hazard distance.
The hydrogen flare radiation model was applied to various release conditions.
article info
abstract
Article history:
Flare stacks, used for emergency venting of redundant hydrogen, can cause jet fires that
Received 24 April 2023
pose thermal hazards to the surrounding environment. To accurately predict the hazard
Received in revised form
distance of hydrogen flare, it is necessary to develop a new flare radiation model. Also, the
7 June 2023
numerical simulations of hydrogen flame are carried out to assess the radiation hazard
Accepted 27 June 2023
area of the flares. The results show that the hazard distances predicted by the numerical
Available online xxx
method and the new model agree well with the HSL data fitted by exponential regression,
and the errors are less than ±5%. Furthermore, the new model and simulations were used
Keywords:
to analyze the distribution of thermal radiation for hydrogen flare under various release
Flare stacks
conditions. Increasing the release rates will drive the hazard boundary of flare system to
Hazard distance
expand. Additionally, as flare height increases, the radiation damage from the flare flame
Hydrogen flame
on ground is reduced due to buoyancy of combustion products.
Thermal radiation
© 2023 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction
Hydrogen is regarded as an important means for addressing
climate change and building the decarbonized society [1].
The rapid advancement of hydrogen energy technology has
resulted in a significant increase in both the quantity of
hydrogen being stored and the storage pressure required to
contain it [2,3]. Meanwhile, the increasing application scenes
of such hydrogen necessitates a deep understanding of the
consequences resulting from potential accidents involving
large-scale hydrogen leakage or hydrogen fire. Generally,
hydrogen ignition release is an effective measure for safe
disposal of redundant hydrogen in emergency situations. The
hydrogen flare stack is an essential component of the safety
protection system for the hydrogen energy storage and
transportation chain [4], and the hazard distances for
hydrogen flare is a crucial consideration in the design of the
* Corresponding author.
E-mail addresses: heyongch@126.com (Y. He), hongbotan@xjtu.edu.cn (H. Tan).
https://doi.org/10.1016/j.ijhydene.2023.06.319
0360-3199/© 2023 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
2
international journal of hydrogen energy xxx (xxxx) xxx
Nomenclature
Ceq
d0
D
De
Fs
HSL
I
l
L
L0
Lf
m_
m_ ng
MPS
Mair
Mp
PH2 O
PCO2
Q
Qi
Ri
Rh
Weighted carbon dioxide equivalent for CO2, N2,
H2O components
the flare exit diameter (m)
Hazard distance (m)
Equivalent gas source diameter (m)
Stoichiometric mass fraction fuel in mixture
The Health and Safety Laboratory
Incident radiation at the receiver (kW/m2)
Lift-off distance (m)
Flat section length of flame model (m)
Flame length in still air (m)
Distance from flare tip to flame end (m)
Release rate of gas fuel (kg/s)
Release rate of natural gas in the Chamberlain's
model (kg/s)
Multi-point source
Molecular weight of air
Molecular weight of combustion products
Impact of H2O in air on t
Impact of CO2 in air on t
Total energy released per unit time from fuel gas
combustion (kW)
Thermal quantity of the radiant point source i (kW)
Distances between radiative point sources i and
the receiver (m)
Ambient relative humidity (%)
hydrogen production, storage, delivery and terminal site
plan.
Many scientists and companies have carried out a great
deal of experimental and theoretical studies on the jet flame
and its thermal radiation generated by the hydrogen ignition
releases [5e10]. Brzustowski et al. [11] performed the
hydrogen diffusion flame tests in a crosswind and measured
the flame length. Fishburne et al. [12] conducted a series of
large-scale hydrogen ignition releases experiments at the
Rocketdyne test site in the United States, with flare vent diameters ranging from 6 to 27 inches and release rates ranging
from 2 to 126 kg/s. Thermal radiation from a large buoyant
flame was predicted using only a few parameters. The Health
and Safety Laboratory (HSL) [13] carried out the hydrogen flare
tests under variable flow conditions, as well as measurements
of flame geometry and heat flux at various locations. In
addition, the geometry of the hydrogen flame has a significant
influence on radiative heat transfer, which is typically determined by parameters such as flame length, lift-off distance,
tilt angle, etc. Bradley et al. [14,15] and Kalaghatigi et al. [16]
investigated the lift-off distances in choked and subsonic
hydrogen flames, and discovered that hydrogen behavior
differs obviously from that of hydrocarbon flames. Carboni
et al. [17] analyzed the effect of boundary conditions on the
hydrogen flame length using experimental and simulation
means. Considering the effect of crosswind on hydrogen and
hydrocarbon jet flames, literatures [18e20] demonstrated that
the hydrogen flame tilt angle is more sensitive to
RiðL0 Þ
RiðDe Þ
SPS
Smm
Tad
Tad;H2
Tair
uw
uj
V
Vi
Wb
Wt
k
ε
a
r0
t
b
d
d0
DH
Richardson number associated with the flame
length in still air
Richardson number associated with the
equivalent diameter of the flare
Single point source
Saturated water pressure at ambient temperature
(mm Hg)
Adiabatic combustion temperature (K)
Adiabatic combustion temperature of pure
hydrogen (K)
Ambient temperature (K)
Wind velocity (m/s)
Fuel velocity at flare exit (m/s)
Total volume of flame geometry model (m3)
Volume of the flame model for region i (m3)
Section base width of the flame model (m)
Section top width of the flame model (m)
Density correction parameters
Radiant heat fraction (%)
Tilt for natural gas flames using the Chamberlain
model
Air density (kg/m3)
Air transmissivity
Angle between the vertical axis of the flare and the
hydrogen flame axis
Flame velocity ratio
Corrected flame velocity ratio
Lower heating value of fuel gas (J/kg)
environmental factors. The flare stack tests conducted by HSL
among the above experiments provide more comprehensive
information on hydrogen flames and thermal radiation, and
the results can be used to validate numerical models of largescale flare flames.
In general, the great costs and risks make it difficult to
conduct hydrogen industrial flare tests, so numerical methods
become the most appreciated research tools. Singh et al. [21]
used CFD methods to model industrial flares and laboratorygrade flames, and the findings improved prediction accuracy
of combustion efficiency significantly. Considering the thermal radiation hazard of jet fires, Cirrone et al. [22,23] conducted numerical simulations to study cryogenic hydrogen jet
fires and assessed the thermal radiation damage. Jang et al.
[24] used the CFD software KFX to analyze the thermal radiation distribution of the large-scale fire in a factory, demonstrating that the results can be used to generate emergency
plans or prepare safety measures to avoid thermal radiation
hazards from fire. In addition, Jung et al. [25] employed the
CFD software FDS to assess the thermal radiation impacts
associated with emergency flaring of a floating LNG bunkering
terminal. This analysis was conducted to determine an
appropriate hazard distance for the facility.
In the field of engineering, researchers often utilize
computational models that were originally developed by early
oil companies to calculate the range of thermal radiation effects occurring during flare operations. Chamberlain's flare
radiation model [26] was constructed using a significant
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
3
international journal of hydrogen energy xxx (xxxx) xxx
amount of natural gas data to derive empirical equations for
flame length, flame tilts and radiation fraction. However,
when applied to hydrogen flames, the model may overestimate the radiation fraction at lower flow rates due to their
greater sensitivity to wind compared to natural gas flames
[27]. The API 521 model [28], which utilizes multiple types of
gas data and was initially designed for pool fire modeling,
tends to overestimate flame parameters when the release
rates of gases approaches the choke flow. It is well known that
these semi-empirical models are derived from hydrocarbon
release currently. In comparison with the release of hydrocarbons to the atmosphere, there are remarkable differences
in hydrogen flame geometry and thermal radiation behaviors.
As a result, this paper is based on Air Products' modified
method [29] of calculating hydrogen flame parameters to
more accurately predict hydrogen flare flame geometry,
allowing for the development of new hydrogen flare radiation
models with a more comprehensive approach for determining
hazard distances.
The new model advances the determination of a hazard
distances for hydrogen ignition release through the consideration of two primary factors: the precise characterization of
flame geometry and the assessment of thermal radiation intensity resulting from hydrogen flame at the receiver. In this
study, a CFD model for evaluating the hazard distance of a
hydrogen flare was validated. Based on an improved theoretical model, the hazard distance of the hydrogen flare was
predicted for varying release conditions. These findings offer a
valuable theoretical foundation for developing large-scale
hydrogen safety disposal strategies in the future.
Physical model
Base case
The hydrogen ignition releases experiment performed by HSL
in 2011 is employed to establish the physical model. Around
6 m of horizontal pipework were connected to the hydrogen
tube trailer to deliver gas to the vent stack, which was set up
outside in a center location without any building obstruction.
Hydrogen was released vertically from a 5.5 m high stack with
a 5.08 102 m nominal bore vent pipes, as seen in Fig. 1 [13].
According to HSL reported, two sets of experiments were
conducted for the ignition release of hydrogen with a mass
Fig. 1 e Hydrogen ignition releases experiment conducted
by HSL.
Table 1 e Experimental parameters.
Parameters
Flare stack height (m)
Flare exit diameter ( 102 m)
Mass flow rate (kg/s)
Atmospheric temperature (K) at release height
Experiment 1: atmospheric humidity (%)
Experiment 1: wind velocity (m/s) at release height
Experiment 2: wind velocity (m/s) at release height
Experiment 2: flame height (m)
Experiment 2: flame width (m)
Experiment 2: flame tip ( )
Values
5.50
5.08
0.40
273
90
3.20
10.0
7.68
4.31
33
flow rate of 0.4 kg/s. Experiment 1 monitored the incident
radiation from the hydrogen flame while the mean wind velocity at release height is 3.2 m/s, and experiment 2 monitored
the hydrogen flame geometry while the mean wind velocity at
release height is 10.0 m/s. More experimental details are
shown in Table 1 [13,29].
Model scale and boundary conditions
According to the HSL test, the computational model is built
with the size of 60 m 30 m 10 m in x, y, and z directions.
The circular hydrogen vent source faces upwards vertically
and the center of which locates at point (0, 5.5, 0). In addition,
eight fast response radiometers were arranged along the
downwind direction to measure the heat flux from the
hydrogen flame, which were mounted on poles at a height of
1.8 m and angled in towards the release. These sensors were
placed at horizontal distances of 2 m, 3 m, 4 m, 5 m, 7 m, 9 m,
25 m and 40 m from the center of the vent stack, respectively.
The corresponding sketch is drawn in Fig. 2.
The vent source face is a semicircle with a radius of
2.54 102 m, of which the boundary condition is mass flow
inlet. The boundary condition of the z ¼ 0 plane is symmetric to
save the computing resources. Also, the planes of y ¼ 30 m and
z ¼ 10 m are similarly designated as symmetric boundary
conditions, keeping both planes far away from the radiative
field of hydrogen flame to avoid the effects. The boundary
condition of the x ¼ 10 plane is velocity inlet. Finally, the
plane of x ¼ 50 m is set as the pressure outlet boundary
condition.
Fig. 2 e Physical model of hydrogen ignition releases.
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
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international journal of hydrogen energy xxx (xxxx) xxx
Continuity equation:
vrm
þ V $ ðrm !
vm Þ ¼ Sm
vt
(1)
vm represent the density and average velocity of
where rm and !
the mixture, the source term Sm refers to the mass that diffuses from other phases into the continuous phase, for
example, the phenomenon of liquid droplets evaporation exists in the model. However, the HSL test is a diffusion combustion phenomenon in which hydrogen combustion occurs
at the flare exit, without considering the evaporation of
droplets, that is, Sm ¼ 0.
The continuity equation is transformed as follows:
vrm
þ V $ ðrm !
vm Þ ¼ 0
vt
(2)
Momentum equation:
Fig. 3 e Grid independence test.
Mesh independence
The grids around the vent source and in the radiometer
placement zone are refined whereas the far-field grids can
become increasingly sparse. The grid number of control volumes is tested four times, and the numbers are 380,634,
530,073, 737,171, and 995,834. The Incident radiation at the
radiometers of near field (3, 1.8, 0) and far field (40, 1.8, 0) are
selected as the monitoring indicators. The test results are
shown in Fig. 3.
It is evident that as the grid number of control volumes
increases from 380,634 to 737,171, the incident radiation at the
sensor of near field has an apparent increase. When the grid
number of control volumes comes to 995,834, the incident radiation changes less than 3%. Moreover, the mesh number
increases from 530,073 to 995,834, there is almost no change in
incident radiation with far field. As a result, the following study
has assigned the grid number of control volumes as 737,171.
Mathematical model
Governing equations
When using flare stacks for hydrogen ignition release, the
vertical upward turbulent diffusion flames are commonly
regarded as non-premixed combustion cases. The radiation
emitted by the flare flame will then pass through the fluid
medium of the atmospheric environment, with a portion of
the radiation being absorbed and scattered along any given
path, potentially causing heat damage to surrounding
workers.
The mixture gas (hydrogen-air) is assumed to be incompressible and keep the ground as an adiabatic wall, the conservation equations for mixture mass, momentum, and
energy are solved to predict the flame combustion and thermal radiation behaviors of hydrogen ignition releases. The
continuity, momentum, energy and species equation are
expressed as follow [30]:
v
T
ðr !
vm Þ þ V $ ðrm !
vm $ !
vm þ V !
vm Þ ¼ Vp þ V½mm ðV !
vm Þ
vt m
g
þ rm !
(3)
where mm is the molecular viscosity, p is the static pressure.
g is the gravitational body force.
rm !
Energy equation:
v
v !
v
vT ! ðrm EÞ þ
ð vm ðrm E þ pÞÞ ¼
þ vm tij eff þ Sh
keff
vt
vxi
vxj
vxj
(4)
where E is the total energy. keff is the effective thermal conductivity. ðtij Þeff denotes the deviatoric stress tensor related
with the effective dynamic viscosity. Sh is the source term,
including the effect of enthalpy transport caused by species
diffusion.
Species transport model:
vðrm Yi Þ
!
þ V $ ðrm !
vm Yi Þ ¼ V $ Ji þ Pi
vt
(5)
where Yi represents the mass fraction of the species i, Pi is the
!
net rate of production of species i by chemical reaction. Ji
represents the diffusion flux of species i, which can be obtained by ðrm Di;m þmt =St ÞVYi . Di;m is the diffusion coefficient,
mt is the turbulent viscosity and St is the turbulent Schmidt
number.
Combustion model
In order to accurately describe the turbulent chemical reaction
of H2-Air, the combustion model was derived through the
Eddy Dissipation Concept (EDC) model [23,31], the concrete
expression is as follows:
. *
t 1 ðx* Þ3
Ri ¼ rm ðx* Þ2 $ Yi* Yi
x* ¼ Cx
(6)
1=4
nε
k2
(7)
n1=2
ε
(8)
t* ¼ Ct
where x* is the volume fraction of the fine scales and Yi* is the
species mass fraction over a time scale t* , n is the kinematic
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
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international journal of hydrogen energy xxx (xxxx) xxx
5
viscosity. Cx is a volume fraction constant equal to 2.1377, and
Ct is a time scale constant equal to 0.4082.
Simulation method and model validation
Turbulence model
General settings
The literature shows that the standard k-ε model is widely
used in industry due to its high stability, wide application, and
ability to produce accurate results quickly [32e34]. This study
utilizes the standard k-ε model as the turbulence model for
simulating flame combustion. The widely adopted twoequation model of the standard k-ε model relates turbulent
viscosity to turbulent energy and dissipation rate. The model
includes the turbulent kinetic energy equation k and the
diffusion rate equation ε:
The numerical simulation is carried out using the commercial
CFD code Ansys Fluent. Given the goal of modeling established jet flames with constant release conditions, a threedimensional steady-state flame combustion model was performed. Pressure velocity coupling is solved by Coupled
scheme. For the spatial discretization of momentum, energy,
turbulent kinetic energy, and turbulent dissipation rate, the
second-order upwind scheme is used. Both the energy and P-1
models had relaxation factors of 0.95. Residuals are all set as
106 for the solution convergence. Convergence is typically
achieved by allowing the scaled residuals for each equation to
reach a specific value. However, due to the nature of the
initialization, relying solely on scaled residuals for this study
could be misleading. To more accurately determine the
convergence of the solution, flow properties were monitored
to confirm that measurement of radiation was not changing
with additional iterations. Remote targets to record incident
thermal radiation were defined 1.8 m above the ground surface at horizontal distances of 2 m, 3 m, 4 m, 5 m, 7 m, 9 m,
25 m and 40 m, from the center of the flare stack. The location
of monitors is shown in Fig. 2.
v
v
v
ðr kÞþ ðrm kui Þ¼
vt m
vxi
vxj
m vk
mþ t
þ Gk þGb rm ε YM þ Sk
sk vxj
(9)
v
v
v
ðr εÞ þ
ðr εui Þ ¼
vt m
vxi m
vxj
m vε
mþ t
sε vxj
(10)
ε
ε2
þ C1ε ðGk þ C3ε Gb Þ C2ε r þ Sε
k
k
where Gk and Gb are the generation of turbulence kinetic energy due to the mean velocity gradient and buoyancy,
respectively. In compressible turbulent flows, YM represents
the contribution of fluctuating dilatation to the global dissipation rate. C1ε , C2ε and C3ε are constants. Sε and Sk are userdefined source terms. The turbulent viscosity mt , is
2
computed by combining k and ε and as mt ¼ rm Cmm kε , and Cmm is
a constant.
Radiation model
The radiative heat transfer from the flare flame depends not
only on the flame temperature but also on the fluid medium's
radiation absorption and scattering capacity. It is crucial to
consider the product H2O resulting from a large-scale
hydrogen fire when analyzing radiative heat transfer. The
absorption coefficient of the gas medium is acquired using a
weighted sum of gray gases model (WSGGM) [35,36]. The P-1
model was employed to simulate radiation hydrogen flame
[37]. When dealing with media that can absorb, emit, and
scatter radiation, the radiative transfer equation (RTE) at a
given position !
r and direction !
s can be expressed as
follows:
Z4p
4
!
dIð!
r ;!
sÞ
ss
!
!
2 sT
þ ðl þ ss ÞsIð r ; s Þ ¼ lw
þ
Ið!
r ;!
s ÞFð!
s ; s0 ÞdU0
ds
p
4p
0
(11)
!
where !
r is the position vector, !
s is direction vector, s0 is the
direction vector of scattering, s is the length along the path of
radiation, l is the absorption coefficient, w is the refractive
index, ss is the scattering coefficient, s is the StephenBoltzmann constant with a value of 5.67 108 W/m2$k4, I is
the intensity of thermal radiation, depending on !
r and !
s , F is
the scattering coefficient of condensed phase, U0 is the solid
angle, ðl þss Þs is the extinction coefficient of medium.
Model validation against HSL test
The numerical model was validated through the selection of
two sets of experiments in the HSL test. In Experiment 1, the
incident radiation was monitored using eight radiometers
while the shape of the hydrogen flame was captured by an
infrared camera. However, the thermal emissivity of the
hydrogen flame could not be accurately adjusted by the thermal imaging camera, which made it impossible to measure the
flame length and tilt angle [13]. As a complement, the visible
hydrogen flame was measured for its length, width, and tilt at
constant release conditions in experiment 2. However, the
incident radiation was not recorded during these tests.
Fig. 4 shows a high level of similarity between the flame
geometries of experiments 1 and numerical simulations. Besides, Fig. 5 compares the incident radiation of the hydrogen
flame from experiments 1 and numerical simulations. From
near-field to far-field, the simulated incident radiation is
gradually decreased from 7.68 to 0.23 kW/m2, compared with
the actual situation (the average value decreased from 9.43 to
0.27 kW/m2) [13,29], the maximum error is within 18%. It is
obvious that the environmental disturbances have an impact
on the shape of the flame. As a result, the experimental data
from HSL exhibits slight discrepancies when compared to the
simulated values of the near-field incident radiation, particularly at the measurement points (5, 1.8, 0). When the radiometer is placed in the far-field, the shape of the flare flame
has minimal impact on the far-field thermal radiation.
Therefore, it is assumed that the thermal radiation from the
flame is emitted from a point source. The hazard distance for
the thermal radiation from the flare is usually located in the
far field, and the simulated incident radiation is in good
agreement with the experimental data.
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
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international journal of hydrogen energy xxx (xxxx) xxx
Fig. 4 e Model validation 1: flame geometry of experiment 1. (a) Numerical simulation. (b) HSL infrared image.
Fig. 5 e Model validation 2: incident radiation of
experiment 1.
In experiment 2, hydrogen flame geometry captured by
infrared camera at night, the visual flame length is obtained
directly [13], and the corresponding data were reported in the
literature [29]. The boundary and initial conditions in experiment 1 and 2 were identical, except for the wind velocity. In
addition, the temperature threshold is the most commonly
used method in CFD to determine the flame length. In
hydrogen combustion experiments, Schefer et al. [9,38] used
the combustion temperature of 1300e1500 K as a criterion for
the hydrogen flame boundary, which is used to determine the
flame geometry in this study. According to the actual situation
of HSL experiment, the flame geometrical sizes of hydrogen
flame were simulated. Fig. 6 demonstrates the comparison of
the flame height, width and tilt between the experiments 2 and
the numerical simulations. It can be seen that the geometry
corresponding to flame height, width and tilt are 6.95 m, 4.53 m
and 34.50 , respectively, which is highly correlated with the
reported geometrical sizes of hydrogen flame in Table 1 [13,29],
proving the accuracy of the numerical model.
Based on the validation studies described above, it is
confident to say that the proposed model is reliable in simulating the geometry of hydrogen flame and the transfer
behavior of thermal radiation.
Fig. 6 e Model validation 3: hydrogen flame geometrical
sizes of experiment 2.
New model for developing hydrogen flares
hazard distances
Model fundamentals
Hydrogen ignition release is an effective measure for safe
disposal of redundant hydrogen in emergency situations. The
hazard distances for hydrogen flare is a crucial consideration
in the design of the hydrogen production, storage, delivery
and terminal site plan. In general, scholars have used semiempirical models developed to study the thermal radiation
behavior from flare stack. The single point source (SPS) model
is widely used in engineering calculations because it is simple
to calculate, but its results are only accurate in the far field
[39]. The multi-point source (MPS) model considers incident
radiation received by the target as a superposition of radiation
from each point source distributed along the centerline of the
flame [40]. The solid flame model accurately predicts the nearfield and far-field thermal radiation of the flare stacks, but the
complexity of computational process makes it not widely used
in the engineering field. Subsequently, Chen et al. [41] established a sub-regional and multi-point source model for
calculating the hazard distance of elevated flares, which
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
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international journal of hydrogen energy xxx (xxxx) xxx
7
Fig. 7 e Schematic diagram of theflare radiation model.
combines the respective advantages of the point source flame
model and the solid flame model.
In this paper, first of all, the cone frustum model [41e43] is
used to assume the geometry of the flare flame and the schematic diagram is shown in Fig. 7. From the flare tip to the flame
end, the jet flame temperature shows a trend of increasing and
then decreasing. Then, the jet flame can be divided into three
regions based on the surface temperature and the thermal
radiation properties [6,44e46]. The thermal radiation in each
region is represented by a radiation source, which means that
the jet flame as a whole is considered as three radiation sources. Finally, the amount of radiation emitted by the radiation
source in each region is determined by the volume ratio of the
region to the total volume of the jet flame.
It is well known that these semi-empirical models are
derived from hydrocarbon release currently. In comparison
with the release of hydrocarbons to the atmosphere, there are
significant differences in hydrogen flame geometry and thermal radiation behaviors [29]. Based on the model described
above, the paper optimized the calculation method for the
hazard distance of hydrogen flare. A new flare radiation model
based on sub-regional and multi-point sources is being
developed through MATLAB software, which is applicable to
hydrogen ignition releases. The following is a brief overview of
the calculation steps.
1. Determine the flame length L0 in still air and equivalent gas
source diameter De.
2. Determine flame geometry, flame length Lf in crosswind,
lift-off distance l, and flame tilt b.
3. Establish a sub-regional and multi-point source model
based on flame geometry.
4. Add up the thermal radiation received by the target point
from each region to determine the hazard distances.
Flame length in still air
Diffusion flame length L0 in still air is widely used in flare radiation models, and Chamberlain developed an expression for
L0 based on Kalaghatigi [16], as shown in Eq. (12). The difference in fuel gas properties renders the above equation inapplicable to the hydrogen combustion reaction, whereas the
correction for adiabatic combustion temperature Tad increases the applicability of the equation.
ðDe k=L0 Fs Þ2=3 ¼ A þ B$RiðL0 Þ
k¼
1=2
Mair $Tad
Mp $Tair
100Tad ¼ Tad;H2 73:95C2eq þ 3:66Ceq þ 99:72
(12)
(13)
(14)
where RiðL0 Þ is the Richardson number in still air, represented
by RiðL0 Þ ¼ ðg=ðDe uj Þ2 Þ1=3 $L0 . Fs is stoichiometric mass fraction
fuel in mixture. The equivalent gas source diameter can be
0:5
_
obtained by De ¼ ð4m=ðpr
0 uj ÞÞ , m. A and B are constants
equal to 0.200 and 0.024. uj is the fuel velocity at flare exit, m/s.
m_ is release rate of gas fuel, kg/s. k represents the density
correction parameters. Tad;H2 is adiabatic combustion temperature of pure hydrogen. Mair and Mp represent the molecular weight of air and combustion products. Tair is ambient
temperature. Ceq represents the weighted carbon dioxide
equivalent for CO2, N2, H2O components.
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international journal of hydrogen energy xxx (xxxx) xxx
flame velocity ratio, and the x can be expressed by x ¼
3 $RiðL0 Þ $m_ =ðm_ ng $400Þ.
Flame tilt
The predicted angle of tilt for natural gas flames using the
Chamberlain model is represented by a [26], while b refers to
the angle between the vertical axis of the flare stack and the
hydrogen flame axis.
a¼
d < 0:05
8000d=RiðL0 Þ
.
1726ðd 0:026Þ0:5 þ 134 RiðL0 Þ d 0:05
(15)
where d is the flame velocity ratio, represented by d ¼ uw =uj ,
and uw is the wind velocity, m/s. r0 is the air density, kg/m3.
The tilt at which the hydrogen flame bends due to crosswind conditions is greater than that of the hydrocarbon. A
correction term is used to improve the accuracy of the
computational model [29], as shown in Eq. (16).
b¼a
m_ ng
m_
(16)
In which,
m_ ng ¼ 255:42d20 $Yng
100Yng ¼
(17)
8
< 200:74X2 101:03Xng þ 1:85; Xng > 0:665
ng
: 78:73X2:9013
;
ng
Xng 0:665
.
Xng ¼ L0 174:83d0:8794
0
(18)
Hydrogen flame geometry model
In Fig. 7, a schematic diagram of a cone frustum flame
model is presented [41e43], where the actual geometry is
calculated based on the above corrected parameters and
divided into three regions. And the geometry model is
derived as follows:
Flat section length of flame model:
1=2
l cosðaÞ
L ¼ L2f l2 sinðaÞ
(25)
Lift-off distance l in Chamberlain's method, which has
been found to be adequate for hydrogen, is directly used in the
new model.
8
b¼0
< 0:2Lf (26)
l ¼ Lf sin 0:185e20d þ 0:015 $a sinðaÞ 0 < b < p
:
0:015Lf
b¼p
The section base width of the flame model is expressed as
below:
qffiffiffiffiffiffiffiffiffiffiffi Wb ¼ De $ 13:6e6d þ 1:5 $ 1 0:067 1 r0 rj e70$RiðDe Þ$wd
(27)
(19)
where, m_ ng (kg/m3) is the release rate of natural gas in the
Chamberlain's model. Xng is the ratio of L0 to still-air flame
length at given Mach number, in Chamberlain's model [26,29].
Yng is derived from Xng , which can be seen in Eq. (18). d0 is the
where, RiðDe Þ is the Richardson number associated with the
equivalent diameter of the flare, which is calculated as RiðDe Þ ¼
ðg=ðDe uj Þ2 Þ1=3 $De , and the w can be obtained by ð1000e100d þ0:8Þ.
The section top width of the flame model can be expressed
by the following equation:
d
Wt ¼ Lf $ 0:18e1:5 þ 0:31 $ 1 0:47e25d
(28)
flare exit diameter, m.
Incident radiation at the point of interest
Flame length in crosswind
According to Chamberlain model, the length of the natural gas
flame decreases as the wind velocity increases, see Eq. (20)
[26]. Actually, the literature [11,29] indicates that there is a
positive correlation between flame length and wind velocity
when the hydrogen flame tilt angle exceeds 60+ approximately. As a result, it is necessary to correct the flame length
in crosswind conditions to make the model more widely
application, as shown in Eq. (21).
Lf ¼ L0 0:51e0:4uw þ 0:49
Lf L0 ¼
aebb ;
b p=3
0
0:51e0:4d uj þ 0:49; b > p=3
(20)
(21)
In which,
a ¼ e90b
(22)
0
b ¼ 0:033 ln 1 0:51e0:4d uj þ 0:49
(23)
d0 ¼
0:026 þ
x;
2
60$RiðL0 Þ$m_ m_ ng 134 1726 ; x > 0:05
x 0:05
(24)
where Lf is the distance from flare tip to flame end, m. a and b
are correction parameters of flame length, d0 is the corrected
Total volume V (m3) of the flame geometry model is expressed
as below:
V ¼ ðpL = 12Þ$ Wb2 þ Wt2 þ Wb Wt
(29)
Similarly, the volume of the flame model is calculated for
each of the three regions sequentially.
Determine the thermal quantity Qi of the radiant point
source i, which can be expressed by the following equation:
Qi ¼
Vi
Q ði ¼ 1; 2; 3Þ
V
(30)
where, Q is total energy released per unit time from fuel gas
_
combustion, which can be obtained by m$DH,
DH is lower
heating value of fuel gas, J/kg. Vi is the volume of the flame
model region i (i ¼ 1, 2, 3).
Assuming that the horizontal distance between the
receiver and the flare stack is D, the incident radiation
received by the target is the total radiative heat flux I generated by three radiation point sources superimposed at the
receiver, as shown in the following equation.
IðrÞ ¼
n
X
εQi t
i¼1
4pR2i
(31)
where, I is the incident radiation value at the receiver,
kW/m2. The distances between radiative point sources i
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
9
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 8 e Comparison of various methods for predicting the distribution of thermal radiation from hydrogen flares.
(a) Incident radiation from the hydrogen flare. (b) Hazard distance of the hydrogen flare.
and the receiver are represented by Ri (i ¼ 1, 2, 3), and
n ¼ 3.
ε is radiant heat fraction, which was obtained by AP flame
model using publicly available hydrogen data [29]. The radiant
heat fraction is highly correlated with the mass flux at the
flare exit under vertical release conditions, and the ε of a small
ignition-released flame has a minimum value of 0.05 [47].
(32)
ε ¼ Max 0:1691 0:01 ln Mflux ; 0:05
Mflux ¼
4m_
pd20
(33)
Air transmissivity t, reported by Wayne, was defined as the
fraction of radiant heat from the flame that is transmitted
through the air to the receiver [48]. It should be noted that the
method was developed through hydrocarbon combustion, but
the findings are also applicable to hydrogen flames. The expressions are shown below:
2
1000t ¼ 1006 11:71 $ log10 PH2 O 23:68 log10 PH2 O
(34)
2
31:88 $ log10 PCO2 þ 1:164 log10 PCO2
8
PH2 O ¼ 288:651ðRh Ri Smm =TÞ
>
>
>
>
<P
CO2 ¼ 273ðRi =TÞ
>
>
3816:42
>
>
: Smm ¼ 0:0075 exp 23:18986 T0 46:13
1=2
2
R2i ¼ ðx xi Þ2 þ y yi þ ðz zi Þ2
(35)
(36)
where PH2 O and PCO2 are impact of H2O and CO2 in air on t,
respectively. Rh represents the ambient relative humidity, %.
Smm is the saturated water pressure at ambient temperature,
mm Hg.
Then, assuming that the incident radiation at the target
point of interest is the radiative hazard threshold for long
exposure, the hazard distance D of the hydrogen flare can be
solved using the above description.
ignition release, using the modified model mentioned above.
Additionally, a comparison was made between the new model
and conventional SPS model and MPS model, the discrepancies in the results were further analyzed. To compare with
the new model presented in this study, a conventional MPS
model was used to calculate the engineering example with the
same number of point sources as the new model (three). The
results are presented in Fig. 8. To avoid potential hazards to
surrounding personnel and equipment caused by heat radiation from jet fires, it is critical to understand the distribution
characteristics of thermal radiation during flare stack operations. The hazard criteria [49] in Table 2 are used to assess the
hazard distances of thermal radiation from a jet fire, and
determine the hazard distance in accordance with the hazard
threshold of acceptable thermal radiation for personnel.
Using HSL experimental data as the reference, Fig. 8(a)
demonstrates the predicted results of the new model show
good agreement in both the near-field and far-field, but the
results of both the SPS model and the MPS model are significantly over-estimating the whole incident radiation of the
flare flame. In comparison to the SPS and MPS models, the
new model improves the prediction accuracy of incident radiation in the flare near-field by about 105.0% and 71.0%,
respectively. It is observed that by modifying the flame geometry parameters, the new model improves the prediction
accuracy of the heat flux near the release venting. As the
downwind distance increases, the predictions almost exactly
match the HSL experimental data in the far field.
A suggested hazard threshold for long exposure to radiation from a jet fire is 1.60 kW/m2. The hydrogen flare hazard
distances calculated from the SPS model, MPS model, new
model, simulation results and the exponential regression fit of
HSL experimental data approximately are 27.0, 25.5, 21.0, 19.5
and 20.0 m, respectively (see Fig. 8(b)). Although there are
Table 2 e Hazard criteria.
Hazard caused
Validity analysis
The accuracy of the new model was validated by predicting
the hazard distance of the HSL experiment during hydrogen
Hazard distance for long exposures
Threshold of first degree burn in 20 s
Second degree burn after 20 s
100% lethality in 60 s
I (kW/m2)
1.6
4e5
9.5
25
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
10
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 9 e Hazard distances of hydrogen flares predicted by the new model with different release rate conditions.
Fig. 10 e Incident radiation contours in plane z ¼ 0 predicted by simulation with different release rates. (a) 0.2 kg/s, (b) 0.4 kg/
s, (c) 0.6 kg/s, and (d) 0.8 kg/s.
some errors in the predicted incident radiation in the nearfield of the hydrogen flare, the prediction errors of the new
model and simulation are only 5.0% and 2.5%, respectively.
The new model improves the prediction accuracy of flare
hazard distance by about 30.0% and 22.5% over the SPS and
MPS models. It was fully confirmed that the new model has
high suitability for engineering applications in determining
the hazard distance of hydrogen flares.
Model application
It is evident that alterations in the flare height and the prevailing release rates can lead to significant variations in the
hazard distance associated with a jet fire. This section shows
several cases of hydrogen ignition release conditions, in
combination with numerical simulations to fully illustrate the
rationality of the new model for assessing the hazard distance
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
international journal of hydrogen energy xxx (xxxx) xxx
11
Fig. 11 e Hazard distances of hydrogen flares predicted by the new model with different flare height conditions.
of the hydrogen flare. The hydrogen release rate was set to
0.2 kg/s, 0.4 kg/s, 0.6 kg/s and 0.8 kg/s, respectively, and the
other experimental conditions remain constant.
The distribution characteristics of incident radiation from
hydrogen flare flames, using a series of inlet release rates at
the same conditions, were calculated by new model and
Fluent model. The calculations obtained are shown in Figs. 9
and 10. As depicted in Fig. 9(a and b), the hazard distances of
at least approximately 16.0, 21.0, 26.0 and 28.5 m are recommended to restrict the incident radiation to a level of 1.60 kW/
m2 at the release rates of 0.2 kg/s, 0.4 kg/s, 0.6 kg/s and 0.8 kg/s,
respectively. The hazard distance increases by 31.2%, 23.8%,
and 9.6% for every 0.2 kg/s increase in hydrogen release rate.
The radiation affected area of the large-scale jet flame expands as the hydrogen release rate increases, indicating the
need to expand the safety boundary of flare system, see the
incident radiation contours in Fig. 10(aed).
Furthermore, an appropriate increase in the height of the
flare stack can keep the hydrogen plume buoyantly away from
the ground (personnel and equipment), reducing the radiation
Fig. 12 e Incident radiation contours in plane z ¼ 0 predicted by simulation with different flare height. (a) 5.5 m, (b) 6.5 m, (c)
7.5 m, and (d) 8.5 m.
Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319
12
international journal of hydrogen energy xxx (xxxx) xxx
hazard. The flare height was set to 5.5 m, 6.5 m, 7.5 m and
8.5 m, respectively, and the other experimental conditions
remain constant.
Flare jet flames produce a thermal radiation injury area, and
hot air currents in the surrounding environment are harmful
to humans. As show in Fig. 11, it is obvious that as the increase
of the flare height, the damage of thermal radiation from the
flare flame on ground personnel and equipment is reduced due
to buoyancy of combustion products. On the other hand, the
momentum-dominated hydrogen plume moves away from
the ground, see Fig. 12. When the flare height begins at 5.5 m,
the radiation hazard distance is reduced by 21.4%e30.4%
approximately for every 1 m increase. As can be seen, the
hazard distance is the minimum distance between the hazard
source and the object (people, equipment, environment),
which will weaken or even isolate the impact of potential accidents and prevent the extension of more serious accidents.
Conclusion
In this study, to assess the thermal radiation hazard area as
well as the hazard distance of the hydrogen flare, a steadystate numerical model of hydrogen ignition release and a
flare radiation model applicable to hydrogen were developed.
The main findings are summarized as follows.
(1) The incident radiation predicted by the numerical
method and the new model have been demonstrated
good agreement in both the near and far fields.
(2) In comparison with the release of hydrocarbons to the
atmosphere, there are significant differences in
hydrogen flame geometry and thermal radiation behaviors. The new model performances the sensitivity of
geometric parameters such as flame length and tilt
angle to environment and gas type, emphasizing the
importance of accurately constructing flame geometry
models to develop flare hazard distance studies.
(3) Compared with the experimental HSL data fitted by
exponential regression, the error in the hazard distance
predicted by the numerical simulation and the new
model is less than ±5.0%. And the new model improves
the prediction accuracy of flare hazard distance by
about 30.0% and 22.5% over the SPS and MPS models.
(4) The recommended hazard distances increased by
31.2%, 23.8%, and 9.6% for every 0.2 kg/s increase in
hydrogen release rate. In addition, increased flare stack
height effectively reduces the heat radiation hazard
area. When the flare height begins at 5.5 m, the radiation hazard distance decreases by 21.4%e30.4% for
every 1 m increase.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgments
This research work is supported by the National Key Research
and Development Program of China (No. 2020YFB1506200,
2020YFB1506203, 2020YFB1506205).
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Please cite this article as: He Y et al., Development and application of hydrogen flare radiation model for assessing hazard distance,
International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2023.06.319