Modeling of jet spreading and flame hazard distances for high pressure hydrogen releases

Hydrogen is a promising clean and sustainable energy carrier. Hydrogen is usually stored at high pressure due to its low density. Hydrogen releases from high pressure storage can result in underexpanded jets that will mix with air, forming a large combustible cloud. If the jets are ignited, jet flames will form with a large hazard area. This study simulated hydrogen jets and jet flames for storage pressures of 1~70 MPa and nozzle diameters of 1~2 mm using the HyRAM software. The results show that the jet diffusion distance increased with the hydrogen stagnation pressure and the nozzle diameter. The diffusion distances were correlated with the nozzle diameter and the hydrogen stagnation pressure. The jet flames and thermal radiations were then analyzed to show that the flame length and hazard distance both increased with the stagnation pressure and nozzle diameter. Correlations for radiation major harm distance, harm distance and no harm distance were developed to predict the jet flame hazard range. The present study can provide references for the safety design of hydrogen applications.


Introduction
The fossil fuel crisis and air pollution have become increasingly serious in recent years.Hydrogen has been increasingly used as a promising clean and sustainable energy carrier [1][2][3].Over 30 governments have pledged to incorporate hydrogen as a clean energy vector into their energy systems.At present, the storage technology of high-pressure gaseous hydrogen is well developed, with the advantages of well-established technology, low energy consumption, and fast hydrogen filling.Hydrogen is flammable and explosive, with wide flammability limits in the air.Therefore, hydrogen safety is a serious issue requiring utmost attention in hydrogen applications.Hydrogen releases and ignitions are potential accident scenarios, which are important for the design of hydrogen storage scenarios and developing the safety codes and standards.
The flow is choked at the nozzle when hydrogen releases from a high pressure source, forming an underexpanded, supersonic jet.Many researchers have measured and simulated underexpanded hydrogen jets to study the shock structures and jet parameter distributions [4][5][6][7][8][9][10][11].There are complex shock stuctuures near the outlet of underexpanded hydrogen jets.The Mach disk location has been correlated as a function of the pressure ratio and the nozzle diameter.The field parameter distributions are self-similar.The jet axial concentration and velocity decay hyperbolically, while the radial concentration and velocity distributions conform to the Gaussian distributions.Hydrogen releases from high-pressure sources will form jet flames if ignited, leading to disastrous consequences.The jet flame characteristics have been measured in several studies [12][13][14].The flame shape was visualized for various release conditions.The flame length and width were correlated as functions of the stagnation pressure and nozzle diameter [12,13].There are also some studies simulated hydrogen jet flames and predicted the flame temperature distributions using Computational Fluid Dynamics (CFD) methods [15][16][17][18].In addition, the effect distances of hydrogen jets and jet flames are important for the safety design of hydrogen plants and stations.However, the research on the effect distances of jet spreading and jet flames is still inadequate.
HyRAM is an integrated platform for hydrogen safety research, which was developed by the Sandia National Laboratory with the support of the US Department of Energy [19].In HyRAM the system configurations can be defined by the user and then the multiple risk and harm metrics can be calculated [20].The HyRAM calculating results will provide insights for stakeholders in the safety, codes, and standards community.The quantitative risk assessment in HyRAM incorporates generic failure probabilities for hydrogen components, the thermal hazard probabilistic model and the overpressure hazard probabilistic model.LaFleur et al. [21] calculated risk values for developing riskequivalent designs and documented the performance-based process by HyRAM.Xing et al. [22] used HyRAM to analyze the high-risk unit for urban hydrogen refueling stations and determine the fatality zone, flammable area and safe distances.Park et al. [23] studied accidents at hydrogen refueling stations and analyzed individual and societal risks using the HyRAM software.HyRAM also incorporates experimentally validated models of releases and flames.Simulations using HyRAM enable fast calculation of jet and flame characteristics compared to CFD methods.
In this study, the jet and jet flame after leakage of hydrogen stored at high pressure were simulated using HyRAM.The hydrogen mole fractions were predicted for stagnation pressures of 1~70 MPa and nozzle diameters of 1~2 mm.The jet diffusion distance was correlated with the stagnation pressure and nozzle diameter.The jet flame temperatures and radiative heat flux distributions were then calculated for stagnation pressures of 1~70 MPa and nozzle diameters of 1~2 mm.The major harm, harm and no harm distances of flame thermal radiation were also analyzed and correlated.

Problem description
The high pressure hydrogen was released horizontally from circular nozzles with diameters of 1 and 2 mm at stagnation pressures of 1 to 70 MPa.Underexpanded jets will form if the hydrogen is not ignited after leakage, while a jet flame will form if the hydrogen is ignited during leakage.The jets and jet flames were simulated using HyRAM in this paper.The hydrogen stagnation temperature and ambient air temperature were both 300 K.The stagnation pressures and the nozzle diameters for simulated cases are listed in Table 1.

HyRAM simulation for jets
The one-dimensional model [24] was used in HyRAM for jet modeling.The accuracy of the jet model in HyRAM has been validated [25].The jet bending in axial direction caused by buoyancy effects was considered in the model.The disributions of the jet velocity (v), density (ρ), and product of density and hydrogen mass fraction (Y) are assumed to be Gaussian [20], as follows: HEET-2023 Journal of Physics: Conference Series 2723 (2024) 012003 IOP Publishing doi:10.1088/1742-6596/2723/1/012003 ( ) The derivatives of the spatial dimensions are The conservation equations can be written as [20] ( ) ( ) ( ) ( ) where r is perpendicular to the jet flow direction, B is the half-width, λ is the ratio of density spreading to velocity, E is the entrainment, θ is the angle relative to horizontal, h is the enthalpy, the subscript cl represents centerline, amb represents ambient.The ideal gas equation of state is used to calculate the physical properties of atmospheric pressure mixtures.

HyRAM simulation for jet flames
The jet flame radiative heat flux was predicted by a weighted multi-source model.The heat flux can be described as [20] where τ is the transmissivity, VF is the view factor, which is proportional to the heat flux, Af is the flame surface area, and Srad is the total emitted radiative power from a flame, calculated by

Results and discussion
3.1.High pressure hydrogen jets 3.1.1.Concentration distributions.The hydrogen mole fractions were simulated using the physical module in HyRAM.Figure 1 shows the hydrogen mole fraction distributions for various stagnation pressures and nozzle diameters.The white curve in Figure 1 indicates the hydrogen mole fraction of 0.04, which is the lower flammable limit (LFL) of hydrogen in air.The area within the white curve represents the area of the flammable cloud.The flammable cloud spreading range increases with the nozzle diameter for a given pressure and increases with the stagnation pressure for a given nozzle diameter.

Flammable cloud spreading distances.
The flammable cloud spreading distance variation as a function of the stagnation pressure is shown in Figure 2. The spreading distance increases with the hydrogen stagnation pressure for a given nozzle diameter.For the nozzle diameter of 1 mm, the spreading distance is 0.77 m with a stagnation pressure of 1 MPa and increases to 5.68 m with a stagnation pressure of 70 MPa.In addition, the spreading distance increases with increasing nozzle diameter for a given stagnation pressure.For the stagnation pressure of 70 MPa, the spreading distance is 5.68 m with 1 mm diameter nozzle and increases to 11.25 m with 2 mm diameter nozzle.
The spreading distance was non-dimensionalized by the nozzle diameter to develop an empirical correlation.Figure 3 shows the correlation between the dimensionless spreading distance, DLFL/d, and the hydrogen stagnation pressure.The black line in Figure 3 is the fitting curve using the least square method.The correlation between the spreading distance, the nozzle diameter and the hydrogen stagnation pressure was developed as (16) where the coefficients "0.81" and "0.46" were determined by the least square method.The determination coefficient (R²) is 0.9995, which shows that the fitting curve agrees well with the data.

Flame thermal radiation effects.
The thermal radiation flux can be evaluated relative to the harm degree and safety distance of jet flame.The thermal radiation heat flux distributions of hydrogen jet flame were simulated for various stagnation pressures and nozzle diameters, as shown in Figure 5.The three colors in Figure 5 represent different harm degrees for equipment and people.The heat flux of 25.24 kW/m 2 is considered as the major harm criterion, which can cause equipment damage.The heat flux of 4.73 kW/m 2 is considered as the harm criterion, which can cause injury to people.The heat flux of 1.58 kW/m 2 is considered as the no harm criterion, which has no harm to equipment and people [26].

Thermal radiation hazard distances.
The major harm distance variation as a function of the hydrogen stagnation pressure is shown in Figure 6.For the nozzle diameter of 1 mm, the major harm distance increases from 0.42 to 3.16 m with the stagnation pressure increasing from 1 to 70 MPa.For the nozzle diameter of 2 mm, the major harm distance increases from 0.85 to 6.48 m with the stagnation pressure increasing from 1 to 70 MPa.
The major harm distance was nondimensionalized by the nozzle diameter.Figure 7 shows the correlation between the dimensionless major harm distance, DMajor harm/d, and the hydrogen stagnation pressure.The black line in Figure 7 is the fitting curve using the least square method.The correlation between the major harm distance, the nozzle diameter and the hydrogen stagnation pressure was developed as (17) where the coefficients "0.43" and "0.47" were determined by the least square method.The determination coefficient (R²) is 0.9993, which shows that the fitting curve agrees well with the data.Figure 9 shows the correlation between the dimensionless harm distance, DHarm/d, and the hydrogen stagnation pressure.The black line in Figure 9 is the fitting curve using the least square method.The expression between the harm distance, the nozzle diameter and the hydrogen stagnation pressure was developed as (18) where the coefficients "0.46" and "0.50" were determined by the least square method.The determination coefficient (R²) is 0.998, which shows that the fitting curve agrees well with the data.Figure 9. Correlation of the dimensionless harm distance.Figure 10 shows the no harm distances for various stagnation pressures and nozzle diameters.For the nozzle diameter of 1 mm, the no harm distance increases from 0.53 to 4.72 m with the stagnation pressure increasing from 1 to 70 MPa.For the nozzle diameter of 2 mm, the major harm distance increases from 1.11 to 10.24 m with the stagnation pressure increasing from 1 to 70 MPa.
Figure 11 shows the correlation between the dimensionless harm distance, DNo Harm/d, and the hydrogen stagnation pressure.The black line in Figure 11 is the fitting curve using the least square method.The expression between the no-harm distance, the nozzle diameter and the hydrogen stagnation pressure was developed as (19) where the coefficients "0.56" and "0.51" were determined by the least square method.The determination coefficient (R²) is 0.995, which shows that the fitting curve agrees well with the data.

Conclusions
This study simulated high pressure hydrogen jets and jet flames for stagnation pressures of 1~70 MPa with 1 and 2 mm diameter circular nozzles using the HyRAM software.The experimentally validated models in HyRAM were used to calculate the hydrogen jet and flames.The hydrogen jet concentration distributions were predicted for various hydrogen stagnation pressures and nozzle diameters.The flammable cloud spreading distance increases with increasing stagnation pressure and increasing nozzle diameter.The spreading distance correlation was developed as a power function of the nozzle diameter and the hydrogen stagnation pressure to calculate the jet effect distance of hydrogen stored at high pressure.The hydrogen jet flame temperatures and radiation heat flux were also predicted for various conditions.The thermal radiation harm degrees and distances were then analyzed.The thermal radiation hazard degrees were divided into major harm, harm and no harm.The major harm distance, harm distance and no harm distance were correlated as power functions of the nozzle diameter and the stagnation pressure to assess the effect distances of high pressure hydrogen jet flames.
The results can provide a scientific basis for the safety design of hydrogen plants and stations.
mass flow rate, ΔHc represents the combustion heat, which equals to 120 MJ/kg, Xrad represents the radiant fraction, ap equals to 0.23, which represents the Planck-mean absorption coefficient, τf represents the residence time of flame, ρf represents the flame density, Pamb represents the ambient pressure, Wmix represents the mean molecular weight of the combustion stoichiometric products, and R represents the gas constant.The accuracy of the flame model in HyRAM has been validated[25].

Figure 2 .
Figure 2. Spreading distances of the flammable cloud.

Figure 3 .
Figure 3. Correlation of the dimensionless spreading distance.

3. 2 . 4 .
High pressure hydrogen jet flames 3.2.1.Jet flames.The jet flame trajectories and temperatures were simulated for various stagnation pressures and nozzle diameters, as shown in Figure 4.The results show that larger leak diameters and stagnation pressures result in longer flame lengths.For the nozzle diameter of 1 mm, the flame length increases from 0.42 to 3.07 m with the stagnation pressure increasing from 1 to 70 MPa.For the stagnation pressure of 70 MPa, the flame length increases from 3.07 to 6.15 m with the nozzle diameter increasing from 1 to 2 mm.(a) p=1 MPa, d=1 mm (b) p=1 MPa, d=2 mm (c) p=10 MPa, d=1 mm (d) p=10 MPa, d=2 mm (e) p=30 MPa, d=1 mm (f) p=30 MPa, d=2 mm (g) p=70 MPa, d=1 mm (h) p=70 MPa, d=2 mm Figure Hydrogen jet flame temperatures for various stagnation pressures and nozzle diameters.

Figure 6 .
Figure 6.Major harm distances of jet flames.Figure 7. Correlation of the dimensionless major harm distance.The harm distances for various stagnation pressures and nozzle diameters are shown in Figure 8.For the nozzle diameter of 1 mm, the harm distance increases from 0.45 to 3.77 m with the stagnation pressure increasing from 1 to 70 MPa.For the nozzle diameter of 2 mm, the major harm distance increases from 0.93 to 7.95 m with the stagnation pressure increasing from 1 to 70 MPa.

Figure 7 .
Figure 6.Major harm distances of jet flames.Figure 7. Correlation of the dimensionless major harm distance.The harm distances for various stagnation pressures and nozzle diameters are shown in Figure 8.For the nozzle diameter of 1 mm, the harm distance increases from 0.45 to 3.77 m with the stagnation pressure increasing from 1 to 70 MPa.For the nozzle diameter of 2 mm, the major harm distance increases from 0.93 to 7.95 m with the stagnation pressure increasing from 1 to 70 MPa.

Figure 8 .
Figure 8. Harm distances of jet flames.Figure9.Correlation of the dimensionless harm distance.Figure10shows the no harm distances for various stagnation pressures and nozzle diameters.For the nozzle diameter of 1 mm, the no harm distance increases from 0.53 to 4.72 m with the stagnation pressure increasing from 1 to 70 MPa.For the nozzle diameter of 2 mm, the major harm distance increases from 1.11 to 10.24 m with the stagnation pressure increasing from 1 to 70 MPa.Figure11shows the correlation between the dimensionless harm distance, DNo Harm/d, and the hydrogen stagnation pressure.The black line in Figure11is the fitting curve using the least square method.The expression between the no-harm distance, the nozzle diameter and the hydrogen stagnation pressure was developed as

Figure 10 .
Figure 10.No harm distances of jet flames.Figure 11.Correlation of the dimensionless no harm distance.

Figure 11 .
Figure 10.No harm distances of jet flames.Figure 11.Correlation of the dimensionless no harm distance.

Table 1 .
Stagnation pressures and the nozzle diameters for simulated cases.