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Preliminary numerical study of cryogenic liquid hydrogen Release through a small orifice

H Aghajani and J X Wen*

The Centre for Fire and Explosion Studies, Faculty of Engineering

Kingston University, Friars Avenue, London, SW15 3DW, UK

* Correspondence: j.wen@kingston.ac.uk Abstract Hazard analysis related to hydrogen release from cryogenic hydrogen storage has been the subject of several experimental, theoretical and computational studies in recent years. In the present study, we investigate liquid hydrogen spray behaviour, which may arise in many practical situations from accidental release of cryogenic hydrogen stored under pressure. This paper reports on the preliminary results from a systematic programme to develop numerical models for pressurised liquid hydrogen release. The aim is to gain insight of this accidental phenomenon. The scenario has been modelled by releasing of liquid hydrogen jet through a small orifice in to a cylinder. Such configuration has been recently tested in laboratory conditions by Nakamichi et al. [22]. The numerical study is conducted with OPENFOAM, an open source CFD code written in C++ and constructed in modular format. Detailed correlations have been implemented for the properties of liquid hydrogen. Predictions are made for the evaporation time of the injected liquid hydrogen and the droplets distribution. Work is ongoing to further modify the code for more thorough studies of the phenomenon. Key words: Hydrogen release, droplet formation, evaporation Introduction

Hydrogen is currently regarded as a promising energy carrier for the future with many potential applications. Hydrogen offers the prospect of solutions to issues such as reduction of air pollution, security of energy supply and climate change, especially when produced with renewable energy sources. It is estimated that a transition to hydrogen as the main automotive energy carrier could be completed by the middle of this century [1]. In association with different types of hydrogen storage, various accident scenarios need to be considered. Examples could include the formation of a liquid hydrogen pool on the ground and vaporization of the liquid, catastrophic failure of the tank resulting from high internal pressure with the instantaneous release of the whole content and release of a jet stream of liquid or gas or a two-phase mixture trough a small opening in a pressurized system. From phenomenological point of view, cryogenic liquefied gases are characterized by boiling points well below the ambient temperature. If released from a pressurised vessel, the pressure relief from system to atmospheric pressure results in a so called, spontaneous (flash) vaporization of a certain fraction of the liquid. Depending on leak location and

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thermodynamic state of the cryogen, a two-phase flow will develop due to the formation of aerosols which vaporize in the air without touching the ground. This can significantly reduce the mass released. The conditions and configuration of the source has dominant influence on the composition, release height, initial plume distribution, time dependant dimensions and energy balance in the resulting vapour cloud [2]. Previous investigations on liquid hydrogen release into atmosphere have included experimental, theoretical and computationally studies. Most of the reported experiments were concerned with large scale releases. In the 1960s, Little [3] conducted large scale liquefied hydrogen dispersion experiments to examine the atmospheric dispersion of hydrogen in relation to potential accidental scenarios in the use of liquid hydrogen for space aviation. This was followed by a series of tests conducted by Witcofski and Chirivella [4-5] to investigate the generation and dispersion of flammable clouds formed as a result of large, rapid spills of liquid hydrogen. Such spills might occur as the result of the rupture of a large storage facility. Preliminary results from these experiments indicated that for rapid spills thermal and momentum-induced turbulence can cause the cloud to disperse to safe concentration levels and become positively buoyant long before mixing due to normal atmospheric turbulence becomes a major factor. Later, Schmidtchen et al. [6] investigated the cryogenic pool spreading and vaporization, the generation of a gas/air mixture cloud and its dispersion adjacent to buildings. More recently, small-scale Liquid Hydrogen leakage and dispersion experiments were performed in the framework of WE-NET project [7,8]. Early phase and steady phase pool spreading and evaporation as well as the cloud evolution were measured during these tests. Verfondern and Dienhart [9-11] investigated in detail pool spreading and vaporization on a liquid and solid ground. It was found that liquid hydrogen spillage onto a water surface could create a massive ice layer with radial ice tracks attached. They also developed a computer model LAuV to simulate pool spreading and vaporization of a liquefied gas under various conditions such as different grounds. Chitose et al. [12] simulated the NASA tests [4-5] using the CHAMPAGNE code by performing two-dimensional two-phase flow calculations. They also modified the evaporation model to account for the generation and dispersion of flammable clouds [16]. CFD pre-test calculations of the BAM tests conducted by Schmidtchen et al. [6] were performed using BASSIM [13]. However, no post-experimental validation was reported. Post-test CFD dispersion calculations were performed using FLUENT [14] and ADREA-HF [15-16] codes. Other numerical approaches can be found through [17-21]. There lacks detailed investigations concerning the release of cryogenic liquid hydrogen in the form of a jet stream of liquid or two-phase mixture through a small orifice in a pressurized system. Here the formation of aerosols in the air and its flash evaporation further complicates the underlying physics. In the present study, a numerical model is being developed to address this complicated physical process. Preliminary simulations have also been conducted for the laboratory scale flashing and evaporation tests conducted by Nakamichi et al [22].

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Numerical model

The present model is being developed within the frame of OPENFOAM [23-26], which is an object-oriented open source code written in C++. The modular format of the code renders it reasonably straightforward to implement new sub-models into the whole code structure. For the present study, the dieselFoam solver, which uses a combination of Eulerian and Lagrangian representations, is used to account for aerosol formation physics. Its evaporation is considered to be similar to diesel fuel spray in an internal combustion engine combustion chamber. The air in the domain is described using an Eulerian framework while the liquid spray is discretised into computational ‘parcels’, each described by Lagrangian coordinates. In the simulation, we inject part of the spray and track its position in time. The parcels may consist of any number of droplets, which are considered to be identical and their characteristics depend on values set by the user. Each of these parcels is subject to the same processes as a real liquid hydrogen aerosol, including atomization, break-up, collision, evaporation, heat transfer and turbulence. The aforementioned physical processes, such as heat transfer, occur as integral operations over the particle's entire surface. However, full resolution of the particle surfaces is computationally prohibitive. Therefore, a 'point particle' approximation is typically made, which requires a large number of sub-models to empirically account for integral fluxes over the particle surfaces. Further sub-models, requiring still more empiricism, are needed to model physical processes such as atomization. Unfortunately, most of the sub-models available today are quite unreliable, and depend on the user to supply constants that have limited physical interpretability.

The computational details

The geometry used to study effects of liquid hydrogen spray behaviour and flash vaporization is shown in Figure 1. The 20mm×50mm×20mm chamber, surrounded by rigid walls, is divided into 40×50×40 computational cells in x, y and z directions.

Figure 1: Geometry outline and the grid

Using Eulerian-Lagrangian approach comes to capability of using uniform grids, otherwise implementing fine grids to capture aerosols in computational domain was mandatory. The orifice diameter is 0.1 mm to simulate a very small opening and the upstream pressure as 40

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bar which is typical for liquid hydrogen storage. Normal hydrogen1, property constants shown in Table 1.

Table 1: Hydrogen constants PROPERTY UNITS VALUE

Molecular Weight kg kmol⁄ 2.016

Critical Temperature � 33.18

Critical Pressure Pa 1.313E+06

Critical Volume m� kmol⁄ 0.06415

Critical Compress Factor 0.305

Melting Point � 13.95

Triple Pt Point � 13.95

Triple Pt Pressure 7.220E+03

Normal Boiling Point � 20.39

Liquid Molar Volume m� kmol⁄ 0.028604

IG Heat of Formation J kmol⁄ 0.0

IG Gibbs of Formation J kmol⁄ 0.0

IG Absolute Entropy � ���⁄ . � 1.3057E+05

Heat Fusion at Melt Pt J kmol⁄ 1.1715E+05

Stand Net Heat of Comb J kmol⁄ -2.4182E+05

Acentric Factor -0.2150

Radius of Gyration � 3.7080E-11

Solubility Parameter �� ��⁄ ��.� 6.6478E+03

Dipole Moment �. � 0.0

van der Waals Volume m� kmol⁄ 0.00621

van der Waals Area �� ���⁄ 1.3790E+08

Refractive Index 1.0001

Flash Point � -

Flammability Limits ��� % 4.0 to 75.0

Auto ignition Temp � 673.15

Values for Temperature dependant properties of Hydrogen have been calculated using National Standard Reference Data Series (NSRDS) functions, eq.(1)-(7), introduced by Daubert and Danner [27].

� � � � � � � � � ! � � " # (1)

� � exp '� � � ⁄ � � �( � ! )* (2)

� � � + 1 � � � ! �- (3)

� � � � � � � � � ! . � " / (4)

� � � ��01�023 4⁄ �5�⁄ (5)

� � ��1 6 7��+14381938:1)38;� (6)

1 75% ortho-hydrogen, 25% para-hydrogen. Above 280 K equilibrium hydrogen mixture is normal hydrogen

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� � � � �'�� ⁄ � sinh�� ⁄ �⁄ *� � !'�" ⁄ � cosh�" ⁄ �⁄ *� (7)

The coefficients A-E in functions listed in eq.(1)-(7) and the appropriate equation from those

mentioned in this equation are listed in Table 2.

Table 2: NSRDS Equation Coefficients for Hydrogen

Property EQN A B C D E

Liquid Density (5) 5.3840E+00 3.4730E-01 3.3180E+01 2.7560E-01 -

Vapour Pressure (2) 1.2752E+01 -9.5133E+01 1.0947E+00 3.3593E-04 2.0000E+00

Heat of Vaporization (6) 1.2199E+06 1.4286E+00 -2.9817E+00 1.9370E+00 -

Solid Heat Capacity (1) 5.7300E+03 - - - -

Liquid Heat Capacity (1) 2.2560E+04 -1.9859E+03 1.1547E+02 -1.2598E+00 -

Ideal Gas Heat Capacity (7) 2.7617E+04 9.5600E+03 2.4660E+03 3.7600E+03 5.6760E+02

Second Virial Coefficient (4) 2.4500E-02 -2.8500E+00 -3.7300E+02 6.2700E+08 -7.5400E+09

Liquid Viscosity (2) -1.1986E+01 2.6260E+01 -1.7740E-01 -4.4000E-16 1.0000E+01

Vapour Viscosity (3) 1.5600E-07 7.0600E-01 -5.8700E+00 2.1000E+02

Liquid Thermal Conductivity (1) -4.9360E-01 1.0082E-01 -6.5500E-03 1.9908E-04 -2.3500E-06

Vapour Thermal Conductivity (3) 2.5470E-03 7.4440E-01 9.0000E+00 - -

Surface Tension (6) 5.3360E-03 1.0622E+00 - - -

The injected liquid hydrogen,0.6�C, with the temperature of 21K was sprayed in 0.005s. The injection velocity is calculated from the injection Pressure Profile according to eq.(8),

D � E2�G7HIHJK 6 LMN�O (8)

Where Pamb is the average pressure in the computational domain and updated at each

injection. The average velocity for injector is 476.748 � S⁄ .

In modelling the evaporation of a droplet, the key parameter is the lifetime, or evaporation relaxation time of the droplet. In the present study, we have adopted Rutland’s flash boil model [28],

τU � ρWd�6D. Sh. ρ[ln �1 � X[,^ 6 X[,_1 6 X`,^ � (9)

where τU, ρ[, X`,^, X[,_, D are relaxation time, liquid vapour density, mass fraction of fuel

vapour at droplet surface, mass fraction of fuel vapour far away and mass diffusion coefficient, respectively. The Sherwood number Sh in the eq. (9) calculated using modified form of Ranz-Marshall correlation [29] to model flashing of superheated liquid hydrogen,

ab � 2 � 0.6cd0 �⁄ ae0 �⁄ (10)

ab � 2 � �ab 6 2�/gN (11)

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gN � h1 � X[,^ 6 X[,_1 6 X`,^ i�.j . log �1 � X[,^ 6 X[,_1 6 X`,^ � X[,^ 6 X[,_1 6 X`,^k (12)

The heat transfer model is based on the convective heat transfer of a particle with a uniform temperature [29].

Results and discussion

Predictions were made for the injection of liquid hydrogen jet from a 40 bar storage container to 14 bar environment. The preliminary results are shown in Figure 2, where you can see the temporal development of liquid hydrogen spray behaviour following the injection. The pressure has been chosen 14 bar, while in this phase the effect of saturation was not of interest, critical pressure is 13.13 bar. The time varying spray penetration length are estimated as 0.0168�, 0.0233�, 0.02495�, 0.0255�, 0.029� and 0.0296� at the different moments shown in Figure 2 and reached 0.0324m at the end of injection time, 0.005Sde, and the aerosols mean diameter were estimated in the range of 102�� 6 2"2#.

Figure 2: Temporal development of liquid hydrogen spray during injection, oLMN=14 bar

The predicted total evaporation time from CFD simulation is 0.3945 sec with the Rutland flash evaporation model and seems reasonable. For similar cases of 15bar and 20bar, the evaporation time was 0.5771 and >2 second, respectively.

Hydrogen concentration, monitored in Figure 3 and Figure 4, undergoes very fast point decay near orifice after spray duration has been finished. It is due to hydrogen’s buoyancy tends to accumulate the evaporated hydrogen gas at top of cylinder, Figure 4-b. Although, the values depends on cylinder length, but the graph shown in Figure 3 can present the general physics

p � 0.0005

p � 0.001

p � 0.0015

p � 0.002

p � 0.0025

p � 0.003

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and behaviour of evaporated liquid hydrogen. Furthermore spray core shown schematically in Figure 2, surrounds by hydrogen vapour during spray evolution, while the region is most potential place of cryogenic droplets.

In Figure 5, the centreline variation of Hydrogen at time of 0.005 sec has been monitored to investigate space coordinate distribution of evaporated liquid in depth. Because of higher density of liquid droplets in the middle, the concentration faced a boost in the magnitude and going further in time would shift all gas hydrogen to top levels of cylinder.

Figure 3: Temporal hydrogen near nozzle concentration

Figure 4: Evaporated hydrogen distribution at a) end of spray b) end of last aerosol vaporization

b

p � 0.005 Sde

p � 0.3945 Sde

a

Figure

In the Figure 6, temperature profile spray time, 0.005 Sde. The minimum numerically captured temperatudomain is 40K, well above injected liquid is about 0.0037m from orifice

As stated earlier the droplet injection velocity at the injector is in the order ofit decays to the order of 340 tension of air which also helps to droplets further breakup.cylinder air with a slow velocity.

The pressure remained approximately Figure 8, because of low amount of injection.

Figure 6: Temperature

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Figure 5: Hydrogen Concentration along centreline

profile in the computational field has been shownhe minimum numerically captured temperatu

njected liquid temperature21�. The blue to read transition length is about 0.0037m from orifice, in this case.

stated earlier the droplet injection velocity at the injector is in the order of � S⁄ after injection, as can be seen in Figure tension of air which also helps to droplets further breakup. As a result, it circulated tcylinder air with a slow velocity.

approximately unchanged in the cylinder till the end of spray time, low amount of injection. The equilibrium value reached to

: Temperature profile [K] at the end of spray time

computational field has been shown at the end of he minimum numerically captured temperature in the solution

The blue to read transition length

stated earlier the droplet injection velocity at the injector is in the order of, 470 � S⁄ , but Figure 7, due to surface

As a result, it circulated the in-

till the end of spray time, The equilibrium value reached to1.49482e+6

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Figure 7: Velocity of a) air in Eulerian System b) aerosol [m/s] in Lagrangian system

a

b

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Figure 8: Pressure Variation in the environment [Pa]

Conclusion

This paper reports on the preliminary results to develop numerical models for pressurised liquid hydrogen release. The scenario has been modelled by releasing small amount of liquid hydrogen through a small orifice, which was modelled as spray of liquid through an injector, in to a cylinder. The numerical study is conducted with an open source CFD code written in C++, so called OpenFOAM. Detailed correlations have been implemented for the properties of liquid hydrogen. Heat transfer of injected liquid as well as its spray length and centreline distribution has been investigated.

It have been understood that spray length reaches a constant level and the penetration sees an exponential function. Evaporation occurs around aerosols and the result vapour accumulated at top of cylinder as expected. Temperature variation is only dominant during injection period. Work is ongoing to further modify the code to consider the cavitations of superheated liquid after entering to ambient pressure less than its critical pressure.

References

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