OpenFOAM-based study on near-field formation and mixing of high nozzle pressure ratio hydrogen jets from leakages

Abstract

A gas stored at high-pressure leaking through a small hole forms a complex series of shock structures as it accelerates and expands to ambient conditions. The near-field region of the jet includes the initial jet expansion, Mach disc formation, and starting vortices, all of which can affect hydrogen mixing with the surrounding air and have an associated combustion risk. Through the use of a modified OpenFOAM solver, simulations of hydrogen stored at 10 and 100 bar leaking into atmospheric conditions through 1.5 mm diameter circular nozzles were performed to determine the transient temperature profile, shock locations, and hydrogen mixing profiles of the hydrogen jet in its initial expansion and propagation stages. From these transient simulations, it was shown that starting vortices form pockets of mixed hydrogen and air that are within hydrogen flammability limits. This new simulation data shows mixed hydrogen pockets can linger in the nozzle near-field region and present a flammability risk that is not easily accounted for when using existing numerical models optimized for far-field flame behavior, showing this new open-source tool can resolve hydrogen mixing behavior in the nozzle near-field region without compromising on shock resolution capabilities.

Keywords

Hydrogen leakages / High storage pressure / OpenFOAM simulations / Hydrogen jet / Flammability risk

CRediT authorship contribution statement

Rui Jovan Yeo: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation. T.H. New: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. W.L. Chan: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Tze How New is a guest editor for special issue: “Hydrogen Potential in Industrial Decarbonization”, and was not involved in the editorial review or the decision to publish this article. Other authors declare that there are no competing interests.

Acknowledgements

The computational work for this article was partially performed on resources of the High-Performance Computing Center of NTU (https://www.ntu.edu.sg/hpcc) and National Supercomputing Center, Singapore (https://www.nscc.sg).

References

[1] Abdollahi, S.A., Ranjbar, S.F., Gerdroodbary, M.B., Ehghaghi, M.B., 2025. Enhancing hydrogen mixing efficiency using extruded nozzles behind struts in supersonic combustion chambers. Int. J. Hydrogen Energy 143, 728-739. https://doi.org/10.1016/j.ijhydene.2025.05.234.

[2] Ali, H., Vuorinen, V., Rintanen, A., 2025. Large-eddy simulation of highly underexpanded hydrogen jets using a low dissipative solver. Int. J. Hydrogen Energy 182, 151331. https://doi.org/10.1016/j.ijhydene.2025.151331.

[3] Asahara, M., Iwatsuki, K., Kang, D., Kambayashi, I., Saburi, T., Iwasaki, K., Uehara, T., Miyasaka, T., 2024. Characterization of hydrogen jets considering leakage from high-pressure storage tanks using shadowgraphy. Int. J. Hydrogen Energy 61, 1456-1472. https://doi.org/10.1016/j.ijhydene.2024.02.074.

[4] Ashkenas, H., Sherman, F.S., 1965. Structure and Utilization of Supersonic Free Jets in Low Density Wind Tunnels. NASA-CR-60423.

[5] Ba, Q., Zhao, Z., Zhang, Y., Liu, Y., Christopher, D.M., Ge, P., Li, X., 2024. Modeling of cryogenic compressed hydrogen jet flames. Int. J. Hydrogen Energy 51, 917-927. https://doi.org/10.1016/j.ijhydene.2023.06.265.

[6] Cao, C., Ye, T., Zhao, M., 2015. Large eddy simulation of hydrogen/air scramjet combustion using tabulated thermo-chemistry approach. Chin. J. Aeronaut. 28, 1316-1327. https://doi.org/10.1016/j.cja.2015.08.008.

[7] Crist, S., Glass, D.R., Sherman, P.M., 1966. Study of the highly underexpanded sonic jet. AIAA J. 4, 68-71. https://doi.org/10.2514/3.3386.

[8] Crowl, D.A., Jo, Y.D., 2007. The hazards and risks of hydrogen. J. Loss Prev. Process. Ind. 20, 158-164. https://doi.org/10.1016/j.jlp.2007.02.002.

[9] Dauptain, A., Cuenot, B., Gicquel, L., 2010. Large eddy simulation of stable supersonic jet impinging on flat plate. AIAA J. 48, 2325-2338. https://doi.org/10.2514/1.J050362.

[10] Duronio, F., De Vita, A., 2024. Cfd analysis of hydrogen and methane turbulent transitional under-expanded jets. Int. J. Heat Fluid Flow 107, 109381. https://doi.org/10.1016/j.ijheatfluidflow.2024.109381.

[11] Franquet, E., Perrier, V., Gibout, S., Bruel, P., 2015. Free underexpanded jets in a quiescent medium: a review. Prog. Aero. Sci. 77, 25-53. https://doi.org/10.1016/j.paerosci.2015.06.006.

[12] Gerdroodbary, M.B., 2020. Scramjets: Fuel Mixing and Injection Systems. Butterworth-Heinemann.

[13] Gerdroodbary, M.B., Bishehsari, S., Hosseinalipour, S., Sedighi, K., 2012. Transient analysis of counterflowing jet over highly blunt cone in hypersonic flow. Acta Astronaut. 73, 38-48.

[14] Gerdroodbary, M.B., Jahanian, O., Mokhtari, M., 2015. Influence of the angle of incident shock wave on mixing of transverse hydrogen micro-jets in supersonic crossflow. Int. J. Hydrogen Energy 40, 9590-9601.

[15] Gong, L., Jin, K., Yang, S., Yang, Z., Li, Z., Gao, Y., Zhang, Y., 2020. Numerical study on the mechanism of spontaneous ignition of high-pressure hydrogen in the l-shaped tube. Int. J. Hydrogen Energy 45, 32730-32742. https://doi.org/10.1016/j.ijhydene.2020.08.267.

[16] Hassan, I., Ramadan, H.S., Saleh, M.A., Hissel, D., 2021. Hydrogen storage technologies for stationary and mobile applications: review, analysis and perspectives. Renew. Sustain. Energy Rev. 149, 111311. https://doi.org/10.1016/j.rser.2021.111311.

[17] Hoste, J.J.O., Casseau, V., Fossati, M., Taylor, I.J., Gollan, R., 2017. Numerical modeling and simulation of supersonic flows in propulsion systems by open-source solvers. In: 21st AIAA Int. Space Planes and Hypersonics Tech. Conf., p. 2411. https://doi.org/10.2514/6.2017-2411.

[18] Inagaki, M., Kondoh, T., Nagano, Y ., 2002. A mixed-time-scale SGS Model with Fixed Model-Parameters for Practical LES. Elsevier Science Ltd, Oxford.

[19] Keenan, J., Makarov, D., Molkov, V., 2017. Modelling and simulation of high-pressure hydrogen jets using notional nozzle theory and open source code OpenFOAM. Int. J. Hydrogen Energy 42, 7447-7456. https://doi.org/10.1016/j.ijhydene.2016.07.022.

[20] Khodadadi, R., Heidari, A., Wen, J.X., 2018. A computational fluid dynamic investigation of inhomogeneous hydrogen flame acceleration and transition to detonation. Flow Turbul. Combust. 101, 1009-1021. https://doi.org/10.1007/s10494-018-9977-4.

[21] Kurganov, A., Noelle, S., Petrova, G., 2001. Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23, 707-740. https://doi.org/10.1137/S1064827500373413.

[22] Kurganov, A., Tadmor, E., 2000. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comp. Physiol. 160, 241-282. https://doi.org/10.1006/jcph.2000.6459.

[23] Li, X., 2015. Dispersion of Unintended Subsonic and Supersonic Hydrogen Releases from Hydrogen Storage Systems. Tsinghua University, Beijing.

[24] Li, X., Christopher, D.M., Hecht, E.S., Ekoto, I.W., 2017. Comparison of two-layer model for hydrogen and helium jets with notional nozzle model predictions and experimental data for pressures up to 35 MPa. Int. J. Hydrogen Energy 42, 7457-7466.

[25] Liu, X.Y., Luan, M.Y., Chen, Y.L., Wang, J.P., 2020. Flow-field analysis and pressure gain estimation of a rotating detonation engine with banded distribution of reactants. Int. J. Hydrogen Energy 45, 19976-19988. https://doi.org/10.1016/j.ijhydene.2020.05.102.

[26] Loving, C., Mastantuono, G., Terracciano, A.C., Vasu, S.S., Pigon, T., Hernandez, A., Cloyd, S., 2023. Auto-ignition test results of hydrogen and natural gas fuels at atmospheric and elevated pressures for gas turbine safety. In: Turbo Expo: Power for Land, Sea, and Air. American Society of Mechanical Engineers. https://doi.org/10.1115/GT2023-102674.

[27] National Institute of Standards and Technology, 2022. Saturation properties for hydrogen - pressure increments. https://webbook.nist.gov/cgi/fluid.cgi?Action=Load&ID=C1333740&Type=SatT&Digits=5&PLow=.5&PHigh=1.5&PInc=.1&RefState=DEF&TUnit=K&PUnit=atm&DUnit=kg/m3&HUnit=kJ/mol&WUnit=m/s&VisUnit=uPa*s&STUnit=N/m.

[28] Nista, L., Saracoglu, B.H., Ispir, A.C., 2019. A detailed combustion solver for detonation engines simulations. In: AIAA Scitech 2019 Forum, San Diego, California, AIAA2019-2250.

[29] O Conaire, M., Curran, H.J., Simmie, J.M., Pitz, W.J., Westbrook, C.K., 2004. A comprehensive modeling study of hydrogen oxidation. Int. J. Chem. Kinet. 36, 603-622. https://doi.org/10.1002/kin.20036.

[30] Radulescu, M.I., Law, C.K., 2007. The transient start of supersonic jets. J. Fluid Mech. 578, 331-369. https://doi.org/10.1017/S0022112007004715.

[31] Rahantamialisoa, F., Zembi, J., Miliozzi, A., Sahranavardfard, N., Battistoni, M., 2022. CFD simulations of under-expanded hydrogen jets under highpressure injection conditions. J. Phys.: Conf. Ser. 2385, 012051. https://doi.org/10.1088/1742-6596/2385/1/012051.

[32] Ren, Z., Wen, J.X., 2020. Numerical characterization of under-expanded cryogenic hydrogen gas jets. AIP Adv. 10. https://doi.org/10.1063/5.0020826.

[33] Ruggles, A.J., Ekoto, I.W., 2012. Ignitability and mixing of underexpanded hydrogen jets. Int. J. Hydrogen Energy 37, 17549-17560. https://doi.org/10.1016/j.ijhydene.2012.03.063.

[34] Salim, S.M., Cheah, S., 2009. Wall Y+ strategy for dealing with wall-bounded turbulent flows. In: Proceedings of the International Multiconference of Engineers and Computer Scientists, pp. 2165-2170.

[35] Shang, J., Wang, K., Wang, A., Wang, Q., Zhao, W., 2023. Detonation wave structure and thrust variation of a ram accelerator with different projectile velocities. Aero. Sci. Technol. 143, 108717. https://doi.org/10.1016/j.ast.2023.108717.

[36] Traxinger, C., Pfitzner, M., 2021. Effect of nonideal fluid behavior on the jet mixing process under high-pressure and supersonic flow conditions. J. Supercrit. Fluids 172, 105195. https://doi.org/10.1016/j.supflu.2021.105195.

[37] Viti, V., Neel, R., Schetz, J.A., 2009. Detailed flow physics of the supersonic jet interaction flow field. Phys. Fluids 21, 046101. https://doi.org/10.1063/1.3112736.

[38] Yip, H.L., Srna, A., Liu, X., Kook, S., Hawkes, E.R., Chan, Q.N., 2020. Visualization of hydrogen jet evolution and combustion under simulated direct-injection compression-ignition engine conditions. Int. J. Hydrogen Energy 45, 32562-32578. https://doi.org/10.1016/j.ijhydene.2020.08.220.

[39] Zang, B., Vevek, U., Lim, H.D., Wei, X., New, T.H., 2018. An assessment of OpenFOAM solver on rans simulations of round supersonic free jets. J. Compos. Sci. 28, 18-31. https://doi.org/10.1016/j.jocs.2018.07.002.

[40] Zhang, H., Zhao, M., Huang, Z., 2020. Large eddy simulation of turbulent supersonic hydrogen flames with OpenFOAM. Fuel 282, 118812. https://doi.org/10.1016/j.fuel.2020.118812.