DOI: 10.3303/CET23104020 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 12 April 2023; Revised: 13 July 2023; Accepted: 4 October 2023 
Please cite this article as: Giannini L., Tincani G., Collina G., Salzano E., Cozzani V., Ustolin F., 2023, Modelling of Fireballs Generated After 
the Catastrophic Rupture of Hydrogen Tanks, Chemical Engineering Transactions, 104, 115-120  DOI:10.3303/CET23104020 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 104, 2023 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Sabrina Copelli, Ernesto Salzano 
Copyright © 2023, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-06-9; ISSN 2283-9216 

Modelling of Fireballs Generated after the Catastrophic 

Rupture of Hydrogen Tanks 

Leonardo Gianninia,*, Gabriele Tincanib, Giulia Collinab, Ernesto Salzanob, Valerio 

Cozzanib, Federico Ustolina 

a Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology NTNU, Richard 

Birkelands vei 2B, 7034 Torndheim, Norway  
b Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Università degli studi di Bologna, Via Terracini 28, 

40131 Bologna, Italy 

 leonardo.giannini@ntnu.no 

The interest towards hydrogen skyrocketed in the last years. Thanks to its potential as an energy carrier, 

hydrogen will be soon handled in public and densely populated areas. Therefore, accurate models are 

necessary to predict the consequences of unwanted scenarios. These new models should be employed in the 

consequence analysis, a phase of risk assessment, and thus aid the selection, implementation, and optimization 

of effective risk-reducing measures. This will increase safety of hydrogen technologies and therefore favour their 

deployment on a larger scale. Hydrogen is known to be an extremely flammable gas with a low radiation flame 

compared to hydrocarbons. However, luminous fireballs were generated after the rupture of both compressed 

gaseous and liquid hydrogen tanks in many experiments. Moreover, it was demonstrated that conventional 

empirical correlations, initially developed for hydrocarbon fuels, underestimate both dimension and duration of 

hydrogen fireballs recorded during small-scale tests (Ustolin and Paltrinieri, 2020). The aim of this study is to 

obtain an analysis of hydrogen fireballs to provide new critical insights for consequence analysis. A comparison 

among different correlations is conducted when predicting fireball characteristics during the simulation of past 

experiments where both gaseous and liquid hydrogen tanks were intentionally destroyed. All the models 

employed in this study are compared with the experimental results for validation purposes. Specific models 

designed for hydrogen can support the design of hydrogen systems and increasing their safety and promote 

their future distribution. 

1. Introduction 

The REPowerEU ambitious strategy for hydrogen implementation foresees a great increase in the domestic 

renewable hydrogen production within the European union (European Commission, 2022), thus implying a vast-

scale diffusion of hydrogen technologies, even in high densely populated areas. However, safety aspects of 

hydrogen technologies still constitute a bottleneck to their implementation for several reasons, one of them being 

hydrogen’s high flammability, which could promote the occurrence of hazardous scenarios and accidents 

(Campari et al, 2023). Hence, the definition of safety procedures for hydrogen handling encompasses several 

different challenges. More precisely, the very low minimum ignition energy of 0.017 mJ (Ono et al, 2007) is just 

one characteristic that raises concern among scientists and engineers. Moreover, the occurrence of rare, yet 

severe phenomena referred to as hydrogen fireballs is deemed to be not only critical in terms of safety, but also 

in terms of perceived risk, which limits the public acceptability of these technologies. In fact, the concreteness 

of disastrous scenarios is known to socially impact hydrogen refuelling stations, making them more challenging 

to site, permit, and operate, thus limiting the development of a widespread hydrogen infrastructure (Huijts et al, 

2019). For these reasons, the necessity of specific and reliable models describing hydrogen fireballs arises as 

a first-order variable in the development of the hydrogen value chain, therefore affecting the overall energy 

transition scenario. This work proposes new models which aim to estimate both the duration and the diameter 

of hydrogen fireballs. These models are considered as an evolution of the ones often found in literature, since 

they are developed for hydrogen and based on experiments concerning both pressure vessel bursts (PVBs) 

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and liquid hydrogen (LH2) boiling liquid expanding vapor explosion (BLEVE). In particular, the proposed models 

aim at the description of the fireball generated during the recently concluded “Safe Hydrogen Fuel Handling and 

Use for Efficient Implementation” project (SH2IFT, 2021) and in this paper a comparison with other experimental 

hydrogen fireballs is performed for validation purposes. However, there still is a deep need for new experimental 

activities to further validate and improve these models. Experimental studies can in fact help improving the 

accuracy and reliability of the new models by providing more data on real-world conditions and scenarios. These 

studies can also help identify different hazards or factors that may influence the behaviour of hydrogen fireballs, 

thus leading to better safety standards and practices. 

2. Hydrogen Fireballs 

BLEVEs and PVBs are defined as explosions involving the catastrophic rupture of a vessel. A BLEVE is 

characterized by the violent burst of a boiling liquid, which involves both the rapid expansion of the gaseous 

phase and the flashing of a fraction of the liquid phase, as a consequence of rapid depressurization (Ustolin et 

al, 2020). A PVB may show a similar aftermath, but it is characterized by the burst of a vessel containing gas at 

elevated pressure (CCPS, 2010). In both cases, the high mechanical energy released (Ustolin et al, 2022) 

implies consequences that are often severe, involving generation of pressure waves, fragments projection and, 

if the released fluid is flammable, fireballs. Hence, a distinction of fireballs from BLEVEs and PVBs is provided 

below, to describe the different experiments the proposed models are based on. 

2.1 Fireballs from BLEVEs 

Hydrogen BLEVEs are rare scenarios, often classified as atypical accident scenarios (Ustolin et al, 2020). In 

addition, experiments concerning these explosions and their major consequences (i.e., hydrogen fireballs) are 

also difficult to be found in literature, and a limited number of data is currently available. Moreover, the cryogenic 

conditions of liquid hydrogen (LH2) impose considerable costs for the purchase of specific equipment, reducing 

the availability of experimental evidence and data. Within this work, two important set of experiments were 

considered to study the fireball generated from hydrogen BLEVEs: 

 

• “Cold” LH2 BLEVEs from safety tests conducted by BMW car manufacturer in the 1990s (Pehr, 1996) 

hereafter BMW tests. 

• “Hot” LH2 BLEVE from the SH2IFT project (SH2IFT, 2021), hereafter SH2IFT test. 

 

Where “cold” and “hot” indicate the event triggering type, being “cold” a cutting charge located on the exploding 

vessel and “hot” implying the presence of a propane burner placed under the LH2 tank to engulf it in a fire. The 

experiments resulted in the generation of fireballs, which were unique in terms of their fundamental 

characteristics (i.e., duration and diameter). More precisely, the mass content is deemed to be a crucial 

parameter for the development of the fireball, which is also confirmed by several models in literature (Roberts, 

1981). During the execution of the SH2IFT test, a leakage of LH2 happened before the BLEVE event, which 

reduced the initial mass (27 kg of LH2) to an unknown value. This event affected both the fireball dimension and 

duration, but a hydrogen mass ranging between 13 kg and 27 kg is deemed as a plausible value at the moment 

of the explosion. Moreover, the exact mass of LH2 is also unknown for the BMW tests, since the experimental 

data indicate a hydrogen mass ranging from 1.8 kg and 5.4 kg. Therefore, it is expected that these uncertainties 

affect the overall accuracy of the models. However, the obtained results suggest that further tests could validate 

these findings, as explained in Sec. 4.  

2.2 Fireballs from PVBs 

Similarly to the LH2 BLEVE, a hydrogen fireball is likely to occur as a consequence of a H2 PVB. Experimental 

hydrogen PVBs are usually conducted to investigate the consequences of loss of containment scenarios 

involving high pressure vessels, such as hydrogen vessels designed for the automotive sector. Hence, data are 

available for different pressure levels, ranging from 34.5 MPa to almost 100 MPa for different experiments, which 

in some cases simulate PVBs generating from road accidents (Zalosh, 2007). In particular, the following 

experiments are considered in this paper: 

 

• PVBs triggered by propane flames applied to different vessel types (type III and IV) without pressure relief 

valves (PRVs), hereafter, Zalosh-1 test (Zalosh and Weyandt, 2005) and Zalosh-2 test (Zalosh, 2007). 

• Fire tests conducted on different types of high-pressure hydrogen vessels (type III and IV), hereafter 

Tamura-1 test, and Tamura-2 test (Molkov, 2021). 

• Fireball generated by a cup head failure of a type III vessel, hereafter Shen tests 2018 (Shen, 2018)  

 

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Table 1 summarizes the experiments and provides the available measures concerning fireball diameters and 

durations: 

Table 1: Experimental data for hydrogen BLEVEs and PVBs (abbreviation: FB: fireball). 

Test  Year Type [-]  Mass Content [kg] Pressure Burst [MPa] FB diameter [m] FB duration [s] 

BMW  1996 BLEVE 1.80 ÷ 5.40 < 1.29 20 4.0 

SH2IFT 2021 BLEVE 27.00 5.00 26 5.0 

Zalosh-1 2005 PVB 1.64 35.70 8 2.0 

Zalosh-2 2007 PVB 1.87 34.50 24 2.0 

Tamura-1 2006 PVB 1.41 99.50 18 2.0 

Tamura-2 2006 PVB 1.37 94.50 18 2.0 

Shen 2018 PVB 3.90 43.70 7 ÷ 8 1.5 

 

It is worth noticing that three out of the seven tests reported in Table 1 are described as flattened fireballs, hence 

characterized by a particularly elongated horizontal dimension. As it will be discussed in Section 4, the 

experiments that resulted in the flattened fireball are Tamura-1, Tamura-2, and Zalosh-2 tests (Makarov, 2021). 

3. Methodology 

The models proposed within this work are obtained by fitting the experimental data of the BMW and SH2IFT 

tests. Hence, the PVBs experiments are reported to investigate the models’ accuracy for these events and for 

validation purposes. Before discussing these models, the adopted methodology is explained in Sections 3.1 and 

3.2. 

3.1 Literature Correlations 

Several empirical correlations can be found in literature to predict dimensions and duration of fireballs generated 

after the loss of containment of flammable fuels. Among these formulae, the Hord equation (Hord, 1972) gained 

the most appeal (Eq. 1). This correlation considers the fireball diameter as a function of the fuel mass, while the 

fireball duration can be evaluated considering it as momentum-driven or buoyancy-driven (Eq. 2 and Eq. 3). 

Again, this distinction is based on the fuel mass contained in the exploding vessel, as reported below. 

D = 7.93 m𝑓
1

3⁄  (1) 

t = 0.45 m𝑓
1

3⁄   momentum-driven (2) 

t = 2.60 m𝑓
1

6⁄   buoyancy-driven (3) 

Where D indicates the fireball diameter in meters, t its duration in seconds, and m𝑓 being the fuel mass in 

kilograms. These equations, in accordance with others found in literature, consider the fireball as spherical. 

However, recent studies (Makarov, 2021) propose different empirical correlations (Eq. 4 and Eq. 5) to estimate 

the diameter of a hydrogen fireball, considering it to develop in a hemispherical shape. 

Dℎ𝑚𝑠 = 9.8 m𝐻2

1
3⁄  (4) 

Dℎ𝑚𝑠_𝑐𝑜𝑛𝑠 = 19.5 m𝐻2

1
3⁄  (5) 

Where Dℎ𝑚𝑠 and  Dℎ𝑚𝑠_𝑐𝑜𝑛𝑠 indicate the hydrogen fireball diameter in meters considering it as hemispherical 

(Eq. 5 being more conservative) and m𝐻2
being the hydrogen mass in kilograms. Eq. 5 predicts particularly 

conservative results, since it is based on a flattened fireball experiment (obtained by placing an obstacle above 

the exploding tank) which resulted in an increased horizontal dimension (Makarov, 2021). 

3.2 Proposed Correlations 

As mentioned, the models proposed within this work are obtained by fitting the experimental data of the BMW 

and the SH2IFT tests and tuning existing correlations described in Sec. 3.1. The correlations aim at predicting 

both diameter and duration of hydrogen fireballs. Eq. 6 and Eq. 7 estimate the fireball diameter fitting the BMW 

and the SH2IFT tests respectively, while Eq. 8 and Eq. 9 calculate the fireball duration. In addition, Eq. 8 and 

Eq. 9 are conceived to predict the fireball duration similarly to the buoyancy-driven case, but they are built fitting 

the experimental data of both the BMW and the SH2IFT BLEVEs respectively. In fact, the buoyancy-driven 

model is more accurate for hydrogen fireballs than the momentum-driven, as it is shown below. 

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D = 16.44 m𝑓
1

3⁄  BMW-fit (6) 

D = 10.97 m𝑓
1

3⁄  SH2IFT-fit (7) 

t = 3.63  m𝐻2

1
6⁄   BMW-fit (8) 

t = 3.26 m𝐻2

1
6⁄   SH2IFT-fit (9) 

In accordance with the models found in literature, these correlations are also based on the fuel mass contained 

in the exploding vessels, so a high accuracy in the mass measurement is deemed as necessary for future 

experimental tests.  

4. Results and Discussion 

The obtained results (Figure 1a) show how the models proposed with this work (Eq. 6 and Eq. 7) generally 

overestimate the PVBs fireball diameters, with the exception of the flattened fireball of the Zalosh-2 test, which 

was characterized by an exceptionally higher horizontal dimension. Figure 1a also depicts the two new models, 

named BMW-fit (Eq. 6) and SH2IFT-fit (Eq. 7), which fit the data of the BMW and SH2IFT BLEVE experiments, 

respectively. The uncertainties concerning the mass values at moment of the explosion are also illustrated in 

Figure 1a and 1b, along with the PVBs and BLEVEs experimental data. Given these results, it could be 

speculated that the hydrogen mass prior the SH2IFT BLEVE was closer to the expected value of 13 kg, thus 

implying a leakage of about 14 kg of hydrogen (thin dashed line with black circles). This aspect could be also 

inferred by taking into account the experimental data of the BMW tests (thin dashed line with black squares) 

which might indicate that the 20 m fireball diameter was obtained with a filling value close to 5.4 kg of LH2. 

Moreover, Eq. 6 seems to accurately predict the dimensions of both the Tamura fireballs, which were described 

as flattened. In addition, the measured fireball dimensions are higher for the LH2 BLEVEs, with the exception of 

the results of flattened fireballs (Tamura-1, Tamura-2, and Zalosh-2 tests). Interestingly, both Eq. 1 (Hord, 1972) 

(blue curve) and Eq. 4 (Makarov, 2021) (green curve) underestimate the fireball diameters for LH2 BLEVEs, 

while the fitting equation of the extremely flattened fireball obtained for the Zalosh-2 test (red line) results in the 

most conservative prediction.  

  

       a)      b) 

Figure 1: Comparison between experimental data and predictions fireball (a) diameters and (b) durations for 

different hydrogen masses. The uncertainties concerning the liquid hydrogen BLEVE masses are indicated by 

the thin dashed lines.   

While the flattening of fireballs resulted in a relevant scattering of the experimental diameters, the data 

concerning the fireball durations seem to show more consistency. Figure 1b illustrates this aspect, since each 

PVB experiment resulted in a fireball duration of around two seconds, except for the Shen test, in which a shorter 

duration was measured for a higher hydrogen mass with respect to the other experiments. On the other hand, 

the fireballs generated from BLEVEs seem to show longer durations with respect to the ones generated by 

PVBs. This aspect can be also noted in Table 2, which collects the calculation errors for the BMW-fit model. 

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This model produced the most conservative estimations for the fireball duration, and it was developed 

considering the exploding mass equal to 1.8 kg of LH2. 

Table 2: Comparison between the experimental results and the most conservative model (BMW-fit) outcomes. 

 Experimental data Simulation 

Test  Diameter [m] Duration [s] Diameter [m] Duration [s] Diameter Error [%] Duration Error [%] 

BMW  20 4.0 20 4.0 0 0 

SH2IFT 26 5.0 38 5.5 46 11 

Zalosh-1 8 2.0 23 3.9 188 96 

Zalosh-2 24 2.0 20 4.0 -15 103 

Tamura-1 18 2.0 18 3.8 2 92 

Tamura-2 18 2.0 18 3.8 2 89 

Shen 7 ÷ 8 1.5 30 3.9 275 160 

As mentioned, the obtained results could be a hint indicating that the hydrogen fireballs are more likely to behave 

in a more buoyancy-driven manner, given the hydrogen extremely low density, and therefore high buoyancy in 

air. However, Eq. 3 seems to underestimate the duration of the BLEVE fireballs, which could affect the 

predictions on the overall thermal dose, ultimately leading to an underestimation of the related hazard. Hence, 

the models proposed with this work seem to overestimate the fireball durations, but further experimental 

evidence is needed to investigate their suitability. Furthermore, the effect of hydrogen elevated buoyancy should 

be investigated with respect to the fireball duration, since it appears that the buoyancy-driven model might be 

more suitable than the momentum-driven one, even if CCPS (2010) suggests applying Eq. 3 to masses higher 

than 30,000 kg, which are three orders of magnitude higher than the ones considered in this work. One may 

recommend estimating the fireball duration by means of the buoyancy-driven model for the PVBs, and the 

correlations developed in this work for BLEVEs. Finally, the building of an ad-hoc model to estimate both LH2 

fireballs diameter and duration is deemed as necessary, since conventional models seem to provide possible 

hazardous underestimations. Hence, additional experimental data is needed to validate the new models and 

provide reliable evidence concerning the mass involved in the explosion, which seems to be the main parameter 

in the hydrogen fireball development.  

5. Conclusions 

Conventional models aimed at the prediction of fireballs behaviour and generated by vessels loss of integrity 

have proven not to be suitable for hydrogen accidental scenarios. In fact, an overall underestimation of both the 

fireball dimension and duration was obtained with respect to experimental hydrogen BLEVEs. Hence, new 

models were built based on experimental data of LH2 BLEVEs obtained during the BMW tests and the SH2IFT 

project, which seem to achieve more conservative predictions. In addition, the necessity of new experimental 

evidence concerning this hazardous scenario was underlined. Moreover, the implications of the lack of specific 

models describing the consequences of LH2 ignited releases (e.g., liquid hydrogen fireballs) is deemed to 

potentially affect the safety of hydrogen equipment in general, thus ultimately inhibiting the spread of hydrogen 

technologies. 

Nomenclature 

BLEVEs – boiling liquid expanding vapor explosion. 

D – fireball diameter. 

Dhms – hemispherical fireball diameter. 

Dhmsc – hemispherical conservative fireball diameter. 

FB – fireball. 

LH2 – liquid hydrogen. 

PVBs – pressure vessel bursts. 

t – fireball duration. 

Acknowledgments 

This work was undertaken as part of the research project Safe Hydrogen Fuel Handling and Use for Efficient 

Implementation (SH2IFT), and the authors would like to acknowledge the financial support of the Research 

Council of Norway under the ENERGIX programme (Grant No. 280964). This work was undertaken as part of 

the ELVHYS project No. 101101381 supported by the Clean Hydrogen Partnership and its members and the 

European Union. UK participants in Horizon Europe Project ELVHYS are supported by UKRI grant numbers 

10063519 (University of Ulster) and 10070592 (Health and Safety Executive). 

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