=Paper=
{{Paper
|id=Vol-3777/paper18
|storemode=property
|title=Mathematical Modeling of Pressure Effects from Hydrogen Explosion
|pdfUrl=https://ceur-ws.org/Vol-3777/paper18.pdf
|volume=Vol-3777
|authors=Yurii Skob,Oleksandr Khimich,Oksana Pichugina,Andrii Hulianytskyi,Oleksii Kartashov
|dblpUrl=https://dblp.org/rec/conf/profitai/SkobKPHK24
}}
==Mathematical Modeling of Pressure Effects from Hydrogen Explosion==
https://ceur-ws.org/Vol-3777/paper18.pdf
Mathematical Modeling of Pressure Effects from
Hydrogen Explosion
Yurii Skob1, Oleksandr Khimich2, Oksana Pichugina1, Andrii Hulianytskyi3, and Oleksii
Kartashov1
1
National Aerospace University “Kharkiv Aviation Institute”, 17, Vadim Man’ko st., Kharkiv, 61070, Ukraine
2
V.M. Glushkov Institute of Cybernetics, 40, Glushkov ave., Kyiv, 03187, Ukraine
3
Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska str., Kyiv, 01601, Ukraine
Abstract
The statement of the problem and algorithm of computational modeling of the processes of formation of
the hydrogen-air mixture in the atmosphere, its explosion (taking into account chemical interaction) and
dispersion of the combustion materials in the open space with complex relief are presented. The finite-
difference scheme was developed for the case of the three-dimensional system of gas dynamics equations
complemented by the mass conservation laws of the gas admixture and combustion materials. The
algorithm of the computation of thermal and physical parameters of the gas mixture appearing as a result
of the instantaneous explosion taking into account chemical interaction was developed. The algorithm of
computational solution of the difference scheme obtained on the basis of Godunov method was
considered. The verification of the mathematical model showed its acceptable accuracy in comparison
with known experimental data. It allows using the developed model for the modeling of pressure and
thermal consequences of possible failures at the industrial enterprises which store and use hydrogen. The
computational modeling of an explosion of the gas hydrogen cloud appearing as a result of instantaneous
destruction of high pressure containers at the fueling station was carried out. The analysis of different
ways of protection of the surrounding buildings from destructive effects of the shock wave was
conducted. The recommendations considering the choice of dimensions of the protection area around the
fuelling station were worked out.
Keywords
hydrogen-air mixture, hydrogen release, dispersion, blast wave, overpressure, volume concentration,
safety evaluation, explosion consequences 1
1. Introduction
Hydrogen is widely used as an alternative transport fuel [1] which is harmless to the environment
[2]. However, such characteristics of hydrogen [3] as low density, high combustion energy and
rapid transition from burning to detonation cause the problems of safe storage [4] and delivery of
the hydrogen fuel [5] and right allocation of fuelling stations with regard to residential areas [6].
The equipment seal failures, destruction of storage volumes of high compressed hydrogen, cause
its release into the atmosphere and formation of an explosive hydrogen-air mixture [7]. It creates a
real threat of the hydrogen inflammation, detonation explosions [8] and, as a result, considerable
material damage [9].
A physical experiment modeling these gas-dynamics phenomena is very expensive [10]. Its
results cannot be easily used under real conditions of industrial enterprises. For this reason, it is
more advantageous to use computational methods, which can have varying degrees of complexity
and accuracy [11]–[26]. As a rule, overpressure and shock wave impulse are determined using
semi-empiric equations of regression to predict construction loadings after an explosion [17].
However, experimental data are usually obtained in the open space, not taking into account
ProfIT AI 2024: 4th International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2024), September 25–27,
2024, Cambridge, MA, USA
y.skob@khai.edu (Y. Skob); KhimichOM@nas.gov.ua (O. Khimich); o.pichugina@khai.edu (O. Pichugina);
andriihul@knu.ua (A. Hulianytskyi), o.kartashov@khai.edu (O. Kartashov)
0000-0003-3224-1709 (Y. Skob); 0000-0002-8103-4223 (O. Khimich); 0000-0002-7099-8967 (O. Pichugina); 0000-0001-
5269-097X (A. Hulianytskyi); 0000-0002-6282-553X (O. Kartashov)
© 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Workshop ISSN 1613-0073
Proceedings
complex relief [27]. Modern computation methods of burning-to-detonation transition (e.g. [28]–
[32]) are developed for model problems. Therefore, the problem of the creation of the mathematical
model describing adequately time-dependent processes of formation of explosive gas mixtures in
the three-dimensional space (due to evaporation from liquid hydrogen spill [33] taking into
account ambient conditions [34]), their explosion (taking into account chemical interaction of the
mixture components) and further dispersion of the combustion materials in the atmosphere is very
important. A computer system realizing such a mathematical model will allow analyzing and
forecasting three-dimensional fields of the explosive admixture concentration, mixture
thermodynamics parameters in time (before and after explosion) and space, evaluating possible
after-explosion infrastructure destruction, suggesting rationally designed protection devices which
will provide a sufficient level of safety for people in the accident zone [35] and their sustainable
strength so as not to collapse themselves [36]. Moreover, an adequate mathematical model of the
reacting gas mixture flow will allow not only to evaluate the dimensions of the protective device,
but also to select the material for its manufacture for an explosion of different power [37]. It is also
necessary to take into account the model’s ability to provide the necessary data for deterministic
[38] or probabilistic [12] approaches to assess the consequences of accidents for the surrounding
area.
2. Mathematical model
An adequate description of physical processes of hydrogen release and further mixture dispersion
in the atmosphere is possible only using the system of Navier-Stokes time-dependent equations
(NSE) for compressible gas. The limited capabilities of the computing technology available to
engineers do not allow carrying out direct computational solution of these equations effectively. In
many cases, the computation modeling of turbulent flows is realized by solving Reynolds-averaged
NSE, complemented by a turbulence model [39]–[41]. But a great majority of the turbulence
models do not describe different types of flows adequately. It especially relates to flows with an
intensive boundary flow separation and/or heavy changes of such flow parameters as temperature
or pressure. Therefore, it is necessary to create new mathematical models and finite-difference
schemes for a computation modeling of such flows.
The main purposes of this work are to develop a simplified mathematical model describing
adequately time-dependent processes of explosive gas mixtures formation in the three-dimensional
space, their explosion and dispersion of combustion materials in the atmosphere as well as to
create a computational modeling algorithm of these processes.
It is assumed that the mass, impulse and energy transfer impacts for the most part on actual
physical processes. Thus, it is reasonable to apply roughened NSE without taking in account
viscosity (Euler equations with sources [42]).
The computation area Ω is a parallelepiped located in the right-hand coordinate system (fig. 1)
and it is partitioned to spatial cells, the scale of which depends on characteristic sizes of the
computation area (roughness of streamlined surfaces, dimensions of streamlined objects).
Figure 1: Computational model of gas cloud explosion: 1 – entrance air flow with speed vector 𝑞⃗! ;
2 – hydrogen cloud with concentration Q; 3 – combustion products; 4 – exit mixture flow
The system of gas mixture motion differential equations can be represented as follows [43]:
𝜕𝑎⃗ 𝜕𝑏(⃗ 𝜕𝑐⃗ 𝜕𝑑⃗
+ + + = 𝜌𝑓⃗, (1)
𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑧
where vectors 𝑎⃗, 𝑏(⃗, 𝑐⃗, 𝑑⃗, 𝑎𝑛𝑑 𝑓⃗ look like this:
𝑎⃗ = [𝜌, 𝜌𝑢, 𝜌𝑣, 𝜌𝑤, 𝐸]" , (2)
𝑏(⃗ = [𝜌𝑢, 𝑃 + 𝜌𝑢# , 𝜌𝑢𝑣, 𝜌𝑢𝑤, (𝐸 + 𝑃)𝑢]" , (3)
𝑐⃗ = [𝜌𝑣, 𝜌𝑢𝑣, 𝑃 + 𝜌𝑣 # , 𝜌𝑣𝑤, (𝐸 + 𝑃)𝑣]" , (4)
𝑑⃗ = [𝜌𝑤, 𝜌𝑢𝑤, 𝜌𝑣𝑤, 𝑃 + 𝜌𝑤 # , (𝐸 + 𝑃)𝑤]" , (5)
𝑓⃗ = [0, 0, −𝑔, 0, −𝑔𝑣]" , (6)
where time is represented by t, the flow speed vector 𝑞⃗ – by the following components u, v, w,
pressure – by P, density – by r , and total energy of mixture volume unit – by E:
𝐸 = 𝜌 @𝑒 + 1D2 (𝑢# + 𝑣 # + 𝑤 # )E, (7)
where e – mixture mass unit internal energy; components of the vector 𝑓⃗ – volume distributed
sources components; g is an acceleration of gravitation.
The equation of motion of every admixture (combustible gas, combustion materials) is as
follows [43]:
𝜕(𝜌𝑄) 𝜕(𝜌𝑢𝑄) 𝜕(𝜌𝑣𝑄) 𝜕(𝜌𝑤𝑄)
+ + + = 𝜌$! , (8)
𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑧
where Q represents the admixture mass concentration, 𝜌$! – mixture component diffusion source
member (according to Fick dependence [44], [45] looks like this 𝜌$! = 𝑑𝑖𝑣(𝜌𝑄% 𝑔𝑟𝑎𝑑𝑄), and the
diffusion coefficient 𝑄% can be evaluated using the theory of Berlyand [46]–[48])
The set of equations (1-8) is incomplete. It is complemented with equations defining thermal
and physical properties of mixture components [43]. For polytropic gas, internal energy e can be
found from 𝑒 = 𝑃⁄I(𝑘 − 1)𝜌K.
It is assumed that any component of air flow velocity is subsonic. The approaching flow is
defined by the values of total enthalpy 𝐼& = 𝑘D𝑘 − 1 𝑃D𝜌 + 1D2 (𝑢# + 𝑣 # + 𝑤 # ), entropy function
𝑆& = 𝑃⁄𝜌' , flow velocity vector (angles 𝛼( , 𝛼) ), and relative admixture mass concentration 𝑄 (𝑄£1
if the gas admixture flows in). The entry flow parameters are defined by equations (3, 4) (if angles
𝛼( , 𝛼) are set) using the "left" Riemann invariant correlation [49]. On the impermeable
computational cells’ surfaces, the “no flowing” condition is satisfied: qn = 0 (where n is a normal to
the considered cell surface). Exit boundary conditions are set on the computational cells’ surfaces
where the mixture flows out using the "right" Riemann invariant correlation [49]–[53].
At start time in all "gaseous" cells of the computational space, the ambient parameters are
assigned. In the cells occupied by an admixture cloud, the relative mass concentration of the
admixture equals 𝑄 = 1 (100%).
3. Gas mixture explosion model
According to the suggested combustion model, it is assumed that the global instantaneous chemical
reaction takes place in the volume where the concentration of the admixture is in the
inflammability range (a control volume). It means that the values of the parameters of the gas
mixture in the control volume are instantly changed by the values of the corresponding parameters
of combustion materials and remnants of the one of the mixture components (combustible gas in
the case of thin mixture or air in the case of rich mixture). It is assumed that the flame front
propagates with infinitely large speed.
The main purposes of this work are to develop a simplified mathematical model describing
adequately time-dependent processes of explosive gas mixtures formation in the three-dimensional
space, their explosion and dispersion of combustion materials in the atmosphere as well as to
create a computational modeling algorithm of these processes.
Mass of combustible participating in burning is determined for computational cells where the
admixture concentration is in the range between minimal and maximal concentration limits of
inflammability 𝑄*+, ≤ 𝑄 ≤ 𝑄*-( :
𝑚.. = R(𝜌𝑄∆𝑉). (9)
The mass of the combustible not participating in the burning process is determined only for the
computational cells where the admixture concentration 𝑄 > 𝑄*-( :
𝑚&.. = R(𝜌𝑄∆𝑉). (10)
The total mixture mass in the volume where the burning process occurs is determined for
computational cells where the admixture concentration 𝑄*+, ≤ 𝑄 ≤ 𝑄*-( :
𝑚 = R(𝜌∆𝑉). (11)
On the other hand, the total mixture mass m includes the masses of an oxidant m¢ , burning
combustible m¢¢ and not burning combustible m0¢¢. Hence the oxidant mass in the mixture is:
𝑚. = 𝑚 − 𝑚.. − 𝑚&.. . (12)
The mass concentration (averaged on computation space volume) of mixture components are
determined as follows:
𝑄.. = 𝑚.. ⁄𝑚; 𝑄&.. = 𝑚&.. ⁄𝑚; 𝑄. = 𝑚. ⁄𝑚 = (1 − 𝑄.. − 𝑄&.. ). (13)
The excessive air factor in the mixture a is as follows:
𝛼 = 𝑚. ⁄(𝜗& 𝑚.. ) = (1 − 𝑄.. − 𝑄&.. )⁄(𝜗& 𝑄.. ), (14)
. ⁄ .. .
where 𝜗& = 𝑚/0 𝑚 is a stoichiometric number, 𝑚/0 – air mass which is necessary in theory for
the complete combustion of 1 kg of the fuel.
The lower combustion value of the admixture Hu is set from the tables of thermophysical
properties of the matters. The molar mass µc and the adiabatic coefficient kc of the combustion
materials are determined on the basis of reversibility hypothesis of the realized chemical reactions.
In the case when ∝≥ 1 the thermophysical properties of the gas mixture after an explosion are
determined as follows:
1 − (𝜗& + 1)𝑄.. − 𝑄&.. (𝜗& + 1)𝑄.. 𝑄&.. (15)
𝜇 = 1D[ .
+ + .. \,
𝜇 𝜇1 𝜇
𝐶2 = [1 − (𝜗& + 1)𝑄.. − 𝑄&.. ]𝐶2. + (𝜗& + 1)𝑄.. 𝐶21 + 𝑄&.. 𝐶2.. , (16)
.. .. . .. 1 .. ..
𝐶3 = [1 − (𝜗& + 1)𝑄 − 𝑄& ]𝐶3 + (𝜗& + 1)𝑄 𝐶3 + 𝑄& 𝐶3 , (17)
In the case when ∝< 1 the thermophysical properties of the gas mixture after an explosion are
determined in such a way:
(𝜗& + 1)𝑄. 𝜗& − (𝜗& + 1)𝑄.
𝜇 = 𝜗& D[ + \, (17)
𝜇1 𝜇..
𝐶2 = _1 − 𝑄1⬚ `𝐶2.. + 𝑄1⬚ 𝐶21 , (19)
𝐶3 = _1 − 𝑄1⬚ `𝐶3.. + 𝑄1⬚ 𝐶31 , (20)
In any case such properties of the gas mixture as adiabatic coefficient, pressure, temperature
and density are as follows:
𝑘 = 𝐶2 ⁄𝐶3 . (21)
.. (𝑘 .. .. ..
𝐻5 𝑚/0 − 1) 𝐻5 (1 − 𝑄 − 𝑄& )𝑚⬚ (𝑘 − 1) (22)
𝑃= + 𝑃- = ..
+ 𝑃- ,
𝑉 𝜗& 𝑄 𝑉
𝑃𝑉𝜇 (23)
𝑇= .
𝑚𝑅5,
𝜌 = 𝑚⁄ 𝑉 . (24)
From here, it is assumed that an explosion is instantaneous; combustion takes place in the
permanent volume occupied by an explosive mixture with the combustible concentration within
the limits of inflammability. After the explosion in the localized volume the fluid dynamics
parameters of two-reactant mixture (air and combustible gas) are modified to the fluid dynamics
parameters of the three-component mixture (air, products of combustion and fuel remnants).
4. Algorithm and method of computational solution
The vector equation (1) can be presented in an integral form for every computational cell:
⬚ ⬚ ⬚
𝜕
d 𝑎𝑑𝑉 + e 𝐴g𝑑𝜎 = d 𝜌𝑓𝑑𝑉 , (25)
𝜕𝑡
6 7 6
where the volume of computational unit is represented by V, the surface of the volume unit 𝜎⃗ is
defined by normal vector 𝑛(⃗ (𝜎⃗ = 𝜎 𝑛(⃗), 𝐴g is the tensor of conservative variables 𝑎⃗.
The differential equation (8) can be interpreted in an integral form:
⬚ ⬚ ⬚
𝜕
d 𝜌𝑄𝑑𝑉 + e 𝜌𝑄𝑞𝑑𝜎 = dI𝜌$! K𝑑𝑉, (26)
𝜕𝑡
6 7 6
The computational solution of the equations (27, 28) is based on the scheme of an arbitrary
break of fluid parameters (Godunov method [49]–[53]). In the moment of an explosion in the
volume of the computation space occupied by the explosive mixture with the admixture
concentration within the limits of inflammability (𝑄*+, ≤ 𝑄 ≤ 𝑄*-( ) the gas dynamics
parameters of two-component mixture (air and fuel) instantly become the parameters of three-
component mixture (air, combustion materials and fuel remnants). The mixture parameters after an
explosion are determined according to the equations (9-26).
An explicit Godunov method is used to solve Euler equations complemented by the
conservation law of the gas mixture concentration in the integrated form. The first order finite-
differential scheme is used to approximate Euler equations. The second order central differences
are used for the diffusion source member of the conservation law of the gas mixture concentration.
The simple pressure interpolation in the vertical dimension is applied. Godunov method has a
robust algorithm resistant to disturbances of flow parameters.
The presented model is used in the research bundled software «Fire» which allows forecasting a
gas admixture concentration and pressure development in an acceptable time using stand-alone
computers.
5. Mathematical model validation
A release of the gas inflammables into the atmosphere and their explosion cause the formation and
propagation of the shock waves, personnel affection and damage of the vitally important objects.
An overpressure in the front of the shock-wave generated by an explosion is usually used to
evaluate building surface loadings.
The validation of the developed model against experimental results was carried out. An
explosion of the hemispheric homogeneous stoichiometric hydrogen-air mixture cloud was
modeled (experiments at Fraunhofer ICT [54]) under the following conditions: the total volume of
the cloud 2094 m3; the initial pressure 98.9 kPa; the initial temperature 283 K; the diameter of the
hemispheric cloud 20 m. The pressure development at the distances of 35 m (the point B on the fig.
2) and 80 m (the point C) from the epicenter of the explosion (the point A) was examined during
the computation.
The computation space had the following dimensions: the length of 200 m; the width of 100 m,
the height of 30 m. The dimensions of the computational grid were 200x100x30 cells. The computer
and code had the following characteristics: processor Intel® Core(TM) i7–3630QM CPU @ 2.40
GHz 2.40 GHz, 16 Gb RAM, Windows 7, 0.2 h CPU time.
The flow pressure distribution near the ground at the moment when the shock-wave passes the
point B is presented on the fig. 2. It is obvious that a zone of decreased pressure has been formed
around the epicenter of the explosion. The further propagation of the explosion shock-wave along
the computation area to the control point C is accompanied by decreasing of the intensity of
overpressure (fig. 3).
Figure 2: Pressure distribution in the plane XOZ near the ground (t=0.33 s)
Figure 3: Pressure distribution in the plane XOZ near the ground (t=0. 44 s)
The overpressure dynamics at the control milestones B and C is presented on the fig. 4-5 against
the experimental results and the computational results obtained using other different codes [54]–
[62]. More sharp form of the calculated curve can be explained by particular features of the
accepted combustion model (global instantaneous chemical reaction). More intensive decrease of
the overpressure as the shock-wave propagates from the point B to the point C may be obviously
referred to the first order scheme of the Godunov method.
As a whole the computational results have quite a good agreement with the experimental data.
It allows using the developed mathematical model and code for a simulation of the large-scale
explosions of the hydrogen-air mixtures in the open atmosphere and prediction of pressure
consequences of such explosions on surrounding buildings.
An explosion of stoichiometric propane-air mixture (the volume of combustible cloud – 1495 m3,
energy of explosion – 4640 MJ) was also carried out in order to validate the developed model and
code.
The computational results (fig. 6) show acceptable accuracy comparing with experimental data
and regressive dependence [17] (in the fig. 6: 𝑅& = 𝑅⁄𝐸 !⁄8 . is a dynamic radius, where R –
distance from the epicenter of explosion, m; E – energy of explosion, J).
6. Computation of hydrogen cloud explosion
The hydrogen dispensing station [63] and local area around it is considered. The station has a
cryogenic tank with liquid hydrogen (5,7 m3). The tank feeds 36 high-pressure cylinders (18,4 m3 in
overall) with gas hydrogen. During operation of the fuel station different emergencies caused by
gas and liquid hydrogen leaks from the defective equipment (or as a result of its destruction) can
happen. It results in formation of the explosive cloud of the hydrogen-air mixture and its
dispersion in the atmosphere. One of the most dangerous scenarios (taking into account potential
catastrophic consequences threatening to the equipment of the station, its personnel and near-by
residential area buildings) is an explosion of hydrogen-air mixture as a result of large-scale
instantaneous release into the atmosphere of all the volume of compressed gas hydrogen from the
all high pressure dispensing cylinders [63]–[65].
Figure 4: Overpressure history in the point B near the ground
Figure 5: Pressure history in the point C near the ground
Figure 6: Overpressure distribution in the shock wave front: 1 – computational results,
2 – regressive dependence, 3 – experimental data
This scenario was modeled using the developed mathematical model. The hydrogen cloud had
such initial parameters: volume 798 m3; hydrogen mass 687.4 kg; hydrogen mass concentration
100%; pressure 1031371.3 Pa; temperature 288 K. It was assumed that the cloud had been dispersing
during 0.06 s after instantaneous destruction of high pressure cylinders (a physical explosion).
Then a detonation explosion of the hydrogen-air mixture (a chemical explosion) took place. The
chemical explosion caused appearance of high temperature combustion materials and shock wave
which had a pressure impact on the station equipment and residential buildings. The location plan
is presented in the fig. 7.
Figure 7: The location plan of the area around the fuelling station (A, B – possible location sites of
the station; C – a control point on the building wall; – infrastructure objects)
The height of the buildings was 5–12 m. The location of the station (positions A and B in the fig.
7) was varied in relation to the buildings location. The different types of the shield installations
(banks, bumper wall) around the station against destructive influence of the shock wave
overpressure were also considered. The pressure history was analyzed at the explosion epicenter
and point on the building (A, B and C on the fig. 7, accordingly).
6.1. Hydrogen cloud explosion nearby infrastructure objects
The case when the fuel station location is close to the residential area is considered (position B
in the fig. 7). Any shield installation from destructive influence of an explosion shock wave is used.
The distribution of the hydrogen volume concentration in the just before an explosion is presented
in the fig. 8. Obviously, the radius of a hemispheric zone of the detonation burning makes
approximately 25 m and surpasses the height of the building.
Figure 8: The distribution of the hydrogen volume concentration before a moment of nearby
explosion in the YOZ plane (B – explosion epicenter, C – control point on the building)
The pressure distribution near the ground and in YOZ-plane when the pressure at point C
reaches the maximal is presented in fig. 9. The analysis shows that pressure in the wave front on
the building near the ground is approximately twice as higher as in open space.
Figure 9: Pressure distribution in the planes: XOZ near the ground (a), YOZ (b)
The pressure history in the control points B and C is presented in the fig. 10. Two peaks of
pressure in the point B (fig. 10 a) correspond to the moments of time when physical and chemical
explosions occur. As the explosion epicenter is moved away from the residential area, the value of
the shock wave pressure amplitude decreases quickly (fig. 10 b).
6.2. Distant hydrogen cloud explosion
The case when the fuel station location is distant from the residential area is also considered
(position A in the fig. 7). The distance from the fuel station to the nearest buildings is selected from
the recommendations [63]–[65]. Any shield installation against the destructive influence of an
explosion shock wave is used. The analysis of the hydrogen volume concentration distribution
shows that the size and the form of the detonation burning zone are similar to the case with the
near-by location of the station (fig. 8). The pressure distribution in the planes XOZ (near the
ground) and YOZ when overpressure in the control point C reaches the maximum is presented in
the fig. 11.
Figure 10: Pressure history in the points: B (a) and C (b)
Figure 11: The pressure distribution in the case of a distant location of the fuel station in the
planes: XOZ near the ground (a), YOZ (b)
The pressure history in points A and C is presented in the fig. 12. Two peaks of pressure in the
point A (fig. 12 a) correspond to the moments when explosion occur. The distancing of the
explosion epicenter from the residential area significantly decreases (approximately five times) the
maximal pressure loading on the building walls (fig. 12 b, 10 b).
Figure 12: Pressure history in the characteristic points: A (a) and C (b)
6.3. Distant banked explosion of a hydrogen cloud
A similar to 5.2 case of the distant location of the fuel station from the residential area is
considered (position A in the fig. 7). To shield the buildings against the destructive impact of the
explosion the banks (7 m high) surrounding the station are installed. The analysis of the hydrogen
volume concentration distribution shows that the overall dimensions and the form of the
detonation zone have been changed under the influence of complex relief of banks (fig. 13).
Figure 13: The hydrogen volume concentration distribution before a moment of the banked
distant explosion in the YOZ plane (A – an explosion epicenter)
The pressure distribution in the cross-planes XOZ (near the ground) and YOZ (through the
point C on the building) when the overpressure in the control point C reaches maximum
(fig. 14) has changed insignificantly comparing to the remote explosion 5.2.
Figure 14: The pressure distribution in the planes: XOZ near the ground (a), YOZ (b)
6.4. Distant partly banked explosion of the hydrogen cloud
A similar to 5.3 case of the distant location of the fuel station from the residential area is
considered (position A in the fig. 7). To shield the buildings from the impact of an explosion the
banks (7 m high) partly surrounding (in the north-east) the station are installed. Overall
dimensions and a form of the detonation zone have been changed under the influence of the banks
relief (fig. 15).
The pressure distribution in the planes XOZ (near the ground) and YOZ when the overpressure
at the control point C reaches the maximum is presented in the fig. 16. The partly banking of an
explosion site has insignificantly changed the overall pressure field comparing to the explosion 5.3.
6.5. Distant explosion partly surrounded with higher banks
A similar to 5.4 case of the distant location of the fuel station from the residential area is
considered (position A in the fig. 7). To protect the buildings from an explosion impact the higher
banks (13 m high) which partly (in the north-east) and more distantly surrounding the station are
installed (fig. 17, 18 a). The pressure distribution in the planes XOZ (near the ground) and YOZ
when the overpressure at the control point C reaches the maximum is presented in the fig. 18. The
data analysis shows that the higher partly banking of an explosion site allows decreasing slightly
the pressure loading on the buildings (fig. 18 b).
Figure 15: The hydrogen volume concentration distribution before a moment of partly banked
distant explosion in the YOZ cross plane (A – an explosion epicenter)
Figure 16: The pressure distribution in the planes: XOZ near the ground (a), YOZ (b)
Figure 17: The hydrogen volume concentration field before a moment of a distant explosion partly
surrounded with the higher banks in the YOZ cross plane (A – an explosion epicenter)
6.6. Distant hydrogen explosion with the use of bumper walls t, s
A similar to 5.2 case of distant location of the fuel station from the residential area is
considered. To protect the buildings from an explosion impact the bumper walls (8 m high, 3 m
thick) are installed immediately in front of the buildings (fig. 19 a). The pressure distribution in the
planes XOZ (near the ground) and YOZ when the pressure at the control point C reaches the
maximum is presented in fig. 19. The data analysis makes it clear that an installation of the bumper
wall near the buildings causes a decrease of pressure by approximately 10 percent comparing with
a case without protection (fig. 20).
Figure 18: The pressure distribution in the planes: XOZ near the ground (a), YOZ (b)
Figure 19: Pressure distribution in planes: XOZ near the ground (a), YOZ (b)
Figure 20: Pressure history in a point C
It should be noted that all the considered types of the protective installations do not allow
bringing maximal overpressure down in the control point on the wall of the building to the safe
level.
7. Conclusion
The mathematical model of the gas-dynamics processes of the two-agent explosive gas mixture
formation, its explosion and dispersion of the combustion materials in the open atmosphere was
developed. The finite-difference approximation was developed for the case of three-dimensional
system of the gas dynamics equations complemented by the mass conservation laws of the gas
admixture and combustion materials. The algorithm of the computation of the thermo-physical
parameters of the gas mixture resulting after instantaneous explosion taking into account the
chemical interaction was developed. The smoothing effect of the first-order finite-difference
scheme can be compensated by a denser computational grid. The verification of the mathematical
model showed an acceptable accuracy in comparison with the known experimental data that
allowed using it for the modeling of consequences of the possible failures at industrial objects
which store and use hydrogen.
The computational modeling of the gas hydrogen explosion at the fuel station was carried out.
The analysis of the different ways of protecting the surrounding buildings from the shock wave
destructive impact was conducted. It was revealed that the considered types of the protective
installations (partial or complete banking, bumper walls) had an influence on the pressure
distribution in the computation area but did not allow bringing the maximal overpressure down to
the safe level. It was concluded that a bumper wall immediately in front of the protected object was
one of the most effective protective installation. It is necessary to take into account a three-
dimensional character of the shock wave in order to select safe dimensions of the protection zone
around the hydrogen storage facilities.
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