=Paper=
{{Paper
|id=Vol-3641/paper15
|storemode=property
|title=Mathematical Modelling of Gas Admixtures Release, Dispersion and Explosion in Open Atmosphere
|pdfUrl=https://ceur-ws.org/Vol-3641/paper15.pdf
|volume=Vol-3641
|authors=Yurii Skob,Sergiy Yakovlev,Oksana Pichugina,Mykola Kalinichenko,Kyryl Korobchynskyi
|dblpUrl=https://dblp.org/rec/conf/profitai/SkobYPKK23
}}
==Mathematical Modelling of Gas Admixtures Release, Dispersion and Explosion in Open Atmosphere==
https://ceur-ws.org/Vol-3641/paper15.pdf
Mathematical Modelling of Gas Admixtures Release,
Dispersion and Explosion in Open Atmosphere
Yurii Skob1, Sergiy Yakovlev1,2, Oksana Pichugina1, Mykola Kalinichenko1 and Kyryl
Korobchynskyi1
1 National Aerospace University “Kharkiv Aviation Institute”, 17, Chkalov st., Kharkiv, 61070, Ukraine
2 Institute of Information Technology, Lodz University of Technology, 90-924 Lodz, City, Poland
Abstract
The method of the numerical solution of a three-dimensional problem of atmospheric release,
dispersion and explosion of gaseous admixtures is presented. It can be equally applied for gases of
different densities, including hydrogen. The system of simplified Navier-Stocks equations received by
truncation of viscous members (Euler equations with source members) is used to obtain a numerical
solution. The algorithm is based on explicit finite-difference Godunov scheme of arbitrary parameters
breakup disintegration. To validate the developed model and computer system comparisons of
numerical calculations with the published experimental data on dispersion of methane and
hydrocarbons explosions have been carried out. Computational experiments on evaporation and
dispersion of spilled liquid hydrogen and released gaseous hydrogen at different wind speed values
have been conducted. The largest mass concentrations of hydrogen between bottom and top limits of
flame propagation and cloud borders have been determined. The problem of explosion of hydrogen-air
cloud of the complex form generated by large-scale spillage of liquid hydrogen and instant release of
gaseous hydrogen has been numerically solved at low wind speed. Shock-wave loadings affecting the
buildings located on distance of 52 m from a hydrogen release place have been shown.
Keywords
gas mixture, admixture release, evaporation, explosion pressure wave, overpressure, mass
concentration, probit analysis, accident consequences 1
1. Introduction
Hydrogen is widely applied in the different industries. Particular danger of its application is
conditioned by the large energy of combustion, fast transition from burning to detonation, and,
as a consequence, powerful explosion of the cloud in the atmosphere after release. Hydrogen
differs essentially from other explosive compressed gases and liquids, firstly, by very small
density, and, secondly, by very low liquid stage temperature. The quantity of hydrogen
participating in explosion is defined by conditions of its evaporation (in case of release and
spillage in liquefied form), dispersion and mixing with air. These processes will be influenced by
specified above properties of liquefied and compressed hydrogen [1]. Spilled liquids evaporate
from spillage surface mixing with fresh air and forming dangerous mixtures. These physical
processes substantially depend on shape of the spill spot [2], environment conditions,
especially, wind speed [3], earth surface relief [4].
Usually, accidental release of dangerous liquids takes place after malfunction of storage or
transportation equipment (Figure 1Figure 1Figure 1Figure 1). Released admixture mixes with
fresh air and creates air-gas cloud with some gas concentration, and the mixture could explode.
ProfIT AI 2023: 3rd International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2023), November
20–22, 2023, Waterloo, Canada
y.skob@khai.edu (Y. Skob); svsyak7@gmail.com (S. Yakovlev); o.pichugina@khai.edu (O. Pichugina);
m.kalinichenko@khai.edu (M. Kalinichenko) ; k.korobchinskiy@khai.edu (K. Korobchynskyi)
0000-0003-3224-1709 (Y. Skob); 0000-0003-1707-843X (S. Yakovlev); 0000-0002-7099-8967 (O. Pichugina);
0000-0002-8685-065X (M. Kalinichenko); 0000-0002-3676-6070 (K. Korobchynskyi)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Industrial Hydrogen Formation of Explosion of Explosion
Environment
equipment release into hydrogen-air combustible wave
impact
failures atmosphere cloud mixture propagation
Figure 1: Typical accidental process development scheme
Accidental gas releases and could explosions cause significant damage to the environment
and create such dangerous factors as shock-impulse loads on humans and building
constructions [5] in hazard zones, toxic inhalation dozes (if admixtures are toxic) [2], and
thermal radiation dozes from high-temperature combustion products [6] and fire flame fluxes
[7]. Safety experts need all the information about distribution of dangerous factors around
accident epicenter in order to assess the consequences for environment and provide protection
measures to mitigate them [8] reaching acceptable risk levels and check if protection
construction could withstand explosion loads without destruction [9]. Mathematical modeling
of physical processes during accidental release and explosion of combustible gases (Figure 2),
instead of full experiment, could significantly reduce the costs of risk assessment work.
Gas release Control of Determination Environment
dispersion and hazardous of damage impact
explosion parameters factors evaluation
model
Figure 2: Typical consequences assessment procedures scheme
Atmospheric dispersion of gaseous admixtures is traditionally modeled under the
assumption of Gaussian distribution of the admixture concentration and on the basis of
corresponding analytical functional dependences [10]. But for neutral, heavy and light gases
only the partial solutions are obtained, and such important factors as relief and gas
compressibility under explosion condition can not be taken into account. The most adequate
description of the physical processes of dispersion of chemically reacting gases is possible only
using the Navier-Stokes system of non-stationary equations for compressible gas [11].
Currently, numerical simulation of turbulent flows is carried out by solving the Reynolds-Favre-
averaged Navier-Stokes equations, supplemented by a model of turbulence [12]. However, most
turbulence models do not describe with an equal degree of adequacy the various types of flows
that can appear [13]. This is especially true for flows with intense flow breaks and/or large
pressure and temperature gradients. That is why, more simple than Navier-Stokes equations
model but sophisticated enough in order to take into account relief, flow compressibility, and to
avoid difficulties to select adequate turbulence model is needed aiming to extract mass
concentration admixture and overpressure distributions as hazardous risk factors.
In presented work an attempt to solve numerically a three-dimensional problem of the
admixture dispersion in the atmosphere and explosion equally applied for different density
gases (including hydrogen) have been made.
2. Mathematical model
2.1. Model brief description
A mathematical model of the physical process of the emergency release and dispersion of a gas
impurity into the atmosphere, its dispersion in the surface layer of the atmosphere with the
formation of a gas-air mixture and its explosion allows us to obtain non-stationary fields of the
mass concentration of the impurity and pressure in the accident zone. These distributions of
hazardous parameters can be further used to calculate the fields of hazardous factors (excess
pressure and impulse of the compression phase in the shock wave front) to assess the
consequences of their impact on the environment (operating personnel and man-made facility
structures) in order to develop recommendations for reducing the operation risks of high
danger enterprises.
To evaluate the spacious distribution of hazardous admixture mass concentration during the
release and dispersion processes the basic equations system of air-gas mixture movement in the
near-Earth atmosphere layer is used based on Euler approach supplemented with admixture
conservation equation. An instant explosion model is used to define overpressure fields and
asses explosion consequences. Admixture mass concentration is controlled during the
calculation process to localize the area where admixture concentration is within flammability
limits, and in the moment of explosion air-gas mixture flow parameters are replaced on
detonation parameters. After that explosion products concentration and pressure distributions
are controlled to evaluate overpressure and impulse at the explosion wave front. This useful
information can be used in future versions of the model to calculate human damage probability
using probit analysis model.
The computational domain is a parallelepiped located in the right Cartesian coordinate
system (Figure 3). It is divided into spatial cells which dimensions are determined by the scale
of the characteristic features of the area (surface roughness, objects dimensions).
2.2. Basic equations
An adequate description of physical processes of nonreactive gas mixture with air and
further admixture dissipation in the atmosphere (or enclosed ventilated premise) is possible
only with the use of time-dependent Navier-Stocks equations for compressible gas. The limited
resources of modern computers do not allow obtaining effectively the direct numerical solution
of these equations. As a rule, numerical modeling of large space turbulent flows is carried out by
solving of Reynolds-averaged Navier-Stocks equations [14] added by turbulence model [15].
However the majority of turbulence models do not describe with an identical degree of
adequacy all various types of flows. It especially relates to flows with intensive stream
separation and large-scale gradients of pressure and temperature.
Figure 3: Calculation scheme: 1 – spill spot; 2 – ground surface; 3 – air wind vector; 4 –
evaporation process; 5 – total evaporation rate; 6 – mixture; 7 – explosion products; 8 –
overpressure explosion wave
As a result of the flow structural analysis and decomposition of the full gas-dynamic
mathematical model it is assumed that the convective mass exchange mainly influences on the
process considered. Thus, for the description of processes of two-component gas mixture and
dissipation it is enough to use the simplified Navier-Stocks equations received by the truncation
of viscous members (Euler approach with source members).
The calculated space Ω is a parallelepiped located in the right-hand Cartesian system of
coordinates (X, Y, Z) with the basis in plane XOZ (axis Y is directed opposite to the Earth's
gravity). The calculated space is broken into spatial cells. The full system of the time-dependent
equations describing three-dimensional two-component gas mixture flow looks like [16], [17],
[18]:
𝜕𝑎⃗ 𝜕𝑏⃗⃗ 𝜕𝑐⃗ 𝜕𝑑⃗
+ + + = 𝜌𝑓⃗, (1)
𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑧
where a, b, c, d, f represent the following vector-columns:
𝑎⃗ = [𝜌, 𝜌𝑢, 𝜌𝑣, 𝜌𝑤, 𝐸]𝑇 , (2)
𝑏⃗⃗ = [𝜌𝑢, 𝑃 + 𝜌𝑢2 , 𝜌𝑢𝑣, 𝜌𝑢𝑤, (𝐸 + 𝑃)𝑢]𝑇 , (3)
2 𝑇
𝑐⃗ = [𝜌𝑣, 𝜌𝑢𝑣, 𝑃 + 𝜌𝑣 , 𝜌𝑣𝑤, (𝐸 + 𝑃)𝑣] , (4)
⃗
𝑑= [𝜌𝑤, 2 (𝐸
𝜌𝑢𝑤, 𝜌𝑣𝑤, 𝑃 + 𝜌𝑤 , + 𝑃)𝑤] , 𝑇 (5)
𝑇
𝑎⃗ = [0, 0, −𝑔, 0, −𝑔𝑣 + 𝑒𝑠 ⁄𝜌] , (6)
where t represents time, u, v, w are the components of air speed vector, P, – pressure and
density, and E is full energy of a volume unit of gas mixture:
𝐸 = 𝜌 (𝑒 + 1⁄2 (𝑢2 + 𝑣 2 + 𝑤 2 )), (7)
where e – internal energy of gas mass unit; components of the vector 𝑓⃗ – projections of the
distributed volumetric sources; g – gravitational acceleration; 𝑒𝑠 – intensity of a thermal
emission in gas volume unit as a result of chemical reaction.
If consider leaked and evaporated explosive admixture [19] and combustion products as
separate gases [20], the law of each admixture component transfer, taking into account a
diffusion speed, looks like [21]:
𝜕(𝜌𝑄) 𝜕(𝜌𝑢𝑄) 𝜕(𝜌𝑣𝑄) 𝜕(𝜌𝑤𝑄)
+ + + = 𝜌𝑄𝑡 + 𝜌𝑄𝑠 , (8)
𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑧
where Q – relative mass density of an admixture (the ratio of gaseous admixture substance
density to the mixture density); 𝜌𝑄𝑡 – an admixture density change rate as a result of diffusion
(according to Fick law [22], 𝜌𝑄𝑡 = 𝑑𝑖𝑣(𝜌𝑄𝐷 𝑔𝑟𝑎𝑑𝑄), and the factor of diffusion 𝑄𝐷 is defined
according to Berljand [23]); 𝜌𝑄𝑠 – an admixture density change rate as a result of chemical
reaction.
The system of the equations (1, 8) is completed by the mixture component heat-transfer
properties equations [24]. For ideal gas the value of e is related to the values of P and of the
mixture by the following dependence 𝑒 = 𝑃⁄((𝑘 − 1)𝜌).
2.3. Boundary conditions
It is assumed that the air flow quantity component of velocity does not surpass sound speed.
Entry boundary conditions are set on the finite-difference cells surfaces through which
atmospheric air enters. The approaching flow is defined by values of total enthalpy
𝑘 𝑃
𝐼0 = + + 1⁄2 (𝑢2 + 𝑣 2 + 𝑤 2 ), (9)
𝑘 −1𝜌
entropy function
𝑃
𝑆0 = 𝑘 , (10)
𝜌
flow velocity vector (angles 𝛼𝑥 , 𝛼𝑧 ), and relative admixture mass density Q (Q 1 if the gaseous
admixture flows in). The entry flow parameters are defined by equations (3, 4) (if angles 𝛼𝑥 , 𝛼𝑧
are set) using "left" Riemannian invariant correlation [24]. On impermeable computational cells’
surfaces the “no passing” conditions are satisfied: 𝑞𝑛 = 0 where 𝑛⃗⃗ is a vector of normal to
considered surface. Exit boundary conditions are set on the computational cells surfaces
through which the mixture flows out (except for the atmospheric pressure 𝑃𝐴 , the "right"
Riemannian invariant correlation [24] is used).
2.4. Initial conditions
At start time in all "gaseous" cells of the computational space the parameters of an ambient
air are assigned. In cells, where the admixture cloud takes place, relative mass concentration of
an admixture equals 1 (100%). In cells with hydrogen evaporation (or outflow) the law of
admixture consumption variation is set.
2.5. Algorithm of the numerical solution
The vector equation (1) is a consequence of the mass, impulse and energy conservation laws
which can be presented in the integrated form for each calculated cell
𝜕
∭ 𝑎𝑑𝑉 + ∯ 𝐴̂𝑑𝜎 = ∭ 𝜌𝑓𝑑𝑉 , (11)
𝜕𝑡
𝑉 𝜎 𝑉
where V is a volume of an elementary computational cell, 𝜎⃗– a limiting surface of the given
cell which has an external normal vector 𝑛⃗⃗ (𝜎⃗ = 𝜎 𝑛⃗⃗) ( = σn ) , 𝐴̂ – a tensor of the flow density
of conservative variables 𝑎⃗ which columns are vectors b, c and d, accordingly.
The mixture component transfer law (8) can be presented also in the integrated form for
each computational cell:
𝜕
∭ 𝜌𝑄𝑑𝑉 + ∯ 𝜌𝑄𝑞𝑑𝜎 = ∭(𝜌𝑄𝑡 + 𝜌𝑄𝑠 )𝑑𝑉 , (12)
𝜕𝑡
𝑉 𝜎 𝑉
The equations (11, 12) suppose occurrence and existence of parameters break surfaces of
two types: shock waves and tangential breaks. The functions, satisfying to the equations (11,
12), can be considered as the gas dynamics equations generalized solutions. The use of
integrated conservation laws as initial for construction of finite-difference equations provides
the formation of breakup solutions without isolation of breaks.
The set of gas-dynamic parameters in all computational cells at the moment of time t n
represents the known solution. Gas-dynamic parameters at the moment of time t n+1 = t n +
are calculated by means of explicit finite-difference approximations for equations (5) according
to Godunov method [24]. At first stage continuous distribution of parameters is replaced with
piecewise constant integral-averaged values in each computational cell. At the same time the
borders of a cell represent unstable surfaces of arbitrary breakup which disintegrate to steady
wave elements: a shock wave, a contact surface and a wave of rarefaction. For each such
breakup the streams of mass, impulse and energy through sides of gas cells are defined. The
stability of the finite-difference scheme is provided due to a choice of time step size.
On the basis of mathematical model the computer system of the engineering analysis of the
gas-dynamic processes of release, mixture and dispersion was developed which is used in the
research computer information system. It allows predicting an admixture concentration change
in time and space in the calculated area and computing shock-wave parameters formed after
detonation in the atmosphere during fuel-air mixture dispersion process with the use of
personal computers for practically reasonable time.
3. Mathematical model validation
Since we did not possess hydrogen experimental data, we have used propane and methane
experimental data to verify mathematical model and developed computer system.
3.1. Propane evaporation from a water surface
In order to verify the developed model for gaseous admixture dispersion in the atmosphere
the comparison of the computation results with experimental data [25] was conducted (Figure
4Figure 4Figure 4).
Figure 4: The maximal propane concentrations: 1, 2 and 3 – computations, 4, 5 and
6 – experimental data [25] at heights 0.8, 1.4 and 2.3 m, accordingly
The evaporation process of liquid propane from a spillage pond occupying the area of 256 m2
was modeled at ambient air parameters: pressure 101325 Pa, temperature 291 K, wind speed
8.1 m/s. The propane evaporated with the consumption of 27.6 kg/sec and had the temperature
230 K in a gaseous stage. The calculated propane concentration distributions at heights 0.8, 1.4
and 2.3 m at the moment of time 450 sec from the evaporation start time in comparison with
experimental gauging [25] are well enough conformed to experimental data.
3.2. Gas cloud explosions in the atmosphere
For validation of calculation model of atmospheric gas cloud explosions a comparison of
calculated results with experimental data [26] іs conducted (Figure 5).
An explosion of a stoichiometric propane-air mix cloud was calculated at conditions of
experiment: volume of the gas mixture cloud - 1495 m3; energy of explosion - 4940 МJ. On the
basis of these data initial conditions for calculation, pressure and temperature of combustion
products in the cloud, have been defined:
𝐸(𝑘 − 1) 4940𝑒 6 (1.29 − 1)
𝑃= + 𝑃𝐴 = + 101325 = 1.06 𝑀𝑃𝑎, (13)
𝑉 1495
𝑃𝜇𝑚𝑖𝑥 1.06𝑒 6 0.029
𝑇= = = 2868 𝐾, (14)
𝜌𝑚𝑖𝑥 𝑅 1.29 8.31
where V – volume of the gas mixture cloud; E – energy of explosion; k – adiabatic coefficient; PA
– atmospheric pressure; mix – molar mass of the mixture; mix – mixture density; R – universal
gas constant.
For obtaining parameters of gas detonation, more sophisticated models [27] can be used to
assess explosion hazards [28]. In work [26] on the basis of experiments of explosion of clouds of
acetylene, propane and methane with air and propane and methane with oxygen the correlation
dependence was received that allows to define the overpressure Pf in the shock wave front
from distance from an epicenter for the assigned energy of explosion:
0.6 10−1 1.4 10−2 2.5 10−3
∆𝑃𝑓 = + + 𝑖𝑓 𝑅0 ≥ 0.3, (15)
𝑅0 𝑅02 𝑅03
0.052
∆𝑃𝑓 = 1.7 𝑖𝑓 0.08 ≤ 𝑅0 < 0.3, (16)
𝑅0
1
where 𝑅0 = 𝑅⁄𝐸 3 – dynamic radius; R – distance from an explosion epicenter; E – energy of
explosion.
Figure 5: Explosion waves parameters in comparison with experimental data [26] and
analitical correlation dependance [26]
In Figure 5 the results of numerical calculations are presented which well enough coincide
with experimental data and with correlation dependence [26].
4. Numerical computations of hydrogen releases
4.1. Release conditions
Processes of gaseous hydrogen release (spilled liquid hydrogen evaporation), hydrogen-air
mixture formation, explosion and further dispersion of hydrogen-air cloud in the atmosphere
(taking into account the movement of the air, gravity, presence of buildings, and
thermodynamic gas properties) are considered. Usually, the evaluation of safety measures of a
hydrogen fueling station is provided using physical modeling [30], and then quantitative risk
assessment can be done [31] to satisfy safety regulation documents [32].
Some possible scenarios at hydrogen dispensing station are modeled [29]. The station has
the large cryogenic hydrogen tank (5.7 m3) that feeds three 12-cylinder packages in total
amount 799.2 m3 in which gaseous hydrogen is stored at ambient temperature. The hydrogen
under pressure is dispensed to vehicles’ tanks. The station is separated from residential area by
three zones.
• The region in the immediate vicinity of the equipment to protect the personnel from
small leaks.
• An exclusion zone in the immediate area of the facility (23 m) to provide protection
against unplanned minor releases of hydrogen.
• An additional margin, as large as 53 m is necessary to protect against large potentially
catastrophic release of hydrogen.
The most dangerous scenarios from the potential catastrophe point of view have been
numerically simulated using the created mathematical model and developed computer system.
1. Spillage from the tank of all volume of liquid hydrogen, consecutive evaporation of cold
liquid, mixture of gaseous hydrogen with moving air and the further dispersion of a mix
towards residential area.
2. Release of all volume of the gaseous hydrogen compressed under a high pressure from
cylinders of distribution with formation of a cloud and its further dispersion in a stream of
air.
3. Explosion of a hydrogen-air cloud that is formed as a result of evaporation of spilled
liquid hydrogen or instant gaseous hydrogen release.
4.2. Spillage of liquid hydrogen
According to the scenario 1, numerical computations of an instant spillage of all volume of
liquid hydrogen from the cryogenic tank of dispensing station with formation of a spillage pond
with total area of 65.7 m2 were conducted. Liquid hydrogen evaporation productivity was
evaluated of 11.56 kg/sec [29]. The wind blew with speeds of 1, 3 and 10 m/sec, and its
direction was towards residential area. The calculation space has the following dimensions: the
length along OZ axis – 70 m, width (OX) – 22 m, and height (OY) – 20 m.
Hydrogen mass concentration distributions near the surface of the ground are presented on
Figure 6. With an increase in wind speed the rate of dispersion increased too (Figure 7).
According to comparison of hydrogen time-space concentration distributions at different wind
conditions in the case of spilled liquid hydrogen its buoyancy is insignificant because of low
vapor temperature and, as a consequence, small difference between densities of hydrogen and
air.
Figure 6: Numerical computations of spilled liquid hydrogen dispersion (wind speed 1 m/sec:
a – the plane XOZ near the ground; b – the plane YOZ view
Mass concentration fields are very important data for safety experts to carry out following
risk assessment. They can evaluate the total amount of hydrogen mass that potentially could
explode (mass concentration has to be between flammability limits). This parameter
characterizes the power of the explosion and the hazardous area where overpressure exceeds
acceptable safe levels.
Figure 7: The maximum hydrogen concentration distribution along the OZ–direction for
different wind speed conditions: a – evaporation from spill spot ; b – instant release of all the
hydrogen amount
4.3. Dispersion of gaseous hydrogen cloud
An instant release of all gaseous hydrogen from a package of dispensing high-pressure
cylinders with the formation of a cloud in volume 799.2 m 3 have been numerically simulated
according to the scenario 2. According to results of numerical experiments, buoyancy of
hydrogen is essential only at low wind speeds (Figure 8).
Figure 8: Hydrogen concentration distribution in 5 sec after release in planes XOZ and YOZ for
different wind speed conditions: a, d – 1 m/sec; b, e – 3 m/sec; c, f – 10 m/sec
It should be noted that the fields of mass concentration of flammable impurities significantly
depend not only on wind speed, but also on the presence of obstacles in the form of buildings in
the actual space, which distort the flow velocity fields, which will subsequently affect the
distribution of pressures in the zone of emergency release and explosion.
With an increase of wind speed the air flow prevents the cloud movement up pressing it to
the ground. Calculation results are similar to the results of the physical experiment [33]
provided in the photographs of the hydrogen cloud plume, which arises as a result of
evaporation from the liquid hydrogen spill spot under different wind conditions (Figure 9).
Figure 9: Liquid hydrogen evaporation from the spill spot surface (physical experiment [33])
for different wind speed: a – 1.6 m/sec; b – 3.8 m/sec; c – 6.3 m/sec
Obviously, if wind speed is greater then hydrogen buoyancy, hydrogen behaves as a neutral
gas. Both in the case of spilled hydrogen dispersion and dispersion of instantly released gaseous
hydrogen, the presence of construction facilities and residential buildings essentially affect flow
symmetry decreasing transfer and mixing processes in the space before the buildings and
accelerating these processes between constructions.
4.4. Explosion of hydrogen cloud
In computations on dispersion the dependence of hydrogen mass in the cloud between top
and bottom concentration limits of flammability was determined (Figure 10). The largest mass
of hydrogen and, consequently, maximal explosion energy will be under low wind speed
conditions. But, as evident from Figure 10, a, an explosive cloud with less hydrogen mass and
larger energy of explosion can be located closer to residential constructions.
Figure 10: The history of total mass of gasious hydrogen which mass concentration is within
flammability limits (the air-hydrogen mixture could explode) during the dispersion process for
different wind speed conditions : a – evaporation after spillage; b – after instant gas release
In case of instant release of compressed gaseous hydrogen, the cloud is compact enough
(Fig. 10, b) and it can be considered as spherical cloud. But, in case of presence of constant
source of assigned productivity (hydrogen spillage evaporation), the hydrogen mixture that
explodes according to the mathematical model occupies the space of complex shape (Figure 11)
in the calculated area. The air-gas mixture with mass concentration that is lower than bottom
flammability limit does not explode because of lack of fuel component. If mass concentration is
greater than top flammability limit, the mixture will not explode too because of lack of oxidant.
Figure 11: Mass concentration distribution of hydrogen within flammability boundaries in YOZ
plane (wind speed makes up 1 m/sec)
The numerical results of blast wave parameters for the wind speed option 1 m/sec at
detonation of the cloud generated after an instant gaseous hydrogen release are presented in
Figure 12. The mass of hydrogen in the cloud equals 63 kg at the moment of explosion.
Figure 12: Pressure distribution after hydrogen explosion: a – near the ground; b – in YOZ
plane
An increase of pressure takes place between residential constructions, as it would be
expected. Overpressure affecting the walls of buildings (on the right side of the Figure 12, a) is
about 28 kPa that allows suggesting the possibility of serious destructions of residential
buildings and industrial facilities threatening to health or even life of industrial object personnel
and residential area inhabitants.
5. Conclusions
The three-dimensional model of the release and explosion of gaseous admixtures in the
atmosphere has been developed. The validation of the numerical results shows acceptable
accuracy in comparison with known experimental data.
Numerical computations for dispersion of evaporated spilled liquid and instantly released
gaseous hydrogen and for explosion of the hydrogen-air cloud generated during dispersion
have been carried out.
Obtained results can be usually predicted at qualitative level but presented numerical
computations have allowed making quantitative forecasting with no contradictory physical
picture.
Numerical modelling of the harmful admixture dispersion in the atmosphere generated as a
result of air-fuel mixture distribution in three-dimensional space with the use of developed
computer information system is applicable to engineering calculations for different
technological systems, including ones which work on liquefied and gaseous hydrogen.
Presented mathematical model can be used in more complex information system as a
predictor of distribution of such a hazardous flow parameter as pressure during an accidental
gas explosions. Calculated pressure field is an origin of such hazardous factors values as
maximum overpressure and impulse of pressure phase at the front of the explosion wave which
moves away from an accident epicenter and influences harmfully on humans and buildings. This
information about the explosion wave can be used to evaluate distribution of damage
probability and to assess the risks of dangerous industrial objects by safety experts.
References
[1] W. G. Houf, W. S. Winters, Simulation of High-pressure Liquid Hydrogen Releases, Int. J.
Hydrog. Energy 38 (2013) 8092–8099. doi:10.1016/j.ijhydene.2013.01.052
[2] Y. Skob, M. Ugryumov, E. Granovskiy, Numerical Evaluation of Probability of Harmful
Impact Caused by Toxic Spill Emergencies, Environ. Clim. Technol. 23 (2019) 1–14.
doi:10.2478/rtuect-2019-0075
[3] Y. Skob, M. Ugryumov, E. Granovskiy, Numerical Evaluation of Wind Speed Influence on
Accident Toxic Spill Consequences Scales, Environ.Clim. Technol. 27(1) (2023) 450–463.
doi: 10.2478/rtuect-2023-0033
[4] Y. Skob, S. Yakovlev, K. Korobchynskyi, M. Kalinichenko, Numerical Assessment of Terrain
Relief Influence on Consequences for Humans Exposed to Gas Explosion Overpressure,
Computation 11(2) (2023) 19. doi:10.3390/computation11020019
[5] Y. Skob, M. Ugryumov, E. Granovskiy, Numerical assessment of hydrogen explosion
consequences in a mine tunnel, Int. J. Hydrog. Energy 46 (23) (2021) 12361–12371.
doi:10.1016/j.ijhydene.2020.09.067
[6] W. Houf, R. Schefer, Predicting radiative heat fluxes and flammability envelopes from
unintended releases of hydrogen, Int. J. Hydrog. Energy 32 (2007) 136–151.
doi:10.1016/j.ijhydene.2006.04.009
[7] G. Hankinson, B. J. Lowesmith, A consideration of methods of determining the radiative
characteristics of jet fires, Combust. Flame 159 (2012) 1165–1177.
doi:10.1016/j.combustflame.2011.09.004
[8] Y. Skob, M. Ugryumov, Y. Dreval, Numerical Modelling of Gas Explosion Overpressure
Mitigation Effects, Mater. Sci. Forum 1006 (2020) 117–122. doi:
10.4028/www.scientific.net/msf.1006.117
[9] Y. Skob, M. Ugryumov, Y. Dreval, S. Artemiev, Numerical Evaluation of Safety Wall Bending
Strength during Hydrogen Explosion, Mater. Sci. Forum 1038 (2021) 430–436.
doi:10.4028/www.scientific.net/msf.1038.430
[10] J. Lee, S. Lee, H. Son, W. Yi, Development of PUFF–Gaussian dispersion model for the
prediction of atmospheric distribution of particle concentration, Scientific Reports 11
(2021) 6456. doi:10.1038/s41598-021-86039-y
[11] B. Andersson, R. Andersson, L. Hakansson, M. Mortensen, R. Sudiyo, B.van Wachem,
Computational Fluid Dynamics for Engineers, New York, Cambridge University Press Publ.,
2012, 212. doi:10.1017/CBO9781139093590
[12] V. Molkov, V. Shentsov, S. Brennan, D. Makarov, Hydrogen non-premixed combustion in
enclosure with one vent and sustained release: Numerical experiments, Int. J. Hydrog.
Energy 39(20) (2014) 10788–10801. doi: 10.1016/j.ijhydene.2014.05.007
[13] S. Jayanti, Computational Fluid Dynamics for Engineers and Scientists, Springer Dordrecht,
2019, 402. doi:10.1007/978-94-024-1217-8
[14] R. W. MacCormack, Numerical Computation of Compressible and Viscous Flow, 2014.
doi:10.2514/4.102646
[15] P. Majumdar, Computational Fluid Dynamics and Heat Transfer, 2nd. ed., CRC Press, Boca
Raton, 2021. doi:10.1201/9780429183003
[16] S. Serovajsky, Mathematical Modelling, 1st ed., Chapman and Hall/CRC, New York, 2021.
doi:10.1201/9781003035602
[17] J. W. Murdock, Fundamental Fluid Mechanics for the Practicing Engineer, 1st ed., CRC Press,
Boca Raton, 1993. doi:10.1201/9781315274065
[18] R. Brun, Eight Elements of Gas Dynamics, in: R. Brun (Ed.), Introduction to Reactive Gas
Dynamics, Princeton University Press, Princeton, 2020, pp. 224–258.
doi:10.1093/acprof:oso/9780199552689.003.0010
[19] E. Kim, J. Park, J. H. Cho, I. Moon, Simulation of hydrogen leak and explosion for the safety
design of hydrogen fueling station in Korea, Int. J. Hydrog. Energy 38 (2013) 1737–1743.
doi:10.1016/j.ijhydene.2012.08.079
[20] B. Karlsson, J. G. Quintiere, Enclosure Fire Dynamics, 2nd. ed., CRC Press, Boca Raton, 2022.
doi:10.1201/b22214-9
[21] I. Yakovenko, A. Kiverin, Numerical Modeling of Hydrogen Combustion: Approaches and
Benchmarks, Fire 6(6) (2023) 239. doi:10.3390/fire6060239
[22] M. E. Berlyand (Ed.), Air pollution and atmospheric diffusion, John Wiley & Sons, Chichester,
1973.
[23] M. E. Berlyand (Ed.), Air pollution and atmospheric diffusion, Vol. 2, John Wiley, Chichester,
1974.
[24] E. F. Toro, Godunov Methods. Theory and Applications, Springer, New York, NY, 2001.
doi:10.1007/978-1-4615-0663-8
[25] G. S. Puttock, G. W. Colenbrander, D. R. Blackmore, Marlin Sands experiments 1980:
Dispersion results from continuous releases of refrigerated liquid propane, in: Heavy Gas
and Risk Assessment – II, Springer, Dordrecht, pp. 147–161. doi:10.1007/978-94-009-
7151-6_9
[26] S. M. Kogarko, V. V. Adushkin, A. G. Lyamin, Investigation of spherical detonation of gas
mixtures, Combust. Explos. Shock Waves 1 (1965) 15–22. doi:10.1007/bf00757224
[27] Q. Liu, Y. Zhang, S. Li, Study on the critical parameters of spherical detonation direct
initiation in hydrogen/oxygen mixtures, Int. J. Hydrog. Energy 40(46) (2015) 16597–16604
doi:10.1016/j.ijhydene.2015.09.053
[28] H. D. Ng, Y. Ju, J. H. S. Lee, Assessment of detonation hazards in high-pressure hydrogen
storage from chemical sensitivity analysis, Int. J. Hydrog. Energy 32(1) (2007) 93–99.
doi:10.1016/j.ijhydene.2006.03.012
[29] X. Zhang, G. Qiu, S. Wang, J. Wu, Y. Peng, Hydrogen Leakage Simulation and Risk Analysis of
Hydrogen Fueling Station in China, Sustainability 14(19) (2022) 12420.
doi:10.3390/su141912420
[30] J. Sakamoto, H. Misono, J. Nakayama, N. Kasai, T. Shibutani, A. Miyake, Evaluation of safety
measures of a hydrogen fueling station using physical modeling, Sustainability 10 (2018)
3846. doi:10.3390/su10113846
[31] H. R. Gye, S. K. Seo, Q. V. Bach, D. Ha, C. J. Lee, Quantitative risk assessment of an urban
hydrogen refueling station, Int. J. Hydrog. Energy 44 (2019) 1288–1298.
doi:10.1016/j.ijhydene.2018.11.035
[32] L. Zhiyong, P. Xiangmin, M. Jianxin, Quantitative risk assessment on a gaseous hydrogen
refueling station in Shanghai, Int. J. Hydrog. Energy. 35(13) (2010) 6822–6829.
doi:10.1016/j.ijhydene.2010.04.031
[33] R. D. Witcofski, J. E. Chirivella, Experimental and Analytical Analyses of the Mechanisms
Governing the Dispersion of Flammable Clouds Formed by Liquid Hydrogen Spills, Int. J.
Hydrog. Energy 9(5) (1984) 425–435. doi:10.1016/0360-3199(84)90064-8