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```COMPUTATIONAL MODELING
OF PRESSURE EFFECTS FROM
HYDROGEN EXPLOSIONS
Granovskiy E.A., Lifar V.A., Skob Yu.A.,
Ugryumov M.L.
Scientific Center of Risk Investigations
“Rizikon“, Ukraine
Mathematical model
Computational model of gas cloud explosion
Total system of the time-dependent equations
describing the three-dimensional multi-component
gas mixture flow
 



a b c d
    f
t x y z

T
a   , u, v, w, E



c  v, vu, P  v , vw,( E  P )v

d  w, wu, wv, P  w ,( E  P )w
T

2
b  u, P  u , uv, uw,( E  P )u
T
2
2

T
f  0,0,g ,0,gv
T
transfer
( Q ) ( uQ ) ( vQ ) ( wQ )



 Q
t
x
y
z
Gas mixture explosion model
 mass of combustible participating in burning:
m  QV , Qmin  Q  Qmax
 mass of combustible not participating in
burning:
m0  QV , Q  Qmax
 total mixture mass in the volume where the
burning process occurs:
m  V , Q  Qmin
 the oxidant mass in the mixture:
m  m  m  m0
 The mass concentrations of mixture components
m
Q 
m
m0
Q0 
m
m
Q   1  Q  Q0
m
 the excess air factor in the mixture:
1  Q  Q0
m


0 m
0 Q
where stoichiometric number:

mth
0 
m
 In the case when
 1
the thermophysical
properties of the gas mixture after an explosion :
1

1  0  1Q  Q0 0  1Q Q0



c
 
C p  1  0  1Q  Q0 Cp  0  1QC cp  Q0Cp
c







Cv  1  0  1Q  Q0 Cv  0  1Q Cv  Q0Cv
k
Cp
Cv
 In the case when
 1
the thermophysical
properties of the gas mixture after an explosion :
0

1  0 Q  0  1  0 Q
c
 
c


C p  1  Qc C p  QcC p
c


Cv  1  Qc Cv  QcCv
k
Cp
Cv
 pressure, temperature and density of gas mixture
 k  1
H u mth
H u 1  Q  Q0 mk  1
P
 Pa 
 Pa
V
0 QV
PV
T
mRун
m

V
mathematical model verification
(experiments at Fraunhofer ICT)
Pressure distribution in the plane XOZ near the ground (t=0.33 s)
Pressure distribution in the plane XOZ near the
ground (t=0. 44 s)
Pressure history in the point B near the ground
Pressure history in the point C near the ground
Overpressure distribution in front of the shock wave
(explosion of stoichiometric propane-air mixture)
1 –computational results, 2 – regressive dependence, 3 – experimental data
Computation of hydrogen cloud explosion
 Hydrogen cloud explosion nearby residential area
The distribution of the hydrogen volume concentration
before a moment of explosion
Pressure distribution in the planes:
XOZ near the ground (a), YOZ (b)
Pressure history in the points: B (a) and C (b) explosion
 Distant hydrogen cloud explosion
pressure distribution
Pressure history in the points: B (a) and C (b) explosion
 Distant banked explosion of hydrogen cloud
hydrogen volume concentration distribution before a
moment of the banked distant explosion
Pressure distribution
 Distant partly banked explosion of hydrogen cloud
hydrogen volume concentration distribution before a
moment of the partly banked distant explosion
Pressure distribution
 Distant explosion partly surrounded with higher
banks
hydrogen volume concentration distribution before a
moment explosion
pressure distribution in the planes:
XOZ near the ground (a), YOZ (b)
 Distant hydrogen explosion with the use of bumper
walls
Pressure distribution in planes: XOZ near the ground (a), YOZ (b)
Pressure history in a point C
CONCLUSIONS
 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 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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