A. Beccantini, A. Malczynski and E. Studer- Comparison of TNT-Equivalence Approach, TNO Multi-Energy...

8/3/2019 A. Beccantini, A. Malczynski and E. Studer- Comparison of TNT-Equivalence Approach, TNO Multi-Energy Approach a

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COMPARISON OF TNT-EQUIVALENCE APPROACH, TNO

MULTI-ENERGY APPROACH AND A CFD APPROACH IN

INVESTIGATING HEMISPHERIC HYDROGEN-AIR VAPOR

CLOUD EXPLOSIONS.

A. Beccantini1, A. Malczynski1,2 and E. Studer1

1CEA Saclay, DEN/DM2S/SFME/LTMF1,2

Warsaw University of Technology

ABSTRACT

In this work, we investigate the pressure wave generated by a so-called vapor cloud explosion (VCE),

in the particular case in which the hydrogen-air mixture is homogeneous, presents a hemispheric

geometry and the ignition occurs at the center of the hemisphere. Then we compare the resultsobtained on this particular geometry using three different approaches, namely TNT-equivalence

approach, TNO multi-energy approach and ``1D point-symmetric deflagration'' approach, which

solves the Fluid Dynamics equations (Computational Fluid Dynamics or CFD approach) in the case of

1D point-symmetric flows. These three approaches have been compared on a large-scale experiment

performed at Fraunhofer Institute of Chemical Technology. As we will show, the TNT-equivalence

method have shown not to be a good candidate to investigate VCE. The CFD approach gives a

pressure field which fits the experimental one, providing that the flame speed is correctly evaluated.

Concerning the multi-energy approach, it is possible to establish a relation between its strength index

and the fundamental flame speed, a part from a region close to the one containing the burnt gas.

INTRODUCTION

The introduction and commercialization of hydrogen as an energy carrier of the future makes

great demands on all aspects of safety [1]. For instance, the use of automobiles which use hydrogen

as its primary source of power for locomotion implies the existence of gas refueling stations having

hydrogen dispensing pumps. In the case of accidental hydrogen release and explosion, one of the most

important issue is the safety of the working personnel and of the general public living around. In

Nuclear Industry, as presented in [2], the possibility of using the high temperature gas of Nuclear Gas

Cooled Reactors to massively produce hydrogen is under evaluation (see an example of layout of a

combined plant in [3]). In this case, one of the most important issue is to guarantee the integrity of the

nuclear power plant under the accidental case of hydrogen explosion in the coupled chemical plant as

well as the safety of the working personnel and of the general public living around.

There are several method to investigate the pressure wave generated by so-called vapor cloudexplosions (VCE) [4]. In this work, we restrict our attention to the case in which the hydrogen-air

mixture is homogeneous, presents a hemispheric geometry and the ignition occurs at the center of the

hemisphere. Then we compare the results obtained on this particular geometry using three different

approaches, namely TNT-equivalence approach, TNO multi-energy approach and ``1D point-

symmetric deflagration'' approach, which solves the Fluid Dynamics equations (Computational Fluid

Dynamics or CFD approach) in the case of 1D point-symmetric flows.

All of them present one parameter which must be specified by the ``user'' (and, as we will see,

blast parameters result to be very sensitive to). In the TNT-equivalence method, a parameter between

1 and 0 must be fixed, the so-called efficiency factor, which artificially decreases the energy released

by the explosion of the TNT-equivalent mass, thus pretending to take into account the real mass which

burns and the combustion regime. The TNO multi-energy method involves the so-called strength

index, arising from 1 (weak deflagration) to 10 (strong detonation); there exist tables which help in thechoice of such parameter. In the CFD approach here considered, the fundamental flame speed must be

Proceedings of the 5th International Seminar on Fire and Explosion Hazards, Edinburgh, UK, 23-27 April 2007

159 www.see.ed.ac.uk/feh5


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specified. In the literature, there exist correlations which specify the flame speed as function of the

mixture composition and of the obstacles array (if present) [13].

This paper is divided into several part. First, we describe the three approaches. Then we analyze

the problem of the hemispherical vapor cloud explosions in the case of constant speed deflagration. In

particular, we present the governing equations of the problem (and the hypothesis they are based on),

perform the dimensional analysis, show the problem solution. Afterward, we perform a parametric

study of the different approaches on this problem, namely we investigate how the efficiency for the

TNT approach, the strength index for the TNO multi energy approach and the fundamental flame

speed for the CFD approach affect the maximum overpressure and the positive impulse. As we will

show, if we are interested in evaluating the maximum overpressure and the positive impulse, as certain

blast criteria require, in the particular case of hemispherical vapor cloud explosion there exists a

relation between the fundamental speed and the strength index of the TNO multi-energy method

(although there is a little difference between these two approaches in the combustion region).

Conversely, no relation between the parameter involved in the TNT-equivalence method and the CFD

approach can be established. This is due to the difference of mode of combustion energy released in

the TNT (the energy is immediately released in a small region) and the vapor cloud (the energy is

distributed on a large domain in a finite time). Finally, the CFD results are compared with some

experimental results provided on a large-scale experiment performed at Fraunhofer Institute ofChemical Technology and which has been the object of a code benchmark for the participants of the

Hysafe project [5]. In this experiment, a 10 meter radius polyethylene hemispheric balloon has been

filled with a stoichiometric and homogeneous mixture of hydrogen-air. The mixture has been ignited

at the center. Experimental results show that the combustion of the mixture occurs at almost constant

speed of about 63 m/s and gives a maximum overpressure of 50 millibar. As we show, the CFD

approach gives a pressure field which fits the experimental one, providing that the flame speed is

taken equal to the one given by experimental results. Conclusion follows.

1. DESCRIPTION OF THE APPROACHES

In this section we briefly present the TNT-equivalence method, the TNO multi-energy method

and the ``1D point-symmetrical deflagration'' approach to evaluate the overpressure caused by thecombustion of a ``hemispherical vapor cloud'' on the ground.

1.1 TNT-equivalence approach

The TNT-equivalence method has been widely used to express the explosive load of vapor

clouds using an equivalent weight of a TNT-charge.

In order to estimate the maximum overpressure and the positive impulse at a specified distance,

the chemical energy available in a vapor cloud is converted into an equivalent weight of TNT using

the formula

,Q

Qm=W

TNT

2H

2H

TNT

Where TNTW is the equivalent mass of TNT, is an efficiency factor, 2Hm is the total mass of

hydrogen in the gas cloud,2

HQ the heat of combustion of hydrogen (123 MJ/kg), and TNTQ is the

heat of combustion of the TNT (approximately 4.184 MJ/kg). Once computed TNTW , there exist

diagrams, obtained via TNT explosions, which give the non-dimensional maximum overpressure and

the positive impulse as function of the Sachs scaled distance ( )( )3/10TNT // PWr :




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( )

( ) ( )

3/1

0TNT

3/1

0TNT0

0

3/1

0TNT0

max

//

/

PWrf=

PWPcI

PW

rf=

P

P

+

(1)

Here r(m in the SI system) is the distance from the center of symmetry, 0P (Pa) is the atmospheric

pressure, ( ) 3/10TNT / PW ((kg/Pa)3/1

) is the Sachs scale distance (or the energy scaled distance), 0c

(m/s) is the speed of sound in the undisturbed air; the maximum overpressure and the positive impulse

are defined by

( ) ( )( )

( ) ( )( )( ) t,Ptr,P=rI

Ptr,P=rP

+

t

d0max

max

0

0max

The efficiency factor pretends to take into account the fact that in the cloud the combustion occursat deflagration regime, by simply postulating that the effects of a VCE in which a deflagration occurs

is equal to the ones of a TNT explosion with a released energy reduced of a factor . Note from (1)that, by varying , the graphic maximum overpressure maxP versus radius r is scaled of a factor

inversely proportional to3/1 on the r-axis; the graphic positive impulse +I versus radius r is

scaled of a factor inversely proportional to3/1 on the r-axis and of a factor proportional to 3/1 on

the+I axis.

1.2 TNO multi-energy method

This model is based on the assumption that a blast is generated in a vapor cloud explosion only

where the flammable mixture is partially confined and/or obstructed while, on the other hand, a

unconfined/unobstructed mixture does not generate a blast. The total domain occupied by the vapor

cloud is divided into several sub-domains. In each sub-domain, the mixture is concentrated in a

hemisphere and treated as homogeneous and stoichiometric. There exists abacuses which give the non-

dimensional maximum overpressure and the positive impulse as function of the Sachs scaled distance

and of a strength index arising from 1 (weak deflagration) to 10 (strong detonation). These abacuses

have been obtained by using the semi-analytical solution of the 1D point-symmetrical flame in a

homogeneous medium and numerically studying its time-evolution as the combustion stops. There

exist rules for the choice of the index (see for instance [7]). There exist also rules for summing non-

dimensional maximum overpressures and positive impulses. Nevertheless the choice of the index as

well as of the domain decomposition is quite user-dependent.

1.3. 1D point-symmetrical deflagration approach

In this approach we suppose to deal with a mixture of thermally-perfect gases. We neglect

viscosity effects. We suppose that the chemical combustion is governed by the one step irreversible

chemical reaction

.+ OHO

2

1H 222

We also suppose that the mixture occupies a hemisphere close to the (rigid) ground, the solution is 1D




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point-symmetrical, the flame is infinitely thin and the fundamental flame speed (the flame speed with

respect to the unburnt gas close to the flame surface) is equal to 0K . The problem we solve will be

presented in section 2. Let us briefly describe the numerical method we use (see [8] and [9] for

details). In an operator splitting strategy, we first solve the non-reactive Euler equations; then we

update the energy and the densities of the species by taking into account the chemical reaction.

Concerning the non-reactive part, we solve the Euler equations in conservative form via anexplicit algorithm in time. We suppose that we are dealing with a mixture of ideal gases. The variation

of specific heats with respect to temperature is taken into account. We compute the average of the

conservative variables (namely densities, momentum and total energy (sensible plus kinetic energy)

per unit volume) via a cell-centered Finite Volume approach. Far from shocks and discontinuities,

second order space accuracy is obtained via the linearly-exact reconstruction on primitive variables

(namely total density, speed, pressure, species mass fractions) of [10]. At each interface we compute

the flux vector using the shock-shock Flux Difference Splitting [9].

Concerning the reactive part, we update the total energy and the density of the species by

observing that the quantity of unburnt gas which crosses the flame at each time is given by

,SK=t

mffu, 0

d

d (2)

where fu, is the density of unburnt gas ahead of the flame and22 ff r=S is the surface of the

hemisphere at the flame position r. As one can read in [13], the apparent speed of a spherical flamedepends on the burning velocity and the ratio between the real surface of the flame and the surface of

the sphere at the flame position. If the flame were perfectly spherical, this ratio would be equal to one;

nevertheless, because of instability effects, the flame surface is crisped; then this ratio is larger than

one. In the CFD approach here presented, the fundamental flame speed 0K incorporates this ratio,

namely its value is equal to the (apparent) flame speed flamD divided by the expansion ratio (ratiobetween densities of unburnt and burnt gases).

2. HEMISPHERIC VCE

We have a hemisphere (radius hemr ) with a stoichiometric mixture of hydrogen-air inside and

air outside, everything at constant pressure and temperature ( 0P and 0T ). We suppose that the flame

is initiated in the center and the flow keeps 1D point-symmetrical and occurs at the fundamental flame

velocity 0K . We also suppose to deal with a mixture of thermally-perfect gases, that viscous effects

are negligible and that the chemical combustion is governed by a one step irreversible chemical

reaction.

2.1 Dimensional analysis

The governing equations (Euler Equation in 1D spherical geometry) can be written as

( )

( )

( )

=

+

=

++

+

+

=+

+

=

+

jj

j

j jj

urYrrt

Y

huP

eurrr

ue

t

r

PPrru

rrt

u

urrrt

&

&

2

2

02

2

2

2

222

2

2

2

1

2

1

2

21

01

(3)




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where the pressurePand the internal energy e are linked via the Equation of States (EOS)

( ){ }

T

jv,j

j

j

j

jj

j

cY=e

TRY=TM

RY=P

0

*

d

Here r(m in the SI system) is the distance from the center of symmetry, (kg/m 3 ) the density, u(m/s) the speed, e (J/kg) the sensible internal energy, T(K) the gas temperature, jM (kg/mole) the

molar weight for thej-th gas involved in the mixture,0

jh (J/kg) its formation enthalpy at 0 K, jY its

mass fraction, j& (s1

) its reaction rate, ( )Tc jv, (J/(Kg K)) its constant volume specific heat, jR

(J/(Kg K)) its gas constant and*

R the universal gas constant (8.314 J/(mole K)). Actually, because ofthe hypothesis of irreversible chemical reaction and infinitely thin flame (i.e. infinitely fast reaction),

the evolution of the densitiesj

Y during the combustion phase is evaluated using (2) instead of thereaction rates.

Concerning the initial conditions, we have a stoichiometric mixture of hydrogen and air inside the

hemisphere and air outside; everything is at ambient conditions (pressure and temperature 0P and

0T ). Actually, because of the hypotheses previously presented, we can treat the problem as if we were

dealing with three gases only: the air (air), the unburnt mixture (u) and the burnt mixture (b). Then, at

the beginning we have an hemisphere filled with the unburnt mixture and air outside.

The solution of the problem can be expressed as follows:

( )00vvvair0,0,hem0, bub,u,air,bu hh,c,c,c,R,R,RTP,rKt,r,=U ,U being the vector of the conservative variables (densities, momentum and total (sensible plus

kinetic) energy per unit volume), i.e. it depends on 13 parameters1

including the independent variablesr and t. Since there are 4 independent dimensions involved (mass, length, temperature and time),

according to the Buckingam -theorem, the non-dimensional solution depends on 13-4=9 parameters.If we chose as dimensionally-independent reference quantities 0P , 0T , hemr and airR , the non-

dimensional conservative variables can be expressed as

=

=

0air

00

air

v

air

v

air

v

airair0air

0

0air

00

air

v

air

v

air

v

airairair

air

0

0

0

0

hem

hem

0air

0

hem

0air

hem

~~~

~~

TR

hh,

R

c,

R

c,

R

c,

R

R,

R

R,

TR

K,t,rU

TR

hh,

R

c,

R

c,

R

c,

R

R,

R

R,

R

R,

T

T,

P

P,

r

r,

TR

K,

r

TRt,

r

rUU

bub,u,air,bu

bub,u,air,bu

They are solutions of the Euler equations (3) subjected to the EOS

( )

=

=

T

j

jv,

j

j

j

j

R

TcY=e

TR

RY=P

~

0 airb,u, air

0

airairb,u,

d~

~~~

1 Strictly speaking, specific heats are not parameters but function ofT. Then, if these functionsare approximated using 4-th order temperature polynomials, each specific heat involves 5 parameters.




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As one can see, with this particular choice of the dimensionally-independent variables, the values of

the initial pressure and of the radius of the hemisphere do not affect the non-dimensional solution. The

initial value of temperature is involved in the non-dimensional numbers ,TRK 0air0 /

( ) 0air00 / TRhh bu . The first non-dimensional number represents the ratio between the fundamentalflame speed and the unperturbed sound speed in the air (divided by the square root of the air specific

heat ratio air ). The second one is representative of the ratio between the energy released in the

combustion per mass unit and initial sensible energy in the air (divided by a factor close to ( )1air ).If the gas is thermally perfect but non-calorically perfect (as it is in this case), the initial value of the

temperature also affects the non-dimensional specific heats, which are temperature functions. It

follows that, if we change the value of 0T and we keep constant the other independent variables and

parameters, the non-dimensional solution is affected. Conversely, if the mixture involved calorically

perfect gases, the initial value of the temperature would not affect the non-dimensional solution.

2.1 Solution of the problem

Let us restrict our attention to a problem the conditions of which are similar to the large-scale

experiment performed at Fraunhofer Institute of Chemical Technology. As already mentioned in the

previous section, the values of the initial pressure and of the radius of the hemisphere do not affect the

non-dimensional solution, while the initial temperature does. We have a 10 m radius hemisphere with

a stoichiometric mixture of hydrogen-air inside and air outside, everything at almost atmospheric

conditions ( 0P and 0T equal to 0.989 bar and 283 K). This corresponds to 522H=m kg of hydrogen

which, if completely burns, releases .=Q MJ106.293

In this section we present the solution of the problem under the hypothesis of constant

fundamental speed 0K equal to 22.6 m/s (nevertheless, from a qualitative point of view, we have

similar results if we take a different value). The solution is obtained using the numerical approach

previously described. We can distinguish between 3 different phases. In the first one, the flow consists

of a precursor shock, followed by an isentropic compression and by the flame surface. In this phase,

neither the shock wave nor the flame has reached the surface separating the combustible mixture with

the outside gas. In the second phase, the shock wave has reached the separating surface but the flame

has not. In the third phase, the flame has reached the separating surface and there is no more

combustion.

Before the precursor shock reaches the surface of the balloon (first phase), the solution is self-

similar (and it coincides with the propagation of a constant speed flame in an homogeneous medium

[11, 12]). The evolution of the pressure with respect to variable r/tis qualitatively shown in Figure 1.Here 0 is the undisturbed state ahead of the shock wave. The surface between 0 and 1 is a shock wave,

moving with speed 0sh c>D , 0c being the sound speed in the unperturbed medium. This surfaceseparates the perturbed and the unperturbed flow. 1 is the state behind the shock wave. The region

between 1 and 2 is an isentropic compression, in which pressure, density and speed of sound increase

as we approach the flame surface. In this region, the flow velocity u increases to the value

0flam KD just ahead of flame surface, flamD being the speed of the flame with respect to the

unperturbed state (as already mentioned 0flam K=D , where is the expansion ratio); moreover theflow is identical to the one generated by a spherical expanding piston the (constant) speed of which is

smaller than flamD and larger than 0flam KD=u . 2 is the state ahead of combustion. The dotted

line represents the infinitely thin flame, which separates the unburnt and the burnt mixture. 3 is the

state behind the flame (flow at rest). Note that the pressure is maximum just ahead of the flame and

slightly decreases once the flow crosses the flame. In Figure 2 we show the computed pressure asfunction of the distance, before the shock wave reaches the balloon surface. The precursor shock speed




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is about 400 m/s, i.e. almost equal to the speed of sound in the hydrogen-air mixture, accordingly to

the fact that in this case the shock strength is small (note that the larger the fundamental flame speed,

the stronger the shock). The flame speed flamD is about 160 m/s (i.e. the ratio between the flame speed

and the speed of sound in the unperturbed mixture of hydrogen and air is 4.0/ cloud,0flam cD ).

In Figures 3 and 4 we showPversus randPversus r/tafter the compression wave has reachedthe interface (phase 2). As one can see, because of this interaction, the pressure increases even in the

unburnt region. This is due to that fact that the compression wave enters into a gas with different

properties, i.e. air with density larger than the one of the hydrogen-air mixture. Since the compression

wave can be considered as an ensemble of shock waves of infinitesimal strength, the reason can be

easily understood by considering the problem of the interaction of a right-traveling (i.e. toward

increasing values forr) shock wave with a contact discontinuity (see Figure 5).Once a shock wavereaches a contact discontinuity, we have the formation of a new discontinuity with a left state equal to

the left state of the shock and a right state equal to the right state of the contact discontinuity. This

state differs from the right state of the shock only for the densities. The discontinuity thus formed

constitutes a so-called Riemann problem, i.e. in the pressure-velocity plane, we have to look for the

intersection of the rarefaction and shock curves2. As one can see in [8], given the state R, the slope of

the left shock curve in the pressure velocity plane in R is

( ) ( ) .P=c=u

PRR

R

d

d

It follows that, if the specific ratio is the same (as it is in our case), we can distinguish between two

cases: if the density on the right of the contact discontinuity (R' in Figure 5) is larger than the density

on the right of the shock (R in Figure 5), as it is in our case, then the solution of this Riemann problem

involves a left and a right-traveling shock, with a pressure larger than the one of the original shock; if

the density on the right of the discontinuity is smaller than the density on the right of the original

shock, then the solution involves a left-traveling rarefaction and a right-traveling shock, with a

pressure smaller than the one of the original shock. In both cases the discontinuity starts moving from

the left to the right. In our case, the pressure increases. Note also that the shock wave is slower than in

the first phase (340 m/s in phase 2 versus 400 m/s in phase 1) and this is due to the fact that the soundspeed in air is smaller than the sound speed in the stoichiometric mixture of hydrogen and air.

Phase 3 (t> 0.1 s) starts once the flame surface reaches the surface between the mixture and theair, i.e. once the combustion stops and there is no more chemical energy provided to the fluid. Once

again, when the flame reaches the interface between the stoichiometric mixture and the air, we have

the formation of a discontinuity. On the left we have zero velocity, while on the right we have a right-

moving flow. The pressure is almost constant at the interface. This structure generates two rarefaction

waves, one moving left and one moving right. The latter is faster than the precursor shock, therefore it

weakens the pressure in the flow head. The former moves toward the center of symmetry and then it

weakens the pressure in this region; then it is reflected and starts moving in the opposite direction. At

the end, in each point, the pressure reaches the atmospheric value (see Figure 6).

2.2 Characteristic scales.

Let us now present some characteristic scales for this problem. First of all, let us present the

value of some quantities (density, pressure, temperature and sound speed, in SI units) inside the

hemisphere before the combustion occurs and after and Adiabatic Isobaric Complete Combustion

(AIbCC).

( )3m/kg P(bar) T (K) c (m/s)

Inside 0.878 0.989 283 405

2 Given one state, we define left (right) shock curve the set of the states which can be connected to this stateby a left (right) shock. In the same manner, we define the rarefaction curve.




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( )3m/kg P(bar) T (K) c (m/s)AIbCC 0.116 0.989 2510 1030

Let us present some characteristic scales for the velocity (m/s).Fundamental flame speed 0K 8.5

3

Flame speed in the laboratory 0flam K=D 634

Sound speed in the unburnt gas cloud0,c 405

Sound speed in the burnt gas 1030

Sound speed in unperturbed air outc 338

Let us present some characteristic scales for the distance (m).

(Sachs) Energy based length ( ) 3/10/2Q P 50.3

Initial hemisphere radius hemr 10.0

Final hemisphere radius3/1

hemhem r='r 19.6

Acoustic distance flamouthemac /Dc'rr 1055

As characteristic scale for time, we have the time at which the combustion stops (s).

flamhem /D'r 0.316

The sound speed represents the speed at which the perturbations (as well as weak shocks) travel in a

medium. The energy based scale represents the dimension of a box at which the released energy

generates an overpressure of the same order as the initial pressure. The acoustic distance represents

the distance lasted by a weak shock once the combustion stops. We also emphasize that in the case of

8.50 =K m/s (Fraunhofer experiment), once the combustion stops, 30% of the released energy has

contributed to increase the internal energy inside the combustion region; the rest of the released energy

has contributed to increase the total energy outside the hemisphere. We emphasize that the larger the

flame speed, the larger the overpressure in the burnt region, the larger the density in the burnt region,

the smaller the final radius of the vapor containing the burn mixture, the larger the quantity of releasedenergy which contributes to increase the energy inside the combustion region. In the particular case of

spherical detonation, once the combustion stops, the dimension of the hemisphere has not changed and

outside of the sphere the flow is completely undisturbed.

3. PARAMETRIC STUDY OF THE DIFFERENT APPROACHES

The average of the flame speed measured in the experiment performed at Fraunhofer Institute

3 Fundamental flame speed corresponding to the average flame speed in the Fraunhofer experiment.

4 Value of the average flame speed in the Fraunhofer experiment.

5 Distance last by the acoustic wave once the reaction stops, corresponding to the average flame speed in theFraunhofer experiment.

6 Duration of the combustion , corresponding to the average flame speed in the Fraunhofer experiment.




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of Chemical Technology is 630flam =K=D m/s, which gives a fundamental flame speed 8.50 K m/s. Here we compute the propagation of the pressure waves due to a vapor cloud explosion, by

taking our initial conditions and different fundamental flame speeds ( 0K from 5.65 to 43.2 m/s,

which corresponds to flamD from 40 to 320 m/s, i.e. cloud0,flam / cD from 0.1 to 0.8). For the TNT

equivalence method we take the efficiency factor equal to 10, 50 and 100%. Generally, 10% is thevalue recommended for the case of a deflagration [4]. In the TNO multi-energy model, we take the

initial blast strength equal from 1 for insignificant deflagration to 7 for strong deflagration. Strict

application of the multi-energy method would lead to the choice of 1 since the cloud is completely

unconfined and there are no obstacles in the patch of the flame [7]. As presented in [13], there exist

blast damage criteria which involve maximum overpressure and positive impulse. For this reason, we

compare the different approaches on these two quantities.

In Figure 7 we compare the results obtained using the TNT-equivalent approach and the CFD

approach on the maximum pressure and the positive impulse as function of the distance from the

center. As one can see in [6, 11], the pressure field generated by a TNT-explosion (or by a point

explosion) is not the same as the one originated by a vapor cloud explosion in deflagration regime. In

the former case, the energy is immediately released in a small volume, while in the latter, as we havealready mentioned, the combustion energy is released in a volume the dimension of which depends on

the flame speed. In the case of TNT explosion, each point sees an incoming shock followed by a

rarefaction wave, while in the latter case a compression wave is followed by the rarefaction wave. The

decaying of the overpressure is not the same and it is more pronounced in the case of the TNT

explosion. In Figure 7 we see that, although equal to 10% also reduces the slope of theoverpressure as function of the distance (with respect to the one with efficiency factor equal to 100%),

there is a severe intersection between this curve and the one corresponding to a fundamental speed

equal to 22.6 m/s at r=80 m. This implies that, in a deflagration with fundamental speed equal to 22.6m/s, the overpressure is less important than in a TNT explosion involving 10% of the released

combustion energy before the intersection point, but more important after this intersection point.

Moreover, if we check the behavior of the positive impulse versus distance in Figure 7, we see that the

one given by the TNT approach with the equivalent factor equal to 10% is much smaller than the onegiven by the deflagration with fundamental speed equal to 22.6 m/s. Indeed, although maximum

overpressure in both cases are quite close, the decaying of a blast generated by a TNT wave is more

important, which explains this behavior. Then, even if we artificially reduce the released energy by

introducing an efficiency parameter, it is not possible to establish a relation with this parameter and

the flame speed. In our opinion, these differences make the TNT approach a bad candidate for

analyzing VCE explosions.

In Figure 8 we compare the results obtained using the TNO multi-energy approach and the CFD

approach on the maximum pressure as function of the distance from the center. As already mentioned,

abacuses in the TNO multi-energy method have been obtained by considering constant velocity 1D

point-symmetric deflagration of hemispherical vapor clouds. As one can see in Figure 8, once a

strength index is given, the TNO multi-energy approach predicts a constant (in-space) maximum

overpressure in the region occupied by the burnt gases at the end of the combustion. This is in

contradiction with the fact that there is an interaction between the separation discontinuity and the

compression wave ahead of the flame; this interaction increases the value of the maximum

overpressure in the region close to the surface which separates the burnt gases and the air.

Nevertheless, far from the combustion region, (r > 30 m), a correlation between the blast strength and

the fundamental speed can be established. TNO strength index 2 corresponds to 60 K m/s; strength

index 3 corresponds to 90 K m/s; strength index 4 corresponds to 150 K m/s; strength index 5

corresponds to 200 K m/s; strength index 6 corresponds to 300 K m/s; finally, strength index 7

corresponds to 400 K m/s. Results on positive impulses are in accord with the considerations done

for maximum overpressure curves.




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4. EXPERIMENTAL RESULTS VERSUS CFD RESULTS.

Finally, let us compare the computational results and the ones of the large-scale experiment

performed at Fraunhofer Institute of Chemical Technology. As already mentioned, in this experiment,

a 10 meter radius polyethylene hemispheric balloon is filled with a stoichiometric and homogeneous

mixture of hydrogen-air. The mixture is ignited at the center, by ignition pills of 150 J. When the

flame reaches the half of the radius, the balloon bursts at the seams bordering the ground and along

longitudinal welds. Experiments give the position of the flame as a function of time, 0< t


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speed is given (see [13] in which analytical formulas are given or [16] in which blast curves are

given). Nevertheless, 1D CFD approach can be also used for investigating flows generated by flame

acceleration. Validation of this tool for such purpose will be the object of another work.

REFERENCES

[1] Safety of Hydrogen as an Energy Carrier. In http://www.hysafe.org. 2006

[2] Y. Inaba and T. Nishihara and M.A. Groethe and Y. Nitta. Study on explosion characteristics of

natural gas and methane in semi-open space for the HTTR hydrogen production system.

Nuclear Engineering and Design, vol. 232. 2004.

[3] T. Takizuka. Reactor technology development under the HTTR project. Progress in Nuclear

Energy, vol. 47. 2005

[4] Y. Mouilleau and J.F. Lechaudel. Guide des mthodes d'valuation des effects d'une explosion

de gaz l'air libre. INERIS Technical Report. (Available and downloadable from the INERIS

web sitehttp://www.ineris.fr/).1999[5] E. Gallego, J. Garcia, E. Migoya, A. Crespo, A. Kotchourko, J. Yanez, A. Beccantini, O.R.

Hansen, D. Baraldi, S. Hoiset, M.M. Voort, and V. Molkov. An intercomparison exercise on the

capabilities of CFD models to predict deflagration of a large-scale H2-air mixture in openatmosphere. International Conference on Hydrogen Safety. Pisa, September 8-10. 2005

[6] W.E. Baker. Explosions in air. Wilfred Baker Engineering. 1983

[7] M.W. Roberts and W.K. Crowley. Evaluation of flammability hazards in non-nuclear safety

analysis. 14-th EFCOG Safety Analysis Workshop. San Francisco, CA. (Available and

downloadable from http://www.llnl.gov/es_and_h/sawg2004/pdf/34_roberts.pdf). 2004[8] A. Beccantini. Solveurs de Riemann pour des mlanges des gaz parfaits avec capacits

caloriphiques dpendant de la temprature. PhD Thesis/CEA Report CEA-R-5973. 2001.

[9] A. Beccantini. Colella-Glaz splitting scheme for thermally perfect gas. In Godunov methods:

theory and application (E.F. Toro, ed.), Kluwer/Plenum Academic Press, 2001.

[10] T.J. Barth, D.C. Jespersen. The design and application of upwind schemes on unstructured

meshes. AIAA 89-0366. 1989

[11] L.I. Sedov. Similarity and dimensional methods in Mechanics. Academic Press. 1959[12] A.L. Kuhl, M.M. Kamel and A.K. Oppenheim. Pressure waves generated by steady flames.

Fourteenth (international) symposium on Combustion, The Combustion Institute. 1973

[13] S.B. Dorofeev. Evaluation of safety distances related to unconfined hydrogen explosions.

International Conference on Hydrogen Safety. Pisa, September 8-10. 2005

[14] M. Kustnetzov, J Grune. Planned HyTunnel experiments at FZK. Proc of 3rd

IEF Workshop on

velocity measurements in gases and flames, April 5-6 2006, HSL, Buxton, UK, 2006

[15] Y.A. Gostintsev, A.G. Istratov, Y.V. Shulenin. Self-similar propagation of a free turbulent

flame in mixed gas mixture. Fizika Gorenika i Vzryva. Vol. 24. 1988

[16] M.J. Tang, Q.A. Baker. A New Set of Blast Curves from Vapor Cloud Explosion. Process

Safety Progress (Vol 18). 1999




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FIGURES

Figure 1. Solution of the problem. Steady 1D point-symmetrical flame in a homogeneousmedium.

Figure 2. Solution of the problem. Phase 1. Computed pressure Pversus distance r.




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Figure 3.. Solution of the problem. Phase 1. Computed pressure Pversus the characteristicvariable r/t. As one can see, the solution is self-similar.

Figure 4. Solution of the problem. Phase 2. Computed pressure Pversus distance r.




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Figure 5. Solution of the problem. Shock contact discontinuity interaction. (P,u) diagram inthe phase space on the left, pressure versus distance on the right. On the top, the situationbefore the right traveling shock reaches the contact discontinuity. L and R are the left andright states of the shock. R and R' are the left and right states of the contact discontinuity (R'and R differs only for the densities). Once the shock reaches the contact discontinuity(pictures on the medium and on the bottom), we have the formation of a new discontinuity(new Riemann problem to deal with). In the (P,u) diagram, R and R' coincide. In the picture

on the medium, RR > ' and the slope of the shock curve for R' is larger than slope the ofthe shock curve for R (dot line). Two shocks and one contact discontinuity connect L and R'.

In the pictures on the bottom RR


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Figure 7. Parametric study of the different approaches. CFD approach versus TNT-equivalent approach. Maximum overpressure and positive impulse versus distance.




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Figure 8. Parametric study of the different approaches. CFD approach versus TNO-approach. Maximum overpressure and positive impulse versus distance.




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Figure 9. Experimental results versus CFD results. Pressure versus time in r=5 m.





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A. Beccantini, A. Malczynski and E. Studer- Comparison of TNT-Equivalence Approach, TNO Multi-Energy...

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