# Analysis of TROI-13 Steam Explosion Experiment

Authors: Mitja Uršič; Matjaž Leskovar
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

The prediction of steam explosion inducing loads in nuclear power plants must be based on results of experimental research programmes and on simulations using validated fuel-coolant interaction codes. In this work, the TROI-13 steam explosion experiment was analysed with the fuel-coolant interaction MC3D computer code. The TROI-13 experiment is one of several experiments performed in the TROI research program and resulted in a spontaneous steam explosion using corium melt. First, the TROI-13 premixing simulations were performed to determine the initial conditions for the steam explosion simulations and to evaluate the melt droplets hydrodynamic fragmentation model. Next, a number of steam explosion simulations were performed, varying the steam explosion triggering position and the melt droplets mass participating in the steam explosion. The simulation results revealed that there is an important influence of the participating melt droplets mass on the calculated pressure loads, whereas the influence of the steam explosion triggering position on the steam explosion development was less expressive.


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## Body

## 1. Introduction

A steam explosion in
a nuclear power plant may develop when the molten corium interacts with the
water inside the reactor vessel or in the reactor cavity.
During the
fuel-coolant interaction (FCI),  the corium thermal energy is intensively transferred
to the water. The water vaporizes at high pressure and expands, doing work on
its surroundings. Although the steam explosion has a low probability of
occurrence, it is an important nuclear safety issue in case of a severe reactor
accident. Namely, the high pressures occurring during a steam explosion can
potentially induce severe dynamic loadings on surrounding safety relevant
systems, structures, and components of the nuclear power plant. One of the most
severe potential consequences of an ex-vessel steam explosion in a nuclear
power plant is an early containment integrity loss, which can lead to an early radioactive
material release into the environment. [1]The prediction of steam
explosion induced loads must be based on results of experimental research programs
(e.g., TROI, KROTOS, FARO) and on simulations using validated FCI models (e.g.,
MC3D, IKEMIX, COMETA). Experiments provide experimental data for the steam
explosions fundamental issues investigation, the structural loadings evaluation,
and the severe accident management improvement. Since the experimental results
are in general not directly applicable to reactor conditions, above all due to the
different scales, FCI models are needed for experimental findings extrapolation
to reactor conditions. To be able to make reliable predictions, the FCI models
have to be validated on experimental data. In the complex FCI phenomenon,
multiple processes are involved during the different steam explosion stages, that
is, premixing (corium fragmentation when mixing with water), steam explosion
triggering, explosion propagation (the corium thermal energy is converted into coolant
thermal energy), and expansion (the coolant thermal energy is converted into
mechanical energy), which have to be adequately modelled. The modelling contributes
to the FCI phenomenon understanding and highlights issues that are not well
understood or require further experimental investigation and model validation. Only
adequate FCI processes and consequences understanding enable the FCI codes development
to a sufficient high level, appropriate for steam explosion risk assessment in
nuclear power plants. [2–4]Among several
experiments performed in the TROI research program, the TROI-13 FCI experiment
was chosen for the simulation with the FCI computer code MC3D. The TROI-13 experiment
was selected since in this experiment the steam explosion occurred
spontaneously and resulted in the strongest explosion among the TROI
experiments performed with corium melt. The purpose of the performed analysis
was to establish the modelling capabilities of the MC3D code and to get
additional insight into the complex FCI phenomenon.As follows, first,
the description of the TROI facility and the main TROI-13 experimental results is
provided. Next, the simulation results of the TROI-13 steam explosion
experiment are being presented and discussed in comparison with the
experimental measurements. Finally, conclusion remarks are given.


## 2. Troi-13 Experiment Set Up and Results

Test for real
corium interaction with water (TROI) is one of the research programs, which
was established to provide experimental data to investigate the steam
explosions fundamental issues, to enable the structural loadings evaluation,
and to improve the severe accident management in nuclear power plants. The
program started in 1997 at Korea Atomic Energy Research Institute (KAERI). [5]As shown in Figure1, the TROI facility has a 3D geometry and consists of a furnace vessel, a
pressure vessel, and a sliding valve. The furnace vessel contains a cold
crucible (copper tubes), a release assembly (plug and puncher), and
instrumentation for transient pressure (designator FSVP) and melt temperature
(pyrometer) measurements. The melt is prepared in the cold crucible. The
sliding valve is opened after the melting is completed. The melt is being
released when the plug is removed and the puncher breaks the crust formed at
the melt bottom. The puncher actuation time is the starting time for the
dynamic data acquisition system and the camera. The melt is delivered into the
pressure vessel, which contains the test section and the instrumentation for
the measurement of the coolant temperature (designator IVT), the dynamic
pressure in the coolant (designator IVDP), the dynamic load at the test section
bottom (designator IVDL), the atmosphere temperature (designator PVT), the transient
pressure (designator PVSP), the dynamic pressure (designator PVDP), the gas
sampling (designator GAS), and the visualization (cameras). The melt is poured
into the water inside the test section, which is 150 cm high and has an inner
diameter of 60 cm. Due to FCI, a steam explosion may develop inside the test
section. [5]Figure 1
Schematic diagram of TROI facility (not in scale; unit in cm) [5].Among
several experiments performed in the TROI facility, the TROI-13 experiment was
chosen for the simulation with the MC3D code (Section3). In the TROI-13
experiment, a eutectic corium composition was used. The mass fraction of UO2 was 70%, and the mass fraction of ZrO2 was 30%. In the
crucible, 13.7 kg of corium were heated to a temperature of nearly 3500 K. Melted
corium with the mass 7.735 kg was then poured into the test vessel, which was
filled up to 67 cm with water at a temperature 292 K. The free fall height of
the molten corium was 3.8 m. The free volume of the pressure vessel was 8.032 m3,
and the initial air pressure was 0.108 MPa. [5]In
the TROI-13 experiment, a spontaneous steam explosion occurred. The steam
explosion energy conversion ratio from thermal to mechanical energy was 0.4%. The
steam explosion started at about 1220 milliseconds, when the jet reached the
test vessel bottom. A pressure peak of 7 MPa and duration of 1 millisecond was
measured at 1224 milliseconds. At the test vessel bottom, the dynamic load was
measured. The dynamic force was higher than 250 kN, and the duration of the
pressure load was about 15 milliseconds. The most important TROI-13
experimental measurements results are summarized in Table1.   In Table 1, also
specific results of some other TROI experiments,  which had a similar
experimental set up as the TROI-13 experiment, are given. [5]Table 1
Selected experimental results from TROI facility [5]. SDM
is the mean Sauter diameter of the debris, X<0.425 mm is the mass
fraction of debris particles whose size was lower than the sieve size of 0.425 mm, SE indicates whether a spontaneous steam explosion occurred or not, pdynamic is the dynamic pressure peak, and F is the dynamic force peak at the test
vessel bottom.
ResultUnitTROI-9TROI-10TROI-11TROI-12TROI-13TROI-14SDMmm1.871.082.990.680.710.81X<0.425⁢mm%2.38.70.520.918.915.7SEN/ANoYesNoYesYesYespdynamicMPaN/ANo dataN/A1.07.00.8FkNN/ANo dataN/A210250210As
seen in Table1, not all experiments resulted in a spontaneous explosion. Based
on the TROI experimental program and other comprehensive experimental programs
(e.g., KROTOS, FARO), one can conclude that the explosivity of the premixture
and the strength of the steam explosion depend on a number of conditions [2, 4],
the most important are the following:(i)
melt material
properties (the energy conversion ratio in steam explosion experiments with
prototypic materials was one order of magnitude lower than with stimulant
materials),(ii)
melt pouring mode
(multiple pours form a more extended premixture than single pours),(iii)
system confinement
(confined systems allow more time for heat transfer between the melt and
coolant),(iv)
water subcooling
(with higher water subcooling, the premixture void fraction is lower, resulting
in a stronger steam explosion),(v)
noncondensable
gases (noncondensable gases hinder the direct melt water contact, reducing the
explosivity of the premixture),(vi)
system pressure (with a higher system pressure, the vapour film around the melt droplets becomes more stable, reducing the explosivity of the premixture).


## 3. Simulation of Troi-13 Experiment

The TROI-13
experiment was simulated and analyzed with the computer code MC3D, version 3.5,
patch 3 [6, 7]. MC3D is being developed by IRSN, France. MC3D is built mainly
for the complex FCI phenomenon evaluation. MC3D has two main applications,
which are being developed for the premixing and steam explosion calculations. The
geometry model of the TROI-13 experiment, which was used for the premixing and
steam explosion simulation, is given in Figure 2.Figure 2
Geometry and mesh of the TROI-13
experiment model.The melt description
in the MC3D premixing application is made with three fields, describing the
continuous corium, the melt droplets, and the melt fragments. The corium continuous
field is used to describe the corium jet. The second field corresponds to the
melt droplets (order of cm in diameter) issued from the jet fragmentation. The
last field is used to describe the melt fragments (less than 100μm in diameter) issuing from the melt droplet
fine fragmentation. In the TROI-13 premixing simulation, the melt fragment field
was not taken into account, since in the TROI experiments the amount of melt fragments
smaller than 0.425 mm was small if the steam explosion did not occur (Table 1).
The relations of jet fragmentation and coalescence are used to describe the
mass transportation between the continuous corium and the melt droplets field. Inside
the melt droplets field,  the melt droplets hydrodynamic fragmentation is driven
by the coarse drop break up process. [6]The appropriate melt
droplets amount determination during the premixing simulation is important,
since the melt droplets drive the heat transfer and also present the source for
fine fragmentation in the MC3D steam explosion application [6].In the simulations,
the creation of the noncondensible hydrogen during the interaction of corium
with water vapor was not modelled. Noncondensible gases in general reduce the
strength of the steam explosion since they increase the premixture void
fraction and hinder the direct melt water contact [2].


### 3.1. Premixing Simulation

The initial
conditions for the premixing simulations were obtained or estimated based on
[5]. The jet was injected at a height of 1.75 m with a velocity of 7.35 m/s and
a diameter of 2 cm [5, 8]. The MC3D default or recommended numerical and model
parameters values were used as far as possible in the premixing simulation,
although information from [5, 8, 9] was used to estimate those simulation parameters
which could have an influence on the jet fragmentation mechanisms, the
coalescence process, the melt droplets hydrodynamic fragmentation, and the melt
droplets solidification effects.Both, the jet
fragmentation and the coalescence processes depend on the molten corium material
properties, which had to be defined reasonably. First, the appropriate poured molten
corium temperature (Tjet) was established, since the experimental
measurements of Tjet were not reliable. On one hand, the measured melt
temperature was given to be 2600 K, what is below the corium solidus
temperature, but on the other hand, the temperature was estimated to be most
probably near 3500 K or even higher [5]. Therefore, the temperature of 3300 K
was chosen, based on the simulations performed in the scope of the OECD program
SERENA [8]. Next, the appropriate temperature (Tsol−liq), below
which the melt droplets fragmentation and coalescence is suppressed due to
droplets solidification, had to be determined. In the MC3D code, the temperature
Tsol−liq presents the threshold temperature below which the melt
droplets are treated as solid spheres. In MC3D, the melt droplets temperature
is defined with the melt droplets bulk temperature. So, if the melt droplets
bulk temperature is higher than Tsol−liq, the melt droplets are
treated as liquid, allowing droplets fragmentation and coalescence, otherwise the
melt droplets are treated as solid. The droplets bulk temperature is a good
measure for the droplets solid/liquid state only if the melt inside the droplet
is well mixed. However, it is believed that the melt inside the droplet is not
well mixed, and that consequently, a solid crust forms on the droplet much
earlier than the droplets bulk temperature decreases below the solidification
temperature [9]. Since in MC3D the droplets crust formation is not modelled,
for Tsol−liq a temperature higher than the default corium solid
temperature 2800 K has to be taken. We decided to perform our simulations using
for Tsol−liq the temperature 2820 K, where corium is still liquid
and which is only slightly higher than the default one.For the melt
droplet hydrodynamic fragmentation, the coarse drop break up model is used in
the MC3D code. The model is based on wave crest stripping followed by
catastrophic break up, and depends on the Weber’s number (We). If the melt
droplets We are above the critical value (Wecrit), then melt droplet
hydrodynamic fragmentation could occur. Below Wecrit, internal
forces inside the melt droplet cannot overcome the cohesive forces of the melt droplet
surface tension and the hydrodynamic fragmentation stops. For Wecrit,
the most commonly used value 12 was taken. The coarse drop break up correlation
used in MC3D should hold only for We above 350. For We below 350, two additional
damping functions are introduced to take into account also other hydrodynamic fragmentation
modes presented at lower We. The first damping function is introduced for We
below 20, and the second damping function for We below 350. A sensitivity study
was performed to evaluate the damping functions influence on the premixing
results (Figure 3). [6]Mean Sauter diameter (SDM) history (a) and
melt droplets fraction history (b) for TROI-13
premixing simulations using different melt droplets
fragmentation modelling options.
(a)(b)On Figure3(a),
the simulated mean Sauter diameter (SDM) results are given. SDM is defined as the mean sphere diameter that
has the same volume/surface area ratio as the particles of interest. Based on
the nonexplosive TROI-9 experiment, a SDM of around 2 mm could be expected in
the premixing phase (Table 1). In the case of the
nonexplosive TROI-11 experiment, SDM was overestimated since part of UO2 pellets
was not fully melted. The comparison of simulation results with the
experimental results in Table 1 indicates that the use of both damping
functions (designator BDF—both damping functions) overestimates SDM. If
both damping functions were suppressed (designator NDF—no damping function), SDM was strongly
underestimated due to the hydrodynamic fragmentation process overestimation. By
suppressing, only the second damping function SDM is still underestimated
(designator FDF—first damping function). The SDM values for
FDF were around 1.5 mm as long as the effect of the melt droplets coalescence
did not become dominant. Therefore, one can conclude that the simulated SDM for
case FDF is in reasonable agreement to the expected 2 mm in the nonexplosive
cases. The final SDM decrease (to around 1 mm in case FDF) was due to the
coalescence of larger melt droplets, which were still liquid at the end of the
premixing phase. The results indicate that there is a need for further
investigation of the melt droplet hydrodynamic fragmentation modelling.Additionally,
Figure3(b) shows also the melt droplets fraction with regard to the total
injected corium jet mass. The melt droplets coalescence was estimated to be low
in TROI-13-like experiments, since no information about an observed cake was
given in [5]. Although it was expected to achieve a low coalescence with the
increased Tsol−liq (from the default 2800 K to 2820 K) and by
selecting the lower Tjet (SERENA value 3300 K instead of quite
probable 3500 K or even higher), the coalescence still remained important once
the jet reached the test vessel bottom at premixing time around 0.25 second
(Figure 3). Since the steam explosion occurred already before the coalescence
could become significant, we did not try to improve the coalescence modelling
in our premixing simulations. As seen on Figure 3, the suppression of damping
functions (FDF, NDF) strongly influences the SDM values and the coalescence.
The coalescence reduction for smaller melt droplets could be explained with
more extensive melt droplets freezing, since frozen droplets cannot
coalescence. The coalescence was overestimated in all simulated cases if
compared to the experimentally observed low coalescence. A way to improve the
coalescence behavior is to improve the melt droplet solidification model.


### 3.2. Initial Conditions for Explosion Simulation

The initial conditions inside the test vessel for the TROI-13 steam
explosion simulations were determined based on the FDF premixing simulation case
(Figure4), where the agreement with experimental measurements was the best.
The steam explosion was triggered at premixing time 0.25 second, which was selected
based on general experimental observations that a spontaneous steam explosion usually
triggers by the contact of the molten corium with the bottom of the test vessel.Figure 4
Volume fractions of water
(TXLIQ), vapor (TXVAP), and melt droplets (TXGOU) inside the test vessel at
triggering time in the premixing simulation.In the explosion
simulation, the area of water inside the test vessel was initially divided into
three zones (interaction zone, trigger zone, and bulk zone). It was estimated from
the premixing results (Figure4) that the interaction zone extends from the
water surface (0.70 m) to the test vessel bottom (0.03 m) and has a radius of 4 cm. A homogenous distribution of the melt droplets, vapour, and water was set.
The volume fraction of melt droplets in the interaction zone was determined
based on the corium jet mass entered in the water at time 0.25 second (~1.9 kg). The volume fraction of melt droplets participating in the steam explosion
was varied in the performed simulations to consider the influence of the
incomplete jet break up and the influence of droplets freezing. Based on the
premixing simulation, the molten droplets temperature and diameter were set to
3150 K and 1.6 mm (Figure 3). The vapor volume fraction 0.43 and the vapor temperature
2760 K inside the interaction zone were set to values estimated from premixing
results. Since the sum of the  volume fractions must be 1 by definition, the water
volume fraction inside the interaction zone was set according to the vapor and
melt droplets volume fractions. The water temperature in the interaction zone
was set to 310 K and was also estimated from premixing results. The steam
explosion triggering was modelled with a trigger zone placed inside the
interaction zone at the central axis. The conditions in the trigger zone were
set reasonable according to the interaction zone conditions. The triggering
pressure of 1 MPa was chosen based on a sensitivity study, where the triggering
pressure influence on the steam explosion results was investigated. It turned out
that the triggering pressure has a negligible influence on the simulation
results if set inside a reasonable range. The position of the trigger zone in vertical
direction was varied to establish the influence of the assumed trigger location
on the steam explosion development. In the bulk zone, only water and vapor were
present. The vapor volume fraction in the bulk zone was estimated from the premixing
results and was set to 0.01. The water temperature in the bulk zone was set to
the initial premixing water temperature (292 K) and the vapour temperature to
the saturation temperature. In the simulation, also the increase of the water
level, due to the presence of the jet and vapor in the premixture, was taken
into account based on premixing results.


### 3.3. Results of Explosion Simulation

The main steam
explosion simulations results are given on Figure5. Additionally,   also a part
of the experimentally measured dynamic pressure, digitalized from [5], is shown
for comparison. The time delay between the calculated and measured pressure
peak on Figure 5 should not be taken into consideration, since in the
experiment pressure fluctuations occurred already before the strong pressure
escalation, and so the time shift depends on the definition of the spontaneous
triggering time in the experiment. The simulation results are given for
different trigger zone positions. In the simulations, the steam explosion was
triggered between the bottom (0.03 m) and the near-mid (0.3 m) parts of the
test vessel. The melt droplets mass participating in the steam explosion was
set to fractions 40%, 60%, 80%, and 100% of the total corium mass entered in
the water at triggering time. The pressure was tracked at the pressure
detectors IVDP101 and IVDP102 positions (Figures 1 and 2).Simulated pressure histories at
the positions of pressure detectors IVDP101 and IVDP102 in comparison to
TROI-13 experimental measurements. Triggering was performed at positions 0.03,
0.1, 0.2, and 0.3 m. The melt droplets mass involved in the steam explosion is
given as 40%, 60%, 80%, and 100% fractions of the total corium mass entered in
the water at the steam explosion triggering time. Time zero on the figures
corresponds to steam explosion triggering.
(a)(b)(c)(d)(e)(f)(g)(h)The results on
Figure5 reveal that the melt droplets mass significantly influences the
pressure peak height and its position. With a larger melt mass, more melt
droplets are available for fine fragmentation, resulting generally in higher
pressure peaks and larger pressure impulses. With larger melt droplets mass,
also the steam explosion develops faster due to more intense interactions, and
so the pressure peaks occur earlier. The calculated pressure peak becomes
comparable with the measured data if around 40–80% of the injected corium mass in the water,
presented as melt droplets, were taken into account in the explosion
simulations. This observation is in agreement with the premixing simulation
results, where around 80% of the jet inside the water were fragmented into melt
droplets at triggering time, and we have to consider that part of these corium
droplets is already frozen and so cannot efficiently participate in the steam
explosion [9]. The so established melt droplets mass involved in the steam
explosion (i.e., fine fragmentation) is comparable also with the experimentally
measured mass of fine fragments (smaller than 0.425 mm) in Table 1. On Figure 5,
we see that the influence of the assumed triggering position on the steam
explosion development is quite stochastic and less expressive. So, we can
conclude that the strength of a steam explosion is governed mainly by the
premixture conditions at triggering time.Figure6 shows the
pressure field propagation inside the test vessel during the steam explosion.
The steam explosion was triggered at the test vessel bottom. It was assumed
that in the interaction zone 80% of the corium mass are in form of molten
droplets, which can participate in the steam explosion. The pressure field
first developed along the interaction zone and then propagated towards the test
vessel wall, where also the pressure detectors IVDP101 and IVDP102 were placed
(Figures 1 and 5). The pressure increase near the wall was due to the incoming
and reflecting pressure superposition. After the heat transfer process from the
hot melt to water ceased, the pressure started to decrease.Calculated pressure field inside
the test vessel between 0.5 and 3 milliseconds with time step 0.5 millisecond.
The explosion was triggered in the test vessel center at position 0.03 m. The
initial conditions were set for premixing time 0.25 second. The melt droplets
mass fraction was 80% of the corium mass entered in the water at triggering
time.
(a)(b)(c)(d)(e)(f)


## 3.1. Premixing Simulation

The initial
conditions for the premixing simulations were obtained or estimated based on
[5]. The jet was injected at a height of 1.75 m with a velocity of 7.35 m/s and
a diameter of 2 cm [5, 8]. The MC3D default or recommended numerical and model
parameters values were used as far as possible in the premixing simulation,
although information from [5, 8, 9] was used to estimate those simulation parameters
which could have an influence on the jet fragmentation mechanisms, the
coalescence process, the melt droplets hydrodynamic fragmentation, and the melt
droplets solidification effects.Both, the jet
fragmentation and the coalescence processes depend on the molten corium material
properties, which had to be defined reasonably. First, the appropriate poured molten
corium temperature (Tjet) was established, since the experimental
measurements of Tjet were not reliable. On one hand, the measured melt
temperature was given to be 2600 K, what is below the corium solidus
temperature, but on the other hand, the temperature was estimated to be most
probably near 3500 K or even higher [5]. Therefore, the temperature of 3300 K
was chosen, based on the simulations performed in the scope of the OECD program
SERENA [8]. Next, the appropriate temperature (Tsol−liq), below
which the melt droplets fragmentation and coalescence is suppressed due to
droplets solidification, had to be determined. In the MC3D code, the temperature
Tsol−liq presents the threshold temperature below which the melt
droplets are treated as solid spheres. In MC3D, the melt droplets temperature
is defined with the melt droplets bulk temperature. So, if the melt droplets
bulk temperature is higher than Tsol−liq, the melt droplets are
treated as liquid, allowing droplets fragmentation and coalescence, otherwise the
melt droplets are treated as solid. The droplets bulk temperature is a good
measure for the droplets solid/liquid state only if the melt inside the droplet
is well mixed. However, it is believed that the melt inside the droplet is not
well mixed, and that consequently, a solid crust forms on the droplet much
earlier than the droplets bulk temperature decreases below the solidification
temperature [9]. Since in MC3D the droplets crust formation is not modelled,
for Tsol−liq a temperature higher than the default corium solid
temperature 2800 K has to be taken. We decided to perform our simulations using
for Tsol−liq the temperature 2820 K, where corium is still liquid
and which is only slightly higher than the default one.For the melt
droplet hydrodynamic fragmentation, the coarse drop break up model is used in
the MC3D code. The model is based on wave crest stripping followed by
catastrophic break up, and depends on the Weber’s number (We). If the melt
droplets We are above the critical value (Wecrit), then melt droplet
hydrodynamic fragmentation could occur. Below Wecrit, internal
forces inside the melt droplet cannot overcome the cohesive forces of the melt droplet
surface tension and the hydrodynamic fragmentation stops. For Wecrit,
the most commonly used value 12 was taken. The coarse drop break up correlation
used in MC3D should hold only for We above 350. For We below 350, two additional
damping functions are introduced to take into account also other hydrodynamic fragmentation
modes presented at lower We. The first damping function is introduced for We
below 20, and the second damping function for We below 350. A sensitivity study
was performed to evaluate the damping functions influence on the premixing
results (Figure 3). [6]Mean Sauter diameter (SDM) history (a) and
melt droplets fraction history (b) for TROI-13
premixing simulations using different melt droplets
fragmentation modelling options.
(a)(b)On Figure3(a),
the simulated mean Sauter diameter (SDM) results are given. SDM is defined as the mean sphere diameter that
has the same volume/surface area ratio as the particles of interest. Based on
the nonexplosive TROI-9 experiment, a SDM of around 2 mm could be expected in
the premixing phase (Table 1). In the case of the
nonexplosive TROI-11 experiment, SDM was overestimated since part of UO2 pellets
was not fully melted. The comparison of simulation results with the
experimental results in Table 1 indicates that the use of both damping
functions (designator BDF—both damping functions) overestimates SDM. If
both damping functions were suppressed (designator NDF—no damping function), SDM was strongly
underestimated due to the hydrodynamic fragmentation process overestimation. By
suppressing, only the second damping function SDM is still underestimated
(designator FDF—first damping function). The SDM values for
FDF were around 1.5 mm as long as the effect of the melt droplets coalescence
did not become dominant. Therefore, one can conclude that the simulated SDM for
case FDF is in reasonable agreement to the expected 2 mm in the nonexplosive
cases. The final SDM decrease (to around 1 mm in case FDF) was due to the
coalescence of larger melt droplets, which were still liquid at the end of the
premixing phase. The results indicate that there is a need for further
investigation of the melt droplet hydrodynamic fragmentation modelling.Additionally,
Figure3(b) shows also the melt droplets fraction with regard to the total
injected corium jet mass. The melt droplets coalescence was estimated to be low
in TROI-13-like experiments, since no information about an observed cake was
given in [5]. Although it was expected to achieve a low coalescence with the
increased Tsol−liq (from the default 2800 K to 2820 K) and by
selecting the lower Tjet (SERENA value 3300 K instead of quite
probable 3500 K or even higher), the coalescence still remained important once
the jet reached the test vessel bottom at premixing time around 0.25 second
(Figure 3). Since the steam explosion occurred already before the coalescence
could become significant, we did not try to improve the coalescence modelling
in our premixing simulations. As seen on Figure 3, the suppression of damping
functions (FDF, NDF) strongly influences the SDM values and the coalescence.
The coalescence reduction for smaller melt droplets could be explained with
more extensive melt droplets freezing, since frozen droplets cannot
coalescence. The coalescence was overestimated in all simulated cases if
compared to the experimentally observed low coalescence. A way to improve the
coalescence behavior is to improve the melt droplet solidification model.


## 3.2. Initial Conditions for Explosion Simulation

The initial conditions inside the test vessel for the TROI-13 steam
explosion simulations were determined based on the FDF premixing simulation case
(Figure4), where the agreement with experimental measurements was the best.
The steam explosion was triggered at premixing time 0.25 second, which was selected
based on general experimental observations that a spontaneous steam explosion usually
triggers by the contact of the molten corium with the bottom of the test vessel.Figure 4
Volume fractions of water
(TXLIQ), vapor (TXVAP), and melt droplets (TXGOU) inside the test vessel at
triggering time in the premixing simulation.In the explosion
simulation, the area of water inside the test vessel was initially divided into
three zones (interaction zone, trigger zone, and bulk zone). It was estimated from
the premixing results (Figure4) that the interaction zone extends from the
water surface (0.70 m) to the test vessel bottom (0.03 m) and has a radius of 4 cm. A homogenous distribution of the melt droplets, vapour, and water was set.
The volume fraction of melt droplets in the interaction zone was determined
based on the corium jet mass entered in the water at time 0.25 second (~1.9 kg). The volume fraction of melt droplets participating in the steam explosion
was varied in the performed simulations to consider the influence of the
incomplete jet break up and the influence of droplets freezing. Based on the
premixing simulation, the molten droplets temperature and diameter were set to
3150 K and 1.6 mm (Figure 3). The vapor volume fraction 0.43 and the vapor temperature
2760 K inside the interaction zone were set to values estimated from premixing
results. Since the sum of the  volume fractions must be 1 by definition, the water
volume fraction inside the interaction zone was set according to the vapor and
melt droplets volume fractions. The water temperature in the interaction zone
was set to 310 K and was also estimated from premixing results. The steam
explosion triggering was modelled with a trigger zone placed inside the
interaction zone at the central axis. The conditions in the trigger zone were
set reasonable according to the interaction zone conditions. The triggering
pressure of 1 MPa was chosen based on a sensitivity study, where the triggering
pressure influence on the steam explosion results was investigated. It turned out
that the triggering pressure has a negligible influence on the simulation
results if set inside a reasonable range. The position of the trigger zone in vertical
direction was varied to establish the influence of the assumed trigger location
on the steam explosion development. In the bulk zone, only water and vapor were
present. The vapor volume fraction in the bulk zone was estimated from the premixing
results and was set to 0.01. The water temperature in the bulk zone was set to
the initial premixing water temperature (292 K) and the vapour temperature to
the saturation temperature. In the simulation, also the increase of the water
level, due to the presence of the jet and vapor in the premixture, was taken
into account based on premixing results.


## 3.3. Results of Explosion Simulation

The main steam
explosion simulations results are given on Figure5. Additionally,   also a part
of the experimentally measured dynamic pressure, digitalized from [5], is shown
for comparison. The time delay between the calculated and measured pressure
peak on Figure 5 should not be taken into consideration, since in the
experiment pressure fluctuations occurred already before the strong pressure
escalation, and so the time shift depends on the definition of the spontaneous
triggering time in the experiment. The simulation results are given for
different trigger zone positions. In the simulations, the steam explosion was
triggered between the bottom (0.03 m) and the near-mid (0.3 m) parts of the
test vessel. The melt droplets mass participating in the steam explosion was
set to fractions 40%, 60%, 80%, and 100% of the total corium mass entered in
the water at triggering time. The pressure was tracked at the pressure
detectors IVDP101 and IVDP102 positions (Figures 1 and 2).Simulated pressure histories at
the positions of pressure detectors IVDP101 and IVDP102 in comparison to
TROI-13 experimental measurements. Triggering was performed at positions 0.03,
0.1, 0.2, and 0.3 m. The melt droplets mass involved in the steam explosion is
given as 40%, 60%, 80%, and 100% fractions of the total corium mass entered in
the water at the steam explosion triggering time. Time zero on the figures
corresponds to steam explosion triggering.
(a)(b)(c)(d)(e)(f)(g)(h)The results on
Figure5 reveal that the melt droplets mass significantly influences the
pressure peak height and its position. With a larger melt mass, more melt
droplets are available for fine fragmentation, resulting generally in higher
pressure peaks and larger pressure impulses. With larger melt droplets mass,
also the steam explosion develops faster due to more intense interactions, and
so the pressure peaks occur earlier. The calculated pressure peak becomes
comparable with the measured data if around 40–80% of the injected corium mass in the water,
presented as melt droplets, were taken into account in the explosion
simulations. This observation is in agreement with the premixing simulation
results, where around 80% of the jet inside the water were fragmented into melt
droplets at triggering time, and we have to consider that part of these corium
droplets is already frozen and so cannot efficiently participate in the steam
explosion [9]. The so established melt droplets mass involved in the steam
explosion (i.e., fine fragmentation) is comparable also with the experimentally
measured mass of fine fragments (smaller than 0.425 mm) in Table 1. On Figure 5,
we see that the influence of the assumed triggering position on the steam
explosion development is quite stochastic and less expressive. So, we can
conclude that the strength of a steam explosion is governed mainly by the
premixture conditions at triggering time.Figure6 shows the
pressure field propagation inside the test vessel during the steam explosion.
The steam explosion was triggered at the test vessel bottom. It was assumed
that in the interaction zone 80% of the corium mass are in form of molten
droplets, which can participate in the steam explosion. The pressure field
first developed along the interaction zone and then propagated towards the test
vessel wall, where also the pressure detectors IVDP101 and IVDP102 were placed
(Figures 1 and 5). The pressure increase near the wall was due to the incoming
and reflecting pressure superposition. After the heat transfer process from the
hot melt to water ceased, the pressure started to decrease.Calculated pressure field inside
the test vessel between 0.5 and 3 milliseconds with time step 0.5 millisecond.
The explosion was triggered in the test vessel center at position 0.03 m. The
initial conditions were set for premixing time 0.25 second. The melt droplets
mass fraction was 80% of the corium mass entered in the water at triggering
time.
(a)(b)(c)(d)(e)(f)


## 4. Conclusion

Fuel coolant
interaction computer codes have to be validated with steam explosion
experimental data to be able to perform reliable simulations. The purpose of
the presented work was to model the TROI-13 steam explosion experiment with the
computer code MC3D to establish the modelling capabilities of the code and to
get additional insight into the FCI phenomenon. The experiment was modelled
according to public available experimental data, applying recommended or
default MC3D numerical and model parameters. For the explosion simulation, the
correct determination of the premixture conditions at steam explosion
triggering is essential. Therefore, first, the premixing conditions were
simulated and discussed in details to enable the appropriate determination of
the mass, size, temperature, and distribution of the corium droplets at steam
explosion triggering. The corium droplets are so important because they drive the
heat transfer and represent the source for fine fragmentation during the steam
explosion.The comparison of
premixing results with experimental measurements revealed that the premixing
simulations overestimate the melt droplets mean Sauter diameter if the MC3D
coarse drop break up model damping functions are used, and underestimate it if
they are suppressed. The melt droplet coalescence was overestimated in any
case, if the damping functions were used or if they were not used. It turned
out that using only the first damping function, quite reasonable premixing
results are obtained in the initial stage of the melt pour, lasting also beyond
the steam explosion triggering time. Therefore, these premixing results were
used to define the initial conditions for the steam explosion simulations. The
steam explosion simulations results were in reasonable agreement with the
experimental measurements. The results revealed that there is an important
influence of the involved melt droplets mass on the steam explosion process.
The influence of the assumed steam explosion triggering location on the steam
explosion strength was less expressive. Due to the importance of the adequate
active melt droplets mass prediction at triggering time on the subsequent
development of the steam explosion, it is of utmost importance to appropriately
consider in the FCI codes also melt droplets solidification phenomena.



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*Source: 852047-2008-08-25.xml*