Fukushima
Daiichi accident that took place in March 2011 affected entire industry and
raised huge amount of new challenges in field of safety justification of
post-accident nuclear facilities. One of consequences of the accident is corium
– highly radioactive lava-like remains of reactor core. It is essential to
avoid any emergency processes during corium handling operations. One of such
dangerous operations is corium extraction.
In
present times, some of corium is located at the bottom of reactor cavities of
Fukushima’s damaged units and being cooled with water, but Tokyo Electric Power
Company (TEPCO) is planning to extract corium from its current location with
the aim of holding it in proper place. First part of extraction process will include
crushing corium to small pieces (debris), second is debris extraction itself,
during this stage debris particles can fall to the water and can approach to recriticality [1-3]. Safety justification of such situation is not an easy task;
it consists of CFD modeling of particles falling process in order to get their
time-dependent positions and following neutronic Monte Carlo simulation with
obtained geometry. Since nobody knows real isotopic composition of corium and
its structure i.e. possible layers and other spatial heterogeneities, it is
essential to find most limiting conditions of distribution of debris particles
and their isotopic composition in order to fully justify safety of such
operations. Proper data visualization is a good way to do so.
Aim
of this work is to create a tool for visualizing neutron fluxes and reaction
rates in fuel debris falling to the water in case of accident during corium
extraction procedure. Data set for visualization was obtained at the first part
of joint Russian-Japanese work related to safety justification of corium
handling operations. The following parts of the aforementioned work will be
characterized, inter alia, by the complexity of geometry, so visualization tool
should have possibility to work with it.
Model
of interest in this work is the system of one thousand debris particles (cubes
with edge equals to 1 cm) which fall to the water on concrete bed. Compositions
of debris and concrete are based on compositions for post-accident BWR type
reactors. Time dependent positions of falling cubes were obtained with help of
ParticleWorks CFD code [4]. Entire falling process takes approximately one
second, but only five system snapshots were chosen for further analysis with
precise neutronic Monte Carlo codes; these snapshots are enough to perform
recriticality analysis because they represent the key states of the system,
i.e. states with different uranium-water ratios and debris particle densities.
Each cube for all five moments of time has its own position and rotation, they
may overlap each other and concrete bed, but it does not have much of impact on
simulation. Particle distribution for each time moment is presented in figure 1.
Figure 1. – Particle distribution for
each time moment.
As
can be seen in figure above, each time snapshot significantly differs from
others. From neutronic point of view, it leads to different uranium-water ratio
and hence to different multiplication properties of system at each moment of
time. Density of particles and heterogeneity of their distribution lead to considerable
variation of neutron flux and reaction rates across the system. Visualization
of these values can give additional information about the system’s state and
help to improve current and further analysis of it.
Data
set for visualization is flux and various reaction rates in debris particles,
obtained via precise Monte Carlo simulation, and their standard deviations. Data
presented in this work is result of simulation in code Serpent [5] developed at
VTT Technical Research Centre of Finland.
Data
from Serpent’s output files was extracted via simple Python script and saved in
format, suitable for further use in visualization software. Such approach
(separation of data preparation and visualization process) allows to use
results of every Monte Carlo code after proper preparation.
In
order to visualize data for such a complex system nonstandard approach is
required, since it cannot be done with common plotting libraries and environments.
The
target function of the visualization software is to render system of cubes giving
to each cube color, based on value of interest in corresponding debris particle.
Then system can be viewed in 3D or user can make a capture of interesting
system’s sections. There are many ways to visualize distributions in complex
geometry. First is to use graphical engines (e.g. OpenGL) such approach was
implemented in [6] to visualize space debris distribution, graphical engines
are widely used for visualization of biological structures [7, 8] and for mesh
visualization [9], also they may be used as graphical part of complex systems [10]
when scientists and developers have no choice but use them. Thus, graphical
engines are used when optimization or integration with other software is
required. Second approach consists in using 3D modeling software (e.g. Blender)
authors of [11] used it to visualize wave function dynamic, also it may be used
for visualization of molecular diffusion [12] and dynamic [13]. Third is to use
something more high-level, for example, game engines, since using of first two
approaches may be not an easy task, because graphical engines are too low-level
and require a lot of programming, while 3D modeling software is aimed to solve
different kind of problems and, in some cases, not suitable for visualizing
purposes.
We
have chosen the Unreal Engine 4 for this work due to its scalability and simplicity
for render tasks. Unreal Engine 4 is an open source game engine developed by
Epic Games [14]. In present time, it is used not only for game development, but
also as real-time render engine in filmmaking, architecture etc. Unreal Engine
has built in optimization features which are enough for visualization purposes
of almost every scale (not for cases mentioned above), a lot of programming
work has already been done by engine’s developers, thus Unreal Engine is the
simplest tool for creating visualization software. In context of scientific
visualization, it is usually used when some interactivity is required [15, 16].
User
interface of visualization software is presented in figure 2. Via this GUI user
can choose moment of time and value to visualize, also it is possible to look
at system from every angle and make a picture of desirable section of model.
Left bottom part of GUI allows to choose section plane (shown as red grid with
an arrow) for further capturing from its position.
Figure 2. –
Graphical user interface.
In
the future, on next steps of correlated work, form of debris particles may
change to spherical or something more complex; this was taken into account
during development process of the software.
Integrated
neutron flux and fission reaction rate were chosen as most significant and
useful data. Their distribution is presented on figures 3 and 4. One can notice
debris cubes that overlap concrete bed, this feature of model, which was
mentioned above, is the result of direct modeling of falling process.
Figure 3. – Integrated neutron flux, YZ
plane.
Figure 4. – Integrated fission reaction
rate, YZ plane.
As
can be seen from figures below, distributions of fluxes and fission reaction
rates do not match. This can be explanated by different neutron spectrums
across geometry. While integrated flux is higher in the center of debris
cluster, fission reaction rate “pike” is shifted towards water, where neutron
spectrum is thermal.
Figure
5 shows distribution of standard deviation of integrated neutron flux in each
cube. As expected, distribution of this value is reversed comparing with
integrated flux distribution.
Figure 5. – Standard deviation of
integrated neutron flux, percentage, YZ plane.
We
have developed a new programming tool that targets the visualization of highly
distributed neutronic functionals in fuel debris particles. The visualization
software allows representing the scientific data of complex systems that is obtained
by precise Monte Carlo modeling. Images, obtained via the software, are good
illustrative material that helps improving safety justification of
corresponding systems. The software was designed with mind of extension for
further work.
This
work was financially supported by the Ministry of Science and Higher Education
of the Russian Federation (unique identifier of the project RFMEFI61419X0003).
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