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COMPARATIVE ANALYSIS OF NUMERICALMETHODS USED FOR THERMAL MODELING OF SPENT NUCLEAR FUELDRY STORAGE SYSTEMS

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Management of spent nuclear fuel is a very important part in the whole cycle of nuclear energy generation. Usually "dry" storage technology in casks is selected for the interim storage of spent nuclear fuel for up to 50 years after pre-storage time in water pools. In this paper, two case studies were carried out to highlight the differences and similarities between Ukraine and Lithuania in spent nuclear fuel storage.
Methodology of SNF thermal state simulation in modular storage NON-VENTILATED CASKS This paper presents the modeling results of decay heat removal from metal-concrete CONSTOR nonventilated casks that are used only for RBMK-1500 SNF at the Ignalina NPP. Modeling is performed for casks in an open type storage facility for summer conditions. The body of a CONSTOR cask contains 2 low-alloy steel cylinders of different inner and outer dimensions. The annular space is filled with heavy concrete. The heavy concrete is also poured into the space between panels and at the bottom of the cask. A massive metal ring is welded at the top of cask steel cylinders. The cask lid and two guard plates are fastened and fixed to the ring. The cask described is a storage vessel for a stainless steel basket where the SNF bundles are placed. The basket contains 51 assemblies cut in halves (102 fuel rod bundles). Once the basket is within the cask, the cask lid and the guard plates are tightly closed. When the water is pumped out, the cask dries out and helium is pumped in. Then the cask is put onto a concrete base at the open storage facility and a reinforced concrete cover is used as additional cover. A shock-absorbing damper is fastened to the bottom of the cask to prevent possible shocks during its transfer to the storage site. A loaded concrete cask weights approx. 88 tones. For thermal analysis, the ALGOR code [8] was used. It is a general-purpose code which can be used for two-and three-dimensional modeling using the finite element method. The ALGOR code is widely used for modeling the mechanical stress and structural integrity of the equipment and thermal processes. The cask in this paper was modeled as two-dimensional in cylindrical r-z coordinates assuming steady state conditions (Fig. 3). Modeling is performed based on effective
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ISSN 1562-6016. PASТ. 2019. №5(123), p. 75-79.
COMPARATIVE ANALYSIS OF NUMERICAL METHODS USED FOR
THERMAL MODELING OF SPENT NUCLEAR FUEL
DRY STORAGE SYSTEMS
S. Alyokhina1,2, Y. Matsevity1,2, V. Dudkin2, R. Poskas3, A. Sirvydas3, K. Rackaitis3, R. Zujus3
1A. Podgorny Institute of Mechanical Engineering Problems of the National Academy
of Sciences of Ukraine, Kharkiv, Ukraine
E-mail: alyokhina@ipmach.kharkov.ua, tel. +38(057)294-27-94;
2V.N. Karazin Kharkiv National University, Kharkiv, Ukraine;
3Lithuanian Energy Institute, Nuclear Engineering Laboratory, Kaunas, Lithuania
Management of spent nuclear fuel is a very important part in the whole cycle of nuclear energy generation.
Usually “dry” storage technology in casks is selected for the interim storage of spent nuclear fuel for up to 50 years
after pre-storage time in water pools. In this paper, two case studies were carried out to highlight the differences and
similarities between Ukraine and Lithuania in spent nuclear fuel storage.
PACS: 47.27.te
INTRODUCTION
Interim dry storage in containers is one of the rather
widely used technologies for the management of spent
nuclear fuel (SNF) in countries with an open fuel cycle.
In Ukraine, it is planned to use two types of storage
facilities: at the Zaporizhska NPP, SNF from WWER-
1000 reactors is stored in concrete ventilated containers
VSC-24, produced by Sierra Nuclear Corporation and
Duce Engineering and Services (USA); at the
Chernobyl NPP, the SNF of RBMK-1000 reactors will
be stored in containers placed in ventilated concrete
modules developed by Holtec Int. (USA). In both cases,
the storage facilities are open type facilities; the SNF is
placed in containers after storing in pools for at least
5 years. The service life of the storage facilities is at
least 50 years.
Lithuania decided to use the dry storage method and
to store spent nuclear fuel from RBMK-1500 reactors of
the Ignalina NPP after storage in pools for at least
5 years in an open-type storage facility using initially
unventilated containers of the CASTOR RBMK-1500
type and further CONSTOR RBMK-1500 type.
CASTOR containers are made from metal, CONSTOR
containers from reinforced concrete. In 1999, a storage
facility was built that can hold up to 120 containers and
is now completely full. In 2017, the operation of a new,
closed-type intermediate storage facility was started,
where SNF is stored in new type reinforced concrete
containers CONSTOR RBMK-1500/M2. The total
storage capacity is about 190 containers. The life of
both storage facilities is 50 years.
The determination of the thermal state of containers
with SNF is an important component in ensuring the
safety of the SNF dry storage during the entire service
life of the storage facility. Therefore, a number of
thermal state studies have been carried out for storage
containers with SNF from WWER-1000 [1, 2] (the
method will be transformed for storage modules with
RBMK-1000 fuel) and RBMK-1500 [3, 4] reactors.
This paper presents the modeling methodology and
results of decay heat removal from CONSTOR RBMK-
1500 and storage modules used for the Chernobylska
NPP dry SNF storage facility.
1. METHODOLOGY
VENTILATED STORAGE MODULE
In Ukraine, the SNF of RBMK-1000 reactors is
stored in concrete modules (Fig. 1). The cooling of a
cask with spent fuel assemblies is conducted by
atmospheric air, which goes through the module due to
natural draught. The module includes a storage cask,
which is covered by a thermal shield; the entry port of
the module is closed by a concrete lid.
Fig. 1. The storage module used for SNF
of RBMK-1000
The multi-stage approach [5] for the current problem
consists of the components shown in Fig. 1. At the first
stage, the storage basket with spent fuel assemblies was
considered as a solid unit with equivalent thermal
properties [6, 7] and the thermal state of the whole
storage module is defined.
Then, the thermal conditions on the surface of the
basket were obtained on the basis of the calculated
information about heat transfer processes inside the
storage container. These conditions include the
temperature of the basket surface or the heat transfer
rate through the basket surface or the temperature of the
cooling air in the ventilating channels together with the
heat-transfer coefficient on the basket surface. This
information is used as boundary conditions at the next
stage. At the second stage, the basket alone is
considered with more detailed geometry than at the
previous stage: the helium domain and domains of solid
parts of the basket are taken into account, but each SNF
assembly is considered as a solid unit with equivalent
thermal properties. The thermal state of the basket is
calculated with the boundary conditions on its surface
that were obtained at the first stage, and the thermal
conditions on the surfaces of the solid units
corresponding to the SNF assemblies are calculated
similar to the conditions on the basket surface at the first
stage. At the third stage, each SNF assembly is modeled
with more detailed geometry and the boundary
conditions obtained at the second stage. Finally, this
approach (Fig. 2) allows determining the temperature
fields of each fuel element.
1. Storage module
2. Storage cask with SNF
3. Spent fuel assembly
4. Spent fuel rod
Boundary conditions on the
surface of the storage cask Equivalent thermophysical
properties of the storage cask
Boundary conditions on the
surfaces of guide tubes Equivalent thermophysical
properties of the fuel assembly
Boundary conditions on the
surfaces of fuel rod Equivalent thermophysical
properties of fuel rod
Fig. 2. Methodology of SNF thermal state simulation in
modular storage
NON-VENTILATED CASKS
This paper presents the modeling results of decay
heat removal from metal-concrete CONSTOR non-
ventilated casks that are used only for RBMK-1500
SNF at the Ignalina NPP. Modeling is performed for
casks in an open type storage facility for summer
conditions.
The body of a CONSTOR cask contains 2 low-alloy
steel cylinders of different inner and outer dimensions.
The annular space is filled with heavy concrete. The
heavy concrete is also poured into the space between
panels and at the bottom of the cask. A massive metal
ring is welded at the top of cask steel cylinders. The
cask lid and two guard plates are fastened and fixed to
the ring.
The cask described is a storage vessel for a stainless
steel basket where the SNF bundles are placed. The
basket contains 51 assemblies cut in halves (102 fuel
rod bundles). Once the basket is within the cask, the
cask lid and the guard plates are tightly closed. When
the water is pumped out, the cask dries out and helium
is pumped in. Then the cask is put onto a concrete base
at the open storage facility and a reinforced concrete
cover is used as additional cover. A shock-absorbing
damper is fastened to the bottom of the cask to prevent
possible shocks during its transfer to the storage site. A
loaded concrete cask weights approx. 88 tones.
For thermal analysis, the ALGOR code [8] was
used. It is a general-purpose code which can be used for
two- and three-dimensional modeling using the finite
element method. The ALGOR code is widely used for
modeling the mechanical stress and structural integrity
of the equipment and thermal processes. The cask in this
paper was modeled as two-dimensional in cylindrical
r-z coordinates assuming steady state conditions
(Fig. 3). Modeling is performed based on effective
thermal conductivities and thermal conductivities. So, in
such a case, the ALGOR code is a rather effective tool.
Fig. 3. Schematic view of the cask computer model:
1 fuel load active part; 2, 3 fuel load lower and
upper parts; 4 basket bottom; 5 lid; 6a metal parts
of the body, 6b heavy concrete; 7 reinforced
concrete cover; 810 horizontal lower, vertical and
horizontal upper helium gaps
The elements of the cask are meshed separately. The
grid of the computer model was created following
ALGOR code recommendations for the effective
conductivity/conductivity cases. To demonstrate the
grid independence, the modelling was also performed
using a 1.5 times finer grid. In such a case the maximum
rod cladding temperature decreased by ~ 2% but the
cask body outer surface temperature increased by ~ 1%.
This demonstrates that the selected grid is reasonable
and gives conservative values for rod cladding
temperatures.
When modeling the following processes and
parameters are accepted: the decay heat of the fuel, heat
conduction (or effective conductivity) coefficients of all
materials of the cask (which depend on the
temperature), ambient temperature, the influence of
adjacent casks in the storage facility, the heat transfer
coefficient by natural convection from the cask’s outer
surface, the emissivity for external radiation from the
cask surfaces and the heat fluxes from solar insolation.
A cask just loaded with 102 SNF rod bundles that
had been stored in water pools for 5 years emits
approximately 6.1 kW of decay heat. Since our model
doesn’t take into account decay heat variation in axial
direction (the maximum deviation is 17), therefore in
modeling the 17% enlarged decay heat of fuel load
homogeneous zone is assumed to be Q 7.14 kW. The
decay heat gradually decreases during the succeeding
period of SNF storage.
A scheme of heat transfer from the fuel rods through
the cask is presented in Fig. 4. The heat from the fuel
load by conduction is transferred to the outer surfaces of
6a
6a
6b
the cask, and then by radiation and natural convection to
the environment. For the modeling, effective axial and
radial heat conductivity coefficients were used to
evaluate the heat transfer through the fuel load. They
were obtained experimentally by research institutions.
Fig. 4. Processes of decay heat removal from the cask in
summer time. Solar insolation was taken into account
only for the reinforced concrete cover
For the determination of the heat transfer coefficient
from the vertical cylindrical surface of the cask by
natural convection an empirical correlation [9] was
used:
1/3
Nu 0.13Ra ,
(1)
where Nu = αconv l/0 is the Nusselt number; Ra = GrPr
is the Rayleigh number; Gr = gl3 (TcaskTa)/02 is the
Grashof number; Pr = 0cp0/0 is the Prandtl number;
g = 9.81 m/s2 is the gravitational acceleration; β is the
coefficient of volumetric expansion; λ0, ν0, and 0 are
coefficients of air conductivity and dynamic and
kinematic viscosity, respectively; cp0 is air specific heat;
l is a reference geometrical parameter. The reference
geometrical parameter here is the cask’s height, and the
reference temperature is the ambient temperature.
For the upper horizontal surface of the protective
concrete cover of the cask the heat transfer coefficient is
calculated from the empirical correlation [9]:
1/3
Nu 0.15Ra .
(2)
The reference geometrical parameter here is half of
the cask’s radius, and the reference temperature is the
ambient temperature. The calculation of the parameters
mentioned is a iterative process since the values of heat
transfer coefficients and surface temperatures depend on
each other.
For evaluating heat transfer through the He gaps,
only conduction was taken into account. Based on [10],
an increase in heat transfer by natural convection is
negligible when the Rayleigh number, characterizing
natural convection, is less than 1000. Heat transfer by
radiation through the He gaps also can be neglected
conservatively because the temperature differences in
the He gaps are relatively small and He thermal
conductivity is rather high.
In the modeling, heat from solar insolation was
taken into account. This was evaluated based on IAEA
recommendations [11]. It is recommended that the heat
flux from solar insolation during daylight (12 h) to
horizontal surfaces is 800 W/m2, and to vertical surfaces
is 200 W/m2. In this study heat fluxes from solar
insolation were distributed during 24 h. So, heat flux to
the horizontal surface was 400 W/m2 and to the vertical
surface 100 W/m2. Also, the effect of neighboring
containers for vertical surfaces was taken into account,
since, in a storage facility, casks are arranged at
intervals of 3 m.
Furthermore, heat radiation from the outer
cylindrical surface of the cask to the environment was
not taken into consideration because the wall
temperatures of surrounding casks are similar. The
summary of the real and modeled processes is presented
in Fig. 4.
In this study, when the modeled cask is in an open
storage facility in summer time, it is affected by solar
insolation and the ambient temperature is 37 °C. Such a
temperature was evaluated by taking into account the
average temperature of the hottest season in Lithuania
and adding 10 °C due to the effect of the adjacent casks.
A decrease of the temperature during the night was
conservatively not taken into account.
Further, the temperature and the heat flux
distributions in the fuel load and the cask’s body were
modeled and an assumption was made that the
maximum fuel load temperature coincides with the
central heat generating rod temperature. Modeling was
performed till 300 years of container storage. Validation
of the numerical model was performed by comparing
modelling results of cask surface temperatures with
surface temperature measurements of a commercial cask
for winter conditions (ambient temperature -6 °C)
taking into account real burnup of the loaded fuel
bundles [12]. The surface temperature difference
between modelling results and measurements was till
2.0 °C.
2. RESULTS DISCUSSION
VENTILATED STORAGE MODULE
At the beginning of the research on the Ukrainian
SNF storage system, only the first level of the
calculation methodology was used. One concrete
module with a storage cask was considered. The
atmospheric air comes to the module and, already
cooled, flows up the cask, which is placed horizontally
(Fig. 5). The heated ventilating air then flows out
through two outlet vents. The outlet vent placed above
the entry port conducts more air than the other due to
the specifics of the cooling channels inside the storage
module.
The existing velocity field organizes relevant
temperature field (Fig. 6). The maximum temperature is
observed inside the storage cask but above the central
axis. It is caused by the structure of the cooling flow,
which is stopped by the thermal shield placed above the
storage cask.
Fig. 5. Velocity contour of ventilated air inside storage
module with SNF of RBMK-1000
Fig. 6. Temperature field of storage module with SNF
of RBMK-1000
The velocity and the thermal contours are physically
correct and therefore the problem formulation is correct
too and could be used in real simulation of the storage
module for the Chernobyl NPP.
NON-VENTILATED CASKS
Fig. 7 gives the distribution of isotherms inside
casks (in fuel load) and in a body of cask for summer
conditions after 5 (just loaded SNF into cask) and 300
year of storage. In Fig. 7,a it can be observed that the
maximum temperature is in the center of fuel load. As it
mentioned above, this temperature coincides with the
central heat generating rod temperature. Receding from
the center in axial, as well as in radial direction, the
temperature decrease, but in radial direction the
temperature gradients are substantially higher. The
temperatures are varying similarly in the cask body. The
highest temperatures are in the center of the inner
surface of cask body and protective cover. The lowest
temperatures are in the body corners. The typical feature
is that because of the influence of solar insolation the
temperatures of the upper surface of protective cover are
higher than the temperatures of cylindrical surface.
a b
Fig. 7. Distribution of isotherms inside the casks for
summer conditions: a in case of 5 year of storage;
b in case of 300 years of storage
In the case of 300 years of storage (see Fig. 7,b), the
maximum fuel load temperature is about 180 °C lower
due to decreased decay heat, and it reaches about 92 °C
but it is displaced to the top of the cask because of the
effect of solar insolation. The maximum surface
temperature is about 40 °C lower in comparison with the
maximum temperature in the case of 5 year of storage.
CONCLUSIONS
After the thermal analysis of two SNF storage casks,
the following conclusions have been drawn:
The techniques used by Lithuanian and
Ukrainian scientists in the study of the thermal state of
the spent fuel of the RBMK-1500 and RBMK-1000
reactors are similar. Both groups have used CFD-
methods, effective thermal conductivity of some
elements and showed good results in the analysis of the
thermal safety of dry storage facilities.
Simulation of heat removal from the CONSTOR
RBMK-1500 container with rather conservative
assumptions has shown that the temperature of the
hottest fuel element does not exceed the allowable
temperature (300…350 °C).
The temperature in the fuel storage module of
RBMK-1000 reactors does not exceed the limits for
thermal safety either.
ACKNOWLEDGEMENTS
Results were obtained and publication is prepared in
frame of the LithuanianUkrainian Cooperation
Program in the Fields of Research and Technologies
according to Research Council of Lithuania (research
contract No. S-LU-18-5) and Ministry of Education and
Science of Ukraine (research contract M-81) R&D
project “Comparative analysis of the modelling
methodologies and results for evaluation of the RBMK-
1000 (Ukraine) and RBMK-1500 (Lithuania) spent
nuclear fuel’s radiation/thermal parameters in dry
storage conditions”.
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Article received 13.02.2019
СРАВНИТЕЛЬНЫЙ АНАЛИЗ ЧИСЛЕННЫХ МЕТОДОВ, ИСПОЛЬЗУЕМЫХ
ДЛЯ ТЕПЛОВОГО МОДЕЛИРОВАНИЯ СИСТЕМ ХРАНЕНИЯ
ОТРАБОТАВШЕГО ЯДЕРНОГО ТОПЛИВА
С. Алёхина, Ю. Мацевитый, В. Дудкин, Р. Пошкас, А. Сирвидас, К. Рачкайтис, Р. Зуюс
Управление отработанным ядерным топливом является очень важной частью всего цикла производства
ядерной энергии. Обычно технология «сухого» хранения в контейнерах выбирается для временного
хранения отработанного ядерного топлива в течение до 50 лет после времени предварительного хранения в
водных бассейнах. В этой статье были проведены два тематических исследования, чтобы подчеркнуть
различия и сходства между Украиной и Литвой в области хранения отработавшего ядерного топлива.
ПОРІВНЯЛЬНИЙ АНАЛІЗ ЧИСЕЛЬНИХ МЕТОДІВ, ЩО ВИКОРИСТОВУЮТЬСЯ
ДЛЯ ТЕПЛОВОГО МОДЕЛЮВАННЯ СИСТЕМ ЗБЕРІГАННЯ ВІДПРАЦЬОВАНОГО
ЯДЕРНОГО ПАЛИВА
С. Альохіна, Ю. Мацевитий, В. Дудкін, Р. Пошкас, А. Сірвідас, К. Рачкайтис, Р. Зуюс
Управління відпрацьованим ядерним паливом є дуже важливою частиною всього циклу виробництва
ядерної енергії. Зазвичай технологія «сухого» зберігання в контейнерах вибирається для тимчасового
зберігання відпрацьованого ядерного палива протягом до 50 років після часу попереднього зберігання у
водних басейнах. У цій статті були проведені два тематичних дослідження, щоб підкреслити відмінності і
подібності між Україною та Литвою в області зберігання відпрацьованого ядерного палива.
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The safe thermal conditions of spent nuclear fuel storage are the important component of complex safety of the dry spent nuclear fuel storage facility. The multistage approach for numerical definition of thermal fields in storage containers with spent fuel assemblies is proposed. The approach is based on solving of the series of the conjugate heat transfer problems with different geometrical detailing. The developed approach is used for estimation of thermal state of ventilated containers with spent nuclear fuel of WWER-1000 reactors of Zaporizhska nuclear power plant. The results of the thermal calculations for single-placed container on open-site storage platform were presented. The safety of containers usage in normal and extreme ambient temperatures was proven. Copyright © 2015 John Wiley & Sons, Ltd.
Article
The main characteristics, such as temperatures of the fuel rod cladding and cask surface, dose rates at the surface and at the some distance for CASTOR RBMK-1500 and CONSTOR RBMK-1500 casks loaded with spent nuclear fuel are presented. These casks are used for an interim dry storage of spent nuclear fuel at Ignalina Nuclear Power Plant. Numerical modeling (calculation of the equivalent dose rates, activities of nuclides, etc.) and experimental measurements of the equivalent dose and gamma spectrum on the cask surface at dry storage facility were performed for assessment of radiation characteristics. Temperatures were evaluated using only numerical modeling. Rather good agreement between experimentally determined and calculated dose rates for CASTOR RBMK-1500 and CONSTOR RBMK-1500 casks was obtained. Also it was revealed that maximum fuel rod cladding temperature is higher for CONSTOR RBMK-1500 cask, but never exceeds the maximum allowable value. The cask surface temperatures are similar for both cask types.
Thermal Analysis of Certain Accident Conditions of the Dry Spent Nuclear Fuel Storage // Nuclear Engineering and Technology
  • S Alyokhina
  • A Kostikov
S. Alyokhina, A. Kostikov. Unsteady heat exchange at the dry spent nuclear fuel storage // Nuclear Engineering and Technology. 2017, v. 49, p. 1457-1462. 2. S. Alyokhina. Thermal Analysis of Certain Accident Conditions of the Dry Spent Nuclear Fuel Storage // Nuclear Engineering and Technology. 2018, v. 50, issue 5, p. 717-723; DOI: 10.1016/j.net.2018.03.002. 3. R. Poškas, V. Šimonis, P. Poškas, A. Sirvydas. Thermal analysis of CASTOR RBMK-1500 casks during long-term storage of spent nuclear fuel // Annals of Nuclear Energy. 2017, v. 99, p. 40-46.