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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; 8–10 – 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 = Gr∙Pr

is the Rayleigh number; Gr = g∙∙l3 (Tcask–Ta)/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 Lithuanian–Ukrainian 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.