#### Abstract

The analysis of the thermal condition of spent FA (fuel assembly) of BN-350 reactor in a six-place cask for dry storage is presented. Simulation of the thermal condition of the cask is conducted with finite elements method using ANSYS software. Calculations of fuel temperature, fuel cladding, and assembly structural elements are the part of the safety analysis for storage of spent FA. In conclusion, the results of the thermal calculations in the cases of filling cask with argon and atmospheric air are given when the thickness of the insulation cask with concrete is 0.5 and 1 m. As a result of the calculated studies, the parameters of SNF (spent nuclear fuel) storage are determined, under which the fuel temperatures will have minimum and maximum values.

#### 1. Introduction

SNF is most often transferred to a dry storage method after reducing the level of radioactivity and the residual energy release. The general principle of SNF dry storage is that spent fuel is stored in sealed metal baskets, and the baskets are located in the casing of the protective cask [1–3]. Fuel elements or assemblies inside the casks are usually in an inert gas medium, which protects the materials from corrosion and helps to remove residual heat.

The main characteristics for the SNF integrity in dry storage are values of fuel temperature and the cladding. There is a need for thermal calculations related to storage conditions to assess the safety of long-term storage of spent assemblies of BN-350 reactor in the cask. The paper shows the results of calculations of the stationary temperature field of a six-place cask with spent FA of the BN-350 reactor. Cases of the cask filling with argon and atmospheric air, when the thickness of the insulation cask concrete is 0.5 and 1 m, are considered; the parameters of the storage in which the fuel temperature will have maximum and minimum values are determined.

#### 2. Initial Data for Thermal Calculation

Spent fuel assemblies of the BN-350 reactor are packed in six-place casks. The layout of fuel assemblies in a dry storage cask is shown in Figure 1 [4]. Figure 2 shows the layout of the fuel elements in FA, where the temperature distribution calculation area is marked by a circle in the center of FA.

The temperature distribution is determined in the area of the central fuel element of one of the fuel assemblies of BN-350 reactor in a six-place cask for dry storage. Materials and geometric dimensions of the cask elements and fuel assemblies are given as follows:

Cask: material, austenitic stainless steel 12Х18Н10Т; outer diameter, 406.4 mm; inner diameter, 396.4 mm; height, 3854 mm.

Inner basket (six-place): material, austenitic stainless steel 12Х18Н10Т; outer diameter of the cell, 130 mm; inner diameter of the cell, 129 mm.

Hexagonal tube: material, austenitic stainless steel 12Х18Н10Т; width across flats, 96 mm; the thickness of hexagonal tube, 2.175 mm; height, 1050 mm.

FEs: number of FEs in FA, 127 pcs; material of FE cladding, austenitic stainless steel 0Х16Н15М3B; outer diameter, 6.9 mm; inner diameter, 6.1 mm; height, 1060 mm; the gap among FEs, 1.05 mm.

Fuel: material, mixture of plutonium dioxide and uranium dioxide; diameter of fuel pellet, 6 mm with the central hole of ⌀1.7 mm.

Calculation is conducted for FA power of 120 and 190 W. Calculations of the profile of temperature distribution are conducted for cases of cask filling with argon and atmospheric air. The cask is surrounded with the concrete of 0.5 or 1 m.

#### 3. Calculation

Calculation is conducted with ANSYS software, which implements the method of finite elements [5, 6].

For calculations two-dimensional model was used which is provided in Figures 1 and 2. The finite element grid of the model consists of 572143 units and 464000 elements; higher grid resolution is concentrated in the FA area.

The surface temperature of the concrete is estimated as equal to 293 K. Calculation of stationary distribution of the temperature in the average height of the cross-section of the six-place cask (as most of the heat-stressed section) is conducted for two values of the residual energy in the fuel: ~54.3 kW/m^{3}, which corresponds to the power of FA equal to 190 W, and ~34.3 kW/m^{3}, which corresponds to the power of FA equal to 120 W.

The energy release values were determined by the following formula:

wherein is power of FA (120 and 190 W); is number of FEs in FA ( = 127 pcs); is volume of FE ( = 2.756 × 10^{−5} m^{3}).

It is assumed that the energy release in the fuel is constant in height and radius of FA, and the energy release in the construction of FA materials and the cask is equal to zero.

The heat flow from the end surfaces of the cask is assumed to be zero.

Heat transfer from fuel elements to the rest part of the model is conducted using thermal conductivity and natural convective heat transfer [7]. wherein is coefficient of convection; is coefficient of medium heat conductivity (argon, air), W/(m·K).

Coefficient of convection is determined by the following formula:wherein is Grashof number; is Prandtl number.

When , ; when , .

Grashof number is equal towherein is temperature coefficient of volume expansion of the filler, 1/K; is gravitational acceleration, m/sec^{2}; is determining size, m (hydraulic diameter, for cask, is 0.191 m, for FA it is equal to 0.0033 m); is maximum temperature of the medium, K; is minimal temperature of the medium, K; is coefficient of kinematic viscosity of the medium, m^{2}/sec.

Prandtl number is as follows:wherein is dynamic viscosity coefficient of the medium, Pа×sec; is specific heat capacity of the medium under the constant pressure, J/(kg×K).

The average calculated value of the convection coefficient when filling the cask cavity with argon under the FA power of 120 W is and for argon, filling the FA cavity. Thus, heat transfer in the FA cavity is conducted only due to thermal conductivity. This is because the value of the Rayleigh number for argon in the FA cavity is less than 10^{3} (is 6.8); in this case, the convection coefficient is assumed to be equal to one.

An iterative solution is required to account the effect of natural convection using the above method. The model is calculated with reference values of the thermal conductivity of the medium in zero-order approximation. Then convection coefficients are calculated for the medium that fills the cask cavity. The model is recalculated. The process is repeated until the difference between the calculated values of the temperature of two successive iterations model will be below 0.1 K.

Thermophysical properties of materials depending of temperature used for calculations are presented in Tables 1, 2, and 3 [8, 9].

According to experimental data, calculation error in ANSYS is from 5 to 10 %.

#### 4. Analysis of Obtained Results

Figures 3–5 show the calculated temperature field in the average height of the cross-section of the cask filled with argon at FA power of 120 W, while the thickness of concrete is 0.5 m. Figures show that the maximum temperature of the fuel will not exceed 553 K.

Table 4 shows the calculated temperature values determined in the positions indicated in Figures 3–5 for the eight calculation options. Argon and air were used as the filler of the cask and fuel assemblies. The thickness of the cask insulation with concrete is 0.5 and 1 m.

The data obtained as a result of the calculations show that, with an increase of concrete thickness from 0.5 m to 1 m, the fuel temperature increases by 42 K at FA power of 120 W and with filling the cask with argon and by 41 K when cask filling with air.

With increasing of the concrete thickness from 0.5 m to 1 m, fuel temperature increases by 66 K at FA power of 190 W and filling of the cask with argon and by 64 K when filling the cavity of the cask with air.

When cask filling with air instead of argon, the maximum temperature of the model will be reduced by ~54 K at FA power of 190 W and by ~37 K at FA power of 120 W.

It is also worth noting that the maximum value of the temperature is shifted from the center of FA for certain distance. When filling the cask with argon, the maximum temperature will be shifted by ~7 mm, if the gas medium is air, and then displacement will be ~11 mm. Maximal value of the fuel temperature exceeds the temperature of the central fuel element by no more than 3 K.

Maximal change in the material temperature in the fuel elements section is not more than 1 K. Since the thermal conductivity of the fuel element repeatedly exceeds the thermal conductivity of the gas medium, the temperature distribution over the cross-section of the cask is uneven.

#### 5. Conclusion

The temperature field in the average height of the cross-section of the cask with the fuel assemblies of BN-350 reactor for dry storage was determined as a result of the calculations.

Results of thermal calculation allow considering the optimum alternation for storage, where temperature of construction elements will have minimum value. Requirements for BN-350 SNF storage safety assume that as a result of passive cooling temperature of fuel element cladding will not exceed 673 K [10].

The calculated maximum fuel temperature is equal to 745 K, obtained in case of cask filling with argon with the concrete thickness of 1 m and FA power of 190 W.

The minimum temperature of the fuel among the considered calculation options is 516 K (the maximum in the model for this calculation option) was obtained in the case of cask filling with air, with concrete thickness of 0.5 m and FA power of 120 W.

When using air as cask filler instead of argon, the maximum temperature of the model will be reduced by ~54 K at FA power of 190 W and at ~37 K at FA power of 120 W, which is due to the higher conductivity of air compared to argon.

It is determined that the maximum temperature in FA is shifted to the center of the cask in the result of calculations. The temperature of the central fuel element is below the maximum temperature by ~3 K. If the cavity of the cask is filled with argon, the displacement of the maximum temperature from the FA axis to the center of the cask will be ~7 mm, if air is used as a gas medium, then displacement will be ~11 mm.

#### Data Availability

All data of this study are included within the article.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Authors’ Contributions

M.K. Skakov contributed to task definition; Ye. T. Koyanbayev collected baseline data for calculations; D. A. Ganovichev and Ye. A. Martynenko contributed to calculation; M. K. Skakov, А. А. Sitnikov, Ye. T. Koyanbayev, and D. A. Ganovichev contributed to result analysis and conclusions; Ye. T. Koyanbayev and D. A. Ganovichev are responsible for article writing; Ye. T. Koyanbayev, D. A. Ganovichev, and Ye. A. Martynenko provided feedback on reviewers’ comments.

#### Acknowledgments

The research was financially supported by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan for 2018 *«*Investigation of Structure Degradation and Material Properties of Standard SFA of BN-350 Reactor due to Irradiation and Long-Term Isothermal Effect*»* (Contract no. 71 dated 02.04.2018).