# Development of the model to determine the fuel temperature field in a two-dimensional problem statement

6/24/2019 2019 - #02 Modelling processes at nuclear facilities

Gorbunov V.A. Ivanova N.B. Lonshakov N.A. Belov Ya.V.

https://doi.org/10.26583/npe.2019.2.15

### UDC: 621.039.517.5; 004.942

Water-cooled water-moderated reactors (VVER) are widely used at Russian nuclear power plants. The VVER reactor core is formed by fuel assemblies consisting of fuel rods. The fuel in fuel rods is uranium dioxide. The safety of the reactor operation is ensured through stringent requirements for the maximum nuclear fuel temperature. Calculation of temperature fields within the reactor core requires associated problems to be solved to determine the internal energy release in fuel based on neutronic characteristics. Dedicated software for such calculations is not accessible to a broad range of users. At the present time, there are numerical thermophysical modeling packages available for training or noncommercial applications which are used extensively, including Elcut, Flow Vision, Ansys Fluent, and Comsol Multiphysics. Verification of the obtained results is becoming an important issue in building models using these calculation packages. An analytical solution was obtained as part of the study for the fuel temperature field determination. A program was developed in MathCAD based on this solution. A model was developed in Comsol Multiphysics to determine the fuel temperature field with constant thermophysical properties in a two-dimensional problem statement. The numerical model was verified using the analytical solution. The influence of the number of the grid nodes on the solution accuracy was established. The analytical solution can be used to determine the fuel temperature field at any radial coordinate of the reactor.

The temperature field determination model developed in MathCAD can be used to verify numerical models of the fuel temperature field determination developed in dedicated packages.

### References

- Perimov R.R., Sorokin G.A., Sorokina T.V. Modeling of thermal-mechanical reliability of the fuel rod with different variants of change of energy; guideline and temperatures. Promyshlennaya teplotekhnika. 2004, v. 26, iss. 5, pp. 150-153 (in Russian).
- Kolpakov G.N., Selivanikova O.V. Designs of Fuel Rods, Channels and Cores of Power Reactors. Tomsk. Tomskij Politihnicheskij Universitet Publ., 2009, 118 p. (in Russian).
- Dement’ev B. A. Nuclear Power Reactors. Moscow. Energoatomizdat Publ., 1990, 352 p. (in Russian).
- Dolgov A. Effective fuel solutions using SNF reprocessing. International Forum «AtomExpo», Moscow, JSC «Tvel», May 31, 2016.
- Leskin S.T., Shelegov A.S., Slobodchuk V.I. Physical features and design of the VVER-1000 reactor. Moscow. NIYaU MIFI Publ., 2011, 116 p. (in Russian).
- Golcev A.O, Davydova G.B., Davidenko V.D. The Influence of depression of the neutron flux in the RBMK cell on the magnitude of the maximum and average fuel temperature. Izvestiya Tomskogo politekhnicheskogo universiteta. 2009, v. 314, iss. 4, pp. 5-7 (in Russian).
- Zhukov A. V., Kuzina Y.A., Sorokin A.P. Systematization of Research of Heat Exchange in Fuel Rod Assemblies and Some Tasks of Liquid Metal Cooling. Izvestia Vysshikh Uchebnykh Zawedeniy. Yadernaya Energetika. 2009, no. 4, pp. 95-108 (in Russian).
- Batenin V.M., Beljaev I.A., Listratov J.I. Features of heat exchange of heavy liquid metal in nuclear power plants of new generation]. Proc. of the XIIIth International Scientific and Practical Conference on Atomic Energy «Bezopasnost’, Effektivnost’, Resurs». Sevastopol’. SevNTU Publ., 2017, pp. 79-81 (in Russian).
- Design Codes of New Generation. Available at: http://www.ibrae.ac.ru/contents/68/ (accessed Jun 10, 1018) (in Russian).
- Vishnyakova A.D., Gulina O.M., Salnikov N.L. The possibility of using the neural network apparatus for predicting erosion and corrosion wear of NPP equipment. Izvestia Vysshikh Uchebnykh Zawedeniy. Yadernaya Energetika. 2015, no. 4, pp. 61-71 (in Russian).
- Velesjuk A., Morgunov I. CFDs-codes: problems and prospects in nuclear power engineering. Atomnyj Ekspert. Appendix to Atomnaya Energiya. 1990, no. 8, pp. 37-39 (in Russian).
- Agranat V., Malin M., Pioro I., Abdullah R., Perminov V.A. CFD Modelling of Supercritical Water Heat Transfer in a Vertical Bare Tube Upward Flow. Proc. of the ICONE-23, May 17-21, Chiba, Japan, 2015. Paper 1163. 11 p.
- Kartashov K.V., Bogoslovskaya G. P. Calculations for optimization of geometric and regime parameters of VVER-SKD fuel assemblies for different operating modes of the reactor at supercritical water parameters. Izvestia Vysshikh Uchebnykh Zawedeniy. Yadernaya Energetika. 2012, no. 2, pp. 3-11.
- Ushakov P.A., Subbotin V.I. Approximate calculations of hydrodynamic characteristics of turbulent fluid flow in ring channels. Teplofizika Vysokikh Temperatur. 1972, v. 10, no. 5, pp. 1025-1030 (in Russian).
- Loginov V.S. Approximate Methods of Thermal Calculation of Active Elements of Electrophysical Installations. Moscow. Fizmatlit Publ., 2009, 273 p. (in Russian).
- Starkov V.A., Marihin N.Yu. Method and program of calculation of stationary temperature field in the system of multi-zone cylindrical fuel rods. Izvestia Vysshikh Uchebnykh Zawedeniy. Yadernaya Energetika. 2013, no. 1, pp. 54-62 (in Russian).
- Scherbakova T.S., Gorbunov, V.A. The study of problems of accuracy of the solution with boundary conditions of 2nd kind of heating in the multipurpose computing complex of Phoenics. Proc. of the All-Russian Student Olympiad, Scientific and Practical Conference and Exhibition of Students, Postgraduates and Young Scientists «Energo- i resursosberezhenie, energoobespechenie, netraditsionnye i vozobnovlyaemye istochniki energii». Ekaterinburg. UGTU-UPI Publ., pp. 174-175 (in Russian).
- Gorbunov V.A. Predicting the accuracy of results in solving heat transfer problems based on neural network technologies. Promyshlennaya Energetika. 2011, no. 8, pp. 48-52 (in Russian).
- Gorbunov V.A. Experience in using the software complex at Ivanovo state power engineering University n.a. V.I. Lenin. ANSYS Advantage (Russkaya Redaktsiya). 2011, no. 15, pp. 38-39 (in Russian).
- Palmer L.D., Swanson L.L. Measurements of Heat Transfer coefficients, Friction Factors and Velocity Profiles for Air Flowing Parallel to Closely Spaced Rods. Proc. of the Conf. of ASME, AIChE and Inst. Ch. E. on Internat. Developments in Heat Transfer. ASME, part 3, August 1961, pp. 535-542.

fuel rod fuel temperature field analytical solution mathematical model to determine fuel temperature fields verification of numerical calculations influence of tuning coefficients safety of fuel rod heating