Mathematical and Computer Modeling of the Forms of Multi-Zone Fuel Elements with Plates

Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 25, no. 4, 2022 (December)
Pages 32-38
Cited by J. of Mech. Eng., 2022, vol. 25, no. 4, pp. 32-38



Kyrylo V. Maksymenko-Sheiko, A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), e-mail:, ORCID: 0000-0002-7064-2442

Tetiana I. Sheiko, A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), e-mail:, ORCID: 0000-0003-3295-5998

Denys O. Lisin, V. N. Karazin Kharkiv National University (4, Svobody sq., Kharkiv, 61022, Ukraine), e-mail:, ORCID: 0000-0002-6718-7389

Nykyta D. Petrenko, A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), ORCID: 0000-0002-4631-9020



Seeing the significant increase in the number of nuclear power plants, as well as models and modifications of nuclear reactors, it becomes important to find out/establish the advantages of certain plants. At the same time, designers face a number of questions for which optimal solutions have not yet been found. At nuclear plants, there is the largest turnover of financial funds and the smallest gain in economy brings huge profits, but one should not forget about reliability and costs during the plant construction. This is a complex problem that is solved at the design stage. Calculations of the reactor at the design stage make it possible to determine the main parameters of the active zone, temperature values, etc. Thermohydraulic calculation of the active zone of the reactor is one of the cornerstones in justifying the safe operation of the nuclear power plant. Calculations of coolant parameters and temperatures of fuel elements are carried out at all stages of designing and proving the safety of nuclear power plants. Twisted pipes and finned heat transfer surfaces are widely used in engineering to increase the effective heat transfer coefficient. In particular, longitudinal, transverse, and spiral edges are used for finning the shells of fuel elements of nuclear reactors and the outer surfaces of steam generator pipes. Finning not only increases the heat transfer surface on the side where the heat transfer coefficient has a low value, but also significantly affects the hydrodynamics of the flow, and thus affects this coefficient. It is obvious that the better the medium is mixed in the main flow and in the intercoral zone, the higher the heat transfer coefficient is. The most profitable forms of fuel elements shells finning are chevron and polyzonal finning, which are performed in the form of a multiturn spiral with a large step. The R-function theory turned out to be quite convenient for building mathematical models of finned shells of fuel elements with straight and helical plates, as well as for building the corresponding objects on a 3D printer. From a practical point of view, the relevance of the problem is also determined by the significant spread of twisted cylindrical bodies, twisted channels, coils in the energy, chemical, oil, gas, metallurgical industries and in heat engineering equipment. The flows that arise at this time make it possible to intensify the processes of heat and mass exchange and achieve savings in energy resources.


Keywords: shells of fuel elements, fuel elements with chevron and polyzonal finning, R-function theory, 3D printer.


Full text: Download in PDF



  1. Petukhov, B. S., Genin, L. G., & Kovalev, S. A. (1974). Teploobmen v yadernykh energeticheskikh ustanovkakh [Heat exchange in nuclear power plants]. Moscow: Atomizdat, 367 p. (in Russian).
  2. Andreyev, P. A., Gremilov, D. I., & Fedorovich, Ye. D. (1969). Teploobmennyye apparaty yadernykh energeticheskikh ustanovok [Heat exchangers of nuclear power plants]. Leningrad: Sudostroyeniye, 352 p. (in Russian).
  3. Antufyev, V. M. (1966). Effektivnost razlichnykh form konvektivnykh poverkhnostey nagreva [Efficiency of various forms of convective heating surfaces]. Moscow, Leningrad: Energiya, 184 p. (in Russian).
  4. Rvachev, V. L. (1982). Teoriya R-funktsiy i nekotoryye yeye prilozheniya [The R-functions theory and some of its applications]. Kyiv: Naukova dumka, 552 p. (in Russian).
  5. Maksimenko-Sheyko, K. V. (2009). R-funktsii v matematicheskom modelirovanii geometricheskikh obyektov i fizicheskikh poley [R-functions in the mathematical modeling of geometric objects and physical fields]. Kharkiv: IPMash NAS of Ukraine, 306 p. (in Russian).
  6. Choporov, S. V., Gomenyuk, S. I., Lisnyak, A. A., Al’-Omari, M. A. V., & Alatamnekh, Kh. Kh. (2016). Triangulyatsiya poverkhnostey pri gibridnom parametricheskom i neyavnom predstavlenii [Surface triangulation using hybrid parametric and implicit representation]. Vestnik Khersonskogo natsionalnogo tekhnicheskogo universitetaBulletin of Kherson National Technical University, no. 3 (58), pp. 542–549 (in Russian).
  7. Maksymenko-Sheiko, K. V., Sheyko, T. I., Lisin, D. O., & Dudinov, T. B. (2022). Mathematical and computer modeling of convective heat transfer in fuel cartridges of fuel elements with different shapes and packing of rods. Journal of Mechanical Engineering – Problemy Mashinobuduvannia, vol. 25, no. 1, pp. 40–54.
  8. Lisin, D. O. (2012). Kompiuterna prohrama “Systema vizualizatsii ta pobudovy sitky na poverkhni heometrychnykh obiektiv, yaki opysani za dopomohoiu matematychnykh zasobiv teorii R-funktsii “RFPreview” [Computer program “System of visualization and construction of a grid on the surface of geometric objects, which are described by mathematical means of the theory of R-functions “RFPreview”]: Certificate of registration of copyright to the work no. 45951 (in Ukrainian).


Received 13 November 2022

Published 30 December 2022