Zborovskii V.G.1,2, Khoruzhii O.V.1,2, Likhanskii V.V.1,2, Elkin N.N.1, Chernetskii M.G.1, Averchenko P.A.1,3, Grachev D.S.1,3, Khorokhorin M.V.1,3, Belousov V.I.1, Davidenko V.D.1, Dachkov I.I.1, Ioanissian M.V.1, Malkov M.R.1
The paper deals with extended validation of the FRC-SCP module and its coupling to the neutron transport code KIR. The software module FRC-SCP performs thermohydraulic simulation of a coolant under supercritical pressure (SCP) and a cooled fuel rod. The software package KIR solves accurately steady-state and time-dependent neutron transport equations using Monte Carlo method. SCP coolant under pseudophase transition exhibits specific behavior as its density and heat transfer coefficient change significantly. Existing feedback dependencies on coolant density and fuel temperature are important for the nuclear safety analysis of the reactor. To solve thermohydraulic and neutron transport problems consistently the codes FRC-SCP and KIR are combined into the KIR-TH complex. We discuss various iteration procedures to solve the coupled problems. Iterations involve heat generation profile as well as thermal state of a fuel rod and a coolant including its density. Test calculations for a fuel rod cooled by SCP water show that the KIR-TH complex is capable of coupled thermal and neutron transport simulation. The paper also covers the Grass heat transfer correlation which is built upon physical considerations and its application to heat transfer analysis. We present the extended validation against experiments on the heat transfer to SCP water in heated tubes for various thermal parameters. It shows a good agreement between calculations and measurements under normal heat transfer conditions when Kurganov, Deev, or Grass correlations are used. The study reveals the possibility of consistent thermal and neutron simulation for SCP water reactor including the conditions of pseudophase transition.
1. Kirillov P.L. Supercritical water cooled reactors. Thermal Engineering, 2008, vol. 55, pp. 361–364.
2. Kirillov P.L. Vodookhlazhdayemyy reaktor VVER SKD (predvaritel'nyye razrabotki) [Water Cooled Reactor VVER SCP (preliminary elaboration)]. Izvestiya vuzov. Yadernaya Energetika, 2013, no. 1, pp. 5–14. DOI: https://doi.org/10.26583/npe.2013.1.01.
3. Kurganov V.A. Teploobmen v trubakh pri sverkhkriticheskikh davleniyakh teplonositelya: nekotoryye itogi nauchnogo issledovaniya [Heat exchange in pipes at supercritical heat carrier pressures: some results of scientific research]. Trudy RNKT-4 [Proc. of RNKT-4]. Moscow, 2006, vol. 1, pp. 74–83.
4. Makhin V.M., Churkin A.N. Kontseptual'nyye predlozheniya po vodookhlazhdayemomu reaktoru so sverkhkriticheskimi parametrami (obzor zarubezhnykh i rossiyskikh razrabotok SCWR) [Conceptual proposals on supercritical water-cooled reactor (review of foreign and Russian SCWR designs)]. Voprosy atomnoy nauki i tekhniki. Seriya: Fizika yadernykh reaktorov – Problems of Atomic Science and Engineering. Series: Physics of Nuclear Reactors, 2017, issue 1, pp. 48–65.
5. Oka Y. Research and development of the supercritical pressure light water cooled reactors. Proc. of the 10th Intern. Topical Meeting on Nuclear Thermal Hydraulics (NURETH-10). Seoul, Korea, October 5–9, 2003, Paper KL-02.
6. Zborovskii V.G., Khoruzhii O.V., Likhanskii V.V., Elkin N.N., Chernetskii M.G. Raschotnyy modul' dlya opredeleniya fizicheskikh parametrov v kanale reaktora s teplonositelem zakriticheskogo davleniya [Software module for calculating thermophysical parameters in hydraulic channels of supercritical water reactor]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2022, issue 4, pp. 131–146. DOI: http://doi.org/10.55176/2414-1038-2021-4-131-146.
7. Davidenko V.D., Zinchenko A.S., Harchenko I.K. Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method. Physics of Atomic Nuclei, 2016, vol. 79, pp. 1252–1256. DOI: https://doi.org/10.1134/S106377881708004X.
8. Gomin E.A., Davidenko V.D., Zinchenko A.S., Harchenko I.K. Calculation of the neutron importance function and the delayed neutron effective fraction by the Monte Carlo method. Physics of Atomic Nuclei, 2017, vol. 80, pp. 1392–1398. DOI: https://doi.org/10.1134/S1063778817080051.
9. Gomin E.A., Davidenko V.D., Zinchenko A.S., Harchenko I.K. Calculation of prompt fission neutron lifetimes by the Monte Carlo method. Physics of Atomic Nuclei, 2017, vol. 80, pp. 1387–1391. DOI: https://doi.org/10.1134/S106377881708004X.
10. Gomin E.A., Davidenko V.D., Zinchenko A.S., Harchenko I.K. Simulation of nuclear reactor kinetics by the Monte Carlo method. Physics of Atomic Nuclei, 2017, vol. 80, pp. 1399–1407. DOI: https://doi.org/10.1134/S1063778817080063.
11. Grass G., Herkenrath H., Hufschmidt W. Anwendung des Prandtlschen Grenzschichtmodells auf den Wärmeübergang an Flüssigkeiten mit stark temperaturabhängigen Stoffeigenschaften bei erzwungener Strömung. Warme- und Stoffubertragung, 1971, Bd. 4, S. 113–119 (1971). DOI: https://doi.org/10.1007/BF01929761.
12. Petukhov B.S., Genin L.G., Kovalev S.A., Soloviev S.L. Teploobmen v yadernykh energeticheskikh ustanovkakh [Heat transfer in nuclear power plants]. Moscow, MEI Publ., 2003. 548 p.
13. Grabezhnaya V.A., Kirillov P.L. Heat-transfer degradation boundary in supercritical-pressure flow. Atomic Energy, 2006, vol. 101, issue 4, pp. 714–721. DOI: https://doi.org/10.1007/s10512-006-0158-5.
14. Deev V.I., Kharitonov V.S., Baisov A.M., Churkin A.N. Heat transfer in rod bundles cooled by supercritical water – Experimental data and correlations. Thermal Science and Engineering Progress, 2020, vol. 15, p. 100435. DOI: https://doi.org/10.1016/j.tsep.2019.100435.
15. Shitsman M.E. Ukhudshennyye rezhimy teplootdachi pri zakriticheskikh davleniyakh [Deterioration of the heat transfer at supercritical pressures]. Teplofizika vysokikh temperatur – High Temperature, 1963, vol. 1, pp. 237–244.
16. Kirillov P.L, Terent’eva M.I., Bogoslovskaja G.P., Churkin A.N. Banki eksperimental'nykh dannykh po teplootdache k potoku vody sverkhkriticheskogo davleniya v trube [Experimental data banks on heat transfer to the supercritical pressure water flow in a pipe]. Sb. Trudy 9-y MNTK “Obespecheniye bezopasnosti AES s VVER” [Proc. of the 9 th ISTC “Safety of NPP with WWER”]. Podol'sk, 2015. Available at: http://www.gidropress.podolsk.ru/files/proceedings/mntk2015/autorun/article114-ru.htm.
17. Mokry S., Pioro I., Kirillov P., Gospodinov Y. Supercritical-water heat transfer in a vertical bare tube. Nuclear Engineering and Design, 2010, vol. 240, issue 3, pp. 568–576. DOI: https://doi.org/10.1016/j.nucengdes.2009.09.003.
18. Kirillov P., Pomet'ko R., Smirnov A., Grabezhnaia V., Pioro I., Duffey R., Khartabil H. Experimental study on heat transfer to supercritical water flowing in 1- and 4-m-long vertical tubes. Proc. of GLOBAL 2005 Int. Conf. on Nuclear energy systems for future generation and global sustainability. Tsukuba, Japan, 2005, Paper No. 518.
19. Mokry S., Pioro I., Farah A., King K., Gupta S., Peiman W., Kirillov P. Development of supercritical water heat-transfer correlation for vertical bare tubes. Nuclear Engineering and Design, 2011, vol. 241, issue 4, pp. 1126–1136. DOI: https://doi.org/10.1016/j.nucengdes.2010.06.012.
20. Pis’menny E.N., Razumovskiy V.G., Maevskiy E.M., Koloskov A.E., Pioro I.L. Heat transfer to supercritical water in gaseous state or affected by mixed convection in vertical tubes. Proc. of ICONE14 Int. Conf. on Nuclear Engineering. Miami, Florida, USA, 2016, ICONE14-89483, pp. 523-530. Available at: https://asmedigitalcollection.asme.org/ICONE/proceedings-abstract/ICONE14/42436/523/315859.
21. Yamagata K., Nishikawa K., Hasegawa S., Fujii T., Yoshida S. Forced convective heat transfer to supercritical water flowing in tubes. International journal of heat and mass transfer, 1972, vol. 15, no. 12, pp. 2575–2593.
22. Understanding and prediction of thermohydraulic phenomena relevant to supercritical water cooled reactors (SCWRs). Final report of a coordinated research project. IAEA-TECDOC-1900, Vienna, 2020. 546 p. Available at: https://www-pub.iaea.org/MTCD/publications/PDF/TE-1900web.pdf.
23. Pernice M., Walker H.F. NITSOL: a Newton iterative solver for nonlinear systems. SIAM J. Sci. Comput., 1998, vol. 19(1), pp. 302–318. DOI: https://doi.org/10.1137/S1064827596303843.
24. Valtavirta V. Development and applications of multi-physics capabilities in a continuous energy Monte Carlo neutron transport code. Doctoral dissertaion. Helsinki, Finland, 2017. 172 p. Available at: http://montecarlo.vtt.fi/download/S150.pdf.
