DOI: 10.55176/2414-1038-2021-4-131-146
Authors & Affiliations
Zborovskii V.G.1,2, Khoruzhii O.V.1,2, Likhanskii V.V.1,2, Elkin N.N.1, Chernetskii M.G.1
1 National Research Center “Kurchatov Institute”, Moscow, Russia
2 Lebedev Physical Institute of the Russian Academy of Science, Moscow, Russia
Zborovskii V.G. – Leading Researcher, Cand. Sci. (Phys.-Math.), Lebedev Physical Institute of the Russian Academy of Science, Senior Researcher, National Research Center “Kurchatov Institute”. Contacts: 1, Akademika Kurchatova pl., Moscow, 123182. Tel.: +7 (926) 569-38-48; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Khoruzhii O.V. – Leading Researcher, Dr. Sci. (Phys.-Math.).
Likhanskii V.V. – Head of the Department, Dr. Sci. (Phys.-Math.).
Elkin N.N. – Leading Researcher, Dr. Sci. (Phys.-Math.).
Chernetskii M.G. — Engineer.
Abstract
The paper describes the software module FRC-SCP intended for thermohydraulic simulation of a coolant under supercritical pressure (SCP) and a cooled fuel rod. Several designs of supercritical water reactors utilize the transition of the coolant from the pseudoliquid state to pseudogas while it is heated in the reactor core. SCP coolant under pseudophase transition exhibits specific behavior as its density changes significantly. Furthermore, coolant thermophysical properties (density, heat capacity, viscosity, thermal conductivity) can also vary across the coolant channel affecting heat transfer from the fuel rod to the coolant and consequently the fuel temperature. Existing feedback dependencies on coolant density and fuel temperature are important for the nuclear safety analysis of the reactor. The paper considers the present version of the FRC-SCP module. It implements the steady-state thermohydraulic channel solver to calculate coolant parameters: temperatures of the flow core and a heater, as well as coolant pressures, densities etc. User-specified correlations define the heat transfer law under the normal conditions. The module solves the thermal problem for the fuel rod consistently with the channel thermohydraulic problem. It is also possible to couple the FRC-SCP module with the neutron physical codes. Thermohydraulic module is tested against experiments on the heat transfer to SCP water in heated tubes. We discuss the behavior of the fuel cladding under conditions imitating the deteriorated heat transfer modes and the effect of the nuclear fuel thermal conductivity.
Keywords
coolant, fuel rod, nuclear fuel, cladding, supercritical pressure, pseudophase transition, thermohydraulic simulation, heat transfer coefficient, temperature field, experiments with heated tubes, deteriorated heat transfer modes
Article Text (PDF, in Russian)
References
- Kirillov P.L. Supercritical water cooled reactors. Thermal Engineering, 2008, vol. 55, issue 5, pp. 361–364.
- Guzonas D., Novotny R. Supercritical water-cooled reactor materials – Summary of research and open issues. Progress in Nuclear Energy, 2014, vol. 77, pp. 361–372.
- Novotny R., Guzonas D. Material research for the supercritical water-cooled reactor – summary and open issues. Nuclear Corrosion. Woodhead Publishing, 2020. Pp. 403–435. doi: https://doi.org/10.1016/B978-0-12-823719-9.00012-3.
- Kirillov P.L., Yur’ev Yu.S., Bobkov V.P. Spravochnik po teplogidravlicheskim raschetam (yadernyye reaktory, teploobmenniki, parogeneratory) [Handbook of thermal-hydraulic calculations (nuclear reactors, heat exchangers, steam generators)]. Moscow, Atomenergoizdat Publ., 1990. 360 p.
- Mikheev M.A., Mikheeva I.M. Osnovy teploperedachi [Fundamentals of heat transfer]. Moscow, Energiya Publ., 1977. 344 p.
- Kutateladze S.S. Teploperedacha i gidrodinamicheskoye soprotivleniye: Spravochnoye posobiye [Heat transfer and hydrodynamic resistance: handbook]. Moscow, Energoatomizdat Publ., 1990. 367 p.
- Deev V.I., Kharitonov V.S., Churkin A.N. Uchet peremennosti teplofizicheskikh svoystv teplonositelya v uravnenii teplootdachi k vynuzhdennomu potoku vody sverkhkriticheskogo davleniya [Taking into account the variability of the thermophysical properties of the coolant in the equation of heat transfer to the forced flow of supercritical pressure water]. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta “MIFI” – Bulletin of the National Research Nuclear University “MEPhI”, 2014, vol. 3, no. 3, p. 353.
- Löwenberg M.F. Wärmeübergang von Wasser in vertikalen Rohrströmungen bei überkritischem Druck. Diss. Karlsruhe: FZKA, 2007. 179 p. Available at: https://elib.uni-stuttgart.de/bitstream/11682/1749/1/Dissertation_M_Loewenberg.pdf (accessed 17.11.2021).
- Loewenberg M.F. et al. Supercritical water heat transfer in vertical tubes: A look-up table. Progress in Nuclear Energy, 2008, vol. 50, no. 2–6, pp. 532–538.
- Kurganov V.A. Teploobmen i soprotivleniye v trubakh pri sverkhkriticheskikh davleniyakh teplonositelya. Ch. 1. Osobennosti teplofizicheskikh svoystv zhidkosti, gidrodinamiki i teploobmena. Rezhimy normal'noy teplootdachi [Heat transfer and pressure drop in tubes under supercritical pressure. Part 1: Specifics of the thermophysical properties, hydrodynamics, and heat transfer of the liquid. Regimes of normal heat transfer]. Teploenergetika – Thermal Engineering, 1998, vol. 45, issue 3, pp. 2–10.
- Kurganov V.A., Maslakova I.V. An integral method of calculation of stabilized heat transfer in tubes in single-phase near-critical region. High Temperature, 2010, vol. 48, no. 4, pp. 541–554.
- Kurganov V.A., Maslakova I.V. Normal and deteriorated heat transfer upon heating of turbulent flows of heat carriers with variable physical properties in tubes. High Temperature, 2016, vol. 54, no. 4, pp. 577–598.
- 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.
- 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.
- Kurganov V.A., Zeigarnik Y.A., Maslakova I.V. Heat transfer and hydraulic resistance of supercritical pressure coolants. Part III: Generalized description of SCP fluids normal heat transfer, empirical calculating correlations, integral method of theoretical calculations. International Journal of Heat and Mass Transfer, 2013, vol. 67, pp. 535–547.
- Kurganov V.A. Heat transfer and pressure drop in tubes under supercritical pressure. Part 2. Heat transfer and friction at high heat fluxes. The influence of additional factors. Enhancement of deteriorated heat transfer. Thermal engineering, 1998, vol. 45, no. 4, pp. 301–310.
- Kurganov V.A., Zeigarnik Y.A., Maslakova I.V. Heat transfer and hydraulic resistance of supercritical pressure coolants. Part IV: Problems of generalized heat transfer description, methods of predicting deteriorated heat transfer; empirical correlations; deteriorated heat transfer enhancement; dissolved gas effects. International Journal of Heat and Mass Transfer, 2014, vol. 77, pp. 1197–1212.
- Valueva E.P. Numerical modeling of heat exchange and turbulent flow of fluid within tubes at supercritical pressure. High Temperature, 2012, vol. 50, no. 2, pp. 278–285.
- Deev V.I., Rachkov V.I., Kharitonov V.S., Churkin A.N. Analysis of relations for calculating normal heat transfer to supercritical pressure water flow in vertical tubes. Atomic Energy, 2016, vol. 119, no. 3, pp. 169–176.
- Deev V.I., Kharitonov V.S., Baisov A.M., Churkin A.N. Universal dependencies for the description of heat transfer regimes in turbulent flow of supercritical fluids in channels of various geometries. The Journal of Supercritical Fluids, 2018, vol. 135, pp. 160–167.
- 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.
- Wang H., Bi Q.C., Wang L., Lv L., Leung L.K.H. Experimental investigation of heat transfer from a 2×2 rod bundle to supercritical pressure water. Nucl. Eng. Des., 2014, vol. 275, pp. 205–218.
- Wang H., Bi Q., Ni Z., Lv H., Gui M. Experiments of heat transfer to supercritical water in a 2×2 rod bundle with wire-wrapped spacers. Proc. 7th International Symposium on Supercritical Water Cooled Reactors (ISSCWR-7). Helsinki, Finland, March 15–18, 2015, paper 2060.
- Wang H., Bi Q.C., Leung L.K.H. Heat transfer from a 2×2 wire-wrapped rod bundle to supercritical pressure water. Int. J. Heat Mass Transf., 2016, vol. 97, pp. 486–501.
- Gu H.Y., Hu Z.X., Liu D., Xiao Y., Cheng X. Experimental studies on heat transfer to supercritical water in 2×2 rod bundle with two channels. Nucl. Eng. Des., 2015, vol. 291, pp. 212–223.
- Hu Z.X., Li H.B., Tao J.Q., Liu D., Gu H.Y. Experimental study on heat transfer of supercritical water flowing upward and downward in 2×2 rod bundle with wrapped wire. Ann. Nucl. Energy. 2018, vol. 111, pp. 50–58.
- Churkin A.N. Neodnoznachnost' temperatury obogrevayemoy stenki v potoke zhidkosti sverkhkriticheskogo davleniya [An ambiguity of the heated wall temperature in a supercritical pressure fluid flow]. Voprosy atomnoy nauki i tekhniki. Seriya: Obespecheniye bezopasnosti AES. Reaktornyye ustanovki s VVER – Problems of Atomic Science and Technology. Series: NPP Safety Assurance. Reactor Plants with WWER, 2011, vol. 30, pp. 122–125.
- Churkin A.N., Deev V.I. Neodnoznachnost' rezul'tatov rascheta teplootdachi k vode pri ispol'zovanii empiricheskikh korrelyatsiy v oblasti sverkhkriticheskikh davleniy [Ambiguity of the results of calculating heat transfer to water using empirical correlations in the region of supercritical pressures]. Voprosy atomnoy nauki i tekhniki. Seriya: Obespecheniye bezopasnosti AES. Reaktornyye ustanovki – Problems of Atomic Science and Technology. Series: NPP Safety Assurance. Reactor Plants, 2012, vol. 32, pp. 65–75.
- Wolery T.J. H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water (Rev. 1), LLNL-TR-805304, May 18, 2020.
- IAPWS R6-95(2018). Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, September 2018. Available at: http://www.iapws.org/release.html (accessed 17.11.2021).
- IAPWS R12-08. Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance, September 2008. Available at: http://www.iapws.org/release.html (accessed 17.11.2021).
- IAPWS R15-11. Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance, September 2011. Available at: http://www.iapws.org/release.html (accessed 17.11.2021).
- Pernice M., Walker H.F. NITSOL: A Newton Iterative Solver for Nonlinear Systems. SIAM J. Sci. Comput., 1998, vol. 19(1), pp. 302–318.
- Forsythe G.E., Malcolm M.A., Moler C.B. Computer methods for mathematical computations. Prentice Hall, 1977. 259 p.
- Samarskii A.A., Andreev V.B. Raznostnyye metody dlya ellipticheskikh uravneniy [Difference methods for elliptic equations]. Moscow, Nauka Publ., 1976. 352 p.
- Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D. LAPACK Users' Guide. 3rd ed. SIAM, Philadelphia, PA, 1999.
- Ierusalimschy R., de Figueiredo L.H., Celes W. Lua 5.1 Reference Manual. Available at: https://www.lua.org/manual/5.1/ (accessed 17.11.2021).
- Zborovskii V. Lua (and Fortran) in thermomechanical simulations. Lua Workshop 2018, Kaunas, Lithuania, 2018. Available at: https://www.lua.org/wshop18/Zborovskii.pdf (acccessed 17.11.2021).
- The HDF Group. Hierarchical Data Format, version 5. Available at: http://www.hdfgroup.org/HDF5/ (accessed 17.11.2021).
- Shitsman M.E. Ukhudshennyye rezhimy teplootdachi pri zakriticheskikh davleniyakh [Impairment of the heat transmission at supercritical pressures]. Teplofizika vysokikh temperatur – High Temperature, 1963, vol. 1, pp. 237–244.
- 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 9th ISTC “Safety of NPP with WWER”]. Podol'sk, 2015. Available at: http://www.gidropress.podolsk.ru/files/proceedings/mntk2015/autorun/article114-ru.htm (accessed 11/17/2021).
- 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 (accessed 17.11.2021).
- 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.
- 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 (accessed 17.11.2021).
- Blinkov V.N., Gabaraev B.A., Melikhov O.I., Soloviev S.L. Nereshennyye problemy teplo- i massoobmena vodookhlazhdayemykh reaktornykh ustanovok so sverkhkriticheskimi parametrami teplonositelya [Unsolved problems of heat and mass transfer in water-cooled reactors with supercritical parameters of a coolant]. Moscow, NIKIET Publ., 2008. 85 p.
- Kurganov V.A., Zeigarnik Yu.A., Yan’kov G.G., Maslakova I.V. Teploobmen i soprotivleniye v trubakh pri sverkhkriticheskikh davleniyakh teplonositelya: itogi nauchnykh issledovaniy i prakticheskiye rekomendatsii [Heat transfer and friction in tubes under supercritical pressures of a coolant: results of scientific studies and practical guidelines]. Moscow, “Shans” Ltd. Publ., 2018. 302 p.
- Grabezhnaya V.A., Kirillov P.L. Heat-transfer degradation boundary in supercritical-pressure flow. Atomic Energy, 2006, vol. 101, issue 4, pp. 714–721.
UDC 621.039.546:536.24
Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2021, issue 4, 4:12
