Vertikov E.A.1, Zubkov A.G.1, Oleksyuk D.A.1, Baisov A.M.2, Bosenko S.V.2, Churkin A.N.2
 1 National Research Centre “Kurchatov Institute”, Moscow, Russia
2 Experimental and Design Organization “GIDROPRESS”, Podolsk, Russia
Vertikov E.A. — Engineer. Contacts: 1, pl. Akademika Kurchatova,  Moscow, Russia, 123182. Tel.: +7 (985) 191-60-16; e-mail: 
 Zubkov A.G. – Researcher.
 Oleksyuk D.A.  – Head of Department, Cand. Sci. (Tech.).
 National Research Centre “Kurchatov  Institute”.
 Baisov A.M. – 1st Category Design Engineer, Cand. Sci. (Tech.).
 Bosenko S.V. – 1st  Category Design Engineer.
 Churkin A.N. – Head of the Department, Cand. Sci. (Tech.), Experimental and Design Organization “GIDROPRESS”.
Abstract
At present, thermal-hydraulic codes using the subchannel method of modeling coolant flow within rod bundles are the main means of substantiating the thermal reliability of nuclear reactor cores under steady-state operating conditions. The article gives an overview of the existing Russian subchannel thermal-hydraulic codes developed and used in various organizations of the nuclear industry for reactors with water coolant: SC-1, SC-INT and SC-Core (NRC “Kurchatov Institute”), PUCHOK-1000, TIGRSP, TEMPA-1F and TEMPA-SK (OKB GIDROPRESS JSC), KANAL (JSC “Afrikantov OKB Mechanical Engineering”), VYAZ-M, MIF-SKD (IPPE JSC). For each code a brief history of development is given, as well as the key features in terms of numerical methods used, the field of application and availability of certification passport. Questions about the interaction of computational tools using the subchannel approximation with codes that have a different scale of modeling the computational domain are discussed. As a part of system thermal-hydraulic codes, the subchannel method can be used as an additional module for detailed calculation of the core, which will allow to reasonably reduces the degree of conservatism in determining the departure from nucleate boiling ratio within the framework of modeling transient and emergency processes in comparison with the “hot channel” approximation. Computational fluid dynamics codes, which allow three-dimensional modeling of coolant flow, can be used, firstly, to clarify existing and create new closing relations for calculation of friction coefficients, local hydraulic coefficients and turbulent mixing efficiency, which are put into subchannel codes, and, secondly, to obtain boundary conditions for distribution of coolant flow rate by fuel assemblies at the inlet of the core. In order to improve the quality of description of heat and mass transfer processes in smooth rod bundles taking into account the presence of spacer and intensifier grids as further ways to improve subchannel codes, the following necessities are emphasized: expansion of the validation database, transition to a two-fluid description of the flow of two-phase flows and realization of the possibility of full-scale calculation of cores.
Keywords
heat and mass transfer,  subchannel method, calculation codes, VVER, core, fuel assembly, smooth rod  bundles
Article Text (PDF, in Russian)
- Bestion D. et al. Multi-Scale Thermalhydraulic Analyses Performed in NURESIM and NURISP Projects. Proc. of the 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference. Anaheim, California, USA, 2012, pp. 581–590. DOI: 10.1115/ICONE20-POWER2012-54891.
- Sorokin A.P., Bogoslovskaya G.P. Metody teplogidravlicheskikh raschetov teplovydelyayushchikh sborok aktivnoy zony bystrykh reaktorov [Methods of thermal-hydraulic calculations of fuel assemblies of the active zone of fast reactors]. Teploenergetika – Thermal Engineering, 1997, no. 3, pp. 21–26.
- Vasilenko V.A., Migrov Yu.A., Semakin S.G., Kasterin D.S., Mickevich A.V. Napravleniya razvitiya sistemnykh teplogidravlicheskikh raschetnykh kodov novogo pokoleniya [Directions for the development of new-generation system thermal-hydraulic calculation codes]. Tekhnologii obespecheniya zhiznennogo tsikla yadernykh energeticheskikh ustanovok – Technologies for ensuring the life cycle of nuclear power plants, 2022, no. 1 (27), pp. 54–72. DOI: 10.52069/2414-5726_2022_1_27_54.
- Asmolov V.G., Blinkov V.N., Melihov V.I., Melihov O.I., Parfenov Yu.V., Emel'yanov D.A., Kiselev A.E., Dolganov K.S. Current state of system thermohydraulic codes and trends in their development abroad. High Temp, 2014, vol. 52, issue 1, pp. 98–109. DOI: https://doi.org/10.1134/S0018151X14010027.
- Semenovich O.V. Analiz subkanal'nyh modelej termogidrodinamicheskogo raschyota sterzhnevyh TVS: klassifikaciya i tendencii razvitiya [Analysis of subchannel models of thermohydrodynamic calculation of rod fuel assemblies: classification and development trends]. Preprint OIEYAI-Sosny-40 NAN Belarusi – Preprint of JIPNR-Sosny-40 NAS of Belarus. Minsk, 2009. 36 p.
- Sorokin A.P., Kuzina Yu.A., Sorokin G.A., Denisova N.A. Modelirovaniye protsessov teplo- i massoobmena v TVS bystrykh reaktorov v ramkakh pokanal'nogo metoda rascheta. Obobshchennyye kharakteristiki obmena dlya odnofaznykh potokov zhidkikh metallov [Modeling of heat and mass transfer processes in fuel assemblies of fast reactors as part of the channel-by-channel calculation method. Generalized exchange characteristics for single-phase flows of liquid metals]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2020, no. 2, pp. 104–130.
- Sorokin A.P., Kuzina Yu.A., Denisova N.A. Gidrodinamika i teploobmen v TVS aktivnoy zony bystrykh reaktorov s spiral'nymi provolochnymi navivkami na tvelakh [Experimental studies internals hydraulic processes with coolant stratification in primary circuit of the fast reactors with an integrated equipment arrangement in various operating regimes]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2022, no. 1, pp. 181–209.
- Zalesov A.S. Gidrodinamika i teploobmen v TVS aktivnoy zony bystrykh reaktorov s spiral'nymi provolochnymi navivkami na tvelakh [Simulation by the MATADOR code for heat and mass transfer processes in fuel assemblies of fast reactors with wire wrapped spacing]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2024, no. 3, pp. 224–237.
- Vertikov E.A., Oleksyuk D.A., Zubkov A.G., Malyutin M.A. K voprosu o validatsii poyacheykovykh kodov dlya rascheta aktivnykh zon reaktorov tipa VVER [On the Issue of Validation of Subchannel Codes for Calculating of the VVER Type Reactors Core]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2025, no. 1, pp. 232–244.
- Moorthi A., Sharma A.K., Velusamy K. A review of sub-channel thermal hydraulic codes for nuclear reactor core and future directions. Nuclear Engineering and Design, 2018, vol. 332, pp. 329–344. DOI: 10.1016/j.nucengdes.2018.03.012.
- Yang B.W., Nikotana H., Long J., Liu A., Han B. Subchannel analysis – Current practice and development for the future. Nuclear Engineering and Design, 2021, vol. 385, p. 111477. DOI: 10.1016/j.nucengdes.2021.111477.
- Borisov V.D. Poperechnoye peremeshivaniye teplonositelya v puchkakh sterzhney [Transverse mixing of coolant in rod bundles]. Preprint IAE-3269/5. Moscow, 1980. 27 p.
- SC-1. Certification passport of the program for electronic computers No. 123, 2000.
- Oleksyuk D.A. Razrabotka i eksperimental'noye obosnovaniye programmy dlya poyacheykovogo teplogidravlicheskogo rascheta aktivnykh zon reaktorov tipa VVER. Dis. kand. tekh. nauk. [Development and experimental justification of the program for cell-by-cell thermal-hydraulic calculation of WWER reactor cores. Diss. cand. tech. sci.]. Moscow, 2002. 194 p.
- Kobzar L.L. Oleksyuk D.A. Programma SC-1 [Program SC-1]. Voprosy atomnoy nauki i tekhniki. Seriya: Fizika yadernykh reaktorov – Problems of Atomic Science and Technology. Series: Physics of Nuclear Reactors, 2005, no. 3, pp. 62–64.
- Bolobov P.A., Oleksyuk D.A. Neutronic and thermal hydraulic code package PERKMAK-3D/SC-1 in 3D pin-by-pin analysis of the core. Proc. of the 17th Symposium of AER on VVER Reactor Physics and Reactor Safety. Yalta, Ukraine, 2007. Available at: https://inis.iaea.org/records/pv9rg-6hn44 (accessed 06.08.2025).
- Bolobov P.A., Oleksyuk D.A. The development of the code package PERMAK-3D/SC-1. Proc. of the 21st Symposium of AER on VVER Reactor Physics and Reactor Safety. Dresden, Germany, 2011. Available at: https://inis.iaea.org/records/q8143-h7a03 (accessed 06.08.2025).
- Oleksyuk D.A., Kobzar' L.L., Hamaza V.A., Kovalishin A.A., Krapivin M.A., Laletin I.N. Inzhenernyy kod SC-REACTOR [Engineering code SC-REACTOR]. Certificate of state registration of computer program No. 2020660375, Russian Federation, 2020.
- Perepelitsa N.I. Grids with Mixing Elements for VVER Fuel Assemblies. At Energy, 2020, vol. 128, issue 3, pp. 129–135. DOI: https://doi.org/10.1007/s10512-020-00663-x.
- Kobzar L.L., Oleksyuk D.A., Semchenkov Y.M. Experimental and computational investigations of heat and mass transfer of intensifier grids. Kerntechnik, 2015, vol. 80, no. 4, pp. 349–358. DOI: 10.3139/124.110508.
- Kireeva D.R., Kobzar L.L., Oleksyuk D.A. Razrabotka metodiki otsenki vliyaniya reshetok-intensifikatorov teploobmena na krizis teplootdachi v puchkakh sterzhney [Development of a Methodology for Assessing the Effect of Heat Transfer Enhancement Grids on the Heat Transfer Crisis in Rod Bundles]. Yadernaya fizika i inzhinirng – Nuclear Physics and Engineering, 2015, vol. 6, no. 1–2, pp. 20–24. DOI: 10.1134/S2079562915010078.
- Oleksyuk D.A., Kireeva D.R. Validation of the SC-INT code using experimental data on coolant mixing in a 37-rod fuel assembly with heat exchange intensifying spacer grids. Proc. of the M&C 2017 – International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering. Jeju, Korea, 2017. Available at: https://www.kns.org/files/int_paper/paper/MC2017_2017_8/P339S08-07KireevaD.pdf(accessed 06.08.2025).
- Kobzar L.L., Oleksyuk D.A. Experimental Studies of the Efficiency of Heat-and-Mass Transfer Intensifier Spacer-Grids. At Energy, 2019, vol. 125, issue 5, pp. 290–296. DOI: https://doi.org/10.1007/s10512-019-00483-8.
- Oleksyuk D.A., Kireeva D.R., Kobzar L.L. Experimental research of critical heat fluxes on 37-rod bundles with various types of intensifying grids. Proc. of the 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2019. Portland, USA, 2019, pp. 1528–1541.
- Balay S. et al. PETSc/TAO Users Manual Revision 3.19. Argonne National Lab. (ANL), Argonne, IL (United States), 2023. No. ANL-21/39.
- Oleksyuk D.A., Kobzar’ L.L. SC-INT. Certificate of state registration of the computer program No. 2016617793 Russian Federation, 2016.
- SC-INT. Certification passport of the program for electronic computers No. 578, 2023.
- Vertikov E.A., Oleksyuk D.A. Razrabotka subkanal'nogo teplogidravlicheskogo koda SC-Core dlya rascheta polnomasshtabnykh aktivnykh zon reaktorov s vodoy pod davleniyem [Development of the subchannel thermal hydraulic code SC-Core for calculating full-scale active zones of pressurized water reactors]. Materialy XVII Minskogo mezhdunarodnogo foruma po teplomassoobmenu [Proc. of the XVII Minsk International Forum on Heat and Mass Transfer]. Minsk, Belarus, 2024. Available at: https://www.itmo.by/conferences/abstracts/mif-17/mif17-proceedings.pdf (accessed 06.08.2025).
- Pinegin A.A., Oleksyuk D.A., Ryzhov A.A. Lowering engineering factor for DNBR margin for fuel assemblies TVS-2M and TVSA. Proc. of the 23rd Symposium of AER on VVER Reactor Physics and Reactor Safety. Strbske Pleso, Slovakia, 2013. pp. 513–528.
- Vertikov E.A., Oleksyuk D.A., Zaporzhin K.V., Zubkov A.G. Razrabotka statisticheskogo metoda rascheta inzhenernogo koeffitsiyenta po podogrevu teplonositelya [Development of a statistical method for calculating the engineering coefficient for heating the coolant]. Tezisy dokladov mezhdunarodnoy nauchno-tekhnicheskoy konferentsii “Bezopasnost', effektivnost' i ekonomika atomnoy energetiki” (MNTK-2024) [Proc. of the International Scientific and Technical Conference “Safety, Efficiency and Economy of Nuclear Power Engineering” (MNTK-2024)]. Moscow, Russia, 2024, pp. 204–205.
- Patankar S. Chislennyye metody resheniya zadach teploobmena i dinamiki zhidkosti [Numerical methods for solving heat transfer and fluid dynamics problems]. Moscow, Energoatomizdat Publ., 1984. 152 p.
- Abramov V.I., Konovaltsev Yu.M., Levin E.I. et al. Opredeleniye lokal'nykh teplogidravlicheskikh kharakteristik i analiz krizisnykh usloviy v puchke teplovydelyayushchikh sterzhney [Determination of local thermal-hydraulic characteristics and analysis of crisis conditions in a bundle of fuel rods]. Sbornik dokladov seminara “Teplofizika-74” [Proc. of the Seminar “Thermophysics-74”]. Moscow, USSR, 1974. Available at: https://inis.iaea.org/collection/NCLCollectionStore/_Public/09/392/9392330.pdf (accessed 06.08.2025).
- Abramov V.I., Kobzar L.L., Konovaltsev Yu.M. et al. Sravneniye rezul'tatov raschetov teplogidravlicheskikh kharakteristik puchka sterzhney po metodu yacheyek s opytnymi dannymi [Comparison of the results of calculations of thermal hydraulic characteristics of a rod bundle using the cell method with experimental data]. Sbornik dokladov seminara “Teplofizika-78” [Proc. of the Seminar “Thermophysics-78”]. Budapest, Hungary, 1978, pp. 791–805.
- PUCHOK-1000. Certification passport of the program for electronic computers No. 129, 2001.
- PUCHOK-1000. Certification passport of the program for electronic computers No. 415, 2017.
- Bosenko S.V., Churkin A.N. Rezul'taty dopolnitel'noy validatsii programmy PUCHOK-1000 dlya poyacheykovogo rascheta teplovydelyayushchikh sborok VVER-1200 [Results of additional validation of the PUCHOK-1000 program for cell-by-cell calculation of VVER-1200 fuel assemblies]. Materialy XVII Minskogo mezhdunarodnogo foruma po teplomassoobmenu [Proc. of the XVII Minsk International Forum on Heat and Mass Transfer]. Minsk, Belarus, 2024. Available at: https://www.itmo.by/conferences/abstracts/mif-17/mif17-proceedings.pdf (accessed 06.08.2025).
- TIGRSP. Certification passport of the program for electronic computers No. 209, 2005.
- Galkin I.Yu., Strebnev N.A., Abramov V.I., Konovaltsev Yu.M. TIGRSP. Certificate of state registration of the computer program No. 2015611032, Russian Federation, 2015.
- Churkin A.N. Matematicheskoye modelirovaniye protsessov teplomassoperenosa v puchkakh teplovydelyayushchikh sterzhney. Dis. kand. tekh. nauk [Mathematical modeling of heat and mass transfer processes in bundles of fuel rods. Diss. cand. tech. sci.]. Podolsk, 2006. 167 p.
- Gentry R.A., Martin R.E., Daly B.J. An Eulerian differencing method for unsteady compressible flow problems. Journal of Computational Physics, 1966, vol. 1, no. 1, pp. 87–118. DOI: 10.1016/0021-9991(66)90014-3.
- Shary N.V., Semishkin V.P., Piminov V.A., Dragunov Yu.G. Prochnost' osnovnogo oborudovaniya i truboprovodov reaktornykh ustanovok VVER [Strength of the Main Equipment and Pipelines of WWER Reactor Installations]. Moscow, IzdAT Publ., 2004. 496 p.
- Churkin A.N., Semishkin V.P., Mokhov V.A., Parshin N.Ya. Raschet eksperimentov s odinochnymi tvelami, vypolnennykh na stende PARAMETR [Calculation of Experiments with Single Fuel Elements Performed on the PARAMETR Facility]. Voprosy atomnoy nauki i tekhniki. Seriya: Obespecheniye bezopasnosti AES – Problems of Atomic Science and Technology. Series: Ensuring NPP Safety, 2006, no. 15, pp. 132–144.
- Churkin A.N., Yagov P.V., Mokhov V.A. and Shchekin I.G. Computer Code TEMPA SC: Simulation of Thermal-Hydraulic Processes in the Core of VVER-SCP Reactor. Proc. of the Fourth International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-4). Heidelberg, Germany, 2011, pp. 1–10.
- Yagov P.V., Churkin A.N., Mokhova O.V. Analiz teplogidrodinamicheskoy ustoychivosti techeniya teplonositelya i neravnomernosti podogrevov v teplovydelyayushchikh sborkakh VVER-SKD [Analysis of thermal and hydrodynamic stability of coolant flow and non-uniformity of heating in WWER-SKD fuel assemblies]. Voprosy atomnoy nauki i tekhniki. Seriya: Obespecheniye bezopasnosti AES – Problems of Atomic Science and Technology. Series: Ensuring NPP Safety, 2011, no. 29, pp. 82–91.
- Baisov A.M. Razrabotka obobshchennykh sootnosheniy dlya rascheta koeffitsiyenta teplootdachi v teplovydelyayushchikh sborkakh yadernykh reaktorov, okhlazhdayemykh vodoy sverkhkritiche-skogo davleniya. Dis. kand. tekh. nauk [Development of generalized relationships for calculating the heat transfer coefficient in nuclear reactor fuel assemblies cooled by supercritical water. Diss. cand. tech. sci.]. Moscow, 2022. 208 p.
- Baisov A.M., Churkin A.N. Validatsiya programmy TEMPA-SK na eksperimentakh s puchkami teplovydelyayushchikh sterzhney, okhlazhdayemykh vodoy sverkhkriticheskogo davleniya [Validation of the TEMPA-SK program in experiments with fuel rod bundles cooled by supercritical water]. Voprosy atomnoy nauki i tekhniki. Seriya: Fizika yadernykh reaktorov – Problems of Atomic Science and Technology. Series: Physics of Nuclear Reactors, 2022, no. 3, pp. 4–15.
- 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: 10.1016/j.tsep.2019.100435.
- KANAL. Certification passport of the program for electronic computers No. 273, 2022.
- Samoilov O.Yu. et al. Eksperimental'nyye issledovaniya teplogidravlicheskikh kharakteristik na modelyakh TVSA VVER-1000 [Experimental studies of thermal-hydraulic characteristics on TVSA WWER-1000 models]. Sbornik trudov chetvertoy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii “Obespecheniye bezopasnosti AES s VVER” [Proc. of the Fourth International Scientific and Technical Conference “Ensuring the Safety of NPPs with WWER”]. Podolsk, Russia, 2005, pp. 23–27.
- Dmitriev S.M., Lukyanov V.E., Samoilov O.B. Obosnovaniye korrelyatsii dlya rascheta kriticheskogo teplovogo potoka v teplovydelyayushchikh sborkakh al'ternativoy konstruktsii s peremeshivayushchimi reshetkami-intensifikatorami dlya VVER-1000 [The Substantiation of the Correlation for Critical Heat Flux Calculation for Alternative Design Fuel Assemblies with Mixing Spacer Grids in VVER-1000]. Izvestiya vuzov. Yadernaya energetika, 2012, no. 1, pp. 99–108. DOI: 10.26583/npe.2012.1.12.
- Samoilov O.B., Falkov A.A., Shipov D.L., Lukyanov V.E., Morozkin O.N. Teplogidravlicheskie harakteristiki usovershenstvovannogo topliva VVER na baze TVSA s peremeshivayushchimi reshetkami-intensifikatorami [Thermo-hydraulic characteristics of the WWER advanced fuel with the TBCA with mixing grids]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2016, no. 3, pp. 54–60.
- Gushchin E.V., Kolmakov A.P. Programma pokanal'nogo teplogidravlicheskogo rascheta VYAZ-M i nekotoryye rezul'taty raschetov [VYAZ-M channel-by-channel thermal-hydraulic calculation program and some calculation results]. Sbornik trudov vtoroy vserossiyskiy nauchno-tekhnicheskoy konferentsii “Obespecheniye bezopasnosti AES s VVER”[Proc. of the Second All-Russian Scientific and Technical Conference “Ensuring the Safety of NPPs with WWER”]. Podolsk, Russia, 2001. Vol. 5, pp. 125–131.
- Bogoslovskaya G.P., Kirillov P.L., Loshinin V.M., Pometko R.S. et al. Eksperimental'nyye i raschetnyye issledovaniya teploobmena v TVS aktivnoy zony v obosnovaniye effektivnosti i bezopasnosti vodookhlazhdayemykh reaktorov novogo pokoleniya [Experimental and computational studies of heat transfer in fuel assemblies of the core to substantiate the efficiency and safety of new-generation water-cooled reactors]. Sbornik statey k 65-letiyu sozdaniya Teplofizicheskogo otdela FEI [Proc. for the 65th anniversary of the creation of the Thermophysical Department of IPPE]. Obninsk: GNC RF – FEI Publ., 2019. Pp. 157–169. Available at: https://www.ippe.ru/science-info/books/1033-thermal-physics (accessed 06.08.2025).
- Bogoslovskaya G.P., Karpenko A.A., Kirillov P.L. et al. MIF-SKD computation code for thermohydraulic design of a reactor core cooled by supercritical-pressure water. Therm. Eng., 2009, vol. 56, issue 3, pp. 214–217. DOI: https://doi.org/10.1134/S0040601509030057.
- Kartashov K.V. Provedeniye raschetov po optimizatsii geometricheskikh i rezhimnykh parametrov TVS reaktorov VVER-SKD dlya razlichnykh rezhimov ekspluatatsii reaktora na sverkhkriticheskikh parametrakh vody [Subchannel Thermohydraulic Calculations for Fuel Subassembly of Reactor Core on Supercritical Water]. Izvestiya vuzov. Yadernaya Energetika. 2012, no. 2, pp. 95–101. DOI: https://doi.org/10.26583/npe.2012.2.12.
- Kartashov K.V. Pokanal'nyy teplogidravlicheskiy raschet aktivnoy zony reaktora VVER-SKD 30 MVt (tepl.) pri nominal'nykh rezhimakh raboty [Subchannel thermohydraulic calculations of reactor core for WWER-SCP 30 MW (TH) under nominal conditions]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2016, no. 3, pp. 127–131.
- Kazachkovsky O.D., Sorokin A.P., Zhukov A.V. et al. Metod sosredotochennykh parametrov v zadache o temperaturnom pole v formoizmenennykh TVS bystrykh reaktorov s neadiabaticheskimi granichnymi usloviyami [The method of lumped parameters in the problem of the temperature field in modified fuel assemblies of fast reactors with non-adiabatic boundary conditions]. Preprint FEI-1972 – Preprint IPPE-1972. Obninsk, FEI Publ., 1985.
- Gordienko P.V.Modelirovaniye nestatsionarnykh neytronno-fizicheskikh protsessov v reaktorakh VVER s potvel'noy detalizatsiyey. Dis. kand. tekh. nauk [Modeling of non-stationary neutron-physical processes in WWER reactors with fuel-pin detailing. Diss. cand. tech. sci.]. Moscow, 2014. 100 p.
- Konyukhova A.I. Razvitiye metodov raschetnogo obosnovaniya bezopasnosti RU VVER s pri-meneniyem potvel'nogo modelirovaniya aktivnoy zony. Dis. kand. tekh. nauk [Development of methods for the computational justification of the safety of WWER reactor plants using fuel-pin modeling of the core. Diss. cand. tech. sci.]. Moscow, 2021. 134 p.
- Artemov V.G., Artemova L.M., Korotaev V.G., Mikheev P.A., Shemaev Yu.P. Sopryazhennyye neytronno-fizicheskiy i teplogidravlicheskiy raschety pri analize temperaturnogo sostoyaniya tvelov [Coupled neutron-physical and thermal-hydraulic calculations in the analysis of the temperature state of fuel elements]. Tekhnologii obespecheniya zhiznennogo tsikla yadernykh energeticheskikh ustanovok – Technologies for ensuring the life cycle of nuclear power plants, 2016, vol. 3, no. 5, pp. 37–47.
- Artemov V.G., Artemova L.M., Korotaev V.G., Mikheev P.A. Primeneniye potvel'noy neytronno-fizicheskoy i teplogidravlicheskoy modeli dlya issledovaniya temperaturnogo sostoyaniya tvelov v avariynykh rezhimakh reaktornykh ustanovok [Application of a fuel-element neutron-physical and thermal-hydraulic model for studying the temperature state of fuel elements in emergency modes of reactor plants]. Tekhnologii obespecheniya zhiznennogo tsikla yadernykh energeticheskikh ustanovok – Technologies for ensuring the life cycle of nuclear power plants, 2018, vol. 2, no. 8, pp. 15–25.
- Jeong J.J., Lee W.J., Chung B.D. Simulation of a main steam line break accident using a coupled «system thermal-hydraulics, three-dimensional reactor kinetics, and hot channel analysis» code. Annals of Nuclear Energy, 2006, vol. 33, no. 9, pp. 820–828. DOI: 10.1016/j.anucene.2006.04.008.
- Zhang K., Sanchez-Espinoza V.H. Optimization and verification of the coupled code TRACE/SubChanFlow using the VVER-1000 coolant mixing benchmark data. Nuclear Engineering and Design, 2019, vol. 353, p. 110238. DOI: 10.1016/j.nucengdes.2019.110238.
- Kucukboyaci V.N. et al. VERA-CS Modeling and simulation of PWR main steam line break core response to DNB. International Conference on Nuclear Engineering, 2016, vol. 50046, p. V004T10A026. DOI: 10.1115%2FICONE24-60865.
- Zhang H. et al. Developing fully coupled subchannel model in RELAP-7. USA, 2014. No. INL/EXT-14-33102.
- Krapivtsev V.G., Kudryavtsev O.V., Solonin V.I. Modelirovaniye techeniya na vkhode v aktivnuyu zonu reaktorov VVER [Modeling of the flow at the inlet of the WWER reactor core]. Vestnik MGTU im. N.E. Baumana. Seriya: Mashinostroyeniye – Bulletin of Bauman Moscow State Technical University. Series: Mechanical Engineering, 2012, no. 2, pp. 70–80.
- Krapivtsev V.G., Solonin V.I. Model Studies of Coolant Flow Hydrodynamics at VVER-1000 Core Entry. At Energy, 2021, vol. 130, issue 1, pp. 13–19. DOI: https://doi.org/10.1007/s10512-021-00766-z.
- Volkov V.V., Golibrodo L.A., Krutikov A.A., Kudryavtsev O.V., Nadinsky Yu.N., Nechaev A.T., Skibin A.P. Razrabotka polnomasshtabnoy teplogidravlicheskoy CFD-modeli pervogo kontura reaktornoy ustanovki AES-2006 [Development of a full-scale thermal-hydraulic CFD model of the primary circuit of the AES-2006 reactor plant]. Sbornik trudov mezhdunarodnoy konferentsii “Superkomp'yuternyye dni v Rossii” [Proc. of the International Conference “Supercomputer Days in Russia”]. Moscow, Russia, 2018. Available at: https://2018.russianscdays.org/files/pdf18/770.pdf (accessed 06.08.2025).
- Dmitriev S.M., Dobrov A.A. Primeneniye CFD-programmy LOGOS dlya polucheniya granichnykh usloviy dlya programmy poyacheykovogo rascheta TVS aktivnoy zony [Application of the LOGOS CFD-program to obtain inlet boundary conditions for the program of subchannel thermal hydraulic analysis of reactor core fuel assembly]. Voprosy atomnoy nauki i tekhniki. Seriya: Yaderno-reaktornyye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2023, no. 2, pp. 222–230.
- Bykov M.A., Moskalov A.M., Shishov A.V., Belova O.V., Posysaev D.A., Kudryavtsev O.V., Petrov V.E. Opredeleniye gidravlicheskikh kharakteristik TVS-2M s ispol'zovaniyem programmnykh kompleksov STAR-CD i ANSYS CFX [Determination of hydraulic characteristics of TVS-2M using STAR-CD and ANSYS CFX software packages]. Sbornik trudov pyatoy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii “Obespecheniye bezopasnosti AES s VVER” [Proceedings of the Fifth International Scientific and Technical Conference “Ensuring Safety of NPPs with WWER”]. Podolsk, Russia, 2007. Available at: http://www.myshared.ru/slide/212668/ (accessed 06.08.2025).
- Dobrov A.A., Ivanov K.G., Legchanov M.A., Kurbatova N.P., Lyakhov I.Yu. Polucheniye v CFD-programme LOGOS koeffitsiyentov gidravlicheskogo soprotivleniya yacheyek TVS s distantsioniruyushchey reshetkoy dlya modeli odnomernogo poyacheykovogo rascheta aktivnoy zony [Obtaining hydraulic resistance coefficients of fuel assembly cells with a spacer grid in the LOGOS CFD program for a one-dimensional cell-by-cell calculation model of the core]. Trudy NGTU im. R.Ye. Alekseyeva – Proc. of NSTU named after R.E. Alekseev, 2018, no. 1 (120), pp. 91–97. DOI: 10.46960/1816-210X_2018_1_91.
- Palomino L.M., El-Genk M.S. Friction factor correlation for hexagonal bundles of bare tubes/rods and with flat and scalloped walls. Nuclear Engineering and Design, 2019, vol. 353, p. 110230. DOI: 10.1016/j.nucengdes.2019.110230.
- Bae J.H., Park J.H. Analytical prediction of turbulent friction factor for a rod bundle. Annals of Nuclear Energy, 2011, vol. 38, no. 2–3, pp. 348–357. DOI: 10.1016/j.anucene.2010.10.008.
- Stepanov O.E., Galkin I.Yu., Melekh S.S. et al. Verification of the TIGRSP Computer Code as Applied to a 19-Rod Fuel Assembly Using CFD Computations. Therm. Eng., 2019, vol. 66, issue 7, pp. 457–464. DOI: https://doi.org/10.1134/S0040601519070097.
- Stepanov O.E., Galkin I.Yu., Kurnosov M.M., Korolev V.V., Strebnev N.A. Krossverifikatsiya modeli poyacheistogo rascheta TVS koda TIGRSP s primeneniyem CFD-koda na primere 7-sterzhnevoy cborki [Cross-verification of the cellular calculation model of fuel assemblies of the TIGRSP code using the CFD code using the example of a 7-rod assembly]. Voprosy atomnoy nauki i tekhniki. Seriya: Fizika yadernykh reaktorov – Problems of Nuclear Science and Technology. Series: Physics of Nuclear Reactors, 2016, no. 2, pp. 54–66.
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Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2025, no. 3, 3:13

 
	