Sorokin A.P., Kuzina Ju.A., Orlov A.I.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
The similarity analysis and the following criteria as well asymptotic solutions must be fully applied at planning and carry out the experimental study and generalizing its results. As academician S.S. Kutateladze notes "The external simplicity of the foundations of this analysis and the everincreasing multi-parametric nature of the problems for physical and mathematical modeling lead to many misunderstandings and direct mistakes”. Liquid metals form a special class of coolants characterized by a significant volumetric heat capacity and high thermal conductivity, which have the coefficient of kinematic viscosity much lower than the coefficient of thermal diffusivity, its Prandtl number is much less than one. The analysis results of the application of the similarity theory of the thermophysical processes to the modeling of hydrodynamics and heat transfer in liquid metals are presented in this report for: channels of complex shape, rod systems (reactor core and heat exchangers), temperature fields and coolant velocity in a hot chamber of a fast reactor in different operating modes. Practically the direct modeling can be applied unlimitedly only for processes in which determined similarity numbers are functions of only geometric simplices of the system and one defining criterion. For example the presence of two defining criteria such as the numbers Re and Pr during heat exchange makes modeling much more difficult. With three defining criteria the direct modeling is usually not feasible. In such cases it is necessary to caring out the systematic multivariate experiments. The purpose of such modeling experiments is the real detection of effects solved by a very general mathematical model but not impossible to carry out at the modern level of mathematical technologies, either analytically or in numerical studies.
1. Rachkov V.I., Arnoldov M.A., Efanov A.D., Kalyakin S.G., Kozlov F.A., Loginov N.I., Orlov Yu.I., Sorokin A.P. Use of liquid metals in nuclear, thermonuclear energy and other innovative technologies. Thermal Engineering, 2014, no. 5, pp. 20–30 (in Russian).
2. Sorokin A.P., Poplavsky V.M., Trufanov A.A., Kozlov F.A., Orlov Yu.I., Kamaev A.A., Chernonog V.L. Research in the field of thermophysics of new generation nuclear reactors. Proc. IV Int. Sci. and Techn. Conf. “Innovative projects and technologies of nuclear energy (MNTK NIKIET-2016)”. Moscow, 2016. 12 p. (in Russian).
3. Zhukov A.V., Sorokin A.P., Matjukhin N.M. Interchannel exchange in FA of fast reactors (theoretical bases and physics of the process). Moscow, Energoatomizdat Publ., 1989 (in Russian).
4. Zhukov A.V., Sorokin A.P., Matjukhin N.M. Interchannel exchange in FA of fast reactors (calculation programs and practical application). Moscow, Energoatomizdat Publ., 1991 (in Russian).
5. Pershukov V.A., Arkhangelsky A.V., Kononov O.E., Sorokin A.P. Thermophysical bench base of nuclear energy of Russia and Kazakhstan. Sarov, FSUE “RFNC – VNIIEF” Publ., 2016. 160 p. (in Russian).
6. Gukhman A.A., Kirpichev M.V. Theory of models. News of the Leningrad Polytechnic Institute name after M.I. Kalinin, 1927, vol. 30, pp. 1–50 (in Russian).
7. Sedov L.I. Methods of similarity and dimension in mechanics. Moscow, State publication of scientific and technical literature, 1957 (in Russian).
8. Kirpichev M.V., Mikheev M.A. Modeling of thermal devices in mechanics. Moscow-Leningrad, Publishing house of the USSR Academy of Sciences, 1936 (in Russian).
9. Gukhman A.A. Introduction to the theory of similarity. Moscow, High School Publ., 1973 (in Russian).
10. Kutateladze S.S. Analysis of similarity in thermal physics. Novosibirsk, Nauka Publ., 1982 (in Russian).
11. Gukhman A.A. Application of the theory of similarity to the study of heat and mass transfer processes. Moscow, Higher School Publ., 1973 (in Russian).
12. Kutateladze S.S. Analyzes of similarity and physical models. Novosibirsk, Nauka. Sib. Department Publ., 1986 (in Russian).
13. Kutateladze S.S. Analyzes of similarity and physical models. Novosibirsk, Science. Sib. Department Publ., 1989. Pp. 410–416 (in Russian).
14. Kirillov P.L., Yuriev Yu.S., Bobkov V.P. Handbook of thermohydraulic calculations (nuclear reactors, heat exchangers, steam generators). Moscow, Energoatomizdat Publ., 1990 (in Russian).
15. Kirillov P.L, Terentyeva M.I., Deniskina N.B. Thermophysical properties of materials of nuclear technology. Moscow, IzdAt Publ., 2007 (in Russian).
16. Gurvich L.V., Veyts L.V. Medvedev V.A. et al. Termodinamicheskie svoystva individual'nykh veshchestv [Thermodynamic properties of individual substances]. Moscow, Nauka Publ., 1978.
17. Shpilrayn E.E., Yakimovich K.A., Totskiy E.E. et al. Teplofizicheskie svoystva shchelochnykh metallov [Thermophysical properties of alkali metals]. Moscow, Standart Publ., 1970.
18. Konakov P.K. Slip coefficient for smooth pipes. News of the Russian Academy of Sciences, 1948, no. 7, pp. 1029 (in Russian).
19. Kanaev A.A. Heat transfer and hydraulic resistance during the flow of mercury in tubes. Kotloturbostroenie, 1953, no. 2 (in Russian).
20. Tolstoy D.M. Gliding of mercury through glass. DAN USSR, 1952, vol. 75, no. 6, pp. 1329–1332 (in Russian).
21. Warburg E. About the flow of mercury in glass capillaries. Annalen der Physik, 1870, pp. 367.
22. Kondratiev N.S. Hydraulic resistance in the motion of liquid metals in pipes. Moscow, Publishing House of the USSR Academy of Sciences, 1959 (in Russian).
23. Brighton J. Fully developed turbulent flow in the channel of the annular section. Theoretical bases of engineering calculations, 1964, no. 4, pp. 240.
24. Subbotin V.I., Ibragimov M.Kh., Ushakov P.A., Bobkov V.P., Zhukov A.V., Yuriev Yu.S. Gidrodinamika i teploobmen v atomnykh energeticheskikh ustanovkakh [Hydrodynamics and heat transfer in nuclear power plants]. Moscow, Atomizdat Publ., 1975. 408 p.
25. Zhukov A.V., Sorokin A.P., Kirillov P.L., Ushakov P.A., Kiryushin A.I., Kuzavkov N.G. Methodical instructions and recommendations for thermal-hydraulic calculation of fast reactors core. Obninsk, IPPE Publ., 1988. 436 p. (in Russian).
26. Rachkov V.I., Efanov A.D., Zhukov A.V., Kalyakin S.G., Sorokin A.P. Thermohydraulic researches of nuclear power plant (to the 60 anniversary of start-up of the First atomic power station). Izvestiya vuzov. Yadernaya energetika – Proseedings of Universities. Nuclear Power Engineering, 2014, no. 1, pp. 39–63 (in Russian).
27. Rachkov V.I., Sorokin A.P., Zhukov A.V. Thermohydraulic investigations of liquid-metal coolants in nuclear power plants. High temperature, 2017, vol. 56, no. 1, pp. 121–136.
28. Lyon R. Heat transfer coefficient in liquid metals. Chemical Engineering Progress, 1951, vol. 47, no. 2, pp. 75–81.
29. Kirillov P.L. Heat exchange of liquid metals in round tubes (single-phase and two-phase flows). Author's abstract. Dr. techn. sci. diss. Moscow, JIHT USSR, 1969 (in Russian).
30. Ibragimov M.Kh., Subbotin V.I., Ushakov P.A. Investigation of heat transfer in turbulent flow in pipes of liquid metals. Atomnaya energiya - Atomic Energy, 1960, vol. 8, no. 1, pp. 54–56 (in Russian).
31. Talanov V.D., Ushakov P.A. Heat exchange in round, circular and square channels. Moscow, Atomizdat Publ., 1967. Pp. 9–15 (in Russian).
32. Subbotin V.I., Ushakov P.A., Gabrianovich B.N. et al Heat transfer during the flow of liquid metals in round tubes. Journal of Engineering Physics and Thermophysics, 1963, vol. 4, no. 4, pp. 16–21.
33. Petukhov B.S., Genin L.G., Kovalev S.A. Heat transfer in nuclear power plants. Moscow, Energoatomizdat Publ., 1986 (in Russian).
34. Kirillov P.L. Heat transfer in a turbulent flow. Part 2. Distribution of velocity and temperature. Atomnaya energiya – Atomic Energy, 2017, vol. 122, no. 4, pp. 192–203 (in Russian).
35. Kirillov P.L. Accounting of contact thermal resistance to heat exchange of liquid metal in a circular pipe. Preprint FEI-284 – Preprint IPPE-284. Obninsk, 1971 (in Russian).
36. Subbotin V.I., Ivanovsky M.N., Orlov Yu.I. Thermal contact resistance when cooling channels with liquid metal. High temperatures, 1967, vol. 5, no. 6, pp. 1025–1031.
37. Ushakov. P.А. Approximate thermal simulation of cylindrical fuel elements. Moscow, Atomizdat Publ., 1967. Pp. 137—148 (in Russian).
38. Subbotin V.I., Ivanovsky M.N., Ushakov. P.A. Hydrodynamics and heat transfer in nuclear power plants (basics of calculation). Moscow, Atomizdat Publ., 1975 (in Russian).
39. Ushakov P.А., Zhukov A.V., Matjukhin N.M. Heat transfer to liquid metals in correct fuel rod grids. High temperature, 1977, vol. 15, no 5, pp. 1027–1033 (in Russian).
40. Borishansky V.М., Gotovsky М.А., Firsova E.V. Teplootdacha k zhidkim metallam v prodol'no omyvaemykh puchkakh sterzhney [Heat transfer to liquid metals in longitudinally washed bundles of rods]. Atomnaya energiya – Atomic Energy, 1969, vol. 27, no. 6, pp. 549–551 (in Russian).
41. Ushakov P.А., Zhukov A.V., Matjukhin N.M. Temperature fields of rod fuel rods located in regular lattices, with a laminar flow of coolant. High temperature, 1976, vol. 14, no 3, pp. 538—545 (in Russian).
42. Buleev N.I., Mironovich R.Ja. Heat transfer in a turbulent fluid flow in a triangular lattice of rods. High temperature, 1972, vol. 10, no 5, pp. 1031 (in Russian).
43. Ushakov P.А., Zhukov A.V., Matjukhin N.M. Azimuthal non-uniformities in the temperature of fuel elements located in regular lattices, under turbulent flow of liquid metals. High temperature, 1977, vol. 15, no 1, pp. 76–82 (in Russian).
44. Ushakov P.А., SubbotinV.I., Gabrianovich B.N., Zhukov A.V. Heat transfer during the flow of mercury and water in a tightly packed pin bundles. Atomnaya energiya – Atomic Energy, 1962, vol. 9, no. 6, pp. 461–469 (in Russian).
45. Ushakov P.А., Subbotin V.I., Gabrianovich B.N. Heat transfer and hydraulic resistance in tightly packed pin bundles. Atomnaya energiya – Atomic Energy, 1962, vol. 13, no. 2, pp. 162—169 (in Russian).
46. Zhukov A.V., Kirillov P.L., Matjukhin N.M. et al Thermohydraulic calculation of TBC fast reactors with liquid metal cooling. Moscow, Energoatomizdat Publ., 1985 (in Russian).
47. Hofmann F., Essig C., Georgeours S., Tenchine D. Investigations on Natural Convection Decay Heat Removal by Natural Convection in Fast Reactors. Evaluation of Decay Heat Removal by Natural Convection. Specialists Meeting of IAEA. Japan, 1993, pp. 15–25.
48. Weinberg D., Hoffmann H., Ohira H, Schnetgoke G. The Status of Studies Using RAMONA and NEPTUN Models on Decay Heat Removal by Natural Convection for the Europian Fast Reactor. Evaluation of Decay Heat Removal by Natural Convection. Specialists Meeting of IAEA. Japan, 1993, pp. 51–57.
49. Birbraer P.N., Gorbunov V.S., Zotov V.S., Kuzavkov N.G., Pykhonin V.A., Ryzhov V.A., Sobolev V.A. Comparision of Decay Heat Exchangers Arrangerment in the Primary Circuit of Pool Type Fast Reactor. Evaluation of Decay Heat Removal by Natural Convection. Specialists Meeting of IAEA. Japan, IAEA, 1993, pp. 119–126.
50. Sobolev V.A., Voronov V.N., Kuzavkov N.G. Analysis of Decay Heat Removal from the Core Using Passive Cooling Systems. Proc. Int. Top. Meeting on Sodium Cooled Fast Reactor Safety. Obninsk, 1994, vol. 4, pp. 6–12.
51. Betts C. et al Europe on Studies on Fast reactor Core Interwrapper Flows. Proc. Int. Conf. Fast Reactors and related Fuel Cycles. Kyoto, Japan, 1991, vol. III, pp. 1–15.
52. Takeda H., Koga T., Kanno J. Study on similarity rule for natural convection water test of LMFBR. Specialists Meeting of IAEA “Evaluation of Decay Heat Removel by Natural Convection”. IAEA, 1993, pp. 58–66.
53. Ushakov P.A., Sorokin A.P Problems of simulation on the water of an emergency escape of residual heat release by natural convection in the chambers of fast reactors. Preprint FEI-2585 - Preprint IPPE-2585. Obninsk, 1997 (in Russian).
54. Ushakov P.A., Sorokin A.P. Modeling problems of emergency natural convection heat removal in the upper plenum of LMR using water. Proc. 9th Intern. Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9). California, San Francisco, 1999.
55. Ushakov P.A., Sorokin A.P. The role of hydraulic resistance in natural convection simulation in fast reactor vessels. Thermal Engineering, 2000, no. 5, pp. 9–14 (in Russian).
56. Ushakov P.A., Sorokin A.P. Modeling problems of emergency natural convection heat removal in the upper plenum of LMR using water. Proc. 8th Int. Conf. on Nuclear Engineering (ICONE-8). USA, Baltimore, 2000.
57. Opanasenko A.N., Sorokin A.P., Zaryugin D.G., Rachkov V.I. Stratification of the coolant in nuclear power plants. Atomnaya energiya - Atomic Energy, 2011, vol. 111, no. 3, pp. 131—136 (in Russian).
58. Opanasenko A.N., Sorokin A.P., Zaryugin D.G., Fedorov A.V. Experimental studies of the temperature and structure of the coolant flow on the model of a fast reactor in the elements of the first circuit during the transition to cooling by natural circulation. Obninsk, IPPE Publ., 2015. Pp. 102–111 (in Russian).
59. Opanasenko A.N., Sorokin A.P., Trufanov A.A., Denisova N.А., Sviridov E.V., Razuvanov N.G., Zagorsky V.G., Belyaev I.A. Experimental investigations of the temperature and velocity fields on the integrated water model of a fast reactor in various operating modes. Atomnaya energiya – Atomic Energy, 2017, vol. 123, no. 1, pp. 21–27 (in Russian).
60. Opanasenko A.N., Sorokin A.P., Zaryugin D.G., Trufanov A.A. Fast reactor: an experimental study of thermohydraulic processes in various operating modes. Thermal Engineering, 2017, no. 5, pp. 1–10 (in Russian).
61. Opanasenko A.N., Sorokin A.P., Zaryugin D.G., Trufanov A.A. Fast Reactor: an Experimental Study of Thermohydraulic Processes in Different Operating Regimes. Thermal Engineering, 2017, vol. 64, no. 5, pp. 336–344.
62. Shulz H. Experience with thermal fatigue in LWR piping caused by mixing and stratification. Specialists Meeting Proceedings. Paris, 1998, pp. 13–18.