A.M. Zagrebayev1

1 Federal State Budgetary Educational Institution of Higher Vocational Education National Research
  Nuclear University MEPhI (Moscow, Russia)
 

In this paper the mathematical model and application for nuclear reactor’s neutron flux statistical investigation are described. The goal for developing the application was verification of the possibility to determine the significant parameters for accident-free nuclear reactor running via neutron flux statistical characteristics in passive experiment.

As mathematical model authors use correlated equation of reactor neutron physics with fluctuating absorption cross-section, thermal physics and control equations. Mathematical model numerical realization in application uses finite-difference implicit method. The application can be divided into four parts according to functionality: calculation, input, output and statistical processing. In the application it is possible to build the model dynamically i. e. the user can choose witch feedbacks (including control system) should be included into calculation. Also user can set output characteristics and feedback parameters, such as constants, reactivity coefficients structure and values.

Numerical calculations proved that the application correctly represent physical processes in nuclear reactor and can be used for statistical researches.

Zagrebayev A.M. Nuclear reactor’s neutron flux modeling application in case of technological characteristics random perturbations. Information-measuring and Control Systems. 2023. V. 21. № 2. P. 51–60. DOI: https://doi.org/10.18127/j20700814-202302-07 (in Russian)

1. Vejnberg A., Vigner E. Fizicheskaya teoriya yadernyh reaktorov: Per. s angl.. Pod red. Ya.V. Sheveleva. M.: Izd-vo inostr. lit. 1961 (in Russian).
2. Adamov E. O., Orlov V. V., Gabaraev B. A., Filin A. I. dr. Innovacionnyj proekt AES s reaktorom BREST i pristancionnym toplivnym ciklom dlya ploshchadki Beloyarskoj AES. Atomnaya energetika. Sostoyanie i perspektivy: Materialy 3-j nauchno-tekhnich. konf. Minatoma Rossii. Moskva, 5 iyunya 2002 g. S. 85–107 (in Russian).
3. Krayushkin A.V., Kubarev A.V. Programma STEPAN-S dlya rascheta harakteristik yadernoj bezopasnosti. V sb. «Vnutrennyaya bezopasnost' yadernyh energeticheskih ustanovok». M.: CNIIatominform. 1991. S. 228, 229 (in Russian).
4. Feynman R. P., F. De Hoffmann, and R. Serber. Dispersion of the Neutron Enlission in U-235 Fission.. Journal of Nuclear Energy. 1956. № 3. P. 64
5. Pal L. On the Theory of Stochastic Processes in Nuclear Reactors. NuovoCimento (supplement). 1958. № 7. P. 25.
6. Pal L. «Statistical Fluctuations of Neutron Multiplication». Geneva Conference. 1958. V. 16, 687, P. 1710.
7. Urig R. Statisticheskie metody v fizike yadernyh reaktorov. M.: Atomizdat. 1974 (in Russian).
8. Gohn G.E. A Simplified Theory of Pile Noise. Nuclear Science and Engineering. 1960. V. 7. № 5. P. 472.
9. Sheff J.R., Albrecht R.W. The Space Dependence of Reactor Noise. Nuclear Science and Engineering. 1966. V. 24. № 3. P. 246.
10. Sheff J.R., Albrecht R.W. The Space Dependence of Reactor Noise. Nuclear Science and Engineering. 1966. V. 26. № 2. P. 207.
11. Herr J.D., Thomas J.R. Noise analysis for monitoring the moderator tem-perature coefficient of pressurized water reactors. Nuclear Science and Engineering. 1991. V. 108. P. 341–346.
12. Housiadas C., Antonopoulos-Domis M. The effect of fuel temperature on the estimation of the moderator coefficient in PWRs.. Annals of Nuclear Energy. 1999. V. 26. P. 1395–1405.
13. Kostic L.J., Runkel J., Stegemann D. Thermohydraulics surveillance of pressurized water reactors by experimental and theoretical investigations of the low frequency noise field. Progress in Nuclear Energy. 1988. V. 21. P. 421–430.
14. Kostic L. Monitoring of the temperature reactivity coefficient at the PWR nuclear power plant. Annals of Nuclear Energy. 1997. V. 24. P. 55–64.
15. Laggiard E., Runkel J. Evaluation of the moderator temperature coefficient of reactivity in a PWR by means of noise analysis. Annals of Nuclear Energy. 1997. V. 24. P. 411–417.
16. Laggiard E., Runkel J. Noise analysis estimation of the moderator temperature coefficient for a PWR fuel cycle. Annals of Nuclear Energy. 1999. V. 26. P. 149–156.
17. Pazsit I. Two-phase flow identification by correlation technique. Annals of Nuclear Energy. 1986. V. 13. P. 37–41.
18. Shieh D.J., Upadhyaya B.R., Sweeney F.J. Application of noise analysis technique for monitoring the moderator temperature coefficient of reactivity in pressurized water reactors. Nuclear Science and Engineering. 1987. V. 95. P. 14–21.
19. Sweeney F.J. In-core coolant velocity measurements in a pressurized water reactor using temperature-neutron noise cross-correlation. Transactions of the American Nuclear Society. 1984. V. 46. P. 736–738.
20. Thomas J.R., Herr J.D., Wood D.S. Noise analysis method for monitoring the moderator temperature coefficient of pressurized water reactors. I. Theory. Nuclear Science and Engineering. 1991. V. 108. P. 331–340.
21. Upadhyaya B.R., Shieh D.J., Sweeney F.J., Glockler O. Analysis of in-core dynamics in pressurized water reactors with application to parameter monitoring. Progress in Nuclear Energy. 1988. V. 21. P. 261–269.
22. Williams M.M.R. The effect of random material density on reactor criticality. Atomkernenergie. 1973. V. 22. P. 248–250.
23. Voroncov B.A., Emel'yanov I.Ya., Podlazov L.N. i dr. Voprosy diagnostiki fizicheskih harakteristik RBMK po nejtronnym shumam. Atomnaya energiya. 1980. T. 48. Vyp. 3. S. 145–48 (in Russian).
24. Stepanov A.V. Srednyaya plotnost' potoka nejtronov v neodnorodnyh sredah. NeutrjnThermalizationandReactjrSpectra, International atomic energy agency. Vienna. 1968. V. 1. P. 193–222 (in Russian).
25. Galanin A.D. Teoriya vozmushchenij dlya uravneniya s odnoj gruppoj nejtronov. Atomnaya energiya. 1986. T. 60. Vyp. 4. S. 267–273 (in Russian).
26. Karpov V.A., Nazaryan V.G., Postnikov V.V. Issledovanie sluchajnoj sostavlyayushchej raspredeleniya teplovydeleniya v yadernom reaktore. Atomnaya energiya. 1976. T. 40. Vyp. 6. S. 456–460 (in Russian).
27. Filipchuk E.V., Potapenko P.T., Postnikov V.V. Upravlenie nejtronnym polem yadernogo reaktora. M.: Energoizdat. 1981.
28. Goryunov V.K. Prostranstvennye flyuktuacii raspredeleniya nejtronov i moshchnosti v kriticheskom reaktore. Atomnaya energiya. 1978. T. 44. Vyp. 4. S. 357–359 (in Russian).
29. Goryunov V.K. Perekosy polya nejtronov v reaktorah pri sluchajno raspredelennyh vozmushcheniyah makrosechenij. Atomnaya energiya. 1980. T. 49. Vyp. 5. S. 321–323 (in Russian).
30. Gomin E.A., Gorodkov S.S. O nekotoryh svojstvah flyuktuacij nejtronnogo polya v yadernom reaktore. Atomnaya energiya. 1979. T. 46. Vyp. 3. S. 187–188 (in Russian).
31. Dollezhal' N.A., Emel'yanov I.Ya. Kanal'nyj yadernyj energeticheskij reaktor. M.: Atomizdat. 1980 (in Russian).
32. Zagrebaev A.M., Nasonova V.A. Veroyatnostnye harakteristiki plotnosti potoka nejtronov v yadernom reaktore pri sluchajnyh vozmushcheniyah v svojstvah sredy. Izv. vuzov. Ser.: Yadernaya energetika. 2009. № 4. S. 71–78 (in Russian).
33. Zagrebaev A.M., Nasonova V.A., Ovsyannikova N.V. Matematicheskoe modelirovanie yadernogo reaktora pri sluchajnyh vozmushcheniyah tekhnologicheskih parametrov. Monografiya. M.: NIYaU MIFI. 2011. 180 s. (in Russian).
34. Zagrebaev A.M., Nasonova V.A. Issledovaniya statisticheskih harakteristik plotnosti potoka nejtronov pri sluchajnyh vozmushcheniyah v svojstvah sredy. Estestvennye i tekhnicheskie nauki. 2010. № 6. S. 562–564 (in Russian).
35. Zagrebaev A. M., Nasonova V. A., Ovsyannikova N. V. Statisticheskie issledovaniya plotnosti potoka nejtronov v yadernom reaktore pri sluchajnyh vozmushcheniyah svojstv sredy. Atomnaya energiya. 2011. T. 111. № 2. C. 88–92 (in Russian).
36. Zagrebaev A.M. Ocenka veroyatnosti obrazovaniya lokal'nyh nadkriticheskih zon pri sluchajnyh vozmushcheniyah svojstv sredy. Algoritmy obrabotki informacii v slozhnyh sistemah. M.: Energoatomizdat. 1991 (in Russian).
37. Zagrebaev A.M. Veroyatnost' obrazovaniya lokal'nyh nadkriticheskih zon pri sluchajnyh vozmushcheniyah material'nogo parametra sredy. Nejtronno-fizicheskie problemy bezopasnosti yaderno-energeticheskih ustanovok: Tezisy dokl. VI Vsesoyuznogo seminara po problemam fiziki reaktorov. Moskva, 4–8 sentyabrya. 1989 g. CNII ATOMINFORM (in Russian).
38. Zagrebaev A.M. Ob ocenke veroyatnosti vybrosa izbytka koefficienta razmnozheniya nejtronov v fazovom ob"eme Trudy H Mezhdunar. nauchno-tekhn. seminara «Sovremennye tekhnologii v zadachah upravleniya, avtomatizacii i obrabotki informacii». 2001 (in Russian).
39. Zagrebaev A.M. O svyazi fizicheskih i statisticheskih harakteristik polya nejtronov pri sluchajnyh vozmushcheniyah svojstv sredy. Inzhenernaya fizika. 2005. № 4. S. 7–11 (in Russian).
40. Zagrebaev A.M., Koz'min L.A., Krajko M.A. Matematicheskoe obespechenie dlya opredeleniya postoyannoj vremeni grafitovoj kladki reaktora RBMK-1000 v passivnom eksperimente. Trudy HIII Mezhdunar. nauch.-tekhn. seminara «Sovremennye tekhnologii v zadachah upravleniya, avtomatiki i obrabotki informacii». M.: Izd-vo MGU. 2004 (in Russian).