Development of Cross-Section Library for DYN3D Code

Development of Cross-Section Library for DYN3D Code

At present, SSTC NRS uses the HELIOS code for generation of few-group cross-section libraries for WWER core calculations. There is an urgent issue of selecting the appropriate approach to implement the cross-section library into the DYN3D code. The paper overviews the application of approaches us...

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Datum:2014
Hauptverfasser: Ovdiienko, I., Ieremenko, M., Kuchin, A., Khalimonchuk, V.
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Sprache:English
Veröffentlicht: Державне підприємство "Державний науково-технічний центр з ядерної та радіаційної безпеки" Держатомрегулювання України та НАН України 2014
Schriftenreihe:Ядерна та радіаційна безпека
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/97633
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Zitieren:Development of Cross-Section Library for DYN3D Code / I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk // Ядерна та радіаційна безпека. — 2014. — № 4. — С. 22-25. — Бібліогр.: 6 назв. — англ.

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spelling irk-123456789-976332016-04-01T03:02:18Z Development of Cross-Section Library for DYN3D Code Ovdiienko, I. Ieremenko, M. Kuchin, A. Khalimonchuk, V. At present, SSTC NRS uses the HELIOS code for generation of few-group cross-section libraries for WWER core calculations. There is an urgent issue of selecting the appropriate approach to implement the cross-section library into the DYN3D code. The paper overviews the application of approaches used by SSTC NRS, such as a multidimensional table and polynomial dependences. The capabilities and possible extension of each approach are described with inherent advantages and disadvantages. In addition, the model development and cross-section preparation for the WWER-1000 radial reflector taking into account discontinuity factors are discussed. Brief results of calculations with the use of different approaches are presented. На даний час ДНТЦ ЯРБ використовує спектральний код HELIOS для підготовки малогрупових бібліотек нейтронно-фізичних констант тепловидільних збірок (ТВЗ) активних зон ВВЕР. У процесі розробки моделей ТВЗ виникає актуальна проблема вибору правильного підходу до реалізації бібліотеки констант у коді DYN3D. У даній роботі надано результати досліджень підходів, що використовує ДНТЦ ЯРБ, — реалізації бібліотеки у вигляді багатовимірної таблиці й поліноміальних залежностей. Розглянуто підходи ДНТЦ ЯРБ до вирішення проблеми розробки моделі та підготовки нейтронно-фізичних констант радіального відбивача для ВВЕР-1000 з урахуванням факторів розривності. Наведено короткі результати розрахункових досліджень при використанні різних підходів. В настоящее время ГНТЦ ЯРБ использует спектральный код HELIOS для подготовки малогрупповых библиотек нейтронно-физических констант тепловыделяющих сборок активных зон ВВЭР. В ходе разработки моделей тепловыделяющих сборок возникает актуальная проблема выбора правильного подхода к реализации библиотеки констант в коде DYN3D. В данной роботе представлены результаты исследований подходов, используемых ГНТЦ ЯРБ, — реализации библиотеки в виде многомерной таблицы и полиномиальных зависимостей. Показаны подходы к решению проблемы разработки модели и подготовки нейтронно-физических констант радиального отражателя для ВВЭР- 1000 с учетом факторов разрывности. Даны краткие результаты расчетных исследований при использовании различных подходов. 2014 Article Development of Cross-Section Library for DYN3D Code / I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk // Ядерна та радіаційна безпека. — 2014. — № 4. — С. 22-25. — Бібліогр.: 6 назв. — англ. 2073-6231 http://dspace.nbuv.gov.ua/handle/123456789/97633 621.039.512 en Ядерна та радіаційна безпека Державне підприємство "Державний науково-технічний центр з ядерної та радіаційної безпеки" Держатомрегулювання України та НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description At present, SSTC NRS uses the HELIOS code for generation of few-group cross-section libraries for WWER core calculations. There is an urgent issue of selecting the appropriate approach to implement the cross-section library into the DYN3D code. The paper overviews the application of approaches used by SSTC NRS, such as a multidimensional table and polynomial dependences. The capabilities and possible extension of each approach are described with inherent advantages and disadvantages. In addition, the model development and cross-section preparation for the WWER-1000 radial reflector taking into account discontinuity factors are discussed. Brief results of calculations with the use of different approaches are presented.
format Article
author Ovdiienko, I.
Ieremenko, M.
Kuchin, A.
Khalimonchuk, V.
spellingShingle Ovdiienko, I.
Ieremenko, M.
Kuchin, A.
Khalimonchuk, V.
Development of Cross-Section Library for DYN3D Code
Ядерна та радіаційна безпека
author_facet Ovdiienko, I.
Ieremenko, M.
Kuchin, A.
Khalimonchuk, V.
author_sort Ovdiienko, I.
title Development of Cross-Section Library for DYN3D Code
title_short Development of Cross-Section Library for DYN3D Code
title_full Development of Cross-Section Library for DYN3D Code
title_fullStr Development of Cross-Section Library for DYN3D Code
title_full_unstemmed Development of Cross-Section Library for DYN3D Code
title_sort development of cross-section library for dyn3d code
publisher Державне підприємство "Державний науково-технічний центр з ядерної та радіаційної безпеки" Держатомрегулювання України та НАН України
publishDate 2014
url http://dspace.nbuv.gov.ua/handle/123456789/97633
citation_txt Development of Cross-Section Library for DYN3D Code / I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk // Ядерна та радіаційна безпека. — 2014. — № 4. — С. 22-25. — Бібліогр.: 6 назв. — англ.
series Ядерна та радіаційна безпека
work_keys_str_mv AT ovdiienkoi developmentofcrosssectionlibraryfordyn3dcode
AT ieremenkom developmentofcrosssectionlibraryfordyn3dcode
AT kuchina developmentofcrosssectionlibraryfordyn3dcode
AT khalimonchukv developmentofcrosssectionlibraryfordyn3dcode
first_indexed 2025-07-07T05:17:46Z
last_indexed 2025-07-07T05:17:46Z
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fulltext 22 ISSN 2073-6237. ßäåðíà òà ðàä³àö³éíà áåçïåêà 4(64).2014 УДК 621.039.512 I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk State Scientific and Technical Center for Nuclear and Radiation Safety, Kyiv, Ukraine Development of Cross­Section Library for DYN3D Code At present time SSTC NRS uses the HELIOS code for generation of few- group cross-section libraries for WWER core calculations. There is an actual problem choosing the appropriate approach to implement the cross-section library into the DYN3D code. The paper overviews the application of approaches used by SSTC NRS, such as a multidimensional table and polynomial dependences. The capabilities and possible extension of each approach are described with inherent advantages and disadvantages. In addition, the model development and cross-section preparation for the WWER-1000 radial reflector taking into account discontinuity factors are discussed. Brief results of calculations with the use of different approaches are presented. K e y w o r d s: WWER; cross-section library; fuel assembly; reflector. Ю. М. Овдієнко, М.Л.Єременко, А. В. Кучин, В. А. Халімончук Розвиток бібліотеки нейтронно-фізичних констант для коду DYN3D На даний час ДНТЦ ЯРБ використовує спектральний код HELIOS для підготовки малогрупових бібліотек нейтронно-фізичних констант тепловидільних збірок (ТВЗ) активних зон ВВЕР. У процесі розробки мо- делей ТВЗ виникає актуальна проблема вибору правильного підходу до реалізації бібліотеки констант у коді DYN3D. У даній роботі надано ре- зультати досліджень підходів, що використовує ДНТЦ ЯРБ, — реалізації бібліотеки у вигляді багатовимірної таблиці й поліноміальних залеж- ностей. Розглянуто підходи ДНТЦ ЯРБ до вирішення проблеми розроб- ки моделі та підготовки нейтронно-фізичних констант радіального від- бивача для ВВЕР-1000 з урахуванням факторів розривності. Наведено короткі результати розрахункових досліджень при використанні різних підходів. К л ю ч о в і с л о в а: ВВЕР; нейтронно-фізичні константи; тепловидільна збірка; відбивач. © I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk, 2014 T he DYN3D code is widely used at SSTC NRS in li- censing activities both for steady-state calculations in reviews of safety substantiation for fuel reload- ing and transient calculations for emergency modes of WWER reactors of Ukrainian NPPs. Since 2006 SSTC NRS has been using the modern spectral HELIOS code for preparation of few-group cross-section librar- ies instead of the out-of-date one-dimensional NESSEL code. It allowed SSTC NRS to increase the accuracy in calculations of the entire complex DYN3D/cross-section library. The basic parameterization of cross-sections in DYN3D is given in the following way: ( ) ( ){ } ( ) ( ){ } ( ){ } mod mod, 0 mod mod, 0 mod mod, 0 mod mod, 0    Σ = Σ + α − ×       × + β γ − γ + β γ − γ × × + δ γ − γ + δ γ − γ × × γ − 0 mod mod,0 2 , 1 , 2 2 , 1 , 0 , 2 , 0 mod 1 1 1 1 1 exp , s s s s b b s b b s f T T C C C C T T where Σ is the actual cross-section; 0 is the reference cross- section; αs, βs,1, βs,2, δs,1, δs,2, γs are parameterization coefficients; Òmod, Òf , γmod, Ñb are actual thermophysical parameters; Òmod, 0, γmod, 0, Ñb,0 are parameters of reference state. Each parameterization coefficient is represented as a sec- ond-order polynomial dependence versus fuel burnup B, as Pi = Pi,0*(1+αi,1B+αi,2B 2). In general, results with use of the basic parameterization of cross-sections are quite acceptable besides the reactivity co- efficient on moderator temperature; particularly on hot zero power states where it shows low absolute values and relative errors more than 100 %. The significant drawback of the basic cross-section library parameterization is the impossibility to use discontinuity fac- tors. The use of discontinuity factors for WWER-1000 fuel as- semblies does not have a significant effect. However, the cross- section for the radial reflector without discontinuity factors gives too high discrepancy in power distribution that can reach up to 10 % for peripheral assemblies. This occurs because the HELIOS library for fuel assemblies uses old parameteriza- tion for the radial reflector in which cross-sections were ad- ditionally adapted by auxiliary program for application without discontinuity factors. Elaboration of basic XS parameterization. The parameteriza- tion was improved by adding the third-order polynomial depen- dence of moderator density β3 and boron acid concentration δ3. ( ) ( ) ( ){ } ( ) ( ){ ( ) } ( ){ } mod mod, 0 mod mod, 0 mod mod, 0 mod mod, 0 mod mod, 0 mod mod, 0 0 mod mod,0 2 3 1 2 3 2 1 , 0 2 , 0 3 3 , 0 mod 1 1 1 1 1 exp . b b b b b b f T T C C C C C C T T    Σ = Σ + α − ×       × + β γ − γ + β γ − γ + β γ − γ × × + δ γ − γ + δ γ − γ + +δ γ − γ × × γ − Additionally, the linear dependence of change in the mod- erator density with parameterization coefficients on boron ISSN 2073-6237. ßäåðíà òà ðàä³àö³éíà áåçïåêà 4(64).2014 23 Development of Cross-Section Library for DYN3D Code acid concentration was introduced in form of δi= δi0 + acij (∆γ). The third-order polynomial dependence on fuel burnup Pi = Pi, 0(1 + αi,1B + αi, 2B 2 + αi,3B 3) was also added. The improved basic cross-section library parameteriza- tion allowed a slight increase in the accuracy of calculating the boron concentration and axial power distribution. However, the reactivity coefficient on moderator temperature remained unsatisfactory. Further elaboration of the basic cross-section parameteriza- tion consisted in introducing the discontinuity factors and pin power distributions from the spectral code with the possibility to increase the calculation accuracy and extend the capabilities of DYN3D code. XS library in form of multidimensional tables. The new cross- section library was prepared for WWER-1000 based on the OECD/NEA and U.S. NRC PWR MOX/UO2 core transient benchmark. This is a five-dimensional table of cross- section with dependence on burnup, moderator density, boron concen- tration, fuel and moderator temperature. The accuracy of this multidimensional table cross-section library will depend on meshing of the whole range of thermo- hydraulic variables. The meshing should be based on balance between the error caused by linear interpolation of cross-sec- tions and the reasonable total number of branch calculations that will define calculation time for library preparation. Based on this analysis, we chose 7 branches for moderator density, 4 branches for boron concentration and fuel temperature, and 3 branches for moderator temperature (Table 1). The total num- ber of branches to cover the whole range of change in thermo- hydraulic parameter amounts to 336. Further meshing causes difficulties with calculation time for library preparation because adding of one branch increases the total number of branches by two times. Table 1. Chosen parameters for multidimensional tables ¹ burnup step Burnup, Moderator density, 3 Boron concentration, Fuel temperature, K Moderator temperature, K 1 0.0 200.0 0.0 293.0 293.0 2 0.5 400.0 4.0 793.0 563.0 3 1.0 500.0 8.0 1393.0 623.0 4 3.0 600.0 16.0 2593.0 – 5 6.0 700.0 – – – 6 9.0 800.0 – – – 7 12.0 1000. – – – … … Total 336 branches for different thermo-hy- draulic parameters25 66.0 Use of the multidimensional table cross-section library (with chosen parameters of branches) increases the accuracy of calculating neutron-physical characteristics of reactor core in comparison with the parameterization form of library, first of all accuracy of reactivity coefficient on moderator tem- perature at HZP (Table 2). It also covers the whole range of changes in core thermal-hydraulic parameters both for normal operation (hot and cold states) and for accidents with admis- sible accuracy. Besides the much greater total number of calculating branch- es in comparison with the library with improved parameteriza- tion (336 vs. 44), this form of library has one more disadvantage. The use of multidimensional table library significantly increases the DYN3D calculating time — by approximately three times. Moreover, in some calculating cases, the iterations were not converged in contrast to the library with improved parameter- ization under the same convergence parameters. Table 2. Reactivity coefficient on moderator temperature at HZP with different types of XS library NPP unit number Experiment BIPR DYN3D (polyn. param.) DYN3D (table param.) KhNPP-2, loading ¹ 1 –6.68( T) –7.38( T) –6.93 –6.16 –5.41 KhNPP-2, loading ¹ 2 –4.3 –5.73 –10.23 –6.47 KhNPP-2, loading ¹ 3 –9.3 –9.16 –13.16 –9.40 KhNPP-2, loading ¹ 4 –12.0 –11.10 –15.36 –11.65 ZNPP-1, loading ¹ 22 –5.60 –4.23 –12.64 –8.96 ZNPP-1, loading ¹ 23 –7.60 –5.54 –13.61 –9.96 ZNPP-1, loading ¹ 24 –8.80 –9.09 –13.55 –9.66 Preparation of cross-section for radial reflector. The aim of preparing the advanced cross-section library for radi- al reflector is to increase the accuracy of power distribution in the core owing to more precise geometry of in-core com- ponents. Specifically, five different XS sets (Fig. 1) calculated by HELIOS were introduced into the library instead of one set in one-dimensional geometry calculated by the NESSEL code. Fig. 1. Five reflector cells of advanced cross-section library for radial reflector The advanced cross-section library for the radial reflector was supplemented with reflector discontinuity factors. The dis- continuity factors were calculated by analytical solution of the 24 ISSN 2073-6237. ßäåðíà òà ðàä³àö³éíà áåçïåêà 4(64).2014 I. Ovdiienko, M. Ieremenko, A. Kuchin, V. Khalimonchuk diffusion equation for two-dimensional hexagonal reactor geometry in non-multiplying material with the approach de- scribed in [4]. The model of each reflector cell for HELIOS calculations represents a macro cell of the considered cell surrounded by six neighboring ones, some of them (from 1 to 3) are fuel assembly cells (Fig. 2). The RDFs calculated with the mentioned approach for in- troduction into the advanced cross-section for radial reflec- tor were averaged over sides of the reflector cells neighboring the core. It is necessary to note that the cross-section with improved parameterization allows the introduction of RDF for each of the six hexagon sides. Effect from the introduction of advanced cross-section for radial reflector was estimated for several fuel campaigns of Ukrainian NPPs. Typical assembly-wise power distributions with use of the averaged 1D reflector NESSEL XS and prepared sets of 2D reflector HELIOS XS are presented in Fig. 3. As fol- lows from the figure, the prepared sets of XS do not only in- crease the accuracy of power distribution for peripheral assem- blies, but also decrease its maximal discrepancy near the core center (for the case from δkq = 0.057 up to δkq = 0.037). Fig. 2. One (third) cell of radial reflector and model with surrounded cells for HELIOS model Fig. 3. Assembly-wise power distributions with use of averaged 1D reflector NESSEL XS (a) and prepared sets of 2D reflector HELIOS XS (b) à b ISSN 2073-6237. ßäåðíà òà ðàä³àö³éíà áåçïåêà 4(64).2014 25 Development of Cross-Section Library for DYN3D Code The multidimensional table cross-section library gives the possibility to take into account spectral effect during reactor core burnup calculation using the DYN3D code. The DYN3D code includes the approach for spectral effect accounting based on usage of plutonium-239 concentration as the spectral history indicator [5]. For this purpose, the multidimensional table cross-section library was supplement with an additional sub-library. The fol- lowing parameters were prepared for the sub-library: - 239Pu and 238U concentrations in standard depletion, - microscopic cross-sections needed for 239Pu calculation, - history coefficients. In the sub-library, these cross-sections and their historical coefficients are also given in multidimensional tables. The consideration of spectral effect is quite appreciable al- ready for the first fuel campaign, starting from zero fuel bur- nup (AER-19 benchmark, first loading, Fig. 4). The calcula- tion accuracy increased not only for axial profile but also for boron acid concentration. The trend of distortion of axial power profile in the core upper part agrees well with results of direct accounting of spectral effect by moderator density for the fuel campaign presented in [6]. Conclusions 1. Use of the multidimensional table cross-section library (with chosen parameters of branches) increases the accuracy of calculating neutron-physical characteristics of reactor core in comparison with the parameterization form of library, first of all accuracy of reactivity coefficient on moderator tempera- ture at HZP. It also covers the whole range of changes in core thermal-hydraulic parameters both for normal operation (hot and cold states) and for accidents with admissible accuracy. 2. The main disadvantages of the multidimensional table cross-section library include a much higher total number of cal- culating branches and worse convergence of iteration process, significantly increasing the DYN3D calculating time. 3. Introduction of advanced cross-sections for the radial reflector increases the accuracy of power distribution for pe- ripheral assemblies and decreases its maximal discrepancy near the core center. 4. The accounting of spectral effect increases the calcula- tion accuracy both for axial profile and for boron acid concen- tration and agrees with results of other approaches to spectral effect accounting. References 1. Grundmann U., Rohde U., Mittag S., Kliem S. (2005), “DYN3D, Version 3.2, Code for Calculation of Transient in Light Water Reactors (LWR) with Hexagonal or Quadratic Fuel Elements. Description of Models and Methods”, Report FZR-434, Rossendorf. 2. Lötsch T., Khalimonchuk V., Kuchin A. (2009), “Proposal of a Benchmark for Core Burnup Calculations for a VVER-1000 Reactor Core”, Proceeding of the 19th Symposium of AER on VVER Reactor Physics and Reactor Safety. 3. “HELIOS methods. Version 1.10”, Studsvik® Scandpower, April 2008. 4. Mittag S., Petkov P.T., Grundmann U. (2003), “Discontinuity Factors for Non-Multiplying Material in Two-Dimensional Hexagonal Reactor Geometry”, Annals of Nuclear Energy 30, pp. 1347—1364. 5. Bilodid I., Mittag S. (2010), “Use of the Local Pu-239 Concentration as an Indicator of Burnup Spectral History in DYN3D”, Annals of Nuclear Energy, Vol. 37, Issue 9, pp. 1208—1213. 6. Bilodid I., Ovdiienko I., Mittag S., Kuchin A., Khalimonchuk V., Ieremenko M. (2012/04), “Assessment of Spectral History Influence on PWR and WWER core”, Kerntechnik, pp. 278—285. Îòðèìàíî 27.10.2014. Fig. 4. Effect of accounting of spectral effect for boron acid concentration (a) and axial power profile in the most loaded FA (b) (AER-19 benchmark, first loading) à b

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