The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors
The mathematical method of optimizing the amount of the alloying element Fe in structural zirconium alloys Zr1%Nb of fuel elements cladding of nuclear reactor-cores of nuclear power plants on the basis of physical experiments to increase their corrosion resistance is considered. Alloying the Zr1%Nb...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Cite this: | The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors / O.V. Yefimov, M.M. Pylypenko, L.M. Lyubchyk, T.V. Potanina, V.P. Kravchenko, T.O. Yesypenko, T.A. Harkusha // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 46-51. — Бібліогр.: 10 назв. — англ. |
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Yefimov, O.V. Pylypenko, M.M. Lyubchyk, L.M. Potanina, T.V. Kravchenko, V.P. Yesypenko, T.O. Harkusha, T.A. 2023-12-10T12:54:11Z 2023-12-10T12:54:11Z 2023 The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors / O.V. Yefimov, M.M. Pylypenko, L.M. Lyubchyk, T.V. Potanina, V.P. Kravchenko, T.O. Yesypenko, T.A. Harkusha // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 46-51. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 81.05.-t, 89.30.Gg, 02.60.-x DOI: https://doi.org/10.46813/2023-144-046 https://nasplib.isofts.kiev.ua/handle/123456789/196101 The mathematical method of optimizing the amount of the alloying element Fe in structural zirconium alloys Zr1%Nb of fuel elements cladding of nuclear reactor-cores of nuclear power plants on the basis of physical experiments to increase their corrosion resistance is considered. Alloying the Zr1%Nb alloy with Fe is promising in the development of the technology for the production of domestic materials for fuel elements claddings for reactors with high reliability and safety. To process the results of experimental studies of corrosion of zirconium alloy with different Fe content, a mathematical method of two-dimensional polynomial comb regression was proposed with its implementation in the Python programming language based on the theory of “machine learning”. The application of this method made it possible to determine the optimal amount of the alloying element Fe for zirconium alloy Zr1%Nb of fuel elements cladding of nuclear power plant reactors with pressurized water. Розглянуто математичний метод оптимізації кількості легуючого елемента заліза Fe в конструкційних цирконієвих сплавах Zr1%Nb оболонок твелів активних зон ядерних реакторів АЕС на основі фізичних експериментів для підвищення їх корозійної стійкості. Легування сплаву Zr1%Nb залізом Fe є перспективним при розробці технології виготовлення вітчизняних матеріалів оболонок твелів для реакторів з високою надійністю і безпекою. Для опрацювання результатів експериментальних досліджень утворення корозії сплавів цирконію з різним вмістом заліза було запропоновано математичний метод двовимірної полiномiнальної гребеневої регресії з реалізацією його мовою програмування Python на основі теорії “машинного навчання”. Застосування цього методу дозволило визначити оптимальне значення необхідної кількості легуючого елемента заліза (Fe) для цирконієвих сплавів Zr1%Nb оболонок твелів реакторів АЕС з водою під тиском. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Thermal and fast reactor materials The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors Метод оптимізації вмісту заліза в конструкційному матеріалі Zr1%Nb для оболонок тепловиділяючих елементів ядерних реакторів АЕС Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors |
| spellingShingle |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors Yefimov, O.V. Pylypenko, M.M. Lyubchyk, L.M. Potanina, T.V. Kravchenko, V.P. Yesypenko, T.O. Harkusha, T.A. Thermal and fast reactor materials |
| title_short |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors |
| title_full |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors |
| title_fullStr |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors |
| title_full_unstemmed |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors |
| title_sort |
method for optimizing the iron content in the structural material zr1%nb for fuel element cladding of npp nuclear reactors |
| author |
Yefimov, O.V. Pylypenko, M.M. Lyubchyk, L.M. Potanina, T.V. Kravchenko, V.P. Yesypenko, T.O. Harkusha, T.A. |
| author_facet |
Yefimov, O.V. Pylypenko, M.M. Lyubchyk, L.M. Potanina, T.V. Kravchenko, V.P. Yesypenko, T.O. Harkusha, T.A. |
| topic |
Thermal and fast reactor materials |
| topic_facet |
Thermal and fast reactor materials |
| publishDate |
2023 |
| language |
English |
| container_title |
Problems of Atomic Science and Technology |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Метод оптимізації вмісту заліза в конструкційному матеріалі Zr1%Nb для оболонок тепловиділяючих елементів ядерних реакторів АЕС |
| description |
The mathematical method of optimizing the amount of the alloying element Fe in structural zirconium alloys Zr1%Nb of fuel elements cladding of nuclear reactor-cores of nuclear power plants on the basis of physical experiments to increase their corrosion resistance is considered. Alloying the Zr1%Nb alloy with Fe is promising in the development of the technology for the production of domestic materials for fuel elements claddings for reactors with high reliability and safety. To process the results of experimental studies of corrosion of zirconium alloy with different Fe content, a mathematical method of two-dimensional polynomial comb regression was proposed with its implementation in the Python programming language based on the theory of “machine learning”. The application of this method made it possible to determine the optimal amount of the alloying element Fe for zirconium alloy Zr1%Nb of fuel elements cladding of nuclear power plant reactors with pressurized water.
Розглянуто математичний метод оптимізації кількості легуючого елемента заліза Fe в конструкційних цирконієвих сплавах Zr1%Nb оболонок твелів активних зон ядерних реакторів АЕС на основі фізичних експериментів для підвищення їх корозійної стійкості. Легування сплаву Zr1%Nb залізом Fe є перспективним при розробці технології виготовлення вітчизняних матеріалів оболонок твелів для реакторів з високою надійністю і безпекою. Для опрацювання результатів експериментальних досліджень утворення корозії сплавів цирконію з різним вмістом заліза було запропоновано математичний метод двовимірної полiномiнальної гребеневої регресії з реалізацією його мовою програмування Python на основі теорії “машинного навчання”. Застосування цього методу дозволило визначити оптимальне значення необхідної кількості легуючого елемента заліза (Fe) для цирконієвих сплавів Zr1%Nb оболонок твелів реакторів АЕС з водою під тиском.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/196101 |
| citation_txt |
The method for optimizing the iron content in the structural material Zr1%Nb for fuel element cladding of NPP nuclear reactors / O.V. Yefimov, M.M. Pylypenko, L.M. Lyubchyk, T.V. Potanina, V.P. Kravchenko, T.O. Yesypenko, T.A. Harkusha // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 46-51. — Бібліогр.: 10 назв. — англ. |
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46 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144
https://doi.org/10.46813/2023-144-046
THE METHOD FOR OPTIMIZING THE IRON CONTENT IN THE
STRUCTURAL MATERIAL Zr1%Nb FOR FUEL ELEMENT CLADDING
OF NPP NUCLEAR REACTORS
O.V. Yefimov
1
, M.M. Pylypenko
2
, L.M. Lyubchyk
1
, T.V. Potanina
1
,
V.P. Kravchenko
3
, T.O. Yesypenko
1
, T.A. Harkusha
1
1
National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine
E-mail: AVEfimov@kpi.kharkov.ua;
2
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine;
3
Odessа Polytechnic National University, Odessa, Ukraine
The mathematical method of optimizing the amount of the alloying element Fe in structural zirconium alloys
Zr1%Nb of fuel elements cladding of nuclear reactor-cores of nuclear power plants on the basis of physical
experiments to increase their corrosion resistance is considered. Alloying the Zr1%Nb alloy with Fe is promising in
the development of the technology for the production of domestic materials for fuel elements claddings for reactors
with high reliability and safety. To process the results of experimental studies of corrosion of zirconium alloy with
different Fe content, a mathematical method of two-dimensional polynomial comb regression was proposed with its
implementation in the Python programming language based on the theory of “machine learning”. The application of
this method made it possible to determine the optimal amount of the alloying element Fe for zirconium alloy
Zr1%Nb of fuel elements cladding of nuclear power plant reactors with pressurized water.
PACS: 81.05.-t, 89.30.Gg, 02.60.-x
INTRODUCTION
The main structural materials for fuel element
cladding of water-cooled thermal neutron reactors both
in our country and abroad are zirconium alloys, which,
unlike other structural materials, have a very small
thermal neutron absorption cross-section (0.18 barn),
which is necessary for the use of low-enriched nuclear
fuel. Such zirconium alloys used in the nuclear power
industry of various countries (Ukraine, Canada, USA,
France, Japan, etc.) include alloys Zircaloy-4 (Zry-4),
E110, E635, E125, M4, M5, MDA, and others. In the
USA, Canada, and Western Europe, two main
zirconium alloys are used for fuel element cladding,
shrouds and channels of light-water and heavy-water
reactors: Zircaloy-4 and Zircaloy-2, and the first is
mainly used for fuel element reactors PWR, the second
– for reactors BWR [1, 2].
In Table 1 shows the chemical composition and
mechanical properties of some zirconium alloys.
Comparison of the mechanical properties of Zry's and
Zr-Nb alloys shows the difference of the zirconium
alloys in both strength and elongation.
In the programs of work carried out in the world to
improve nuclear fuel for new-generation WWER
(PWR) reactors and which are aimed at further
improving the operational reliability of fuel cells with
fuel burn-up to 70…75 (GW·days)/t U) and a campaign
length of up to 6…7 years, much attention is paid to
increasing the resource characteristics of zirconium fuel
element cladding and components of fuel assemblies.
One of the most important requirements for the
structural materials of nuclear reactor cores is their high
corrosion resistance, which should ensure the reliability
and safety of operation of both the reactor plant and the
entire power unit as a whole. Meeting the corrosion
resistance requirement is particularly important for
structural materials of reactor fuel element shells, which
are made of Zr1%Nb zirconium alloy. With a minimum
wall thickness (0.65 mm) for neutron absorption, they
are in the most difficult operating conditions in the core.
That is, during operation, the material of fuel element
shells can deform as a result of radiation damage to the
nuclear fuel in the fuel element, large thermal stresses
occur in the cladding due to significant temperature
changes, and the material of the cladding can change its
physical and mechanical properties under the influence
of neutron irradiation. Therefore, ensuring high
corrosion resistance of fuel element cladding of nuclear
reactors of nuclear power plants is an urgent scientific
and technical problem of the world nuclear power
industry [1, 3].
The results of long-term studies of the purification
processes of zirconium and alloy Zr1%Nb, which was
obtained using Ukrainian technology in the form of
ingots in the NSC KIPT of the National Academy of
Sciences of Ukraine, are presented in [3–6]. Various
methods in laboratory conditions were used for those
researches, and properties of the alloys were determined
using mathematical methods for processing
experimental data, taking into account the uncertainty of
the initial data. Research on the structure, chemical
composition, thermal desorption, hardness and
microhardness of Zr1%Nb alloy samples, as well as its
corrosion resistance were carried out.
Zirconium alloy Zr1%Nb, in which Nb is an
alloying element, contents of about 20 impurities (Hf,
Al, Ti, Fe, N, F, C, Si, Cl, etc.). At the same time, it is
known that Al, Ti, N, C reduce the corrosion resistance
of zirconium in water at high temperatures, and Fe
increases the corrosion resistance of zirconium in water
and steam environments [7].
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 47
Table 1
Chemical composition of zirconium alloys [1, 3]
Parameter Zircaloy-2 Zircaloy-4 Е110 Е125
Chemical composition, wt.%
Zr 98.6…97.8 98.4…97.8 ~99.0 ~97.5
Nb – – 1.0 2.5
Sn 1.2…1.7 1.2…1.7 – –
Fe 0.05…0.15 0.18…0.24 – –
Cr 0.07…0.20 0.07…0.13 – –
Ni 0.03…0.08 – – –
Σ (Fe+Cr+Ni) 0.18…0.38 – – –
Σ (Fe+Cr) – 0.28…0.37 – –
O2 0.09…0.15 0.10…0.15 – –
N2 < 0.006 < 0.006 – –
Mechanical properties at 20 °С
Elongation ratio δ, %, at 300 °С 28…40 28…40 37…50 17…26
Ultimate strength σВ, kgf/mm²
(МN/m
2
)
22
(216)
22
(216)
15…19
(147…186)
22…34
(236…333)
Yield strength σ0.2, kgf/mm²
(МN/m
2
)
11
(108)
11
(108)
12…16
(118…157)
20…30
(196…294)
For studies of the effect of iron on the properties of
the Zr1%Nb alloy, samples of the alloy with an iron
content from 0.012 to 0.192 wt.% were made at the
NSC KIPT. Sponge (magnesium-thermal) zirconium
was used as the base of the alloy, which provides an
increase in the heat resistance of fuel element cladding
in the conditions of the loss-of-coolant accident
(LOCA) for light-water reactors.
Additional alloying of zirconium and its alloy
Zr1%Nb with iron is promising in the development of
alloys for reactors with high reliability and safety of
operation, since an increase in the iron content in the
zirconium alloy provides the material of the cladding
tubes with the necessary creep resistance and hardening
under irradiation, which ensures the design margin of
stability and increases its corrosion and radiation
resistance in the conditions of the nuclear reactor
operation [5]. It is also known that with an increase in
the iron content of the Zr1%Nb alloy in the structure of
cladding tubes, the amount of Laves phase – Zr(Nb,Fe)2
secretions increases, which favorably affects their
corrosion resistance in water environment, especially
for cladding tubes made of alloys based on sponge
zirconium. Iron under the action of irradiation comes
out from the Laves phase into the matrix with the
formation of secondary finely dispersed precipitates and
thus delays the formation of dislocation loops <с>-type
which are responsible for accelerating the radiation
growth of the alloy. At the same time it was established
that as a result of additional alloying with iron the
technological efficiency of the Zr1%Nb alloy decreases
requiring the development of a new deformation and
thermal scheme of tube manufacturing [6, 7].
Therefore, determination of the optimal iron content,
which will not reduce the manufacturability of the alloy,
but will increase the performance characteristics of the
Zr1%Nb alloy and its service life, is an urgent task.
INITIAL DATA AND TASK SETTING
Thus, the problem statement can be formulated as
follows:
You need to restore the V (F, T) dependency, where
V is the corrosion rate, mg/(dm
2
·h); T is the observation
period, h; F – iron content, %.
Features of this task:
– small sample of observations, which is associated
with the high cost of conducting the experiment – (7
pairs of samples with a fixed mass content of iron for
each pair were studied);
– lack of a priori information about the type of
dependency you are looking for, which does not allow
you to set its analytical model in advance.
To solve this problem, these features determine the
feasibility of using the “machine learning” method.
The data of the results of experimental
measurements of weight gain of Zr1%Nb samples after
long-term corrosion tests are given in Table 2.
According to Table 2 formed a training sample
(training dataset in the terminology of “machine
learning”), presented in Table 3.
48 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144
Table 2
Results of experimental corrosion tests of zirconium alloy samples with different iron content
Parameters
Iron content F, wt.%
0.012 0.042 0.072 0.102 0.132 0.162 0.192
1000 h testing
Weight gain, mg/dm
2
36.3
35.3
36.6
33.3
32.8
31.8
28.7
29.9
31.3
31.5
33.3
32.4
32.54
33.98
Average weight gain,
mg/dm
2
35.8 34.95 32.3 29.3 31.4 32.85 33.26
Average corrosion
rate, mg/(dm
2
·h)
0.0358 0.03495 0.0323 0.0293 0.0314 0.03285 0.03326
2000 h testing
Weight gain, mg/dm
2
67.1
68.23
58
50.89
53.17
48.52
42
44.13
46.7
45.75
46.12
48.2
48.7
46.7
Average weight gain,
mg/dm
2
67.665 54.445 50.845 43. 065 46.225 47.185 47.7
Average corrosion
rate, mg/(dm
2
·h)
0.033833 0.027223 0.025423 0.021533 0.023113 0.023593 0.02385
3000 h testing
Weight gain, mg/dm
2
77.42
81.77
64.47
66.25
65.87
57.87
56.21
58.1
60.69
61.75
64.74
63.16
67.63
63.12
Average weight gain,
mg/dm
2
79.595 65.36 61.87 57.155 61.22 63.95 65.375
Average corrosion
rate, mg/(dm
2
·h)
0.026532 0.021787 0.020623 0.019052 0.020407 0.021317 0.021792
4000 h testing
Weight gain, mg/dm
2
92.74
92.42
85.18
88.75
80.79
85.24
73.2
79.1
81.03
82.58
83.19
85. 09
90.61
88.73
Average weight gain,
mg/dm
2
92.58 86.965 83. 015 76.15 81.805 84.14 89.67
Average corrosion
rate, mg/(dm
2
·h)
0.023145 0.021741 0.020754 0.019038 0.020451 0.021035 0.022418
Table 3
Training Dataset
Т, h
F, %
0.012 0.042 0.072 0.102 0.132 0.162 0.192
1000 0.0358 0.03495 0.0323 0.0293 0.0314 0.03285 0.03326
2000 0.033833 0.027223 0.025423 0.021533 0.023113 0.023593 0.02385
3000 0.026532 0.021787 0.020623 0.019052 0.020407 0.021317 0.021792
4000 0.023145 0.021741 0.020754 0.019038 0.020451 0.021035 0.022418
RESULTS AND DISCUSSION
Two-dimensional polynomial ridge regression was
used to restore the dependence V (F, T). The degree of
the polynomial and the regularization coefficient were
selected using a cross-validation procedure.
The dependency recovery algorithm is implemented
in the Python programming language using the scikit-
learn, pyswarm, and matplotlib libraries [8–10].
As a result of calculations, the degree of polynomial
3 and the regularization coefficient 0.6734 were
selected.
The restored dependency is obtained in the
following form:
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 49
2 2 3 2 2 3
0 1 2 3 4 5 6 7 8 9( , ) .V F T a a T a F a T a TF a F a T a T F a TF a F (1)
The coefficients of the approximating polynomial
are shown in Table 4.
A three-dimensional visualization of the restored
dependence of V (F, T) and the training dataset is shown
in Fig. 1.
Table 4
Coefficients of the approximating polynomial
-0.68953395 -0.59437232 -0.22295343 0.36915152 0.0747594
0.33696609 -0.09272832 0.14789556 -0.05873025 -0.09225197
a
b
Fig. 1. Restored dependence V (F, T) and training dataset
50 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144
The function V (F, T) is shown using contour graphs in Fig. 2.
a b
Fig. 2. Contour graphs of the restored dependency V (F, T)
In Fig. 3 shows sections of the approximating dependence V (F, T) for different values of the observation time.
Fig. 3. Sections of the approximating dependence V (F, T)
CONCLUSIONS
Long-term corrosion tests of samples of alloy
Zr1%Nb with different iron content, obtained by
Ukrainian technology, in the water environment in
composition and parameters (temperature 350 °C,
pressure 16.5 MPа), which corresponds to the coolant of
the primary circuit WWER-1000 when working at
power, and mathematical processing of the results of
these studies allowed us to determine the optimal
amount of iron, which leads to an increase in the
corrosion resistance of alloy Zr1%Nb in working
conditions in the core of WWER-1000.
The results obtained allow us to conclude that the
dependence V (F, T) at a fixed T has a pronounced one-
extreme character, which indicates the presence of an
optimal value of the mass content of iron, which
provides a minimum rate of corrosion, and is localized
around F = 0.1%. Consequently, the optimal amount of
iron, which will increase the corrosion resistance of the
alloy Zr-1%Nb under operating conditions in the core of
WWER-1000, it is 0.1 wt.%.
The presence of an optimal value of the alloying iron
content is typical for all zirconium alloys of Zr-Nb
system. In the future, this opens up the possibility of
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 51
producing fuel element cladding of increased corrosion
resistance for the nuclear fuel cycle of Ukraine.
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Article received 06.01.2023
МЕТОД ОПТИМІЗАЦІЇ ВМІСТУ ЗАЛІЗА В КОНСТРУКЦІЙНОМУ МАТЕРІАЛІ Zr1%Nb
ДЛЯ ОБОЛОНОК ТЕПЛОВИДІЛЯЮЧИХ ЕЛЕМЕНТІВ ЯДЕРНИХ РЕАКТОРІВ АЕС
О.В. Єфімов, М.М. Пилипенко, Л.М. Любчик, Т.В. Потаніна, В.П. Кравченко,
Т.О. Єсипенко, Т.А. Гаркуша
Розглянуто математичний метод оптимізації кількості легуючого елемента заліза Fe в конструкційних
цирконієвих сплавах Zr1%Nb оболонок твелів активних зон ядерних реакторів АЕС на основі фізичних
експериментів для підвищення їх корозійної стійкості. Легування сплаву Zr1%Nb залізом Fe є
перспективним при розробці технології виготовлення вітчизняних матеріалів оболонок твелів для реакторів
з високою надійністю і безпекою. Для опрацювання результатів експериментальних досліджень утворення
корозії сплавів цирконію з різним вмістом заліза було запропоновано математичний метод двовимірної
полiномiнальної гребеневої регресії з реалізацією його мовою програмування Python на основі теорії
«машинного навчання». Застосування цього методу дозволило визначити оптимальне значення необхідної
кількості легуючого елемента заліза (Fe) для цирконієвих сплавів Zr1%Nb оболонок твелів реакторів АЕС з
водою під тиском.
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://doi.org/10.46813/2021-135-077
https://doi.org/10.46813/2021-135-077
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://vant.kharkov.ua/ARTICLE/VANT_2018_1/article_2018_1_003.pdf
https://scikitlearn.org/
https://www.worldcat.org/search?q=au%3ARhinehart%2C+R.+Russell%2C&qt=hot_author
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