High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator
At high-temperature oxidation of nuclear graphite, the oxidant flow in the near-surface region is taken into account. Macro- and microscopic modeling of the oxidation of the near-surface layer was carried out. The calculation of the diffusion coefficient of gaseous components as a function of temper...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator / A.I. Komir, N.P. Odeychuk, V.I. Tkachenko, A.L. Ulybkin, A.A. Nikolaenko // Вопросы атомной науки и техники. — 2018. — № 1. — С. 142-147. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-1370132020-12-08T15:12:41Z High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator Komir, A.I. Odeychuk, N.P. Tkachenko, V.I. Ulybkin, A.L. Nikolaenko, A.A. Физика и технология конструкционных материалов At high-temperature oxidation of nuclear graphite, the oxidant flow in the near-surface region is taken into account. Macro- and microscopic modeling of the oxidation of the near-surface layer was carried out. The calculation of the diffusion coefficient of gaseous components as a function of temperature and concentration is given. The influence of the motion of the surface layer of the oxidizer on the concentration of gaseous components is studied. При високотемпературному окисленні ядерного графіту врахований потік окислювача в приповерхневій області. Проведено макро- і мікроскопічне моделювання окислення приповерхневого шару. Наведено розрахунок коефіцієнта дифузії газоподібних компонент у залежності від температури і концентрації. Досліджено вплив обліку руху приповерхневого шару окислювача на концентрацію газоподібних компонентів. При высокотемпературном окислении ядерного графита учтен поток окислителя в приповерхностной области. Проведено макро- и микроскопическое моделирование окисления приповерхностного слоя. Приведен расчет коэффициента диффузии газообразных компонент в зависимости от температуры и концентрации. Исследовано влияние учета движения приповерхностного слоя окислителя на концентрацию газообразных компонентов. 2018 Article High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator / A.I. Komir, N.P. Odeychuk, V.I. Tkachenko, A.L. Ulybkin, A.A. Nikolaenko // Вопросы атомной науки и техники. — 2018. — № 1. — С. 142-147. — Бібліогр.: 9 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/137013 621.039.53 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Физика и технология конструкционных материалов Физика и технология конструкционных материалов |
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Физика и технология конструкционных материалов Физика и технология конструкционных материалов Komir, A.I. Odeychuk, N.P. Tkachenko, V.I. Ulybkin, A.L. Nikolaenko, A.A. High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator Вопросы атомной науки и техники |
| description |
At high-temperature oxidation of nuclear graphite, the oxidant flow in the near-surface region is taken into account. Macro- and microscopic modeling of the oxidation of the near-surface layer was carried out. The calculation of the diffusion coefficient of gaseous components as a function of temperature and concentration is given. The influence of the motion of the surface layer of the oxidizer on the concentration of gaseous components is studied. |
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Article |
| author |
Komir, A.I. Odeychuk, N.P. Tkachenko, V.I. Ulybkin, A.L. Nikolaenko, A.A. |
| author_facet |
Komir, A.I. Odeychuk, N.P. Tkachenko, V.I. Ulybkin, A.L. Nikolaenko, A.A. |
| author_sort |
Komir, A.I. |
| title |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| title_short |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| title_full |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| title_fullStr |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| title_full_unstemmed |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| title_sort |
high-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2018 |
| topic_facet |
Физика и технология конструкционных материалов |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/137013 |
| citation_txt |
High-temperature oxidation of nuclear graphite with account of movement of the surface layer of oxidator / A.I. Komir, N.P. Odeychuk, V.I. Tkachenko, A.L. Ulybkin, A.A. Nikolaenko // Вопросы атомной науки и техники. — 2018. — № 1. — С. 142-147. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-10T02:17:26Z |
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| fulltext |
ISSN 1562-6016. PASТ. 2018. №1(113), p. 142-147.
UDC 621.039.53
HIGH-TEMPERATURE OXIDATION OF NUCLEAR GRAPHITE
WITH ACCOUNT OF MOVEMENT OF THE SURFACE LAYER
OF OXIDATOR
A.I. Komir, N.P. Odeychuk, V.I. Tkachenko, A.L. Ulybkin, A.A. Nikolaenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: komir@kipt.kharkov.ua
At high-temperature oxidation of nuclear graphite, the oxidant flow in the near-surface region is taken into
account. Macro- and microscopic modeling of the oxidation of the near-surface layer was carried out. The
calculation of the diffusion coefficient of gaseous components as a function of temperature and concentration is
given. The influence of the motion of the surface layer of the oxidizer on the concentration of gaseous components
is studied.
INTRODUCTION
Macro- and microscopic modeling of the processes
of high-temperature oxidation of nuclear graphite of the
MPG grade was carried out taking into account the
motion of the gas flow near the surface layer of the
oxidizer.
Currently, experiments and calculations are being
carried out to justify passive safety in the event of an
emergency situation for nuclear power systems of the
IV generation. In view of the possibility of
distinguishing the properties of graphite within 10% in
one structural element, a fairly general way of justifying
the safety without violating the structural integrity of the
structural element and for a wide class of carbon
materials is required.
As part of the solution of this problem is given
modeling technique which takes into account the
microstructure of the oxidation of the sample, and based
on the data obtained allows the simulation of the
oxidation process.
To investigate the rate of oxidation of nuclear
graphite, a series of experiments were carried out,
during which activation energies and degrees of
oxidation reaction for different types of nuclear graphite
were obtained.
In the experimental work [1], the researchers used
the stream from the He-O2 mixture with the stream
through the reaction chamber 7…18 of the STLP
(Standard liters per minute), which is a rather large flux
through reaction chamber with allowance for a small
macroscopic reaction surface of 39.58 cm
2
, and a high
oxidation temperature of 813…903 K, a number of
other investigators used oxidation conditions with fluxes
given in Table 1.
Table 1
Comparison of flows through the reaction chamber and
temperatures of graphite oxidation experiments [1, 2]
Temperature,
°С
Concentra-
tion O2
Gas
flow,
SLPM
Activation
energy
450…750 0.2 0.496 201
550…650 0.2 – 210
650…900 0.013 0 324
700…1500 0.05…0.19 0.2…4.5 199.72
540…630 0.03…3.2 7…18 218
The method for separating the modes of oxidation of
nuclear graphite in the 3 stages indicated in Fig. 1.
Fig. 1. Modes of oxidation of nuclear graphite [3]
The oxidation regime limited by chemical kinetics
(a) is characterized by a slight change in the
concentration of the oxidant in the interior of the sample
and by the restriction of the rate of oxidation by the
processes of chemical kinetics at a given temperature.
This mode, according to Mohamed El-Genk, is in the
temperature range 400…800 K.
The oxidation regime limited by diffusion in the
internal space (b) is characterized by an increased
temperature in comparison with regime a of
800…1000 K. Under this oxidation regime, the
concentration of the oxidant decreases substantially with
increasing distance from the surface and is the main
limiting factor in the oxidation of nuclear graphite.
The oxidation regime of the near-surface layer (c) is
characterized by high oxidation temperatures > 1200 K
and the presence of an oxidizer only in a small near-
boundary layer.
Within the framework of this separation by
temperature, the dimensionality factor of the samples
was not taken into account, which is quite significant.
This question was partially considered in the framework
of the study [4] which presents analytical solutions of
differential diffusion equations that indicate the depth in
which 5% of the oxidant concentration is concentrated
mailto:komir@kipt.kharkov.ua
relative to the concentration of the near-surface level,
Fig. 2.
Fig. 2. Depth of 5% oxidant concentration relative to
the near-surface concentration level [4]
In Fig. 2 shows the difference between the
calculated and changed values of the oxygen
concentration, which, based on the extrapolation of the
data, can differ by an order of magnitude in the
oxidation regime a.
The modeling based on the representation of
graphite in the form of a continuous medium was made
by the researchers in the work [3], shown in Fig. 3. The
diameter of the sample was 21 mm, height 30 mm.
Based on the analytical solution for nuclear graphite
H451 with an activation energy of 186…960 J/mole
oxidation during air oxidation [4]. It can be argued that
for simulated temperatures, it is necessary to take into
account the volume of the participating in the oxidation,
since for a temperature of about 900 K the sample will
transfer from the oxidation regime limited by diffusion
to the oxidation regime of the boundary layer, since a
5% concentration will be at a depth of less than half the
width of the sample, if it is assumed that the difference
in the distribution of the oxidant concentration in the
interior of the sample for these types of graphite is not
significant.
Fig. 3. Simulation of oxidation of nuclear graphite [2]
Based on the modeling presented in the study [2],
Fig. 3, semi-empirical formulas on the reaction rate
were obtained. The ratio of the resulting concentration
of the gas mixture, it was suggested that the main
determining factor for the oxidation rate is the near-
surface concentration of the oxidant, which is quite true
for temperatures over 1200 °C. However, the diffusion
to the volume of the sample needs to be clarified for the
modeling temperatures used in this work –
700…1500 °C.
In work [2], to obtain a sufficiently accurate
correspondence between the accuracy of the simulation
and the experimental data, a number of correction
coefficients were introduced, including for the
Sherwood number.
PURPOSE OF THE WORK
The aim of the work was to consider the distribution
of the oxidant concentration in the volume of nuclear
graphite taking into account the motion of the surface
layer of the oxidizer.
In considering the task posed, the following were
decided:
• Macroscopic modeling of oxidizer fluxes in the
reaction chamber to find the oxidizer flow rate in the
near-surface layer.
• Calculation of the diffusion coefficients for the
modeling temperature of 873 K.
• Microscopic modeling of the oxidation of nuclear
graphite, taking into account the results of macroscopic
modeling with the distribution of the concentration of
reaction products.
THE PROCEDURE FOR MODELING
OXIDATION PROCESSES
As part of this work was proposed use direct
modeling to justify approaching the numerical solution
of the problem of oxidation of nuclear graphite
temperature range takes into account the diffusion of
oxidation mode.
To determine the flows of the near-surface layer of
the oxidizer, modeling was carried out using the
software package Solid Works Flow Simulation [5] in
the model volume of the oxidation chamber.
To simulate microscreen oxidation of nuclear
graphite, a package was used to solve the problem of
applied hydrodynamics Open FOAM, taking into
account the bulk and surface reactions.
The surface reaction was taken into account:
22 2 , (190...116) kJ/mole.surfC O CO
The bulk reaction considered in the simulation:
2 22 2 , 213 kJ/mole.volumeCO O CO
Changes in the coefficients of self-diffusion and
mutual diffusion of the oxidant and reaction products as
a function of temperature were taken into account.
Based on the work [6], the calculation was used for
the diffusion coefficients for each component of the
three component gas mixture:
,
, ,
1
,A
A mixture
B C
A B A C
x
D
x x
D D
where ,A mixtureD – the diffusion coefficient,
respectively, of component A of the gas mixture relative
to the whole mixture, m
2
/s; ,A BD and ,A CD –
coefficient of mutual diffusion, respectively, of
components A and B, and A and C of the gas mixture
component; Ax , Bx , and Cx – molar fraction,
respectively; of components A, B, and C of the gas
mixture.
(1)
To calculate the diffusion coefficients of a binary
mixture, we used the expression [6]:
7
12
3
1 2 1 2
2 (1,1)
12 12 12
2.6280 10
( ) / 2
,
*( *)
D
T M M M M
p T
(2)
where
12D is the diffusion coefficient of the binary
mixture, m
2
/s; T – the temperature, K;
1M ,
2M
– the
molecular weight of the first and second components; p
is the pressure, atm;
12 *T – the reduced temperature is
equal, is a dimensionless quantity
12
kT
;
12 , Å;
12
k
,
K – parameters of the potential energy of molecules,
characterizing the interaction of molecules of types 1
and 2;
(1,1)
12 12*( *)T is the collision integral for
molecular diffusion, which is a function of the reduced
temperature.
To calculate the diffusion coefficient in the first
approximation, it is sufficient to use an integral with
values l,s equal to 1, both for pure gas and for a gas
mixture [7], indices 1, 2 denote the types of two
molecules participating in the collision.
For the components of a binary gas mixture, the
Lennard-Jones potential constants were calculated from
the following expressions [6]:
,AB A B
(3)
.
2
A B
AB
(4)
To calculate the diffusion tensor, the values of the
Lennard-Jones potential constants for the simulated
gases are required [7], and the results of calculations for
the binary diffusion of O2-CO, O2-CO2, CO-CO2
(Tabl. 2).
Based on the Lennard-Johnson constants (Tabl. 3)
we find the values of the reduced temperature.
The intermediate values of the collision integral
(1,1) * were calculated by linear interpolation based on
the nearest values.
The tabulated values of the collision integral were
taken from the work [8].
Table 2
The Lennard-Jones potential constants
Gas , K
k
, Å
O2 113 3.433
CO 110 3.590
CO2 190 3.996
O2-CO 111.49* 3.5115**
O2-CO2 146.53* 3.7145**
CO-CO2 144.57* 3.793**
*Calculated on the basis of (1), **calculated on the
basis of (2).
Table 3
The reduced temperature and the values of the collision
integral for gases and mixtures of gas components
Gas and
mixtures
*T
(1,1) *
873.2 K 1073.2 K
O2 9.4973 0.7490
CO 9.7564 0.7456
CO2 5.6484 0.8229
O2-CO 9.6260 0.7473
O2-CO2 7.3241 0.7836
CO-CO2 7.4234 0.7818
Based on the data obtained in Tables 2 and 3 values,
the diffusion tensors of the three-component mixture
were found for three simulated temperatures (Tabl. 4).
Table 4
The diffusion tensor
T, K The diffusion tensor
ijD , x10
-4
m
2
/s
873.2
1,85 1.83 1.4
1.83 1.82 1.4
1.4 1.4 1.06
Index 1 corresponds to O2, 2 – CO, 3 – CO2.
In calculating the diffusion coefficients, 3 significant
figures were taken, since the proposed approach has an
accuracy in percent of the change to experimental data
[6], which is the third significant figure.
The law of an ideal gas was used to obtain the gas
density as a function of temperature.
In microscopic modeling, a reconstructed graphite
microstructure was used in the size of 50 samples with a
size of 5000x1000 μm.
The porous structure of the nuclear graphite was
reconstructed using the S gems multicriteria statistics
package, the source codes of which are available in free
access. Subsequently, the result of the reconstruction
was ported as the initial geometry for modeling in a
freely distributed package for solving the problems of
numerical hydrodynamics Open FOAM [9].
THE DISCUSSION OF THE RESULTS
Figs. 4–7 shows the results of simulating gas flows
in the oxidation chamber.
Fig. 4. Distribution of velocities in the volume of the
oxidation chamber in the section of the YZ plane
Fig. 5. Distribution of velocities in the volume of the
oxidation chamber in the section of the XZ plane
Fig. 6. Flow trajectories in the volume of the
oxidation chamber in the section of the YZ plane
Fig. 7. Flow trajectories in the volume of the oxidation
chamber in the section of the XZ plane
Fig. 8. Increased cross section of gas flow velocities
near the samples
Based on the simulation results presented in Figs. 4–
8, we can conclude that at 873 K the near-surface
currents have velocities in the range 0.001…-0.027 m/s.
These data were used as the basis for specifying a near-
surface flow for modeling the oxidation of the micro-
structure of nuclear graphite.
RESULTS OF MICROSCOPIC MODELING
The results of microscopic modeling are shown in
Figs. 9–13.
Fig. 9. Distribution of CO concentration in the near-
surface region with a speed of oxidizer 0.027 m/s
Fig. 10. Distribution of CO2 concentration in the near-
surface region with a speed of oxidizer 0.027 m/s
The presented results indicate a decrease in the
reaction products in the porous volume of graphite by
more than 2 times, which can significantly influence the
modeling of the diffusion oxidation regime in samples
with a significant decrease in the oxidant concentration
in depth and with geometric dimensions comparable to a
depth of 95% of the oxidant concentration for the
simulated temperature.
It can be seen from the simulation of a slight change
in the oxidant concentration in the meso porosity.
Fig. 11. The distribution of the velocities of gas flows in
the near-surface region of nuclear-graphite modeling
Fig. 12. Distribution of CO concentration in the near-
surface region without taking into account the motion of
the near-surface layer
Fig. 13. Distribution of CO2 concentration in the near-
surface region without taking into account the motion of
the near-surface layer
CONCLUSIONS
1. For the first time, macroscopic and microscopic
modeling of the oxidation of the near-surface layer of
nuclear graphite was carried out, taking into account the
motion of the near-surface layer.
2. The tensor of binary diffusion of gaseous oxidant
components and reaction products is calculated for the
temperature of 873 K.
3. In simulation, the concentration of reaction
products is shown to be smaller by a factor of 2, taking
into account and without taking into account the motion
of the near-surface layer, which implies a comparable
influence of the motion of the near-surface layer and the
diffusion of gaseous reaction products when considering
mesoprostability.
4. The necessity of modeling the microstructure of
nuclear graphite is shown, in view of the presence of an
essentially unchanged oxidant concentration in the
mesopores, which can significantly affect the oxidation
dynamics upon transition to higher temperature
oxidation modes of the samples, with linear dimensions
comparable to the penetration depth of the oxidizer.
REFERENCES
1 E.S. Kim, H.C. No. Measurements of Kinetic
Parameters of Nuclear Graphite IG-110 for HTGR //
Air-ingress. In Korean Nuclear Society Spring Meeting,
2004, 13 p.
2 E.S. Kim, H.C. No. Experimental study on the
oxidation of the nuclear graphite and development of an
oxidation model // Journal of Nuclear Materials. 2006,
v. 349 (1-2), p. 182-194;
doi:10.1016/j.jnucmat.2005.10.015
3 M.S. El-Genk. Diffusion Velocity Correlation for
Nuclear Graphite Gasification at High Temperature and
Low Reynolds Numbers // ICAPP-2012. 2012, v. 505,
p. 415-421.
4 R.P. Wichner, T.D. Burchell, C.I. Contescu.
Penetration depth and transient oxidation of graphite by
oxygen and water vapor // Journal of Nuclear
Materials. 2009, v. 393 (3), p. 518-521.
5 Solid Works. https://www.solidworks.com/ –
Title from the screen.
6 D. Hirschfelde, C. Curtiss, R. Byrd. Molecular
theory of gases and liquids / E.V. Stupochenko, Ed.
(Translated from). Moscow, 1961.
7 Ed. Nikolsky B.P. Chemical Handbook
(Chemistry), 1982.
8 S. Bretschneider. Properties of gases and liquids.
M., 1966.
9 OpenFOAM. http://www.openfoam.com/ – Title
from the screen.
Article received 22.11.2017
ВЫСОКОТЕМПЕРАТУРНОЕ ОКИСЛЕНИЕ ЯДЕРНОГО ГРАФИТА С УЧЕТОМ
ДВИЖЕНИЯ ПРИПОВЕРХНОСТНОГО СЛОЯ ОКИСЛИТЕЛЯ
А.И. Комир, Н.П. Одейчук, В.И. Ткаченко, А.Л. Улыбкин, А.А. Николаенко
При высокотемпературном окислении ядерного графита учтен поток окислителя в приповерхностной
области. Проведено макро- и микроскопическое моделирование окисления приповерхностного слоя.
Приведен расчет коэффициента диффузии газообразных компонент в зависимости от температуры и
концентрации. Исследовано влияние учета движения приповерхностного слоя окислителя на концентрацию
газообразных компонентов.
ВИСОКОТЕМПЕРАТУРНЕ ОКИСЛЕННЯ ЯДЕРНОГО ГРАФІТУ З УРАХУВАННЯМ
РУХУ ПРИПОВЕРХНЕВОГО ШАРУ ОКИСЛЮВАЧА
А.І. Комір, М.П. Одейчук, В.І. Ткаченко, А.Л. Улибкін, А.О. Ніколаенко
При високотемпературному окисленні ядерного графіту врахований потік окислювача в приповерхневій
області. Проведено макро- і мікроскопічне моделювання окислення приповерхневого шару. Наведено
розрахунок коефіцієнта дифузії газоподібних компонент у залежності від температури і концентрації.
Досліджено вплив обліку руху приповерхневого шару окислювача на концентрацію газоподібних
компонентів.
|