Numerical study of hyperstoichiometric fuel creep (UO2+x) in fuel clad interaction of WWER1000

Annals of Nuclear Energy 133 (2019) 950–959

Contents lists available at ScienceDirect

Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Numerical study of hyperstoichiometric fuel creep (UO2+x) in fuel clad interaction of WWER1000 M. Safari, M. Aghaie ⇑, A. Minuchehr, Gh. Allahyarizadeh Engineering Department, Shahid Beheshti University, G.C., P.O. Box: 1983963113, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 17 October 2018 Received in revised form 14 May 2019 Accepted 15 July 2019

Keywords: Fuel pellet Densification Swelling Fuel creep WWER1000 Hyperstoichiometric fuel (UO2+x)

a b s t r a c t Nuclear fuel is faced with extreme thermomechanical environments during its operating time. In this period, fuel mechanical response is deeply influenced by inherent heterogeneous microstructures, dependent on stress and temperature. Under the reactions occurring inside the reactor, the fuel crystal will change, and the UO2 will be UO2±x. Creep as a slow deformation process, strongly affected by this irradiation. Indeed, the hyperstoichiometric crystals effect the creep rate and mechanical stresses. In this article, the thermomechanical behavior of WWER1000 fuel pellets considering the hyperstoichiometric fuel (UO2+x) is studied. Fuel swelling, densification, thermal stress and creep are numerically considered and pellet clad interactions (PCIs) are evaluated. For validating the model, the results for pellet clad interactions are compared with experimental data. The hyperstoichiometric study of fuel cladding mechanical interaction in WWER1000 shows advancement of mechanical interaction during fuel burnups. It is found while the fuel and clad interaction occurs in 50.8 MWd/kgU for UO2, by increasing the amount of x and hyperstoichiometric fuel in the pellet, the pellet clad interactions will occur in lower burnups. These advancements for several hyperstoichiometric fuels are calculated and results are discussed. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Nuclear fuels are subject to severe thermal conditions. Fuel mechanical response is deeply affected by an inhomogeneous microstructure that inherently dependent on stress levels and temperature (Baron and Hallstadius, 2012). Evaluation of these microstructures is crucial to obtain the macroscopic response associated with these environments to predict the mechanical and transient fuel efficiency (Van Brutzel et al., 2015). Microstructures are affected by irradiation and creep rate changes. The activation energy of creep is very sensitive to the stoichiometry (Gao et al., 2010). The addition of oxygen atoms increases the plastic deformation of UO2 thus increases the creep rate and affects thermal conductivity. Stoichiometry changes the cations diffusion. Therefore, the threshold stress depends on stoichiometry (Fink, 2000). However, the coefficient of cation diffusion is still uncertain. For tensions less than threshold stress, in general, it is accepted that the creep rate is inversely proportional with the square of the grain size (Goyal et al., 2015). Studies show that the creep rate increases as porosity increases (Van Brutzel et al., 2015). Despite, the pores shape effect, like the interior porosity and inward grains, is not

⇑ Corresponding author. E-mail address: [email protected] (M. Aghaie). https://doi.org/10.1016/j.anucene.2019.07.040 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

yet rated and these parameters are not existing in the creep models that have been used. The microscopic physical phenomena of this behavior are not yet fully explained. It has been explained that the creep decreases, if radiation with heavy ions increases (Ye et al., 2013). Fission products, as sediments or exhaust gases, reduce fuel creep (Van Brutzel et al., 2015). Creep, in material science is the process of slow deformation influenced of stresses and has various roots, thermal, irradiation, or mechanical. In a nuclear reactor, irradiation and thermal creep produce the fuel element dimensional changes which can make so much deformation and reactor events (Michel et al., 2012). Creep in the material increases with increasing temperature and stress. Generally, the creep strain can be divided into three parts: primary, middle and final (see Fig. 1). The calculations and formulas presented up to this time for creep are true only to the middle part and there is no relationship for the final part due to the large deformation of matter. The part of the creep that is considered by the researchers in this area is the mid-section because the time interval of this region is high and the strain rate is almost constant (Naumenko, 2007). Creep is an important phenomenon for reactor safety assessment and material design, that needs to be considered and modeled. Creep performance depends on the activation energy. This energy is a function of the O/U ratio of fuel. If all other properties

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

951

Nomenclature A gf gc G Bu Bu1 tgap Dq0 Ssolid Sgas T Xtran Tc hgap XPost X0 Xpre N,n R D hgas hsolid Kf hrad kc q00 (z)

Oxidation rate of clad Jump distance of fuel surface temperature (m) Jump distance of cladding temperature (m) Grain size (mm) Burnup (MWd kg
1) Burnup to end of last time step (MW-s/kg-U) Gap thickness Total densification that can occur Solid fission product swelling Gaseous fission products swelling Temperature of the oxide-metal interface (K) The oxide layer thickness in transition state (m) Clad temperature Gap conduction The post transition oxide layer thickness (m) The oxide layer thickness in the initial state (m) The oxide layer thickness in pretransition state (m) Number of radial mesh, Iteration counter universal gas constant (J/mol.K) Density (percent of theoretical density) Gas Conduction (W/m2K) Contact conduction (W/m2K) Fuel conduction Radiation conduction (W/(m2K)) Clad conduction (W/m K) Heat flux in the axial direction (W/m2)

are constant, increasing the O/U ratio will increase the creep. Also, the non-stoichiometry of fuel, affects the fuel conductivity. Thermal conductivity of the fuel (UO2+x) was experimentally evaluated for different amount of x (White and Nelson, 2013). Evaluation of fuel pellet performance is inevitable for designing and testing the fuel rods. It is very important for fuel vendors and fuel designers to develop a new fuel pellets with better reliability and material and they interested in developing numerical codes to calculate thermomechanical fuel behavior. So that they can have a precise prediction of the thermomechanical behavior of the fuel rod. The fuels used for nuclear reactors during their operation and storage are exposed to complex thermomechanical processes, which are the result of deformation mechanisms like creep, swelling, densification and interaction between pellet and clad.

kgas BuD ri ro t ttran Tf r h Ea u CD F x

Gas conduction (W/m K) Burnup at which densification is complete Inside clad radius (m) Outside clad radius (m) Time at temperature (day); at creep model (hr) Time of transition Fuel temperature Radial direction Gap conductance (W/m2K) Creep activation energy Radial displacement For temperatures below 750 °C is given by 0.0086, above 750 °C it is 1.0 Fission rate (fissions/m3)/s Deviation of O/M ratio from 2.0

Greek characters ec Clad emissivity r Stefan–Boltzmann constant, 5.6697E-8 (W/m2K4) e_ f Fuel creep rate (1/s) q Density (kg/m3) rf Stress (pa) u Fast neutron flux (1/m2/s) ef Fuel emissivity eD Densification of fuel e_ h Clad creep hoop strain rate (1/s)

Deformation of fuel is one of the most important aspects that needs more model development with understanding for new design of fuel and qualification programs. A common based paradigm needs development for few decades and is completely not an appropriate option for calculating different plans for a future energy candidate (Van Brutzel et al., 2015). In this work, using numerical methods, a model has been developed to predict the steady state behavior of a fuel rod considering the fuel creep and hyperstoichiometric effects. In other word, the effect of hyperstoichiometric crystals on deformation of irradiated fuels is evaluated. The excess oxygen in UO2+x changes the physical properties of the fuel and creep rate changes. In this way a numerical model for thermomechanical evaluation of the PCIs for several burnups is developed. This model has three part for analysis. The

Fig. 1. Schematic representation of creep strain as a function of time.

952

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

first part, which gains temperature in coolant, clad and fuel in axial and radial direction and calculates thickness of the clad oxide layer. The second part, which gains creep, stress, displacement and strain in clad and fuel and calculates fuel swelling, densification and pellet-cladding interaction. The third part contains the properties of materials including irradiated fuels, creep rate and thermal conductivity. 2. Fuel rod model The geometry of the fuel rod model is shown in Fig. 2. Cylindrical fuel pellets are symmetrically placed within a clad and surrounded by a fluid. In addition, it is assumed that there is gas volume in the upper part of the fuel. In this work, the thermal and mechanical parameters are calculated in one dimensional and it is developed for each axial section. Fig. 3 shows the flow diagram of computations. 2.1. Thermal calculation The thermal response involves distributing the temperature along with radial direction of the fuel rod. The fluid temperature is calculated in axial direction, and then the transfer of heat between the fluid and the outer surface of the oxide layer for the single-phase flow, using the Dittus-Boltter and in the two-phase flow, derives from the Jens-Lutz equation (Berna et al., 1997). 2.1.1. Oxide layer and clad thermal calculations For calculation of oxide layer temperature, oxide layer thickness must be calculated. Oxidation properties of the clad depend on temperature and oxide layer thickness. The thickness of the oxide layer in the transition is described by Eq. (1), the pre-transmission thickness is calculated using Eq. (2) and post-transfer thickness using Eq. (3) (Allison et al., 1993). 790 X tran ¼ ð7:749  10
6 Þ  eð
T Þ

ð1Þ

n o13 15660 X pre ¼ ð4:976  10
9 Þ  A  t  eð
T Þ þ X 30

ð2Þ

X post ¼ 82:88  A  ðt
t tran Þ  eð


ð3Þ

A ¼ 1:203  102  eð
7:11810


3

ÞþX

14080 T

tran

Fig. 3. The flow diagram of computations. TÞ

ð4Þ Using Eq. (5), the clad temperature is calculated for each axial section (Berna et al., 1997).

DT c ¼

  q00 ðzÞ  r o  ln rroi kc

ð5Þ

2.1.2. The gap heat transfer model The heat transfer model for the gap consist of three mechanisms; gas conduction, radiation and contact conduction (Imani et al., 2015).

hgap ¼ hrad þ hgas þ hsolid

ð6Þ

The radiation conduction is gained by Eq. (7) (Berna et al., 1997) and gas conduction is computed with Eq. (8) (Ross and Stoute, 1962).

(

hrad ¼

hgas ¼ Fig. 2. Geometry of the fuel rod model.

r 1

ef

)

þ ec
1 1

kgas t gap þ g f þ g c



T 4f
T 4c Tf
Tc

ð7Þ

ð8Þ

953

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

2.1.3. Pellet thermal analysis For the fuel thermal analysis, the differential heat transfer equation is solved in cylindrical geometry, which considers radial thermal flux in fuel. 2

d Tf 1 dkf dT f 1 dT f q00 þ þ ¼
2 kf dr dr r dr dr kf

parameter Af, these processes are defined which depends on grain size, departure of the stoichiometric, density and fission products. The exact description of this parameter is very essential for modeling. The MATPRO experimental correlations (Allison et al., 1993) have been used to compute this work.

ð9Þ

The thermal conductivity of the fuel described with Jiang et al. (2011).

e_ ¼

 Q 1 ðA1 þ A2 FÞrf e
RT ðA3 þ DÞG2 ( h

Q 1 ¼ 17884:8 e

2.2. Mechanical analysis of pellet

 Q  2 Q  ðA4 þ F Þrf 4:5 e
RT 3 þ þ A7 rf Fe RT A6 þ D

i


20
8 ln ðxÞ

)
1 þ1

  J þ 72124:23 mol

Calculation of displacement, strain, stress and creep is important for examine the mechanical interaction between fuel and clad (Garcia et al., 2016). In this analysis, these parameters are calculated with below methods.

Q 2 ¼ 19872 e

2.2.1. Swelling Solid fissile and gas products cause fuel inflation. To consider this work, the experimental correlations of MATPRO (Allison et al., 1993) are used. Solid swelling is:

    s s2 ; A2 ¼ 1:3100E
19 m6 : ; A1 ¼ 0:3919 m3 : kg kg   s2 A3 ¼
87:7; A6 ¼
90:5; A7 ¼ 3:72264E
35 m4 : ; kg   J Q 3 ¼ 2:6167E3 mol

Ssolid ¼ 7:435  10
13  q  ðBu
Bu1 Þ

ð10Þ

For gaseous swelling:


10

qBuÞ

ð11Þ

2.2.2. Densification of fuel Density of fuel pellet is created by the destruction of internal porosity if they are emitted from the reactor. The calculation of fuel density is done with ESCORE model (Williamson, 2011):

( 

eD ¼ Dq0  e



Buln ð0:01Þ C D BuD

)
1

ð12Þ

2.2.3. Clad creep The creep at steady-state and transitions affects the mechanical interaction of the pellet-clad (PCMI) and the thickness of the gap affects the temperature of the fuel. Therefore, the creep plays an important role in the modeling of fuel rod performance. The calculation of the creep is done with CIEMAT model (Herranz and Feria, 2010):

e_h ¼ f 1 ðrh Þ  f 2 ðT c Þ  f 3 ðutÞ  t
0:5

i
20
8 ln ðxÞ

)
1 þ1

 þ 111543:5

 J mol

ð19Þ

ð20Þ

ð21Þ

2.3. Calculation of fuel and clad interaction (gap size)

Sgas ¼ 2:617  10
39  q  ðBu
Bu1 Þ  ð2800
T f Þ11:730  e
0:01620ð2800
T f Þ  eð
2:4010

( h

ð18Þ

ð13Þ

Where:

In this analysis, at the first step the thermal calculations are carried out. In second step, the mechanical parameters are evaluated and in next according to Eqs. (10)–(23), the radiuses of fuel and clad are respectively calculated. The fuel radius changes due to thermal expansion, swelling, creep and densification. Clad radius changes due to thermal expansion and creep. Now these calculations are repeated with new radiuses and this loop continues while the convergence criteria obtain (see Fig. 3). The fuel and clad radius changes over time, which changes the width of the gap between the fuel and clad (gap size). By calculating the radius of fuel and clad, the gap size can be calculated. The pellet and clad interaction is indicated by zero gap size.

rnew ¼ f

N X

h i Dr fi 1 þ efuelswelling þ efueldensification þ efuelcreep þ unf
un
1 f i i i

i¼1

ð22Þ ¼ rnew c

N X

h i Dr cj 1 þ ecladcreep þ unc
un
1 c j

ð23Þ

j¼1

3. Hyperstoichiometric fuel

1 f 1 ðrh Þ ¼  a  rbh 2

ð14Þ


c3

f 2 ðT c Þ ¼ eðT c þ273Þ

ð15Þ

f 3 ðutÞ ¼ eð
c4 utÞ

ð16Þ

2.2.4. Fuel creep An equation for calculating the creep is given by Billy Norton’s law (Eq. (17)).



e_ f ¼ Af ðTÞrf n exp


Ea rT f



ð17Þ

The creep response depends directly on the microstructure processes that occur in the material during the deformation. In

Uranium dioxide is an important ceramic mainly used as a fuel in nuclear power plants. All uranium dioxide pellets are produced by high-temperature sintering in hydrogen atmosphere (Gao et al., 2009). Even though uranium fuel starts out stoichiometric is achieved during fabrication and operation of the fuel with a chemical formula of UO2+x where x is concentration of excess oxygen present fuel (Rakesh et al., 2016). The features of UO2 at high burn-up and temperatures bring many restrictions for fuel elements design of nuclear reactor. UO2 is stoichiometric compound of UO2+x. This technical indicator is important for UO2+x fuel, O/U more affects the melting point of fuel pellet, evaporation rate, interaction between fuel and clad and thermal conductivity. Table 1 shows the thermal conductivity of UO2+x specimens (White and Nelson, 2013). As seen, changing O/U atom ratio can increase the fuel and clad compatibility and change nuclear fuel elements

954

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

Table 1 Thermal conductivity of UO2+x specimens (White and Nelson, 2013). T(K)

1673 1623 1573 1523 1473 1423 1373 1323 1273 1223 1173 1123 1073 1023 973 923 873 823 773 723 673 623 573 523 473

x 0.042 0.063 Thermal conductivity k (W/m.K)

0.072

0.104

1.889 1.921 1.963 2.002 2.044 2.082 2.133 2.187 2.249 2.312 2.370 2.448 2.524 2.595 2.687 2.774 2.869 2.974 3.079 3.205 3.725 4.231 4.651 4.977 5.311

1.846 1.860 1.867 1.905 1.933 1.959 1.997 2.036 2.073 2.018 2.154 2.198 2.241 2.300 2.349 2.405 2.459 2.525 2.584 2.771 3.114 3.459 3.705 3.958 4.178

1.905 1.905 1.934 1.945 1.964 1.982 2.004 2.028 2.054 2.073 2.107 2.135 2.166 2.193 2.230 2.259 2.294 2.326 2.376 2.572 2.888 3.165 3.386 3.569 3.732

1.839 1.855 1.877 1.897 1.963 1.967 1.999 2.040 2.089 2.125 2.176 2.224 2.286 2.337 2.402 2.462 2.530 2.603 2.682 2.871 3.245 3.613 3.933 4.186 4.449

(y = 0.95,0.9,0.85) is simulated and the pellet-cladding interactions with hyper stoichiometric creep rate is calculated. In this way, this work includes the effect of x and y on pellet-cladding interactions during burnups. In this study, for numerical simulation 60 nodes in radial direction and 10 nodes for axial direction are considered. Clad temperature in the outer surface is dependent on the temperature of the fluid and the inner surface temperature is dependent on fuel rod linear heat rate. Fig. 4 shows the thickness of the oxide layer for different burnups. The amount of clad oxidation in various states is calculated using the Eqs. (1)–(3). The thickness of oxide layer effects on the temperature distribution in fuel pellet. As seen in Fig. 4, the oxidation of clad occurs in different rates for various burnups. Fig. 5 shows the clad and fuel radiuses at the fifth axial node of fuel rod. The experimental results by Smirnov, have been used for comparison (Smirnov et al., 2004). Fig. 6 shows the size of the gap in different burnups. The gap size changes with changing the fuel swelling, conductivity, densification and creep. Interaction of fuel and clad for WWER1000 is in line with the expected momentum

safety at high temperatures (Hui, 2014). In this analysis, the effect of the hyperstoichiometric fuels on PCIs considering the creep rate is evaluated.

4. Model validation in WWER1000 (BNPP) fuel rod In this work, to study the effect of hyper stoichiometric creep on pellet-cladding interactions, a fuel rod is simulated. Table 2 shows the required parameters of WWER1000 fuel rod for this analysis. For evaluation of the model, the result for pellet-cladding interactions have been compared with experimental data. These comparisons show good agreement with experimental data. In following, the hyperstoichiometric creep effect for 0.9UO2 + 0.1UO2+x fuel pellets (x = 0.042, 0.063, 0.072, 0.104) is evaluated. Indeed, in this section the variation of the x is studied and the thermomechanical results are discussed. In the next section, the effect of amount of hyperstoichiometric fuel in the form of yUO2 + (1
y)UO2+x

Fig. 4. Thickness of oxide layer via burn up.

Table 2 Main design parameters of WWER1000 fuel rod (FSAR, 2005; Aghaie et al., 2012). Parameter

Value

Average linear power Average mass flux Coolant pressure Coolant inlet temperature Fill gas initial pressure Heating length Pitch Nominal fuel density Maximum Fuel densification Gap width Fuel rod diameter Radius of the fuel pellet The volume of the gas plenum No. of radial segments for fuel No. of radial segments for clad No. of axial segments in fuel rod Burnup at full densification

170 w/cm 3850 kg s
1 m
2 15. 2 MPa 291 °C 2 MPa 3.58 m 1.275 cm 95.5% Theoretical 2.8% Of theoretical density 80 lm 0.91 cm 3.785 mm 1.8283e-5 m3 100 50 10 5 MWday/kgU Fig. 5. The fuel and clad radiuses via burn up.

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

Fig. 8. Hoop strain of fuel via burn up. Fig. 6. Gap between fuel and clad via burn up.

(Smirnov et al., 2004). Interaction burnup that calculated is 50.80 MWd/kgU, that consistent with these experimental. Fig. 7 shows the surface and center temperatures of the fuel in the fifth axial node during burnups. In first steps, temperature of fuel increases rapidly due to fuel densification. Then, due to the fuel swelling, fuel-clad creep and the size of the gap, the temperature of the fuel decreases until interaction of the fuel and clad is occurred. The Fig. 8 shows the fuel hoop strain and Fig. 9 shows the fuel radial strain at different burnups. As shown in these Figures, the center of fuel has maximum strain in hoop and radial strains. The Fig. 10 shows the appropriate fuel radial displacement and the Fig. 11 depicts the fuel surface axial stress at different burnups. As fuel densification increases, the fuel axial stress (with a negative sign) increases. With the loss of the densification effect, as a result of fuel swelling and creep, fuel axial stress reduces. These changes appear from thermal expansions and fuel pressures. Fig. 12 shows the fuel radial stress and Fig. 13 shows the fuel hoop stress. As shown in Fig. 13, due to temperature profile and gas pressure, the fuel center is under pressure and the fuel surface is under tensile stress. It causes crack formation on the fuel surface.

Fig. 7. The temperature of fuel (center and surface) via burn up.

Fig. 9. Fuel radial strain via burn up.

Fig. 10. Fuel radial displacement via burn up.

955

956

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

Fig. 14 shows the clad radial creep during burnups. As shown, with increasing time (burnup), the clad radial creep increases linearly. The Fig. 15 shows the radial displacement of the clad in different burnups. As shown, with increasing the burnup and temperature, the radial displacement of the clad increases. The Figs. 16 and 17 show the hoop and radial strains of the clad in different burnups. As shown, because of the temperature gradient and pressure, the radial strain in the inner surface of the clad is more than the outer surface. The Figs. 18–20 show the clad stresses in radial, hoop and axial direction in different burnups, respectively. As shown, because of the coolant pressure, the radial stress on the outer surface of the clad is almost constant and for inner surface, with increasing the gas pressure the stress increases. Fig. 21 shows the gap between clad and fuel considering 0.9UO2 + 0.1UO2+x (x = 0.042, 0.063, 0.072, 0.104) pellets. As shown, with increasing the x, the maximum of gap size between fuel and clad decreases and the interaction between fuel and clad is earlier occurred. This is a notable matter in thermomechanical evaluation of the fuel rods. For instance, for UO2 pellets the maxiFig. 11. Fuel axial stress via burn up.

mum gap size is 0:12  10
3 m. For 0.9UO2 + 0.1UO2.042 the maximum

gap

size

reduces

to

0:1178  10
3 m

and

for

0.9UO2 + 0.1UO2.063 the maximum gap size is 0:1169  10
3 m. In

Fig. 12. Fuel radial stress via burn up.

Fig. 14. Radial clad creep via burn up.

Fig. 13. Fuel hoop stress via burn up.

Fig. 15. Clad radial displacement via burn up.

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

Fig. 16. Clad hoop strain via burn up.

Fig. 19. Clad hoop stress via burn up.

Fig. 17. Clad radial strain via burn up.

Fig. 20. Clad axial stress via burn up.

Fig. 18. Clad radial stress via burn up.

Fig. 21. Gap width for 0.9UO2 + 0.1UO2+x.

957

958

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959

following, Fig. 22 shows the fuel conductance for 0.9UO2 + 0.1UO2+x (x = 0.042, 0.063, 0.072, 0.104). As shown, due to changes in fuel crystal, fuel properties including the fuel thermal conductivity, change. Increasing the , the fuel thermal conductivity is decreased. For instance, for UO2 pellets the maximum conductance is 3:4966 mW2 K. For 0.9UO2 + 0.1UO2.042 the maximum fuel conductance reduces to 3:3794 mW2 K and for 0.9UO2 + 0.1UO2.063 the maximum fuel conductance is 3:3593 mW2 K. Fig. 23 shows the fuel center temperature considering 0.9UO2 + 0.1UO2+x. As shown, with increasing the x the fuel center temperature increases. For UO2 pellets the maximum fuel center temperature is 1544.5 Kelvin. For 0.9UO2 + 0.1UO2.042 the maximum fuel center temperature reaches 1559.5 Kelvin and for 0.9UO2 + 0.1UO2.063 the maximum fuel center temperature enhances to 1561.4 Kelvin. Table 3 shows the effect of UO2þx on the mechanical interaction point, maximum fuel center temperature and maximum gap between fuel and clad. As shown, with decreasing the 1
y (amount of hyper stoichiometric fuel) in yUO2 + (1
y)UO2+x, fuel center temperature decreases, maximum gap size increases and interaction between fuel and clad later occurs. From results for 0.9UO2 + 0.1UO2+x and yUO2 + (1
y) UO2+x , it is clear by increasing the x or 1
y that means reaching to higher hyperstoichiometric states the PCIs are earlier occurs. The

Table 3 The effect of UO2:104 present on the mechanical interaction between fuel and clad. Fuel

Gap sizemax (m)

Tmax fuel (K)

PCI (MWd/kgU)

UO2 0.95UO2 + 0.05UO2.104 0.9UO2 + 0.1UO2.104 0.85UO2 + 0.15UO2.104

0.1200e-3 0.1176e-3 0.1149e-3 0.1118e-3

1.5445e3 1.5520e3 1.5602e3 1.5696e3

50.8 50.5 50.3 50.0

hyperstoichiometric parameter in this simulation effects directly on the fuel creep rate and the thermal conductivity of the fuel (Table 1). 5. Conclusion In this paper, considering hyperstoichiometric effects the fuel behavior using numerical methods has been investigated. The mechanical interaction between fuel and clad is evaluated and temperature, stress, strain, displacements and gap size in fuel rod for long-term burnups are presented. It is shown, while the fuel clad mechanical interaction in normal fuel occurs at 50.8 MWd/ kgU, this interaction happens earlier with hyperstoichiometric effects. It is shown, changing O/U of fuel pellet can change the fuel pellets and clad compatibility at high temperatures. It is observed that in the case of hyperstoichiometric fuel, the fuel creep rate increases and heat transfer coefficient decreases. Increasing the creep rates in high temperatures leads to faster PCIs although it has smaller effect than burnup. The hyper stoichiometric parameter in this simulation effects directly on the fuel creep rate and the thermal conductivity of the fuel. From results for 0.9UO2 + 0.1UO2+x and yUO2+(1
y)UO2+x pellets, it is clear by increasing the x or 1
y, that means reaching to higher hyperstoichiometric states the PCIs are earlier occurs. Acknowledgement The authors are gratefully indebted to Shahid Beheshti University G. C., for partial support of this work. Appendix A. Supplementary data

Fig. 22. Thermal conductivity for 0.9UO2 + 0.1UO2+x.

Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.07.040. References

Fig. 23. Fuel center temperature for 0.9UO2 + 0.1UO2+x.

Aghaie, M., Zolfaghari, A., Minuchehr, A., 2012. Coupled neutronic thermal– hydraulic transient analysis of accidents in PWRs. Ann. Nucl. Energy 50, 158– 166. Allison, C.M., Berna, G.A., Chambers, R., Coryell, E.W. et al., 1993. SCDAP/RELAP5/ MOD3.1, MATPRO – A Library of Materials Properties for Light-Water-Reactor Accident Analysis. NUREG/CR-6150. Baron, D.D., Hallstadius, L., 2012. Compr. Nucl. Mater. 2 (19), 481–514. Berna, G.A., Beyer, C.E., Davis, K.L., 1997. FRAPCON-3: A Computer Code for the Calculation of Steady-state, Thermal–Mechanical Behavior of Oxide Fuel Rods for High Burnup NUREG/CR-6534-Vol. 2. System Technology Office of Nuclear Regulatory Research, Washington, p. 2. Fink, J.K., 2000. J. Nucl. Mater. 279, 1–18. Final Safety Assessment Report (FSAR) for BNPP, 2005. Russia Federal Agency on Nuclear Energy (RFANE). Book 1, Moscow. Gao, Jia-cheng, Wang, Liang-fen, et al., 2009. High-temperature creep properties of uranium dioxide pellet. Trans. Nonferrous Metals Soc. China 20, 238–242. Gao, J., Wang, L., Wang, 2010. High temperature creep properties of uranium dioxide pellet. Trans. Nonferrous Met. Soc. China 20 (2010), 238–242. Garcia, P., Struzik, C., Agard, M., Louche, V., 2016. Mono-dimensional mechanical modelling of fuel rods under normal and off-normal operating conditions. Nucl. Eng. Des. 2016, 183–201. Goyal, A., Phillpot, S.R., Subramanian, G., Andersson, D.A., Stanek, C.R., Uberuaga, B. P., 2015. Phys. Rev. B 91, 13. 094103. Herranz, L.E., Feria, F., 2010. Extension of the FRAPCON-3.3 creep model to dry storage conditions. Prog. Nucl. Energy 52 (7), 634–639.

M. Safari et al. / Annals of Nuclear Energy 133 (2019) 950–959 Hui, W., 2014. Research on preparation technology, sintering performance, microstructure of UO2-x fuel pellets. J. Eur. Ceram. Soc. 35 (2015), 1081–1087. Imani, M., Aghaie, M., Zolfaghari, A., Minuchehr, A., 2015. Numerical study of fuel– clad mechanical interaction during long-term burnup of WWER1000. Ann. Nucl. Energy 80, 267–278. Jiang, Y., Cui, Y., Huo, Y., Ding, Sh., 2011. Three-dimensional FE analysis of the thermal–mechanical behaviors in the nuclear fuel rods. Ann. Nucl. Energy 38 (2011), 2581–2593. Michel, B., Sercombe, J., Nonon, C., Fandeur, O., 2012. Compr. Nucl. Mater. 3 (22), 677–712. Naumenko, K., 2007. Modeling of Creep for Structural Analysis. Springer. Rakesh, K., Behera, A., Watanabe, Taku, 2016. Diffusion of oxygen interstitials in UO2x using kinetic Monte Carlo simulations: Role of O/M ratio and sensitivity analysis. J. Nucl. Mater. 472, 89–98.

959

Ross, A.M., Stoute, R.L., 1962. Heat transfer coefficient between UO2 and Zircaloy-2, Atomic Energy of Canada Technical Report, AECL-1552. Smirnov, A.V., Markov, D.V., Ovchinikov, V.A., Polenok, V.S., Ivashchenko, A.A., 2004. Pellet-cladding Interaction in WWER Fuel Rods. Pellet-clad Interaction in Water Reactor Fuels, France. Van Brutzel, L., Dingreville, R., Bartel, T.J., 2015. Sandia National Laboratories, NEA/ NSC/R (2015)5. White, J.T., Nelson, A.T., 2013. Thermal conductivity of UO2+x and U4O9-y. J. Nucl. Mater. 443 (1–3), 342–350. Williamson, R.L., 2011. Enhancing the ABAQUS thermomechanics code to simulate multipellet steady and transient LWR fuel rod behavior. J. Nucl. Mater. 415 (2011), 74–83. Ye, Bei, Oaks, A., Kirk, M., Yun, Di, Chen, Wei-Ying, Holtzman, B., 2013. Irradiation effects in UO2 and CeO2. J. Nucl. Mater. 441 (2013), 525–529.