Development and validation of thermo-mechanical analysis code of metallic fuel under steady-state conditions in LMFR

Annals of Nuclear Energy 138 (2020) 107221

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

Development and validation of thermo-mechanical analysis code of metallic fuel under steady-state conditions in LMFR Hongping Sun, Yapei Zhang, Wenxi Tian, Suizheng Qiu, G.H. Su Science and Technology on Reactor System Design Technology Laboratory, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 6 June 2019 Received in revised form 30 September 2019 Accepted 16 November 2019

Keywords: Thermal-mechanical analysis Metallic fuel Steady state LMFR

a b s t r a c t Thermal characteristics and mechanical analysis are particularly essential in the performance and safety analysis of metallic fuel for Liquid Metal Fast Reactor (LMFR). Therefore, the development of advanced thermo-mechanical analysis code is significant for the safety design of metallic fuels. In order to meet the future demand for metallic fuel application in China, the FRAC code was developed to analyze the metallic fuel performance during steady-state conditions. The code was benchmarked against the open-literature EBR-II experimental database. In comparison with the experimental data given, the code calculated Zr mole fraction, fuel temperature distribution, fission gas release and clad strain distribution are in good agreement with the data, which indicates that the code is reliable and can be applied into safety analysis of metal fuel design in China. The overall code assessment shows that the prediction error is within acceptable range. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Liquid metal fast reactor (LMFR) is an advanced reactor that can realize nuclear fuel proliferation, long-life fission product transmutation and support closed fuel cycle. It is a key reactor that can support nuclear energy as a clean and sustainable advanced energy and regain world attention. The main fuel types of fast reactor are mixed oxidized fuel (PuO2-UO2), metallic fuel (U-Pu-Zr or UZr) and nitride fuel (UN-PuN). Metal fuel is the core technology for developing advanced fast reactor in the future. The Schematic diagram of metallic fuel pin is shown in Fig. 1. The main advantages of metal fuels include high thermal conductivity, high fission atomic density, easy processing and so on. However, one of the main problems facing the design of metal fuels during irradiation is that the irradiation swelling is serious and the higher burnup depth can’t be achieved. The irradiation experiments of EBR-II metal fuel show that the maximum burnup of metal fuel using D-9 cladding is 18.4% and that using HT-9 cladding is 19.9% (Walters, 1999). Perhaps this problem can be overcome when major advances in fuel materials science are made in the future. Performance analysis of fuel rod design is particularly important to ensure its safety under irradiation conditions. Therefore, it is very significant to study the irradiation behavior and performance analysis of metal fuel in fast reactor.

E-mail address: [email protected] (Y. Zhang) https://doi.org/10.1016/j.anucene.2019.107221 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

In the past, many countries have carried out experimental and theoretical studies on the performance of metal fuels under irradiation conditions. Pahl (1990) has carried out the experimental study of U-Pu-Zr fuel pins in the Experimental Breeder Reactor-II (EBR-II). Mark-I, Mark-II and Mark-III experiments have been carried out in the JOYO facility (Masayoshi Ishida, 2017). For theoretical research, many codes have been developed for the performance analysis of metal fuels. The codes for steady and transient analysis of metal fuels are as follows, LIFE-METAL (Billone, 1986), FEAST-METAL (Aydın Karahan, 2010). Codes for steadystate analysis include MACSIS (Woan Hwang, 1998), SESAME (Hirokazu OHTA, 2011), ALFUS (Ogata and Yokoo, 1999) and so on. Having successfully operated FBTR with carbide fuels, the fuel cycles for both the mixed oxide fuel and the metallic fuel needs to be developed expeditiously (Baldev Raj, 2005). There was also an investigation on unprotected loss of flow accident in metal fueled 500 MWe fast rector (Neethu Hanna Stephen, 2015), physics parameters of metal fuel studies (Riyas, 2008) and criticality safety studies for U-Pu metal fuel (Neethu Hanna Stephen, 2013) in India. China is in its infancy in the field of metal fuels and is formulating plans for the development of metal fuels (Mi, 1999). Therefore, it is necessary to develop an independent fast reactor metal fuel analysis code in order to meet the design requirements. The main objective of this work is to develop a thermo-mechanical coupled code for the analysis of metal fuels, and to be able to be used for the performance analysis of metal fuels. Based on advanced models, a code named FRAC was developed to analyze the metallic fuel

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H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221

Upper end plug Gas plenum Cladding Sodium bond Fuel slug Lower end plug

Fig. 1. Schematic diagram of metallic fuel pin.

under steady-state conditions. The EBR-II experimental database of metallic fuel were selected for comparative validation analysis. And according to the comparative results, an error prediction evaluation of the code is made in this work.

2. Overview of the FRAC code The FRAC code has been developed to analyze the thermohydraulic characteristics and mechanical performance of fuel in liquid metal fast reactor (LMR). It mainly contains many subroutines to calculate the behavior of LMR fuel under irradiation conditions. This code was written in FORTRAN-95 program language, which is mainly complied in FORTRAN compiler. FORTRNA language is widely used in the world because of its powerful numerical computing ability and high precision computing function. The flow chart of the FRAC is shown in the Fig. 2. Users need to define fuel geometry, composition and operating conditions through a simple input file. The main operating conditions include coolant inlet temperature, mass flow rate, power distribution and so on. Fig. 3 shows the geometrically model of computation in the program. Overall, there are three regions in the fuel pellet part: (1) Central void; (2) Columnar grain; (3) Unrestructured fuel. For nodes partition up to 12 fuel nodes can be modeled in the radial direction, and there are also three additional cladding nodes, one coolant node and one structure node. In the axial direction, up to 20 nodes can be divided, as shown in Fig. 4. The latest models in the field of metal fuels are used to explore solutions to fuel irradiation swelling, low melting point alloy phase formation, fuel composition restructuring, fission gas retention and release, mechanical phenomena, etc. The calculation process of the program mainly includes input and output module, temperature distribution, fuel/clad swelling, fuel densification, fission gas retention and release, mechanical calculation. The code uses advanced numerical methods to solve the mathematical models. Such as the two-dimensional cylindrical coordinate nodes is applied to calculate heat transfer, the axisymmetric two-dimensional finite element method is used to analyze stress and strain. By implementing numerical techniques, the independence of modules greatly reduces the running time of code.

Fig. 2. Calculation flowchart of FRAC.

Structure Coolant Outer cladding radius, rco Fuel-cladding gap Inner cladding radius, rci Outer fuel radius, ro Columnar grain growth radius, rb Central void formed by densification radius, rv Fabricated central void radius, rm Fig. 3. Fuel, cladding and coolant heat transfer geometry.

3. Mathematical models of FRAC In this section, the main advanced models used in the program are described, including temperature distribution, fuel composition recombination, fission gas retention and release, mechanical models, and other related models are briefly introduced.

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fuel thermal conductivity. The effect to the fraction of theoretical density can be obtained by porosity correction factor (Theodore H. Bauer, 1995):

 9 =  1  kkNa0 3=2 PNa h  i  1  Pg Pf ¼ 1  3  kNa : ; 1  Pg 1:16 þ 1:84 8 <

ð6Þ

k0

where is Pf the porosity correction factor, kNa is the logged sodium thermal conductivity, PNa is the sodium-filled porosity fraction, P g is the gas-filled porosity fraction, k0 is the thermal conductivity of unirradiated fuel. 3.1.2. Coolant temperature distribution The heat transferred from the fuel rod to the coolant will raise its temperature. Therefore, an energy equation can be used to solve the coolant temperature rise at each axial node:

  DT c ¼ ql Dz  ccp Mf 

where ql ¼ qp r 2o  r v is linear power on the surface of each axial node of fuel pin, Dz is the node height, ccp is the heat capacity of coolant, Mf is the coolant mass flow rate, r o is the outer fuel radius and r v is the fabricated central void radius. In the FRAC code, an assumption is made that the coolant mass around the fuel pin is uniform.

Fig. 4. Radial and axial nodes of heat transfer calculation.

3.1.3. Cladding temperature distribution There are thin films between cladding and coolant, and the temperature rise is calculated by defining the heat transfer coefficient:

3.1. Temperature distribution calculation models 3.1.1. Fuel temperature distribution In FRAC program, the fuel axial node is assumed to be adiabatic because temperature gradient is very small in typical LMFBR fuel. Thus the axial heat conduction between axial nodes can be almost neglected. The code calculates the steady-state temperature distribution of fuel rods in cylindrical coordinates as shown in the Fig. 4. The theoretical heat conduction equation for steady fuel rods is calculated as follows:

r  ðkrT Þ ¼ q

ð1Þ

where k is the thermal conductivity, T is the temperature and q is the volumetric heat generation rate. Actually due to the axial symmetry, the equation can be written as:




 1 @ @T rk ¼ qðr Þ r @r @r

ð2Þ

The thermal conductivity can be expressed as the function of fuel temperature and alloy composition (Billone, 1986):

k0 ¼ K 1 þ K 2 T þ K 3 T

2

ð3Þ

Where the coefficients K 1 ,K 2 and K 3 are mainly related to the weight fraction of zirconium in fuel. Theses coefficients can be expressed as (Billone, 1986):

K 1 ¼ 17:5

ð1  2:23W Zr Þ ; K2 ð1 þ 1:61W Zr Þ

¼ 1:54  102

ð1 þ 0:061W Zr Þ ; K 3 ¼ 9:38  106 ð1 þ 1:61W Zr Þ

ð4Þ

Based on the early experimental data, a reasonable fitting methodology has been developed for calculating the thermal conductivity of metal fuels (Theodore H. Bauer, 1995):

kf ¼ Pf ð1  pÞ1:5ðeÞ k0

ð7Þ  2

ð5Þ

where e ¼ 1:72 for metal fuel with gas filled pores andpis the fraction of theoretical density (fuel porosity). In this work, the sodium bond infiltration effect was considered to calculate the irradiated

DT ¼

ql AH

ð8Þ

where H is the film coefficient and the A is the surface area per unit length. Thus, the outer cladding temperature can be get by:

T co ¼ T c þ

ql 2pr co H

ð9Þ

where Tco is the outer cladding temperature, T c is the coolant temperature andr co is the outer cladding radius. The cladding temperature distribution calculation is similar to that of fuel pellets, except that the volume heat generation rate is 0:


 1 @ @T rk ¼0 r @r @r

ð10Þ

Thus, the inner surface temperature of the cladding can be calculated according to following equation:

T ci ¼ T co þ

ql  lnðrci =r co Þ 2pk

ð11Þ

where r ci is the inner cladding radius. 3.2. Fuel constituents migration It was found that there was component redistribution in metallic fuels under irradiation conditions. This phenomenon was first reported by Murphy (Murphy, 1969) in the metallic U-Pu-Zr fuels. Based on the experimental analysis, he regionalized the whole constituent redistribution zone into three structural zones in U-Pu-Zr and U-Zr alloys during irradiation. The phenomenon of fuel constituent redistribution is particularly essential for the analysis of core disruptive accident (CDA) in fast reactor. Because this phenomenon can change the structure of the metal fuel matrix, thus affecting the melting temperature of the fuel. In previous studies, many researchers (Ishida, 1993; Ogawa, 1991) have established theoretical models to analyze this phenomenon. The model used in FRAC is mainly Hoffman model (Hofman, 1996), which is widely used in the world. He found that

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the radial temperature gradient of metallic fuel was a key factor in fuel constituent redistribution. Many assumptions are taken into account as follows:  The cross-terms which relate the flux of one substance to the chemical potential gradient of another substance are neglected.  Uranium flux is equal to negative zirconium flux.  Plutonium element is immovable, thus the equilibrium phases of ternary U-Zr-Pu alloy is calculated by using quasi-binary UZr alloy calculation method. The model is mainly used to calculate the flux of Zr in singlephase and two-phase fields. First, the Zr interdiffusion flux in a single-phase field located in temperature gradient can be get by:

J Zr ¼ DUZr 


 @C Zr Q  C Zr @T  þ @r RT 2 @r

ð12Þ

where JZr is the Zr interdiffusion flux, DU-Zr is the U-Zr interdiffusion coefficient, C Zr is the Zr concentration, R is the ideal gas constant andQ  is the thermos-transport parameter. The thermal transport behavior of binary phases in several alloys has been studied in the past (Jaffe, 1964). These theoretical studies have been successfully applied to experimental analysis. In a two-phase field of Hoffman model, the Zr interdiffusion flux can be get by:

J Zr ¼ DUZr C Zr

V f ðDHs þ Q  Þ @T  @r RT 2

ð13Þ

where Vf is the phase volume fraction and DHs is the solution enthalpy of Zr in U, which can be calculated from the U-Zr phase figure. FRAC first calculates the phase field of the node based on the temperature and constituents distribution, and then determines the Zr concentration at nodes based on the phase diagram polynomial equations and evaluates material physical properties. 3.3. Fission gas retention and release model

mgb ¼ C s

X  ðniþ1  ni Þ fi  2 i

ð15Þ

where Cs is the correction coefficient. This parameter is mainly used for atoms concentration of grain boundary per unit surface area, hence the effective number of bubbles, fi, can be calculated accord

ing to the Cs andf i : 

f i ¼ Cs  f i

ð16Þ

Actually, most fission gases remain in the matrix. The slow diffusion of fission gas under the combined action of temperature and fission peak will affect the crystal structure. There are channels through which fission gases can reach grain boundaries and gradually form bubbles. In this work, a simple two-dimensional cubic structure is used to simulate the critical fraction of bubbles at grain boundaries (Woan Hwang, 1998):




r gb Rgb

 ¼ crit

pr2gb ð2r gb Þ2

¼

p 4

ð17Þ

where rgb is the gas bubble radius and Rgb is the circular unit cell radius of grain boundary. Hence, the saturation conditions per unit area of grain boundary can be get by:

1 X  2 ¼ r lb;i  f i 4 i

ð18Þ

The release of fission gas will lead to the increase of gas plenum pressure. The plenum pressure is mainly contributed by four parts, including filled gas brought to operating conditions, sorbed gas, vapor in the fuel and released fission product gases. Thus the pressure can be get by:

    Pp ¼ V f þ V s þ V v þ V r  T c  Patm = 273  V p

ð19Þ

whereV f ,V s ,V v andV r are the volumes of the filled gas, sorbed gas, vapor and fission gas, respectively.Patm is the one atmosphere of pressure andV p is the effective plenum volume. 3.4. Mechanical models

It is well known that fission gas production increases with the increase of fuel power density. Accurate prediction of fission gas behavior under any operating conditions is of great significance for radiation safety analysis. Fission gas release mainly consists of two processes, one is that fission gas generated in fuel matrix moves to the boundary and forms bubbles, the other is that the bubbles on grain boundary are released into fuel rod gas plenum through channels. The main characteristics of fission gas retention and release include bubble nucleation, growth, migration, and saturation conditions at grain boundaries. The whole process of diffusion of fission gas atoms in the matrix to grain boundaries and formation of bubbles is described in the literature (Woan Hwang, 1998). In this work, the BOOTH classical diffusion theory is used to simulate the fission gas release (BOOTH, 1957). The average number of bubbles per unit volume is related to the size range of bubbles (Hwang et al., 1991), thus the relationship of each group in the grain boundary multi-bubble distribution can be get by:

Z

niþ1

ni



F ðm; s; nÞdn ¼ f i ðniþ1  ni Þ

ð14Þ 

where i is the group number of bubbles, f i is the average number of bubbles, ni is the number of bubbles and s is a dimensionless parameter representing reduced time. Then total number of gas atoms of the grain boundary can be get by the following balance equation:

Cladding is the first barrier to prevent the release of fission products. Therefore, it is particularly important to assess the failure of cladding by stress-strain calculation in fuel behavior analysis. The main phenomena under irradiation include fuel cladding swelling and related stress-strain changes. Especially when the hoop stress of cladding is higher than ultimate tensile stress, the cladding will fail. 3.4.1. Fuel swelling model The thermal expansion of fuel is evaluated by calculating the radial displacement of volume. Therefore, the thermal expansion coefficient is first calculated for each fuel node:

af ¼ aof þ aTf  T

ð20Þ

whereaf is the thermal expansion coefficient of fuel, aof and aTf are input quantities. Then the average thermal expansion can be get by: 

DDf =Df ¼

R

R ro af Trdr DDf =Df rdR R  ¼ r v 2 rdr 1=2 ro  r2v

ð21Þ

The trapezoidal rule is used to solve the equation numerically. Therefore, the radius of the fuel under operating conditions can be calculated as:

  r0f ¼ ðro þ DDs Þ  1:0 þ DDf =Df

ð22Þ

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H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221



where r 0f is the ‘‘hot” fuel radius and DDs is the fuel swelling

P¼

coefficient. 3.4.2. Cladding swelling model The thermal expansion of the cladding is calculated by input linear function, thus the change of radius can be get by:

DL=L ¼ ðaoc þ aTc T ÞðT  T R Þ

ð23Þ

where aoc and aTc are input parameters, T R is the room temperature andDL=Lis the length change fraction. Then the cladding radius can be get by:

r 0c ¼ r co ð1:0 þ DL=LÞ  ð1:0 þ DV c =V c Þ

ð24Þ

where DV c =V is the cladding swelling faction, which depends on the cladding materials. 3.4.3. Stress–strain calculation model Fig. 5 shows the schematic diagram elastic Fuel-Cladding Mechanical Interaction (FCMI). In order to simplify the calculation, many assumptions are used in the calculation of stress and strain of cladding and fuel:     

Only elastic deformation considered Neglection of the thermal-stress contribution Elastic isotropy materials for fuel and cladding Neglection of the axial stress The radial stress is equal to the interface pressure

Based on these assumptions, the radial stress of fuel and cladding can be calculated as (Harris, 1963): rrc ¼ 1ðEvc c Þ2  ðerc þ v c ehc Þ ¼ P at rfc (25)   Ef rrf ¼ (26) ¼ P at rfc 2  erf þ v f ehf 1ðv f Þ The hoop stress of fuel and cladding can be calculated as:  P r 2c þr 2fc

rhc ¼ 1ðEvc c Þ2  ðehc þ v c erc Þ ¼ 

r 2c r 2

þ

fc

rhf ¼

Ef 1ðv f Þ

2











P r 2f þr 2fc

ehf þ v f erf ¼  



2Pe r 2c



(27)

r2c r 2

fc

(28)

r 2 r 2 fc

f

And the relationship between fuel-cladding interference and hoop strain can be calculated as: ehc  ehf ¼ Dr=rfc (29) Then according the above equations, the interface pressure can be get by:



vc

   P p r 2f Pe r 2c Ec þ 2 r2 þr 2 þ r 2 r 2 Ef c c fc fc
  1 r 2c þr 2fc r2f þr 2fc þ r2 r2 þ r2 r2  v f  EEc Dr E r fc c

c

fc

fc

c

(30)

f

where rrc and rhc are the cladding radial and hoop stresses at rfc , rrf and rhf are the fuel radial and hoop stresses at rfc ,erc and ehc are the cladding radial and hoop strains at rfc , erf and ehf are the fuel radial and hoop strains at rfc , Ec and Ef are the cladding and fuel Young’s Modulus, v c and v f are the cladding and fuel Poisson’s radios, P p is the plenum pressure, P e is the external cladding pressure, P is the interface pressure, rfc is the fuel-cladding interface radius, rf is the fuel inner radius, r c is the cladding outer radius, Dr is the fuel-cladding interference. 3.5. 3.5. Other relative models In order to satisfy the detailed thermo-mechanical analysis of the code, other models are also considered in the FRAC. These models are mainly used for heat transfer calculation. Before accurately calculating the heat transfer coefficient between fuel and cladding, it is necessary to know the gap change between them. The residual gap correlation (David F. Shanno, 1967) has been developed based on the gap measurements data. Next the fuel-cladding heat transfer coefficient can be get from the fuel-cladding gap conductance correlation, which is a simplification of the Ross-Stoute gap conductance model (Cox, 1972; Horn, 1972; Leggett, 1972). The radiant heat transfer model between two concentric circles comes from the Ref. (Echer, 1959). The heat transfer through the effective gap of filling gas and the solid-to-solid heat transfer models (Ross, 1962) are also included in FRAC as well as physical properties calculation modules of materials, such as gas thermal conductivity (Brokaw, 1955) and so on. 4. Validation of FRAC To validate the FRAC code, the EBR-II tests database was chosen to compare with the code prediction. Meanwhile, the steady-state prediction results are also compared with that of MACSIS, LIFE-M and ALFUS code. There are many metallic fuel irradiation tests in the EBR-II core, and fuel materials used in the experiment include U-Pu-Zr and U-Zr alloy. In this work, the X425 (Yacout, 1996; Hofman, 1996), X441 (Pahl, 1992) and X447 (Pahl, 1993) of the EBR-II test assemblies were selected to for the code validation due to the available data in the literature. The fuel design data of these three assemblies are shown in the Table 1. In this section,

Fig. 5. Schematic diagram elastic fuel-cladding mechanical interaction.

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H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221

Table 1 Fuel design data of EBR-II assemblies. Parameters

Values

Fuel assembly Fuel composition Clad materials Clad inner radius (mm) Clad outer radius (mm) Fuel slug diameter (mm) Fuel active length (cm) Smear density (%) Peak linear power (W/cm) Peak clad temperature (°C)

X425 U-19Pu-10Zr HT 9 2.54 2.92 4.32 34.3 72.3 400 590

X441 U-19Pu-10Zr HT 9 2.54 2.92 4.67 34.3 85.0 510 600

X447 U-Zr HT 9 2.54 2.92 4.40 34.3 75.0 330 660

it mainly includes two parts, the comparison calculation of code and benchmark steady-state results and the analysis of code prediction error. 4.1. Benchmark calculation During the establishment of the experimental model, 18 nodes were divided in the axial direction, 12 fuel pellet nodes in the radial direction and 3 cladding nodes in the fuel rod. More detailed experimental conditions can be found in the literature mentioned above. Based on available experimental data, a comparative analysis of Zr composition and temperature distribution, fission gas release and strain distribution is made in this section. 4.1.1. Zr and temperature distribution The code calculated the Zr constituent migration phenomenon was validated against the available data of DP-81 and DP-11 rods from X447 assembly (Yacout, 1996; Hofman, 1996). The DP-81 and DP-11 rods were tested at a peak burnup of 5 at.% and 10 at. %, respectively. In the code, the diffusion coefficients are set to be the same as the Hofman’s model. The model assumes a 10-fold increase in the ex-reactor diffusion coefficients of under radiation effects. Fig. 6 shows the comparison of Zr constituent predicted by the code with experimental data. Due to different content of Zr, the whole fuel region in the radial direction can be divided into

three regions according to the U-Zr binary phase diagram, i.e. the c, the b + c and the a + b region as shown in the Fig. 6. The migration direction of two-phase zirconium component is determined by many factors in Eq. (13). When the thermos-transport parameter was set to be 100 kJ/mol, the results yields the best agreement with the data. The common phenomenon in the two figures is that a large amount Zr is depleted in the intermediated two-phase zone (b + c) and enriched in the single-phase zone (c), which indicates that most of the Zr in the b + c zone migrates to the c zone. For the boundary of phase transition position, in DP-11 test, the r/Ro of single-phase to two-phase conversion is 0.45, and the conversion position between b + c zone and a + b zone is 0.64, while in the code prediction, the two values are 0.48 and 0.70, respectively. In DP-81 test, the experimental values of the two positions are 0.21 and 0.62, while the code calculated the two values are 0.27 and 0.56, respectively. Fig. 7 shows more intuitively the Zr component distribution in the fuel radial direction calculated by the code. With the increase of the burnup, more Zr atoms in the b + c zone migrate to the central zone and enrich. Fig. 8 shows the comparison between the temperature distribution of DP-11 rod at the end of life (EOL) predicted by the code and the data. When the sodium band infiltration is not considered, the calculated value is over-predicted. The reason is that the logged sodium in the fuel slug can improve the thermal conductivity of the fuel and then enhance the heat transfer as in the Eq. (6). When the effect of fuel constituents migration (FCM) is neglected, the predicted fuel temperature in the b + c region is slightly lower than the measured data, while the temperature in the a + b zone is close to the data. Based on the eq., the increase of thermal conductivity will lead to a smaller temperature difference when the Zr depletes in the b + c zone. However, increased U component in this region will generate more heat production, which leads to an overall temperature rise. 4.1.2. Fission gas release The fraction of fission gas release is proportional to the increase of fuel burnup. The calculated fission gas release fraction of U-19Pu-Zr fuel in X425 compared with data (Pahl, 1990) is shown in Fig. 9. The figure shows that the calculated values are consistent

Fig. 6. Zr radial distribution of fuel pin (X447).

H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221

7

Fig. 7. Calculated the Zr radial distribution of fuel pin.

Fig. 8. Fuel temperature distribution of DP-11 at the EOL.

Fig. 10. Fission gas release fraction comparison with X447 data (U-Zr).

in X425 test comes from the effect of fuel composition, which has a great influence on the crystal structure of fuel during fission gas release at different burnup. As explained above, the calculation method of U-Pu-Zr alloy fuel is the same as that of U-Zr alloy fuel, thus the influence of composition on fuel structure causes this deviation with some uncertain experimental errors. It can be seen that the code prediction of fission gas release for U-Zr fuel is obviously more accurate than that of U-Pu-Zr fuel. According to the comparison results. The consistency between data and prediction is excellent.

Fig. 9. Fission gas release fraction comparison with X425 data (U-19Pu-Zr).

with the experimental data. The fission gas release fraction of X425 fuel assembly test is about 74% at the EOL, and the core prediction of the peak fraction is about 77.5%. The calculated fission gas release of U-Zr fuel in X447 compared with data (Pahl, 1993) is displayed in Fig. 10. The fission gas release fraction is about 75–79% at the EOL in X447 fuel assembly and the code prediction value is about 80%. The most important deviation at low and high burnup

4.1.3. Clad strain distribution The diametral strain calculated by the FRAC at 15.8 at.% peak burnup compared with data is shown in Fig. 11. And cladding axial strain distribution of code prediction compared with data at 5 and 10 at.% peak burnup in X441 is shown in Fig. 12. The calculated results are in good agreement with the experimental ones and the axial strain distribution of the cladding is consistent with the data trend. The possible reasons for the deviation of predicted axial cladding strain for 5 and 10 at.% burnup in X441can be attributed to uncertainties in irradiation conditions and mechanical properties of HT9 materials, as pointed out in the literature (Pahl, 1991). As the figure shows, due to the lower temperature at the bottom of the metal fuel and the lower opening ratio lead to the higher hardness at the bottom of the metal, the effect of FCMI is more remarkable, which reflects that the cladding strain is greater. However, the upper part of the fuel is softer and more flexible, resulting in lower strain. Table 2 and Table 3 show the comparison

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H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221

peak cladding strain are 16%, 9.2% and 5.5% for the X425 tests at 10.4%, 15.8% and 18.9 at.% peak burnup, respectively. And the calculated relative errors of peak cladding stain were 4% and 3% in X441 test with 5% and 10 at.% burnup, respectively. It can be seen that the maximum prediction error of peak cladding strain is less than 20%, which is within acceptable range. 4.2. Code assessment

Fig. 11. Comparison of X425 cladding axial strain distribution at 15.8 at.% peak burnup.

In this section, the error assessment of the validation results of FRAC program is carried out in order to show more intuitively the calculation performance of the code for metal fuels. Thus, a comparison is made between the experimental data and the corresponding code predicted values. Fig. 13 shows the comparison between calculated valves by the code and the experimental data of X447. The prediction error of the code is less than ±30% for most of the experimental data. As shown in the Fig. 14, The temperature distribution from clad midwall to fuel centerline is compared with that of MACSIS (Woan Hwang, 1998) and LIFE-METAL code (Billone, 1986) in the same case. The code prediction of fuel temperature is consistent with that of the two codes, which shows that the FRAC code can predict fuel rod temperature distribution well. Code prediction of fission gas release compared with measured data during different irradiation conditions is illustrated in Fig. 15. As the figure shown, the overprediction error of the code for experimental data is +20%, while the error for underestimation is 15%. And only two points are outside the two ranges. Fig. 16

Fig. 12. Comparison of X441 cladding axial strain distribution at 5 and 10 at.% peak burnup.

of the FRAC and AFLUS (Ogata and Yokoo, 1999) code prediction with data corresponding related peak burnup for X425 and X441 fuel assemblies. The peak strain of cladding increases along with the increase of fuel burnup. The relative errors of code in predicting

Fig. 13. Calculated Zr atom fraction vs. measured data.

Table 2 Peak clad strain in X425. Peak burnup at.%

Exp. Data

FRAC

AFLUS

Clad strain (%)

Relative error (%)

Clad strain (%)

Relative error (%)

10.4 15.8 18.9

0.25 0.98 2.00

0.21 1.07 2.11

16 9.2 5.5

0.37 0.86 1.55

48 14 22.5

Peak burnup at.%

Exp. Data

FRAC

5.0 10.

0.25 1.65

Table 3 Peak clad strain in X441. AFLUS

Clad strain (%)

Relative error (%)

Clad strain (%)

Relative error (%)

0.24 1.60

4 3

0.21 2.12

14.2 20.9

H. Sun et al. / Annals of Nuclear Energy 138 (2020) 107221

9

is at 5% in X441 test, about half of the data is outside the error range of +20%. This shows the code has some deviation in calculating the axial stress distribution of the clad at low burnup case. According to the above comparison results, the overall prediction error of the program for the experiment is within acceptable level and the code will be further optimized in the future for the stress deviation in low burnup calculation. 5. Conclusions

Fig. 14. Fuel temperature distribution.

Fig. 15. Code prediction of fission gas release vs. measured data.

A new code named FRAC has been developed to analyze the thermo-mechanical performance of metallic fuels under different steady-state irradiation conditions. Based on the basic models, the code considers the important behavior of metal fuels under irradiation conditions, such as sodium band effect, fuel constituents migration, fission gas retention and release behavior, and the mechanical effect of fuel-cladding and so on. The database of EBR-II metal fuel irradiation tests were selected for comparative analysis to validate the performance of the code. The comparison results show that the calculation trend of Zr constituent and fuel temperature distribution, fission gas release and cladding axial strain distribution by the code is consistent with the experimental data. However, more experimental data are needed for a significant quantitative assessment of code capability, such as fuel swelling, fuel axial slug deformation, clad wastage and so on. Error analysis of the overall calculation results shows that the prediction error of Zr constituent distribution is less than 30%, while that of fission gas release and cladding strain distribution is less than 20%, and the prediction error is within acceptable range. After evaluating the prediction error of experimental data, there are still some deviations in predicting clad strain under low burnup conditions. Further optimization of the code is needed in the future. The code is mainly used for the performance analysis of metal fuel under steady-state conditions, and the transient version is currently under development. The code can also be applied to the safety design and analysis of metallic fuels in liquid metal fast reactor. Acknowledgments The authors appreciate the financial support from National Natural Science Foundation of China. References

Fig. 16. Code predicted strain distribution vs. measured data (U-19 wt%Pu-10 wt% Zr pin).

displays the comparison between the code calculated stress distribution and the experimental data. Similarly, the prediction error of the code is within ±20% for most data. However, when the burnup

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