Study on the Steady-State Performance of the Fuel Rod in M²LFR-1000 Using KMC-Fueltra

Abstract

Operating conditions in the liquid metal fast reactor, like higher power density, higher temperature gradient, and higher burnup, are more severe to the fuel rod comparing to the light water reactor. The integrity and safety of the fuel rod is very essential to the reactor safety. In this study, the fuel rod designed for M²LFR-1000, which is a typical pool type lead cooled fast reactor, is evaluated using a fuel performance analysis code named KMC-Fueltra. Irradiation behaviors and material properties for the MOX fuel and T91 cladding are established and introduced into the code. The steady-state performance of the fuel rod is analyzed. Results concerning both fuel and cladding performance are discussed based on indicative design limits collected from the open literatures. This study is useful to improve the conceptual design of the M²LFR-1000.

1 Introduction

Ensuring the integrity and safety of the fuel rod, which is the core component in the reactor, is the most essential issue in the design of a nuclear reactor [1]. For the fast reactor, the power density, temperature gradient and burnup are higher than light water reactor. This brings a greater challenge for the fuel rod in the fast reactor.

Many materials have been developed and studied in order to meet the above characteristics of fast reactors. Material properties and irradiation behaviors are implemented into the fuel performance code to evaluate their performance in the specific reactor. Considering the transmutation and proliferation, MOX fuel has been widely used in fast reactors. The cladding material are mainly stainless steel. One is austenitic stainless steel; the other is ferritic martensitic stainless steel. Due to the better thermal creep resistance, the austenitic steel 15-15-Ti has been chosen to be the cladding material in the ALFRED, MYRRHA and ASTRID reactors [2]. Marcello extended the TRANSURANS code [3] and it is adopted for the simulation of the fuel and cladding performance covering the average and the hottest reactor conditions in the ALFRED reactor [2]. 316SS is also used in fast reactors like JOYO and EBR-II [4], but the it has poor compatibility with lead coolant. Corrosion with lead coolant should be considered at certain coolant velocity and temperature in the lead cooled fast reactor. Benefit from the good corrosion resistance to the lead coolant, T91 is selected as the cladding in 1000Mth Medium-size Modular Lead-cooled Fast Reactor (M²LFR-1000) [5]. In order to ensuring the safety of the reactor, the integral performance of the fuel rod design should be investigated under the operational condition in M²LFR-1000.

In this paper, material properties and irradiation behaviors of MOX fuel and T91 cladding are incorporated into the fuel performance code KMC-Fueltra. The widely used failure mechanism and design limits of some important parameters applicable for the fast reactors are collected from the public literatures to evaluate the fuel rod design. The steady-state performance of the fuel rod in M²LFR-1000 is studied using KMC-Fueltra. Results are discussed and some improvements are suggested.

2 Material Properties

Material properties are of great importance to the fuel performance analysis. The thermal and mechanical properties of the MOX fuel and T91 cladding implemented in the KMC-Fueltra are presented in this part. The main point is put on the basic material properties. The unique irradiation behaviors did not list but can be found in the former work.

2.1 MOX Fuel

• (1) Thermal conductivity

Many correlations have been proposed for MOX fuel concluded from the fresh or irradiation fuel data. A wide set of factors like fuel temperature, burnup, plutonium content, stoichiometry, and porosity have effects on the MOX fuel thermal conductivity. Magni et al. [6] assessed the most recent and reliable experimental data statistically and proposed a new correlation for the MOX fuel with above factors taking into consideration. The correlation of thermal conductivity for the fresh MOX fuel is:

$$ \begin{gathered} k_{0} \left( {T,x,\left[ {Pu} \right],p} \right) = \left( {\frac{1}{{A_{0} + A_{x} \cdot x + A_{Pu} \cdot \left[ {Pu} \right] + \left( {B_{0} + B_{Pu} \left[ {Pu} \right]} \right)T}} + \frac{D}{{T^{2} }}e^{{ - \frac{E}{T}}} } \right) \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {1 - p} \right)^{2.5} \hfill \\ \end{gathered} $$

(1)

where T is the temperature, $K$; $\left[ {Pu} \right]$ is the plutonium atomic fraction; $p$ is the porosity fraction; Considering the thermal conductivity of degradation at certain burnup values, the correlation after the irradiation is:

$$ k_{irr} \left( {T,x,\left[ {Pu} \right],p,bu} \right) = k_{inf} + \left( {k_{0} \left( {T,x,\left[ {Pu} \right],p} \right) - k_{inf} } \right) \cdot e^{{ - \frac{bu}{\varphi }}} $$

(2)

where $k_{0} \left( {T,x,\left[ {Pu} \right],p} \right)$ is the fresh MOX thermal conductivity; $bu$ is the burnup, $GWd/tHM$; $k_{inf}$ asymptotic thermal conductivity, $W/m/k$; $\varphi$ is the fitted coefficient, $GWd/tHM$; Parameters used in this correlation is listed in the Table 1.

Table 1. Parameters in the correlation

• (2) Young’s modulus and Poisson’s ratio

Young’s modulus of MOX fuel is related to the Pu content and stoichiometric state [7]. The relation can be expressed as:

$$ E = E\left( {UO_{2} } \right) \cdot \left( {1 + 0.15w_{Pu} } \right)exp\left( { - Bx} \right) $$

(3)

where $B$ is constant, 1.34 for the hyper-stoichiometric fuel and 1.75 for the hypo-stoichiometric fuel; $x$ is the deviation from stoichiometry; $w_{Pu}$ is the weight fraction of $PuO_{2}$; $E\left( {UO_{2} } \right)$ is the Young’s modulus of $UO_{2}$ and can be denoted as:

$$ E\left( {UO_{2} } \right) = 2.334 \times 10^{11} \left[ {1 - 2.752\left( {1 - D} \right)} \right]\left( {1 - 1.0915 \times 10^{ - 4} } \right) \cdot T $$

(4)

where $D$ is the theoretical density fraction; $T$ is the temperature, $K$.

Possion’s ratio of MOX fuel is given as a function of the weight fraction of $PuO_{2}$:

$$ v\left( {MOX} \right) = w_{Pu} \cdot v\left( {PuO_{2} } \right) + \left( {1 - w_{Pu} } \right) \cdot v\left( {UO_{2} } \right) $$

(5)

$$ v\left( {PuO_{2} } \right) = 0.276 + \frac{T - 300}{{2800}}\left( {0.5 - 0.276} \right) $$

(6)

$$ v\left( {UO_{2} } \right) = 0.316 + \frac{T - 300}{{2800}}\left( {0.5 - 0.316} \right) $$

(7)

where $v\left( {UO_{2} } \right)$ and $v\left( {PuO_{2} } \right)$ is the Possion’s ratio of $UO_{2}$ and $PuO_{2}$ respectively; $T$ is the temperature, $K$; $w_{Pu}$ is the weight factor of $PuO_{2}$.

• (3) Thermal expansion

Thermal expansion of the MOX fuel is obtained by weight factor of different components [8].

$$ \varepsilon^{th} \left( {MOX} \right) = \left( {1 - w_{Pu} } \right) \cdot \varepsilon^{th} \left( {UO_{2} } \right) + \left( {w_{Pu} } \right) \cdot \varepsilon^{th} \left( {PuO_{2} } \right) $$

(8)

where, $\varepsilon^{th}$ is thermal expansion, %; $w_{Pu}$ is the weight factor of $PuO_{2}$. Thermal expansion of $UO_{2}$ and $PuO_{2}$ is expressed by:

$$ \varepsilon_{i}^{th} = K_{1} \cdot T - K_{2} + K_{3} exp\left( { - \frac{{E_{D} }}{kT}} \right) $$

(9)

The subscript $i$ takes 1 and 2, which represent $UO_{2}$ and $PuO_{2}$, respectively. Parameters used in this correlation is listed in the Table 2.

Table 2. Parameters used in thermal expansion model

• (4) Creep model

Creep can effectively release the stress caused by irradiation behaviors like swelling and thermal expansion in the fuel, which can protect the fuel from reaching the safety limits [9]. Creep of the MOX fuel is divided into two parts: thermal creep and irradiation creep [4]. Thermal creep is composed of diffusional creep and dislocation creep and is expressed as follows:

$$ \varepsilon^{ \cdot }_{th} = 3.23 \times 10^{9} \cdot \frac{{\sigma_{eff} }}{{a^{2} }}\exp \left( { - \frac{{Q_{1} }}{RT}} \right) + 3.24 \times 10^{6} \cdot \sigma_{eff}^{4.4} \cdot exp\left( { - \frac{{Q_{2} }}{RT}} \right) $$

(10)

where $\varepsilon^{ \cdot }_{th}$ is the fuel thermal creep rate, $1/h$; $a$ is the grain size, $\mu m$; $\sigma_{eff}$ is the equivalent stress, $MPa$; $Q_{1} = - 92500$ and $Q_{2} = - 136800$ are activation energy; $R$ is the universal gas constant.

Irradiation creep is denoted as;

$$ \varepsilon^{ \cdot }_{irr} = 1.78 \times 10^{ - 26} \sigma_{eff} \cdot \varphi $$

(11)

where $\mathop {\varepsilon_{irr} }\limits$ is the fuel irradiation creep rate, $1/h$; $\varphi$ is the fission rate, $fission/\left( {m^{3} \cdot s} \right)$.

2.2 T91 Cladding

• (1) Thermal conductivity

Thermal conductivity of the cladding is denoted as a function of temperature as follows [10]:

$$ k = 21.712 + 0.011T - 9.5483 \times 10^{ - 6} T^{2} + 3.627 \times 10^{ - 9} T^{3} $$

(12)

where $T$ is the temperature, $K$.

• (2) Young’s modulus and Poisson’s ratio

Young’s modulus of the cladding is a function of temperature and can be expressed as [11]:

$$ E = 2.11458 \times 10^{5} - 21.24 \cdot T - 7.94 \times 10^{ - 2} \cdot T^{2} $$

(13)

where $E$ is Young’s modulus, $Mpa$; ${ }T$ is the temperature, °C, with the range of applicability in $20 < T < 760$ °C.

Possion’s ratio of the cladding is set as a constant:

$$ v = 0.3 $$

(14)

• (3) Thermal expansion

Thermal expansion of the cladding is expressed as [10]:

$$ \begin{gathered} \varepsilon^{th} = \frac{\Delta L}{L} = - 3.0942 \times 10^{ - 3} + 1.1928 \times 10^{ - 5} \cdot T - 6.7979 \times 10^{ - 9} \cdot T^{2} + 7.9606 \hfill \\ \times 10^{ - 12} \cdot T^{3} - 2.546 \times 10^{ - 15} \cdot T^{4} \hfill \\ \end{gathered} $$

(15)

where $\varepsilon^{th}$ is thermal expansion, %; ${\text{T}}$ is the temperature, $K$.

• (4) Creep model

Similar to the MOX fuel, creep model of the cladding is also divided into two parts: thermal creep and irradiation creep. Thermal creep is expressed as [11]:

$$ \dot{\varepsilon }_{th} = A\sigma^{n} exp\left( { - Q/RT} \right) $$

(16)

where $Q = 728 \pm 35\,\rm{kJ}/\rm{mo}$ l is the activation energy; $n = 5$.

Irradiation creep is expressed as:

$$ \varepsilon^{ \cdot }_{irr} = 1.8 \times 10^{ - 22} \varphi_{v} \left( t \right) \cdot \sigma_{eq} $$

(17)

where $\varphi_{v} \left( t \right){ }$ is the neutron flux rate, $n/\left( {cm^{2} \cdot s} \right)$; $\sigma_{eq}$ is the equivalent stress, $Mpa$; $t$ is the time, $h$.

• (5) Plasticity model

Plasticity is an important aspect in the fuel rod mechanical performance, which is related to the fuel failure highly. Plasticity model of the cladding is denoted as a function of temperature [11].

$$ \sigma_{y} = 536.1 - 0.4878 \cdot T + 1.6 \times 10^{ - 3} \cdot T^{2} - 3 \times 10^{ - 6} \cdot T^{3} + 8 \times 10^{ - 10} \cdot T^{4} $$

(18)

where $\sigma_{y}$ is the yield stress, $Mpa$; ${ }T$ is the temperature, °C, with the range of applicability in $20 < T < 700$ °C.

• (6) Cumulative damage function

Fuel rod failure time is a critical parameter to the reactor safety. Predicting this parameter as accurately as possible is one of the main tasks of fuel performance analysis. The traditional cumulative damage function (CDF) is used to evaluate the fuel rod failure.

$$ CDF = \sum\nolimits_{i = 1}^{n} {\frac{\Delta t}{{t_{r} \left( {\sigma_{i} ,T_{i} } \right)}}} $$

(19)

where $\Delta t$ is the time step, $s$; $t_{r} \left( {\sigma_{i} ,T_{i} } \right)$ represents time to failure at certain stress and temperature. It can be calculated by the Larson-Miller parameter (LMP) [12], defined as:

$$ LMP\left( \sigma \right) = T\left( {C + \log_{10} t_{r} } \right) $$

(20)

For the T91 cladding, the LMP is fitted by the polynomial function.

$$ LMP\left( \sigma \right) = 38387.008 - 84.880\sigma + 0.403\sigma^{2} - 1.15 \times 10^{ - 3} \sigma^{3} + 1.254 \times 10^{ - 6} \sigma^{4} $$

(21)

where $\sigma$ is the equivalent stress, $Mpa$; $C$ is set as 33.

3 Model Implementation

3.1 Description of M²LFR-1000

The 1000MWth Medium-size Modular Lead-cooled Fast Reactor (M²LFR-1000) is a typical pool-type fast reactor developed by USTC [5]. It adopts a rod-shaped fuel element design. The pellet is MOX with Pu enrichment about 20%, the cladding is T91 stainless steel and the coolant is lead. The operating temperature is 400–480 °C. The main design parameters of the fuel rod are outlined in Table 3.

Table 3. Fuel specifications for M²LFR-1000

3.2 Introduction of KMC-Fueltra

KMC-Fueltra is a 1.5D fuel performance analysis code designed for the liquid metal fast reactor. It is applicable for the steady-state and transient operating conditions and covers typical materials used in LMFRs [13, 14]. Figure 1 shows the flow diagram of KMC-Fueltra. It can perform the thermal, thermal migration, fission gas release, and mechanical analysis of the fuel rod. Based on the above calculation results, the fuel rod failure analysis is also performed. Irradiation behaviors considered in this code contain thermal expansion, swelling, densification, relocation, cracking-healing, restructuring, creep, and plasticity for the pellet as well as thermal expansion, swelling, creep, and plasticity for the cladding. In this article, KMC-Fueltra is used to evaluate the steady-state performance of the fuel rod in the M²LFR-1000.

Fig. 1.

Flow diagram of KMC-Fueltra.

3.3 Indicative Design Limits

Design limits are important for the conceptual design of the fuel rod. Luzzi et al. [2] has concluded some conservative design limits for many important parameters that influence thermal and mechanical performance from the open literatures. These limits are adopted for the conceptual design of fuel rods in M²LFR-1000 as well. Some limits are concluded from the view of the corrosion and erosion problem of the lead environment, others are from the material properties or irradiation experiments. Table 4 lists the conservative design limits of some important parameters.

Table 4. Indicative design limits for M²LFR-1000

4 Results and Discussions

4.1 Thermal Performance

The change of fuel rod temperature with time is shown in Fig. 2. The maximum fuel pellet temperature is about 1314.4 °C, which appears at the half height of the fuel rod and is consistent with the axial power distribution. The maximum cladding temperature is about 529.6 °C, which appears at the top of the fuel rod. The margin to the safety limits is abundant. The maximum temperature of the fuel pellet becomes larger with time while the cladding did not show too much change. Burnup effect on the fuel rod can account for this. Thermal conductivity of the fuel pellet in Eq. 2 gets smaller with burnup and the gap conductance also decreases at a certain burnup as can be seen in Fig. 3. These factors lead to the deterioration of heat conduction in fuel rod. Gap conductance is affected by many factors including the gap with, gas temperature, plenum pressure, and gas content. Its change depends on which factor is dominant in the operational life. Due to the swelling in the fuel pellet, the gap width decreases with time, which improves the gap conduction at the initial stage. However, the gap conductance decreases later because of the increasing released fission gases.

Fig. 2.

Evolution of the fuel rod maximum temperature.

Fig. 3.

Evolution of the gap conductance and gap width.

4.2 Fission Gas Release

Figure 4 gives the change of fission gas release fraction in MOX fuel. At the initial stage, fission gases diffuse and agglomerate in the fuel matrix with the fission process, so the release fraction is almost zero. When the fission gases atoms accumulate to a certain amount in the gas bubbles, the migration process starts. These gas bubbles migrate to the intergranular and then to the gap under the temperature gradient. The released fission gases cause the plenum pressure getting larger as shown in Fig. 5. The initial gas pressure is 0.5 MPa and the maximum plenum pressure is about 1.8 MPa at the end of burnup.

Fig. 4.

Evolution of the fission gas release fraction.

Fig. 5.

Evolution of the plenum pressure.

4.3 Mechanical Performance

In addition to the temperature field, the effect of irradiation behaviors on the fuel performance is also shown in the deformation of the fuel rod. Figure 6 illustrates the evolution of fuel rod size. The biggest change is the fuel pellet outer diameter. Irradiation behaviors that occur within the fuel pellet is more intense where the neutron flux is the largest. Thermal expansion and swelling contribute a lot to the expansion of the fuel pellet. Although densification can decrease the pellet deformation, its contribution is small and it ends at the initial stage quickly. The size of the cladding does not show too much change during the entire operational life. Table 5 gives the comparison results of the parameters with the design limits. The safety margin of fuel pellet temperature is very large while the cladding is only 20 °C. This should be paid attention in the later optimization of the fuel rod design. Some burnup related parameters like plenum pressure, total creep strain, maximum cladding stress and CDF is far from the design limits. Meanwhile, due to the low stress state, the plastic strain does not appear in the fuel rod. A major reason is that burnup of the fuel rod, as shown in Fig. 7, is not very large compared to the other fast reactors of the same type. The maximum burnup is about 4.2 at%. For better economy, it can enlarge by modifying the reactor design if needed.

Fig. 6.

Evolution of the fuel rod size.

Table 5. Comparison results of the parameters.

Fig. 7.

Evolution of the fuel rod maximum burnup.

5 Conclusions

In this paper, the steady-state fuel rod performance in M²LFR-1000 has been studied using the fuel performance code KMC-Fueltra. Material properties for the MOX fuel and T91 cladding have been incorporated into the code. An important evaluation model and some indicative design limits are collected from the open literatures to help find out the shortcoming of the fuel rod design. The corresponding thermal and mechanical parameters of the fuel rod are evaluated and discussed. Some important parameters concerning the thermal and mechanical performance of the fuel pellet and cladding do not exceed the design limits, proving the safety of the fuel rod design. Even some parameters are far from the design limits, leaving a lot of room for optimization. Burnup of the fuel rod in M²LFR-1000 is about 4.2 at%, which is not very deep compared to fast reactors of the same type. It can also be optimized in the later design process.