The U-TRU-(40-60)Zr metallic fuel is being considered as the transmutation fuel for HYPER in Korea. U-TRU-15Zr is also considered as the reference fuel for critical system. The MACSIS-H for an metallic fuel is being developed as the steady-state performance computer code. The fuel temperature calculation schemes were developed and implemented into the MACSIS-H code to analyze the fuel rod performance.

A constituent migration subroutine has been made and installed into the MACSIS code to simulate constituent redistribution. The He production rates calculated by the other code were inserted into the swelling/FGR routine of the code. The burnup limits and CDF(cumulative damage fraction) were analyzed by MACSIS-H code. There are lots of uncertainties on the modeling, so some experimental tests are needed for clarifying the uncertainties of fuel modeling.

Introduction

Metallic fuel is being considered as the transmutation fuel for the HYPER(Hybrid Power Extraction Reactor) in Korea[1]. U-TRU-Zr is being considered for the alloy fuel slug, and the cladding material is the HT9. The performance analysis in fuel rod design is essential to assure adequate fuel performance and integrity under irradiation conditions. In this paper, parametric study has been performed by the MACSIS-H (Metal fuel performance Analysis Code for Simulating the In-reactor behavior under Steady-state conditions-HYPER)[1]. This code will be used for simulating operational limits of metal fuel under steady state conditions.

Present studies represent parametric results and the capability for efficiently predicting the performance parameters as a function of burnup. There were a few fuel characteristics relating to TRU material, so the material data of the U-Pu-Zr were used for those of the U-TRU-Zr. The radial fuel constituent migration subroutine has been made and installed into the MACSIS-H code to simulate constituent redistribution. The He production rates calculated by the other code are inserted into the swelling/FGR routine of the code. The thermal creep strain limits was analyzed according to the plenum-to-fuel ratio by MACSIS-H. A statistical failure analysis was performed to analyze the rupture behavior of the metallic fuel pins. The failure probabilities were estimated in terms of CDF, based upon the known Weibull statistical failure model.

Code description

MACSIS-H is a metallic fuel performance computer code which calculates thermal performance characteristics and dimensional changes of the fuel rods in a fast neutron environment. MACSIS-H code calculates temperature distribution, mechanical deformations, fission gas release, and the constituent migrations of the fuel elements during irradiation. It assumes that the fuel slug is an infinitely long rod concentric with an infinitely long cladding.

The key phenomena which are significant in controlling metallic fuel pin behavior and reliability are known to be large fission gas release and the fuel swelling in the early irradiation stage, the fuel constituent migration and the bonding material behavior and the fuel/cladding eutectic reaction[2].

Main structures of the code consist of the temperature profile calculation routine, the swelling/FGR calculation routine, the chemical/metallurgical behavior calculation routine and the deformation calculation routine.

Design parameter

The alloy fuel consists of a U-TRU-Zr metallic alloy slug and liquid metal thermal bonding in HT9 steel, much like the Experimental Breeder Reactor II (EBR-ll) fuel or fuel developed for the Integral Fast Reactor (IFR) concept. A fission gas plenum is located above the fuel slug. The key design parameter for the alloy fuel is shown in Table 1.

Table 1. Key Design Parameter

Fuel temperature prediction

Thermal conductivity and power-to-melt

The precise prediction of fuel temperature distribution is one of the most important factors in a fuel performance code, because fuel temperature affects almost all of the fuel element behaviors. It is known that the key factors which may affect the temperature distribution of metallic fuel are porosity formation, bonding material infiltration, and heat generation rate and thermal conductivity dependence on fuel constituent migration.

The thermal conductivity of the unirradiated U-TRU-Zr alloy, k_0, can be expressed as the function of temperature and alloy composition[3].

(1)

where, T is the temperature in kelvin and Wz is the weight fraction of zirconium.

Thermal conductivity for more than 20wt% of Zr or more than 30wt% TRU is given by [4].

(2)

The porosities and bonding material infiltration effect should be considered in calculating the thermal conductivity of irradiated metallic fuel. These effects can be determined by porosity correction factor, P_f, which was derived by Bauer and Holland[5].

The predicted temperatures of U-Zr metal fuel by MACSIS-H versus LIFE-M, etc.[3,6~10] are plotted in figure 1 which is an evaluation of the various temperatures from cladding mid-wall to fuel centerline. It is apparent that MACSIS-H has reasonably good capability in predicting fuel pin rod temperatures.

Figure 2 shows several cases of temperature variation with respect to linear heat generation of the typical HYPER and critical system fuel pin. In the design of a metallic fuel pin, fuel temperature limits on fuel melting should be considered from a temperature point of view. Based on the aggregate of TREAT tests, ANL concluded that centerline fuel melting, even extensive melting exceeding 80 % of a given radial cross-section, is not a problem and does not result in pin failures[11]. However, the prevention of centerline fuel melting is regarded as a design limit of metallic fuel pins for conservatism. It is expected that the solidus temperature of U-42TRU-50Zr and U-20TRU-14.6Zr metallic fuel are 1090 and 1295^oC, respectively. As irradiation proceeds, the thermal conductivity of metallic fuel is degraded to approximately 50 % of the initial value at around 1 at% burnup. For further irradiation, the conductivity is restored by bonding material infiltration into the fuel slug. In the case of 50 % degraded thermal conductivity, which is the worst condition in terms of fuel temperature, the calculated power-to-melt for U-42TRU-50Zr and U-20TRU-14.6Zr metallic fuel were about 420 and 500 W/cm respectively.

Fuel constituent migration

The radial fuel constituent migration related to the formation of three distinct phasal zones is a general phenomenon in irradiated U-Pu-Zr and U-Zr alloys[12]. This phenomenon may affect the in-reactor performance of metallic fuel rods, such as melting temperature, thermal conductivity, power generation rate, phase boundaries and eutectic temperature of the fuel slug. Thus, constituent migration modeling is essential to develop a metallic fuel performance code. The constituent migration model adopted in MACSIS-H was based on the Ishida’s model[13] and Hofman’s theory[14].

Ishida’s model is a ternary diffusion model that considers a quasi-binary U-Zr phase diagram with constant plutonium contents for the U-Pu-Zr system, but Zr weight is limited to about 20wt%. So the quasi-binary U-Zr phase diagram has been reconstructed by several polynomial equations only for the fuel slug of the critical system. The diffusion coefficients used in this model are based on the Hofman’s model[14]. The fuel constituent migration model for more than 40wt% Zr will be developed in the future.

Figure 3 shows the calculated radial profile of Zr and measured Zr concentration for the U-19Pu-10Zr. The dashed line shows the initial Zr composition. As shown in figure 3, significant amount of Zr is depleted in the middle zone.

Figure 4 shows the simulated Zr redistribution for U-20TRU-14.6Zr fuel. The main reason for Zr addition to metallic fuel is to increase melting point of the fuel and to enhance the chemical compatibility between fuel and cladding. In this regard, the fuel constituent migration may affect the integrity of fuel pin. At around 650 ^oC of fuel temperature, the model predicts the Zr fraction in fuel center reaches 0.5, and there will be no centerline Zr depletion expected in all range of temperature. The model also predicts that the sharp Zr depletion occurs when the fuel surface temperature is approached the upper limit of (z+g) phase boundary.

Margin to slug centerline melting

Figure 5 and 6 show the radial distribution of the temperature of the slug center. The centerline peak temperature is very lower than the solidus temperature. It can be concluded, therefore, that the metallic fuel has a sufficient margin to the slug melting temperature.

Figure 5 also shows the temperature distribution for the case of the fuel constituent migration. Zr fraction in the fuel center is increased by the fuel constituent migration. This indicates fuel centerline melting will be retarded as redistribution occurs during off-normal conditions. But Zr depletion at fuel surface may affect deleterious effect on fuel pin integrity. This phenomenon has not been confirmed yet experimentally, but the fuel designers might be careful on this effect for setting up their operating temperature limit.

Fission gas release and He rate insertion

Fission gas retention and release

The production rate of the fission gas products is proportional to power density, and a predictive capability for the behavior of fission gas in nuclear fuel during normal and off-normal conditions is essential to any rational estimate of fuel element integrity. The first step of fission gas release is the movement of fission gas created in the fuel matrix to the fuel grain boundary. The second step of fission gas release is the movement of fission gas on the grain boundary through the fission gas tunnels to the fuel rod gas plenum.

Figure 7 shows the percentage gas releases according to burnup variation, predicted by the semi-theoretical models in the MACSIS-H code. According to the experimental results, it appears that fission gas release largely increases at around 1 to 2 at% burnup and the maximum fission gas release at a burnup of 13at% was 74 %. The predictions by MACSIS with the semi-theoretical models agree comparatively well with the experimental results from ANL, according to burnup increase.

Figure 7. Fission Gas Release as function of burnup

He rate insertion

The estimated helium production rates from ²⁴¹Am was 50 ml He per gram of transmuted ²⁴¹Am[16]. As shown in Table 1, initial loaded ²⁴¹Am contents by the heavy metal contents of the HYPER and the critical system were 2.66 and 0.1 wt%, respectively. So the initial loaded ²⁴¹Am weight calculated by the fuel dimensions were 9.1 and 0.5g. It is assumed that the time required to achieve 50% transmutation of ²⁴¹Am is 2.5 years[16]. The He generation rates of the alloy and the inter-metallic dispersion fuel were assumed to be about 40 and 9.36ml/165day.

In the MACSIS-H, the He generation rates were inserted into the FGR (Fission Gas Release) analysis module, and then the volume of the fission gas generated was calculated including the He generation rates.

Burnup limits analysis

Figure 8 shows the cladding thermal creep strain comparison with He effects as a function of the plenum-to-fuel ratio for the fuel of HYPER. The cladding strain of a low-smeared density pin can be accounted for by the plenum pressure stress alone[2]. It was estimated that the swelling and the irradiation creep of the HT9 were very small. The effects on thermal creep strain with different plenum sizes were analyzed by the MACSIS-H code.

A shorter plenum length results in a larger thermal creep strain. The values of thermal creep strain without the He effects were about 0.14 and 0.09% at 25at% for the 1.5 and 1.75 plenum-to-fuel ratios, respectively. But the values of total strain with He effects were about 0.4 and 0.19% at 25at% for the 1.5 and 1.75 plenum-to-fuel ratios, respectively. These results indicate that the He effects will be a very important factor for the higher burnup, even if the He weight were very small.

According to preliminary burnup limits, the thermal creep strain limit is 1%[17]. So the burnup limits of alloy fuel for HYPER were 29 and 33at% for the 1.5 and 1.75 plenum-to-fuel ratio, respectively.

Even though a lot of models such as the eutectic melting and the FCMI by the solid fission products have not been established, it is expected that 1.5 and 1.75 times of the plenum-to-fuel ratios are conservative for satisfying the discharge burnup goal of about 25% by thermal creep strain limit.

Figure 9 shows the cladding thermal creep strain comparison with He effects as a function of the plenum-to-fuel ratio for the fuel of the critical system. The values of thermal creep strain without the He effects were about 2.27 and 0.64% at 9.8at% for the 1.5 and 1.75 plenum-to-fuel ratios, respectively. But the values of total strain with He effects were about 4.8 and 1.2% at 9.8at% for the 1.5 and 1.75 plenum-to-fuel ratios, respectively.

These results indicate that the HT9 cladding is not conservative for satisfying the discharge burnup goal, because of the high coolant outlet temperature. It is estimated that the replacement of cladding material with higher thermal creep resistance may be needed for the critical system.

Cumulative damage fraction analysis

To prevent fuel pin failure, generally two kinds of specific design limits have been used in fast reactor fuel design. One of them is the strain limit approach. However, this approach has a deficiency in that rupture strain is strongly dependent on temperature and strain rate. The other approach is cumulative damage fraction (CDF) method, which utilizes the linear life fraction rule assuming that the damage accumulates linearly. The CDF is determined from time-to-rupture correlation as a function of temperature and stress.

For the evaluation of component reliability, the Weibull statistical model [18] has been widely used in the area of fuel nuclear component as well as other industries. The Weibull analysis is appropriate to describe fuel pin breach because it is derived from the situation where the most severe flaw dominates the failure.

For the steady-state conditions, the probabilistic CDF were estimated as follows;

• The failure distribution functions of metallic pins were derived by Weibull analysis with application of CDF and burnup;

• The cumulative damage fractions of the X447 fuel pins were evaluated from the time-to-rupture correlation by the MACSIS-H code calculations;

• Fuel pin performances were estimated under the HYPER and the critical system conditions.

For the transient conditions, the probabilistic CDF were estimated as follows;

• The cladding performances during transient conditions were evaluated using the result of the WPF (Whole Pin Furnace) tests;

• Cumulative damages about the WPF test fuel pin were estimated by the transient test data and the failure correlation;

• Distribution of the CDF of the WPF data was determined by Weibull probabilistic analysis;

• Fuel pin performance was estimated under the same conditions as the WPF tests.

Generally the limit on the fuel pin failure rate of the fast reactor core is allowed less than 0.01%, so figure 10 also shows the CDF limit of 0.001 was reasonable.

The calculated CDF on 25at% of peak burnup for the fuel pin of HYPER during the steady-state were 1.6´10^-3 and 5.7´10^-4 for the 1.5 and 1.75 plenum-to-fuel ratios, respectively. The fuel pin failure rates were 0.017 and 0.003%, respectively. It was estimated that 1.75 times of the plenum-to-fuel ratio is conservative for satisfying the discharge burnup goal of about 25% by CDF strain limit. .

Failure probability of the HYPER fuel pin during transient condition were lower than that of the WPF pin, because of a higher plenum-fuel volume ratio and lower cladding inner radius vs. thickness ratio. If there were more transient data points of the fuel pin, more accurate probabilistic CDF analysis will be performed.

Figure 10. Cumulative damage fraction Thermal creep strain for the alloy fuel

Conclusions

The metallic fuel is being considered as the transmutation fuel for the HYPER in Korea. The MACSIS-H has been developed for the design of metallic fuel in HYPER, and a parametric study was performed using the MACSIS-H code.

It was estimated that the metallic fuel has a sufficient margin to the slug melting temperature. The constituent migration analysis was performed by the inserting of the quasi-binary U-Zr model into MACSIS-H code. The results show the significant amount of Zr was depleted in the middle zone. So it is expected the centerline melting temperature of U-20TRU-14.6Zr fuel will be increased, but eutectic temperature at fuel surface will be decreased.

In order to evaluate the He effects by ²⁴¹Am transmutation, the He generation rates were inserted into the code. It was estimated that the He effect will be a very important factor.

It was expected that the fuel pin of HYPER is conservative for satisfying the discharge burnup goal of about 25% by thermal creep strain limit of 1%. But the fuel pin of the critical system was not conservative for satisfying the discharge burnup goal, because of the high coolant outlet temperature. It was estimated that the replacement of cladding material with higher thermal creep resistance may be needed.

It was estimated that 1.75 times of the plenum-to-fuel ratio is conservative for satisfying the discharge burnup goal of about 25% by CDF strain limit. Failure probability of the HYPER fuel pin during transient condition were lower than that of the WPF pin, because of a higher plenum-fuel volume ratio and lower cladding inner radius vs. thickness ratio.

There are lots of uncertainties in the modeling such as the material data, the eutectic melting, and the FCMI etc., so some experimental tests are needed for clarifying the uncertainties of the fuel modeling.

Acknowledgments

This work has been carried out under the national nuclear long-term R&D program which is supported by the Korean MOST(Ministry Of Science and Technology).