Measurements and Modeling of Thermal Conductivity of U-Mo/Al Dispersion Fuel for

During this study, a comprehensive investigation of the thermal conductivity of U-Mo/Al dispersion type fuel was carried out. This thesis has been contributed to provide a comprehensive insight for the general understanding of the thermal conductivity of U-Mo/Al dispersion fuel.

Introduction

Background

History of research reactor fuel developments
U-Mo alloy fuel
Irradiation behaviors of U-Mo/Al dispersion fuel

It is composed of the fuel meat (or fuel zone) in which the fissile materials are loaded. KJRR is the first research reactor in the world designed to use U-Mo/Al dispersion fuel [38].

Table 1. Basic properties of uranium intermetallic fuels [7], [8].

Thermal conductivity in research reactor fuel

Role of thermal conductivity in U-Mo/Al dispersion fuel
Literature survey for the thermal conductivity of U-Mo/Al dispersion fuel

For the thermal conductivity of U-Mo/Al dispersion fuel, the measurement data in the literature are scarce due to the difficulties in sample fabrication and measurements. Until now, many uncertain factors in the thermal conductivity of U-Mo/Al dispersion fuel have not been revealed.

Objectives and scope of the research

Finally, a semi-empirical model was developed to consider various microstructure parameters so that it is applicable to various fuel and irradiation conditions. The model is applied to the fuel performance code and more accurate fuel performance analysis is achieved.

Table 3. Comparison of methods for obtaining the thermal conductivity of composite material

Effective thermal conductivity of composite material

Methodology

Maxwell [48] and Rayleigh [49] were the first to develop a theoretical model for an effective material property based on electrostatic theory. In this case, the actual material property refers to the material property of the composite material when it is homogenized so that the material properties are effectively the same regardless of location within the material.

Descriptions of theoretical models

Maxwell and Bruggeman model
Advanced models for a composite material
Models for a coated material
Models for a porous material
Developed models used for U-Mo/Al dispersion fuel

De Zehner and Schlünder [54] developed a semi-empirical expression for the effective thermal conductivity of a packed bed. The thermal conductivity of porous material depends on the thermal conductivity of the pore and the matrix.

Figure 7. Illustrations for temperature distribution showing the interfacial thermal resistance

Thermophysical properties of U-Mo/Al(-Si) dispersion fuel

Sample fabrication

Sample fabrication of aluminum-silicon alloys
Sample fabrication of fresh U-Mo/Al dispersion fuels
Sample fabrication of heat-treated U-Mo/Al dispersion fuels

Consequently, the hot-extrusion method was used for the production of the fresh U-Mo/Al and U-Mo/Al-5Si dispersion samples. A comparison between the hot-extrusion and the hot-rolling process for the production of U-Mo/Al dispersion fuel.

Figure 8. Images of cold pressing machine and hot-pressing machine used in the fabrication of Al-Si alloys

Microstructure characterization

Microstructure analysis of Al-Si alloys

The morphology of Si precipitates in Al-Si alloys has been investigated in the literature [83]- [85]. Microstructure analysis was performed to examine the presence of Si precipitates in the sintered sample.

Figure 16. Microstructure images of sintered Al-Si alloys: (a) Al, (b) Al-02wt.%Si, (c) Al- Al-05wt.%Si, and (d) Al-08wt.%Si

Measurement techniques

Density and coefficient of thermal expansion
Image analysis method
Laser flash method
Differential scanning calorimetry (DSC)

The half time means the time it takes for the sample to heat to half the maximum temperature on the backside. For the thermal diffusivity measurement of Al-Si alloys, the Netzsch LFA 447 model was used (Figure 30 (a)). In general, the DSC measurements for the specific heat capacity analysis require three separate measurements since the specific heat capacity of the samples is unknown (see Figure 32).

First, since the heat was not delivered identically to the reference and sample platforms and the crucibles for the reference and sample have different masses, the base heat flux must be measured. Two platinum (Pt) crucibles were fabricated: one for the sample and the other for the reference.

Figure 27. Images of DIL instrument (DIL 402C, Netzsch)

Thermophysical properties of Al-Si alloy

Physical information of Al-Si alloy samples
Thermal diffusivity of Al-Si alloy samples
Specific heat capacity of Al-Si alloy samples
Thermal conductivity of Al-Si alloy samples
Discussion
Summary

Using the measured data, the thermal diffusivities of sintered Al-Si were fitted to a linear function of temperature:. where α is the thermal diffusivity in mm2·s-1 and T is the temperature in K. The obtained fitting parameters, b1 and b2, are given in table 9 for each of the sample types. From the measured thermophysical data, the thermal conductivity of Al-Si alloy was calculated as a function of temperature and Si content. The differences in the thermal conductivity between Al and Al-Si alloys are predominantly attributed to the difference in the thermal diffusivity.

The measured data for pure Al in Figure 42 was used as the thermal conductivity of Al matrix. Comparison of the thermal conductivity of sintered Al-Si with the predictions of the Bruggeman model at 100 °C.

Figure 35. Density of sintered Al-Si alloys as a function of Si contents at room temperature

Thermophysical properties of fresh U-7Mo/Al dispersion fuel

Physical information of fresh U-7Mo/Al dispersion samples
Thermal diffusivity of fresh U-7Mo/Al dispersion samples
Specific heat capacity of fresh U-7Mo/Al dispersion samples
Thermal conductivity of fresh U-7Mo/Al dispersion samples
Discussion
Summary

Density variations of U-7Mo/Al and U-7Mo/Al-5Si dispersion fuels as a function of temperature. Thermal diffusivity of fabricated U-7Mo/Al and U-7Mo/Al-5Si samples as a function of U-Mo volume fraction. Specific heat capacity of fabricated U-7Mo/Al and U-7Mo/Al-5Si samples as a function of temperature.

For U-7Mo/Al-5Si, thermal conductivity increases with temperature for all U-Mo volume fractions. The trend in the thermal conductivity of U-7Mo/Al and U-7Mo/Al-5Si with temperature depends on the U-Mo volume fraction.

Table 13. Physical properties of the fresh samples in LFA measurement.

Thermophysical properties of heat-treated U-7Mo/Al dispersion fuel

Physical information of heat-treated U-7Mo/Al dispersion samples
Thermal diffusivity of the heat-treated U-7Mo/Al dispersion samples
Specific heat capacity of the heat-treated U-7Mo/Al dispersion samples
Thermal conductivity of the heat-treated U-7Mo/Al dispersion samples
Density of interaction layers
Discussion
Summary

With respect to all uranium densities, the thermal diffusivity decreases monotonically with the IL volume fraction. Thermal diffusivity of heat-treated U-7Mo/Al dispersion fuel as a function of IL volume fraction. Using the measured data, the thermal conductivity of U-Mo/Al dispersion fuel was calculated as a function of temperature, and IL volume fractions.

Thermal conductivity decreases with U-Mo volume fraction quite linearly over ranges of volume fractions. The decrease in thermal conductivity with IL volume fraction significantly exceeds that of the model prediction.

Table 19. Physical information of the heat-treated U-7Mo/Al samples for LFA.

Heat-transfer simulation using a Finite Element Method

FEM model descriptions

Geometry
Boundary conditions and loads
Calculation of effective thermal conductivity

All other sides are set adiabatically to prevent heat from escaping. This condition allows the heat to flow mainly along the z direction, which represents the direction of the plate thickness. Since the side surfaces were assumed to be adiabatic, heat escapes thoroughly through the top and bottom surfaces.

The heat escaping through the lower and upper surfaces was measured after each analysis to ensure consistency of the sum. For the example of heat generation: the heat generated from the particles and the IL flows out through the top and bottom surfaces.

Figure 67. Meshed model with 50 vol.% particle dispersed system.

FEM model verification

Comparison with the measured data of fresh samples
Comparison with the measured data of heat-treated samples

A comparison of thermal conductivity data between simulation predictions and measured data as a function of U-Mo volume fraction. FEM simulation results for the thermal conductivity of U-7Mo/Al(-xSi) dispersion fuel as a function of U-Mo volume fraction. Since the production of IL itself is impossible, the thermal conductivity of IL is left unknown.

The other characteristic point is that the efficiency of IL thermal conductivity becomes larger as the IL volume fraction increases. Comparison of thermal conductivity of U-7Mo/Al dispersion fuels as a function of IL volume fraction between the measured and the simulated results.

Figure 71. Thermal conductivity of U-7Mo/Al and U-7Mo/Al-5Si in terms of interfacial thermal conductance

Parametric study for the thermal conductivity of U-Mo/Al dispersion fuel

Effects of particle size
Effects of heat-generation from U-Mo and IL
Effects of coating
Stereography effect
Effects of porosity
Conversion of IL thickness to IL volume fraction

Therefore, the heat generation from U-Mo and IL can lead to an overall deterioration of the thermal conductivity. Thus, the thermal conductivity of three-dimensional cases is higher than that of two-dimensional cases. As the IL volume fraction cannot be directly measured, the IL thickness was alternatively measured from microstructure images.

To convert the IL thickness to the IL volume fraction, a conversion model was developed by Kim et al. From the particle size data used in the simulation, the IL volume fraction was calculated, assuming no subtraction of overlapping areas .

Figure 76. Images of simulated particles with different particle distribution data.

Semi-empirical model development

Model descriptions

Semi-empirical models for fresh U-Mo/Al dispersion fuel
Semi-empirical models for IL-formed and coated U-Mo/Al dispersion fuel

Thus, two-unit-cell modeling for the path #2 and path #3 was performed and the effective thermal conductivity was calculated by solving the heat transfer equation, respectively. After integrating the above equation, the effective thermal conductivity of unit cell is obtained so that:. where km and kp indicate the thermal conductivity of matrix and particle, hc is the thermal resistance of the interface, and d is the length of the unit cell. This unit cell took into account the thermal conductivity between particles and matrix.

Finally, the effective thermal conductivity of unit cell #2 was obtained by a series model assuming two contact cells attached to the top and bottom:. where tc is the thickness of the differential strip for the particle contact described in Figure 93. and it is expressed as: . For calculation of unit cell #1 and #2: the thermal conductivity of particles is changed to the thermal conductivity of layer structured particles.

Figure 89. A schematic of three heat transfer mechanisms simplified to each unit-cell

Model verification

Prediction of thermal conductivity of as-fabricated U-Mo/Al dispersion fuel
Prediction of thermal conductivity of IL-formed U-Mo/Al dispersion fuel
Prediction of thermal conductivity of coated U-Mo/Al dispersion fuel

Using the semi-empirical model, the thermal conductivity of IL-formed U-Mo/Al dispersion fuel was estimated. Using the semi-empirical model, the thermal conductivity of coated U-Mo/Al dispersion fuel was estimated. Accordingly, the thermal conductivity of coated U-Mo/Al dispersion fuel decreased linearly with the thickness of the coating layer.

The thermal conductivity of coated U-Mo/Al dispersion fuel was evaluated when the thermal conductivity of coating material varies. However, it showed that the thermal conductivity increased slightly as the thermal conductivity of the coating material increases.

Figure 103. Thermal conductivity prediction using the semi-empirical model as a function of temperature

Model application to the RR fuel performance code

Temperature distribution and change
Thermal conductivity evolution and IL growth during the irradiation

The modified code gave a higher rating for the overall temperature distribution due to the modified thermal conductivity. Both show that the temperature increases as combustion increases, but it can be seen that the temperatures reach their temperature saturation much faster in the case of the modified version. After the modification of the thermal conductivity model, it decreases very quickly with the irradiation time.

In the case of the RERTR-4 current history, the thermal conductivity decreased faster than that of constant power because the operating temperature was much higher than that of constant power. However, it is expected that more distinctive differences will be observed if the conversion model from IL thickness to volume fraction will be implemented. a) Power constant (b) Power variation Figure 112.

Table 25. Summary of irradiation test data for plates used in this analysis.

Conclusion

Conclusions

The model prediction verified that it gives a very consistent result as a function of U-Mo volume fraction and layer or IL thickness which successfully proved a good reproducibility and reliability. The developed semi-empirical model was implemented for the research reactor fuel performance code, PRIME. The modification in the thermal conductivity models gave some remarkable changes in the thermal conductivity and temperature, while not a characteristic change in the radiation growth due to the rapid growth in the Al matrix.

The implementation of the model in the fuel performance code has some remaining work such as verification and validation. The development of the semi-empirical model and its application will continue in the future.

Future works

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