9.8.6. Appendix 9.6: Metallic Fuel Thermal Conductivity Model

The metallic fuel thermal conductivity equation given in Ref. [9‑32] for the unirradiated U-Pu-Zr fuel is utilized. It is given as follows:

(9.8-36)\[\begin{split}k_{0s} = a + bT + cT^{2} \\ a = 17.5\left( \frac{1 - 2.23w_{Zr}}{1 + 1.61w_{Zr}} - 2.62w_{Pu} \right) \\ b = 1.54 \times 10^{- 2}\left( \frac{1 + 0.061w_{Zr}}{1 + 1.61W_{Zr}} + 0.9w_{Pu} \right) \\ c = 9.38 \times 10^{- 6}\left( 1 - 2.7w_{Pu} \right) \\\end{split}\]

where \(k_{0s}\) is unirradiated solid metallic fuel thermal conductivity (W/m-K), T is temperature (K), a,b, and c are constants, \(w_{Pu}\), \(w_{Zr}\) are the Plutonium and Zirconium weight fractions in fuel alloy

Irradiated Metal Fuel Thermal conductivity

Irradiated metallic fuel thermal conductivity is developed in this study in parallel with development and validation of MFUEL metallic fuel performance models of SAS.

(9.8-37)\[k_{irr} = X_{Na}X_{p}k_{0}\]

where \(k_{irr}\) effective thermal conductivity of irradiated fuel ( W/m-K), \(X_{Na}\) is the thermal conductivity enhancement factor due to sodium infiltration into the fuel porosity, only applicable in outer \(\left( (\alpha + \zeta) + \delta \right)\) phase region Ref.[9‑16], \(X_{p}\) is the thermal conductivity correction factor due to fission gas porosity, \(P_{tot} = P_{g} + P_{Na}\), \(P_{tot},P_{g},P_{Na}\) are the total, gas filled, and sodium filled porosity.

(9.8-38)\[X_{p} = \left( 1 - P_{g} \right)^{1.5}\]

(9.8-39)\[X_{Na} = 1 - 3\frac{1 - \left( \frac{k_{Na}}{0s} \right)}{1.163 + 1.837\left( \frac{ k_{Na}}{k_{0s}} \right)}\frac{P_{Na}}{1 - P_{g}}\]

where \(k_{Na}\) is the sodium thermal conductivity (W/m-K)