5.2.1 UC

From a heat transfer point of view, there is an interest on carbides of uranium as nuclear fuels due to their high thermal conductivities and high melting points. Carbides of uranium usable for nuclear fuels are Uranium Carbide (UC) and Uranium Dicarbide (UC2). For instance, UC has been proposed as the fuel of choice for a SCWR concept in Russia (Pioro and Duffey, 2007). Uranium sesquicarbide (U2C3) is another carbide of uranium; however, it cannot be manufactured through casting or compaction of a powder. However, UC2 may transform to U2C3 at high temperatures and under stress (Frost, 1963).

UC, which has a Faced-Centered Cubic (FCC) crystal structure similar to those of UN and NaCl, has a high melting point approximately 2507°C and a high thermal conductivity, above 19 W/m K at all temperatures up to the melting point. UC has a density of 13630 kg/ m3, which is lower than that of UN but higher than those of UO2. It should be noted that the density of hypo-stoichiometric UC is slightly higher than that of stoichiometric UC, which is listed in Table 2. Coninck et al. (1975) reported densities between 13730 and 13820 kg/m3 at 25°C for hypo-stoichiometric UC. Moreover, UC has a higher uranium atom density compared to UO2 but lower than that of UN. The uranium atom densities of UC and UN are 1.34 and 1.4 times that of UO2, respectively.

For hypo-stoichiometric UC, the thermal diffusivity a, in m2/s, and thermal conductivity k, in W/m K, correlations are valid for a temperature range of 570 and 2000°C. In Eqs. (5) and (6), T is in degrees Kelvin (Coninck et al., 1975). For stoichiometric UC, Coninck et al. (1975) provided two correlations, shown as Eqs. (7) and (8), which can be used to determine the mean values of the thermal diffusivity and thermal conductivity of stoichiometric UC for a temperature range between 850 and 2250°C, in m2/s and W/m K, respectively.

a = 10“4 • ^5.75 • 10_2+1.25 • 10_6(T-273.15)] (5)

k = 100 • [2.04 • 10_1+2.836 • 10’8(T — 843.15)2] (6)

a = 10“4 • [5.7 • 10_2+1.82 • 10_12(T-1123.15)3] (7)

k = 100 ^1.95 • 10_1+3.57 • 10_8(T-1123.15)2 ] (8)

In addition to Eqs. (6) and (8), Kirillov et al. (2007) have recommended another correlation, shown as Eqs. (9) and (10), for the calculation of the thermal conductivity of UC in W/m K. In the current study, Eq. (21) have been used to determine the thermal conductivity of UC for the calculation of the UC fuel centerline temperature at SCWR conditions, because this equation provides the lowest thermal conductivity values for a wide temperature range, leading to a conservative calculation of the fuel centerline temperature. In Eqs. (9) and (10), T is in degrees Kelvin.

k = 21.7-3.04 • 10-3(T-273.15) + 3.61 • 10-6(T -273.15)2 , 323<T <973 K (9)

k = 20.2 + 1.48×10"3 (T-273.15), 973<T<2573 K (10)

Frost (1963) developed a correlation shown as Eq. (11), which can be used to determine the diametric increase of UC fuel as a function of time-averaged fuel centerline temperature. According to Eq. (11), UC fuel undergoes significant swelling for temperatures above 1000°C. In Eq. (11), Rd and T are percent diametric increase per atom % burn-up and time — averaged fuel centerline temperature in K, respectively. In addition, as shown in Fig. 10, Harrison (1969) provided the volumetric swelling of UC as a function of burn-up for various temperatures.

Rd =0.6 + 0.77 -1

D I 5000