Question 9.4: At full power 1000 MW(t) sodium-cooled fast reactor has cool......
At full power 1000 MW(t) sodium-cooled fast reactor has coolant inlet and outlet temperatures of 350 and 500 °C, and an average fuel temperature of 1,150 °C. The fuel and coolant temperature coefficients are α_ƒ = -1.8 × 10^{-5} /°C and α_c = +0.45 × 10^{-5} /°C
a. Estimate the core thermal resistance and the mass flow rate, taking for sodium c_p = 1,250 J/kg /°C.
b. Estimate the temperature and power defects, assuming a “cold” temperature of 180 °C.
Part a: Take the average coolant temperature from Eq. (8.39) as
\overline T_{c}=1/2(T_{i}+{\bar{T}}_{o})=1/2 (350+500)=425~^{\circ}C
From Eq. (8.32) the thermal resistance is
R_{f}=\frac{\overline{{{T}}}_{f}-\overline{{{T}}}_{c}}{P}=\frac{1150-425}{1000_{c}}=0.725\ ^{\circ}C/\mathrm{MW}
Form Eq. (8.37) the mass flow rate is
W=\frac{P}{c_{p}(\overline{{{T}}}_{o}-T_{i})}=\frac{1000\cdot10^{6}}{1250(500-350)}=5,333\,\mathrm{kg/s}
Part b: With constant temperature coefficients, for the temperature defect Eq. (9.34) simplifies to
D_{T}=\alpha_{T}(T_{i}-T_{r})=(\alpha_{f}+\alpha_{c})(T_{i}-T_{r})
=(-1.8\cdot10^{-5}+0.45\cdot10^{-5})(350-180)=-9.45\cdot10^{-6}
For the power defect Eqs. (9.33) and (9.35) simplify to
D_{P}=\left[R_{f}\alpha_{f}+(2W c_{p})^{-1}(\alpha_{f}+\alpha_{c})\right]P
=\!\left(-1.31\cdot10^{-5}-0.101\cdot10^{-5}\right)\!1000=-1.4\cdot10^{-2}