Question 17.6: If the average values for αM(T), αF(T), and αS(T) (where “s”......
If the average values for α_M(T), α_F(T), and α_S(T) (where “s” refers to the structure) are −0.5 × 10^{–5} per °C, −3.0 × 10^{−5} per °C, and −0.1 × 10^{−5} per °C, for a reactor that is just starting up, what is the total temperature coefficient for the core? Assume the core is 25% fuel, 25% structure, and 50% coolant.
Part 2: Suppose that the temperature of the coolant increases from 310°C to 340°C during a brief transient, and the fuel temperature increases from 1000°C to 1200°C. How much negative reactivity is introduced into the core by this temperature increase?
We need to apply the relationship Δρ = α_TΔT = {α_M(T) + α_F(T) + α_S(T)} ΔT to find the answer to this question. Since the core is 25% fuel, 25% structure, and 50% coolant, the volume-average temperature coefficient is
α_T ={ 0.50 α_M(T) + 0.25 α_F(T) + 0.25 α_S(T)} = { −0.25 × 10^{–5} − 0.75 × 10^{–5} − 0.025 × 10^{–5}} = − 1.025 × 10^{–5} per ° C.
Part 2: However, in a real core, the fuel temperature and the coolant/structure temperature change at different rates. The structure temperature (which affects the neutron leakage rate) changes at about the same rate as the coolant temperature, but the fuel temperature changes much more quickly. In this case, the overall reactivity change will be Δρ = α_MΔT_MV_M + α_FΔT_FV_F + α_SΔT_SV_S = −0.5 × 10^{–5} × 30 × 0.50 − 3.0 × 10^{–5} × 200 × 0.25 − 0.1 × 10^{–5} × 30 × 0.25 = (−7.5 – 150 – 0.75) × 10^{–5} = −158.25 × 10^{–5} = −158.25 pcm.