Question 9.13: A 2,400 MW(t) plutonium sodium-cooled fast reactor has the f......

The reactor undergoes a loss of flow transient with { W}(t)={ W}(0)/(1+t/t_{o}) where t_{o}=5.0\,\mathrm{s}\,. Employ appropriate software to Eqs. (8.36) through (9.40) to analyze the transient: Make plots of the reactor power, fuel and coolant outlet temperatures for 0 < t < 20 s ( Hint, note that \tilde τ cannot be approximated by τ in this problem.)

β1 := 0.00021          \operatorname{c1}:=\mathbb{\beta 1}\cdot {\frac{\operatorname{P0}}{(\lambda1\cdot\Lambda)}}     \mathrm{c}2:=\beta 2.{\frac{\mathrm{P}0}{(\lambda2\cdot\Lambda)}}

β2 := 0.00142            \operatorname{c3}:=\mathbb{\beta 3}\cdot {\frac{\operatorname{P0}}{(\lambda3\cdot\Lambda)}}    \mathrm{c}4:=\beta 4.{\frac{\mathrm{P}0}{(\lambda4\cdot\Lambda)}}

β3 := 0.00128             \operatorname{c3}:=\mathbb{\beta 3}\cdot {\frac{\operatorname{P0}}{(\lambda3\cdot\Lambda)}}    \mathrm{c}4:=\beta 4.{\frac{\mathrm{P}0}{(\lambda4\cdot\Lambda)}}

β5 := 0.0007            \operatorname{c5}:=\mathbb{\beta 5}\cdot {\frac{\operatorname{P0}}{(\lambda5\cdot\Lambda)}}    \mathrm{c}6:=\beta 6.{\frac{\mathrm{P}0}{(\lambda6\cdot\Lambda)}}

β6 := 0.00027

Sample calculations shown for $0.10 below using the stiff differential equations solver Radau (Mathcad) to obtain the vector Y.

\mathrm{Rf}:={\frac{\tau}{\mathrm{MfCf}}}=0.296         \alpha_{\mathrm f}:=-1.8\cdot10^{-5}

\mathrm{Tf0}:=\mathrm{Rf.P0}+\mathrm{Ti}=1.071\times10^{3}     \alpha_{\mathrm c}:=0.45\cdot 10^{-5}

C = 0.096

Y := Radau (y , 0 , 100 , 10000 , DD)

n := 0 .. 10000

Below is an algebraic equation to obtain the coolant outlet temperature using the fuel temperature and the inlet temperature.