Question 9.11: Using the data and initial conditions from problem [10] appl......
Using the data and initial conditions from problem [10] apply appropriate software to
a. Determine what ramp rate of reactivity insertion will cause a power spike with a peak power that exceeds 100 MW(t)
b. Determine what ramp rate of reactivity insertion will cause a power spike with a peak that exceeds 1,000 MW(t)
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
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)}}
β4 := 0.00257
β5 := 0.00075 \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 $0.40 (5000 MW) below using the stiff differential equations solver Radau (Mathcad) to obtain the vector Y.
\mathrm{Rf}:={\frac{\tau}{\mathrm{MfCf}}}=0.141 α1 = -4.2 × 10^{-5}
Rf.WCp = 8.438 dollars := 0.40
\mathrm y := \begin{pmatrix}P0 \\ c1 \\ c2 \\ c3 \\ c4 \\ c5 \\c6 \\ \mathrm {Tf0} \end{pmatrix}
n := 0 .. 10000
Y := Radau(y , 0 50 10000 , DD)
YY := 10000
YYY := 5000
To obtain a power spike of 5,000 MW, a reactivity of $0.40 is used while to obtain a power spike of 10,000 MW, a reactivity of $0.625 is used.
