Question 9.10: Apply appropriate software to Eqs. (9.37) through (9.42) for......
Apply appropriate software to Eqs. (9.37) through (9.42) for a uranium fueled reactor. Use the following parameters, which are typical of a large pressurized water reactor: Λ = 50 × 10^{-6} s , α = -4.2 × 10^{-5} /°C M_ƒc_ƒ = 32 MW/°C , τ = 4.5 s , With an initial steady state power of 10 MW, make a plot of the power for
a. step reactivity increase of 10 cents,
b. a step reactivity increase of 20 cents
c. a step reactivity decrease of. 10 cents,
d. a step reactivity decrease of 20 cents.
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 $0.10 below using the stiff differential equations solver Radau (Mathcad) to obtain the vector Y.
\mathrm{Rf}:={\frac{\tau}{\mathrm{MfCf}}}=0.141 dollars := 0.1
Rf.WCP = 8.438 α1 = -4.2 × 10^{-5}
Tf0 := Rf.P0 + Ti = 551.406
\mathrm y := \begin{pmatrix}P0 \\ c1 \\ c2 \\ c3 \\ c4 \\ c5 \\c6 \\ \mathrm {Tf0} \end{pmatrix}
n := 0 .. 1000
