Page 94 - Dynamics and Control of Nuclear Reactors

References 87

Exercises

7.1. Explain the shape of the curve in Fig. 7.4 in terms of the thermal utilization and
the resonance escape probability in the six-factor formula

For exercises 7.2–7.4: The transfer function of a zero-power reactor is
given by
δNsðÞ=n 0 ð s + λÞ
G 0 ¼ ¼
δρ s ðÞ β
s Λ s + λ +
Λ
7.2. Make a Bode plot of G 0 (s) and determine the low-frequency and high-
frequency break points of the dB-magnitude plot.
Use the following values for the parameters of a typical PWR:
5
1
λ ¼ 0:08s , β ¼ 0:0067, Λ ¼ 10 s.
7.3. Now consider a negative feedback effect, similar to that in a power reactor.
Assume a feedback transfer function of the form
0:03
HsðÞ ¼
s +0:25
(a) Determine the closed-loop transfer function for this case.
(b) Make a Bode plot of the closed-loop transfer function and determine
the low-frequency and high-frequency break points of the dB-magnitude
plot.
(c) Compare these with the results of part (1).

7.4. For the reactor with feedback transfer function specified in the previous exer-
cise, compute the response δn(t)/n(0) for a step change in the reactivity of
0.001. Plot the responses for t max in the range 10–100 s. You may use the
MATLAB command step(sys), with appropriate value for the step magnitude.
Is the time response stable or unstable? Explain.

7.5. Calculate the eigenvalues of matrix A, for K ¼ 8 in Eq. (7.11)

References

[1] J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, New York,
1983.
[2] T.W. Kerlin, E.M. Katz, J.G. Thakkar, J.E. Strange, Theoretical and experimental
dynamic analysis of the H.B. Robinson nuclear plant. Nucl. Technol. 30 (3) (1976)
299–316, https://doi.org/10.13182/NT76-A31645.