Page 60 - Dynamics and Control of Nuclear Reactors

Further reading 51

Exercises

4.1. Show the state variable model for the perturbation form of the point kinetics
equations (six delayed neutron groups) for a step change in reactivity and for a
variable reactivity input.
4.2. What would be the response at one second after a step change in reactivity of
10 cents if there were no delayed neutrons? Use data for a U-235 reactor with a
generation time of 10 5 s.
4.3. Delayed neutron precursors are a reservoir of future neutrons. How does this
relate to the shutdown of a reactor?
4.4. Estimate the magnitude of the response of a reactor to a sinusoidal reactivity
with an amplitude of 10 cents and a frequency of 10 rad per second. Why is
your answer not exact?
4.5. Show that the transfer function of a circulating fuel reduces to the transfer
derived in Chapter 3 when the in-core residence time approaches infinity.
4.6. Why is a period meter useful for a control room display? Why does a reactor
operating at power not fail to have a stable period?

4.7. A U-235 fueled zero power reactor with a generation time of 10 5 experiences
a stable period of ten minutes. What reactivity caused this transient?

References
[1] J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, New York,
1976.

Further reading
[2] H. Klee, Simulation of Dynamic Systems with MATLAB and Simulink, CRC Press, Boca
Raton, FL, 2007.
[3] MATLAB and Simulink User Guides, The MathWorks, Inc., Natick, MA.