Page 131 - Dynamics and Control of Nuclear Reactors

126 CHAPTER 10 Reactor thermal-hydraulics

Exercises

10.1. Reformulate Mann’s model for an assumption that the average coolant tem-
perature is the average of the temperature in each node rather than the tem-
perature in the first node. How would this affect simulation results?
10.2. Compare the computational differences for modeling a boiling channel with
the moving boundary approach and a model with fixed boundaries and updat-
ing of coefficients during a transient.
10.3. Consider a moving boundary model for a once through steam generator with
superheat. How many boundaries are needed for a dynamic model? How
would the boundaries move (up or down) following an increase in primary
side fluid temperature?
10.4. Consider a PWR with dissolved boron in the coolant. Describe differences in
the reactor power response to an increase in inlet coolant temperature for a
condition of low boron concentration and a condition of high boron
concentration.
10.5. A reactor with a negative fuel temperature coefficient of reactivity and a pos-
itive coolant temperature coefficient of reactivity can be stable even if the
magnitude of the positive coefficient is larger than the magnitude of the neg-
ative coefficient. Explain how this is possible and why it might be counter-
intuitive.
10.6. A change in boiling rate caused by a disturbance in a Boiling Water Reactor
causes changes in coolant density as it moves along the channel. BWRs have
negative coolant density coefficients. This effect can be destabilizing.
a. Explain how this happens.
b. Would increasing the coolant flow rate make the system more stable or
less stable? Explain.

References
[1] T.W. Kerlin, Dynamic analysis and control of pressurized water reactors, in: C.T. Leondes
(Ed.), Control and Dynamic Systems, vol. 14, Academic Press, 1978.
[2] S.J. Ball, Approximate models for distributed parameter heat transfer systems, ISA Trans.
3 (1) (1964) 38–47.
[3] M.R.A. Ali, Lumped-Parameter, State Variable Dynamic Model for U-Tube Recirculation
Type Steam Generators, PhD dissertation, The University of Tennessee, 1976.
[4] A. Ray, H.F. Bowman, A nonlinear dynamic model for a once-through subcritical steam
generator, J. Dyn. Syst. Meas. Control 98 (3) (1976) 332–339. Series G.
[5] T.W. Kerlin, E.M. Katz, J. Freels, J.G. Thakkar, Dynamic modeling of nuclear steam gen-
erators, in: Proceedings of the Second International Conference sponsored by the British
Nuclear Energy Society, Bournemouth, England, 1979. October.