Page 168 - Dynamics and Control of Nuclear Reactors

Exercises 165

Exercises

12.1. Verify Eqs. (12.5), (12.7) and (12.8).
12.2. Consider a PWR with a U-tube steam generator with the following properties:
o
α f ¼ 1:3∗10 5 ð ρ= FÞ
o
α c ¼ 2:0∗10 4 ð ρ= FÞ
2
A f ¼ 42;460 ft
2
A SG ¼133,290 (ft ) in three steam generators
2

U f ¼ 200 BTU=hrft Þ
2 o
U SG ¼ 1000 BTU=hr ft F
ð
W ¼ 28;200 lbm=sÞ
o
C ¼ 1:0 BTU= lbm Fðð Þ
a. Prepare a steady state program for the reactor prescribed above for no
change in reactivity.
b. Estimate δθavg for the reactor prescribed above for δT S ¼0 and a reactiv-
ity change of one cent.
c. Estimate δT s for the reactor prescribed above for δθavg¼0 and a reactivity
change of one cent.
12.3. The steady state program for a PWR with U-tube steam generators is shown in
Fig. 12.9
a. Sketch a steady state program for a PWR with a U-tube steam generator
and constant steam temperature.
b. Explain why the variables other than steam temperature are as you show in
your sketch.
c. What are the relative advantages and disadvantages of the steady state pro-
gram of Fig. 12.9 and your constant steam temperature program?
12.4. Section 12.6 includes a diagram that uses arrows to show a sequence of events
following an initial disturbance. Create a similar diagram for a PWR with a
U-tube steam generator. Include control actions and show all important system
variables. Note that some actions influence more than one downstream action
and some actions depend on more than one upstream action. Show these
actions in your diagram.

12.5. Repeat Exercise 12.3 for a PWR with a once-through steam generator.
12.6. The frequency response for a PWR appear in Figs. 12.15 and 12.16.The
plots demonstrate three distinct regions (0 to 0.1rad/s, 0.1 to 2rad/s and above