Page 51 - Dynamics and Control of Nuclear Reactors

42 CHAPTER 4 Solutions of the point reactor kinetics equations

1.008

1.006
1.004

1.002
P/P 0
1

0.998

0.996
0.994
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time (s)
FIG. 4.6
Fractional power response to a sinusoidal reactivity perturbation of frequency 100 rad/s.

0.02

0.015

0.01
Δ P/P(0) 0.005

0

−0.005
−0.01
0 20 40 60 80 100 120 140 160 180 200
Time (s)
FIG. 4.7
Fractional power response to a sinusoidal reactivity perturbation of frequency 0.1 rad/s.

This figure shows several important features:
1. The amplitude of the power response is high at low frequencies (and approaches
infinity as the frequency decreases). This simply means that inserting reactivity
and leaving it inserted for a long time creates a large power response. This is
consistent with behavior observed for a step change in reactivity. Note that
this low frequency response is independent of generation time.
2. There is a mid-frequency plateau where power changes by 1% / cent of reactivity.
The width of the plateau depends on the generation time, but the magnitude