Page 53 - Dynamics and Control of Nuclear Reactors

44 CHAPTER 4 Solutions of the point reactor kinetics equations

100
1E-5
1E-6
1E-7
10

%power/cent 0.1 1

0.01

10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5
(A) Frequency (rad/s)
0
1E-5
1E-6
1E-7
−20
Phase (deg) −40

−60

−80

10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5
(B) Frequency (rad/s)
FIG. 4.10
(A) Frequency response magnitudes for different generation times. (B) Frequency response
phase angles for different generation times.

4. The phase shift is 90 degrees for low frequencies and for high frequencies.
This means that the power response lags behind a sinusoidal reactivity
perturbation by one fourth of a cycle. In the mid-range plateau, the phase
shift approaches zero degrees, indicating that the power variations “keep up”
with reactivity perturbations in this frequency range.

See App. E for details of frequency response analysis of linear constant coefficient
systems. It should be noted that eliminating the large amplitude at low frequencies is
a design objective for power reactors. This is accomplished by design to achieve
appropriate reactivity feedback from quantities such as moderator temperature, fuel
temperature or fluid pressure, and design of control systems. These issues are
addressed in later chapters.