Page 55 - Dynamics and Control of Nuclear Reactors

46 CHAPTER 4 Solutions of the point reactor kinetics equations

Consequently, this value is recommended for one-group calculations for a U-235
fueled reactor. However, since the frequency response is based on a small perturba-
tion model, good agreement is expected only for small perturbations.

4.7 Fluid fuel reactor response
The equations for a fluid fuel reactor, described in Section 3.9, are used for simula-
tions in this section. No reactivity feedback effects are considered in this simulation.
Fluid fuel reactor responses have a unique dependence on the flow rate of the
liquid fuel. The contribution of delayed neutrons depends on the residence time
of the fuel in the reactor. The circulating fuel causes a change in the effective delayed
neutron fraction by an amount equal to ρ 0 , which is the steady state reactivity in the
system. The effective delayed neutron fraction is equal to (β – ρ 0 ). Therefore, a dollar
of reactivity is equal to (β – ρ 0 ), rather than the value β used in solid fuel reactors. See
Section 3.9 for neutronic equations of a fluid fuel reactor.
The most extreme case of flow reduction in a fluid-fuel reactor is a flow stoppage
in which case the in-core residence time goes to infinity. Fig. 4.12 shows the response
of a fluid-fuel reactor following a flow stoppage.
Fig. 4.13 shows the responses to a step increase in reactivity for two different loop
transit times. It should be noted that in an operating fluid-fuel power reactor, reduced
flow results in increased fluid temperature, and an increased feedback effect causing
the power to level off.
Clearly, the reduction of the delayed neutron contribution due to out-of-core pre-
cursor decays makes a fluid-fuel-reactor more responsive than an equivalently fueled
stationary-fuel reactor.

9
8
7
6
P/P(0) 5 4

3
2

1
0
0 1 2 3 4 5 6 7 8 9 10
Time (s)
FIG. 4.12
Fractional power response of a U-235 fueled fluid fuel reactor to flow stoppage at t ¼ 2s.