Page 33 - Dynamics and Control of Nuclear Reactors

24 CHAPTER 3 The point reactor kinetics equations

Dollar, $ (¼ ρ/β)
Cent, ¢ (¼ 0.01$)

Note that one dollar ($) of reactivity is numerically equal to β, the magnitude of the
total delayed neutron fraction. All of these measures are suitable, but a potential
cause for confusion. Reactivity, ρ, and dollar ($) or cent (¢), is used throughout
this book.

3.4 Alternate choices for the neutronic variable
In the above derivations of the point kinetics equations, the neutron density, n, was
chosen as the neutronic variable. Here, we show that the equations may be written
with neutron flux, reactor power or relative reactor power.
First use the relation, Φ¼nv, to replace the neutron density, n, with neutron flux,
Φ. The result is
6
dΦ ð ρ βÞ X
¼ Φ + λ i C 0 i (3.18)
dt Λ
i¼1
dC 0 β
i ¼ i Φ λ i C 0 (3.19)
dt Λ i
where
0
C i ¼ vC i
Note that the precursor terms in this formulation are no longer actual precursor con-
centrations, but are the non-physical quantity, (v C i ). But since the solution variable
of interest is the neutron flux, the physical interpretation of the precursor variable is
inconsequential.
Now reformulate again with power as the variable of interest. Multiply
Eqs. (3.18) and (3.19) by (F Σ f V) where F is the conversion from fission rate to
power ( 3.2 10 11 watt seconds per fission) and V is the reactor volume to obtain
power, P¼F Σ f Φ V. The result is
6
dP ð ρ βÞ X
¼ P + λ i C 00 i (3.20)
dt Λ
i¼1
dC 00 β
i ¼ i P λ i C 00 (3.21)
dt Λ i
where

00
C i ¼ FΣ f VC i
Finally reformulate with relative power, P/P(0), as the variable of interest. Here P(0)
is a nominal power; for example, the 100% power level. The result is