Civil Engineering Reference
In-Depth Information
k
eff
t
ðÞ
ðÞ
¼
Δ
1
ðÞ
k
eff
0
k
eff
t
Reactivity
ρ ðÞ¼
k
eff
0
ðÞ
ρ
(t) is measured in units of the fraction of the delayed neutrons
β
0.0064 for
U-235. Historically it was defined that
100 cents.
The behavior of the reactor power, temperatures or other changes of the steady
state conditions, e.g. variations of the system pressure or coolant velocity can be
described by a system of differential equations [
8
,
11
,
18
,
35
,
36
]. These are:
β ¼
1 dollar (1 $)
¼
- The differential equations for the instationary neutron kinetics (space- and time-
dependent prompt neutron flux distribution and concentrations of the delayed
neutrons and their precursor atoms)
- The differential equations for the space and time dependent temperature fields in
the fuel, the cladding and coolant of the reactor core (including the material
properties of the different materials, e.g. thermal conductivity, heat capacity,
etc.)
- The equations for the feedback effects affecting the effective multiplication
factor, k
eff
,
as,
e.g.
the
fuel-Doppler-temperature
coefficient
and the
moderator/coolant-temperature coefficient
- The equations for the time dependent temperatures and pressures at the inlet of
the reactor core caused by perturbations on the secondary side of the steam
exchangers.
Not in all cases all parts of these coupled systems of differential equations must
be solved together. In case of relatively fast variations of the physical core charac-
teristics (time range of seconds or less), e.g. the core inlet coolant temperature can
be considered to remain constant, as the steam generators parameters change only
slowly.
In many cases the instationary neutron kinetics can be approximated by a system
of coupled ordinary differential equations with initial conditions. In this case the
prompt and delayed neutrons are represented by one ordinary differential equation
and six differential equations for the precursor atoms which emit the delayed
neutrons by radioactive decay. This leads to seven ordinary differential equations.
The solution of these systems of coupled ordinary differential equations shows that
three ranges of k
eff
are of importance:
For supercriticality k
eff
>
1 two ranges of k
eff
must be distinguished.
- The range between k
eff
¼
in which the multiplying chain
reaction is determined by the
delayed neutrons
. In this range of keff the
relatively slowly originating delayed neutrons (from the radioactive decay of
precursor atoms (see Sect.
2.1
)) allow the control of the nuclear reactor in a time
range of seconds to minutes. Control procedures by moving control rods or
changes of the concentration of boric acid in the coolant water are performed in
this range as displayed by Fig.
2.11
.
- The range of k
eff
>
1 and k
eff
<
1+
β
in which the multiplying chain reaction is determined
by the
prompt neutrons
originating promptly from the fission process
1+
β
