Civil Engineering Reference
In-Depth Information
2.10.1 The Fuel-Doppler-Temperature Coefficient
The fuel-Doppler-temperature coefficient is due to the fact that the microscopic
resonance cross sections depend on the temperature of the fuel and the relative
velocities, respectively, of neutrons and atomic nuclei [
8
,
35
].
The resonance cross sections for U-238, U-235, Pu-239, etc. show very pro-
nounced peaks at certain neutron kinetic energies (Figs.
2.3
and
2.4
). An increase in
fuel temperature broadens this shape of the resonance curve and lowers its peak
which, in turn, results in a change in the fine structure of the neutron energy
spectrum. The neutron reaction rates for capture and fission are changed as a
consequence. Above all, the resonance absorption for U-238 increases as a result
of rising fuel temperatures, while the effect of a temperature change in the reso-
nance cross sections of the fissile materials, U-235 and Pu-239, is so small that it
can generally be neglected if the fuel enrichment is not extremely high. For these
reasons, temperature increases in the fuel result in a negative temperature feedback
effect (Doppler effect) brought about by the increase in neutron absorption in
U-238. The Doppler effect is somewhat less pronounced at very high fuel temper-
atures because adjacent resonances will overlap more and more. The resonance
structure then is no longer as pronounced as at low temperatures, which leads to a
reduction of the negative Doppler effect.
As a consequence of the negative fuel-Doppler-temperature coefficient the
criticality or effective multiplication factor, k
eff
, decreases at higher fuel tempera-
tures. Typical values for the fuel-Doppler-temperature coefficient are
10
5
:
-for PWRs
2
5
change in k
eff
per degree of fuel temperature increase
10
5
-for BWRs
2
change in k
eff
per degree of fuel temperature increase
As the fuel-Doppler-temperature coefficient is coupled to the fuel temperature it
is acting practically instantaneously.
2.10.2 The Moderator/Coolant-Temperature Coefficient
of LWRs
The main contribution to the coefficients of moderator or coolant temperatures stem
from changes in the densities of the moderator or coolant and from resultant shifts
in the neutron energy spectrum. Temperature rises decrease the density of the
coolant and accordingly reduce the moderation of neutrons. The neutron spectrum
is shifted towards higher energies. As a result of the lower moderator density and
the correspondingly higher transparency to neutrons of the core it is also possible
that appreciably more neutrons will escape from the reactor core and neutron losses
due to leakage rate will increase [
8
,
34
,
36
].
