atw - International Journal for Nuclear Power | 2.2024

72
Research and Innovation
fuel (UO₂) at the beginning of the fuel length. This is due
to the higher enrichment of the fuel which eventually
burns out at the end of the fuel length. The packing
fractions and enrichment of the FCM fuel kernel result
in a significant difference in keff and burnup at the
beginning and end of the fuel length. The keff and
burnup rate versus the Effective Full Power Day (EFPD)
for one complete fuel length is depicted in Fig. 8 and
Figure 9, respectively. At the beginning of the fuel
length, the reactivity of UO₂, UCO, and UN has been
found to be 23501pcm, 28931pcm, and 29147pcm,
respectively with the boron concentration of 140ppm.
The UN has high reactivity due to the advantage of the
density. The effective multiplication factor of UCO and
UN FCM fuel is relatively 8.5 % higher than the UO₂ at
the beginning of fuel length. However, the effective
multiplication factor decreased monotonically for FCMbased
fuel after 650 EFFDs with 140ppm soluble boron
concentration. Contrary to this the average burn of UO₂,
UCO, and UN FCM fuels remain similar. similar to the
effective multiplication factor the burn up of UCO and
UN-based FCM decreases monotonically after 650
EFPDs of the SMART reactor, resulting in a significant
diminution of fuel cycle length (Fig. 6). It can also be
seen from Figure 10 that the reactivity of FCM fuels
decreases drastically with the burnup.
(1)
(2)
(3)
Where T is the fuel temperature and ρ is reactivity,
which is a function of the criticality of the system and
can be expressed as:
(4)
Using Eq (4) in Eq (3) and differentiating with respect
to temperature gives the Eq (5)
(5)
Similarly, MTC can be expressed as follows.
(6)
(7)
Fig. 10.
The burnup vs the effective multiplication factor
with 140 ppm boron concertation
3.3 Fuel temperature coefficient and
Moderator temperature coefficient
The reactivity coefficients have a significant effect on
the effective multiplication factor, as they alter the
interaction probability of neutrons with fissile and
fertile fuel. These reactivity coefficients are the Fuel
Temperature Coefficient (FTC) and Moderator Temperature
Coefficient (MTC). The FTC is defined as the
change in the reactivity with the change in the fuel
temperature, while the MTC refers to the change in
reactivity due to the change in moderator temperature.
FTC and MTC can be expressed mathematically shown
in Eq1 and Eq 2 [24] whereas the FTC in terms of reactivity
is depicted in Eq 3.
It has been noticed that the FTC of FCM fuels is
less negative compared to the reference fuel (UO₂). The
FTC has been evaluated from 300K to 1200K with the
degree change of 100K. The 300K is considered as the
reference temperature. FTC became less negative with
the increase in fuel temperature. The least value of FTC
has been found -1.82881 pcm/K with the 400K increase
in fuel temperature from the reference temperature
for UO₂. The FTC for the reference fuel remains in
the range of -1.82881 pcm/K to 1.50749 pcm/K for the
increase in fuel temperature from 100K to 900K from
the refence fuel temperature. On the other hand, the
FTC for the of UN and UCO has been found to be less
negative compared to the standard fuel. However, the
FTC for the FCM fuel also increases with the increase
in fuel temperature. The FTC for UN and UCO remained
in the range of -1.39908 pcm/K to -0.99062 pcm/K and
-1.51367 pcm/K to -1.05743 pcm/K respectively with the
increase in fuel temperature from 100K to 9000K from
the reference temperature.
When the coolant temperature increases the density
decreases due to thermal expansion of coolant. The
resonance escape probability decreases, which causes
Ausgabe 2 › März