Development and Verification of Nuclear Calculation Methods for ...

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Se A Xe +0 a.Xe«' *Xe-*I +0 a,Xe» "
To t V W V X ini °- VfT -Oxe+Vxetit
where the absorption term in equation (5.1) has been neglected, n is the
time- and space-dependent concentration after a time step of the length t;
B° the concentration at the beginning of the time step. X is the radioactive
decay constant, and v the fission yield, o is the microscopic absorption
cross section, and o a is supposed to include summation over all energy
groups. Similarly v£f • includes summation over all fissile nuclei and
groups. Equations (5.3) and (5.4) were deduced with the assumption that
q> and £f are constant during the time step. The first term in equation (5.4)
is the asymptotic or equilibrium value which will be obtained for t - "• .
Introduction of these equations in the two-dimensional over-all calculation
will permit investigations of xenon-induced spatial power oscillations.
The physical reason for their existence will be illustrated by a practical
example.
Imagine that the flux in a region of the reactor is suddenly decreased
by, for example, insertion of a control rod. This will leave the production
of Xe nearly unchanged since it is mostly produced by p -decay of I ,
135
whereas the absorption is lowered, thereby increasing the Xe concentration.
The increased poison will again decrease the flux and so on. This development
will continue, and when the I
135
concentration has decreased so
much that the production of Xe
135
is equal to the amount disappearing by
absorption and 8-decay, the whole situation will change. Now a decrease
in Xe
135
concentration will follow and increase the flux and so on. If a
constant power level is maintained, different regions will contribute out
of phase to the over-all oscillation.
Major feedback mechanisms associated with xenon oscillations are
spatial effects due to local Doppler effect, local moderator temperature
and local xenon concentration. For BWR's the usually strong negative void
reactivity effect will damp such oscillations. It seems therefore that the
xenon-induced spatial power oscillations are more expressed for especially
large FWR's, of which a lot of investigations (refs. 24 and 25) give
evidence.