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Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

For purposes of instrument and control-rod design
it is necessary to know the effect of changes in

rod

normally obtained empirically; but lacking a precise graph

The power is shown to be approximately proportional
to the excess reactivity; the latter in turn is given by an

S-shaped curve which is similar to a displaced sine curve.

The variation with position of rod of the power is shown in

the attached figure, adjusted to fit a total value of

The arguments loading to this graph are given

The effect of a cadmium or boron control rod is to depress the neutron flux,
usually to zero at the boundary. If such a rod were inserted axially in a

circular cylinder of length much greater than the diameter, the neutron flux

would be represented, in a bare reactor, by the function

(This is to be contrasted with the undisturbed flux

The critical condition for such a system would be written

(Undisturbed, the k is given by the same relation without the a)

In a finite cylindrical bare pile, there is an axial sinusoidal variation

effective k of a finite cylinder with a

rod partially inserted is the average of

the undisturbed value k

v and the disturbed
value k

d, with weighting factors
portional

namely the respective areas under the flux

this criterion is

If r1 is the excess reactivity value of the
rod and the "rod-in" position corresponds to

distance the rod is pulled up, Z, is given by

In order to translate this into a power graph it is necessary only to note
that if the pile is just critical at zero power with the rod in and the

solution at the temperature of the cooling water, for any other steady state

at power P the excess reactivity due to the rod must just balance the drop due

Calculations on heat removal and experimental data from
an essentially linear rise in allowed power with temperature. Thus

P/P

1 = T/T1
where (P

1,T1) is the maximum operating point, and (P,T) is any other.

If the temperature effect on reactivity is written

- P
l= 10 kw - α = 240 μre/°C
- r
l= 1.7 x 104μre - T
1= 70°C

Thus