ORNL-2106 - the Molten Salt Energy Technologies Web Site

1
ANP PROJECT PROGRESS REPORT
strengths in each region were calculated* from the
output of the multigroup calculations. The
spectrum of the capture gamma rays in beryllium
is divided into two energy groups in ref. 3, and
these groups were combined into one group with
a.n average energy of 6 Mev, for this calculation.
The buildup factor for beryllium at 6 Mev was
used.
In calculating the gamma-ray sources in the
first lnconel shell around the beryllium reflector,
it was assumed that 3% of all neutrons born in
the core escape from the reflector as thermal
neutrons.6 It was further assumed that these
neutrons escape with an isotropic angular distri-
bution from the surface of the reflector. A source
strength, S, in thermal-neutrons/cm2*sec escaping
from the surface of the reflector, was calculated
by using a'reflector radius of 55.04 cm (ref. 1).
Because of the large radii of curvature in this
n
+(
region of the reactor, the neutron absorption rates
were calculated on the basis of slab geometry.
Between the lnconel shell and the reflector
there is a kin. layer of sodium coo1ant.l If it is
assumed that a neutron leaving the surface source
will be absorbed only on a first-flight absorption
collision, the probability of absorption in the
sodium, P,(Na), is derived to be
where
t = thickness of sodium layer (in cm),
Za(Na) = macroscopic thermal-neutron absorption
cross section for sodium
= 5.6 x 10-3cm-1.
It was assumed that the angular distribution of
the neutrons reaching the lnconel was still
isotropic, and a similar expression was obtained
for the Inconel, for which the macroscopic thermal-
32
neutron absorption cross section is 0.18 cm-l.
Then, for the Inconel,
(5) absorption rate in lnconel
= S[l - Pa(Na)] P,(lnconel) .
The capture gamma-ray source strength per unit
volume was then calculated by using the di-
mensions given in ref. 1, the energy per capture
given in ref. 3, and the assumptions given above,
The macroscopic neutron absorption cross sections
at average velocity at 700OC were calculated from
values given in BNL-325.9
It was assumed that the gamma-ray source was
constant in the Inconel. Also, because of 'the
large radii involved, slab geometry was assumed
for the source and for the mediums between the
source and field points.
For a slab source and the buildup factor given
in Eq. 2, the heating for monoenergetic gamma
rays is given by
where
.I /
t I source strength (w/cm3),
pi I linear total gamma-ray cross section
(cm-l) for the ith slab,
ti E thickness of ith slab (cm); i = 1 designates
the source region.
The spectrum of capture gamma rays from lnconel
was divided into seven energy groups3 with
average energies for each group of 0.5, 1, 2, 4,
6, 8, and 10 Mev. In calculating the heating in
the shells adjacent to the lnconel source, the
buildup factor for lnconel was used. Test calculations
have shown '0 that the heating is relatively
insensitive to the type of buildup factor used for
materials which have nearly the same equivalent
Z. The heating in the beryllium reflector was
calculated by using the buildup factor for ' beryllium.
For the shells on the pressure shell side
of the heat exchanger, the buildup factor for the
9D. J. Hughes and J. A, Harvey, Neutron Cross
Sections, BNL-325 (July 1, 1955).
'OH. W. Bertini, C. M. Copenhaver, and R. B.
Stevenson, ANP Quar. Pmg. Rep. March 10, 1956,
ORNL-2061, P 36.
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