# Gamma Decay Heat Distribution in Core:  A Known Issue Revisited

Authors: Gianni Petrangeli; Calogero Sollima
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

Decay heat in fission reactors is almost equally subdivided into two parts, one part due
to beta rays and the other due to gamma photons. Beta rays are absorbed practically where
they are generated while gamma photons travel some distance in core before being absorbed.
The decay power peaking factor is, in fact, affected by this phenomenon of gamma decay
heat redistribution. Calculations have been performed by the Monte Carlo MCNP5 computer code on the experimental LOFT reactor and on a larger 1000 MWe PWR using various initial
power distributions with variable power peak sharpness (midheight peak width). The
results indicate that an average peak energy reduction ratio of 0.82 for gamma (18% peak
reduction) can be used with tolerable error up to a midheight width of the produced
energy peak (neutron flux shape during operation) of 120 cm. Beyond this value, no peak
energy reduction is warranted. This phenomenon of absorbed γ power redistribution in core
may be very significant (100 to150∘K reduction in calculated PCT).


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## Body

## 1. Background and Overview

Decay  heat in   fission
reactors [1, Chapter 3-2] is almost equally subdivided into two parts, one part due
to beta rays and the other due to gamma photons. This fact is not important for
the overall thermal balance of the reactor but it is important for the decay
power distribution within the core and for the possible overheating of the so
called “hot rod” during an accident. Beta rays are absorbed practically where
they are generated while gamma photons travel some distance in core before
being absorbed. The decay power peaking factor is, in fact, decreased by this
phenomenon of gamma decay heat redistribution. If a power peak exists during
reactor operation, this power peak is attenuated during shutdown. This fact
should be taken into account in transient and accident analyses (and
particularly in best-estimate analyses) since it can be very relevant for some
interesting quantities and in particular for the calculated peak cladding
temperature (PCT).Also appendix K to Part
50 of the U.S. C.F.R. states (5) that “The fraction of the locally generated
gamma energy that is deposited in the fuel (including the cladding) may be
different from 1.0; the value used will be justified by a suitable
calculation.”The present
communication is intended to recall the order of magnitude of this effect and
to recommend attention to it in the current practice. Two main assumptions of
this study are that the operation history at power can be assumed as a
continuous, long duration, operation at nominal power (as frequently it is the
case). Consideration is given to decay heat produced by the core after the
decay of delayed neutrons following shut-down.


## 2. Gamma Decay Heat Source

Gamma photons due to
decay of fission products are usually grouped into seven energy groups.Table1 shows these
groups (from Perkins and King [2], and Etherington [3]).Table 1
Groups of decayγ photons
and energies.
GroupEnergy range (Mev)Effective energy[Mev]I0.1–0.40.4II0.4–0.90.8III0.9–1.351.3IV1.35–1.81.7V1.8–2.22.2VI2.2–2.62.5VII>2.62.8Table2. shows the properties of the
various groups at two times after fission, 100 and 10000 seconds, particularly
relevant for accident studies (from Perkins and King [2]).Table 2
Properties of photon groups.
Time after fission (s)10010000Group(Mev/s fission)Disintegr./s% or
probability(Mev/s fission)Disintegr./s% or probabilityI6e-51.5e-482e-65e-619II2.4e-43e-4161e-52.25e-548III1.2e-39.2e-4492.5e-61.9e-67IV4.2e-42.5e-413.46e-63.5e-613V6e-52.7e-51.453.5e-61.6e-66VI2e-48e-54.33.5e-61.4e-65.4VII4.2e-41.5e-485e-71.8e-7.7The average energy per
disintegration is, for 100 seconds, 1.33 Mev/dis. while, for 10000 seconds, it
is 1.07 Mev/dis.


## 3. Model and Calculation Cases

The simple model used for a reactor
is a homogeneous cylinder subdivided into 35 cylindrical rings and into 66
slices normal to the axis, Figure1. The fuel elements grid for loss-of-fluid
Test (LOFT, [4]) core is also shown. The density chosen is an average one (by
the way, the result is dependent, but less than linearly, on density, because
of the “build-up effect” in γ attenuation). The normal operation power
distribution has been simulated by a sinusoidal curve both in the radial and in
the axial directions. For the radial distribution, other shapes have been
explored: the hot rod (simulated by a 1.4 factor energy peak in the central
ring superimposed on a sinusoidal distribution for the whole core) and three
Gaussian distributions for the whole core with σ2 equal to 0.01 (narrow),
0.05 (intermediate), 0.12 (wide), and 0.24 (extra wide). The spectrum of γ
photons has been taken into account.Figure 1
cylindrical core model with LOFT grid.The well known Monte
Carlo code MCNP5 has been used for the calculation of the
distribution in the core of the absorbedγ photons energy corresponding to the
γ photons produced energy, distributed as above mentioned.The cases calculated are as follows:(i)
small  reactor (LOFT) at 100 seconds after shutdown with sinusoidal
distribution,(ii)
small reactor (LOFT) at 10000 seconds after shutdown with sinusoidal
distribution,(iii)
small reactor (LOFT) at 100 seconds after shutdown with hot rod rod (simulated
by multiplication of theγ power in the central cylindrical cell by the factor
1.4),(iv)
small reactor (LOFT) at 100 seconds after shutdown with intermediate
Gaussian distribution (σ2= square
of the standard deviation = 0.05),(v)
small reactor (LOFT) at 100 seconds after shutdown with wide Gaussian
distribution (σ2=0.12),(vi)
large reactor with sinusoidal distribution,(vii)
large reactor with hot rod (simulated by multiplication of theγ power
in the central cylindrical cell by the factor 1.4) at 100 seconds,(viii)
large reactor with narrow Gaussian distribution (σ2=0.01),(ix)
large reactor with very wide Gaussian distribution (σ2=0.24). The main results are the following:(i)
the maximumγ power absorbed in the core is significantly decreased when
the γ photon redistribution is taken into account. Since the decay heat is due
for one half to γ and for the other half to β rays, a certain reduction in
absorbed γ power translates in a reduction of one half of it in γ+β (total)
decay power. In particular,(i)
for the small reactor without hot rod the reduction of absorbedγ power
versus produced power is equal to about 10% at 100 seconds and to about 15% at
10000 seconds after shutdown; the case of a large reactor with local neutron
flux hills (due, e.g., to specific control rod management strategies) can
approximate the case of a small reactor;(ii)
for the small reactor with hot rod, theγ peak at the hot rod
practically disappears and the overall (sine distribution plus hot rod)
reduction in peak energy is equal to about 30% at 100 seconds (this is considered
the most significant result since the γ redistribution, with corresponding γ+β
power decrease of 15%,  may entail a
calculated PCT reduction of the order of 100–150K°); for a
large reactor, the peak energy is reduced by a 12% instead of 30%;(iii)
for the large reactor without hot rod the correspondingγ reduction is much
lower (about 1% for a sine distribution at 100 seconds).


## 4. Detailed Results and Tentative Practical Rule for the Peak Energy Reduction Evaluation

Table3 shows all the results
obtained for a time after shutdown of 100 seconds.Table 3
Results for time after
shutdown of 100 seconds.
Δr,1/2  (cm)Ep (w/cm3)Ea  (w/cm3)(Ep-Ea)/ Ep, %Ep/ EaCase23.332.34300.7LOFTh8.483.332.94120.88LGh182.381.89210.79LOFT 0.0519.52.382.1120.88LOFT 0.12462.382.1690.9LOFTsin67.52.381.85220.78LG 0.01118.42.382.046140.86LG 0.24192.42.382.360.80.99LG sinIn the table the following symbols
have been adopted:(i)
Δr,1/2= mid
height width of the produced energy peak [cm],(ii)
Ep= maximum produced
specific energy [w/cm3] of photons,(iii)
Ea= maximum absorbed
specific energy [w/cm3] of photons,(iv)
σ2= square of the standard deviation of Gaussian distributions of produced
energy,(v)
LOFT: for LOFT core cases with final
letter h for “hot rod” case; sin for sine distribution and a number forσ2 used,(vi)
LG: for large reactor with the same
meaning of the final letters as for LOFT.Figures2, 3, 4, 5 show the
distributions (radial and axial) of produced and absorbed energies for LOFT and
for LARGE REACTOR with sine distribution.Figure 2
LOFT sin,
100 seconds, produced and absorbed power versus radius.Figure 3
LOFT sin,
100 seconds, produced and absorbed power versus height.Figure 4
LARGE
reactor sin, 100 second, produced and absorbed power versus radius.Figure 5
LARGE
reactor sin, 100 seconds, produced and absorbed power versus height.Figures6, 7, 8, 9 show the same
distributions for the case with hot rod.Figure 6
LOFT hot rod,
100 seconds, produced and absorbed power versus radius.Figure 7
LOFT hot rod,
100 seconds, produced and absorbed power versus height.Figure 8
LARGE
reactor hot rod, 100 seconds, produced and absorbed power versus radius.Figure 9
LARGE
reactor hot rod, 100 seconds, produced and absorbed power versus height.An attempt to correlate the maximum
energy reduction due to gamma photon redistribution in core has been made: the
ratio between maximum absorbed and produced gamma energies has been correlated
with the mid-height width of the produced energy peak. Figure10 has been
obtained.Figure 10
Correlation
between absorbed and produced energies ratio with mid-height peak width.The calculated cases, listed  in Table3, have been used.As a first approximation, it can be
said that the average energy reduction ratio of 0.82 for gamma (18% peak
reduction) can be used with tolerable error up to a mid-height width of 120 cm
and at 100 seconds after shutdown; at 10000 seconds after shutdown a figure of
77% can be used instead of 82%. Above this value of mid-height width, no peak
energy reduction is warranted.


## 5. Conclusions

The average energy reduction ratio
of 0.82 for gamma (18% peak reduction) can be used with tolerable error up to a
mid-height width of the produced energy peak (neutron flux shape during operation)
of 120 cm. Beyond this value, no peak energy reduction is warranted.The phenomenon  of absorbedγ power
redistribution in core may be very significant (100 to 150K° reduction in
calculated PCT).A more refined set of calculations
than the ones mentioned here (smaller cells, nonhomogeneous core model, etc.)
could produce more accurate results; however, for the indicative purpose of
this paper and with an accuracy of a few percent in peak photon energy, the
results obtained are already sufficient to draw the above mentioned
conclusions.In any case, for any specific
reactor and anticipated flux shapes and for any set of similar transients
(importance and critical timing of decay heat for hot rod), a specific
evaluation is advisable.



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*Source: 796268-2008-08-03.xml*