Examination and
Improvement of SHEM
multigroup energy structure
Tholakele P. Ngeleka
Radiation and Reactor Theory, Necsa, RSA
Ivanov Kostadin, Levine Samuel
Department of Nuclear Engineering, PSU, USA
Post-Graduates conference, iThemba Labs,
Cape Town, August 11 – 14, 2013
layout
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Introduction
Unit cells
Computational Tools
Method
Conclusions
References
Introduction
• Fine energy group structures allow accurate
calculation of neutron cross sections for reactor
analysis
• SHEM energy group structures were developed for
LWRs
– Addressed the materials in fuel component and
structural material found in LWRs
– Important nuclides were addressed in such that their
resonances are covered
– However, it was uncertain that they are applicable to
HTRs, which are graphite moderated and achieve high
burnup, without any further modifications.
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Introduction
Figure 1: Hydrogen and carbon cross sections (t2.lanl.gov)
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Introduction
Figure 2: Unresolved resonances for U-235 and U-238 (t2.lanl.gov)
Unit cells
• Two types of fuel:
• Prismatic hexagonal blocks are used for GFR and
VHTR
• Pebble sphere fuel element (FE) used in PBR
• Both Prismatic block and pebble FE consist of TRISO
coated particles, embedded in a graphite matrix
Unit cells
Pebble
15000 CP in each pebble sphere
It has 5 cm diameter fuel zone and 6 cm
outer diameter
Figure 3: Pebble FE model
Unit cells
Prismatic
3000 CP in each cylinder
Fuel channel diameter :1.27 cm
Coolant channel diameter: 1.588 cm
Figure 4: Prismatic block model
Computational Tools
• Dragon - deterministic code
– Capabilities of calculating angular flux and adjoint flux
– Adjoint flux allow the computation of importance
function for each energy group which is used to
improve the energy group structure
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Method
• Contributon and Point-Wise Cross Section Driven
method developed at PennState
– It is an iterative method that selects effective fine and
broad energy group structures for the problem of
interest




ˆ
ˆ
C ( E )   dr  d   r, E,   r, E, 
v
4
angular flux

(1)
adjo int flux
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Method
• The procedure for the group structure improvement
is as follows:
– An initial multi-group energy structure was selected
(SHEM-281 or 361)
– Cross sections were generated for the initial multigroup energy structure
– The angular and adjoint flux calculations were
performed to determine the importance function
– After identifying the energy groups with higher
importance, this energy group structure was improved
by dividing the energy group into two or more energy
groups
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Method
– When the improvement process was complete for all
energy groups, the new energy group structure was
used for cross section generation
– The new cross section library was used to calculate the
reaction rates and k-effective
– The reaction rates and k-effective are calculated using
the new library are compared with the results obtained
from the previous library analysis
– If the results are within a specified tolerance, the
procedure ends; otherwise, previous steps are
repeated until the specified tolerance is achieved (1%
deviation of reaction rate and 10pcm relative deviation
of dk/k)
Results
Fig. 5: Importance function for fast
energy region
Fig. 6: Importance function for
epithermal energy region
Results
PEBBLE
Energy Range
Group Structure
Reaction Rates
Thermal
Epithermal
Fast
SHEM-281
Absorption
(collisions/cm3-s)
7.35093E-01
2.58643E-01
6.26975E-03
Nu-Fission
(fissions/cm3-s)
1.40377E+00
1.04519E-01
8.63650E-03
Average Flux
(particles/cm2-s)
1.07132E+00
1.32069E+00
5.97364E-01
K-effective
SHEM_TPN-407
Fig. 7: Importance function for
thermal energy region
1.51692 (convergence = 2.79E-09)
Absorption
(collisions/cm3-s)
7.35662E-01
2.58207E-01
6.13159E-03
Nu-Fission
(fissions/cm3-s)
1.40454E+00
1.03868E-01
8.48825E-03
Average Flux
(particles/cm2-s)
1.08167E+00
1.32958E+00
5.81286E-01
K-effective
1.516901 (convergence = 9.15E-09)
Table 1: Reaction rates (281 and 407 energy group structures)
Results
PEBBLE
Energy Range
Group Structure
Reaction Rates
Thermal
Epithermal
Fast
SHEM-361
Absorption
(collisions/cm3-s)
7.35048E-01
2.58686E-01
6.26171E-03
Nu-Fission
(fissions/cm3-s)
1.40368E+00
1.04725E-01
8.63635E-03
Average Flux
(particles/cm2-s)
1.07127E+00
1.32084E+00
5.97363E-01
K-effective
SHEM_TPN-531
1.51705 (convergence = 3.44E-08)
Absorption
(collisions/cm3-s)
7.35554E-01
2.58361E-01
6.08033E-03
Nu-Fission
(fissions/cm3-s)
1.40434E+00
1.04105E-01
8.43757E-03
Average Flux
(particles/cm2-s)
1.08158E+00
1.33654E+00
5.74212E-01
K-effective
 SHEM-281
SHEM_TPN-407
 SHEM-361
SHEM_TPN-531
 SHEM energy group
structures can be used for HTR
analysis
1.51688 (convergence = 2.45E-08)
Table 2: Reaction rates (361 and 531 energy group structures)
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References
• Ngeleka, T.P., 2012. Examination and improvements
of energy group structures for HTR and HTR design
analysis, PhD Thesis, The Pennsylvania State
University, USA.
• Alpan, F. A., and Haghighat, A., 2005. Development
of the CPXSD methodology for generation of finegroup libraries for shielding applications, Nuclear
Science and Engineering, 149. 51-64.
• Kriangchairporn, N., 2006. Transport Model based on
3D cross section generation for TRIGA core analysis,
PhD Thesis, The Pennsylvania State University, USA.
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Thank you
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