examination and improvement of shem multigroup energy structure tholakele p. ngeleka radiation and...
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Examination and Improvement of SHEM multigroup energy structure
Tholakele P. NgelekaRadiation and Reactor Theory, Necsa, RSA
Ivanov Kostadin, Levine SamuelDepartment of Nuclear Engineering, PSU, USA
Post-Graduates conference, iThemba Labs, Cape Town, August 11 – 14, 2013
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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.
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
Figure 3: Pebble FE model
Pebble 15000 CP in each pebble sphere It has 5 cm diameter fuel zone and 6 cm outer diameter
Unit cells
Prismatic 3000 CP in each cylinder Fuel channel diameter :1.27 cmCoolant channel diameter: 1.588 cm
Figure 4: Prismatic block model
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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
(1) 4
int
ˆ ˆ( ) r, , r, ,v
angular flux adjo flux
C E dr d E E
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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
multi-group 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
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
Fig. 7: Importance function for thermal energy region
PEBBLE
Group Structure Reaction Rates
Energy Range
Thermal Epithermal Fast
SHEM-281Absorption
(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 1.51692 (convergence = 2.79E-09)
SHEM_TPN-407Absorption
(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)
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Results
SHEM-281 SHEM_TPN-407
SHEM-361 SHEM_TPN-531
SHEM energy group structures can be used for HTR analysis
PEBBLE
Group Structure Reaction Rates
Energy Range
Thermal Epithermal Fast
SHEM-361Absorption
(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 1.51705 (convergence = 3.44E-08)
SHEM_TPN-531Absorption
(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 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 fine-group 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.