Examination and Improvement of SHEM multigroup energy structure Tholakele P. Ngeleka Radiation and Reactor Theory, Necsa, RSA Ivanov Kostadin, Levine Samuel.

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

layout

• Introduction• Unit cells• Computational Tools • Method• Conclusions• References

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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.

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Introduction

Figure 1: Hydrogen and carbon cross sections (t2.lanl.gov)

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

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





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





SHEM_TPN-531Absorption





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.

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Thank you

Examination and Improvement of SHEM multigroup energy structure Tholakele P. Ngeleka Radiation and Reactor Theory, Necsa, RSA Ivanov Kostadin, Levine Samuel.

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