1. 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

2. layout Introduction Unit cells Computational Tools Method Conclusions References

3. 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. 3

4. Introduction 4 Figure 1: Hydrogen and carbon cross sections (t2.lanl.gov)

5. Introduction Figure 2: Unresolved resonances for U-235 and U-238 (t2.lanl.gov)

6. 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

7. 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

8. 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

9. 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 9

10. 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) 10

11. 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 11

12. 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)

13. Results Fig. 5: Importance function for fast energy region Fig. 6: Importance function for epithermal energy region

14. Results Fig. 7: Importance function for thermal energy region PEBBLE Group StructureReaction Rates Energy Range ThermalEpithermalFast SHEM-281 Absorption (collisions/cm 3 -s)7.35093E-012.58643E-016.26975E-03 Nu-Fission (fissions/cm 3 -s)1.40377E+001.04519E-018.63650E-03 Average Flux (particles/cm 2 -s)1.07132E+001.32069E+005.97364E-01 K-effective1.51692 (convergence = 2.79E-09) SHEM_TPN-407 Absorption (collisions/cm 3 -s)7.35662E-012.58207E-016.13159E-03 Nu-Fission (fissions/cm 3 -s)1.40454E+001.03868E-018.48825E-03 Average Flux (particles/cm 2 -s)1.08167E+001.32958E+005.81286E-01 K-effective1.516901 (convergence = 9.15E-09) Table 1: Reaction rates (281 and 407 energy group structures)

15. Results  SHEM-281 SHEM_TPN-407  SHEM-361 SHEM_TPN-531  SHEM energy group structures can be used for HTR analysis 15 PEBBLE Group StructureReaction Rates Energy Range ThermalEpithermalFast SHEM-361 Absorption (collisions/cm 3 -s)7.35048E-012.58686E-016.26171E-03 Nu-Fission (fissions/cm 3 -s)1.40368E+001.04725E-018.63635E-03 Average Flux (particles/cm 2 -s)1.07127E+001.32084E+005.97363E-01 K-effective1.51705 (convergence = 3.44E-08) SHEM_TPN-531 Absorption (collisions/cm 3 -s)7.35554E-012.58361E-016.08033E-03 Nu-Fission (fissions/cm 3 -s)1.40434E+001.04105E-018.43757E-03 Average Flux (particles/cm 2 -s)1.08158E+001.33654E+005.74212E-01 K-effective1.51688 (convergence = 2.45E-08) Table 2: Reaction rates (361 and 531 energy group structures)

16. 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. 16

17. Thank you 17