1. СRCD NSC KIPT DiFis 2.0 – 3D Finite Element Neutron Kinetic Code A.I. Zhukov and A.M. Abdullayev NSC Kharkov Institute of Physics and Technology September 24 - 28, 2007 Yalta, Ukraine 17 th AER Symposium on VVER Reactor Physics and Reactor Safety

2. СRCD NSC KIPT Objective Existing 1D kinetic codes too conservative SNRCU intend to require 3D analysis for accidents with reactivity insertion (Control Rod Eject Accident and others)

3. СRCD NSC KIPT Background Westinghouse PHOENIX-H code (XS) Westinghouse Advanced Nodal Code (ANC-H) Westinghouse 1D-3D neutron kinetic code TWINKLE (for PWR square FA lattice) DiFis 1.0 – 3D FE steady-state code FE methodology

4. СRCD NSC KIPT Nuclear Model 2 group approximation

5. СRCD NSC KIPT Thermal Hydraulic Model for fuel, gap, cladding for coolant Average Fuel Rod (one per assembly)

6. СRCD NSC KIPT Feedback Models PHOENIX-H provides all XS with feedback Moderator density correction includes: a.Diffusion coefficient correction b.Moderator absorption correction c.Boron concentration correction d.Spectrum correction Fuel temperature correction Xe, Sm, Pm correction Control Rod correction

7. СRCD NSC KIPT Finite Element Technique - 1 Set of simplex-functions Set of linear functions Expansion of fluxes into series over linear functions 1 5 6 4 2 3

8. СRCD NSC KIPT Finite Element Technique - 2 or Weighted Residual Equations

9. СRCD NSC KIPT Finite Element Technique - 3 1 6 2 3 4 5 1 6 2 3 4 5 7 8 910 1112 1314 15 16 17 1819 2021 2223 24 1 6 43 2 3 4 5 7 8 910 1112 1314 15 16 17 1819 2021 2223 24 26 27 28 25 2930 3132 3334 3536 3738 39 40 42 41 44455253 54 4647 4849 5051 1 5 6 4 2 3

10. СRCD NSC KIPT Finite Element Technique - 4 Fuel Rod Normally Fuel – 7 zones Gap – 2 zones Clad – 5 zones Axial – 24 zones

11. СRCD NSC KIPT Code capabilities Core Power vs. time Spatial and time power distribution Spatial and time temperature distribution in fuel, cladding and coolant

12. СRCD NSC KIPT Example of Steady-State Calculations EOC Relative FA Power ANC DiFis-ANC Max Err = 4.0% Rms Err = 1.6%

13. СRCD NSC KIPT Example of Transient Calculations - 1 Control Rod Eject Accident Timeline 0 s 0.1 s 0.4 s 3.0 s start finish all banks start to drop finish

14. СRCD NSC KIPT Example of Transient Calculations - 2 Rod Cluster Worth 0.18%

15. СRCD NSC KIPT Example of Transient Calculations - 3 Doppler only FA under ejected RCCA

16. СRCD NSC KIPT Example of Transient Calculations - 4 All Banks drop FA under ejected RCCA

17. СRCD NSC KIPT Example of Transient Calculations - 5 Doppler only FA under ejected RCCA

18. СRCD NSC KIPT Example of Transient Calculations - 6 All Banks drop FA under ejected RCCA

19. СRCD NSC KIPT Summary 1. DiFis 2.0 compatible with well-known codes such as PHOENIX-H and ANC-H 2. DiFis 2.0 provides accuracy ~4% (in compare with ANC) for steady-state calculations 3. DiFis 2.0 justification and benchmarking to be continued