1. RRC “Kurchatov Institute”, Russia NEUTRONIC AND THERMAL HYDRAULIC CODE PACKAGE PERMAK-3D/SC-1 IN 3D PIN-BY-PIN ANALYSIS OF THE VVER CORE P.А. Bolobov, D.А. Oleksuk

2. 2 Reporter – P.Bolobov Code package PERMAK-3D/SC-1

3. 3 Code package PERMAK-3D/SC-1 was designed on the basis of 3D computer code PERMAK-3D and a 3D thermal hydraulic computer code SC-1. The code package predicts axial and radial distributions of power densities and coolant parameters, and boiling in the VVER core fragment of seven fuel assemblies.

4. 4 Contents Brief description of PERMAK-3D code Brief description of SC-1 code Calculation model for VVER-1500 core fragment Test tasks and some outcomes of calculations by code package PERMAK-3D/SC-1

5. 5 Brief description of PERMAK-3D Code PERMAK-3D has been developed by the Institute of Nuclear Reactors, RRC “Kurchatov Institute” and was intended for three-dimensional multigroup pin-by-pin neutronic calculation of VVER core.

6. 6 Brief description of PERMAK-3D Neutron balance equation realised in PERMAK-3D In diffusion approximation the distribution of neutron flux in each group can be described by the following equation:

7. 7 Brief description of PERMAK-3D where : h – is a mesh pitch along the core radius, – are mesh pitches along the core height,, j=7, 8, - is neutron source for group k. The finite-difference analogue of equation, which is realised in code PERMAK-3D, looks like (for regular cells):

8. 8 Brief description of PERMAK-3D For the inner and outer boundaries of simulated region the following boundary condition is used:

9. 9 Brief description of PERMAK-3D Code PERMAK-3D may also use an finite-difference mesh, which accounts a breach in the mesh uniformity in the gaps between FAs. Figure 1 shows a PERMAK-3D finite-difference mesh in the vicinity of three VVER fuel assemblies with identical pitch of fuel pins arrangement in the neighbouring FAs.

10. 10 Brief description of PERMAK-3D Fig. 1 Finite-difference mesh in the vicinity of three assembly junction (identical fuel rod in the neighbouring FAs) h1h1 HkHk M 1 M M 2 D’ D C 1 C C 2 C3C3 K BE F A 1 A A 2 G 1 G G 2 G3G3 O P 0 1 2 34 5 6 FA 1 FA 2 FA 3

11. 11 Brief description of PERMAK-3D Code PERMAK-3D may also use an finite-difference mesh for FAs of different pin pitches. Figure 2 shows the finite-difference mesh with different pitches in the neighbouring FAs. It is suggested, that the amount of the mesh sells in the neighbouring FAs is equal.

12. 12 Brief description of PERMAK-3D Fig. 2 Finite-difference mesh in the vicinity of three assembly junction (different fuel rod pitch in the neighbouring FAs) A B C 1V’1V’ 1V”1V” V’ V”V”’ h1h1 h2h2 h3h3 G B C FA 1 FA 2 FA 3

13. 13 Brief description of PERMAK-3D Input Data: Core and reflectors map and geometry, Coolant temp. and density, Boron conc., Power, Neutron-physical constants PERMAK-3D PERMAK-3D input data

14. 14 Brief description of PERMAK-3D For the purpose of PERMAK-3D calculation of the core fragment of seven assemblies, the BIPR7-А and PERMAK-А calculations outcomes of the fuel loadings may be used as input data. For this purpose code PERMAK-А is equipped with the capability to record the required data in a special file for PERMAK-3D code.

15. 15 Brief description of PERMAK-3D BIPR7-АPERМАК-А Т, G, Cb, W PERMAK-3D Core and reflectors map and geometry, Coolant temp. and density, Boron conc., Power,

16. 16 Brief description of SC-1 Code SC-1 Code SC-1 was developed in the Institute of Nuclear Reactors, RRC “Kurchatov Institute”. The code is intended for performing a subchannel analysis of VVER core thermal hydraulic behaviour in steady state and transient conditions.

17. 17 Brief description of SC-1 In reactor core the coolant flow between parallel fuel rods, therefore the thermal hydraulic simulation applies the method of core radial split into parallel subchannels (or cells). The channels interact through turbulent and convective coolant mixing in radial direction.

18. 18 Brief description of SC-1 Code SC-1 realises the model of homogeneous two-phase flow, which takes into concern the non-equilibrium steam, which is formed due to surface boiling and steam slipping the liquid phase. The system of differential equations of such model includes continuity equation, axial energy and momentum equation for each cell, and also radial momentum equation for every tie between the cell couples.

19. 19 Brief description of SC-1 Fig. 3 shows one FA selected from VVER core.

20. 20 Brief description of SC-1 CORE FA FUEL ROD REFERENCE SPACE GAP Fig.3 –Elementary reference space selected in VVER core

21. 21 Brief description of SC-1 Fig. 4 shows one elementary cell selected from the FA, and the related reference space enclosed by two plains, which are perpendicular to the direction of the main flow.

22. 22 Brief description of SC-1 Fig. 4 – Reference space for averaging the parameters FUEL ROD

23. 23 Brief description of SC-1 The averaging the momentum parameters in radial direction was performed in the space different from the space from Fig. 4 due to dependence of transfer direction on the gap orientation. A modified reference space with central point in the middle of gap is shown in Fig. 5.

24. 24 Brief description of SC-1 Fig. 5 – Reference space for radial momentum equation Cells centres

25. 25 Brief description of SC-1 In order to close up the system of four main differential equations, which includes six unknown values it is required to add an equation of state and a fuel pin model.

26. 26 Brief description of SC-1 In SC-1 code has been realised the model of homogeneous two-phase flux with allowance non-equilibrium steam, which forms due to surface boiling and steam slipping off liquid phase. The adopted model of two-phase flow, used in SC-1 code, was developed by V.S. Osmachkin.

27. 27 Calculation model for core fragment Calculation model for VVER-1500 core fragment CALCULATION MODEL FOR VVER-1500 CORE FRAGMENT CONSISTING OF SEVEN FUEL ASSEMBLIES The example of split of a 7-assembly VVER-1500 core fragment into thermal hydraulic cells for the purpose of SC-1 calculations is shown in Figure 6.

28. 28 Calculation model for core fragment Calculation model for VVER-1500 core fragment Рис. 6 RODS Designations - fuel rod - central tube - guide tube - numbers of FA round FA 1

29. 29 Calculation model for core fragment Calculation model for VVER-1500 core fragment In the Figure 6, the Nos. of fuel pins, Gd-pins, guide tubes and central tube fit the cell enumeration adopted in PERMAK-3D code.

30. 30 Calculation model for core fragment Calculation model for VVER-1500 core fragment

31. 31 Test tasks - description Test tasks For the purpose of analysing of coolant boiling in VVER-1500 core fragment the test tasks where used. The maps of these tasks are shown in Fig. 7.1-7.3. Fig. 8 depicts an axial model of VVER-1500 fuel assembly.

32. 32 Test tasks - description Fig. 7.1 Map 1 of FA arrangement for test task Pin enrich. х=4.95% 4 Pin enrich. х=4.95% 1 Pin enrich. х=4.95% 2 Pin enrich. х=4.95% 3 Pin enrich. х=4.95% 6 Pin enrich. х=4.95% 5 Pin enrich. х=4.95% 7

33. 33 Test tasks - description Fig. 7.2 Map 2 of FA arrangement for test task Pin enrich. х=4.95% 4 Pin enrich. х=2.4% 1 Pin enrich. х=2.4% 2 Pin enrich. х=2.4% 3 Pin enrich. х=2.4% 6 Pin enrich. х=2.4% 5 Pin enrich. х=2.4% 7

34. 34 Test tasks - description Fig. 7.3 Map 3 of FA arrangement for test task Pin enrich. х=2.4% 4 Pin enrich. х=2.4% 1 Pin enrich. х=2.4% 2 Pin enrich. х=3.6% 3 Pin enrich. х=2.4% 6 Pin enrich. х=2.4% 5 Pin enrich. х=2.4% 7

35. 35 Test tasks - description Рис. 8 The axial model of VVER-1500 fuel assembly Bottom reflector Top reflector CORE

36. 36 Test tasks - description Three test tasks were generated at the initial stage of work, they are: 1.V1500_3D-1F (Map 1); 2.V1500_3D-2F (Map 2); 3.V1500_3D-3F (Map 3). Output of all seven Fas in all three test tasks is W=124 MW. Total coolant flow is G=2931 m 3 /h.

37. 37 Test tasks - description Three test tasks were generated with power W=124 МW and coolant flow G=2244 m 3 /h : 1. V1500_3D-1G (Map 1); 2. V1500_3D-2G (Map 2); 3. V1500_3D-3G (Map 3). The test task V1500_3D-1W (Map 1) was generated with power W=184 МW and coolant flow G=2931 m 3 /h.

38. 38 Test tasks – outcomes of calculations Fig. 9 Water density distribution at FA 4 outlet in test tasks with the Map 1 V1500_3D-1F (G=2931 m 3 /h, W=124 MW) V1500_3D-1G (G=2244 m 3 /h, W=124 MW) V1500_3D-1W (G=2931 m 3 /h, W=184 MW) 600-650 kg/m 3 550-600 kg/m 3 500-550 kg/m 3

39. 39 Test tasks – outcomes of calculations Fig. 10 Water density distribution at FA 4 outlet in test tasks with the Map 2 V1500_3D-2F (G=2931 m 3 /h, W=124 MW) V1500_3D-2G (G=2244 m 3 /h, W=124 MW) 600-650 kg/m 3 550-600 kg/m 3 500-550 kg/m 3

40. 40 Test tasks – outcomes of calculations Fig. 11 Water density distribution at FA 3 outlet in test tasks with the Map 3 V1500_3D-3F (G=2931 m 3 /h, W=124 MW) V1500_3D-3G 1 (G=2500 m 3 /h, W=124 MW) V1500_3D-3G 2 (G=2244 m 3 /h, W=124 MW) 600-650 kg/m 3 550-600 kg/m 3 500-550 kg/m 3 500-450 kg/m 3 <450 kg/m 3

41. 41 Code package PERMAK-3D/SC-1 evolution A possibility of performing calculations for symmetry sector of VVER core and transient conditions in the core will be provided in code package PERMAK-3D/SC-1.