Development of 3D Space Time Kinetics Model for Coupled Neutron Kinetics and Thermal hydraulics

Transcription

1 Development of 3D Space Time Kinetics Model for Coupled Neutron Kinetics and Thermal hydraulics WORKSHOP ON ADVANCED CODE SUITE FOR DESIGN, SAFETY ANALYSIS AND OPERATION OF HEAVY WATER REACTORS October 2-5, 212, Ottawa, Canada FERNANDO M.P.S. NPCIL, INDIA

2 22 MWe PHWR is small in size and tihtly coupled Safety analysis was carried out usin point reactor model (point kinetics) No incore instrumentation was required for control and protection NEUTRONIC DECOUPLING increases with Size and power flattenin SPATIAL EFFECTs are more pronounced in neutronically less coupled reactor systems 3D Space time kinetics code is required for Safety analysis Requirement of incore instrumentation for control protection (54 and 7 MWe PHWRs) and IAEA Workshop October 2-5, 212, Ottawa

3 Neutronics for Coupled Thermal Hydraulics Nuclear Library Evaluated cross section from Physics Experiments and analysis (ENDF) Material Composition, Geometry, Temperatures of fuel, coolant & moderator Reactivity device Geometry & material Few roup Homoenised Cross section database Lattice Calculations Supercell Calculations Reactor Kinetics Neutron Transport theory Few Group Neutron Transport theory Few roup Homoenized Cross section Power Variation IAEA Workshop October 2-5, 212, Ottawa

4 TYPICAL SUPERCELL Fuel Cluster Reactivity device D 2 O Guide Tube IAEA Workshop October 2-5, 212, Ottawa

5 NEUTRONIC COUPLING Temperatures Densities Thermal Hydraulics ATMIKA NEUTRONICS IQS 3D Power Distribution IAEA Workshop October 2-5, 212, Ottawa 5

6 Neutron Cross section Library Earlier WIMS (1981) 27 Neutron Group Cross section Library (Winfrith Improved Multi roup Scheme) Improved and Latest Libraries from IAEA WIMS Library Update Project ENDF/B-VI 69 neutron roup library (May 22) (Evaluated Nuclear Data File) IAEA Workshop October 2-5, 212, Ottawa

7 69 Neutron Enery Group Library 14 Fast Groups (1 MeV to KeV) Fission Spectrum 13 Resonance Groups (9.118 KeV to 4 ev) 1/E Spectrum 42 Thermal Groups ( 4 to ev) Maxwellian Spectrum IAEA Workshop October 2-5, 212, Ottawa

8 Feed Back Coefficients of Reactivity Temperature Coefficients of Reactivity Moderator Coolant Fuel Channel Coolant Density or Void Coefficient Coolant Isotopic purity Boron in moderator IAEA Workshop October 2-5, 212, Ottawa

9 NEED FOR 3D SPACE TIME KINETICS Half Core void causes lare side to side power tilt (Radial coolant loops) SPATIAL EFFECTs are more pronounced in Decoupled reactor Shut-off rods are inserted from top Asymmetric insertion of Shutdown rods because of 2 missin rods in voided reion IAEA Workshop October 2-5, 212, Ottawa

10 ) 2,... 1, ( ), ( C + ), ( ), ( ) (1 (r,t) ), ( D t ), ( v 1 i i i d ' f p r ' ' ' ' ' G t r t r t r t r t r 2,...6) 1, ( ), ( ), ( ), ( f i t r C t r t t r C i i i i Time-dependent Multi-roup Neutron Diffusion Theory Equation TIME-DEPENDENT PRECURSOR EQUATION HOMOGENISED CROSS SECTION, MULTI-GROUP APPROXIMATION APPROPRIATE BOUNDARY, CONTINUITY AND INITIAL CONDITIONS VARIATION IN CROSSECTION DUE TO FEEDBACK IAEA Workshop October 2-5, 212, Ottawa

11 Flux Factorisation Technique SHAPE FUNCTION 1 v t D ( r, t) n( t) ( r, t) p (1 ) ' f ' ' ' ' ' r 1 n v dn dt 1 n d i i C i AMPLITUDE FUNCTION dn(t) dt d ( (t) i(t) dt ) n(t) i n(t) i i C i(t) E(t) n(t) i i (t) IAEA Workshop October 2-5, 212, Ottawa

12 TIME STRUCTURE FOR SOLUTION b t o b t 1 b t 2 b t 3 b t 4 b t 5 b t 6 i t k b t i = end of the macro-time interval when the shape function is calculated i t k = end of the micro-time interval when the amplitude factor is calculated IAEA Workshop October 2-5, 212, Ottawa

13 IAEA Workshop October 2-5, 212, Ottawa

14 SOR MESH BY MESH SOLUTION SLOR LINE BY LINE SOLUTION KRYLOV SUB SPACE METHODS IAEA Workshop October 2-5, 212, Ottawa

15 IAEA Workshop October 2-5, 212, Ottawa

16 IAEA Workshop October 2-5, 212, Ottawa

17 CSR FORMAT IAEA Workshop October 2-5, 212, Ottawa

18 KRYLOV SUB-SPACE METHOD IAEA Workshop October 2-5, 212, Ottawa

19 IAEA Workshop October 2-5, 212, Ottawa

20 IAEA Workshop October 2-5, 212, Ottawa

21 IAEA Workshop October 2-5, 212, Ottawa

22 Incomplete LU factorization (ILUT) IAEA Workshop October 2-5, 212, Ottawa

23 IAEA Workshop October 2-5, 212, Ottawa

24 THREE DIMENSIONAL BENCHMARK PROBLEM REALISTIC REPRESENTATION OF PHW REACTOR THREE REACTOR ZONES : INNER, OUTER AND REFLECTOR MESH GRID CONSISTS OF 18 * 18 * 1 IN X, Y AND Z DIRECTION TIME INTERVAL FOR CALCULATION OF INTEGRAL PARAMETERS IS.5 SEC AND POINT KINETICS TIME STEP OF 1-4 SEC LOSS OF COOLANT IS SIMULATED BY A LINEAR DECREASE IN THERMAL ABSORPTION CROSS SECTION ASYMMETRIC INSERTION OF SHUTOFF RODS - ADDITION OF INCREMENTAL THERMAL NEUTRON ABSORPTION IN AFFECTED REGIONS (STARTS AT.6 SEC; FULLY INSERTED AT 2.1 SEC) TRANSIENT LASTS UPTO 2.5 SEC IAEA Workshop October 2-5, 212, Ottawa

25 Y- direction (cm) Y- direction mesh space numbers X-direction (cm) X - direction mesh space numbers REFLECTOR OUTER CORE INNER CORE Fiure 3.5a: Vertical cross section showin mesh rid layout in X-Y plane 3-D Benchmark IAEA Workshop October 2-5, 212, Ottawa

26 Z- direction (cm) Z- direction mesh space numbers X-direction (cm) X - direction mesh space numbers Fiure 3.5b: Horizontal cross section showin mesh rid layout in X-Z plane 3-D Benchmark IAEA Workshop October 2-5, 212, Ottawa

27 Y- direction (cm) X-direction (cm) Y- direction mesh space numbers X - direction mesh space numbers REFLECTOR OUTER CORE INNER CORE Reions affected by absorber insertion Fiure 3.6a: Vertical cross section showin reion assinment in X-Y plane for <Z<3 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

28 Y- DIMENSION (cm) X-DIMENSION (cm) Y- direction mesh space numbers X - DIRECTION MESH SPACE NUMBERS REFLECTOR OUTER CORE INNER CORE Reions affected by absorber insertion Fiure 3.6b: Vertical cross section showin reion assinment in X-Y plane for 3<Z<6 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

29 Z- dimension (cm) Z- direction mesh space numbers X-dimension (cm) X - direction mesh space numbers Hatch indicates area throuh which absorber is inserted Fiure 3.6c: Horizontal cross section showin reion assinment in X-Z plane at Y=39 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

30 Relative Total Power IQS3D CERKIN Time (second) IAEA Workshop October 2-5, 212, Ottawa

31 2 4 Y axis Y axis Flux.5Flux X axis X axis 2 Time=. second Time=1. second 2 4 Y axis Y axis Flux Flux X axis Time=1.35 second X axis Time=2.5 second Fiure 3.8: Thermal flux distribution in X-Y plane at Z=27 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

32 2 Z axis 4 2 Z axis Flux X axis Flux X axis 2 Time=. second Time=1. second 2 Z axis 4 2 Z axis Flux.5 Flux X axis Time=1.35 second X axis Time=2.5 second 2 Fiure 3.9: Thermal flux distribution in X-Z plane at Y=36 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

33 2 Z axis 4 2 Z axis Flux 1 Flux Y axis Y axis 2 Time=. second Time=1. second 2 Z axis 4 2 Z axis Flux 1 Flux Y axis Time=1.35 second Y axis Time=2.5 second 2 Fiure 3.1: Thermal flux distribution in Y-Z plane at X=36 cm (3-D Benchmark) IAEA Workshop October 2-5, 212, Ottawa

34 REDUCTION IN CPU TIMES INVOLVED PROBLEM METHOD CPU TIME (sec) 2D AECL BENCHMARK SLOR 377 PGMRES 47 3D AECL BENCHMARK SLOR 461 PGMRES 82 LOR ANALYSIS FOR 7 MWe PHWR FOR 1%FP LOR ANALYSIS FOR 7 MWe PHWR FOR 1%FP SLOR 17 PGMRES 387 SLOR 26 PGMRES 6 IAEA Workshop October 2-5, 212, Ottawa

35 REDUCTION IN NUMBER OF ITERATIONS PROBLEM METHOD NUMBER OF ITERATIONS (MAX) 2D AECL BENCHMARK SLOR 12 PGMRES 2 3D AECL BENCH MARK SLOR 15 LOR ANALYSIS FOR 7 MWe PHWR FOR 1%FP PGMRES 2 SLOR 15 PGMRES 6 LOR ANALYSIS FOR 7 MWe PHWR FOR 1%FP SLOR 15 PGMRES 75 IAEA Workshop October 2-5, 212, Ottawa

36 28 SHUT-OFF RODS INSERTION 6 Y axis Flux X axis 6 Y axis Flux X axis 6 Y axis Flux X axis % IN 3 %IN 5 % IN Flux 6 4 Y axis Flux X axis X axis 6 4 Y axis 2 6 Y axis Flux X axis 8 % IN 95 % IN 1 % IN IAEA Workshop October 2-5, 212, Ottawa

37 26 SHUT-OFF RODS INSERTION 6 Y axis Flux X axis 6 Y axis Flux X axis 6 Y axis Flux X axis % IN 3 %IN 5 % IN 6 6 Y axis 4 Y axis Flux 4 Flux X axis X axis 6 Y axis Flux X axis 8 % IN 95 % IN 1 % IN IAEA Workshop October 2-5, 212, Ottawa

38 SDS#1 Reactivity Profile -1 STATIC REACTIVITY (mk) RODS 26 RODS PERCENT INSERTION IAEA Workshop October 2-5, 212, Ottawa

39 Reactivity (mk) TAPP#4 Phase B Measurements of Shut-off rods Observed 28 SR Expected 28 SR Position % IN IAEA Workshop October 2-5, 212, Ottawa

40 Interleaved core of 7 Mwe Desin With 98 channels, inlet connected to each inlet header bein distributed uniformly across the reactor core. With interleaved confiuration, void ets distributed across the core. Interleaved core of 7 MWe Desin TAPS-3&4 Core Confiuration IAEA Workshop October 2-5, 212, Ottawa

41 IAEA Workshop October 2-5, 212, Ottawa

42 ATMIKA : LOCA ANALYSIS FOR 7 MWe LEGEND DRUM-2 DRUM-4 DRUM-3 DRUM-1 1 BANK-1 86 BLEED BANK-1 FEED FEED BANK-2 BANK-2 REACTOR CORE PHT Sys. Sec. Sys. ECCS Header Interconnection Line FIG NODALIZATION DIAGRAM FOR LARGE BREAK LOCA IAEA Workshop October 2-5, 212, Ottawa

43 IAEA Workshop October 2-5, 212, Ottawa

44 IAEA Workshop October 2-5, 212, Ottawa

45 RRS RPS Moderator PHT AR Position CR Position ZCC Levels SDS-1shutoff Rod Positions SDS-2 Liquid poison Levels Boron Conc (ppm) Mode. Temp Mode. Level Fuel Temps Coolant Temps Coolant Void Fraction N E U T R O N I C MODEL Neutronic Power Zonal Powers Lin-N Lo-N Rate Lo-N SPND Bulk Power Bulk Thermal Power Channel Powers Decay power Fuel Burnup Net(mk) xe VOIDS COOLANT TEMP FueL TEMP Moderator Temp RRS PHT DIS- PLAY IAEA Workshop October 2-5, 212, Ottawa

46 IAEA Workshop October 2-5, 212, Ottawa Method of Solution: Modal synthesis technique The space-time dependent distributions of neutron flux is expanded as a weihted series of fixed number of reactor modes which are linearly independent, with a set of time-dependent weihtin amplitudes M ( r, t) ( r) a m( t) m m The modes, satisfies the followin relation o ro o fo. D m + m ' m' = m ' m' ' ' The form of the factorization for Iodine and Xenon for the perturbed cross sections are substituted as follows

47 The eneralized point kinetics equations for the modal amplitudes and correspondin precursor concentration correspondin to each mode. a m t = ( sck m ) a m 1 m k mk a k i 6 1 i im( t) im( t) t = i a m ( t) m i im( t) I m (t) t = γ I a m (t) λ I I m (t) X m (t) t = γ x a m (t) λ I I m (t) λ X X m (t) σ 2X n M M A 1k 1 mnk X n (t)a k (t) IAEA Workshop October 2-5, 212, Ottawa

48 SOME LAMBDA MODES FOR 7 MWe PHWR IAEA Workshop October 2-5, 212, Ottawa

49 Zone Power Oscillations due to ZCC-1& 2 drainin at 55%FP (without FTC) IAEA Workshop October 2-5, 212, Ottawa

50 Modal amplitudes variations with time due to ZCC-1&2 drainin at 55%FP 3 (1) 1 (8) 6 (13) 4(11) 2 (9) 7 (14) 5 (12) Power tilt (%) with time due to ZCC-1&2 drainin at 55%FP

51 Zone Power Oscillations due to ZCC-1& 2 drainin at 1%FP (without FTC) IAEA Workshop October 2-5, 212, Ottawa

52 Fiure- Modal amplitudes variations with time due to ZCC-1&2 drainin at 1%FP 3 (1) 1 (8) 6 (13) 4(11) 2 (9) 7 (14) 5 (12) Fiure- Power tilt (%) with time due to ZCC-1&2 drainin at 1%FP

53 Fiure- Zone Power Oscillations due to ZCC-1 &2 drainin at 1%FP (with FTC)

54 Fiure- Modal amplitudes variations with time due to ZCC-1&2 drainin at 1%FP (with FTC) 3 (1) 1 (8) 6 (13) 4(11) 2 (9) 7 (14) 5 (12) Fiure- Power tilt (%) with time due to ZCC-1&2 drainin at 1%FP (with FTC)

55 IAEA Workshop October 2-5, 212, Ottawa