MOC BASED CALCULATION SCHEMES IN APOLLO2 · PDF fileMOC BASED CALCULATION SCHEMES IN APOLLO2 FOR GENERATION OF CROSS-SECTION LIBRARIES FOR VVER G.Todorova*, N. Kolev, N.Petrov, N.Zheleva

MOC BASED CALCULATION SCHEMES IN APOLLO2 FOR GENERATION OF CROSS-

SECTION LIBRARIES FOR VVER

G.Todorova*, N. Kolev, N.Petrov, N.Zheleva

Institute of Nuclear Research and Nuclear Energy, Bulgaria* Varna Free University

BgNS International Conference “NUCLEAR POWER FOR THE PEOPLE”8 – 11 November 2011 Bansko, Bulgaria


OUTLINE

1. Objectives

2. APOLLO2 MOC calculation schemes

3. Verification of the schemes

4. XS library generation

5. Conclusions


OBJECTIVES

Implement MOC based calculation schemes in APOLLO2 for XS library generation for VVER

Validate calculation schemes

Generate few-group diffusion XS libraries at the nodal and pin level

Validate the libraries


APOLLO2 code system

Developed by CEA France

Current version: APOLLO v2.8.3:

transport code with CP and MOC solvers

Latest implementation for VVER includes:

CEA2005 v4.1/JEFF3.1.1 data libraries

281g SHEM energy mesh

Capability to provide CDF for hexagonal cells


INRNE experience since 2006

APOLLO2 was implemented for VVER calculations in the frameworks of the NURESIM and NURISP EU projects

VVER assembly problem

VVER-1000 whole core problem - benchmarks

XS library generation at the nodal level

2D limited scope XS library generation

3D XS library - spectral effects are taken into account through node-by-node depletion at local TH parameters (Tm, Dm, Tf), for 30 axial nodes

Pin-by-pin library - ongoing


XS generation methodology - requirements

The XS generation methodology should meet the following requirements:

Verified calculation route – step by step vs. MC reference

Calculation efficiency – introducing advanced A2 calculation schemes and MOC solvers

Covering wide range operating parameters space

Library format :

Code independent NEMTAB like format

Applicable for specific diffusion code


A2 calculation schemes

Elementary cells definition

Update at burnup steps

OUTPUT

Exact unstructured geometry

Assembly geometry structured geometry

Self‐shielding – CP 281g

Flux recalculation – CP 281g

A2 internal library

Convectional scheme in A2 (used in 2D nodal ):

MOC calculations

Optional group collapsingThis scheme applies CP method in the burnup evolution cycle. It was used in the earlier VVER assembly and core calculations


Advanced A2 calculation schemes

Reason to introduce:To improve the accuracy by implementing MOC during the burnup evolution

BUTXS library generation requires large amount of calculations –branching – the calculation efficiency is essential

Difficulties: SS and flux are many times recalculated during the burnup

evolution updating the A2 internal librarySS requires 281g CP calculations281 g MOC is too time consuming

The advanced two-level calculation scheme (2L):Meets requirementsAvoids the difficulties


Two level scheme in APOLLO2

Originally developed by CEA for PWR assembliesImplemented for hexagonal geometry – INRNEMain features in burnup (fixed parameter conditions)

First level (281g CP for self-shielding)Second level (37g MOC, exact geometry)Efficient procedure for first level media update from the secondlevel concentrationsSave media at burnup steps

Main features in branching calculations (fixed burnup level)Media from stored filesCycle over parameters

SS at actual TH state parameters - 281gMOC solution – 37/281gXS space and energy homogenizationOutput in HDF or ASCII format

VVER-1000 reference and optimized scheme

Reference scheme: for reference transport solutionsFirst level

281g15 fuel media grouping in assembly

Second level281g MOCRefined cell models

Optimized scheme: for XS library generationFirst level

281g6 fuel media grouping in assembly

Second level37g MOCCoarse/refined cell models depending of MOC solver LS MOC/Step MOC (two MOC solvers are available in A2)


VVER-1000 assembly

LATTICE FEATURES:Triangular (hex) lattice pitch: 1.25 cm•Assembly pitch: 23.6 cm•1 mm water reflector(2 mm inter-assembly water gap) •Number of fuel pins: 312 •Number of CR guide channels: 18•Instrumentation tube: 1•Total number of cells: 331•Hexagonal cell side: 0.73612 cm•Fuel pellet radius: 0.3785 cm•Inner/outer clad radius: 0.386/0.455cm •Cold service dimensions assumed


Pin – cell types

5 different types of pins:Fuel cell (FC)CR guide tube with absorber (CR)CR guide tube (GT)CR guide tube with burnable absorber (BA)Central instrumental tube (CT)

FC GT CT

CR BA


Spatial discretization

1/6 VVER-1000 fuel assembly.

404 regions, used with LS MOC

1/6 VVER-1000 fuel assembly.

2254 regions, used with Step MOC


Validation of the APOLLO2reference and optimized solutions vs.T4 solutions

Case A2 A2-T4 Δρ

k-infinity δk (pcm) 1/kref-1/k (pcm)

TRIPOLI4 1.29400 ±0.00004 - -

MOC, 281g, 2254 regions 1.29435 35 21

MOC, 281/37g, 2254 regions 1.29568 168 100

LS MOC, 281g, 404 regions 1.29391 -8 -5

LS MOC, 281/37g, 404 regions 1.29564 165 98


reference and optimized schemes validation

SOLVERTRIPOL4 A2

reference 2L MOC

k inf1.29400± 4 pcm 1.29435 1.29568

δ(1/k) = 1/kref-1/k, pcm - 21 100Pin fiss. rate δ max,% - 0.12 0.11Pin abs. rate δ max,% - -0.28 -0.43

A2 reference and optimized schemes vs TRIPOLI4 solution at BU=0


Case A2 A2-T4

k-infinity δk (pcm) 1/kref-1/k (pcm)

MOC, 281/37g , 15 media, 2254 regions 1.29568 168 100

MOC, 281/37g , 6 media, 2254 regions 1.29577 177 105

Effect of media grouping in the first level

2L scheme, refined MOC geometry, BU = 0


Advantage of 2L MOC scheme in burnup

Bias (1/kref‐1/k) of 2L MOC and Pij vs. MOC 281g results


Biases of 281/37g LS MOC vs TRIPOLI4 ref. solution.

Bu=31 MWd/kgHM, 404 regions

2L MOC calculation efficiency

Calculation scheme 281g MOC P0* 2L MOC P0* Time gain factorSolver CPU time, s 40194 (11h) 1819 (0.5h) 22Total calculation time, s 43221 (12h) 5727 (1.6h) 7.5Self-shielding time, s 557 557 -

CPU time for burnup calculation from 0 to 31 MWd/kgHM

Calculation schemeAnisotropy

281g MOC P0*

2L MOCP0*

Time gain

factor

281g MOCP1

2L MOCP1

Time gain factor

Solver CPU time, s

182 23 8 284 32 9

Self-shielding time, s

15 15 - 15 15

CPU time for one solver iteration

Times for 281g MOC and 2L MOC. The calculations are performed on a dual core 2.4

GHz ATHLON 64 with DDR 400MHz and FSB 800 MHz.


MOC calculation parameters for XS library generation

Calculation parameters 2L scheme

Azimuthal angles (Nφ) 24Tracking step 0.04 cm

Polar angles (Nψ), Bickley quadrature 3

Degree of scattering anisotropy (CP) P0*

Degree of scattering anisotropy (MOC) P0*

Degree of scattering anisotropy (MOC) (option) P1

Surface subdivision factor for LS MOC 6

User specified threshold size for surface subdivision when using LS MOC 0.74 cm


Simultaneous calculations on multi-processor system

DEPLETIONEach axial node is calculated on different processor at given parameter conditions

BRANCHINGEach parameter state is calculated on different processor

POST-PROCESSINGDepending on output data format:txt format – NEMO2 post-processing tool – MEMTAB format

HDF format – scripts to convert into NEMTAB- like format for COBAYA3


Nodal 2G diffusion XS library for MSLB analysis

ScopeSpecs as in the OECD VVER-1000 MSLB benchmarkTable interpolation type - NEMTAB formatWide range in TH (Tf, Tm,Dm); given EOL Cb and target burnup3D burnup for Kozloduy-6, Cycle 8 at 270.4 EFPD

TestingTested in steady state in 2D and 3D core diffusion calculations, vs.

A2 whole core solution, vs. 3D solutions with HELIOS generated XS libraryTested vs. plant data at 92% hot power, 270.4 EFPDTested in transient MSLB calculations in COBAYA3/FLICA4 vs.

DYN3D –FLICA calculations

VVER-1000 MSLB nodal XS library

Assembly #5, enrichment 4.4 w/o, twice burnt, 27.04 MWd/kgU4.4w/o

Reference core


Number T-H conditions Control rod positions Scenario

0 HZP Groups 1-10 ARO 11a HZP (near critical) Groups 1-5 up, 6 -81% wd,

7-10 down1

1b HZP Groups 1-10 ARI 12 HFP Groups 1-9 ARO,

group 10 is 80% wd1

3 HZP Groups 1-10 ARI#90 is 100% wd

1


1


2

6 HZP Groups 1-10 ARI#117 & #140 are 100% wd

2

Definition of the steady states for 3D solutions


V1000-MSLB, HZP at 470K, ARO: 2D core

Difference of COBAYA3 - TRIPOLI4 results2G XS from whole core A2 calculation. δk = +109 pcm


V1000-MSLB-C, HZP, ARO: 2D core solutions

COBAYA3 vs.TRIPOLI4 results8 radial reflector nodes with XS from whole core A2 calculation


COBAYA/A2 vs. COBAYA/HELIOS calculated assembly powers

HZP state 0 (ARO): 3D library

-2,570,573

28

-2,090,774

27

-2,040,767

18

-2,530,570

13

-1,251,071

26

2,470,875

1

2,650,959

2

1,021,272

3

0,151,341

4

-0,011,192

5

1,740,817

6

-1,740,860

71,13

1,2208

1,481,130

9

0,851,123

10

1,300,958

11

-1,221,060

121,48

1,13214

1,710,985

15

1,200,977

16

-1,381,181

170,83

1,13419

0,621,026

20

-0,121,061

21

-2,380,821

221,04

0,99323

-1,411,198

24

-2,400,825

25


Core-averaged axial power distribution in HZP state 0

HZP state 0 (ARO): 3D library

0,000

0,500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350

Axi

al p

ower

pro

file

Elevation, cm

DYN3D

COBAYA

COBAYA-A2


Parameters DYN3D COBAYA/HE COBAYA/A2

Keff 1.02988 1.03006 1.02994

Fxy 1.337 1.334 1.341

Fz 2.949 2.947 2.985

COBAYA/A2 vs. COBAYA/HE calculated assembly powers Control rods 81% wd - marked in blue

HZP state 1a: 3D library


HZP state 1a: 3D lybrary

0,000

0,500

1,000

1,500

2,000

2,500

0 50 100 150 200 250 300 350

Axi

al p

ower

pro

file

Elevation, cm

CRONOS

COBAYA

COBAYA-A2


Parameters CRONOS COBAYA/HE COBAYA/A2

Keff 0.99745 0.99773 0.99793

Fxy 1.410 1.418 1.415

Fz 1.863 1.871 1.951

Core-averaged axial power distribution in HZP state 1a

Groups 1-5 up, 6 -81% wd, 7-10 down

COBAYA/A2 vs. COBAYA/HE calculated assembly powers

HZP state 1b (ARI): 3D library


CONCLUSIONS

APOLLO2.8 MOC‐based calculation schemes were applied for VVER

XS library generation at the nodal level

The accuracy of the 281/37g MOC scheme is comparable to that of

281g MOC while the computation time is strongly reduced. The

scheme is appropriate for XS library generation

Application in parallel (simultaneous) calculation mode has been

successfully tested

APOLLO2 generated XS libraries at the nodal level have been

successfully tested in lattice and core calculations



Documents

MOC BASED CALCULATION SCHEMES IN APOLLO2 · PDF fileMOC BASED CALCULATION SCHEMES IN APOLLO2 FOR GENERATION OF CROSS-SECTION LIBRARIES FOR VVER G.Todorova*, N. Kolev, N.Petrov, N.Zheleva