NEUTRON NOISE CALCULATION IN A LARGE SFR CORE AND ANALYSIS OF ITS PROPERTIES
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1 NEUTRON NOISE CALCULATION IN A LARGE SFR CORE AND ANALYSIS OF ITS PROPERTIES Florian Zylbersztejn CEA, DEN, Cadarache, DER/SPEx/LDCI Christian Jammes, Philippe Filliatre. CEA, DEN, Cadarache, DER/SPEx/LDCI Imre Pazsit, Hoai Nam Tran, Paolo Vinai, Christophe Demazière. Chalmers, Nuclear Engineering 30 OCTOBER OCTOBRE 2012 PAGE 1
2 SOMMAIRE TABLE OF CONTENTS: Introduction & ESFR core 1) Reminder of the Neutron noise equations 2) Verification of the CORESIM code 3) Neutron noise calculations: results and analysis Conclusion 30 OCTOBRE 2012 PAGE 2
3 INTRODUCTION Context: Renewal of the fast reactors field with the Generation-IV international forum. Project of industrial prototype (Astrid) by the CEA in France. The next generation of SFR must have improved safety requirements on every topics. Neutron noise simulation: Not explored enough for fast systems. Enhance neutron diagnosis to improve the safety. Development of CORESIM 30 OCTOBRE 2012 PAGE 3
4 1) REMINDER OF THE NEUTRON NOISE EQUATIONS General operator form of diffusion equation : 1 d ( v dt 1 + B) φ = Pφ + k eff Static flux calculation: eigen-values problem Noise equations : source problem in complex formalism Similar equations: same solving algorithm. S 1 D δφ r ω + ω δφ r ω = χ ω ν δφ r ω + δφ r ω + S r ω (, ) ( ) (, ) ( ) (, ) (, ) (, ) 2 g g t, g g g f, g' g' s, g' g g' keff g' g g' g 1 Sg r r r r ( ω) = δ ( ω) φ ( ) + δ ( ω) φ ( ) + χ ( ω) δν ( ω) φ ( ), t, g g s, g' g g' g f, g' g' g' g keff g' g Results of neutron noise: good as long as static flux calculations are good 30 OCTOBRE 2012 PAGE 4
5 MAIN FEATURES OF CORESIM Some characteristics: Solving diffusion equations for static and dynamic states (i.e. noise in frequency domain). 3-D, multi-energy groups, multi-groups of delayed precursors. Finite differences for spatial discretization. Power iterative solution for both static and noise solutions. CMFD acceleration for both static and noise calculations. Language: Matlab scripts. 30 OCTOBRE 2012 PAGE 5
6 GENERAL LAYOUT OF THE ESFR CORE Model chosen for this study: ESFR core Optimized large fast neutron reactor. Core characteristics close the newest core designs. 30 OCTOBRE 2012 PAGE 6
7 2) VERIFICATION OF THE CORESIM CODE Results of static calculations: Comparison with ERANOS: CEA code suite widely validated from integral measurements. Conditions of calculations: Same core model (macro XS) ERANOS: Transport / CORESIM: diffusion Eigenvalue ERANOS Noise simulator k eff OCTOBRE 2012 PAGE 7
8 NEUTRON FLUX SPATIAL DISTRIBUTION Fast groups Thermal groups 30 OCTOBRE 2012 PAGE 8
9 COMPARISON OF NEUTRON FLUX SPECTRA 30 OCTOBRE 2012 PAGE 9
10 COMPARISON OF POWER DISTRIBUTION # ERANOS results # Relative error (%) Difference of power distribution shape: Boundary conditions 30 OCTOBRE 2012 PAGE 10
11 3) NEUTRON NOISE CALCULATIONS: RESULTS AND ANALYSIS Scenario of perturbation: boiling Cross section perturbation: generated with ERANOS Realistic frequency content: white noise [0.1Hz-10Hz] Neutron noise source: Each kind of cross section 30 OCTOBRE 2012 PAGE 11
12 NEUTRON NOISE EVALUATION FROM BOILING SOURCE Source position Fuel C1 Results of Neutron noise: Spatial dependence of the amplitude. Frequency dependence. Evolution of the phase. Fuel C2 Reflector 30 OCTOBRE 2012 PAGE 12
13 NOISE AT LOW FREQUENCY: DEVIATION FROM POINT KINETIC Frequency = 0.01 Hz 30 OCTOBRE 2012 PAGE 13
14 NOISE AT HIGHER FREQUENCIES Frequency = 1.0 Hz Frequency = 100 Hz 30 OCTOBRE 2012 PAGE 14
15 RADIAL NEUTRON NOISE EVOLUTION Fast group Epithermal group 30 OCTOBRE 2012 PAGE 15
16 ANALYSIS OF THE RESULTS OF CALCULATIONS δφ( r, E) CORESIM system code: provide and the phase. The 33 group energy-dependant noise: interesting for the understanding of the physical processes. f 0 Hz : Shape of the neutron noise shape Static flux shape. f : Shape of the neutron noise shape Only a localized component. To compute the measurable neutron noise : integration over a detector XS. Provide the measurable localized components of the neutron noise. Cross section perturbations: realistic model, for energy dependence & amplitude. δφ Φ The relative noise : correct order of magnitude of noise measurement. These calculations could greatly help the neutron noise interpretation. 30 OCTOBRE 2012 PAGE 16
17 MEASURABLE NEUTRON NOISE: SPATIAL DEPENDENCE Source location: first assembly ring Small amplitude: 10% boiling Typical frequency: 1Hz The localized measurable component is not very visible. 30 OCTOBRE 2012 PAGE 17
18 RELATIVE MEASURABLE NEUTRON NOISE: SPATIAL DEPENDENCE The deviation from static flux shape become more visible. The relative amplitude of the noise stabilize to 0.95 % 30 OCTOBRE 2012 PAGE 18
19 MEASURABLE NEUTRON NOISE: SPATIAL DEPENDENCE Another location: at power peak Higher amplitude: 50% boiling Typical frequency: 1Hz The localized measurable component is more visible. 30 OCTOBRE 2012 PAGE 19
20 RELATIVE MEASURABLE NEUTRON NOISE: SPATIAL DEPENDENCE The deviation from static flux shape become visible. The relative amplitude of the noise stabilize to 0.56 % 30 OCTOBRE 2012 PAGE 20
21 CONCLUSIONS The new CORESIM system code: Solving algorithm: Verified with the reliable Ecco-Eranos code. Solve the neutron noise equations: 1rs order perturbations & diffusion. Estimation of the δφ(r,e,ω) neutron noise: Any scenario of oscillating perturbations. 33 group energy meshing: better understanding. Applications for neutron diagnostics. Conclusion on sodium boiling results: Appearance of a localized component in the core. Noise level at detection location can be calculated. No localization possible from out core monitoring Physical model of perturbation can be improved. 30 OCTOBRE 2012 PAGE 21
22 Thank you for you attention 30 OCTOBRE 2012 PAGE 22
23 30 OCTOBRE 2012 PAGE 23
24 30 OCTOBRE 2012 PAGE 24
25 TITRE INTERCALAIRE PAGE OCTOBRE 2012
26 TITRE DE LA DIAPOSITIVE Sous-titre Sandipis cilismo dionseq uiscili smodiamet, secte doloreet,vulputem volore modionsed tat : equisnumipit alis nos exerosalis amcore feuguevercillamet aliquis dolessit veliquat lut ver ipsusciliquat. Amvelessequis adiamiriusciniam, velisat. Docommy nullaor eratuersimvent wis non enibh esto odolor sent loreet incipsum vent at, consequatametue feu facitatummynibh exer sumvel ut la consequatue dipit aliquamet lumsan eui blam et iriure feugiatpraesse quipis nosnos nulluptating eumvelenimquat wisdelestrud tateet adipea feu facillaore tin vel do od dolorperilit prat diatum ing ea acilit am alit - sed tet, sissendiam eum zzrit - quatinisim eraestrud min hendipitnibh - euis ex exero consectecommynos dolorem nisisalisissed 30 OCTOBRE 2012 PAGE 26
27 TITRE DE LA DIAPOSITIVE Sous-titre Sandipis cilismo dionseq uiscili smodiamet, secte doloreet,vulputem volore modionsed tat. Amcore feuguevercillamet aliquis dolessit veliquat lut ver ipsusciliquat. Amvelessequis adiamiriusciniam, velisat. Docommy nullaor eratuersimvent wis non enibh esto odolor sent loreet incipsum vent at, consequatametue feu facitatummynibh exer sumvel ut la consequatue. Esto odolor sent loreet ecte doloreet,vulputem volore modionsed tat. 30 OCTOBRE 2012 PAGE 27
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