Control Rod Homogenization in Heterogeneous Sodium-Cooled Fast Reactors. Mikael Andersson - Chalmers SNEC/SKC student/industry day, 14 June, 2016
Content M. Andersson Control rods in voided SFRs 2 / 12
Objective Neutronic modeling of control rods in axially-heterogeneous sodium-cooled fast reactors Recommend a quick and reliable procedure for control rod homogenization M. Andersson Control rods in voided SFRs 3 / 12
Motivation - for fast reactors Superphe nix start up tests Overprediction 7-25% in CRW Heterogeneity and diffusion theory New methods ± 5% J.C. Gauthier, J.C. Cabrillat, G. Palmiotti, M Salvatores, Measurement and Predictions of Control Rod Worth, Nucl. Sci. Eng. 106, 18-29, 1990 M. Andersson Control rods in voided SFRs 4 / 12
Old and new axial design of SFR Superphénix like core CFV (ASTRID) like core Can we model the control rod correctly, predicting control rod worth, boron absorption and local pin powers? M. Andersson Control rods in voided SFRs 5 / 12
Control rods in SFR Assembly size Natural or enriched Boron carbide in steel cladding Power shaping, reactivity compensation & shutdown M. Andersson Control rods in voided SFRs 6 / 12
Work outline M. Andersson Control rods in voided SFRs 7 / 12
Fertile Fissile Control rod partitioning In total 27 sets of cross sections (CSDs only), 54 sets for both voided and nominal cases S abs/driver 8Driver C 48 Na Plenum Ep I p/f I f/p Cn enrichment - Control rod segment Environments Ef - Fissile Ep - Plenum S 48/na C7 48 Ef Eb - Fertile blanket S na/48 C6 na C5 na I f/b Interface Environments I f/p - Fissile/Plenum (in Fissile) C4 na Fertile I b/f Eb I p/f - Plenum/Fissile (in Na plenum) C3 na C2 na Fissile I f/b Ef I f/b - Fissile/Fertile blanket (in Fissile) I b/f - Fertile blanket/fissile (in Blanket) 10 cm S abs/follower C1 na I f/b z Follower Internal Control rod interfaces S abs/follower - Absorber/Follower interface S abs/driver - Absorber/Driver interface S enr1/enr2 - Enrichment interfaces M. Andersson Control rods in voided SFRs 8 / 12
S-curve - Deviation in control rod worth from Monte Carlo Nominal Voided M. Andersson Control rods in voided SFRs 9 / 12
Main discrepancy - The Follower/Absorber interface Spectral hardness (red hard spectrum, blue soft spectrum) M. Andersson Control rods in voided SFRs 10 / 12
Summary What has been done? 3D generated homogeneous control rod cross sections for core calculations for a CFV core Main findings - traditional vs. environmentally corrected generated control rod cross sections Control rod worth In general good agreement At certain positions (close to the plenum), the 3D effects are important Future? Experimental validation of the 3D effects M. Andersson Control rods in voided SFRs 11 / 12
Thank you!
Publications M. Andersson, et al. Control rod homogenization in fast reactor environments. Part I: Classification of axial spectral regions. Nucl. Sci. Eng. submitted M. Andersson, et al. Control rod homogenization in fast reactor environments. Part II: A 3 dimensional assessment. Nucl. Sci. Eng. submitted M. Andersson, D. Blanchet, H. Nylén, and R. Jacqmin. Infuence of local spectral variations on control-rod homogenization in fast reactor environments. Nucl. Sci. Eng. 181.2 (2015), pp. 204-215 M. Andersson, et al. Impact of control rod position and homogenization on sodium void effect in CFV-type SFR. in: PHYSOR. Idaho Falls, USA: American Nuclear Society, May 2016 M. Andersson, et al. Impact of 3D modeling and homogenization of control rod on reactivity in CFV-type SFR cores. In ANS winter meeting,washington DC, USA, November 2015. American Nuclear Society M. Andersson, et al. Control rod modeling in axial heterogeneous fast sodium cooled reactors. In The 17th meeting on Rector Physics in the Nordic Countries, Gothenburg, Sweden, May 2015. Chalmers M. Andersson, et al. Influence of local spectral variations on control-rod homogenization. In International Youth Nuclear Congress, Burgos, Spain, July 2014. IYNC
Capture rates 180 cm 120 cm
Error in Power in neightboring Fuel subassembly 180 cm 120 cm
Cross-section calculation Capture cross section Σ c,hom = dv Σhet dωψhet ψ + hom dv dωψhet ψ + hom Scattering cross sections Σ g g s,hom = V dv Σg g s,het ( (4π) d2 Ω ψ g het (4π) d2 Ω ψ +g hom ) V dv ( (4π) d2 Ω ψ g het (4π) d2 Ω ψ +g hom Within group scattering cross sections ( V Σ g g dv Σg g s,hom = s,het (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het ( V dv (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het ) Total cross section Σ t,hom = Σ c,hom + g Σ g g s,hom
Fix-ups Handle the negative self scattering term w/o fixup: Σ g g s,hom = with fixup: Σ g g s,hom = ( V dv Σg g s,het (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het ( V dv (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het ( V dv Σg g s,het (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het ( V dv (4π) d2 Ω ψ g het ψ+g hom (4π) d2 Ω ψ +g hom (4π) d2 Ωψ g ) het Handle negative fluxes (for all integrals) w/o fixup: Σ c,hom = with fixup: Σ c,hom = dv Σhet dωψhet ψ + hom dv dωψhet ψ + hom ψhet dv Σhet dω ψ hom + ψhet dv dω ψ hom +
Comparing with ERANOS ERANOS and PARIS (with absolute values on self scattering)
Individual contributions 180 cm XS set δ CRW [%] T4-1866 pcm 2D -4.1 abs/follower -1.1 Na Plenum -5.1 Full 3D -2.1 120 cm XS set δ CRW [%] T4-3999 pcm 2D -0.02 abs/follower 0.1 Fertile blanket -0.2 B(nat) B48% -2.1 Full 3D -2.3 Large impact for internal control rod interfaces Small impact for core environments
Fine partitioning in the plenum Large discrepancies found in the sodium plenum for 3D procedure Main cause, the 10 cm partitioning. Table: Difference in reactivity at the 210 cm control rod position (nominal). C2 na 10 cm C1 na Follower 2.5 cm Cross section set δ CRW [%] 2D 1.5 3D (10 cm) mesh 5.8 3D (2.5 cm) mesh 1.7
Range of the spectral dependencies? 2D models to determine the range Spectral indicators r = σu238 c φ σf u235 φ Homogeneous macroscopic reaction rates R = Σ hom x φ
Follower absorber interface Long range Large differences at interface
Core environments (1) Changes all over! Irregularities at the interfaces
Core environments (2) Main change: about 5 cm from interfaces Much smaller impact than internal interfaces
Adjoint flux, and partitioning size 5 cm region 10 cm region
Capture rates 210 cm
Capture core, 2D
Total follower/absorber interface, 2D
Enrichment boundary, indicators
Enrichment boundary, capture 2D
Enrichment boundary, total 2D