Some remarks on XS preparation with SERPENT

Transcription

1 Some remarks on XS preparation wit SERPENT E. Fridman Text optional: Institutsname Prof. Dr. Hans Mustermann Mitlied der Leibniz-Gemeinscaft

2 Outline Leakae-corrected omoenized XS XS preparation for non-multiplyin media Neutron multiplication due to n,xn reactions Pae 2

3 Pae 3 Leakae-corrected omoenized XS

4 Wy to introduce a leakae correction? (1) Heter. lattice transport calculations are performed to obtain: Σ r, φ r in roup, for every reion r wit volume V r Σ r, φ r, V r Σ r, φ r are omoenized into a system Σ, φ Via flux-volume and volume averain Σ = Σ r φ r V r Σ r V r Homoenized Σ : Represent te lattice To be collapsed into few-roup XSs Σ, φ Pae 4

5 Wy to introduce a leakae correction? (2) Lattice calculations are performed wit reflective BC Infinite lattice of identical cells k = k φ = infinite-medium flux Te actual operatin conditions are not known But are normally different from te infinite lattice conditions Due to te leakae effects Wat can we do? To assume tat te system is a part of a critical confiuration To force lattice k =1 To estimate te criticality spectrum to be used for XS collapsin How? By introducin a leakae model Pae 5

6 B 1 equations Criticality flux can be obtained by solvin B 1 equations Homoeneous, multi-roup, dimensionless 0 Σ t,φ Σs,' φ' ibj χ ' 1 3a Σt,J 3Σs,' J' ibφ were a ' B 1 equations derived assumin Te flux separability in space, and in enery and anle Linear scatterin anisotropy Te solution of B 1 equations yields: Flux and net-current spectra associated wit a bucklin B 2 Diffusion coefficients consistent wit linearly anisotropic scatterin Te criticality flux and current spectra are found iteratively By searcin B 2 wic yields k eff = 1 B1 solver is available in Serpent (version 1.14) f(b,σ t, ) Pae 6

7 Example case: simplified VVER-440 core Core data 2D confiuration 127 fuel assemblies No typical VVER-440 assembly sroud 90 reflector positions Reflector In tis example Serpent was used To provide a reference solution To enerate two XS sets: Inf and B1 Diffusion calculations are done by DYN3D Nodal diffusion code Usin two XS sets To compare K-eff Radial power distribution 3% UO 2 4% UO 2 Pae 7

8 Example result: Serpent vs. DYN3D B 1 XS Difference in radial power: Max.=1.6% RMS=0.5% Difference in k eff : Δk/k = -0.20% Inf XS Difference in radial power: Max.=13.5% RMS=6.1% Difference in k eff : Δk/k = 0.74% Pae 8

9 P1 vs. B1 diffusion coefficients 1 2 P B Rel. diff -21.9% -25.6% Pae 9

10 Pae 10 Reflector modelin

11 Generation of reflector XS for nodal codes Some backround To et a ood nodal solution one sould preserve: Node-averaed reactions rates (RR) Surface-averaed net leakae rates (LR) Tis is done via te use of: Flux-volume weited (FVW) XS Discontinuity factors (DF): DF = φ s et φ s om φ s et surface flux from eter. transport solution φ s om surface flux from omo. diffusion solution obtained wit FVW XS For a sinle reflected fuel assembly: φ s om can be replaced by averaed φ et (K. Smit) Tis is te way ow DF are calculated in Serpent Not valid for reflector reions Pae 11

12 Reflective Generation of reflector XS for nodal codes How it s done wit deterministic transport lattice codes Solve 1D eter. fuel-reflector (F/R) problem To obtain omoenized XS, F/R interface fluxes and currents Reflective Reflective J net Solve 1D omo. diffusion equation wit a fixed source Separately for te fuel and reflector reions Usin omoenized XS Usin net currents as a boundary condition To obtain diffusion surface flux J(0)=J net Calculate DF as a ratio between transport and diffusion surface fluxes Pae 12

13 Generation of reflector XS for nodal codes Estimation of te leakae rates in Serpent Homoenized XS are directly available Interface currents are not In Serpent tere is no MCNP F1-like surface current tally How to estimate te leakae? Via te use of MCNP not sustainable solution Via te nodal neutron balance Eleant solution - requires minor additional effort Proposed by Bryan Herman of MIT LR Σ t, φ G 1 υσ s φ χ k G 1 νσ f, φ Pae 13

14 Reflective Reflective Generation of reflector XS for nodal codes A test problem A sinle raw of PWR fuel assemblies wit reflector Serpent was used To enerate 2-G omoenized XS for te nodal diffusion code DYN3D To provide a reference solution Te compared parameters: K-eff Nodal power distribution Reflective 3.0% UO2 2.1% UO2 Reflector: Reflective H 2 O+structures Pae 14

15 Flux in te F/R reion Serpent direct Via diffusion flux DF DF Pae 15

16 Flux in te F/R reion k Serpent ±0.02% k DYN3D Δk/k -0.12% Pae 16

17 Generation of reflector XS for nodal codes Results of te test case k-eff Δk/k SERPENT DYN3D % σ k-eff =0.005% Pae 17

18 Pae 18 Neutron multiplication due to n,xn reactions

19 Neutron multiplication due to n,xn reactions Neutron balance for roup, leakae excluded: t,... a, n1n, n2n, n3n, Full inroup scatterin source G 1 n1n 2 G 1 n2n 3 G 1 n3n... 1 k Fission source G 1 f, In previous Serpent versions (before ver. 1.15): Only GTRANSFXS (roup transfer XS matrix) was available GTRANSFXS = Σ n1n Pae 19

20 Neutron multiplication due to n,xn reactions Te direct use of GTRANSFXS effectively means: t,... a, n1n, n2n, n3n, Full inroup scatterin source G 1 n,1n 2 G 1 n,2n 3 G 1 n,3n... 1 k Fission source G 1 f, Te question: ow to account for n,xn reactions (x>1) correctly? Pae 20

21 Neutron multiplication due to n,xn reactions Typical few-roup XS libraries used by nodal codes: Can contain only a sinle roup transfer XS matrix Some re-arranement of neutron balance equation is required 1. Lump all n,xn XS into te one production scatterin XS: s n1n 2n2n 3n3n Re-write Σ t in terms of υσ s and Σ n,xn Σ t Σ a υσ s (Σ n2n 2Σ n3n...) 3. Define a modified Σ a mod 2...) 4. Re-write te balance equation in terms of υσ s and modified Σ a a mod a, a ( n2n n3n s, G 1 s 1 k G 1 f, Pae 21

22 Neutron multiplication due to n,xn reactions Relevant modifications in few-roup XS in Serpent 1.15 Modifications GTRANSFXS now includes all n,xn reactions New XS types SCATTPRODXS = production scatterin XS (υσ s ) GPRODXS = production roup transfer XS matrix (υσ s ) RABSXS = modified absorption XS (Σ a mod ) Pae 22

23 Neutron multiplication due to n,xn reactions Numerical example Test case: typical PWR fuel assembly SERPENT MC k-inf Diff, pcm ± 7pcm - Neutron balance in 2 usin ABSXS + GTRANSFXS Neutron balance in 2 usin RABSXS + GPRODXS Pae 23

24 In deterministic codes From Helios metods: Pae 24

25 Summary In tis presentation you saw Some issues associated wit few-roup XS eneration As well as possible solutions Supported by numerical examples Serpent can be used for few-roup XS eneration For bot multiplyin and non-multiplyin media Future work Automatic scripts for brancin calculations and data manaement Generation of te data for transient nodal calculations Verification via existin numerical bencmarks RIA, boron dilution, etc Pae 25

26 Pae 26 Tank you!