slide 1VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Reactor Physics Analysisof the VHTGR Core

Oak Ridge National LaboratoryDecember 2-3, 2004

Wei Ji, Jeremy L. Conlin, William R. Martin, and John C. LeeNuclear Engineering and Radiological Sciences

University of Michiganwjiz@umich.edu

slide 2VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Introduction

This is one of the tasks of the I-NERI projectI-NERI Project: Develop safety analysis codes and experimental validation for the VHTGR Develop reactor physics models for power distribution and decay heatPerform coupled neutronic/thermal-hydraulic analysis of VHTGR

slide 3VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Development of MCNP models

Detailed microsphere models for analysis of double heterogeneityAssembly-level model for analysis of detailed geometryFull-core models for global calculations of flux and power distributions

slide 4VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

VHTGR fuel (from General Atomic)

slide 5VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

MCNP5 Simulations of Microsphere Cells

Single microsphere cell consists of fuel microsphere and graphite matrix to yield packing fraction = 0.289Enrichment=10.36%Microsphere cell is either heterogeneous (explicit modeling of all regions: fuel kernel, carbon buffer, SiC, and inner/outer pyrolytic carbon shells) or homogenized mixture of microsphere and graphite matrixAnalyzing two region microsphere cell: fuel kernel and remainder of microsphere/graphite matrixReflecting boundaries on six surfaces of cube

slide 6VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

Sensitivity calculation – thermal expansionThermal expansion of graphite taken from CERN report (temperature dependent)MCNP full core calculation (hexagonal block core with reflectors and homogeneous blocks)All linear dimensions multiplied by All densities divided by Results indicate thermal expansion is negligible:

1+ α∆T3(1 + α∆T)

0.00076 1.43788 2000 C

0.000811.43800 1000 C

0.00094 1.43953 Room temp

std devkeffCase

slide 7VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Microsphere cells – microsphere in graphite matrix cube

Fully Heterogeneous Homogeneous

Reflecting b.c. on all sides of cubes

Two-Region Heterogeneous

slide 8VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

MCNP5 Simulations of Microsphere Cells

.00031.1533CenteredFully heterogeneous microsphere cell

.00041.1535CenteredTwo-region heterogeneous microsphere cell

.00041.1515RandomFully heterogeneous microsphere cell (LANL)

.00041.0995- - -Homogeneous microsphere cell

std devkeffKernel location

Configuration

Essential to model the microsphere heterogeneity(at least the fuel kernel portion of the microsphere)

slide 9VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

Alternative method – using modified version of MCNP5 to treat stochastic geometry

Forrest Brown - head of Los Alamos MCNP teamModified MCNP5 to effectively move the microsphere randomly within the graphite cube every time the neutron crossed the cell boundaryAnalyzed a 5x5x5 array of heterogeneous microsphere cells with reflecting b.c. on all sides – used UM dataCompared with 25 realizations of an explicit 5x5x5 simulation with randomly oriented spheres

*Forrest B. Brown and William R. Martin, “Stochastic Geometry in MCNP5,”submitted to Winter 2004 ANS Conference in Washington, DC, LANL report LA-UR-04-4432, June 2004.

slide 10VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

5x5x5 lattice of cubic microsphere cells

- Reflecting b.c on all sides- Spheres randomly oriented wholly within graphite cubes- “On the fly” randomizationversus 25 realizations of 5x5x5 lattice

slide 11VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

LANL MCNP5 simulation results

.00051.1513RandomMultiple (25) realizations of 5x5x5 cells

.00041.1515Random –on the fly

5x5x5 lattice of heterogeneous microsphere cells

.00111.1537CenteredSingle heterogeneous microsphere cell (UM)

.00041.1531Centered5x5x5 lattice of heterogeneous microsphere cells

std devkeffKernel locations

Configuration

slide 12VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Microsphere cells– multi-group radial flux profiles analysis

Fully Heterogeneous

Reflecting b.c. on all sides of cubes

Two-Region Heterogeneous

slide 13VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Radial neutron flux profile in a fully heterogeneous microsphere cell

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 0.003 0.005 0.008 0.01 0.013 0.015 0.018 0.02 0.023 0.025 0.028 0.03 0.033 0.035 0.038 0.04 0.043 0.045 0.048 0.05Radius (cm)

Neu

tron

flux

(/cm

2/pa

rticl

e) (l

og sc

ale)

0-1.4ev 1.4ev-6.17ev6.57ev-6.77ev 6.77ev-0.1Mev 0.1Mev-20Mev

slide 14VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Comparison of the radial neutron flux profiles in resonance energy range 6.57ev - 6.77 ev

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

7.00E+01

8.00E+01

9.00E+01

1.00E+02

1.10E+02

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Radial bins (cm)

Flux

(/cm

2) heterogeous case

two-region case

slide 15VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Neutron spectra in microsphere regions

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+10

1.00E+11

1.00E-09 1.00E-08 1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02

Energy (Mev)

Neu

tron

Flux

(/cm

2/pa

rtilc

e)

Region 1 spectrumRegion 2 spectrumRegion 3 SpectrumRegion 4 SpectrumRegion 5 SpectrumRegion 6 Spectrum

slide 16VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Preliminary conclusions – heterogeneous microsphere cells

Essential to model the detailed geometry of the microsphereThe location of the microsphere within the graphite cube has .2% effect on keff – for the infinite lattice of microspheresThe microsphere is small neutronically for all neutrons except resonance neutronsShould be OK to treat only the fuel kernel and homogenize the outside layers of the microsphere with the graphite matrix

slide 17VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

MCNP5 Simulations of Fuel Compact Cells

Fuel compact and corresponding graphite block (boron-10: 6.9ppm)Hexagonal graphite block with cylindrical fuel regionFuel region consists of cubical microsphere cells (homogeneous and heterogeneous)Cubical microsphere cells “clipped” by cylindrical fuel boundaryCoolant holes and inner/outer/axial reflectors are not represented in the fuel compact cell – only the relative changes in keff are significant

slide 18VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Fuel compact cells – graphite block with microsphere cells

Reflecting b.c. on all surfaces of fuel compact cell

Fully Heterogeneous HomogeneousTwo-Region Heterogeneous

slide 19VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

MCNP5 Simulations of Fuel Compact Cells

.0004

.0004

.0004

std dev

1462.441.3408Two-region heterogeneous case

2872.421.3401Fully heterogeneous case

359.261.2885 Homogeneous case

time (min)keff*fuel compact

The same conclusion: essential to model the microsphere heterogeneity (at least the fuelkernel portion of the microsphere)

*These configurations do not account for coolant holesor reflector regions – change in keff is important

slide 20VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Full core reactor – double heterogeneity

Fuel compact

Microsphere particle

Full core

Fuel block

slide 21VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

MCNP5 Simulations of the Full Core

.0003

.0004

.0001

.0002

std dev

2272.511.0949Doubly heterogeneous-two region

663.741.0583Fuel block-level heterogeneous case

4847.451.0949Doubly heterogeneous-fully

250.241.0153Homogeneous case

time (min)kefffull core

The same conclusion: essential to model the microsphere heterogeneity (at least the fuelkernel portion of the microsphere)

slide 22VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Coupled Nuclear-T/H Calculations

Need to represent feedback effect of axial temperature rise of 350 K on VHTR core power distribution. Used a pseudo-material scheme to interpolate MCNP cross section libraries at a few temperature points. Used homogenized assembly model in 12 axial zones and 3 rings (30/37/36 assemblies) with MCNP5. INEEL provided UM access to RELAP5/ATHENA. Performed 4 iterations between MCNP5 and RELAP5.

slide 23VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

Pseudo-materials

MCNP5 cross section data only provided at specific temperatures, e.g., 294K, 500K, 600K, 900K, and 1200KCoupled neutronic/T-H feedback calculations will require cross sections in the range 294K-1400K or higherPseudo-materials are proposed by mixing generated cross sections linearly with temperatureExample: to get a material at 1000K, create a mixture consisting of 2/3 of material at 900K and 1/3 at 1200KA Python script was written that reads in temperatures and existing libraries and generates material data cards that can be used directly in the MCNP5 input file

slide 24VHTGR Neutronic Analysis | Bill Martin | University of Michigan | 7-6-04

Comparison of keff with pseudo-materials

1.32

1.34

1.36

1.38

1.4

1.42

1.44

1.46

250 350 450 550 650 750 850 950 1050 1150 1250

Temperature (K)

ke

ff

Normal Materials

Pseudo Materials

slide 25VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Axial power distribution in the middle core ring

0 .010

0 .015

0 .020

0 .025

0 .030

0 .035

0 .040

0 .045

0 .050

0 1 2 3 4 5 6 7 8 9 10

A x ia l H e igh t (m )

Po

wer

fract

ion

Itera tion 0Itera tion 1Itera tion 2Itera tion 3Itera tion 4

slide 26VHTR Reactor Physics Analysis | Bill Martin | University of Michigan | 12-03-04

Conclusions and future work

Critical to model double heterogeneity of the fuel microspheresMay be sufficient to treat only the fuel kernel portionCoupled neutronic/T-H calculations are more slowly converging than originally envisionedNeed to study further the effects of criticality calculations due to the stochastic distribution of the microsphere fuel particles