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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
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