1. Evaluation of HEU-Beryllium
Benchmark Experiments to
Improve Computational
Analysis of Space Reactors
John D. Bess
Idaho National Laboratory
Keith C. Bledsoe
www.inl.gov
Bradley T. Rearden
Oak Ridge National Laboratory
Nuclear and Emerging Technologies for Space (NETS-2011)
February 7-10, 2011, Albuquerque, NM
This paper was prepared at Idaho National Laboratory for the U.S. Department of
Energy under Contract Number (DE-AC07-05ID14517)
2. Background for Current Work
• Parry, J. R., Bess, J. D., Rearden, B. T., and Harms, G. A.,
“Assessment of Zero Power Critical Experiments and Needs for
a Fission Surface Power System, NETS 2009, Atlanta, GA, June
14-19, 2009.
• Evaluation of current computational modeling capabilities and
biases
• Minimize necessary nuclear experiments and tests for FSP
• Results:
– Computational bias increases with Be reflector worth
– Bias up to +0.5% Δk/k for HEU Metal Fast Spectrum systems
– Largest bias in subcritical experiments (1.3 – 1.7%)
– Need to improve 235U(n,γ) cross section data
• Dominate uncertainty when modeling an individual experiment
– Need to improve Be cross section data, especially Be(n,n)
• Dominate uncertainty in reactor design using benchmark database
– Cold-critical experiment unnecessary but still useful
– Subcritical submersion experiments still necessary
2
3. Fission Surface Power (FSP) System
• Design concept for this
study
– Lunar outpost power
supply
– 20 – 50 kW
– <8 yr operation
– Ready for launch by
2020
– Provide a power-rich
mission environment
3
4. Previous Evaluation of Benchmark Data
• International • Ideal benchmark:
Handbooks for of – Fast spectrum
Evaluated Criticality – NaK cooled
Safety and Reactor – Stainless steel cladding
Physics Benchmark – HEU-O2
Experiments – Be reflectors
– ICSBEP and IRPhEP – B4C control drums
Handbooks
• Best available:
– ZPPR-20 mockups of
SP-100 experiments
– Four configurations
4
6. Objective of Current Study
• Reduce computational uncertainty in the FSP
design using additional benchmark data
– Identify high-quality experiments
• HEU fuel
• Be reflected
• Fast spectrum
– Benchmark these experiments
– Evaluate benchmark experiments using sensitivity and
uncertainty analysis capabilities found in SCALE 6
– Establish a path forward based on evaluated results
6
7. Oak Ridge Critical Experiments Facility (ORCEF)
• Hundreds of HEU
oralloy experiments
– Bare, graphite-,
polyethylene-, and
beryllium-reflected (3)
• 1960s and 1970s
• Support criticality safety
at Y-12
– Storage, casting, and
handling
– Verification of
calculation methods and
cross section data
7
12. Unique Uncertainty Conditions
• Parts manufactured at • Now uncertainties that
Y-12 to very tight are typically
tolerances insignificant become
– Dimensions: significant
• ±0.0001 in. – Temperature:
– Mass: • ±2 ºF
• ±0.5 g – Reactivity
– Isotopic Composition: measurement:
• ±0.005 wt.% • ±10%
– Part Placement: – Beryllium impurities
• ±0.001 in. • Nominal quantities known
but deviation unknown
12
13. Evaluated Biases
• Small biases are now • Model Simplifications
significant due to small – Removal of impurities
uncertainties – Homogenization of like
components
• Room return • Removal of gaps
• Removal of support • Uniform material
properties
structure • Nominal experiment
– Measured/evaluated by dimensions
experimenter
• Temperature
– Treated as uncertainty
15. Reflector Effects
• Compared reflected Mass Reflector
experiment to bare Experiment Difference Worth (ρ$)
(kg)
HEU configuration in
previous benchmark Top-Reflected 9.922 10.7 ± 0.5
– Mass difference
– Most reactive
portion of HEU discs 13” Annular -13.497 8.5 ± 0.4
replaced with Be for
annuli
15” Annular -3.258 4.2 ± 0.2
• Calculated reflector
worth using MCNP5
Small reflector worths, indicative
of small modeling bias
16. TSUNAMI Analysis
• Tools for Sensitivity and Uncertainty Analysis
Methodology Implementation in Three Dimensions
(TSUNAMI-3D)
– Comprehensive analysis of relative deviation of keff due
to cross-section covariance data
• TSUNAMI-IP (Indices and Parameters)
– Comparison of TSUNAMI-3D analyses for multiple
configurations
– Compute relational parameters between two
configurations to assess a degree of similarity
– i.e. proposed designs to existing experimental data
16
18. Correlation Coefficient, ck
• Rigorous uncertainty analysis
– Propagates tabulated cross-section uncertainty
information to keff
– Energy-dependent sensitivity coefficients
• Represents estimate of the correlated uncertainty
between systems
• Measures degree of similarity of the systems in
terms of relative uncertainty
σ ij
2
ck =
(σ iσ j )
18
19. TSUNAMI-IP Results
• Good correlation
between individual
experiments and the
FSP model
• Less cross-section
uncertainty in the
ORCEF HEU-Be
experiments
19
20. Penalty Assessment (TSUNAMI-IP)
• Determine additional margins of uncertainty where
experimental information is unavailable
• Provides added measure of safety where
validation coverage is lacking
• Covariance data uncertainty reduced to 0.29
%∆k/k, which is mostly from the Be(n,n) reaction
uncertainty, in the original ZPPR-only assessment
• Can be used to assess bias and bias uncertainty
for additional margins in subcriticality experiments
to account for lack of experimental coverage for
beryllium
20
21. Results of the Penalty Assessment
• Addition of three HEU- ZPPR-20 ZPPR-20 &
Be experiments only HEU-Be
FSP cross 2.09 %δk/k 2.02 %δk/k
– Were not sufficient to section
reduce the uncertainty uncertainty
in the Be(n,n) reaction
Penalty 0.29 %δk/k 0.29 %δk/k
– Smaller reflector worth assessment
– Smaller configurations Be(n,n) only 0.28 %δk/k 0.28 %δk/k
– Smaller sensitivities
(see next page)
21
24. TSURFER Analysis
• Tool for Sensitivity/Uncertainty analysis of
Response Functionals using Experimental Results
• Alternative method for uncertainty quantification
• Uses sensitivity data (TSUNAMI-3D) and cross-
section covariance data to determine uncertainty
using the measured keff values of the benchmark
experiments
• Generalized linear least squares approach to
adjusting experimental and nuclear data to
calculate keff values close to their experimental
value
24
26. TSURFER Results
• Slight reduction in the • TSURFER uncertainties
total uncertainty with typically larger than
the addition of the HEU- TSUNAMI-IP penalty
Be experiments calculations
• Some general benefit – Penalties account for
under-coverage of the
but not for the targeted sensitivity data
uncertainty in Be(n,n) – TSURFER assesses the
lack of or inconsistency
in data from multiple
benchmarks
26
27. Future Work
• ORCEF (early 1960s)
space reactor mockup
• HEU-O2 pellets
• SS-347 tubes
• Al container
• Be reflector
• Reactivity Effects
– SS-347, W, Cb (now Nb),
CH2, C, B4C, Al, & Cd
– K coolant
• Fission Rate Distributions
& Cd Ratios
27
29. Conclusions
• Three HEU-Be experiments were evaluated and
compared with the ZPPR-20 benchmarks and FSP
model
– No reduction in Be(n,n) uncertainty
– Sensitivity of experiments to a given cross section is
important when trying to reduce uncertainties
– Overall uncertainty in the FSP system was slightly
reduced
• Evaluation of additional experiments isneeded to
further reduce the uncertainties in the FSP design
– Past experiments (hopefully)
– Future experiments
• Subcriticals, high reflector worth, sensitivity to Be(n,n) reaction
29
32. Simple Benchmark Models
D 38.1 cm (15 in.)
D 17.78 cm (7 in.)
D 17.78 cm (7 in.)
10.16 cm
(4 in.) HEU Be
10-GA50002-54-2 14.12875 cm
Be (5.5625 in.)
D 33.02 cm (13 in.) 24.60625 cm
(9.6875 in.)
D 17.78 cm (7 in.)
10.4775 cm
HEU (4.125 in.)
12.7 cm
(5 in.) HEU Be
09-GA50001-177-2
10-GA50002-54-1
33. Detailed 17.770920
9/16" Be
1.42875
Benchmark 17.770920
1.27
1.42875
0.004826
1.27
Model: 1/2" Be
0.004826
2.54
Top-Reflected 17.770920
2.54 0.004826
Be parts
1" Be 5.08
17.770920
0.004826
5.08
2" Be 3.81
3.81 0.004826
17.770920 0.3175
0.001778
2.543175
1.5" Be
0.001778
0.3175
17.771110
3.814191
2768 HEU
2.543175 0.003556
17.769840
3.816604
2732 HEU
HEU parts
3.814191
17.770856 Drawing not to scale
Diaphragm
location
2734 HEU
Bottom layer
3.816604
17.772060
Dimensions in cm
2733 HEU 09-GA50001-177-4
