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1
Managed by UT-Battellefor the Department of Energy
Monaco / MAVRIC
Shielding in SCALE
John C. WagnerDouglas E. Peplow
Tom M. Evans
Radiation Transport & Criticality GroupNuclear Science & Technology Division
International Nuclear Codes Workshop/MCNEG – 2008
3rd – 6th March 2008
Sellafield Ltd, Risley, Cheshire UK
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Overview
• Introduction– SCALE / Monaco / MAVRIC
• Monaco– Features & Examples
• MAVRIC– Automated Variance Reduction– Features & Examples– Benchmarking
• On-Going & Planned Developments
• Summary Remarks
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What is SCALE? A Modular Code System for PerformingStandardized Computer Analyses for Licensing Evaluation
Calculates reaction rates and fluxes
CSAS Criticality Safety Analysis SequenceSCALEDriverandCSAS
Input
BONAMI
NITAWL
XSDRNPM
KENO-V.a
KMART
End
Cross-section preparation
Used only if cell-weightingcross-sections
Monte Carlo keff calculation
Reaction rate and flux data
KENO3DJavapeno
Goal: Put state-of-the-art methods into reliable and easy-to-use system
Original focus on out-of-reactor safety analysis
System has grown 10-fold since release in 1980Automated sequences make system easy-to-use
Libraries
Data Size
Modules
Document
Code
SCALE 0 SCALE 4.4a SCALE 5
250,00025,000
4,300300
556
10 MB 110 MB
104
400,000
80
650 MB
12
5,800
2
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SCALE
• Developed at ORNL for the NRC beginning in 1976
• Maintained/enhanced under co-sponsorship of NRC and DOE since 1987
• A collection of codes for performing analyses of nuclear facilities and packages. Capabilities include:
– Cross-section processing– Criticality safety– Radiation protection & shielding– Reactor physics– SNF/HLW characterization
(e.g., inventory, decay heat, radiation source and spectra)
• Latest version, SCALE 5.1, released Nov 2006– Next version, SCALE 6, to be released by Dec. 2008
• SCALE website: http://www.ornl.gov/sci/scale/
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SCALE
• Functional modules – physics calculations– KENO, Monaco, ORIGEN-S, NEWT, XSDRNPM,
NITAWL, CENTRM, BONAMI
•Control modules automate the execution and data exchange of individual codes to perform various types of analyses in calculation sequences– CSAS, MAVRIC, TSUNAMI, SAS2H, TRITON
•Multi-group and continuous energy cross-section data
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Current SCALE Shielding Capabilities – Status
• While codes for criticality safety and reactor analysis have been enhanced on a continual basis, the radiation shielding codes have not
• To address this situation, a project was initiated a few years ago to significantly upgrade & advance the Monte Carlo shielding capabilities in SCALE
• This presentation on Monaco & MAVRIC describes some of our progress and what can be expected in the next release of SCALE
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Current SCALE Shielding Modules/Capabilities
• SAS1 – 1-D discrete ordinates Shielding Analysis Sequence– Automates cross-section processing, transport calculation, and
calculation of dose rates outside a defined shield– Combined 1-D criticality/shielding analysis (e.g. CAAS)
• SAS4 – 3-D Monte Carlo Shielding Analysis Sequence– Designed for calculation of radiation doses exterior to a
transport/storage cask– Uses XSDRNPM to calculate 1-D adjoint functions for the generation
of biasing parameters (automated 1-D biasing)
• MORSE – 3-D Monte Carlo code used in SAS4– Unique geometry package, different than that of the SCALE Monte
Carlo criticality (KENO) codes– Legacy code, geometry package and capabilities have not been
substantially updated in >20 years
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Current SCALE Shielding Modules/Capabilities• SAS4 – Shielding Analysis Sequence
– Automated 1-D, deterministic-adjoint-based, axial or radial variance reduction
– Not updated in more than a decade
• Design limitations based on cylindrical cask geometry– Effective for calculating doses at cask mid-plane and top– Not well suited to cask corners or very heterogeneous
geometries– Not effective/reliable for general purpose shielding analyses– Hence, need for modern Monte Carlo tool with automated 3-D
variance reduction (AVR) for general shielding applications
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Principal Goals of UPGRADE Project(Upgrade & advance Monte Carlo shielding in SCALE)
• Establish modern code from which to continue further development
• Unify geometric descriptionsbetween Monte Carlo shielding and criticality codes in SCALE
• Implement general 3-D AVR capability
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Monaco
• 3-D Multi-group Monte Carlo code– MORSE/KENO physics/cross-sections– SCALE Generalized Geometry Package
(same as KENO-VI and TRITON) – Substantial modernization; object-oriented
• Fixed source– Variety of geometric shapes– Mesh-based source capability
• Tallies– Point detectors, region tallies, mesh tallies– Convolves fluxes with detector responses
• Cross-section libraries– ENDF/B-VI & -VII coupled multi-group libraries (200n-47g)
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Monaco
• Variance Reduction– Biased source energy distribution– Source direction distribution– Path-length stretching– Point-detector tallies– Weight windows by region and energy group
• Advanced Variance Reduction– Mesh/energy group based importance map
(weight windows)– Mesh/energy group based biased source
• User-friendly input– Block/keyword format
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Monaco – Model Visualization
• KENO3D enables interactive display of geometry
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KENO3D Examples
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GeeWiz interface
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Monaco Example: Ueki Experiment
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Monaco Example: Ueki Experiment
KENO3D rendering of the benchmark geometry
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Monaco Example: Ueki Experiment
Table 4. Comparison of results to Ueki & Ohashi
0.0100
0.1000
1.0000
0 5 10 15 20 25 30 35T hickness (cm)
Dos
e Eq
uiva
lent
Atte
nuat
ion
Ueki & Ohashi
Monaco
Thickness Ueki & Monaco C/E (cm) Ohashi value rel err
2 0.8288 0.8751 0.0042 1.06 5 0.7217 0.7267 0.0065 1.01
10 0.5261 0.5312 0.0092 1.01 15 0.3649 0.3832 0.0117 1.05 20 0.2532 0.2582 0.0145 1.02 25 0.1705 0.1754 0.0178 1.03 30 0.1126 0.1156 0.0214 1.03 35 0.0742 0.0741 0.0269 1.00
Figure 2. Graphical comparison
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MAVRIC – Monaco with Automated Variance Reduction using Importance Calculations
• SCALE control module that invokes functional modules for the following:– Problem-dependent multi-group cross-section
processing– 3-D Automated Variance Reduction
• Deterministic calculation to compute approximate adjoint function for a desired response
– TORT & GRTUNCL3D or– New parallel SN code – Denovo
• CADIS methodology to convert adjoint function into:– Mesh/energy group based importance map (weight
windows for splitting and roulette)– Consistent mesh/energy group based biased source
– Monte Carlo transport simulation – Monaco
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SCALE 6 Sequence: MAVRIC
SCALEDriverandMAVRIC
Input
Monaco
End
Optional: adjoint cross sections
Optional: 3-D discrete ordinates calculation
3-D Monte Carlo
Resonance cross-section processing
BONAMI / NITAWL orBONAMI / CENTRM / PMC
CADIS
Optional: first-collision source calculation
—PARM=check —
—PARM=tort —
—PARM=impmap —
Optional: importance map and biased source
Monaco with Automated Variance Reduction using Importance Calculations
ICE, DenovoGRTUNCL-3D
TORT
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Features:
1. Utilizes the highly efficient KBA algorithm across processors (MPI).
2. Uses OpenMP to provide task-parallelism on multicore architectures.
3. Uses the Trilinos parallel solver package for highly efficient Krylov solvers and as an interface to the SuperLU direct solver library.
4. Provides DSA preconditioning of within-group solves.
Denovo: New Parallel SN codeKBA Domain DecompositionGoal:
Develop a parallel, deterministic SN code that provides adjoint and forward fluxes for MAVRIC.
KBA Parallel Sweep
1. Sweep each block starting in corner of octant.
2. Communicate outgoing fluxes to neighboring (x,y) blocks.
3. Continue sweep in z-direction.
4. MPI communication across blocks.
5. OpenMP on angles within block.
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Denovo Adjoint Calculations
Denovo provides adjoint fluxes that MAVRIC uses to generate importance maps for forward Monte Carlo calculations.
Tally region in forward problem
forward source region
adjoint currents are plotted to show preference from source to tally region
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In order to calculate the moments of the intensity, we must calculate
which requires ray-tracing through the mesh.
First Collision Source
Ray-effects can result in serious pathologies in SN calculations
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Theory - Adjoint Methodology
• Recognizing the physical meaning of the adjoint function, numerous works have successfully utilized adjoint data for MC VR (for localized quantities)
• Further recognizing the advantages associated with deterministically generated adjoint functions, much work has been done to develop and automate methods based on deterministic importance functions
• Many of these works are reviewed in the following paper:– “Monte Carlo Variance Reduction with Deterministic Importance
Functions,” Progress in Nuclear Energy, 42(1), 25-53, (2003).
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Theory – CADIS
• CADIS – Consistent Adjoint Driven Importance Sampling– Given an objective function, σd, and the corresponding
adjoint importance function, CADIS provides consistent relationships for calculating source & transport biasing parameters based on Importance Sampling
– Biased source is given by:
• numerator is the detector response from a given space-energy element
• denominator is the total detector response• the ratio is the relative contribution from each space-energy
element to the total detector response
RErqEr
ErqErdEdVErqErErq
V E
),(),(),(),(
),(),(),(ˆ+
+
+
==∫ ∫
φφ
φ
9
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Theory – CADIS
• Applying the weight conservation requirement
• The statistical weights are given by
• For use with a weight window technique, the weights can be scaled to calculate lower-weight bounds,
),(),(ˆ),( ErqwErqErw o=
)E,r(R)E,r(w +=
φ
⎟⎠⎞
⎜⎝⎛ +
=⎟⎠⎞
⎜⎝⎛ +
=+
21
21 uu c)E,r(
Rc
w)E,r(wφ w
wcwhere uu =
lw
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CADIS Method
• Provides source biasing parameters and weight windows such that source particles are started with weights that are within the weight windows
• Has been implemented and automated in MAVRIC and the ADVANTG code (based on MCNP) – Both codes are routinely used at ORNL for simulations of
real applications, e.g.,• Ex-vessel detector response• Dose rate in a variety of environments• Nuclear well-logging tool simulations• DPA to HFIR vessel• Analysis of shielding penetrations
– Resulting in considerable experience with the method
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Detector
Core
CavityPressure vessel
Downcomer
Neutron pads
Baffle plates
Flow channel
Core barrel
Concrete shield
Monte Carlo model Deterministic modelx-dimension (cm)
y-di
men
sion
(cm
)
50 100 150 200 250 300
50
100
150
200
250
300
adjoint5.00E+307.46E+291.11E+291.66E+282.48E+273.70E+265.51E+258.23E+241.23E+241.83E+232.73E+224.07E+216.08E+209.07E+191.35E+192.02E+183.01E+174.49E+166.70E+151.00E+15
Adjoint data
,),(),(),(),(),(ˆ
∫ ∫ +
+
=V E
drdEErErqErqErErq
φφ
⎟⎠⎞
⎜⎝⎛ +
=+
21),(
),(ucEr
RErwφ
Calculate VR ParametersSource biasing
Transport biasing (weight windows)
CASE
CPU TIME TO ACHIEVE RE=1%
(h)
SPEEDUP
No VR 8.86E+4 (10.1 yrs) 1 Manual VR 13.6 6500∗ ADVANTG 1.02 87000
∗ Required ~3 weeks by an experienced MC practitioner using all applicable MCNP4C VR capabilities
Results
CADIS Example: PWR Ex-Vessel Thermal (10B) Detector Response
1 eV
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MAVRIC Example – Weight Targets
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MAVRIC Example – Source Biasing
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 2 4 6 8 10Energy (MeV)
Prob
abili
ty p
er M
eV
TrueBiased
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MAVRIC Example – Results
Table 2. Comparison of Results
0.01
0.10
1.00
0 5 10 15 20 25 30 35
Thickness (cm)
Dos
e Eq
uiva
lent
Atte
nuat
ion
Ueki & Ohashi
MAVRIC
Thickness Ueki & MAVRIC C/E (cm) Ohashi value r unc
0 0.8288 0.8728 0.0065 1.05 5 0.7217 0.7270 0.0044 1.01
10 0.5261 0.5358 0.0054 1.02 15 0.3649 0.3761 0.0068 1.03 20 0.2532 0.2553 0.0063 1.01 40 0.1705 0.1717 0.0067 1.01 45 0.1126 0.1121 0.0077 1.00 50 0.0742 0.0731 0.0087 0.99
Figure 2. Results Comparison
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MAVRIC Example – Compare to Analog Monaco
21σTFOM =
FOM FOM Thickness Monaco MAVRIC speedup
(cm) (/sec) (/sec) 0 185.6 677.2 4 2 19.0 169.8 9 5 7.5 460.7 61 10 3.6 168.1 47 15 2.2 62.3 28 20 1.4 55.3 39 25 0.9 37.3 39 30 0.6 26.1 40 35 0.4 21.3 52
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Results – Mesh Tally without CADIS
Exercise 2 Scales
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Results – Mesh Tally with CADIS
Exercise 3 Scales
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MAVRIC Example Results
FOM FOMThickness Monaco MAVRIC speedup
(cm) (/sec) (/sec)0 2.35E+02 1.11E+03 55 5.66E+00 1.30E+02 2310 2.15E+00 7.13E+01 3315 9.12E-01 2.94E+01 3220 4.40E-01 2.38E+01 5425 2.60E-01 2.19E+01 8430 1.16E-01 1.70E+01 14735 6.90E-02 1.49E+01 21640 3.79E-02 9.52E+00 25145 1.41E-02 1.37E+01 96750 5.68E-03 1.15E+01 2027
21σTFOM =
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MAVRIC Cask Example
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MAVRIC Cask Example
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MAVRIC Cask Example
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MAVRIC Cask Example
TORT Monaco
1142 1.50E-09 (2.92%) 4.52E-06 (39.90%)
70 121 1.49E-09 (0.23%) 4.91E-06 (4.05%)
time (min)
uncollided total
Neutron dose rate (rem/hr)
Speed up: 583
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MAVRIC Cask Array Example
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MAVRIC Cask Array Example
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MAVRIC Cask Array Example
Speed up: 28
TORT Monaco
1083 1.05E-08 (0.84%) 2.83E-05 (6.33%)
44 664 1.04E-08 (0.13%) 2.91E-05 (1.47%)
time (min)
uncollided total
Neutron dose rate (rem/hr)
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Need for Simultaneous Optimization
Cask external dose rates
Site boundarydose rates
Nuclear well-logging
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Dose Rates Throughout a PWR FacilityLarge scales, massive shieldingDifficult to calculate dose rates
Turbine Bldg.
Auxiliary Bldg.
85 × 125 × 70 m
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Forward-Weighted CADIS Method• It can be shown that the adjoint source can
be defined to optimize MC for global and semi-global quantities, e.g.,
• For space- and energy dependent flux:
• For total flux:
• For response, e.g., dose:
( )∫ ′′=+
EdErErq
,1),(
φ
( )( ) ( )∫ ′′′
=+
EdErErErErq
d
d
,,,),(
σφσ
( )ErErq
,1),(
φ=+
See: J.C. Wagner, E.D. Blakeman, and D.E. Peplow, "Forward-Weighted CADIS Method for Global Variance Reduction," Trans. Am. Nucl. Soc. 97, 630-633 (2007).
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Forward-Weighted CADIS Method
• The method corresponds to weighting the adjoint source with the inverse of the forward flux/response
• Hence, where the forward flux/response is low, the adjoint importance will be high, and vise versa
• Once the adjoint importance function is determined, the standard CADIS methodology is used– Hence, we refer to the method as Forward-Weighted CADIS
• The method requires:– A forward solution (for adjoint source weighting)– An adjoint solution (for determining biasing parameters)– Both can be automated
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Forward-Weighted CADIS Method
• Perform a forward discrete ordinates calculation
• Estimate the responses R(r,E) everywhere
• Construct a volumetric adjoint source, where the source strength is weighted by 1/R(r,E)
• Perform the adjoint discrete ordinates calculation
• Create the weight windows and biased source
• Perform the Monte Carlo calculation
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SCALE Sequence: MAVRIC
SCALEDriverandMAVRIC
Input
ICE, DenovoGRTUNCL-3D
TORT
MonacoEnd
adjoint cross sections
3-D discrete ordinates calculation
3-D Monte Carlo
Resonance cross-section processing
BONAMI / NITAWL orBONAMI / CENTRM / PMC
CADIS
Optional: first-collision source calculation
—PARM=check —
—PARM=tort —
—PARM=impmap —
Optional: importance map and biased source
ICE, DenovoGRTUNCL-3D
TORT
forward cross sections
3-D discrete ordinates calculationOptional: first-collision source calculation
—PARM=forward —
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Simple Problem: Find Dose Rates EVERYWHERE
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Six Methods: Dose Rate Mesh Tally
1. Analog
2. Standard CADIS, adjoint source in one region
3. Uniformly distributed adjoint source everywhere
4. Exterior adjoint source, with guessed amounts
5. Cooper’s Method, with source biasing
6. Forward-weighted CADIS
Mesh: 40x24x24 = 23040 voxels
Same run time (90 minutes) each
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1. Analogread biasing
windowRatio=10.0targetWeights 27r1.0
18r0.0 end
end biasing
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2. Standard CADISread tortImportance
adjointSource 1boundingBox 500 430
200 -200 200 -200 end
responseID=5end adjointSource
gridGeometryID=8
end tortImportance
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3. Uniformly Distributed Adjoint Sourceread tortImportance
adjointSource 1boundingBox 750 -150 250 -250250 -250 end
responseID=5end adjointSource
gridGeometryID=8
end tortImportance
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4. Exterior Adjoint Sourceread tortImportance
adjointSource 1boundingBox -130 -150250 -250 250 -250 endresponseID=5weight=0.05
end adjointSource
adjointSource 2boundingBox 750 730250 -250 250 -250 endresponseID=5weight=3.0e6
end adjointSource
adjointSource 3boundingBox 750 -150-230 -250 250 -250 endresponseID=5weight=1.0
end adjointSource...gridGeometryID=8
end tortImportance
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5. Cooper’s Methodread tortImportance
gridGeometryID=8
end tortImportance
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6. Forward-Weighted CADIS read tortImportance
adjointSource 1boundingBox 750 -150 250 -250250 -250 end
responseID=5end adjointSource
gridGeometryID=8
forwardWeightingresponseID=5
end tortImportance
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How to Compare Mesh Tallies
• No single measurement like FOM
• Instead compare what fraction of voxels have less than some amount of relative uncertainty.
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100relative uncertain ty (% )
frac
tion
of v
oxel
s greatgoodbadhorrible
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Six Methods: Comparison
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
relative error (% )
frac
tion
of v
oxel
s
analogstandard CADISuniform adj srcexterior adj srcCooper's methodFW-CADIS
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Dose Rates Near A Cask Array
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Standard CADIS - one point at a time
• Slow
• Need a mesh tally & FW-CADIS
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Forward-Weighted CADIS
1. Forward Discrete Ordinates –forward fluxes
2. Forward dose rate estimate
3. Adjoint source, weighted by dose
4. Adjoint Fluxes5. Importance
Map6. Biased Source
1. 2.
3. 4.
5. 6.
21
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Mesh Tally of Dose Rates (photon)
• Dose Rates and relative uncertainties (5 hrs)
Analog FW-CADIS
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Cask Array: Comparison
• FW-CADIS performs well: – A) photon dose from photon source
• From neutron source– B) Neutron dose rate– C) Photon dose rate
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
0 2 0 4 0 60 80 100relative uncertainty (% )
frac
tion
of v
oxel
s
analo gFW-CAD IS
0.0
0 .2
0 .4
0 .6
0 .8
1 .0
0 20 40 60 80 100relative uncertainty (% )
frac
tion
of v
oxel
s
analo gF W -CADIS
0.0
0 .2
0 .4
0 .6
0 .8
1 .0
0 20 40 6 0 80 10 0relative uncertainty (% )
frac
tion
of v
oxel
s
analogFW -CADIS
B)
C)
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Benchmarking Examples• Ueki shielding material experiments
– K. Ueki, A. Ohashi, N. Nariyama, S. Nagayama, T. Fujita, K. Hattori and Y. Anayama, “Systematic Evaluation of Neutron Shielding Effects for Materials,” Nuclear Science and Engineering 124, 455-464 (1996).
• Neutron transmission measurements– E. Sajo, M. L. Williams, and M. Asgari, “Comparison of Measured and Calculated
Neutron Transmission Through Steel for a 252Cf Source,” Annals of Nuclear Energy,20(9), 585–604 (1993).
– B. Jansky, Z. Turik, E. Novak, J. Kyncl, F. Cvachovec, and P. Tiller, “Comparison of Measured and Calculatied Neutron Transmission Through Heavy Water for 252Cf Source Placed in the Center of 30 cm Diameter Sphere,” Annals of Nuclear Energy, 24(15), 1189–1212 (1997).
• CAAS measurements– Gennady Manturov, Yevgeniy Rozhikhin and Lev Trykov, “Neutron and Photon
Leakage Spectra from Cf-252 Source at Centers of Six Iron Spheres of Different Diameters” (ALARM-CF-FE-SHIELD-001), International Handbook of Evaluated Criticality Safety Benchmark Experiments, Volume VIII - Criticality Alarm/Shielding Benchmarks, NEA/NSC/DOC/(95)03, Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA) (September 2007).
– Mark Nikolaev, Natalia Prokhorova, and Tatiana Ivanova, “Neutron Fields in Three-Section Concrete Labyrinth from Cf-252 Source” (ALARM-CF-AIR-LAB-001), International Handbook of Evaluated Criticality Safety Benchmark Experiments, Volume VIII - Criticality Alarm/Shielding Benchmarks, NEA/NSC/DOC/(95)03, Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA) (September 2007).
• Benchmarking will continue indefinitely!
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64 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
MAVRIC Output
• Output from each module concatenated together• Monaco results are at the end
– Summary tables for Region Tallies and Point Detectors
• Separate files – group-wise results for flux and integrated results for each optional response– Mesh Tallies: outputName.mtid.3dmap– Region Tallies:
• Table of results: outputName.rtid.txt• Convergence plot: outputName.rtid.chart
– Point Detector Tallies: • Table of results: outputName.pdid.txt• Convergence plot: outputName.pdid.chart
65 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
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MAVRIC Output
• Mesh File Viewer – Mesh tallies– TORT files– Importance maps– Mesh sources
• Interactive Plotter– Convergence checks– Data from mesh
66 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
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On-Going & Planned Developments
• Monaco– Continuous Energy– Parallel– Continue working on programming modernization and SQA– Continue working to improve features & user-friendliness, e.g.,
• Output to separate (html) tables• Larger variety of source descriptions/flexibilities• Larger variety of tally options – multipliers, totals, etc.
– Pulse-height tallies• Link for ORIGEN sources
– Linkage to CAD package, e.g., BRL-CAD• MAVRIC
– Complete work/testing on new parallel SN code – Denovo (SCALE 6)– CAAS – Criticality Accident Alarm System capability (SCALE 6)
• KENO-VI calculates fission source distribution• MAVRIC calculates deep-penetration to detectors
– Automated VR improvements• Automatic material homogenization for deterministic calculation• Refine standard set of deterministic calculation parameters• Additional diagnostics• AVR for pulse-height tallies
• Testing, Testing, then a bit more Testing
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67 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
Summary Remarks
• Monaco – new MC shielding code for SCALE 6 developed & tested
• MAVRIC offers many ways for automated, advanced variance reduction– Standard CADIS method – for optimizing a specific response at a
specific location– Forward-Weighted CADIS – for optimizing multiple tallies or mesh
tallies over large areas• Easy to use
– In addition to standard MC input description, user provides meshfor SN calculation
– For CADIS, user specifies tally source position or region– For FW-CADIS, user adds a single keyword
• Availability– SCALE 6 – to be released by Dec 2008– Beta versions being made available to “friendly users”
• Contact Steve Bowman, [email protected]
68 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
Summary Remarks
• Advanced methods for VR, which rely on deterministic solutions, are enabling the use of MC for deep-penetration and answers-everywhere applications
• The results of these methods could have significant implications on how MC is used in the future
69 Managed by UT-Battellefor the Department of Energy Monaco / MAVRIC – Shielding in SCALE
Closure
• Contact Info: – John Wagner, [email protected]– Douglas Peplow, [email protected]– Tom Evans, [email protected]
• Questions/Discussion?
• Hands-on tutorial:– Friday, 18 April 2008 – at ICRS-11 / RPSD-2008,
Callaway Gardens, Georgia, USA