Critical Analysis of a Relevant Paper
and Comparison with an MCNP
Simulation of Slowing Down Time
22.106 Term Paper Presentation
Chris Handwerk
10 May 2005
Paper Citation
Benyon, T.D. and Mondal, M. A. W., “The
Application of Space-Dependent
Multigroup Theory to the Analysis of
Neutron Slowing Down Time Experiments
I: Light and Heavy Water
Moderators,”1971, J. Phys. D: Appl. Phys.,
4, 1843-1855.
Focus
• Introduces new numeric solution method
• Solution of Neutron Transport Equation
(NTE)
– P1 Approximation
– Diffusion Approximation
• Comparison with experimental results (3)
– Metric: Neutron Slowing Down
– Only 1 presented here
• MCNP simulation results for 1st experiment
Energy Multigroup Method (Method A)
EHI
Energy
Group
EHI
ΣαΦα
ELOW
g
g+1
g+2
Σg Φ g
Σg+1Φg+1
Σg+2Φg+2
g+3
N
Σg+3Φg+3
ΣN Φ N
Energy Multipoint Method (Method B)
Σα+1Φα+1
Σα+2Φα+2
Σα+3Φα+3
ELOW
Σα+4Φα+4
ΣΘ Φ Θ
Mixed Energy Multigroup/Multipoint Method (Method C)
EHI
g
Σg Φ g
g+1
Σg+1Φg+1
g+3
ΣαΦα
Σα+1Φα+1
ΣΘΦΘ Σg+3Φg+3
N
ELOW
ΣN Φ N
•
•
•
•
Experiment #1
Möller (1966)
1 m3 cube H2O
Dilute Indium
Sulfate
Fast neutron
source
Image removed due to copyright
considerations.
Please see:
Experiment # 1 graph cited
from: Benyon, T. D., and M. A.
W. Mondal. “The Application of
Space-Dependent Multigroup
Theory to the Analysis of
Neutron Slowing Down Time
Experiments I: Light and
Heavy Water Moderators.” J.
Phys. D: Appl. Phys. 4 (1971):
1843-1855.
Image removed due to copyright
considerations.
Experiment #1
Comparison with
MCNP
Simulation
Please see:
Experiment # 1 comparison
graph cited from: Benyon, T.
D., and M. A. W. Mondal. “The
Application of SpaceDependent Multigroup Theory
to the Analysis of Neutron
Slowing Down Time
Experiments I: Light and
Heavy Water Moderators.” J.
Phys. D: Appl. Phys. 4 (1971):
1843-1855.
Possible Sources of Discrepancy
Numeric
Soultion/Experiment
MCNP Simulation
Quantity
Measured
Gamma flux from (n,γ)
capture in Indium
Neutron Flux
Detector
Type
Gamma Point
Flux tally
Detector
Distribution
??
Concentric
Spheres
Source
Isotropy
??
Yes
Conclusions
• New method (C) matches experimental
results well when applied to P1
approximation
• MCNP simulation results differ at greater
distances from source
• Unearthing error will provide greater
insight into original solution/experimental
methods or simulation model
•
•
•
Experiment #2
Chen and Lidofsky (1967)
“Large tank of water”
14.1 MeV neutron source
Images removed due to copyright considerations.
Please see:
Experiment # 2 graph cited from: Benyon, T. D., and
M. A. W. Mondal. “The Application of SpaceDependent Multigroup Theory to the Analysis of
Neutron Slowing Down Time Experiments I: Light and
Heavy Water Moderators.” J. Phys. D: Appl. Phys. 4
(1971): 1843-1855.
Experiment #3
• Möller (1966)
• 1 m3 cube D2O
• Fast neutron
source
Image removed due to copyright considerations.
Please see:
Experiment # 3 graph cited from: Benyon, T. D., and
M. A. W. Mondal. “The Application of SpaceDependent Multigroup Theory to the Analysis of
Neutron Slowing Down Time Experiments I: Light and
Heavy Water Moderators.” J. Phys. D: Appl. Phys. 4
(1971): 1843-1855.
Normalized Flux)
Normalized Flux as a Function of
Time at 4 cm
1.06E+00
1.01E+00
9.60E-01
9.10E-01
8.60E-01
0.6
0.7
0.8
0.9
1
Time (microseconds)
1.1
1.2
Normalized Flux)
Normalized Flux as a Function of
Time at 8 cm
1.06
1.01
0.96
0.91
0.86
0.6
0.7
0.8
0.9
1
Time (microseconds)
1.1
1.2
Normalized Flux)
Normalized Flux as a Function of
Time at 12 cm
1.06E+00
1.01E+00
9.60E-01
9.10E-01
8.60E-01
0.6
0.7
0.8
0.9
1
Time (microseconds)
1.1
1.2
Normalized Flux)
Normalized Flux as a Function of
Time at 16 cm
1.06E+00
1.01E+00
9.60E-01
9.10E-01
8.60E-01
0.6
0.7
0.8
0.9
1
Time (microseconds)
1.1
1.2
Normalized Flux)
Normalized Flux as a Function of
Time at 20 cm
1.06E+00
1.01E+00
9.60E-01
9.10E-01
8.60E-01
0.6
0.7
0.8
0.9
1
Time (microseconds)
1.1
1.2