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© SCK•CEN Academy
G. Bijloos1,2, L. Tubex1, J. Camps1, J. Meyers2
1 SCK•CEN, Belgian Nuclear Research Centre, Boeretang 200, 2400
Mol, Belgium
2 Department of Mechanical Engineering, KU Leuven,
Celestijnenlaan 300, 3000
Leuven, Belgium
The effect of terrain modeling on simulated dose rates
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Near-range atmospheric dispersion can be modelled on various
ways
Ø Different treatments of atmospheric conditions and terrain
effects
Do dose rate simulations benefit from improved physical
descriptions?
Problem statement
2
High
Low
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n Methodologyn Results
n Simulation of Ar-41 routine releasesn Downstream calculations
for a 2 km fetch
n Conclusions
Content
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!"!# + % ⋅ '" = ' ⋅ )'" + *+(- − -/), ∀- ∈ 4 ⊂ ℝ
7 (1)with": the concentration field [;7]%: the wind field
[>/@]): the eddy diffusivity [>A/@]*: the source strength
[;]4: the simulation domain
Step 1: solve " from equation (1) for the near range around the
sourcen buildings are omitted
n terrain and atmospheric conditions are incorporated through
the choice of % and )
Methodology
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Model ! " methodology
Different choices of ! and " lead to different modelsn Assume a
neutral atmospheren Wind field is assumed to be uniform in the
horizontal plane
Methodology
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Model ! " methodologyGaussian model constant:
# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer
experiments)
Analytical solution from 1
(MATLAB)
1 Yi C. 2008. Momentum transfer within canopies. J. Appl.
Meteor. Climatol. 47: 262-275.
Model ! " methodologyGaussian model constant:
# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer
experiments)
Analytical solution from 1
(MATLAB)Particle model power law:
# $ ∝ $&.**Taylor’s statistical turbulence theory
Solve SDE with Euler-Maruyama scheme(MATLAB)
Model ! " methodologyGaussian model constant:
# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer
experiments)
Analytical solution from 1
(MATLAB)Particle model power law:
# $ ∝ $&.**Taylor’s statistical turbulence theory
Solve SDE with Euler-Maruyama scheme(MATLAB)
Vegetation canopy dispersion model
similarity scaling (>canopy)≈ solve NS eqn1(in canopy)
Standard Gradient Hypothesis
Finite volume method(OpenFOAM)
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Step 2: calculate the ambient gamma dose rates "̇# due to the
gamma energy released
per disintegration $# %&' w.r.t. detector location () ∈
ℝ,
̇"# =./012$#
44555
6
7 0 8 (
8 ( 9&:;< ( = ( d( , 8 ( = ( − (′ 9
with
./ = 1.6×10:,GH ⋅ JK ⋅ %&':L a unit conversion factor
012: the absorption coefficient for air [O9/JK]7: the buildup
factor0: the linear attenuation coefficient in air [O:L]⋅ 9: the
Euclidean norm
Kenis K, Vervecken L, Camps J. 2013. Gamma dose assessment in
near-range atmospheric dispersion simulations. SCK•CEN Reports; No.
ER-242. 1:26 p.
Methodology
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n Methodologyn Results
n Simulation of Ar-41 routine releasesn Downstream calculations
for a 2 km fetch
n Conclusions
Content
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n Dose rate measurements for 7 locations on SCK•CEN site (Mol,
Belgium)n Ar-41 releases from the BR1 through the chimney (60
m)
n Data was also distributed in context of the NERIS Atmospheric
Dispersion Modelling (ADM) experiment (J. Camps, Dublin 2018
workshop)
SCK•CEN sitecase study
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BR1
chimney
SCK•CEN forest
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Quantile = cut points that divide the range of a probability
distribution into intervals with equal probabilities
Simulation of Ar-41 routine releasesQ-Q plot
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Gaussian models are biased + underestimate the observed
variance
outliers ?
Particle model seems to perform the best
Canopy model underpredictsoccurrence of dose rates > 120
!"#/ℎ
Gauss (PG) model is biased, but variance is correctly
estimated
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Above 100 nSv/h: mainly underestimations
Simulation of Ar-41 routine releasesOutliers?
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Statistical measures [Chang & Hanna (2004)]: let the
subscript ! denote the observations and " the predictions, then
VG = exp ln,̇-,/,̇-,0
1
, FAC5 = fraction of data that satisfy15≤,̇-,/,̇-,0
≤ 5
Additionally, also a hypothetical ground release (10 C) was
assumed for the same meteorological data as for the stack
release.
Findings
n Stack release: 75% < FAC2 < 90 %, FAC10 ≈ 100% (w.r.t.
measurements)
Simulation of Ar-41 routine releasesStatistical measures
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Release height [m]
L̇M,N L̇M,O PQ [-] RSTU [-] RSTVW [-]
60 Gauss (PG) Canopy 1.20 0.94 1.0
10 Gauss (PG) Canopy 2.52 0.39 1.0
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n Methodologyn Results
n Simulation of Ar-41 routine releasesn Downstream calculations
for a 2 km fetch
n Conclusions
Content
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Concentration discrepancy is much bigger close to the source
than for dose rateØ concentration stronger influenced by terrain
roughness modeling
Downstream calculations for a 2 km fetchRatio’s at ground
level
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Black = concentration ratioRed = dose rate ratio
60 m release (-)10 m release (--)
Ratio = !"#$$ (&!)(")*+, if ≥ 1Ratio = − (")*+,!"#$$ &!
if < −1
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n Higher roughness ⇒ concentration maximum closer to sourcen
Location of max. dose rate is stronger influenced by the source
than by the max.
concentration
Downstream calculations for a 2 km fetchGround profiles
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Low roughness: dose rate doesn’t scale with ground
concentration
60 m release
Black = concentrationRed = dose rate
Canopy (-)Gauss PG (--)
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The canopy and the Gaussian model produce quite different
concentration
distributions for both release heights
Downstream calculations for a 2 km fetchNon-dimensional ground
concentration distributions
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ground release
stack release
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Closer agreement between the models about the location and value
of the max. dose rate than about the max. concentration!
Downstream calculations for a 2 km fetchDiscussion about the
maximum values
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Max. conc. Location [m] Ratio [-]Release height [m]
Canopy Gauss (PG) !"#$%&'"())
60 238 1369 2.610 1 155 3.1
Max. dose Location [m] Ratio [-]Release height [m]
Canopy Gauss (PG) !"#$%&'"())
60 191 310 1.410 0.3 90 2.1
Max. conc. Location [m] Ratio [-]Release height [m]
Canopy Gauss (PG) !"#$%&'"())
60 238 136910 1 155
Max. dose Location [m] Ratio [-]Release height [m]
Canopy Gauss (PG) !"#$%&'"())
60 191 31010 0.3 90
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n Methodologyn Results
n Simulation of Ar-41 routine releasesn Downstream calculations
for a 2 km fetch
n Conclusions
Content
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Despite the different terrain parameterizations, all the three
models were capable of
n Predicting more than 75% of the dose rates within a factor
twon Predicting the right order of magnitude of the dose rates
⇒ dose rates are robust quantities to estimate⇒ interesting
property for source inversion
Conclusions (1)
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An improved physical terrain parametrization can still be
beneficial
n It reduces the bias and improves the variance prediction of
the dose rates
n More important further downstream (>1 km): dose rates were
not found to be
more robust there than concentrations
n Factor 2 – 5 difference between canopy and open field
n Strong influence on the location and value of the max.
concentration
n Important for licensing of nuclear installations
Conclusions (2)
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Thank you!
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