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European Aerosol Conference, Tours, France - Sept 4-9, 2016
The Development and Application of Kinetic Models for the Resuspension of Small Particles in Turbulent Boundary Layers
M W Reeks*
1Mechanical Engineering, Newcastle University, Newcastle upon Tyne, UK
2Department of Aeronautics, Imperial College,, London, SW 7 2AZ
Drag Force
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Acknowledgments
Jim Reed , CEGB/ Edf Energy, UK
Duncan Hall CEGB / SERCO, UK
Luigi Biasi JRC Ispra, It
Martin Kissane IRSN, Fr
Fred Zhang NCL, UK
Richard Perkins ECL, Lyon, Fr
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Background
Important in a range of environmental and industrial processes
Clean air technology,
Dust storms on Earth and Mars (wave of darkening)
Spreading of pollen and crops diseases by fungal spores
Release of radioactive particles in a nuclear accident
Focus on resuspension particles < 5microns in size
principle adhesive forces – Van der Waals intermolecular forces
Import of safety assessment of nuclear reactors
Development and validation of computer codes
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Kinetic Models for Resuspensiosn
Stochastic models which take account of the role of turbulence in particle resuspension
Focus on resuspension rates as well as fraction resuspension
Calculation of a rate constant for resuspension
analogous to the rate constant for desorption of molecules from a surface (relationship to kinetic theory )
Computational very efficicient compared to simulation (particle tracking)
Ideally suited for incorporation into severe accident codes e.g. SOPHAEROS -> ASTEC
kTEe /
European Aerosol Conference, Tours, France - Sept 4-9, 2016
History and Motivation
Radioactive particles released in severe accidents
PWRs - steam spikes (primary circuit), hydrogen deflagration
(containment)
AGRS dropped stringer –accident
HTRs Accumulation of contaminated dust in the coolant circuit – loss of
coolant accident (LOCA)
International Thermonuclear Experimental Reactor (ITER)
Accumulation of contaminated dust in the vacuum vessel
Coolant-water-ingress or Loss of vacuum accident (LOVA)
SARNET
Development of SA Codes / Sophaeros
IRSN
European Aerosol Conference, Tours, France - Sept 4-9, 2016 6
DATABASE
MEDICIS/WEXRUPUICUV
SYSINT
ISODOP
SOPHAEROS
Aerosols and FP
In the reactor circuits
SYSINT
ISODOP
IODE
CPA-AFP
CPA-THY
MEDICIS/WEX
RUPUICUV
SOPHAEROS
CESAR
ELSA
DIVA
d
t
d
t
d
t
d
t
d
t
d
t
d
t
d
t
d
t
Dt
Safety system
management
IODE
Molten core concrete
interaction
Radioactivity inContainment
ELSA
FP relaese
DIVA
Core degradation
CESARCircuit
Thermalhydraulics
CPA-THY
Containment
Thermal hydraulics
CPA-AFP
Aerosols and FP in
containment
Molten core ejection
And direct heating
Of containment
ASTEC
ASTEC integrates the technical knowledge in SARNET
European Aerosol Conference, Tours, France - Sept 4-9, 2016
OUTLINE
Early model RRH model
Escape of particles from surface adhesive potential well
Role of adhesive and aerodynamic removal forces
Mechanisms for removal
• Quasi static
• Energy accumulation
Rock n roll Model
Decay of gas-borne radioactive in a reactor circuit
Model improvements based non-Gaussian removal forces
Extension resuspension from multilayer deposits
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Reeks Reed & Hall Kinetic Model (1987)
nsoscillatio offrequency natural
)( gfluctuatin ;mean ; )(
n
RRRRR tfFtfFF
oscillator harmonic dampedlightly stiffvery
)(12tfmyyy Rn
)(tfR
QDrag Force
removal
<FR > > FAattractive
<FR> < FA
repulsive
FE > FA
particle surface adhesive potential well diagram
Detachment
D
Potential Energy
PE(y)
yd
Q
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resonant energy transfer /energy accumulation
• p is the rate constant for removal s-1
• n typical frequency of the deformation with potential
• Q the height of potential barrier (depends on difference of
adhesive removal forces)
• <PE> average Potential Energy in well
• Resonant energy contribution contribution
• β damping constant
• ER normaled energy spectrum of fR(t)
)( nRE
curvature) of radius energy, surface (JKR, force adhesive
1
/
2 ;
12
1exp
23
2/1222
2
2
rrf
ffn
f
Ffnp
a
nRRn
R
Ra
2
2
2
2
22
2
1exp
2 ;
2
1exp/
2
1
nsferenergy traresonant 1 static quasi 0
R
an
R
Ra
RR
f
fp
f
Ffffp
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Influence of surface micro roughness
Particle surface adhesive force
Distribution of adhesive forces
Fraction remaining after resuspension
Fractional resuspension rate
r
rrrrf aaaaa radius,asperity JKR
23
4~
contact smooth for
adhesionin reduction 01.0~
a
ar
aa
trp
R rdref a
)(
0
),(
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Short term Long term
Hinkley B CAGR gas flow
uτ = 2.2 m s-1
ϱf =1.2 kg m-3
μf = 1.82 x 10-5 kg m-1s-1
= 0.1 ; σa=4
γ= 0.15 Jm-2ar
Short and Long term Resuspension Rate
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Measurements of resuspension factor
Silt from grass at wind
speeds of 5m/s ο 10m/s +
in a wind tunnel Garland
1979
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resuspension measurements / model predictions
nominal 10 micron alumina spherical particles
No resonant energy contribution predictions
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Rock’n’Roll model for particle resuspension
1Γ
2 2L D L D
a rF rF F F F
a
At the point of detachment (ydh) the
adhesive ‘pull off’ force fa = -FA at (ydh), dh af f F
mean
fluctuating
r
0)()( yFtfF A
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Rate constant for Rock’n’Roll model
2
2
2
222
2exp
2exp2),(
f
f
f
fffffW
Gaussian statistically independent pdf
rate constant
number of particles released per sec
/ number of particles attached to surface
2 2
2 2 2
1 1exp 1
2 22 2
dh dhf f f
p erfπ f f f
y
.
detachment
position yd
angular
deformation yd
df df
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resuspension measurements / model predictions
nominal 10 micron alumina spherical particles
No resonant energy contribuition predictions
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Decay of particle concentration in a recirculating flow
CAGR reactor coolant circuit
exponential decay
~t-1
BOILER
TOP DOME
SUB DIAGRID
CORE
Reeks-Hall IDF Equation
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Biasi Correlations adhesive force distribution
geometric mean
geometric spread
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Non- Gaussian removal forces
0)()( tfyfa
European Aerosol Conference, Tours, France - Sept 4-9, 2016
data DNS from /z of onsDistributi1/2
2
1ff
y+=1
Rayleigh Distribution
Rayleigh DistributionRayleigh Distribution
Gaussian Distribution
y+=6 y+=1
European Aerosol Conference, Tours, France - Sept 4-9, 2016
data DNS from /z of onsDistributi 2
2ff
Johnson SU distribution
Gaussian distribution
Johnson SU distribution
y+=6 y+=1
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resuspension rate constant, p
Joint distribution of fluctuating aerodynamic force and its derivative
where A1 , A2 , B1 , B2 , B3 and B4 are all constants depending on y+.
),(;/;/ ; 4321
2/12
2/12
2
22 BBBBBffzfFfzu
fffaaadh
P
European Aerosol Conference, Tours, France - Sept 4-9, 2016
DNS Bfdot A1 A2 ω+
y+ = 6 0.358568 1.83605 1.478360 0.12714 0.346
y+ = 2 0.351181 1.75990 1.431301 0.13126 0.365
y+ = 0.6 0.346911 1.78475 1.446609 0.15203 0.366
y+ = 0.1 0.343658 1.81256 1.463790 0.16419 0.366
Table of resuspension rate parameters
Fffrms
2/12
European Aerosol Conference, Tours, France - Sept 4-9, 2016
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4Normalized resuspension rate constant
zdh
p/
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
10
20
30
40
p/
ratio o
f non-G
aussia
n t
o G
aussia
n
ratio
Gaussian case
non-Gaussian case
Resuspension Rate Constant
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Comparison of Original and Modified R’n’R model
ω+
Modified (DNS) 0.164189 0.366
original 0.0413 0.2
Ff2/1
2
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Comparision of fraction resuspended for 20m Alumina
u (m/s)
Fra
ction r
esuspended a
fter
1s
modified model (DNS)
original R'n'R model
Run - 7
Run - 8
Run - 20
Comparison with Hall’s experimental results
European Aerosol Conference, Tours, France - Sept 4-9, 2016
resuspension fraction after 1s modified versus original models
Hall’s experimental flow and adhesion properties
for 10 micron alumina particles
European Aerosol Conference, Tours, France - Sept 4-9, 2016
fractional resuspension rates for modified and original models
2.0/2/1
2 Ff
2.0/2/1
2 Ff
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Multilayer modelling
Friess and Yadigaroglu (FY), 2001
ξ = adhesive force, flow etc.
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Average radius
(μm)
Fluid density
(kg.m-3)
Fluid kinematic
viscosity (m2.s-1)
Wall friction velocity
(m.s-1)
0.227 0.5730 5.2653 x 10-5 6.25
Surface energy
(J.m-2)
Adhesion
reduction factor
(geometric
mean)
Adhesion spread
factor
(geometric
standard
deviation)
Geometric mean of
normalised adhesive
force
0.5 0.015 1.817 5.94
a
rms
ar
Ff
rz
2/3
– Values of parameters in STORM SR11 Phase 6.
Flow properties correspond to nitrogen gas at 12
bar pressure and temperature of 370 deg C typical
of a PWR severe accident
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resuspension rate of each layer for hybrid generic model STORM Test SR11 flow conditions
Reduction in adhesion 0.0075,spread in adhesion 1.001 Reduction in adhesion 0.015,spread in adhesion 1.87
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Resuspension of each layer vs. time
Reduction in adhesion =0.0075,spread=1.001Reduction in adhesion =0.0075,spread=1.001
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Fractional resuspension rate as a function of number of layers
(particle diameter: 0.45μm) based on STORM test (SR11) Phase 6 conditions
European Aerosol Conference, Tours, France - Sept 4-9, 2016
1 2 3 4 510
-3
10-2
10-1
100
101
102
Layer numbers (L)
Tim
e t
o r
esuspend h
alf o
f part
icle
s (
s)
spread factor = 1.1
spread factor = Biasi(1.8)
spread factor = 4.0
Resuspension half-life vs. layer thickness
European Aerosol Conference, Tours, France - Sept 4-9, 2016
100
101
102
10-4
10-3
10-2
10-1
100
101
layer numbers
Ratio
sf = 1.001, m = 0.0075
sf = 1.001, m = 0.015
sf = 1.1, m=0.015
sf = 1.8, m=0.015
sf = 4.0, m=0.015
- Ratio of short-term (<10-4 s) to long-term resuspension fraction
European Aerosol Conference, Tours, France - Sept 4-9, 2016
• Polydisperse model
Influence of size distribution
• Monodisperse model (single particle size)
• Polydisperse model (distribution of particle size)
2
2
ln( )1 1 1( ) exp
ln 2(ln )2 r r
r rr
r
Size distribution
European Aerosol Conference, Tours, France - Sept 4-9, 2016
0 1000 2000 3000 4000 5000 60000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1STORM SR11 test and multilayer model result (m = 0.01, sf = 1.5)
t (s)
Resuspensio
n f
raction
Experimental data
Monolayer, monodisperse
5 layers, monodisperse
10 layers, monodisperse
Monolayer, polydisperse
2 layers, polydisperse
3 layers, polydisperse
STORM SR11 Test
European Aerosol Conference, Tours, France - Sept 4-9, 2016
BISE Experiment Alloul-Marmor (2002)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Multilayer model results with BISE experiment
t (s)
Resuspensio
n f
raction
Experimental data
Monolayer, monodisperse
50 layers, monodisperse
100 layers, monodisperse
European Aerosol Conference, Tours, France - Sept 4-9, 2016
Summary & Conclusions
Kinetic model for resuspension of particles by a turbulent boundary Rate constant for removal for a particle from a surface
Analogy with desorption rate of molecules from a surface (Arrhenius)
resonant energy transfer/quasi-static removal
Originally developed for removal by lift forces (<F>,f,Ef(n))
Broad distribution of surface adhesive forces log normal) geom spread factor
Factor of 100 reduction in adhesion compared to perfectly smooth contact
Short term (e-pt) and long term resuspension Λ(t)~ξt-1
Decay of gas borne concentration in reactor coolant circuit (deposition and resuspension
Model validation Centrifuge measurements of surface adhesion,
Tangential force easier to remove particles than normal force - ‘rolling over lift off’
Development RnR model using moments of drag forces
• Much better agreement with R&H resuspension measurerments
RnR treatment for non Gaussian removal forces Significant increase in the resuspension rate for rough surface <FR> << g.mean adhesive force
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