2017_02_14_resus_pres_1 - · pdf fileeuropean aerosol conference, tours, france - sept 4-9,...

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


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


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


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 /


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


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


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


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


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

),(


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


Measurements of resuspension factor

Silt from grass at wind

speeds of 5m/s ο 10m/s +

in a wind tunnel Garland

1979


Hall’s measurements of Lift Force


Measurements of adhesion


Resuspension measurements / model predictions

nominal 10 micron alumina spherical particles

No resonant energy contribution predictions


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


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


Resuspension measurements / model predictions

nominal 10 micron alumina spherical particles

No resonant energy contribuition predictions


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


Biasi Correlations adhesive force distribution

geometric mean

geometric spread


Non- Gaussian removal forces

0)()( tfyfa


data DNS from /z of onsDistributi1/2

2

1ff

y+=1

Rayleigh Distribution

Rayleigh DistributionRayleigh Distribution

Gaussian Distribution

y+=6 y+=1


data DNS from /z of onsDistributi 2

2ff

Johnson SU distribution

Gaussian distribution

Johnson SU distribution

y+=6 y+=1


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


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


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


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


resuspension fraction after 1s modified versus original models

Hall’s experimental flow and adhesion properties

for 10 micron alumina particles


fractional resuspension rates for modified and original models

2.0/2/1

2 Ff

2.0/2/1

2 Ff


Multilayer modelling

Friess and Yadigaroglu (FY), 2001

ξ = adhesive force, flow etc.


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


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


Resuspension of each layer vs. time

Reduction in adhesion =0.0075,spread=1.001Reduction in adhesion =0.0075,spread=1.001


Fractional resuspension rate as a function of number of layers

(particle diameter: 0.45μm) based on STORM test (SR11) Phase 6 conditions


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


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


• 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


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


Monolayer, polydisperse

2 layers, polydisperse

3 layers, polydisperse

STORM SR11 Test


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




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

2017_02_14_resus_pres_1 - · pdf fileeuropean aerosol conference, tours, france - sept 4-9,...

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