7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Particle Resuspension Modelling in Turbulent Flows
Fan Zhang*,t Martin Kissanet and Michael Reeks*
*University of Newcastle, School of Mechanical and Systems Engineering,
Stephenson Building, Claremont Road, NewcastleuponTyne
NE1 7RU, United Kingdom
tInstitut de Radioprotection et de Sfiret6 Nucl6aire, Division de la Prevention des Accidents Majeurs, BP 3,
13115 SaintPaullezDurance, France
fan.zhang@irsn.fr
Keywords: adhesion, lift, fluctuations, multilayer deposit, severe accident
Abstract
This work is concerned with the way small particles attached to a surface are resuspended when exposed to a turbulent flow.
Of particular concern here is the dispersal of radioactive particles that could occur during accidents affecting nuclear facilities.
In this context the focus is on very small particles, < 5 microns in size, where the principal force holding the particle onto a
surface arises from Van der Waals intermolecular forces. The reference model is the Rock'n'Roll model which is based on a
statistical approach to resuspension leading to a resuspension rate constant for the escape of particles from a potential well via
the action of the turbulenceinduced fluctuating aerodynamic force. The aspublished Rock'n'Roll model assumes that the
aerodynamicforce fluctuations obey a Gaussian distribution. Here, this model is improved by using calculated statistics for the
fluctuations of both the streamwise fluid velocity and acceleration close to the wall taken from a LES of turbulent channel
flow, i.e., translating these data into the statistical moment of the drag force acting on the particle attached to the surface.
Overall, the influence of morerealistic (nonGaussian) forces on the resuspension rate is seen to be slight increase in total
resuspension. The sensitivity to the adhesive force distribution is also investigated and found to be strong. Further steps to be
taken include using direct numerical simulation (DNS) of turbulence to generate the statistics of fluctuating forces and
compare them with those found using LES. The ultimate model may well be a hybrid development of R'n'R model adapted for
application to multilayer deposits.
Introduction
In the event of an accident affecting a lightwatercooled
reactor (LWR) or other reactor technology such as a helium
cooled hightemperature reactor (HTR) or a thermonuclear
fusion reactor (e.g., ITER), it is expected that mechanical
resuspension of radioactive deposited particles would be a
primary safety concern. In a LWR this phenomenon would
occur, for example, in two principal situations:
 within the reactor coolant system due to socalled steam
spikes (rapid flow accelerations) as the degrading core
collapses into remaining water in the reactor vessel;
within the containment if a hydrogen deflagration takes
place.
The relevance of resuspension and its modelling to safety
assessment of reactors such as ITER and HTR arises from
the accumulation of contaminated dust in the coolant
circuit/torus. For ITER, activation products will accumulate
in deposited particles (graphite, beryllium, tungsten) in the
torus and could, in the event of a coolantwateringress
accident, be resuspended in the flow. For a HTR, the main
accident scenario of coolantcircuit depressurization would
resuspend dusts contaminated with activation products and
small quantities of fission products released during normal
operation such as silver and strontium.
Numerous experiments have been carried out to predict the
level of mechanical resuspension of deposited particles
arising in LWR severe accidents. The most recent are the
STORM tests which examined the resuspension of multi
layer aerosol particles in a pipe by high pressure dry steam
flows typical of those in a LWR lossofcoolant accident
(LOCA) (Capit~o & Sugaroni, 1995). As part of the
STORM programme, the resuspension data were used to
develop and test a number of resuspension models of
various levels of sophistication. Of these, the most useful in
terms of adaptability and predictability was the mechanistic
Rock'n'Roll model (Reeks & Hall, 2001) see below. The
Rock'n'Roll was successfully fitted to STORM results
(despite the significantly smaller size particles and higher
flow rates of these tests relative to those used to develop the
model) and those of other experiments by using the data to
produce values of the surface adhesion that would be
consistent with the measured resuspension. (Biasi et al.,
2001)
The ultimate objective of this work is to develop, validate
and apply a physical model for the resuspension of particles
from multilayer deposits that can account for the
resuspension of clusters of particles from a bed of particles
of variable size and shape. The practical application will be
that of assessing resuspension of particles in a range of
accident scenarios for existing or proposed nuclear facilities
(power and experimental reactors, fusion and fission). The
model could be a hybrid development of the Rock'n'Roll
model adapted for application to multilayer deposits. In this
paper, the modification of several resuspension models will
be described and discussed.
Nomenclature
a distance between two asperities (m)
A, constant of Rayleigh distribution
B, constant of Johnson SU distribution
Cbf coefficient of burst frequency
Crms coefficient of rms of aerodynamic force
f root mean square of resultant force
fa adhesive force (N)
fdh fluctuating aerodynamic force at detachment point
fR particle fraction remaining
F aerodynamic resultant force (N)
Fa adhesive force on smooth surface (N)
FD drag force (N)
FL lift force (N)
Ma adhesive moment (N.m)
MD aerodynamic moment (N.m)
mD root mean square of aerodynamic moment
r particle radius (m)
r' geometric mean of normalised asperities radii
u, friction velocity (m/s)
U, characteristic flow velocity (m/s)
zi normalised force
Z2 derivative of normalised force
Greek letters
F couple of a system (N.m)
y surface energy per unit contact area (J/m^2)
Pf fluid viscosity (Pa.s)
Vf fluid kinematic viscosity (m^2/s)
pf fluid density (kg/m^3)
Ga' spread factor (geometric std of asperities radii)
Tw shear stress at the wall (Pa)
(p(ra') distribution of normalised asperities radii
Subsripts
<> mean
erf() error function
Pure Resuspension Modelling
1 Modification of the NRG4 Model
Generally speaking, the NRG models are forcebalance
models and assume that resuspension occurs when the
aerodynamic force exceeds the adhesive force. The
aerodynamic force includes only the mean drag force,
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
therefore the fluctuating aerodynamic forces and lift force
are not considered in the models though the latter does not
affect much on resuspension comparing to the drag term.
However, it is physically more correct to consider the drag
force as a distribution rather than the mean only. This
subsection is divided into two parts: (i) the modified NRG
model uses the exact approaches for aerodynamic (MD) and
adhesion moment (Ma) as in original NRG4 model (Komen,
2007). (ii) The approaches for aerodynamic resultant force
(F) and adhesive force (fa) in R'n'R model (Reeks & Hall,
2001) are used in NRG4 and its modified model.
1.1 Part I
First of all, the aerodynamic moment, specifically the drag
moment MD, is assumed from a Gaussian distribution with
mean and root mean square mD (fluctuating
component) rather than a fixed value. The mean is obtained
from,
MD =1.399 FDr FD =1.7 67rpfu r2 [Equ 1]
where r is the particle radius, pf is the fluid density and u, is
the wall friction velocity. The r.m.s (mD) is assumed as 0.2
multiplies the mean which is the same assumption used in
R'n'R model for fluctuating aerodynamic force. It will be
shown later how r.m.s coefficient affects the particle
resuspension.
G(M) = exp ) j2]
12mD M f I
[Equ 2]
Therefore, the integration of the aerodynamic moment over
the whole region is applied into the formula which
calculates particle remaining fraction on the surface.
S= G(M)dM I Sqr)dr<
0
Substitute Equ 2 into Equ 3,
[Equ 3]
fR =f G(M)dM (p(r)d4'
0 D
exp fd(p)lr,
il r [Mm J Jd [)d
f0 M >A,
SMD < Ma
Then the above formula can be derived in term of an error
function,
fR= ierf[M MD ) p(rf )dr [Equ 4]
Distribution of normalised asperities radii ((p(r,')) is defined
as a lognormal distribution. The geometric mean value
1
r, = 0.01 is used for all the cases and three different
spread factors Ga' will be used in comparison. Biasi's
correlation (Biasi et al., 2001) (which is tuned based on
Hall's resuspension experiments (Reeks & Hall, 2001) and
describes that the spread factor varies as a function of
particle radius, e.g. for 10pm particles Ga' z 5.216) for
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
spread factor is applied to compare with other two values.
o' =1.8 +0.136(rx106)14
r,'= 0.016 0.0023 (r xl 6 )0.545
[Equ 5]
1.1.2
In this part, the modification of NRG model will be
demonstrated based on the correction of aerodynamic forces
with lift force included. Reeks and Hall's (Reeks & Hall,
2001) method of deriving mean aerodynamic resultant force
is applied.
Figure 1: Rock'n'R
ri
a g P

model geometry (Reeks & Hall,
2001)
[Equ 10]
fR 0
Both the NRG4 and modified model uses the aerodynamic
and adhesive force of R'n'R model. Therefore, they can be
referred to as NRG4RNR and NRGRNR Modified model.
As in 1.1.1, the mean normalised asperity radius is fixed to
0.01 and different spread factor is applied.
Comparison of fraction resuspended for Alumina, sf= 2
1
0 '
0 7/ o"
0 ./ .. *
Ir
o I6
0 I
0 .......... NRG4 l m
S0 // NRG410m
o  NRG420,m
02 ....... NRG Modified lpm
tI S//'  NRG Modified 10m
SNRG Modified 201m
1 2 3 4 5 6
u (m/s)
Figure 2: Comparison of NRG4 and modified NRG with
spread factor = 2
Comparlslon of fraction resuspended for Alumina, sf = 2
First of all, the aerodynamic resultant force F which derived
from the net couple of the system above
a
=a FL + rFD [Equ 6]
2
is assumed generated from a Gaussian distribution with the
mean and the fluctuating component or the root mean
square force f. a is the distance between two asperities. The
resultant aerodynamic force is defined considering on Equ
6. The fluctuating component is defined as 0.2 (r.m.s factor)
times the mean which is the same assumed in Reeks and
Hall (Reeks & Hall, 2001).
(F)= FL)+ FD) f=0.2(F) [Equ7]
2 a
where the geometric factor (r/a) which refers to the ratio of
the particle radius to the distance between asperities is
suggested to be close to 100. The variation of resuspension
depending on the r.m.s factor will be demonstrated later.
The mean drag and lift force are defined as,
(F) =32Pfvf2Li,
v f )
(FL) = 20.9pfv/f2 :
V
[Equ 8]
The adhesion moment is derived following Figure 14 and
the adhesive force fa is simply defined based on scaling on
the adhesive force for the smooth contact surface Fa in the
JKR model, as below
3
Ma =fa =F r'a =2nyrr a
2
u (m/s)
Figure 3: Comparison of NRG4RNR and modified NRG
RNR with spread factor = 2
In both Parts, it can be observed (from Figure 2 and 3) that
for a low roughness surface (the spread factor is small) the
modified models or the models involved a distribution of
aerodynamic force present a remarkable difference (5% ~
7%) to the NRG4 models as the particle size is small. This
may indicate that the fluctuating aerodynamic force has a
strong influence in smaller size (~plm) particles
resuspension on a low roughness surface.
[Equ 9]
The rest of model is similar to Part I, and finally the particle
fraction remaining on the surface is obtained as,
Compassion of fraction resuspended for Alumina, sf= 2
u (m/s)
Figure 4: Comparison of NRG4 and NRG4RNR models
with spread factor = 2
 16
 14
0
8 12.
_o
08
1 2 3 4 5 6 7 8 9 1C
Particle radius (pm)
Figure 5: Ratio of moment system of R'n'R model and
NRG4 model
There is a significant difference between the resuspension
fraction results of NRG4 and NRG4RNR model for small
size particles, as can be seen in Figure 4. The reason of the
huge difference is considered to be from the adhesion
moment systems since the aerodynamic moments in both
Parts have the similar performance. The adhesion moment
in NRG4 model is proportional to r53 whereas in NRG4
RNR model it is proportional to r2, therefore, as the particle
size decreases the adhesion in NRG4RNR model will be
more reduced, that is, the particle resuspension will increase
relatively. Figure 5 shows that as the particle radius is above
6pm the R'n'R moment system (Part II) starts gives less
resuspension than the NRG4 system (Part I).
2 Modification of the Rock'n'Roll Model
Jin (2008) calculated the data of fluid instantaneous velocity
in streamwise and vertical directions using Large Eddy
Simulations (LES) with the commercial CFD code Fluent.
The time interval was 0.0015s and there were 60116 time
steps calculated. The solution agrees rather well with Kim et
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
al. (1987) original model. The parameters are listed below:
pf =1.000kg/m3, uf = 0.0055555 kg/m s
Uc =18.0m/s r, =1.0132Pa
where tf is fluid viscosity, U, is characteristic flow velocity
and Tw is the shear stress at the wall. Then the wall friction
velocity is obtained as 1.0159m/s. The flow instantaneous
velocities are recorded in each time step and the recording
positions are y+ = 1, y+ = 2 and y+ = 6, respectively, away
from the wall.
Assuming the local fluid velocity is similar to the particle
velocity, recall Equ 8, the instantaneous drag forces acting
on the particle is then calculated from the velocities. Since
in R'n'R model the drag force contribute the main part to
the aerodynamic force (from Equ 7, the drag force is
multiplied by a factor of 100 and the lift force is reduced to
half), at the moment it is assumed that the lift force is
neglected and the aerodynamic force is due to the drag.
f (l N) .
Figure 6: Distribution of fluctuating drag force from LES
data (y'=6)
The aerodynamic force contains two parts: the mean and the
fluctuating component. Therefore, the fluctuating
aerodynamic force is obtained by subtracting the mean part
(arithmetic mean of the data) from the instantaneous
aerodynamic force.
f =F F)
Then the data of fluctuating aerodynamic force can be fitted
to a certain distribution. Figure 6 show that the data (for y' =
6) fit well to Rayleigh distributions.
Figure 7: Distribution of derivative of fluctuating drag
force from LES data (y'=6)
The derivative of the fluctuating aerodynamic force a is
The derivative of the fluctuating aerodynamic force y~ is
DislrbuiDon ofautuating dragforce f
calculated by the first order method,
S 2 [Equ 11]
The data of the derivative agrees well to a Johnson SU
distribution. The histogram plots and the fitted distributions
are shown in Figure 7.
Recall R'n'R model Quasistatic case (Reeks & Hall, 2001),
there is a assumption about the joint distribution of
fluctuating aerodynamic force and its derivative says that
the joint distribution is composed by two independent
normal distributions. From the LES data generated above,
the distribution of fluctuating aerodynamic force (Rayleigh
distribution) and its derivative (Johnson SU distribution)
can then replace the normal distribution assumption. Before
regenerating the new joint distribution, the variables need to
be normalised first. Let zi and z2 be the normalised force
and derivative, then
f 2
z1 = Z2
f
[Equ 12]
Then the new joint distribution can be obtained by
z1 A 1 I (z A,_
P(z, 2) A22 2 A,
B1 exp I (B3 +B ln(z + )21
[Equ 13]
where A1, A2, B1, B2, B3 and B4, are all constants depending
Z2 B4
on the fluid condition, z 
B2
The former part of Equ 13 which contains constants A, is the
Rayleigh distribution and the latter which contains B,
constants is the Johnson SU distribution.
Therefore, the resuspension rate constant in R'n'R model
(Reeks & Hall, 2001) is then modified as,
p jfP(ff ,f)df fPp(f,f)fdf
0
= K f) Jz2 P(z ,z2 )dC2 /i P(ziz2 )
f0d
where z V= f fdh is the fluctuating aerodynamic
force at detachment point which equals to the difference
between the adhesion and mean aerodynamic force. Finally,
the modified resuspension rate constant is obtained as
=Bfd ( A exp( 1 z dh A'
lJ2) A2 2 2 A2
/ 1exp_ ( ZdhA12
2 A2
[Equ 14]
The term 2 is assumed as 0.2 multiply the mean
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
aerodynamic force in R'n'R model, here it is calculated as a
constant factor C,,n multiply the mean.
) =C ,,, (F) [Equ 15]
In R'n'R model, the maximum value of p is limited to the
bursting frequency of turbulent motion in a turbulent
boundary layer, the ratio of the r.m.s derivative to the
fluctuating force is given as
= fK [Equ 16]
where Cbf can be called as the coefficient of burst frequency
which equals to 0.0413 in R'n'R model based on Hall's
experiment.
Compansion of resuspension rate for 10pm Alumina
104 102 100
t (s)
Figure 8: Comparison of resuspension rate
The modified model (also called nonGaussian model)
result gives great difference on resuspension rate to the
Gaussian case, shown in Figure 8 which can also be
observed from Figure 9 that for short period of time, the
nonGaussian model returns much more resuspension than
the original R'n'R model.
Comparlslon of fraction resuspended for 10Pm Alumina
09
/,
08. /
07 /
06 I
S05
04 / IJ
u_ I I Modified model t=O 0001
u (m/s)
Figure 9: Comparison of resuspension fraction with
different time
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Comparison of fraction resuspended for 1qm Alumina also concluded and discussed. The future programme
1 includes modifying the model using DNS data and
09 compares it with the current LES results, and then the
multilayer resuspension is considered.
08
0 7 Acknowledgement
0 06.
S6 / The authors thank Prof. R. Perkins (Ecole Centrale de Lyon,
05. France) for valuable discussions.
O 04  RnR,spread factor
S. RnR,spread factor 216 References
S0 3 RnR,spread factor10
02 .......NonGausslan RnR,spread factor Biasi, L., de los Reyes, A., Reeks, M.W. and de Santi, G.F.
 NonGausslan RnR,spread factor 216 (2001) "Use of a simple model for the interpretation of
0 1 NonGausslan RnRspread factor10 experimental data on particle resuspension in turbulent
o flows", Journal of Aerosol Science, Vol.32, p11751200
1 2 3 4 5 6
u(ms) Capitio, J. A. and Sugaroni, F. STORM Benchmarks. Final
Figure 10: Comparison of resuspension fraction with comparison report. EUR 16281 EN (1995).
different spread factor
Fluent. A product of Fluent Inc., Centerra Resource Park, 10
Ratio of fraction resuspended between RnR and NonGausslan RnR model for 10m Alum Cavendish Court, Lebanon, NH 037661442, USA.
o 9 Jin, C. A numerical simulation of particle deposition in
turbulent pipe flow. PhD Thesis, School of Mechanical and
Qo 08 Systems Engineering, Newcastle University. (2008).
0 7 Kim, J., Moin, P. and Moser, R. Turbulence statistics in fully
Developed channel flow at low Reynolds number. J. Fluid
0 6 Mech., Vol.177, pp133166 (1987).
S05
S. Komen, E. M. J. Dispersion of Fission Products and Dust in
4 Direct Cycle HTRs. NRG report 21346/06.60264C,
Revision 2, Petten (2007).
03 ...... spread factor
S spread factor 10 Reeks, M. W. and Hall, D. Kinetic models for particle
o2 ' resuspension in turbulent flows: theory and measurement.
25 s) timeafter s 1 125 Journal ofAerosol Science, Vol.32(1), ppl31 (2001).
Figure 11: Resuspension fraction ratio with different spread
factor
Figure 10 shows how the adhesion spread factor [Equ 5]
affects the resuspension. Generally speaking, as the spread
factor increase the resuspension in both models are reduced.
The ratio of resuspension fraction between original R'n'R
model and nonGaussian model is shown in Figure 11 and
one can observes that there is a huge difference between the
low and high adhesion spread cases when the fluid friction
velocity is relatively small (< Im/s).
Conclusions
The critical difference between NRG4 and Rock'n'Roll
moment systems is concluded and discussed. There is an
improved version of the Rock'n'Roll model based on using
measurements of the statistical fluctuations of both the
stream wise fluid velocity and acceleration close to the wall
from an LES of turbulent channel flow. It is concluded that
the modified Rock'n'Roll model gives approximately 5%
more resuspension than the original model. The effect of
adhesion spread factor and process time on resuspension is
