Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Clustering of monodisperse and polydisperse particles in a "box of turbulence"
Georgios Charalampous* and Yannis Hardalupas*
Imperial College London, Department of Mechanical Engineering,
Exhibition Rd, London, SW7 2BX, U.K
Keywords: particleladen gas, particle clustering, homogeneous and isotropic turbulence
Abstract
The development of a flow for an experimental investigation of particle clustering within a volume of homogeneous and
isotropic turbulence without mean flow, which is often referred to as a "box of turbulence", is presented. The operation of the
flow facility, which is based on driving 8 loudspeakers, placed at the vertices of a cube, with the same frequency and
amplitude, is described. Velocity measurements of the air flow field are presented, which evaluate the degree of homogeneity
and isotropy of the flow turbulence and the extent to which the mean flow velocity remains close to zero. The velocity
measurements showed that isotropic turbulence with nearly zero mean velocity could be established within a volume of a cube
with sides of around 60 mm. The lengthscales and statistics of the flow turbulence were calculated within a region of
40mmx40mm. The clustering of a range of particles, which include micronsized droplets, solid monodisperse polystyrene
spheres and polydisperse water droplets from a spray, due to flow turbulence was quantified in terms of lengthscale and
amplitude and its dependence on particle Stokes number discussed.
of the flow. However, with increasing Reynolds numbers,
the computational demands make numerical simulations
less feasible. Experimental investigation on the other hand
is not affected by this limitation.
Only few experimental facilities have been reported for
the generation of a volume of homogeneous and isotropic
turbulence without mean flow in a gaseous environment. All
implementations have revolved around a chamber, where a
number of jets aim at its centre. The balancing of the
flowrates injected by each jets leads to a region of
homogeneous and isotropic turbulence without mean flow.
The first implementation was proposed by Birouk et al.
(1996) and Birouk et al. ('I 1 i). The approach was to install
eight fans, mounted at the vertices of a cubic chamber,
which pointed at the centre of the chamber where the
desired flow was generated. The injected flowrate from each
fan was controlled by the rotational speed of the fans, in
order to counteract each other at the centre of the chamber
and form a volume with stirred flow but without mean
velocity. Since the gas flow generated by the fans was
supplied from the immediate vicinity of the fan, the faces of
the cubic chamber were closed and the gas flow within the
chamber had several large scale secondary flows, which can
influence the isotropy of the generated turbulence. Salazar
et al. (2I III and De Jong et al. (2I I' followed the same
approach.
A different approach was proposed by Krawczynski et
al. (2006), who constructed a closed chamber with 12 jet
inlets that supplied equal amounts of gas flowrate from a
source outside the chamber. Six of the jets were injected
into the chamber from the top and six jets were injected
from the bottom of the chamber to meet at the centre of the
chamber where, isotropy and homogeneity were satisfied at
the stagnation point at the centre. Since the gas that formed
the jets was supplied from outside the chamber, 10 outlets at
the median horizontal plane removed the excess gas flow
from the chamber.
Introduction
In many natural and engineering particleladen flows,
the centrifuging of particles away from flow regions of high
vorticity causes uneven dispersion and formation of particle
clusters, which are identified as regions with large
deviations of the particle concentration from the spatial and
temporal mean value. The preferential concentration of
particles affects both the flow of the carrier phase (Hwang
and Eaton (2006)) and the disperse phase and can have
consequences on the associated industrial applications. For
example, the evaporation of fuel droplets in a combustor
may be delayed in clusters with high droplet concentration
due to the saturation of the surrounding gas by fuel vapour
in the vicinity of the droplet cluster. This may cause large
variations of the local fuel air ratio in the combustion
chamber leading to less efficient and more polluting
combustion process.
The complexity of turbulent particleladen flows that
are encountered in practical problems makes the isolation of
individual effects and the quantification of associated
correlations between the observables difficult. For example,
it has been shown in particleladen jets that the modification
of the mean flow velocity of the carrier phase due to
momentum transfer from the disperse phase leads to
increase of gas phase turbulence due to the changes of the
mean flow gradients (Hardalupas et al. 1989). As a
consequence, the change of the mean flow of the carrier
phase masks the effects of particles on the structure of the
flow turbulence. However, by considering a simple and well
defined volume of homogeneous and isotropic turbulence
without mean flow, a lot of the complexity of the flow is
removed and particle clustering can be more easily
associated with the flow turbulence characteristics.
Numerical investigation of homogeneous and isotropic
turbulent flows is possible by means of Direct Numerical
Simulation (DNS) that may provide accurate representation
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
is that exchange of gas is allowed between the inside and
the outside of the chamber, which removes the possibility of
the formation of large scale motion. It also makes the
introduction of particles in the chamber easier than for a
closed chamber design. In contrast to Goepfert et al. (2010),
who used 6 loudspeakers, in our implementation we chose
to use 8 loudspeakers as in Hwang and Eaton (2I III) to have
more flexibility it the balancing of the flow within the
chamber.
The flow facility is built around a cubic frame,
constructed from aluminium profiles with an edge of one
meter. Eight loudspeakers from Davis acoustics, model
20MC8A (80W RMS, 6 Ohm impedance) were used to
drive the flow inside the cube. The cone of each
loudspeaker was capped with a PVC plate that was
perforated with circular holes of 6mm in diameter (Figure 1,
Left). The holes were arranged in a regular triangular mesh
pattern with a triangle edge of 20mm and covered an area
with a diameter of 160mm. The function of the perforated
plate is the generation of a uniform array of synthetic jets,
which is formed by the air that is displaced by the pulsating
loudspeaker membrane during its operation. This design of
synthetic jet arrays is identical to the one used by Goepfert
et al. (2010). Each loudspeaker was rigidly mounted on a
flat metal plate by metal rods (Figure 1, Right). The open
loudspeaker support and the open chamber design allowed
air to circulate around the speakers so that the heat that was
produced during operation would dissipate within the
volume of the room and not heat up the air inside the
chamber. The assemblies were mounted on the vertices of
the cubic frame and the centre axis of their cones pointed to
the centre of the cubic frame to form 4 pairs of opposing
synthetic jet arrays. The distance between opposing
synthetic jet array pairs was 590mm.
Paper No
Finally, Hwang and Eaton (2=II 14) developed a closed
chamber, where 8 loudspeakers were mounted at the
vertices of a cube and pointed at the cube centre. This
approach avoids the generation of the largescale flow
motion of the fans and is expected to generate better quality
of isotropic turbulence. The loudspeakers were driven by a
random frequency between 90Hz and 110Hz. The vibrating
motion of the loudspeaker membrane forced the air in the
vicinity of the loudspeaker to pulsate. By fitting a plenum
with a perforated plate at the loudspeaker cone exit, arrays
of synthetic jets were created that met at the box centre to
produce the desired turbulence characteristics. Following
this example, Goepfert et al. (2010) used 6 loudspeakers
placed at the faces of a cubic chamber to generate
homogeneous and isotropic turbulence. They simplified the
design of Hwang and Eaton (2=II 14), by driving the
loudspeakers at a fixed frequency of 42Hz and by simply
attaching a perforated plate directly on the speakers to form
synthetic jet arrays without the need for a plenum. In
addition they considered an open chamber configuration,
This was proposed to remove the possibility of standing
waves, which could develop by using a single frequency to
drive the loudspeakers, or a large scale flow motion that
might develop due to the secondary gas flows within a
closed chamber,
It is the purpose of this paper to describe the
development of a facility for the generation of a volume of
homogeneous and isotropic turbulence without mean flow
in the lines of an open chamber design with synthetic jet
arrays and to characterise the degree to which the
expectations of zero mean flow velocity and of turbulence
homogeneity and isotropy are satisfied. Then, we explore
particle clustering in the flow inside the chamber,
considering, micronsized droplets, which are normally used
as 'seeding' for optical measurements of flows, solid
polystyrene monodisperse particles of 80Clm diameter and
droplets from a polydisperse spray. The paper ends with a
summary of the main findings.
Nomenclature
Particle diameter (m)
Velocity (ms )
RMS velocity (ms )
Figure 1: Synthetic jet array construction. Perforated plate
fixed on loudspeaker (Left). Loudspeaker mounted on
support base (Right)
Each loudspeaker was independently driven by a sine
wave at a frequency of 50Hz. All the sine waves were in
phase to each other. The sine waves were generated by an 8
channel, 16bit National Instruments analogue output card
(PCI 6733). The power output of the analogue card was
insufficient to drive the loudspeakers, so before each of the
sine waves was fed to a loudspeaker, it was amplified by
one channel of four Behringer Europower EP2500 audio
stereo amplifiers (~600W/channel at 6 Ohms). The
amplification of each channel was fixed as the resolution of
the knob switch of the amplifiers was too coarse.
Adjustment of the loudspeaker driving signal amplitude was
only performed by changing the amplitude of the sine wave
from the analogue card. The high resolution of this card
Greek letters
E Energy dissipation rate (W/Kg)
v Kinematic viscosity (Pa s)
SKolmogorov length scale (m)
31 Taylor length scale (m)
SIntegral length scale (m)
Subscripts
x Horizontal direction
v Vertical direction
Experimental Facility
The facility for the generation of the volume of
homogeneous and isotropic turbulence was built following
the example of the open configuration proposed by Goepfert
et al. (2010). The main advantage of an open configuration
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
allowed the fine adjustment of the amplitude of each sine
wave which effectively enabled the precise control of the
intensity of each synthetic jet array.
The flow at the centre of the chamber was quantified
by measurements of the flow velocities on a plane that
passed through the centre of the chamber along the X and Y
axis (figure 2) by means of Particle Image Velocimetry
(PIV) and at a point at the centre of the chamber along the X
and Y axis by means of Laser Doppler Velocimetry (LDV).
For both techniques the air in the room where the chamber
was installed, was seeded with particles in the micron size
range produced by a fog generator located at the far end of
the room. The particles dispersed with a homogeneous
concentration throughout the room and due to the open
configuration of the chamber within the region of interest.
For Particle Image Velocimetry (PIV) measurements,
the 'seeding' particles were illuminated by the second
harmonic of a New Wave Nd:YAG laser at 532nm. The
maximum pulse energy per pulse was 120mJ, but, in
practice, much lower energies were required for the
measurements. The circular laser beam was formed to a
laser sheet with a waist of about 0.5mm FWHH, by a series
of cylindrical and spherical lenses. The flow imaging was
performed by a PCO Sencicam interframe camera with a
resolution of 1340 x 1040 pixels. Considering the
magnification of the imaging lens, the resolution of the
imaged area was 60.5Cum/pixel. An interference filter was
fitted to the camera lens, which filtered out light outside the
laser wavelength to minimise background noise. Processing
of the PIV images was performed by DaVis from LavIsion,
Depending on flow condition, the interrogation region was
set to 32 or 16 pixels with overlapping of either 0% or 50%.
In this way, we attained vector maps from grids of 32x32 up
to 128xl28, which correspond to spatial resolutions between
1.9mm and 0.48mm respectively. Due to the necessity of
checking the balance of the flow from each loudspeaker
entering the chamber from day to day and make small
adjustments to the amplitude of the signals driving the
loudspeakers, a small computational grid was set up to
decrease the processing time of the PIV images. The PIV
system also coupled as an imaging system for the
visualisation of the inertial particles that where considered
for the investigation of clustering.
A two component Dantec LDV system was used mn
backscatter mode for the velocity measurements at the
centre of the chamber. The directions of the LDV
measurements were along the X and Z axes of figure 2. In
this way, it was possible to measure all three velocity
components at the centre of the chamber and confirm that
no net flow was present normal to the PIV plane. The LDV
system was operated in the backscatter mode, at a focal
length of 310mm. The laser source for the LDV
measurement was a Spectra Physics 20W Ar+ laser. For the
two velocity components, the 488nm and the 514nm
wavelengths were used at a combined power of 200mW.
PlV camera
Figure 2: Experimental arrangement showing the
configuration of the 8 loudspeakers, along with the imaging
camera on the left and the LDV system on the right. The
laser sheet can also be seen illuminating the 'seeding
particles.
Initial test on particle clustering were performed using
two types of particles. The possibility of particle clustering
of the 'seeding' microfog droplets used for the velocity
measurements was also considered.
Monodisperse polystyrene particles (density
1050Kg/m3) by Microbeads AS with a specified diameter of
80Cum and coefficient of variation of their diameter certified
to be less than 5% of the central diameter were used. The
particles were introduced into the chamber from a vertical
tube of about 1.5m length directly over the centre of the
chamber. A series of metal meshes were installed along the
length of the tube to assist the even dispersion of the
particles within the tube. The mass flowrate of the particles
into the pipe was controlled by a volumetric screw feeder,
model Schenk 106.
In addition to the monodisperse particles, water
droplets (1000Kg/m ) from an air assist atomiser (Figure 3,
left) from Spraying Systems (type 1/4J) that produced a full
cone spray were introduced into the chamber. The atomiser
was placed on the top face of the frame spraying downwards
directly into the centre of the chamber (Figure 3, right). The
atomiser produced droplets in the region of 20100Clm.
Synt etic jet array
Imaged plane
 o o ooo oo
...
o~too
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
u(mis)
0 10
0 05
0 00
0 05
0 10
Region of
interest
x (mm)
e o Figure 3: Contours of the mean velocity component in the
horizontal direction (X axis of Figure 2), Ux.
Figure 3: Air assist atomiser (L<
the chamber (Right).
Results and Discussion
A. Gas flow in the chamber
Uy(mis)
0 00
0
iRegio tof
The flow at the centre of the chamber needed to be
balanced, so that no significant net flow was present in any
direction. This is a complicated process, as small changes in
the amplitude of the sine wave signals that drove the
loudspeakers caused major changes in the flow at the centre
of the box. The sensitivity of the flow was such that a
change of less than 1% in the relative amplitude of the
driving signals of two opposing jets was sufficient to move
the stagnation point between the two jets by over 30mm.
Finding the correct amplitude for all the driving signals
required an iterative procedure. First, the flowfield on the
XY plane was measured and then the amplitudes of the
driving signal voltages were adjusted to correct the
imbalanced flow. When the flow on the XY plane was
sufficiently balanced the velocity component on the Z axis
was measured by LDV and further adjustment of the
amplitudes of the loudspeaker driving signals took place. An
alteration of PIV and LDV measurements was performed
until all velocity components were balanced. This process is
necessary to repeat on a daily basis in order to correct
daytoday changes of the system.
From the PIV measurements, the contours of the spatial
distribution of the magnitude of the horizontal (Ux) and of
the vertical (U,) components of the mean velocity vector
over a region of 62mm x 62mm along the XY plane, shown
in Figure 2 at the centre of the chamber, are presented in
Figures 3 and 4. In these figures, both Ux and U, are zero
near the centre of the chamber. However, with increasing
distance from the centre of the imaged region, both Ux and
U, begin to deviate increasingly from zero. We chose to
consider a region of 40mmx40mm within which Ux and Ur
remained relatively low. In this region, the range of Ux was
between 0.073 and 0.067m/s and the spatial average Ux
was 0.005m/s. In the vertical direction U, varied between
0.021 to 0.039m/s and Uy was 0.oo5m1/s.
0 04
002
0 01
x (mm)
Figure 4: Contours of the mean velocity component in the
vertical direction (Y axis of Figure 2), U .
While the mean flow was small at the centre of the
chamber, the contour maps of the RMS of the velocity
fluctuations along the X and Y directions, presented in
Figures 5 and 6 respectively, show that the flow is actually
very active inside the chamber. Within the region of interest'
the value of RMSx is between 0.84m/s0.91m/s with a
spatially averaged value RM~Sxof 0.88m/s and RMSy is
between 0.88m/s0.96 with spatially averaged value,
RIS, at 0.92m/s. Comparison of the mean and the RMS
velocities in each direction confirms that the mean flow is
much smaller that the RMS velocity. In the X direction, the
ratio of Ux over RMSx is between 8.6% to 7.6% with the
ratio of the spatially averaged values Ux/MIS, of
0.6% and in the Y direction Uy/RMSy is between 4.2%
and 2.3% witih U,/RMS, at 0.6%. The extent of thre
ranges of the mean velocity over the RMS velocity and their
spatially average values show that the condition of a zero
net flow is satisfied to a good degree.
Air assist atomiser
r L~I I I
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
1.oo j
i .03~ l
001 002 003 004 005
x (mm)
RSY/RMSy
Region of
intereSt
~.92
RMSX(rmr)
09s
092
090
088
085
0 04
S0 03
Region of
interest
0 01 o
001 002 003 004 005 006
x (mm)
Figure 5: Contours of the mean RMS velocity component
in the horizontal direction (X axis of Figure 2), RMSx.
Figure 8: Ratio of RMSy/ RM~S showing degree of
homogeneity of the turbulent velocity fluctuations in the
vertical direction.
The final condition that needs to be satisfied is that of
isotropy of the turbulent velocity fluctuations. The ratio or
RMSx/RMSy in Figure 9 shows that the flow is fairly
isotropic, since the RMS velocity does not change by more
that 10% between the X and Y directions. The RMS velocity
is systematically slightly greater in the Y direction. However,
the degree of anisotropy is small as in the region of interest
RMS,/MS, is 0.95 and the investigation of particle
clustering should not be affected.
!Sy(mis)
095
0906
legion of
interest
O 01 0 02 0 03 0 04 0 05 0 06
X (mm)
Figure 6: Contours of the mean RMS velocity component
in the vertical direction (Y axis of Figure 2), RMSy
The homogeneity of the flow is quantified by the
contour map of the ratio of the RMS velocity to the
corresponding spatially average RMS velocity. In both X
(Figure 7) and Y (Figure 8) directions, the RMS velocity
does not change by more than 6% within the region of
interest which confirms the condition of flow homogeneity.
0 05
1 Region of
1003 interest
0 02 ~1 1 o
0 01 .
0 01 0 02 0 03 0 04 0 05 0 06
x(mm)
Figure 7: Ratio of RMSx/ RM~S showing degree of
homogeneity of the turbulent velocity fluctuations in the
horizontal direction
0 06~ Y
RSxfRMSy
on0
Region of
interest
O 01 0 02 O 03 O 04 O 05 0 06
x (mm)
Figure 9: Ratio of RMSx/RMSy showing the degree of
isotropy of the turbulent velocity fluctuations.
In addition to the contour maps of the mean and RMS
velocities, the spatial correlation coefficients of the velocity
fluctuations between two points in the region of interest
(Figure 11) were computed from the instantaneous PIV
VeoIcity distributions. Also, the 1D energy spectra were
computed and compared with the Kolmogorov 5/3 law.
The longitudinal two point velocity correlation
coefficients are defined as:
F.l (r)= ux (x, y)ux (x + r, y)
Jl ux ~~Jl(x, y~)2
u, (x, y)u (x'y+ r)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
(2)
10
0 9
~07
S0 6
os
,04
g 02
01
00
O Fuu
AGw
OGuu
aFw
oGw(calc)
30 40
lateral twopoint velocity
u;1 \ 1(x,y)Z JI* (x,y+r. )
in the horizontal and in the vertical directions of the PIV
measurement plane and the lateral correlation coefficients
G~lli Y)= x (x, y)ux (x, y + r)
G,,,, (;) ) (3) ')
u, (x +r, y)u (x, y)
G,, (r =
0 10 20
r (mm)
Figure 11: Longitudinal and
correlation coefficients.
where r is the separation distance between two points.
The longitudinal correlation coefficients are in
excellent agreement with each other. In addition, there is
good agreement between the lateral correlation coefficients.
These results support the condition of isotropy of the
turbulent velocity fluctuations, although, for separations
between two points that are close to the size of the region of
interest (>30mm), there is a small departure between the
values of the lateral correlation coefficients.
For isotropic turbulence, the relationship between the
lateral and the longitudinal correlations is given by Bachelor
(1953) as:
r ~F (r)
G (r)= F (r)+ (5)
2 dr
This relationship is well satisfied for most separation
distances. Again, the agreement is not perfect when the
separation distance is close to the size of the region of
interest. It is possible that this imperfection is a consequence
of the small systematic anisotropy that exists as the RMSx
velocities are on average about 5% lower than the RMSy
velocities,
Since the lateral correlation coefficients showed good
agreement between each other, the integral length scale was
estimated by integration over the longitudinal correlation
coefficients. As the correlation coefficients do not become
zero within the considered region, an exponential function
was fitted to the available data. The integral length scale
was found to be 52mm and 50mm for Fuu and Fvy
respectively,
The 1D longitudinal and traverse energy spectra of the
velocity fluctuations were calculated by averaging the
Fourier transform of each line or column of the
instantaneous PIV velocity data and then by averaging over
the number of acquired samples. The 5/3 law for the energy
spectra in the inertial range is given by Kolmogorov (1941)
as:
18 
E;,,, (k~,) = C e ;k"
55
for the longitudinal spectra and as:
E, (k,)=Eg(k)
for the transverse spectra, with C a constant equal to about
1.5 (Davidson (3I III)). In Figure 13, it can be seen that the
5/3 relationship of eq (6) is followed for the lower
wavenumbers. The relationship between the longitudinal
and the transverse spectra of eq (7) is also fairly satisfied.
The above suggest that the flow turbulence at the centre of
the chamber is isotropic.
1E+00 ~r~G
1E01  o Ewx
B Euuy
0 Ewy~
1E02
1E07
1E+02 1E+031E 4
k, (m l)
Figure 13: 1D energy spectra of the velocity fluctuations
Finally, the characteristics of the turbulence at the
Paper No
centre of the chamber are summarised in Table 1. The
spatially average energy dissipation rate was estimated from
twice the turbulent kinetic energy:
2
and the integral length scale A as:
/3
E =C C 2I (9)
C, is the normalized dissipation rate which is taken as 0.5.
The above quantities are sufficient for the calculation of the
spatially averaged Taylor microscale:
A =i~ (10)
Taylor Reynolds number:
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Table 1 (cntd): Summary of turbulent flow characteristics
inside the chamber
Re~ ZE (1 Zk 7
(ns) (nm) ons ga)
296 163 50 1.42 146
B. Particle clustering
The measurements of the velocity of the flow at the
centre of the chamber quantified the homogeneity, the
isotropy of the turbulence and the mean flow velocity and
determined the main characteristics of turbulence. At the
centre of the chamber, the flow was found to be
satisfactorily homogeneous and isotropic in a region of
40mmx40mm, where the investigation of particle clustering
was performed.
The investigation of particle clustering is presented here,
for particles with diameters of about 1l m, which are the
particles used for 'seeding' the gas flow for the velocity
measurements, for monodisperse polystyrene particles with
diameter 80Clm and polydisperse water droplets with size
range between 20 and 100Clm produced by an atomiser. It
should be noted that all the droplet sizes considered here are
smaller than the Kolmogorov scale of the flow turbulence,
which indicates that the influence of the particles to the flow
turbulence is negligible.
The two parameters that are important for particle
dispersion are particle inertia and gravity (Crowe et al.
1998). The particle Stokes number and the settling
parameter quantify the above two parameters.
The particle Stokes number is:
!" i
Re,
St =
eddv turnover time:
42
2
Ee=
with z, being the particle response time and z the
characteristic flow time scale (here the eddy turnover time
(12) and the Kolmogorov time scales).
The settling parameter is:
Kolmogorov length scale:
17 =:E (13)
and Kolmogorov time scale:
Zk =( (14)
Table 1: Summary of turbulent flow characteristics inside the
chamber
=RMS>
(n s) (n s) (n2 s2) (n2 s3, (nm)
0.88 0.92 2.43 7.5 4.9
S """" l p~gd2
u 18puU,
The values of the two parameters for the different types of
particles are presented in Table 2 for liquid water droplets
with diameters throughout the range of interest. Since the
density of polystyrene particles and 'seeding' particles is
similar to that of water, the values of Table 2 apply to those
particles as well. The Stokes number based on the eddy
turnover time is always less than 1. However the Stokes
based on the Kolmogorov time scale is unity for particles of
diameter of 22Clm. The settling parameter is always less
than unity. The effect of gravity becomes influential on
particle dispersion for particles with diameter larger than
around 60 Clm.
Table 2: Inertial and gravitational characteristics of water
droplets at the centre of the chamber
Diameter St, St., S, Pp
(mm) (Kg m3)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
behaviour is due to droplet interaction with instantaneous
turbulent flow structures.
Paper No
1
20
60
80
100
1000
1000
1000
1000
1000
1.9e5
7.5e3
6.7e2
1.2e1
1.9e1
2.1e3 3.4e5
8.6e1 1.4e2
7.7 1.2e1
14 0.22
21 0.34
With the exemption of the 'seeding' particles that were
introduced at the far side of the room, where the chamber
was located and then they were left to disperse into the
chamber, the solid particles and the water droplets were
released into the chamber directly above the region of
interest. The PIV system that was used to image the
'seeding' particles was also used for the imaging of the
heavier particles. A sample image of the polystyrene 80 Clm
particles is shown in Figure 11.
Figure 15: Timeaveraged scattered light intensity of water
droplets at the centre of the chamber. The detected area is
the same as the area of the PIV images (62mmx62mm)
The location of each particle or droplet in each
instantaneous image was determined by thresholding the
images and assigning a value to the geometrical centre of
each intensity peak. An example of the thresholding method
is shown in Figure 16, in which the locations of the detected
particles of image of Figure 14 are presented. The mapping
between the imaged particles and the location of the
detected particles is good, which demonstrated that the
thresholding method is reliable.
Figure 14: Instantaneous image of 80 Clm polystyrene
particles at the centre of the chamber
The polydisperse water droplets, which were injected
from the atomiser, were imaged by recording the intensity of
the scattered light from the droplets after illuminated by the
laser sheet. The intensity of the scattered light is
approximately proportional to the surface area of each
droplet (Domann and Hardalupas (2001), Charalampous,
Hardalupas and Taylor (2= II I4)). The scattered light intensity
was recorded and averaged at each pixel of the images over
the total number of images. In this way, the mean surface
area of the water droplets at each pixel of the imaged region
was estimated (Figure 15). The intensity of the
timeaveraged scattered light intensity is an indication of the
uniformity of the distribution of the surface area of the
droplets inside the chamber. Taking into account the
intensity distribution of the laser sheet, which is responsible
for the horizontal streaks and the lower intensity at the
bottom of the image, the averaged scattered light intensity
across the detected area of the chamber was fairly uniform
(Figure 15). Therefore, we can argue that the timeaveraged
distribution of droplets was uniform and any clustering
Figure 16: Processed instantaneous image of Figure 14
show the location of the detected particles
The preferential concentration of particles was
quantified by the Radial Distribution Function (RDF):
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
N(r)
g~r)= NAVr
where N(r) is the number of particles at a ring with radius r
from the centre of each particle in the region of interest and
width 2dr av(r) is the volume between rdr and r+dr, N is
the total number of particles and AV is the total volume in
the considered region (see Figure 17).
O 000 0 002 0 004 0 006 0 008 0 010 0 012 0 014
r (m)
Figure 18: Radial distribution function of the 1 Ctm PIV
'seeding' particles.
The monodisperse polystyrene 80Clm particles were
introduced into the chamber from above and allowed to
disperse in the flow. The mass loading, in this case, was
estimated by counting the number of particles in each image.
The mass of the solid phase was calculated by multiplying
the number of particles with the mass of each particle,
which is known since the particles are monodisperse. The
mass of the gas phase was estimated by calculating the
volume of the imaged region and multiplying it by the
density of the gas. The mass loading of the particles was
estimated 1.1%+0.6%. The uncertainty margins are rather
high, which is due to the changing number of particles that
entered the region of interest in each image. Figure 19
presents the RDF, which clearly shows that there is
clustering of particles throughout the region of interest. The
density of the particles is constantly increasing with
decreasing radius, and peeks at 1.45 for r=0.4mm, which is
2.7 times the Kolmogorov scale of the flow turbulence.
Figure 17: The particle number density at each distant r is
calculated by counting the number of particles in a volume
dV(r), shown shaded, between rdr and r+dr and normalisng
'vith dV(r).
The RDF is effectively the ratio of the particle number
density at a distance r over the mean particle density in the
considered volume. Deviation from unity indicates that the
particles are not randomly distributed.
We examine first the behaviour of the 'seeding,
particles, which have Stokes number much smaller than 1,
Figure 18 shows the Radial Distribution Function for the
1Ctm particles. The figure shows that value of the RDF
remains equal to 1 down to a scale of 0.7 mm, which
indicates that the particle concentration remains random
down to this scale, which is around 4.8 times the
Kolmogorov length scale. For scales lower than 0.7mm, the
RDF obtains values slightly larger than 1 and becomes
maximum with a value of 1.07 at a scale of 0.4mm, which is
around 2.7 times the Kolmogorov scale. This indicates that
at the small scales particles with very small Stokes number
might not be uniformly dispersed. The mass loading of the
flow for this case can be considered to be negligible, since
the mass of each particle is very small and it would take
millions of particles in the imaged region to attain even a
mass loading of 0.1%.
1 6E+00
1 4E+00
1 2E+00
1 0E+00
8 OE01
60E01
4 0E01
20E01
0 0E+00
0 000 0 002 0 004 0 006 0 008 0 010 0 012 0 014
r(m)
Figure 19: Radial distribution function of 80Cum
monodisperse polystyrene particles.
Finally, the RDF of the polydisperse water droplets is
presented in Figure 20. The water droplets have a range of
sizes between 20 and 100 Clm. As a consequence of the wide
range of droplet sizes, the mass of each detected droplet is
unknown and, therefore, the mass loading of droplets in the
gas phase could not be determined. However, the mass
loading for the droplets is also expected to be small, so that
there was no effect of the droplets on the gas phase
turbulence. The RDF of Figure 20 shows that there is a
nonrandom component at the droplet distribution, which is
more profound at smaller scales than for the monodisperse
particles of 80Cum, since the RDF value increases fast for
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
same scales, there is no significant preferential particle
concentration for the 'seeding' particles and conversely that
there is preferential particle concentration of the
monodisperse particles and the polydisperse water
droplets.
Paper No
scales lower than 2mm at a maximum of around 1.4 at
0.4mm after which it decreases sharply.
1 6E+00 ,, 
O 8 OE01
40E01
2 0E01
010
0 09
0 08
0 07
0 06
O 0 05
0 04
0 03
0 02
o 01
0 00
a Expenrnent
si Polsson
r (m)
Figure20: Radial distribution function of polydisperse
water droplets.
Since the maximum value of the RDF was found to be
at 0.4mm for all 3 cases this could indicate the limits of the
resolution of our current optical implementation since
particles that are separated by smaller distances might
appear as one.
A further test of the randomness of the particle
concentration was performed by dividing the images in
small square cells. Grid sizes of 2mm and 4mm were
considered, which are of the order of the Taylor lengthscale
of the flow turbulence. The number of particles that
appeared in each cell was counted for all acquired imageS
and the frequency of the number of particles in a cell was
calculated. Comparison of the derived distribution was
made with the Poisson distribution:
0 10 20 30 40 50
counts
Figure 21: Distribution of the particle number counts of
polydisperse water droplets for 2mm cells
0 20
0 18
0 16
a 14
O 12
S0 10
0 06
0 04
0 02
0 00
aExperlrnent
aPolsson I
f (n; p) =
HI
0 10 20 30 40 50
Counts
where n is the count of particles and C1 is the mean number
of particles in a grid cell. If the number of particles that
appears in each cell is random, then it should follow a
Poisson distribution. The deviation from a Poisson
distribution was quantified with parameter:
D = G poisso (9
where a is the standard deviation of the measured
distribution and a oisnis the standard deviation of the
Poisson distribution, as suggested by Fessler et al. (1994)
and also used by Hardalupas and Horender (2*== = ). When
D=0, the particles are randomly distributed.
Parameter D was 0.0220.030 for cell sizes of 2mm and
4mm for the 'seeding' particles, which indicates conformity
to a random (Poisson) distribution in which is shoru1 in
Figure 21. In contrast, for the monodisperse 80 Clm
particles, D was 0.411 and 0.445 for 2mm and 4mm cell
sizes and for the polydisperse water droplets D was 0.370
and 0.412 for cell sizes of 2mm and 4mm respectively,
which indicate a nonrandom distribution of the particle
number density. The corresponding distributions are
compared to a Poisson distribution in Figure 22. The above
agree with the findings of the RDF, which shows that for the
Figure 22: Distribution of the particle number counts of
polydisperse water droplets for 2mm cells
Conclusions
A facility was developed for the generation of
homogeneous and isotropic turbulence without mean flow.
The chamber design followed the examples of Hwang and
Eaton (2I III) and Goepfert et al. (2010) using synthetic jet
arrays generated by loudspeakers to stimulate the flow at the
centre of a cubic chamber. For our implementation, we
chose an open chamber configuration to avoid issues that
might arise from large scale motion that can develop within
a closed chamber and used eight loudspeakers placed at the
vertices of a cube.
Planar measurements of the flow velocities at the
centre of the chamber, revealed a region of 40mmx40mm in
which the RMS velocities were of the order of 0.87m/s and
the mean flow velocities about 0.005m/s suggesting that the
zero mean flow is satisfied within that region. In this region,
the spatially averaged ratio between the rms of the velocity
fluctuations in the two directions of the flow was 0.95
showing that the flow turbulence is satisfactorily isotropic
and the range of local RMS velocities were within 6% of the
spatially averaged value in the region confirming
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Fessler, J.R., Kulick, J.D., Eaton, J.K., 1994. Preferential
concentration of heavy particles in a turbulent channel
flow. Phys. Fluids, Vol 6, 37423749 (1994)
Goepfert C., Marie J., Chareyron D., Lance M.,
Characterization of a system generating a homogeneous
isotropic turbulence field by free synthetic jets, Experiments
in fluids, (2010)
Hardalupas, Y. and Horender S. Fluctuations of particle
concentration in a turbulent twophase shear layer,
International Joumnal of Multiphase Flow, Vol 29,
16451667 ('1 IIi)
Hardalupas, Y., Taylor, A.M.K.P. and Whitelaw J.H..
Velocity and particleflux characteristics of particleladen
turbulent jets, Proc. Roy. Soc. Lond. A, Vol 426, 3178
(1989).
Hwang, W and Eaton, J.K., Creating homogeneous and
isotropic turbulence without a mean flow, Experiments in
fluids, Vol, 36, 444454 (21 4 .~
Hwang, W T. and Eaton, J.K. Homogeneous and isotropic
turbulence modulation by small heavy (St similar to 50)
particles, Joumnal of Fluid Mechanics, Vol 564, 361393
(2006)
Kolmogorov, A.N., The local structure of turbulence in an
incompressible viscous fluid for very large Reynolds
numbers, Proceedings of the USSR Academy of Sciences
Vol. 30, 299303 (1941)
Krawczynski J. F., Renou B., Danaila L., Demoulin F. X.,
Smallscale measurements in a partially stirred reactor,
Experiments in fluids, Vol 40, 667682 (2006)
Salazar, J.P.L.C., De Jong, J., Cao, L.J., Woodward, S.H.,
Meng, H. and Collins, L.R., Experimental and numerical
investigation of inertial particle clustering in isotropic
turbulence, Joumnal of Fluid Mechanics, Vol. 600, 245256
Paper No
homogeneity. The turbulent Reynolds number based on
Taylor microscale, Reh, that was realized under these
conditions was 296.
Measurements of particle concentration were
performed for the micronsized water droplets, monosize
polystyrene particles of 80Clm and polydisperse water
droplets in the range 20100 Clm and the particle Radial
Distribution Function (RDF) was quantified. The RDF of
micronsized droplets indicated possible particle clustering
at scales of less than 4.8 times the Kolmogorov scale. The
RDF of the monodisperse 80 Clm particles and the water
droplets showed evidence of clustering at scales lower than
around 3mm, which is around the Taylor lengthscale. The
decrease of the values of the RDF for scales less than
0.4mm in all 3 cases suggests that the resolution of the
imaging system needs to be increased for evaluation of the
RDF at smaller scales.
Acknowledgements
We would like to thank Professor Michel Lance and Dr
JeanLouis Marie for helpful demonstrations of their
experimental facility and assistance with the initial design of
the flow facility. The research has been supported by
Engineering and Physical Sciences Research Council
(EP SRC) through grant EP/EO295 15/1.
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