7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Measurement of Pollen Settling Characteristics in near Homogeneous Isotropic
Turbulence
Lilach Sabban, Rene van Hout
TechnionIsrael Institute of Technology
Department of Mechanical Engineering
Haifa, 32000, Israel
lilsab @technion.ac.il and rene technion.ac.il
Keywords: Bioaerosols, Particle settling, Homogeneous isotropic turbulence, Highspeed inline digital holography
Abstract
In models of atmospheric pollen dispersal, the pollen grains are generally modelled as small spheres and any morphological
features are thought to be irrelevant to their dispersal characteristics. However, most pollen grains have striking morphological
features. Pollen release and dispersal occurs in turbulent atmospheric flows that are known to affect the stillair settling
velocity of small particles. The effect of turbulent eddies on pollen dispersal can be estimated by considering the Stokes
number, defined as the ratio between the particle response time, and a characteristic time scale of the flow, e.g. the
Kolmogorov time scale. Taking into account a range of pollen densities and dissipation rates, Stokes numbers of order one are
obtained, indicating that pollen response to turbulence is of the same order as the Kolmogorov time scale. Therefore, the pollen
settling velocity in a turbulent flow field, an essential input parameter to any dispersal model, is expected to be significantly
different from the stillair settling velocity.
We present results on the settling behavior of particles in near homogeneous, isotropic turbulence generated in a 40 cm3
transparent turbulence chamber. The flow inside the chamber was generated by 8 woofers mounted on the comers. Each
woofer was driven independently at a randomly changing frequency. The generated turbulent flow field was validated using
stereoscopic Particle Image Velocimetry (PIV). Two different pollen types, ragweed (20gm), pine (5060 gm) as well as
polystyrene spheres (80 gm) were released by a high frequency vibrating sieve mounted on the top of the chamber that
prevented clumping of the particles. The settling trajectories were measured using highspeed, inline digital holographic
cinematography. Particle Stokes numbers were of order one, the lowest for ragweed pollen. Holograms were acquired both for
settling in still air as well as in near homogeneous, isotropic turbulence. Results indicate a large effect of the turbulent eddies
on the settling behaviour with the trajectories becoming increasingly meandering in contrast to the straight vertical settling
paths in still air.
Introduction
The efficiency of anemophelous (wind pollinated) pollen
dispersal by male flowers and capture mechanisms by
female flowers is important for the proliferation of the
species (Niklas 1985). Wind pollinated plants produce large
pollen amounts that are released from the male flowers and
entrained into the atmosphere by turbulence. For example,
ragweed (Ambrosia) flowers produce large amounts of
pollen (one billion pollen grains per plant) and its ability to
quickly invade new habitats as well as widespread allergenic
effects demonstrate that pollen dispersal is particularly
efficient in this case. Research indicates that the plant has
invaded China, and parts of Australia, and is now moving
rapidly across Europe (Wang et al. 1985, Bass 2000,
Rybnicek & Jiger 2001). An example of a genetically
modified food crop is corn (Zea Maize), a major food supply
across the world. Corn plants have been genetically
engineered for better resistance against pesticides and
herbicides. However, the risks of gene introgression
between genetically modified plants and natural populations
is poorly understood. Depending on atmospheric conditions,
large amounts of ragweed pollen can be transported over
considerable distances (20 km) and heights (2 km) from
the emitting source (e.g. Hays & Ogden 1974).
Measurements of corn pollen (80 gm) showed that
concentrations decreased with height, i.e. at twice the
canopy height concentrations were reduced to about 30% of
those observed at canopy height (van Hout et al. 2008). In
general, due to a lack of detailed measurements, there is
uncertainty regarding atmospheric parameters that govern
pollen dispersal (Jackson & Lyford 1999). In addition,
pollen entrainment is not continuous but episodic and is
related to wind gusts.
Particle dispersal models commonly predict the dispersion
and deposition of particles assuming that they are emitted
continuously from a point source. Pollen dispersal models
such as those developed by Prentice (1985) and Sugita
(1993) are based on Sutton's equation (Sutton 1953):
Q(x) = exp(4Vdx"/2/nVf C,) (1)
where Q(x) represents the fraction of particles that remain
airborne at a distance x from the source. Q(x) is a function of
the deposition velocity, Vd, the wind speed, Vf, the
turbulence parameter n, and the vertical diffusion coefficient,
Cz. The diffusion coefficient in unstable conditions is
commonly taken between 0.250.32 and the turbulence
parameter as 0.2. The deposition velocity is defined as the
deposited particle rate at a surface divided by the airborne
particle concentration above the surface. In quiescent air, the
deposition velocity equals to the still air, particle settling
velocity.
The settling velocity of pollen grains is an essential input in
any pollen dispersal model. The Stokes settling velocity of a
spherical particle in a quiescent fluid is given by:
Ppd g
V= (2)
18p/
This equation is often used to estimate the settling velocity
of pollen even in turbulent flow conditions assuming that (i)
Stokes flow conditions (Rep = IVpVldlv < 1) hold for
pollen, (ii) the particles are spherical and (iii) the pollen
density equals for example to that of water. Although pollen
grains are saturated with water upon release, previous
studies indicated that pollen grains tend to dry within
seconds after their release. As a result, pollen densities
found in the literature vary widely (Durham 1943). For
example, ragweed pollen density ranges from 840 to 1280
kgm3 depending on the relative humidity (Harrington &
Metzger 1963). In addition, the volume and shape of pollen
grains may also change due to hydration and dehydration,
although some pollen have hard outer shells, e.g. ragweed,
and exhibit very little volumetric change (Payne 1981).
Furthermore, the assumption of a spherical shape does not
hold for pollen grains that are characterized by irregular
shapes and striking morphological surface features. This
will be a further cause for differences between the actual
settling velocity and the estimated settling velocity using Eq.
(2).
Ragweed pollen have spikes (Fig. lb), whereas most conifer
pollen have one to three air filled sacci or bladders, e.g. pine
is a bisaccate pollen grain having two bladders (Fig. la).
(a) (b)
Figure 1: SEM images of pollen (a) Pine (Pinus) (b)
ragweed (Ambrosia)
Still air settling velocities of pollen grains have been
measured in falltowers (Durham 1946, Niklas 1982).
Schwendemann et al. (2007) used stroboscopic photography
to measure the still air settling velocity of pine pollen and
developed a model to predict the settling velocity of pine
pollen with and without sacci. Sacci increase the drag force
by increasing the pollen grain surface area without
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
significantly increasing the pollen grain's mass. The
comparison showed that the settling velocity of pine pollen
without sacci was higher (3.4 cms1) than pine pollen with
sacci (3.07 cms1). Previous numerical studies on the
settling velocity in homogenous isotropic fluid all assume
spherical particles. The pollen grains' irregular shapes may
cause their settling velocity to substantially differ from a
spherical particle settling velocity.
An additional effect that needs to be accounted for when
estimating the actual pollen settling velocity is the ambient
meteorological conditions. Studies on diurnal patterns of
pollen emission have shown that pollen is emitted during
the mornings as the humidity drops and that unstable
conditions, characterized by considerable turbulence have
the most pronounced effect on pollen emission (Ogden et al.
1969, Jackson & Lyford 1999, Barnes et al. 2001, van Hout
et al. 2008).
The objective of this study is to experimentally measure the
effect of a near isotropic, homogeneous turbulent flow field
on pollen settling characteristics. Both PIV and digital
holography techniques are used. First, the experimental PIV
setup used to characterize the turbulence generated inside a
turbulence chamber, is discussed. Next, the inline digital
holographic cinematography used for particle tracking will
be presented. Last, results for particle settling in quiescent
air will be compared to results of settling in near
homogeneous, isotropic turbulence.
Nomenclature
C Constant (1.5x18/55)
C1 Constant (4/3C)
Cs Smagorinsky constant (0.17)
Cz vertical diffusion coefficient
d diameter (m)
E Turbulent kinetic energy spectra (m3S2)
f# Camera'sfnumber
f Focal length of lens (m)
g gravitational constant (ms2)
L Integral length scale (m)
n turbulence parameter
Q Particle fraction that remains airbom
Re Reynolds number
Sl Component of fluctuating strain rate tensor
(s1)
Stokes number
mean flow velocity
(fluctuating) flow velocity (ms 1)
Velocity (ms')
Particle velocity (ms 1)
coordinate (m)
Spatial average of z
ensemble average of z
Greek letters
A band width
e Dissipation rate (m2s3)
l Length scale (m)
c Wave number (m1)
/, Laser wave length (m)
Taylor microscale (m)
Dynamic viscosity (Pas)
Kinematic viscosity (m2s1)
Density (kgm )
Component of stress tensor (Nm2)
Time scale (s)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
followed by a cylindrical lens (f = 10 mm). Cameras and
laser were synchronized using the LaVision programmable
timing unit.
Flow tracers
(oil droplets)
Light sheet
optics
Cutoff
deposition
flow
Direction indices i,j=1,2,3
Particle
settling
Kolmogorov
rms
Spatially resolved
Nd:YAG Laser
r, k

FOV
........ a
Turbulence
chamber
\ Scheimpflug
Ssetup
CCD*
Abbreviations
BF Backward Forward
CCD Charged Coupled Device
CMOS Complementary Metal Oxide Semiconductor
DNS Direct Numerical Simulation
FFT Fast Fourier Transform
FOV Field Of View
LES Large Eddy Simulation
ND Neutral Density
PIV Particle Image Velocimetry
PS PolyStyrene
rms Root mean square
SGS SubGrid Scale
TKE Turbulent Kinetic Energy
Experimental setup: Stereoscopic PIV Experiment
A schematic layout and photograph of the turbulence
chamber together with the stereoscopic PIV system is
shown in Figure 2. The turbulence chamber was designed
following Hwang & Eaton (2004) and consisted of a 40 x 40
x 40 cm3 chamber, with transparent acrylic windows. On
each corner of the cube a woofer was mounted directed
towards the center of the chamber. Each woofer was driven
independently by a sine wave having a constant amplitude,
while the frequency and phase were changed randomly
between 90100 Hz and 010 ms respectively.
The generated flow field inside the turbulence chamber was
measured using a stereoscopic Particle Image Velocimetry
(PIV) system (LaVision Gmbh) consisting of two CCD
cameras (2048x2048 pixel, 7.4pm square pixels), a pulsed
Nd:Yag laser (Quantel, 532 nm) and laser sheet optics. A
scheimpflug setup was used where the cameras were
arranged in BF scattering position. The BF position was
chosen such that the calibration is done while the cameras
are focused on the same plane. Different lens (50 mm
Nikon) f# numbers were used to account for the intensity
differences between the forward and backward scattered
light from the flow tracers. Combinations off# = 8 and 5.6
orf# = 5.6 and 4 were used for the first and second camera,
respectively. The lenses were mounted on a Scheimpflug
adapter in order to achieve focus across the field of view.
The light sheet was formed by a pair of spherical lenses
II
Turbulence
Chamber
a 
figure : Stereoscopic riv setup (a) scnematic layout
(top view) (b) Photograph of setup. Origin of coordinate
system is located at the center of the turbulence chamber.
The flow was seeded with small oil droplets generated by a
portable smoke generator (Colt 4) with oil droplet median
size of 0.20.3pm. Measurements were performed after the
woofers were running for at least 60 s in order to achieve
statistically stationary turbulent flow. The flow
characteristics were measured for two cases A and B at
increasing woofer amplification. At least ten different data
sets were taken at each amplifier setting resulting in a total
number of vector maps that exceeded 500. Image distortion
due to perspective projection was corrected and the
Subscripts
c
d
f
i,j
p
s
k
dewarped (corrected) image had 2086x2050 pixels resulting
in a spatial resolution of 0.022 mm/pix and a FOV of 45.9 x
45.1 mm2.
The resulting PIV images were processed by LaVision
Davis 7.2 software. Velocity distributions (130x128 vectors)
were obtained by multipass cross correlation (FFT based)
with a decreasing window size from 64x64 pixels with 50%
overlap to 32x32 pixels with 50% overlap resulting in a
vector spacing of 0.352 mm.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
stereoscopic PIV setup. Spatial maps of the rms ratios are
displayed in Figure 4 indicating a good degree of isotropy in
the center of the turbulence chamber.
Flow field characteristics
20
(a)
0
[ms1 ]
1.2
1.1
1
0.9
0.8
10 2U
Figure 3: Spatial maps for (a) u', (b) u'2 and (c) u.'3
Case B.
The spatial distributions of the rms values of the three
fluctuating velocity components, u, for case B are
displayed in Figures 3ac. Figures 3a and b show that the
spatial distributions of ul and u' are spatially more
uniform than u3 in accordance with the less accurate
determination of the outofplane velocity component in the
10
20
20 10 0
(c) x1 [mm]
10 20
Figure 4: Isotropy ratio maps. (a) u', /u'2 (b) u'1 /u'3
(c) u'2 /'3. Case B.
The spatially averaged (denoted by overbar) mean and rms
velocities as well as the rms ratios are summarized in Table
1, for cases A and B.
20 10 0
(c) x [mm]
1.75
L .75
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Table 1: Spatial averaged characteristics. Velocity units are [ms 1]
Case U, u', U, U2, U, u U1 2 u 3 u'2/ '3
A 0.06 0.48 0.03 0.49 0.1 0.52 0.98 0.94 0.96
B 0.06 0.58 0.05 0.59 0.03 0.64 1 0.92 0.93
As expected, a higher amplification factor (Case B) leads to
higher rms values. Ratios of spatially averaged rms values
are close to one, indicating near homogeneous, isotropic
turbulence in a statistically averaged sense. Spatially
averaged mean velocities are in most cases less than 10% of
the spatially averaged rms velocities. The higher rms
velocity values in the outofplane direction, i = 3, for both
cases A and B, are probably related to the inherent higher
inaccuracy of determining the outofplane velocity
component in the stereoscopic PIV setup.
Dissipation rate estimation
In order to obtain an estimate for the Kolmogorov time and
length scales given by
r '= and (3)
, = (4)
respectively, we estimate the TKE dissipation rate defined
by (Pope 2000):
v ( u 8u
e = 2vs s+ ) + (5)
In order to accurately resolve the components of the
fluctuating rate of strain, s,, the spatial resolution has to be
smaller than the Kolmogorov length scale. Since PIV
samples the velocity at multiple points along a plane it is an
effective technique for dissipation estimation. However, PIV
velocity vectors are determined using interrogation
windows resulting in a vector spacing that is normally much
larger than the Kolmogorov length scale, such that direct
calculation of the dissipation according to Eq. (5)
underestimates the actual dissipation rate. Several other
methods have been developed to calculate the dissipation
rate (De Jong et al. 2009) such as (i) the LES based method
(Sheng et al. 2000) or an estimate using a 5/3 slope fit of
the inertial range in the spatial energy spectra (e.g. van Hout
et al. 2007).
In LES, the small scale structures are considered universal
(flow independent) and are modeled by SGS models.
Estimation of the dissipation rate using the LES based
method is based on Kolmogorov's theory that TKE is
generated by the large (integral) scales, cascaded down the
inertial range and dissipated by the small scales in the
dissipation range. Thus, the flux of TKE through the inertial
subrange is equal to the turbulence dissipation rate (Sheng
et al. 2000). Therefore, the dissipation approximated by the
averaged SGS dissipation rate is given by:
S(sS)= 2r,,~ ), (6)
where the resolved fluctuating rate of strain is given by:
S= 1/2 (O, /9x,+ Ou,/x ). (7)
Note that the s33 component may be evaluated by solving
the continuity equation:
x 3= xfi + C9 (8)
8x3 [ 1 8x 2
assuming s = (i .j) and 3 = s12 for (i = 1,2) based on
the flow field characteristics discussed in the previous
section.
3 5/3 o E11(1)
103 A 3/4 E2(K1)
o4 0 3/4 E11(K2)
104 A E22(2)
105
106
106
107
1023
101 102 103 1(
K [m]
107
101
102 103
(b) C [m1]
Figure 5: Energy spectra (a) case A (b) case (B).
The Smagorinsky model is used here to approximate the
SGS stress rj, given by:
r =CCA2 s2 (9)
where the Smagorinsky constant is taken as C,=0.17 and the
band width A=27/IKc represents the window size over which
the PIV velocity maps are spatially averaged. The cutoff
wave number Kc (Kc = 44 m 1) lies in the inertial subrange.
In the second method, the spatial energy spectra of TKE,
E,,(K), are calculated through the Fourier transform of two
point velocity correlations. In the inertial subrange,
Kolmogorov's second similarity hypothesis leads to the
following functional form of the longitudinal and transverse
0 El1 (1)
A 3/4 E22(1)
o 3/4E1 (K)
A E22((K2)
energy spectra (e.g. Pope 2000):
E,, (K1) = C2,/3K15/33
S2/315/3' (10)
where C=1.5x18/55 and C1=4/3C. The spatial TKE
spectra are shown Figure 5 for cases A and B together with
the best fitted 5/3 slope in the inertial range.
The estimated dissipations rates based on the LES method
and the slope fit method are shown in Table 2 for cases A
and B. Once the dissipation rate is known, the Kolmogorov
time and length scale may be evaluated (Eqs. 3 and 4; see
Table 2). The LES estimate of E is up to 46% higher (Case
B) then estimated by the 5/3 slope fit. Differences in the
estimated Kolomogorov's time and length scales based on
the two methods are smaller as can be seen in Table 2.
Table 2: The dissipation evaluation
LES 5/3 slope fit
Case F tk Trk F T"k lk
[m2/s3] [ms] [jm] [m2/s3] [ms] [jim]
A 3.2 2.2 180.6 2.6 2.4 190.6
B 5.7 1.6 156.8 3.9 1.9 172.2
The Taylor microscale is defined as AT =(15U1'12 )05 and
equals 4.53 mm and 4.47 mm for cases A and B,
respectively, using the dissipation values according to the
5/3 slope fit. Taylormicroscale Reynolds numbers,
RA ,rul'/v, equal 145 and 168 for cases A and B,
respectively.
Particle settling in near homogeneous isotropic
turbulence
Digital inline holographic cinematography
Digital holography is a full threedimensional technique that
enables to resolve particle position, speed, orientation and
shape in a 3D sampling volume. Hologram reconstruction is
done digitally using "DigiHoloWin" (The Johns Hopkins
University, J. Sheng and J. Katz) which allows fast
processing. Lu et al. (2008) using digital, inline holography,
compared the ability to track particles in a 3D sampling
volume using a single and a dual camera system with
overlapping regions of interest. The comparison showed that
the number of particle links in the single camera
configuration was higher than in the dual camera
configuration that required particle matching by both
cameras. Single camera particle tracks were very similar to
the tracks obtained by the dual camera setup. They further
showed that the pdf's of the Lagrangian particle velocity
components were similar in both configurations. In addition,
there was a good comparison between the lateral
acceleration components, however, accelerations
determined in the depth position were inaccurate in the
single camera configuration.
Here, a single camera setup is used and a schematic layout
of the digital inline holographic cinematography system is
shown in Figure 6. The system consists of a diode pumped
pulsed Nd:YLF laser (L= 523 nm, maximum pulse
frequency 10 kHz, Crystalaser), an ND filter, a spatial filter
followed by a collimator lens that creates a spatially filtered
laser beam that traverses the turbulence chamber and is
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
imaged by a highspeed, lensless CMOS camera (Photron,
Ultima APX, 1024x1024 pixels @ 2000 fps 17jim square
pixels). Since pollen grains tend to clump due to
electrostatic forces and humidity, a specially designed
particle dispenser released the pollen and PS spheres
through a vibrating sieve, thus preventing the particles from
clumping. In different runs, PS spheres, ragweed pollen and
pine pollen were released (separately) by the pollen grain
dispenser. For each run 2048 images were acquired in still
air and in homogenous isotropic flow conditions. The
sample rate in still air was set to 500Hz and in turbulent
flow the sampling rate was 700Hz. As the laser beam
crosses the region of interest it is partially refracted by the
particles and interference patterns (hologram) are generated
on the camera's CMOS sensor.
Pollen grain
dispenser
Collimator
ND filter A
Highspeed
laser Spatial
filter
Figure 6: Schematic layout of
holographic system.
High speed
camera
I'
Turbulence chamber
the digital inline
In order acquire the particle location the holograms must be
reconstructed. Image reconstruction is obtained by
numerically solving the Fresnel diffraction formula (e.g.
Schnars & Jueptner 2005) in planes located at increasing
distances from the hologram as shown in Figure 7. It can be
clearly observed that the particle goes in and out of focus as
the hologram is reconstructed at different xl positions.
Figure 7: Sequence of hologram reconstructions of PS.
Axi= 1 cm between reconstructions.
An inhouse developed MATLAB code for particle tracking
consisted of the following main steps:
a) Background subtraction to reduce noise and spatial
nonuniformities.
b) Hologram reconstruction at a coarse depth resolution.
Resulting reconstructions were collapsed, thresholded
and particle's centroid positions were determined
(Xi,X3).
c) 2D Lagrangian tracking: linking particles in subsequent
frames based on maximum possible displacement and
nearest neighbour position. This criterium was
sufficient due to the low particle density, approximately
2 particles/cm3.
d) Accurate determination of depth location: hologram
reconstruction with Axl = 200 jm. Particle infocus
position determined by the locally minimum particle
intensity.
The uncertainty in particle depth location is given by
dcp2/1 (Yang et al. 2005), thus the smaller the particles, the
higher the depth accuracy for a given wavelength. Various
criteria are suggested in literature for detection of the best
focusing plane of each particle (e.g. Yamaguchi et al. 2006).
Here we defined the particle depth position as the position
where the reconstructed light intensity averaged over the
particle image, was locally minimal. The determined depth
position was further smoothed by a local regression
smoothing method that uses a robust weighting function
(MATLAB's LOWESS function). An example of a 3D
track of a PS sphere before and after smoothing is shown
in Figure 8.
x Evaluated position
...  Smoothed position
S0.5
S
x [cml 1 0.5 x [cm]
^1 L'"J
0.4'
0 10 20
(b) t[ms]
Figure 8: Example of PS sphere (a)
location versus time. At = 1.43 ms.
Pollen settling velocities
The Stokes' settling velocities according to Eq. (2) of
ragweed (Ambrosia) and pine (Pinus) pollen (greer Labs,
USA), and PS spheres in still air (at T = 280C) are presented
in Table 3. The density of the pollen grains was taken as
1000 kg/m3. During the experimental runs, part of the pollen
grains that were released in the turbulence chamber
deposited on microscope slides in order to measure their
size distributions (Matlab's "blob" analysis). Projected area
based pollen diameters and standard deviations were
calculated from 200 pine and 43 ragweed pollen grains,
30 40
3D track. (b) depth
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
respectively. The PS spheres' diameter data were taken from
the manufacturer's specifications (MicroBeads AS,
Beckman Coulter particle sizer measurements).
The measured still air settling velocities presented in Table 3
were averaged over tracks from 372 pine pollen and 142 PS
spheres, resulting in 13187 and 4717 velocity measurements,
respectively. For ragweed pollen the measured still air
settling velocity is not presented due to insufficient
statistics.
Table 3: Settling velocities and particle
ragweed and pine pollen and PS spheres.
characteristics of
Ragweed Pine PS spheres
Quiescent conditions
dp 21.93.2 57.04.5 80.21.5
p 1000 1000 1050
Vs Eq. (2) 1.43 9.72 20.2
V, Exp. 4.030.74 18.73+1.15
N2 12 13187 4717
Re, 0.03 0.15 0.97
T 2.85 4.11 19.11
St 1.5 2.16 10.06
Near homogeneous isotropic turbulence, Case B
1.8745.99 13.1+43.08 18.241.41
6.7543.45 7.0544.04 11.3734.96
Insufficient statistics
Table 3 shows that the measured and calculated settling
velocity for the PS spheres in still air are nearly the same.
This can be expected since the PS spheres are spherical and
the density is well known. Discrepancies may be attributed
to inaccuracy of the actual diameter. On the other hand, the
calculated settling velocity of pine is more than twice as
high as the measured one. Note that the measured value
compares well to the still air settling velocity of pine pollen
measured by Schwendemann et al. (2007), V, = 3.380.67
cm/s, slightly lower than the value determined in the present
study. From Eq. (2), using the measured settling velocity, it
can be deduced that the pine pollen bulk density equals
414.6 kg/m3.
... :.
0
0
0 2
xrcml0 1 2 r
x [cm] 1 2 x [m1
1 L ''
Figure 9: 3D tracks (smoothed) of ragweed pollen grains
(29 separate tracks) released in near homogeneous, isotropic
turbulence. Case B.
3 
3 
The effect of turbulent eddies on particle settling can be
estimated by considering the Stokes number, defined as the
ratio between the particle response time zp, that reflects the
time it takes for the particle to react to changing flow
conditions, and a characteristic time scale of the flow, e.g.
the Kolmogorov time scale, k :
r V /g
St = (11)
Tk (uis)
When Tp;Tk (St 1) the particles should respond to a
substantial fraction of turbulent fluctuations. Experiments in
near homogeneous, isotropic turbulent flow conditions were
carried out for case B. Ragweed and pine pollen as well as
PS spheres were released into the turbulence chamber at
least 60 s after the woofers were activated. An example of
3D trajectories of ragweed pollen obtained from the digital
reconstructions of the holographic cinematography is shown
in Figure 9. It is immediately clear that the ragweed pollen
do not settle in a straight line towards the bottom but exhibit
strongly meandering settling paths. Stokes numbers for
ragweed, pine and PS for tk = 1.9 ms (Table 2, Case B: 5/3
slope fit) are shown in Table 3.
10 ,
0 X
200 100
0
v3 [cm/s]
100 200
200 100 0 100 200
(b v2 [cm/s]
Figure 10: Probability density functions of the velocity
components for ragweed pollen (a) v2 (b) v3
The mean particle velocities, and are summarized
in Table 3 where represents the mean settling velocity
in turbulent conditions and is one of the lateral
components. Ensemble sizes are 1216 (160 particles) for
ragweed pollen, 126 (14 particles) for pine pollen and 183
(10 particles) for PS spheres. Only particle tracks with more
than 5 tracked positions were taken into account. When
comparing the measured settling velocity of PS spheres in
still air (Table 3) to that in turbulence, it is clear that the PS
spheres settling velocity is hardly affected by the turbulence.
This result is in accordance with the PS spheres' high Stokes
number, St = 10.8. Turbulence has the greatest effect on pine
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
pollen increasing its average settling velocity more than
threefold. The ragweed pollen settling velocity in turbulent
flow is only a little higher than the quiescent settling
velocity according to Eq. (2). Note that is of the same
order as the average settling velocity and for ragweed more
than three times as large. The standard deviations of both
velocity components are high and in all cases are about 40
cm/s. These values are similar to those measured by Lu et al.
(2008) for 80 tim water droplets in similar flow conditions.
The pdf's of v2 and v3 of ragweed pollen are presented in
Figure 10. Bothe pdf's have similar shape and although
mean values are relatively low, instantaneous values can be
as high as 100 cm/s.
Conclusions
An experimental study using digital inline holographic
cinematography, on the settling of pine and ragweed pollen
as well as polystyrene spheres in quiescent air conditions
and in near homogeneous, isotropic turbulence has been
presented. Turbulence flow conditions were generated by 8
woofers mounted on the comers of a transparent cubic
chamber. The velocity filed was measured by stereoscopic
PIV and the turbulence flow conditions were validated as
near homogeneous isotropic in the center 40 x 40 x 40 mm3
of the turbulence chamber. Ragweed ( 20 jim) and pine
pollen ( 5060 jim) as well as polystyrene spheres ( 80
jim) were released into the turbulence chamber in both
quiescent and turbulent flow conditions. For the case of
polystyrene spheres, the mean still air settling velocity was
hardly affected by the turbulence in accordance to the high
Stokes number. In contrast for ragweed and pine pollen, the
settling velocity increased.
Acknowledgements
This research is partially supported by The Edmund J. Safra
Philanthropic Foundation, the Wolfsson Family Charitable
Trust, the Technion Fund for Promotion of Research and the
United States Israel BiNational Science Foundation
(BSF) under grant number 2006214
We would like to thank Dr. K. Gommed and undergraduate
students Leonid Klebanov and Gil TovLi for their effort in
designing the turbulence chamber and Mr. Z. Kinstler for
the design of the particle dispenser. In addition, we want to
thank Javier Arca (MSc student) for developing the particle
tracking code.
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