Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 14.1.3 - Experimental study of turbulence-induced collisions of small inertial droplets
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 Material Information
Title: 14.1.3 - Experimental study of turbulence-induced collisions of small inertial droplets Droplet Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Bateson, C.
Molina, A.
Aliseda, A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: inertial droplets
turbulent collision-coalescence
radial distribution function
radial relative velocity
 Notes
Abstract: We have investigated the dynamics of droplets in a size range between 5 and 50 microns immersed in homogeneous, isotropic, turbulent flow. To reproduce this canonical flow under laboratory conditions, droplets were injected inside a wind tunnel through an array of atomizers located at the nodes of a uniformly spaced turbulence-inducing grid that covers the tunnel’s cross section. Measurements were made at sufficient distance downstream from the injectors ( 15M, where M is the grid spacing) that the droplets have lost memory of the injection conditions, and the turbulence is slowly decaying, homogeneous, and isotropic. Droplets size, velocity and time of arrival were measured using a Phase Doppler Particle Analysis (PDPA) system. Processing of the data allows us to calculate the local droplet concentration, global and local velocity statistics, and 1D droplet radial distribution function (RDF). The radial distribution functions for three different downstream locations were analyzed. The results show evidence of significant preferential concentration. A simple power law provided good fits to the RDF data. These fits can be extrapolated to separation distances smaller than the minimum resolution of the PDPA, allowing the RDF to be evaluated at the point of collision, which is an important factor in the droplet collision kernel. The ultimate goal of this project is to use the experimental data for comparison to the results from the hybrid DNS performed by our colleagues at the University of Delaware (see accompanying talk by Parishani et al.) in order to develop and validate droplet collision kernel models.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00340
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1413-Bateson-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Experimental study of turbulence-induced collisions of small inertial droplets


C. Bateson, A. Molina and A. Aliseda

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
cbateson~uw.edu, aaliseda~uw.edu

Keywords: inertial droplets, turbulent collision-coalescence, radial distribution function, radial relative velocity




Abstract

We have investigated the dynamics of droplets in a size range between 5 and 50 microns immersed in homogeneous,
isotropic, turbulent flow. To reproduce this canonical flow under laboratory conditions, droplets were injected inside
a wind tunnel through an array of atomizers located at the nodes of a uniformly spaced turbulence-inducing grid
that covers the tunnel's cross section. Measurements were made at sufficient distance downstream from the injectors
(~ 15M, where Af is the grid spacing) that the droplets have lost memory of the injection conditions, and the tur-
bulence is slowly decaying, homogeneous, and isotropic. Droplets size, velocity and time of arrival were measured
using a Phase Doppler Particle Analysis (PDPA) system. Processing of the data allows us to calculate the local droplet
concentration, global and local velocity statistics, and 1D droplet radial distribution function (RDF). The radial dis-
tribution functions for three different downstream locations were analyzed. The results show evidence of \ignilk~.illl
preferential concentration. A simple power law provided good fits to the RDF data. These fits can be extrapolated to
separation distances smaller than the minimum resolution of the PDPA, allowing the RDF to be evaluated at the point
of collision, which is an important factor in the droplet collision kernel.
The ultimate goal of this project is to use the experimental data for comparison to the results from the hybrid DNS
performed by our colleagues at the University of Delaware (see accompanying talk by Parishani et al.) in order to
develop and validate droplet collision kernel models.


Introduction

The dynamics of droplets in turbulent flows is impor-
tant to many engineering and environmental problems
including fuel sprays, warm rain formation, and the mass
and energy transfer between the ocean and the atmo-
sphere. Rain formation has a particularly \ignlilki.lli
effect on the Earth's atmosphere. Latent heat associ-
ated with water droplet formation is an important energy
source for many meteorological flows, and the rate of
rain formation is directly related to the lifetime of pre-
cipitating clouds. Since the Earth's weather and climate
are strongly affected by the delicate balance between
cloud's absorption and reflection of incoming solar ra-
diation, having the ability to predict cloud variation in
space and time is essential for creating accurate climate
and weather models.
Warm rain formation involves three processes: con-
densation, collision-coalescence due to turbulence, and
collision-coalescence due to gravitational settling. Ini-
tially cloud droplets grow by condensation, but this pro-
cess becomes inefficient when droplets reach a size of
approximately 10p m due to the rate of decrease of the


droplet's surface to volume ratio. Collision-coalescence
is responsible for the continued growth of these droplets.
This process is well understood for large droplets (>
100pm) where gravitational settling dominates the dy-
namics but it is still unclear how it proceeds for smaller
sizes. Droplet growth for the size range in between
10 100pm is hypothesized to be due to turbulence-
induced droplet collisions. When the growth process in
this intermediate regime is modeled using a simplistic
approach that neglects droplet inertia and therefore as-
sumes a random spatial distribution of droplets and rel-
ative velocities equal to the fluctuations of the surround-
ing air motion, the collision rate is extremely slow and
winlislc'lllh over-predicts the time needed for precipi-
tation. These predictions are on the order of hours for
normal cumulus cloud conditions (Jonas 1996), whereas
Doppler measurements made on similar clouds have
shown precipitation forming in a little as 15 minutes
(Szumowski et al. 1997).
Researchers have been investigating the source of this
problem for years. The first study done on the potential
role of turbulence in rain formation was that of Aren-
berg (1939). Using a sinusoidal representation for the







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


lar motion. When the eddies collide, the droplets they
are carrying may collide as well. Reuter et al. (1989)
developed a probabilistic collection kernel that included
the effect of overlapping eddies and used it to calculate
the evolution of a cloud droplet spectrum. They con-
cluded that turbulence contributes to the broadening of
the droplet spectra, and increasing turbulence intensity
increases spectrum broadening, but the droplet growth
rate remains slow even for the most vigorous turbulence
studied.
The publication of the work of Maxey and Riley
(1983) contributed significantly to the understanding of
particle motion in fluid flows. Armed with complete
equations of motion for the particles, researchers could
use their computational tools to study, in detail, particle-
turbulence interactions and as a result they discovered a
number of interesting phenomena.
Maxey performed a series of 2D simulations study-
ing particle motion in simplified representations of tur-
bulence (Maxey and Corrsin 1986; Maxey 1987a,b) and
found that inertia caused heavy particles to concentrate
in regions of high strain and low vorticity. Squires and
Eaton (1990, 1991) found the same was true in their
DNS of turbulence. Wang and Maxey (1993) showed
that this phenomena termed preferential concentration
- follows Kolmogorov scaling; meaning that particles
with response times (7,) approximately equal to the Kol-
mogorov time scale (7a) are most affected by the turbu-
lence. Fessler et al. (1994) validated these results exper-
imentally by measuring preferential concentration in a
turbulent channel flow.
A second phenomena found as a result of these studies
was that turbulence increases particle settling velocity.
When gravitational forces are considered, heavy parti-
cles have a vertical velocity relative to the turbulent fluid
that causes them to interact with vortical structures via a
process known as the "crossing trajectories" effect. The
particles are swept preferentially to the downward re-
gions in the flow and as a result the mean effect of the
turbulence on the particles is an increased settling veloc-
ity (Wang and Maxey 1993).
In general, studies have shown that turbulence en-
hances the collision kernel for cloud droplets in the fol-
lowing ways: (1) differential acceleration and shear in-
crease the relative velocity between droplets; (2) prefer-
ential concentration increases the average pair statistics,
like the RDF, upon which the collision kernel depends
(Pinsky et al. 1997; Sundaram and Collins 1997; Wang
et al. 2000; Zhou et al. 2001); (3) selective changes in the
settling rate increase the relative velocity between drops
(Wang and Maxey 1993; Aliseda et al. 2002); and (4)
turbulence increases collision efficiency (Pinsky et al.
1999, 2000; Wang et al. 2005). Many of these studies,
however, were conducted outside the parameter range


turbulent velocity fluctuations, he considered how tur-
bulence could bring droplets together, but not the condi-
tions necessary for actual collisions. East and Marshall
(1954) took the work on droplet collision efficiencies by
Langmuir (1948) and applied it to a model of collisions
that included both random turbulent motion and gray-
ity. They found that drops with similar sizes have simi-
lar responses to turbulence, but different sized drops can
have \ignlilk~.lill relative velocities due to turbulent air
fluctuations. They concluded that the random motion
of turbulence can be regarded as being equivalent to in-
creasing the acceleration due to gravity. As a result their
model predicts zero increase in the collision rate of sim-
ilar sized drops, but a \ignilk~.lill increase for dissimilar
sized drops. This is due to the fact that their model does
not account for spatial variation in the turbulent fluctua-
tions, which would impose differing velocities on neigh-
boring drops regardless of their size or mass.
Saffman and Tumner (1956) performed what is re-
garded as the seminal work on the problem of
turbulence-induced collisions. They improved on the
analysis of East and Marshall (1954) by including a
mechanism that would allow equal sized drops to col-
lide. They suggested that there are two mechanisms
by which turbulence creates relative velocities between
drops that lead to collision: (1) relative velocities due
to spatial variations in the turbulent air motion, and (2)
relative velocity created by variation in drop responses
to turbulent motions owing to their different inertia.
Saffman and Tumner (1956) dismissed the use of the col-
lision efficiencies reported by Langmuir (1948) since
they were calculated for drops in a steady, laminar flow
around a fixed, large sphere. Instead they assumed colli-
sion efficiencies of 1 for all their drops.
de Almeida (1976, 1979a) performed a battery of
Monte Carlo simulations to study the increase in the ge-
ometric collision efficiency resulting from turbulence.
He then applied these results to calculate the evolu-
tion of cloud droplet size spectra (de Almeida 1979b)
and found that the coalescence process was greatly en-
hanced by turbulence. However, Grover and Pruppacher
(1985) maintain that de Almeida scaled his results with
the wrong part of the turbulent energy spectrum for the
drop sizes he considered, and for this reason he underes-
timated the inertial effects in his calculations. While this
does not totally disqualify his results, they do not have
the same quantitative credibility.
Reuter et al. (1988) published a novel \illdi 1Ih.sI incor-
porated a stochastic model of the drop-collision process
in turbulent air. In addition to shear and inertia effects,
turbulence was thought to create collisions via an "over-
lapping eddy" mechanism. In short, this mechanism can
be described as the interaction between two turbulent ed-
dies carrying with them droplets entrained in their circu-







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


effects of surface tension. For this reason it is safe to
assume that the droplets remained spherical throughout
the experiments.
Two pressure manifolds, for separate air and water
supplies, were used to ensure the respective supply pres-
sures were constant across all the atomizers. The man-
ifolds were constructed out of aluminum pipe (12.7 cm
OD, 11.44 cm ID) with closed covers connected to
flanges welded on each end of the pipe. 81 holes were
drilled and tapped in nine evenly spaced rows of nine
holes equally distributed circumferentially around the
manifolds. Barbed tube fittings were screwed into the
holes in the manifold, and polyurethane tubing con-
nected to the barbed tube fittings ran through holes cut
into the wall of the wind tunnel and into the grid where
they fed the atomizers. Special care was taken to make
all the tubing running between the pressure manifolds
and the atomizers the same length to equalize pressure
losses.
Additional effort was made to account for the mea-
surable pressure difference in the water supply between
the top and the bottom of the grid. In order to com-
pensate for the hydrostatic pressure difference between
the top and bottom of the grid, short lengths of micro-
tubing were glued into the barbed tube fittings in the
water manifold (Figure 3), inducing additional pressure
losses in the injectors with the higher hydrostatic head.
A detailed calculation was done to determine the appro-
priate length of microtubing needed to induce losses in
the water supply lines that would cancel the hydrostatic
head resulting from the height difference between each
row of fittings and its corresponding row of atomizers.
A schematic of the manifold-injector grid arrangement,
including the height difference responsible for the hy-
drostatic pressure differences that need to be canceled
to obtain uniform liquid flow rates at all injectors across
the wind tunnel, is shown in Figure 4. The microtube
lengths were optimized for a range of water flow rates,
so as to minimize the difference in flow rate between the
top and bottom rows of atomizers for all the flow con-
ditions. The height difference between the row of fit-
tings in the manifold and the row of injectors it supplies
in the grid is maximum for the bottom row, decreasing
slightly for each row above, therefore the longest mi-
crotubes were glued into the bottom row of fittings to
counter the largest pressure head and the length of the
microtubes was decreased for each subsequent row of
injectors above. Ultimately, the worst off-design con-
dition resulted in a maximum difference in flow rate of

Measurements to characterize the disperse phase were
made with a Phase Doppler Particle Analyzer (PDPA)
system from TSI Inc. (Shoreview, MN.) By measur-
ing the light scattered by a particle crossing through the


relevant to cloud microphysical processes (Vaillancourt
and Yau 2000). Our research is aimed to help fill this
knowledge gap by using experiments to study the com-
bined effects of coupling droplet inertia and turbulence
on the collision-coalescence of water droplets on a pa-
rameter range scale relevant to warm rain formation.


Experimental Setup

The experiments were conducted in a horizontal, blow-
down style wind tunnel with test section measuring 1.2
m x 1.2 m square cross section and 3 m in length. The
two-stage, axial compressor moves air into a 2:1 expan-
sion ratio section and then through a series of flow con-
ditioning screens and honeycombs. The flow through
the test section had a mean velocity of 1.5 m/s, and a
Reynolds number based on the tunnel width of Re -
10s. The turbulence intensity was measured to be about
30%b, and the Reynolds number based on the Taylor mi-
croscale (Re ) was between 200 and 400.
Before entering the test section, the air passes through
a biplane, turbulence-inducing grid. The grid is com-
prised of nine vertical and nine horizontal hollow (d
2.54cm) aluminum tubes with a mesh spacing of (M =
10.16cm). This results in a grid solidity ratio S
(d/m)(2 d/m) 0.44. The Reynolds number based
on the mesh size, Renc U,M/V, is 104. Two-fluid
atomizers embedded at the nodes of the evenly spaced
mesh introduce the disperse phase into the flow. The ad-
ditional mass flux of air introduced by the high speed
gas jet in the atomizers makes the grid "active". The in-
jection ratio (J), as defined by Gad-el Hak and Corrsin
(1974) is quite low (J7 1 ." I Their study showed
that at our low injection ratio the jet flow will lower
the aerodynamic solidity of the grid and thereby ren-
der the flow downstream more stable and homogeneous.
The atomizers were constructed out of two brass tubes
that were shaped and then brazed together so the high-
momentum air jet impinges almost perpendicular to the
low momentum water jet, atomizing the liquid and pro-
ducing a spray of small droplets. A photo of one of the
atomizers is included as Figure 2.
The atomizers were installed in the grid so the air jets
exit parallel to the mean flow in the wind tunnel. The
droplet size distribution and liquid mass fraction of the
spray can be controlled by the pressure in the air sup-
ply and by the flow rate of water, as shown by Lgzaro
and Lasheras (1992). Data for our experiments was col-
lected at atomizer flow rates of 4 LPM of water and 50
SCFM or air. This produced a volume fraction (a) of
6.6710-s in the tunnel test section. The Weber number
for the droplets was on the order of 10- therefore any
deformation resulting from unsteady pressure forces in
the flow field were quickly dominated by the restoring

























3m (X-axis )


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Manifolds


Figure 1: A diagram of the wind tunnel used for the experiments


intersection of two laser beams, this system allows for
non-intrusive, simultaneous measurements of the panti-
cle's velocity in two dimensions, as well as its diame-
ter. The PDPA also records the particle's time of arrival,
which allows statistics to be calculated that measure lo-
cal droplet concentrations. The intersection of the laser
beams is conforms the probe volume where measure-
ments are taken. For this experiment, the receiver was
positioned at a forward angle of 70 degrees with respect
to the transmitter. This uses the first mode of refraction
for light scattering, which has been shown to be the most
effective for measuring water droplets in air. A more
detailed description of the PDPA operating mechanism
has been published by Bachalo (1994).
The measurement system was positioned at various
stations along the length of the wind tunnel. The velocity
measurements were used to characterize the flow's de-
pendence on distance from the grid. The droplet size dis-
tribution was studied to characterize how droplets chage
size as they interact with the turbulent flow. For this
study, measurements were taken at five stations (.r
0.654m, 1.44m, 1.71m, 2.19m and 2.94m). The grid
is located at the origin, and the value of Jr describes
the distance downstream from the grid. The exact lo-
cations were selected with the intent to distribute the
measurement positions uniformly along the wind tun-
nel test section. Slight adjustment were made to avoid
obstructions in the PDPA optical access caused by the
wind tunnel support structure. To be consistent with the
rich existing literature on grid turbulence, the positions
were non-dimensionalized using the grid mesh size (M).
At each of the five downstream stations, measurements
were made in cross sectional planes across the wind tun-
nel using a 2-axis, motorized traverse,
The velocity data collected at each measurement point
was used to calculate the statistics of the turbulence,
namely, velocity average, root mean square (RMS) of
the velocity fluctuations (ts'), and the longitudinal one


Figure 2: An example of the two fluid atomizers used to
create the disperse phase.


dimensional energy spectrum (E11). In order to charac-
terize the decay of the grid turbulence in our experiment,
the inverse of the turbulent kinetic energy (U/ts')2 was
plotted as a function of distance down the wind tunnel
(Figure 5). Comte-Bellot and Corrsin (1966) proposed
that the turbulence decay follows a power law, and found
that an exponent between 1.2 and 1.3 gave the best fit
to experimental data. However, Wells and Stock (1983)
proposed that in the near region for grid-generated tur-
bulence, which they described as region between 10M
and 150M downstream from the grid, the turbulence in-
tensity decay is inversely proportional to the distance
downstream. Since all but one of the measurements
made for this experiment were within the near region
we expected our data to decay linearly. Two linear re-
gressions to the data were made, one with all the data
points, and a second that excluded the data from the first
station (.r/M 7.5M, Jr 0.65m) since this point lies
outside the near region. The second regression to the
limited data set resulted in a better fit.
Figure 6 is a log-log plot of the longitudinal one di-
mensional energy spectrum at a single measurement sta-
tion. The straight line represents Kolmogorov's -5/3 de-
cay for the inertial subrange. Unfortunately, the data rate
from the PDPA was low, which not only placed an upper
limit on the wave numbers we were able to resolve but
also reduced the precision of the spectra measurements.





7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Turbulence Decay


18
16
14
12

N1 l


Figure 3: A barbed tube fitting with its microtube mod-
ification.


Water
Manifold


10 15 20
Downstream Position (x/M)


25 30


S- Linear Fit=6.454x -2.835 (all data) R2= 0.9795
Linear Fit=7.411x-5.035 (not x/M<10) R2-0.9960


Figure 5: Turbulent intensity (U/')2 decay as a func-
tion of distance (.r/M) downstream of the
grid.


veg = (ve)1/ (4)

Table 1 is a collection of all these parameters calcu-
lated at each of the five measurement stations.


Results and Discussion

In order to quantify the degree of preferential concentra-
tion of droplets in the flow and the potential effect of this
droplet accumulation in the collision probability, we cal-
culated the Radial Distribution Function (RDF) at three
locations along the wind tunnel test section. The RDF is
a measure of the probability of finding a particle within a
certain distance from the center of a particle. Originally
used as a statistical measure of the three dimensional
distribution of the atoms in matter, the RDF was first
used to measure preferential concentration in multiphase
flows by Sundaram and Collins (1997). They showed
that the RDF is an important measurement for studying
droplet collisions because the collision frequency is di-
rectly proportional to the RDF evaluated at the point of
droplet contact, or equivalently, the RDF evaluated at a
distance equal to the sum of the radii of the colliding
droplets.
As derived, the RDF is a three dimensional quantity
and measuring it experimentally is difficult. Droplet
clustering can have characteristic lengths on the order
of the Kolmogorov length scale, which are usually less
than a millimeter even for the high Reynolds numbers
and large scales typical of atmospheric flows. This poses
the problem of imaging the droplets. Current optical


Turbulence
Inducing
Grid


Figure 4: A diagram of how the hydrostatic pressure
difference between the grid and the water
manifold was measured.


Since the lack of precision precludes commenting on the
evolution of the spectra across the measurement stations,
and since all of the spectra were qualitatively similar,
only one is presented here. More accurate characteriza-
tion of the single-phase turbulence statistics, particularly
at the smallest scales, is planned in the near future. This
improved information will allow us to more accurately
scale the droplet statistics and understand the dynamics.
Qualitatively, though, we expect our analysis to stand.
Taking the integral of the premultiplied energy spec-
trum, (1), we were able to get an approximate value for
the turbulent kinetic energy dissipation rate (t). This es-
timate of t is limited in its accuracy by the lack of de-
tailed information about the smallest scales in the tur-
bulent kinetic energy spectrum referred to above. The
value of the Taylor microscale A (used to characterize
the turbulence through the Reynolds number Re ) is
therefore obtained from the ratio to the integral length
scale A/Lil = J~e .

e = 5v kEli~~dk(1)

From t, the rest of the Kolmogorov microscales (2), (3),
(4) can be calculated.

~=yt1/2 (2)

if= (V /t)1/4 (3)












Table 1: Summary of flow parameters.


1 6.4 0.65 1.00 1.23 230 0.0089
2 14 1.44 0.59 0.169 376 0.0098
3 17 1.71 0.56 0.126 405 0.0088
4 22 2.19 0.46 0.0095 434 0.0085
5 29 2.94 0.41 0.0078 456 0.0087


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


RDF Station 2 (x = 14M )


Longitudinal 1-D Energy Spectrum


10"


Figure 6: Longitudinal 1D turbulent energy spectrum at
station 4 (Jr = 22Af).


techniques frequently employ lasers, either in the form
of laser sheets as for Particle Image Velocitmetry (PIV),
or as laser beams like those used by our PDPA system.
Both of these illumination techniques have a finite thick-
ness to their measurement areas, which are comparable
in size to the Kolmogorov length scale, and which ulti-
mately limit their resolution. Additionally, three dimen-
sional imaging techniques are technically challenging
and expensive. Most often, the RDF has to be approxi-
mated with 2D (i.e. PIV) or 1D (i.e. PDPA) measure-
ment techniques. Holtzer and Collins (2002) showed
that these lower dimensional sampling techniques result
in slightly different RDFs. At large separation distances,
the two RDFs converge to the same value, but they di-
verge at separation distances very close to zero. Holtzer
and Collins (2002) also derived equations to describe
the relationship between lower-dimensional and three-
dimensional RDFs, which enables researchers to infer
the behavior of the 3D RDF from their 1D or 2D exper-
imental data.
Our PDPA system makes measurements of the flow
at a fixed point with respect to the wind tunnel. Taking


Figure 7: 1D radial distribution function at station 2.
91D(T/17), ( ); Power law fit, (-).


the difference between droplet arrival times and multi-
plying by the mean velocity gives the distance between
droplets, using Taylor's frozen turbulence by plhsislc\i
Because the probe volume has a finite size, our data
set can be visualized as a long prismatic volume with a
small cross section and a very elongated shape (marked
by the average convective velocity times the sampling
time). This volume contain droplets whos relative dis-
tance is mainly along the long axis of the measurement
volume. Thus, except for small separations, comparable
to the width or height of the prism, the RDF measured is
one dimensional.
We calculated the 1D RDF by counting the number
of droplets within two thin slices of the measurement
volume at the same distance from the location of each
droplet, one slice "ahead" of the droplet in time and the
other "behind". The sum of this droplet counts is added
together for the same distance from all droplet and nor-
malized using the average droplet concentration at that
location of the wind tunnel resulting in a plot of the 1D
RDF (glD F)).
Plots of the RDFs at three locations (Jr








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


RDF Station 3 (x = 17M )

y(x) = a x~n + c
a =16.608
c =1.6445
n =-3.9098
R =0.99692 (lin)


RDF Station 4 (x = 22M )

y(x) = a x~n + c
a =17.488
c =1.4699
n =-4.2367
R =0.9965 (lin)


5 10


5 10


Figure 8: 1D radial distribution function at station 3.
glD(r/p), ( *); Power law fit, (-).




14M, 17M, 22M) are included as Figures 7, 8 and 9.
A simple power law of the form y(x) = ax" + c was fit
to the data set at each measurement location. The values
of the fit parameters, as well as the R-value characteriz-
ing the quality of the fit, are included in the box in the
upper right hand corner of each plot. Qualitatively, the
plots are all very similar, which was to be expected due
to the proximity of the measurement locations and the
slow decay rate of the turbulence intensity. These plots
show the strong evidence of preferential concentration,
At a separation of approximately 14 the droplet concen-
tration is over 8 times the average concentration in the
rest of the tunnel.

As the separation distance increases, and r/4 00o,
all the plots decay to values slightly higher than one.
The actual value for each location is given by the fit
parameter c. Theoretically the RDF should decay to a
value of one as the separation distance increases, which
is equivalent to a concentration equal to the average
droplet concentration. The deviation in our data indi-
cates a small uncertainty in the normalization parame-
ters. As r/4 0 the power law fits suggest that the
glD 00o. An infinite concentration is not physical,
but neither is a zero separation distance. The minimum
separation distance between two drops occurs when they
come into contact. Due to the limitation in the PDPA, we
cannot measure RDF at very small separation (smaller
than the probe volume characteristic length scale), but
these fits will allow the data to be extrapolated to deter-
mine glDr 71 r2), which is necessary for modeling the
collision kernel for two droplets with radius rl and r2.


Figure 9: 1D radial distribution function at station 4.
glD(r/p), ( ); Power law fit, (-).



Conclusions


The dynamics relevant to droplet collisions were stud-
ied using wind tunnel experiments. Water droplets were
injected uniformly into slowly decay, isotropic and ho-
mogeneous grid turbulence. A PDPA system was used
to collect velocity, diameter, and arrival time data for
the droplets. Using these data, the turbulence intensity
decay, the 1D longitudinal kinetic energy spectrum, and
the radial distribution function were computed for multi-
ple locations downstream of the grid. The turbulence in-
tensity was found to decay linearly with distance, which
was the behavior expected for the near region in which
our measurements were made. The energy spectra suf-
fered from a low data rate, and as a result the small-
est scales of the flow could not be resolved. The radial
distribution functions for three different downstream lo-
cations were analyzed. The results showed evidence of
\ignlilk~.lll preferential concentration. A simple power
law provided good fit to the RDF data. These fits can be
extrapolated to evaluate the RDF at separation distances
relevant to collision processes,




Acknowledgements


The authors would like the thank Marita Rodriguez
for her help constructing the experiment. Funding for
this work was provided by NSF through award ATM-
0731248.







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


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