Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 15.1.2 - Measurement of spatial correlation of droplet-gas velocity in a confined spray
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00366
 Material Information
Title: 15.1.2 - Measurement of spatial correlation of droplet-gas velocity in a confined spray Droplet Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Hardalupas, Y.
Sahu, S.
Taylor, A.M.K.P.
Zarogoulidis, K.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: simultaneous measurement of droplet-gas velocity
droplet size and velocity
spatial correlations of velocity
fluctuations
droplet Stokes number
Proper Orthogonal Decomposition
 Notes
Abstract: A novel method of simultaneous measurements of droplet and gas flow characteristics in sprays is described, which combines the out-of-focus imaging technique ‘Interferometric Laser Imaging Droplet Sizing’ (ILIDS) for planar simultaneous droplet size and velocity measurements with the in-focus technique ‘Particle Image Velocimetry’ (PIV) for gas velocity measurements in the vicinity of individual droplets. The measurements are presented in a model co-flowing isothermal spray dryer with a spray injected from a single air-assist solid cone atomizer. The measurements were obtained at 500 mm downstream from the atomiser, at 125 mm off-axial location in the spray and at five different cross-stream locations, situated at 0, 50, 100, 150 and 185mm respectively from the spray axis. The size of the viewing area at each location was 8 × 12 mm2. The experimental method, the image processing algorithm and the method of calculation of spatial correlations of velocity are briefly described. The results include the mean droplet velocity and the rms of the velocity fluctuations for three representative size classes of the spray with corresponding Stokes numbers less than unity, the mean velocity and the rms of the velocity fluctuations of the gas flow, and the spatial correlations of the gas and droplet velocity fluctuations, conditional on droplet size class. At any measurement location, both droplets and gas mean velocities were found to be of similar magnitude, with similar, though not identical, direction. In general, high spatial correlation coefficient between the droplet and gas velocity fluctuations was observed for small distances, while the coefficient was larger for axial, as compared to the cross-stream, velocity component. The spatial correlation coefficients of droplet-gas velocity fluctuations for different size classes were compared with those of the droplet-droplet and gas-gas velocity fluctuations for various cross-stream locations. The selective influence of the large scale eddy structures of the gas phase flow on the droplet-gas flow interaction was examined. The gas flow eddy structures were extracted by applying Proper orthogonal decomposition (POD) on the instantaneous gas velocity data. The contribution of individual POD modes on the spatial correlation of the droplet-gas velocity fluctuations was determined.
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
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00366
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1512-Hardalupas-ICMF2010.pdf

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


Measurement of spatial correlation of droplet-gas velocity in a confined spray


Y. Hardalupasl, S. Sahu2, A.M.K. P. Taylor3 and K. Zarogoulidis4


Department of Mechanical Engineering, Imperial College London
London, SW7 2BX
E-mail: y.hardalupas~,imperial.ac.uk


Keywords: simultaneous measurement of droplet-gas velocity, droplet size and velocity, spatial correlations of velocity
fluctuations, droplet Stokes number, Proper Orthogonal Decomposition




Abstract

A novel method of simultaneous measurements of droplet and gas flow characteristics in sprays is described, which combines the
out-of-focus imaging technique 'Interferometric Laser Imaging Droplet Sizing' (ILIDS) for planar simultaneous droplet size and
velocity measurements with the in-focus technique 'Particle Image Velocimetry' (PIV) for gas velocity measurements in the
vicinity of individual droplets. The measurements are presented in a model co-flowing isothermal spray driver with a spray
inj ected from a single air-assist solid cone atomizer. The measurements were obtained at 500 mm downstream from the atomiser,
at 125 mm off-axial location in the spray and at five different cross-stream locations, situated at 0, 50, 100, 150 and 185mm
respectively from the spray axis. The size of the viewing area at each location was 8 x 12 mm2. The experimental method, the
image processing algorithm and the method of calculation of spatial correlations of velocity are briefly described. The results
include the mean droplet velocity and the rms of the velocity fluctuations for three representative size classes of the spray with
corresponding Stokes numbers less than unity, the mean velocity and the rms of the velocity fluctuations of the gas flow, and the
spatial correlations of the gas and droplet velocity fluctuations, conditional on droplet size class. At any measurement location,
both droplets and gas mean velocities were found to be of similar magnitude, with similar, though not identical, direction. In
general, high spatial correlation coefficient between the droplet and gas velocity fluctuations was observed for small distances,
while the coefficient was larger for axial, as compared to the cross-stream, velocity component. The spatial correlation
coefficients of droplet-gas velocity fluctuations for different size classes were compared with those of the droplet-droplet and
gas-gas velocity fluctuations for various cross-stream locations. The selective influence of the large scale eddy structures of the
gas phase flow on the droplet-gas flow interaction was examined. The gas flow eddy structures were extracted by applying
Proper orthogonal decomposition (POD) on the instantaneous gas velocity data. The contribution of individual POD modes on
the spatial correlation of the droplet-gas velocity fluctuations was determined.


Introduction

The processes determining the spray characteristics
involve spray formation, droplet breakup, interaction
between gas and droplet flow, and, for spray combustion,
heat transfer, droplet evaporation and reaction. The
combination of all these processes makes the understanding
of the physics challenging. Thus, there is a need to study
separately these processes and the emphasis of this paper is
on the droplet-gas flow interaction.
The interaction of a spray with the entrained flow field is
an important part of the evolution of a spray, which may
result in either droplet dispersion by turbulence (one-way
coupling) or turbulence modification by the droplets
(two-way coupling). The interaction of the spray with the
surrounding flow can redistribute spray droplets due to
differences in droplet inertia, momentum and drag, e.g.
Crowe et al. (1998), Sanchez et al. (2I III) and Zimmer et al.
(2 17). The droplet-gas flow interaction is important for
many industrial applications, for example, in spray
combustion, it can cause large variations of the distribution of


droplets leading to variations of fuel concentration that
affects the combustion progress and eventually, combustion
efficiency and pollutant emissions.
In general, for particle-laden flows, considerable amount
of numerical studies, mostly based on direct numerical
simulation (DNS) on particles suspended in an isotropic and
homogeneous turbulent flow, have been reported (Squires
and Eaton, 1990; Boivin et al., 1998; Sundaram and Collins,
1999; Ferrante and Elghobashi, 2003; to name a few). These
studies essentially focused on the prediction of the
modification of turbulent kinetic energy by the dispersed
phase and/or the issue of preferential concentration in the two
phase flows. For a droplet-laden gas flow, the turbulent
kinetic energy equation for the dispersed phase contains
terms, which include correlations of droplet concentration
and velocity fluctuations of the fluid and/or droplets and
droplet-fluid velocity correlations. They represent an 'extra'
source or sink of turbulent kinetic energy in the fluid and
depict the interaction, Kulick et al. (1994) and, Hardalupas
and Horender (2I 1 i). The feasibility of incorporation of the
effect of two-way coupling (i.e modification of turbulence by






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

velocity correlations, for a given location in a polydispersed
spray, was demonstrated in Hardalupas et al. (2 **~.. The
objectives of the paper here are to present two phase
measurements with the combined ILIDS and PIV techniques
in a low Stokes number, polydispersed spray region of a
model spray dryer at various cross-stream locations. The
results include the mean and rms of velocity fluctuations of
the two phases, the spatial droplet-droplet and droplet-gas
velocity correlations conditional on droplet size classes for
different cross-stream locations and comparison between
them. Proper Orthogonal Decomposition (POD) was applied
to the instantaneous gas flow velocity to extract the
large-scale eddy structures (eigen-modes) of the continuous
phase. The contribution of individual POD modes on the
spatial correlation of the droplet-gas velocity fluctuations
was quantified by reconstructing the instantaneous gas
velocity field associated with each mode and recalculating
the spatial correlations of the resulting gas flow with
different droplet size classes. The paper ends with a summary
of the main findings.

Experimental set up for combined ILIDS with PIV
measurements

The fundamental principle of combining the optical
arrangements of ILIDS with PIV and the experimental set-up
are described in detail in Hardalupas et al. (2 1,1 2010). A
brief summary is presented here. As shown in Fig. la, the
reflected and first order refracted light scattered from the
droplet, interfere to produce parallel fringes on a defocused
plane (Glover et al. 1995) and the characteristic
interferogram is observed with a far field arrangement of
receiving optics (Kawaguchi et al. 2002) through camera 1
(Fig. la). The number of fringes present in each of the
imaged fringe patterns and the fringe spacing is proportional
to the diameter. For the purpose of characterizing
simultaneously the velocity of the air flow in the vicinity of
individual droplets, the air surrounding the spray needs to be
seeded with particles and the viewing area is imaged on the
focal plane for PIV measurements. This is achieved by
splitting a part of the incoming scattered light using a beam
splitter and collecting it through a second camera (camera 2)
placed at the focal plane (Fig. la). With this optical system,
bright spots called glare points, corresponding to focused
reflected and refracted rays, appear in camera 2. Hence, the
same droplet is imaged as a rectangular region with a
superimposed fringe pattern on the ILIDS camera and as
distribution of two glare points on the PIV image. The
defocused images from 'seeding' particles appear on the
ILIDS camera, but without any superimposed fringes. The
droplet positions obtained through ILIDS can be used to
detect their corresponding glare points in the PIV image. The
detected glare points can be removed from the PIV image and
the filtered PIV image, when processed, provides gas
velocity around each droplet.
An overview of the experimental rig is shown in Figure
lb. The present work employed a spray dryer rig for two
phase measurements Hardalupas et al. (2II 1~, 2010). The rig
allowed coflowing air to enter from the top in the annulus
around the atomizer, which was a custom-built air-assisted
nozzle placed on the centerline of the cylindrical chamber
with diameter of 0.5m. It produced a solid cone spray with a
characteristic droplet diameter (SMD) of the order of


the particles through interfacial momentum transfer) depends
on successful modelling of these cross-correlation terms.
Also, several important issues, usually absent in numerical
studies, for example, turbulence generation due to particle
wakes and vortices shed by the particles, effect of gravity and
the presence of distribution of particle sizes, should be taken
into account. Thus, experimental characterization of the
droplet-gas flow interaction in sprays is important for the
understanding of the underlying mechanisms and the
provision of appropriate data that can assist the development
and evaluation of computational models. However, only few
experimental studies have been reported in this regard, for
instance, Kulick et al. (1994), Sakakibara et al. (1996),
Prevost et al. (1996), Ferrand et al. ~l; ), Hardalupas and
Horender ( 17), due to difficulties to obtain such
measurements. The measurement difficulty arises from two
challenging factors: first, the estimation of the above
mentioned correlation terms require simultaneous planar
measurement of velocity of both phases, and secondly, the
correlations have to be calculated conditional on droplet
size-classes. However, the literature, till date, is restricted to
single-point measurements and/or mono-sized
droplet/particle consideration. Thus, there is a need of
experimental characterization of, not only the relative
velocity between droplets and gas phase and associated
spatial correlations of velocity fluctuations, but also the
measurement of droplet size simultaneously, which is the
ultimate aim of the present research.
Simultaneous measurements of gas and droplet flow
characteristics in sprays are difficult, because of the need to
discriminate between the two phases. Two phase
measurement techniques, described in the literature, are
based only on Particle Image Velocimetry (PIV), and lack
either the droplet size information or simultaneous
measurements of the two phases. While, in one hand, PIV
alone is not sufficient for the task, on the other hand classical
single-point techniques, though reliable, cannot easily
address issues such as preferential concentration and large
scale flow structure identification in a spray (Prevost et al.
1996). The aim of this paper is to describe the potential
application of an optical instrument to the simultaneous
planar (or whole field) measurement of droplet size and
velocity along with the gas velocity in a spray by combining
the 'out-of-focus imaging' technique ILIDS (Interferometric
Laser Imaging Droplet Sizing) for planar droplet size and
velocity measurements with PIV for gas phase velocity
measurements (Fig.1). The advantage of the present
approach lies in the fact that the position of droplets in a spray,
obtained by ILIDS beforehand, helps in identifying the
images of the same droplets (as glare-points) in the focused
PIV image, thus making it possible to associate the droplet
size to the glare-points. The glare-points from the PIV image
are removed retaining only 'seeding' particles, which follow
the gas phase flow. The PIV images are then processed to
obtain the gas velocity in the vicinity of each droplet.
An unexpected difficulty with the combined technique
was the presence of a discrepancy in droplet centre when
calculated independently through ILIDS and PIV images,
which would lead to erroneous association of droplet size in
the PIV images. The cause of this discrepancy, its
quantification and a method for its elimination were
addressed in Hardalupas et al. (2II 1~, 2010). Application of
the combined technique in calculating the droplet-gas






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

imaged by both cameras, a calibration plate with equally
spaced "crosses" was used. Note that the calibration was
performed with both cameras in focus. The locations of the
centers of the crosses were determined with sub-pixel
accuracy and mapped to the respective pixels by fitting a
mapping function (cubic polynomial), the coefficients of
which were obtained through linear least square
approximation. Thus, the real position in space could be
Obtained, given a location on the image.

Inlage ep Ocessin g

The details of the image processing procedure followed for
the combined ILIDS and PIV techniques can be found in
Hardalupas et al. (2010). The ILIDS images were processed
to detect the fringe pattern and to obtain the droplet size and
velocity thereafter. Similarly, the PIV images were processed
to detect the glare points. In both cases the geometric centre
Of the droplet image (i.e. of either fringe pattern or of glare
points) was assumed to be the actual centre of the droplet. It
might be expected that the centre of any given droplet in the
two images, obtained from ILIDS and PIV respectively,
should coincide within the experimental error of registration.
However, this is not correct. Straightforward combination of
the two optical arrangements results in a discrepancy in the
location of the centre of a droplet, when imaging through
ILIDS and PIV techniques, which may lead to erroneous
identification of the glare points from droplets on the PIV
images. As discussed in Hardalupas et al. (~ I1,2010), the
magnitude of the discrepancy was found to be a function of
position of the droplet image on the CCD array and the
degree of defocus, but almost independent of droplet size.
Specifically, it varies approximately linearly across the
image alOng the direction corresponding to the direction of
prOpagation of the laser sheet for a given defocus setting in
ILIDS. The evaluated error from the measurements with
monodispersed droplets was subtracted from the droplet
centre identified in ILIDS images from a polydispersed spray
without 'seeding' particles. This reduced the discrepancy
between PIV and ILIDS droplet centers from about 1000
micron to about 100 micron and hence increased the
probability of finding corresponding fringe patterns on the
ILIDS image and glare points on the PIV image.
The algorithm for image processing is briefly illustrated
for a pair of ILIDS and PIV images in Figure 2.d In order to
quantify the discrepancy in droplet centre between ILIDS
and PIV images, 50 simultaneous images were captured
through both the ILIDS and PIV cameras, in a dilute region
of the spray without seeding particles in the surrounding air
flow. The discrepancy between the droplet centres in the
object plane, for both the horizontal and vertical directions,
was found and then represented by a linear fit (shown at the
top part of Fig 2). The pair of ILIDS and PIV images of the
spray with seeding particles, the PIV image after filtering out
the glare points (the removed glare points shown as the
dotted circles) and the simultaneous droplet and gas
velocities, obtained after processing PIV images, are also
shown in the same figure.


150-200pm at liquid feed rates of the order of 1.4-1.6x10-3
kg/s and air feed rate of the order of 0.12x10-3 kg/s. The
coflowing air was seeded with aluminium oxide particles
(diameter range 1-5 micron) before entering the rig. The
coflowing air flowrate, carrying the seeding particles, was
200 It/min, resulting in area-averaged air velocity
1.7x10-2m/s around the spray.

(with chn ap lug)


Glare points with
seeding particles


\\ Aiperture Cmrsin
\ \Reflected Opts
Refractedl lane

; LenstCamera-1
Seeding Beam Splitter (with scheimpflug)


ImalenqistionmCeomputer
andlaser


Compression optics i
ILIDS camera


Figure 1: (a) Principle of the combined ILIDS and PIV
technique (b) Experimental set-up

A frequency-doubled, double pulse Nd:YAG laser (120
mJ/pulse at 532 nm; New Wave Research) was used to
illuminate the flow. Thickness of the beam waist was about
Imm. Two identical cameras were used (PCO; Sensicam QE'
12bit, 1040xl376) and positioned on the same side of the
laser sheet. Two identical lenses (Nikon; 135mm focal
length) were used to collect the scattered light from droplets.
The scattered light from droplets was divided into two parts
by using a beam splitter. Because of issues related to optical
aberrations of ILIDS images, both cameras were adjusted to
provide a field of view of approximately 8 x 12 mm2, Which
is comparatively small with respect to that of usual PIV
system operation. The resolution was approximately
9pm/pixel in both directions for both cameras. In all
experiments, the scattering angle was set at a = 690, which is
the optimum scattering angle for ILIDS operation with a
vertically polarized laser sheet. The collecting angle was set
to 5.090, resulting in a resolution of 6.59 [pm/fringe] for the
ILIDS system. Both cameras were aligned under the
Scheimpflug condition. To ensure that the same area was






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


Quantification of
cent hre i epaancyn
vertical directions I '


Subtraction of estimated
Position of centre discrepancy
fringe pattomn in both directions
ILIDSa
Position of
glare ointsIdentify corresponding
frnepatterns and glare points


AMD = 36 4 m cron
SMD = 48 5 m cron


Remove gare poins
n, ,
proc...ine


Droplet size (micron)


YE , I i

Droplet and gas velocity


Figure 3: (a) Measurement locations in the spray and the
coordinate system (b) Probability of droplet size in the 8 x 12
mm2 measurement region at the cross-stream location, R = 0



The combined technique was applied in a polydispersed
spray with 'seeded' coflowing air around it. The increase in
droplet number density, due to the presence of seeding
particles, lowered the signal to noise ratio. As a consequence,
it was sometimes possible to detect images of seeding
particles, along with droplet glare points, during PIV
processing and to decrease the number of validated droplets
during ILIDS image processing. In the present work, results
of the combined ILIDS and PIV measurements are reported
for five different cross-stream locations, 500 mm
downstream of the nozzle exit, as presented in Figure 3a. At
any given measurement location, the notations 'x' and 'y'
refer to the local axial and cross-stream directions
respectively, both lying in the plane of the laser sheet and the
corresponding instantaneous velocities are denoted by 'u u
and v '. Throughout the paper, the subscript 'd' and 'g'
denote droplet and gas respectively. Similarly the subscript
'm' and 'r' respectively denote mean and rms velocities, and
'overbar' over any quantity indicates time-averaging. The
notation 'z' refers to the direction perpendicular to the laser
sheet and is measured from the nozzle axis, and 'R 'refers to
the beginning of any measurement area, at any cross-stream
location, measured from the nozzle axis. Because of the
experimental constraints in the set-up, measurement was
performed at an off-axial position of 125 mm, along the z
direction, in order to maintain the required object distance
between the viewing area and the collecting lenses.
Measurement at nozzle axis required the obj ect distance to be
larger, resulting in very low collecting angle for the given
aperture size of the collecting lens and, thus limiting the
minimum measurable diameter through ILIDS. The
measurement area was approximately 8mm x 12mm and the
cross-stream measurement locations were located at R = 0,
50, 100, 150 and 185 mm respectively from the nozzle axis.
Again, limitations in the experimental set-up did not allow
measurements beyond R = 185mm. For each measurement
location, 1700 image pairs were captured through each of the
cameras. Since the validation rate in the two phase
measurements was low, this large number of images was
required to achieve relatively low statistical uncertainty in
the measured quantities. The time scale of the air flow
turbulence was approximately 0.1 sec (Kavounides, 2006),
signifying that the flow is relatively 'lazy' as compared to
other laboratory scale turbulent flows. Hence, the repetition
rate of the laser was set to 1 Hz, so that the acquired samples
remained statistically independent.


Figure 2: Illustration of the image processing details of the
combined ILIDS and PIV techniques. Boundaries of the
removed glare points from the PIV image are shown as dotted
circles. In the plot of simultaneous droplet and gas velocities,
the blocked disks represent droplets and the associated bold
vectors represent droplet velocity.


Combined ILIDS and PIV measurements


The potential of the combined technique for two phase
spray measurement including estimation of droplet-gas
spatial velocity correlation (conditional on droplet size
classes) was demonstrated for a given location in the spray in
Hardalupas et al. (2 U~. The present paper evaluates, in
detail, the accuracy of the spatial correlation of the
droplet-gas velocity fluctuations for different size classes,
and its comparison with the spatial correlations of droplet and
gas velocity fluctuations. The droplet-gas velocity spatial
correlations for various cross-stream locations in the spray
and their comparison with the other correlations are also
presented. The contribution of the large-scale structures of
the turbulent gas flow surrounding the droplets, obtained
through proper orthogonal decomposition (POD), to the
droplet-gas velocity correlations is quantified.


conowing."


..asu
ocan



R
-


NOZZle .Xis


1


Elevation view


Plan view


rement
tons


Measurement area: 8 mm x 12 mm






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

results in gas velocities associated with a regular, structured
grid, the spatially-averaged mean could be calculated straight
away for each position on the grid, where the gas velocity
could be defined. The spatial resolution for the mean gas
velocity was about 0.15 x 0.15 mm', same as that of
instantaneous velocity, and about an order of magnitude
greater than the largest droplet size considered here. Figure 4
shows vector plots of the droplet mean velocity for droplet
size classes of 20-35Cpm, 35-50Cpm and 50-65 Cm, and for the
gas flow at various cross stream measurement locations (R)
starting from the spray axis and going towards the outer
spray regime. The mean velocity of droplets of a given size
class and the mean gas velocity, at any measurement location,
for both axial and cross-stream velocity components could be
observed to be quasi-uniform across the measuring area.
Thus the choice of window size was not extremely critical in
the present case. The corresponding root mean square (rms)
of velocity fluctuations was also found to show similar trend.
Both mean and rms velocity for droplets and gas was found
to vary within 20-30% across the measuring area at any
given location. This is possibly because of the smaller size of
the viewing area (8x l2 mm2 in the present case) as compared
to the large eddy length scale of the flow (~100mm). The
length scale of the energy containing eddies was assumed to
be 1/5 of the jet width (Tennekes and Lumley, 1972). The top
of Fig. 4, shows that the spray flow field, illuminated by the
laser sheet, spans the whole width of the rig, and so the gas
flow width can be considered the same as the rig diameter, i.e
500 mm.
Considering the case of 1 st measurement location, at R =
0 mm, Table 1 presents the magnitude of the area averaged
mean velocity with the values of the error bar for a 95%
confidence interval and the rms velocity. The statistical
uncertainty of any measurement depends on the rms of the
fluctuations of the variable and the number of samples. In the
present case, the statistical uncertainty increased for higher
droplet size class due to reduction of the number of samples,
as evident from the probability distribution of droplet sizes in
Figure 3b. Typical uncertainty of both axial and cross-stream
velocities was of the order of +0.03 m/s.
In the cross stream direction, since the magnitude of the
velocity is quite low (~ 0.02 m/s), the uncertainty was of the
similar order. This measurement location (R = 0 mm), being
close to the spray axis, the axial component was dominant as
compared to the cross stream component and so, on average
all of the droplets move downward in the same direction. Due
to inertial effects, the average droplet velocity (~ 0. 15 m/s)
was always slightly higher than the average gas velocity (~
0.10 m/s) and the droplet velocity of size class of 50-65 Clm
was about 20% higher than that of size class 20-35 Clm. Thus,
no significant difference is present in the mean velocity
between the droplet size classes, and also between the two
phases. The instantaneous fluctuating velocities (ri and v)
were calculated by subtracting the respective mean values
(ri,, and v,,) from the instantaneous velocities. The root mean
square of the velocity fluctuations (i,. and v,.) were calculated
and found to be of the order of 0.2~- 0.3 m/s for both droplets
of the selected size classes and gas flow, as shown in Table 1.
It should be noted that the rms velocity in the axial direction
was about two orders of magnitude greater than the mean
velocity and also, was of the same order as the rms velocity in
cross-stream direction. The isotropy (i,- / v,-, being close to
'one' and almost spatial invariant, indicates the flow field


The filtered PIV images were far from ideal containing
areas of removed glare-points. The interrogation window size
was chosen to be 32 x32 pixel7 (containing about 10 particles),
as a trade off between accuracy in gas velocity and spatial
resolution. The overlapping in the interrogation window was
about 50%. A higher seeding particle density was not
preferred, since this would have adversely affected the
detection of droplets and so would result in loss of validated
pairs of fringe pattern and glare points. Similarly, an
appropriate value of the laser pulse delay time (AT) between
the acquired pairs of images was carefully selected. A
relatively short value of AT usually resulted in small
displacement, adversely affecting the accuracy of the PIV
image processing, as discussed above: in contrast, a
relatively long AT would increase the chance of particles
moving out of the plane of the laser sheet. Hence, a
compromise had to be struck and AT was chosen to be 150 ps.
A modified FFT based cross correlation algorithm
(Ronneberger et al. 1998) was used for processing the PIV
images, which combines the accuracy of direct correlation
with the faster computing capability of conventional FF T
based correlation algorithm.
The measured droplet size distribution is shown in Figure
3b for the measurement location R = 0 mm. The Arithmetic
mean droplet diameter (AMD) and Sauter mean diameter
(SMD) for this location was 36.4 pm and 48.5 pm
respectively. The size distributions at other measurement
locations were more or less the same, so they are not shown
here. The calculations of the statistical characteristics of the
flow field, include mean droplet velocity, rms of droplet
velocity fluctuations and the spatial correlations of velocity
fluctuations, were performed over three droplet size classes
with overall range of 15pm each. These size classes were
20-35pm, 35-50pm and 50-65pm respectively.

Droplet/gas mean and turbulent velocity

Since ILIDS uses Particle Tracking Velocimetry (PTV) for
calculation of the droplet velocity, the droplet position inside
the measurement area was always random. So, unlike PIV, no
regular grid could be associated with the instantaneous
droplet velocities. Thus, for calculation of the mean velocity-
the observed experimental area was divided into regular and
rectangular sub-areas or windows. The droplet velocities
within each of these windows were averaged over all samples
and the spatially-averaged velocity was associated with each
particular window at its centre. If the size of these sub-areas
were chosen to be too small, the number of samples would be
low and hence the statistical uncertainty would become too
large, while conversely if the sub-area were chosen to be too
large, the spatial resolution would be reduced. Since the
number of detected droplets within a given window depends
on the droplet size class, the window size was varied for
different droplet size classes to ensure accurate statistics.
Also, while deciding the size of the window, the local
gradient of the mean droplet velocity should be taken into
account: a large gradient would require smaller window size.
But since this is not known apriori, in the present case, the
size of the sub-areas (for a given size class) was selected on a
trial and error basis and the final compromise for the spatial
resolution of the droplet velocity was about 2 x 2 mm2 for
droplet size class 20-35Cpm and 3 x 3 mm2 for both droplet
size classes 35-50Cpm and 50-65Cpm. Since PIV processing






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

all locations, was of the similar order as for the case of R = 0
mm. The mean velocity, at any given location, was more or
less independent of the droplet size. Though, a small increase
or decrease (about 20%) in mean axial velocity of larger
droplets (50-65 Clm) was observed as compared to the smaller
droplet size class 20-35 Clm, depending on whether the
droplets move downward closer to the spray centre or
upward against the gravity towards the outer regime of the
Spray. The velocity of droplets with higher size class was
found to be relatively smaller towards outer spray: for
instance the axial mean velocity for 50-65 Clm droplet size
class at R = 1 85 mm was of the order of 0.06 m/s, one third of
the axial velocity at R = 0 mm. Figures 5a and 5b show the
variation of area averaged mean and rms velocity in both
axial and cross-stream direction for droplet size class of
20-35 Clm and gas flow for various measurement positions, R.
The droplets, away from centre of the spray, tend to move
upward, i.e "towards top of the tower". Between R = 50 mm
to 100 mm, at about R = 80 mm, the mean droplet flow field
(not shown here) was observed to be horizontal and inward,
with no axial component. This can be interpreted by the
mOtion of the air surrounding the spray being entrained into
the spray in a recirculating pattern. The droplets are
prevented from drifting downward under the action of gravity,
as might be expected, by the upward component of the gas
velocity.
As shown in Fig. 5a, away from the spray axis, the mean
axial velocity difference in droplets and gas tend to decrease,
while the mean cross stream velocity of the droplets was
higher than that of the gas. Though, no significant difference
in mean velocity could be observed between droplets and gas
at any location R and for any droplet size classes, resulting in
a low value of droplet Reynolds number Re (- 0.05). Figure
5b shows both droplet and gas axial rms velocities are of the
same order (similar to the mean velocity) and slightly
decrease away from the spray axis. However, the
cross-stream rms velocity for both droplets and gas decrease
sharply with R (by about 50% from R = 0 to R = 185 mm),
indicating that away from the spray axis, the flow tends to be
more anisotropic and the production of turbulent kinetic
energy reduces. The rms velocity for droplets, similar to the
mean velocity, was almost independent of the droplet size,
and the rms velocities for either droplets or gas were an order
of magnitude greater than the mean velocity at any given
measurement location.
Figure 6a presents the scatter plot of axial and
cross-stream component of droplet velocity (ud ~ vd) foT
droplet size class of 20-35 Clm at R = 0 mm, which has no
preponderant correlation between the two components of
velocity. This is expected, because the measurement location
in the spray is far from the injector, and also has no strong
normalized Reynolds shear stress, (upv, /urg r < 0.2), as
shown in Figure 6b. The shear stress was normalized with
respect to the respective rms velocities, and was area
averaged. The magnitude of the shear stress was maximum at
R = 100 mm.


(within the viewing area considered here) to be nearly
homogeneous and isotropic closer to the spray axis.


Droplesizheclass:20-35~8 1


..
R m R=1500mm R10m R15


R~ 0mm


100 m


150 mm 185 m


DrOpletsize class 35-50m .

I.



Dropleszreclass 5045pm





:

'- ~~~~ ~~~ I :':.::::.: I



Figure 4: Mean velocity for droplet size classes of 20-35Cpm,
35-50Cpm, and 50-65Cpm and for the gas flow for various
cross-stream measurement locations, R.


Axial Cross-stream Axial Cros-stm
mean vel. mean vel. rms vel. rms vel.
u, (m/s) v,(m/s) ar (m/s) vr (m/s)


D:0.140+0.025 0.013+0.023 0.279 0.261
20-35pm


0.178+0.033 0.031+0.029 0.295 0.265
35-50pm


0.178+0.041 0.022+0.037 0.277 0.255
50-65pm


Gs 0.113+0.019 0.011+0.022 0.268 0.232


Table 1: Area-averaged statistics of velocity of various
droplet size classes and gas flow for the first cross-stream
measurement location, R = 0 mm. The viewing area was
8xl2 mm2.
The mean velocity of the droplets and gas flow, for all
measurement locations (different R) can be compared in
Figure 4. The statistical uncertainty in velocity estimation, at
























0.1



Position of measurement, R (mm)


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


-+- Mean axial droplet velocity
A Mean cross-stmeam droplet velocity
-.5 -*- Mean axial gas velocity
SMean cross-stream gas velocity


U
9
or
c
or
or
I


1.5

1






S0 5


-1 -0.5 0 0.5 1
Axial droplet velocity fluctuation (ud)


0.2




e.2



0.14

o.
l


------------- ^--=---------+-


50 100 150 180
Position of measurement, R (mm)


-Axial droplet rms vel
Cross-stream droplet rms vel ^
-Axial gas rms vel
cross-stream gas rms v''

opposition of measurement, R (mniso


SFigure 6: (a) Scatter plot of instantaneous fluctuating droplet
VeoIcity, ud~ vd for droplet size class 20-35Cpm at R = 0 mm
and (b) Normalized shear stress obtained from the gas
Iss velocity at R = 0 mm.


Figure 5: Area-averaged (a) mean and (b) rms velocity, for
droplet (size class 20-35 Clm) and gas flow for various
cross-stream measurement locations, R.

The Stokes number (St) of a droplet size class is defined
as the ratio of the droplet aerodynamic time constant (r,) to
an appropriate turbulent time scale of the flow (r,). The
Reynolds number of the droplets being very small in the
present case, the assumption of Stokes flow around the
particle remains satisfied. The characteristic time of the jet
(r,) is chosen as the ratio of a large eddy length scale (as
described before) to the axial rms velocity on the jet axis.
Thus, the values of St for the three droplet size classes were
found to be of the order of 0.005, 0.015 and 0.025
respectively. At R = 0 mm, assuming isotropic turbulent flow,
the Taylor (rr) and Kolmogorov time scales (Tk) were
estimated. The Taylor microscale, which was of the order of
0.55 mm, was obtained through the dissipation rate, which, in
turn, was calculated from the spatial gradient of the turbulent
velocity fluctuations (Tennekes and Lumley, 1972). The
Kolmogorov scale was estimated to be the order of 0.085 mm,
again from the dissipation rate (Tennekes and Lumley, 1972).
The Stokes numbers for the 20-35Cpm, 35-50Cpm and
20-35Cpm droplet size classes were of the order of 4.32, 10.7
and 19.6 respectively, based on the Kolmogorov scale, and
1.12, 2.78 and 5.09 respectively, when based on the Taylor
scale. This signifies relatively poor response of the droplets
to the flow at these length scales.


Spatial correlation of droplet and gas velocity fluctuations

Measurement of the droplet-gas and droplet-droplet
velocity correlation terms, appearing in the transport
equations for kinetic stress tensor of the droplets and
turbulent kinetic energy of the gas phase for a droplet-laden
gas flow (with negligible volume fraction of the droplets), is
essential to give further mnsight into the two-phase flow
physics and to validate some new approaches for modeling
the droplet/gas fluctuating motion. However such
measurements are rarely reported in the literature because of
the difficulty in obtaining simultaneous planar measurements
of both phases. The technique of combining ILIDS with PIV
offers such an opportunity. The method of calculating the
spatial correlations is described below.
The velocity correlation terms were calculated over the
whole viewing area for each measurement location, R. Since
no strong spatial gradients of mean and rms velocity in either
axial or cross-stream direction were found within the viewing
area, such averaging was expected to have no influence on
the magnitude of the correlations. The process of calculating
the spatial correlation coefficient of droplet-gas velocity
fluctuations, Rdg(D, r), as a function of droplet size class, D,
is depicted, in Figure 7. For every image sample, I, around
each droplet position, J, a circle with a given radius, named
'radius of separation', r, was defined. For each droplet the
correlation between the fluctuating droplet velocity and all of
the fluctuating gas velocities, index K, which have been
measured inside an annular ring (defined within r + Ar/2),
was calculated. This is done for all droplets belonging to the
size class D in that image sample, and then repeated for all






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

The discrete values of the radius of separation, r, and the
width of the annular ring, Ar, were chosen as a trade-off
between statistical accuracy and spatial resolution of the
correlation coefficient. Though one would always prefer to
obtain the correlation coefficient as close to the droplets as
possible (i.e smaller r), but it should be noted that the number
of instantaneous individual correlations that can be obtained,
between a given droplet and the surrounding gas velocities, is
proportional to both r and Ar. Very small values of r and Ar
would decrease the sample space of the instantaneous
correlations (for a given number of images), causing higher
uncertainty while, the higher values would result in
decreasing the spatial resolution of the calculated correlation
coefficients. In the present case, the increment of r and, the
value of Ar were chosen to be 0.5 mm and 1 mm respectively
for droplet size class 20-35Cpm and 1.5 mm and 3 mm for the
other two higher size classes resulting in lower spatial
resolution of Rdg for the higher size classes owing to their
lower probability of occurrence. The resolution of the gas
velocity vectors from PIV measurements decides the closest
possible distance from a given droplet, where the correlation
can be calculated. In our case this distance, equal to half of
the spatial resolution, is about 0.07 mm. Thus in the present
case, the value of Rdg, at minimum radius of separation, r =
0.5mm, represents the spatially averaged value of the
correlation calculated between r = 0.07 mm to 1 mm. The
plots of droplet-gas velocity correlations for axial and
cross-stream velocity components, represented as Rild*zig and
Rvd*rg TCSpectively, as a function of radius of separation, r, are
Shown in Fig. 8a and Fig. 8b respectively for different droplet
size classes. The statistical uncertainty of the correlation
coefficient for 95% confidence interval is also shown. The
uncertainty of the correlation coefficients was low and of the
order of +0.002 for all droplet size classes.
Fig. 8a shows that the spatial correlation between the
r) velOcity component in the axial direction for droplets of all
SSize classes with gas flow is quite high and decreases with
distance away from the droplets though the change is quite
low (~ 10%). This was somewhat expected. Since the particle
stokes number was very small (St << 1), hence, the droplets
of all three size classes can be expected to closely follow the
gas motion and the flow can be considered to behave
according to one-way coupling between the two phases
within the experimental regime reported here. Also,
comparing the value of Rild*zg for the three size classes, no
significant difference (< 0.1) in the correlation coefficient
could be observed at any r. Thus, Rild*zig can be considered to
be independent of droplet size. However, in cross-stream
direction, the magnitude of the droplet-gas velocity spatial
correlation (Rvd*rg) WaS relatively lower and decreased more
sharply away from the droplets as shown in Fig. 8b. Also, the
magnitude of the correlation was relatively higher for the
smallest droplet size class.
The spatial droplet-droplet velocity correlation, Rdd, WaS
calculated in a similar way as Rdg. However, in this case, for a
given droplet in every image sample, another droplet velocity
(instead of gas velocity) was searched in the annular area
defined within r & Ar/2. The same value of increments for r
and Ar were used as before, thus maintaining the same
resolution for Rdd aS for Rdge for a given droplet size class.
Again, similar to Rdg, Rdd WaS calculated for several
combinations of different droplet velocity components
conditional on different droplet size classes. For example, the


image samples, N. Then, the average of all calculated
correlations was obtained and normalized with the product of
the respective rms of fluctuations of droplet and gas velocity
to obtain the final correlation coefficient, Rdge for the size
class D and for the radius of separation r. It should be
mentioned here that the mean velocity of droplets and gas
used to calculate the fluctuating velocity and, the respective
rms velocity (used for normalization) were the area-averaged
values. Then Rdg iS calculated for different values of 'r' and
for all of the droplet size classes present. Also, the
correlations were calculated for several combinations of the
different velocity components of the droplet and gas flows
and each of the correlations was conditional on different
droplet size classes. For example, Figure 8 shows the
correlation coefficient between the axial components of
droplet and gas velocities as a function of separation distance,
which can be represented as Rild.ig(D, r) and is given as:


udr gUr


Rird*ug (D. r)


Where ui, and u,, are the rms of the fluctuating component
of velocity of droplet (with size class D) and gas in axial
direction and, red and u, are the respective fluctuating
components of velocity.


Average over whole area
and all samples


NC d,I,J (D)x ug,I,K (
2ldr 2gr


Measurement area
Figure 7: The method of calculation of the spatial correlation
of the velocity fluctuations. The formula corresponds to the
droplet-gas velocity correlation in axial direction, as an
example,

It is worth mentioning at this point that, the present
approach of calculating the instantaneous spatial correlations
of velocity fluctuations at any given radius of separation r-
from a given droplet, inherently assumes directional
independency of the correlation around the droplet. The
assumption was verified by calculating the normalized
spatial correlation (Rgg) of the gas flow along both axial (x)
and cross-stream (v) directions separately. The gas
correlation coefficient for axial velocity component along
x-direction (R,,g.,),g was found to lie very close to that along
v-direction. (R,,g.,,g), the difference being of the order of less
than 0.02 at any separation distance. Similar results were
found for the gas correlation for the cross-stream velocity
component, R,gr. .























0.93
as ----------- 20 -35 pm
........... 35 50 pm
z..... **.. ----s-sm
o.ss~ I.";g... ..



*-. .. ... -. ...



0.78


012345678 0
Radius of separation, r (mm)

0.8
1-... *****=**** 20 35 pm
0.75 ***** 35 50 pm


0.7 .-,



0.6 ...

0..


I I I I


'0 2 5 8
Radius of separation, r (mm)




....o**** 35 -50 pm
.8 '*. ****=*** 50 -65 pm



*... *' "::,t ---- ***....







Radius of separation, r (mm)


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

probability of drop size distribution in Fig. 3b, which shows
significant reduction in the probability of the presence of
higher droplet size classes. Also, because of smaller sample
size, the statistical uncertainty was large for smaller radius of
separation for any droplet size class. In Fig. 9a, the value of
the correlation coefficient along axial direction (Rild*zid) foT
SiZe ClaSS of 35-50Cpm and 50-65Cpm, for small separation r,
was found to slightly overshoot 'one'. Considering the
statistical uncertainty involved in instantaneous velocity and
statistics calculation, the droplet-droplet velocity correlation
for all size classes can be considered to be high (> 0.9) and of
the same order for a given r. Though, larger droplets are
expected to have higher correlation, at least for small value of
r, because of higher inertia. Along cross-stream direction
(Fig 9b), the spatial correlation coefficient was lower than the
axial direction and found to decrease with droplet size class.


droplet-droplet spatial correlation coefficient for the axial
components of droplets for the same size class, represented
as Rild*ud(D, r), is given as:


CtradI,.J(D)XllIK (r
Rattiste(D,r)= I J K (2)
tra; xtick
Here, the notation K refers to the droplet velocity found
in the annular ring defined for a given radius of separation r.


Radius of separation, r (mm)


(a)

















(b)


0.9


e" 0.7


I~


----o**** 20 -35 pm
**o**** 35 50 pm
**** **** 50 65 Pm


0

0



a

o

a


Figure 8: Spatial correlation coefficients of droplet-gas
velocity fluctuations for various droplet size classes for (a)
axial component of velocity and (b) cross-stream velocity
component, at R = 0 mm. Error bars indicate the statistical
uncertainty of the correlation coefficient for 95% confidence
interval.

Figures 9a and 9b present the droplet-droplet velocity
spatial correlations for axial and cross-stream velocity
components, represented as Rid*ud and Rvd*rdfreSpectively, as a
function of radius of separation, r, for various droplet size
classes along with the statistical uncertainty (for 95%
confidence interval) for the cross-stream location, at R = 0
mm. In this case, the statistical uncertainty was higher, about
+0.05, +0.1 and 10.15 for the three droplet size classes, the
largest value corresponding to the higher size class. In
comparison to the droplet-gas velocity spatial correlation, the
uncertainty was higher here. This is primarily due to the
decrease in sample record size because the number of
validated droplet velocity in any image was much less than
the number of validated gas velocity vectors (the ratio being
10:5000 in any image). Again, the greater statistical
uncertainty with larger droplet-size class is evident from the


Figure 9: Spatial correlation coefficients of droplet-droplet
velocity fluctuations for various droplet size classes for (a)
axial velocity component and (b) cross-stream velocity
component, at R = 0 mm. Error bars represent the statistical
uncertainty of the correlation coefficient for 95% confidence
interval.

The correlation of droplet axial velocity with gas
cross-stream velocity and vice-verse (Rild*rg and Rvd*rg wr
also obtained for all size classes and found to be of the order
of 0.1-0.2 and almost independent of droplet size. This is
expected in the present flow, which has very small shear
stress in the gaseous phase (the shear stress was of the same
order as shown in Fig. 6b). However, a slight increase in
these correlations was observed at R = 100 mm,






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

velocity almost invariant with respect to the measurement
location R, while the rms velocity in cross-stream direction
decreases (between R = 0 mm and R = 185 mm) by about
50%.


corresponding to the maximum gas shear stress. Thus, it can
be concluded that the droplet/gas motion along either axial or
cross-stream direction do not influence each other.
In order to further elucidate the momentum transfer
between the two phases, the normalized spatial correlation
for the gas flow (Rgg) was obtained, as mentioned before, and
compared with spatial correlations between droplet-droplet
(Rdd) and droplet-gas (Rdg) VeoIcity fluctuations. The spatial
correlation of the axial gas velocity along the axial direction
(Rug.ug and of cross-stream velocity in cross-stream direction
(R,gs~g was calculated. Figure 10 shows the comparison of
the correlations for both velocity components for droplet size
class 20-35 Clm, at the first measurement location, R = 0 mm.
It can be observed that both dispersed and continuous phases
are well correlated with each other and also with themselves
in this flow region, though the correlation is relatively higher
in the axial direction. For smaller radius of separation r or
closer to the droplet, the value of the droplet-droplet
correlation was slightly higher than the gas correlation
because of the higher inertia of the droplets as compared to
gas elements. Away from the droplet, the correspondence of a
droplet with the surrounding gas and also with other droplets
(of same size class) tends to decrease, especially in the
cross-stream direction. This effect is more pronounced for
the droplets with higher relaxation time (compare with the
correlations in Fig. 9a and 9b for higher size classes).
However, the gas remains better correlated with itself even at
large r, and thus for large r, along the cross-stream direction,
Rg > Rdd and Rdg


0.95~ o-

0.9

i9 os


..t . . ....
a
a.
""o....~~~a .


$--......
'~""-0..
s
r

o
'~o
:


E


..o -
a


e R= 0R= mm
0.8~ e- R = 50 mm
"--R =100 mm
0.75 - R =150 mm
--o- R =185 mm


0.9 .




-a 0.7a a ..
tO .s.


o ud'ud
R
ud'ug


vd*vd
Ryd*vg
. R


'0 12 34 56 78 9
Radius of separation, r (mm)
(a)

o.o
R= 0= mm
ooo R =50 mm
R= 100 mm
-- R =150 mm
'-' "-~. ,... --e---R = 185 mm
S 0.7 -

0.6-- ...:



0.40 1 2 3 4 5 6 7 8 0..
Radusof epraton r mm






R.4



FInfuene 1 Coflargescal oflo tutrso spatial correlation cefcet of
droplet-gas velocity futain n()aildrcin(u~g





In general, turbulent flow is characterized by the
existence of several length scales, some of which assume
very specific roles in the description and analysis of the flow,
Tennekes and Lumley (1972). In the context of a
droplet-laden two phase flow, it remains important and
interesting to study the interaction between the dispersed
phase and the large scale motions present in the continuous
phase. Out of the several existing structure education
methodologies, Proper Orthogonal Decomposition (POD),
proposed by Lumley (1981), provides an unbiased method to
extract the large scale structures in a turbulent flow. POD
essentially extracts a complete set of spatial eigen-functions
or modes (also referred as the 'characteristic eddies of
turbulence') from the measured two point velocity
cross-correlation matrix. Thus, the shape of the extracted
modes depends on the particular flow field and serves as a set
of optimal basis functions for expansion of the flow. The


Figure 10: Comparison of spatial correlation coefficients of
droplet-droplet (Rdd) and droplet-gas (Rdg) VeoIcity
fluctuations for droplet size class 20-35Cpm and gas velocity
correlation (Rgg) for both axial and cross-stream velocity
components at the cross-stream measurement location R = 0
mm.


Figures 11a and 11b show the comparison among the
droplet-gas velocity correlations for all of the measurement
locations (R) in axial and cross-stream directions respectively.
Away from the spray axis, the correlation between the two
phases in the axial direction was found to increase though by
a small value (~ 0.1). In cross-stream direction, the value of
the correlation up to R = 100 mm decreased only slightly, but,
towards the outer spray regions (R = 150 mm and 185 mm), it
reduced to low values (~ 0.5). It should be recalled here from
Fig.5b that, both droplets and gas flows have axial rms


1 23 45 67 8
Radius of separation (mm), Lag (mm)






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


velocity field can be represented as a sum of the modes. Also,
because of the fastest convergence property, the number of
energetically significant modes is minimum. In the present
work, the POD modes of the turbulent gas flow are obtained
using the 'method of snapshots', the details of which can be
found in Sirovich (1987).
POD, essentially decomposes the instantaneous
fluctuating velocity data set u(X, t), where X and t are the two
independent variables (denoting space and time respectively),
into a sum product of spatial eigen-functions y;(X) and
temporal coefficients a(t) such that,


u(Xt) = an () n=1
Here, rk iS the rank of the velocity matrix [u]MxN, M is the
number of image samples and N is the number of velocity
data defined in each sample, and the rank rk = min (M,~ N).
Each eigen-function ( y7, ) is associated with an
eigen-value An,, (2 ns are the eigen-values of the two point
velocity cross-correlation matrix) such that, /2, > /2,,, and,


"r (X, t) = ar (t) x P(X)


0.2 (mis)
of t
21
4 -~lr

024681D
(b) t mm > t


y (mm)


y (mm)


ln an 6n Sn n


Figure 12: (a) Contributions of cumulative eigen-values of
the respective POD modes, obtained by applying POD over
instantaneous gas velocity data at R = 0 mm. Flow structures
associated with (b) 1st eigen-mode, (c) 2nd eigen-mode and
(d) 3rd eigen-mode of the POD analysis.

Then the spatial correlations of droplet-gas velocity
fluctuations were calculated following the same procedure,
as described in the previous section. Thus, the correlation is
calculated for each mode conditional on each droplet size
classes. Figures 13a and 13b show the modal contributions
toward the droplet-gas velocity correlation for the droplet
size class 20-35pm for axial and cross-stream velocity
components respectively, at R = 0 mm. In axial direction, the
flow structure represented by the 1st mode produced
maximum correlation value (~ 0.9) and found to be
independent of the radius of separation. The 2nd mOde
showed low correlation, of the order of 0.1, and maintained
the same value at any distance from a given droplet. The
vortical structure, depicted by the 3rd mOde, resulted in
correlation, which was relatively high and positive closer to
any given droplet but was negative away from it. The 4t and
5" modes, containing smaller vertical structures (not shown
here), showed similar behavior, while, the other higher
modes (after 10t mode), which may be characterized as
random fluctuating components, showed very low
correlation (~ 0.05). In contrast to the results in the axial
direction, for cross-stream direction, the 2nd mOde was
dominant instead of the 1st mode. This was somewhat
expected. The 2nd mOde, being always dominant in
cross-stream direction, correlated well with the droplet
velocity in the same direction. Other modes produced a
correlation, more or less similar to the case of axial velocity
component. For other larger droplet size classes, the
contributions of modes for the droplet-gas velocity
correlation, was similar to that of 20-35pm size class.


For any mode, n, the ratio of 2,, to the sum of all
eigen-values ( C4z ) represents the contribution of the
corresponding eigen-mode (yn) towards the total turbulent
kinetic energy.
In the present work, POD was applied over the
instantaneous gas velocity data (for both axial and
cross-stream velocity components) of the two phase spray
measurements, after subtracting the mean velocity, to extract
the large scale eddies. Figure 12a shows the contributions of
the respective cumulative eigen-modes and Fig. 12b, 12c and
12d present the 1st, 2nd and 3rd eigen-modes respectively at
the measurement location, R = 0 mm. The 1st eigen-value
contributes about 30% of the total turbulent kinetic energy
and thus, it is the dominant eddy structure present in the
continuous phase. The figure shows that in total about 30 and
1000 modes are required to represent 60% and 100% of the
total kinetic energy respectively signifying very little
contributions from the higher modes. The largest length scale
of the flow, as described before, being of the order of 100 mm,
the 1 st mode can be expected to be a part of the largest eddies
present in the gas phase flow. The first eigen-mode indicates
that, the effect of these large scale structures (being mostly
axial and upward, Fig. 12b) is to decrease the instantaneous
axial velocity of the gas flow, since the mean gas velocity is
axial and downward (Fig. 4). Similarly the flow structure
corresponding to the 2nd mOde tends to increase the
instantaneous cross-stream velocity away from the spray axis.
The 3rd mOde shows the presence of a vortical structure
spanning the whole measurement area.
It is important to investigate how each individual flow
structure contributes towards the correlation between the
dispersed and continuous phases present in the flow. For this
purpose, for a given eigen-mode, the instantaneous velocity
data were reconstructed by considering that mode only. Thus,
the instantaneous velocity data set obtained by considering rt
mode, can be represented as,


20 5 10 15 20 25 30
10200 400 600 800 1000
3)Eigen aue no














o.1s~ ...




-0.1 e 0-_ .




Radius of separation, r (mm)


0.O

0.2 , j -
0.1s~ -
0.1

o~os


-0.1
0 12 34 56 78 9
Radius of separation, r (mm)


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

droplet size classes, were determined as a function of the
distance of separation between the droplets and gas or droplet
VelOcity vectors and the associated statistical uncertainty was
evaluated. A relatively strong correlation between the axial
components of droplet and gas velocities was observed as
COmpared to the cross-stream velocity component suggesting
that the droplets faithfully follow the gas motion. This
COnclusion is expected from the low values of the turbulent
Stokes number of droplets (St << 1) for the measurement
lOcation considered in the present work. However, for higher
droplet size classes, relatively lower correlation was
Observed. Comparison of spatial correlation of the
droplet-gas velocity fluctuations with the spatial correlations
of droplet-droplet and gas velocity fluctuations was
presented. Along the distance R from nozzle axis and towards
the outer spray, the droplet-gas spatial correlation had a
tendency to increase in axial direction, and decrease in
CTOss-stream direction. The large scale eddy structures,
present in the continuous phase, were extracted by applying
POD over the instantaneous gas velocity data. Contribution
Of individual POD modes on the droplet-gas spatial
Correlation was determined. In axial direction, the 1st mode
and in cross-stream direction, the 2nd mOdes were found to be
the dominant contributors and the associated flow structures
were identified. These results could improve the
understanding of the interaction between the dispersed and
continuous phases in a spray and, also could further elucidate
the capability of the combined technique for two-phase spray
measurements.

References

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techniques. 14th Int Symp on Applications of Laser


::
' .9


. ... ... 0- o. . .o .
o ...... o e... udug
a a OMode 1


Mode 2
Mode 3
Mode 4
Mode 5
Mode 10
Mode 100


e.7 I


vd'vg
. *O Mode 2


Mode l
* Mode 3
- Mode4
+ Mode 5
.a... Mode 10
Mode 100


Figure 13: Contributions of various POD modes on the
spatial correlation of droplet-gas velocity fluctuations for
droplet size class 20-35Cpm at the measurement location R = 0
mm for (a) axial velocity component (Rud*ug) and (b)
cross-stream velocity component (Ryd*vg)

Conclusions

A novel method of simultaneous measurements of
droplet and gas flow characteristics in sprays was described,
which combines the out-of-focus imaging ILIDS technique
with the in-focus imaging PIV technique. ILIDS provides
planar droplet size and velocity measurements, while PIV
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described. The measurement location corresponds to an
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described. The correlation coefficients, conditional on






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

Techniques to Fluid Mechanics, Lisbon, Portugal, 07-10 July cluster measurements. AIAA J, 41:2170-2178 :[ II na)


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