Experiments in Fluids 32 (2002) 252±268 Ó Springer-Verlag 2002
DOI 10.1007/s003480100356
Simultaneous two-phase PIV by two-parameter phase discrimination
D. A. Khalitov, E. K. Longmire
252
Abstract A ¯exible and robust phase discrimination algorithm for two-phase PIV employs second-order intensity
gradients to identify objects. Then, the objects are sorted
into solids and tracers according to parametric combinations of size and brightness. Solids velocities are computed
by tracking, gas velocities by cross-correlation. Tests in a
fully-developed turbulent channel ¯ow of air showed that
the two phases do not contaminate or bias each other's
velocity statistics. Error magnitude and valid data yield
were quanti®ed with arti®cial images for three particle sizes
(25, 33, and 63 lm), two interrogation area sizes (32 and
64 pixels), and volumetric solids loads from 0.0022% to
0.014%. At the channel centerline, the gas valid data yield
was above 98% and the RMS error in gas velocity was less
than 0.1 pixels for all variations of these parameters. The
solid-to-tracer signal ratio was found to be the major
parameter affecting the magnitude of the RMS error.
1
Introduction
Many industrial and environmental processes involve
turbulent dispersed two-phase ¯ows, such as gaseous ¯ows
laden with solid particles or liquid drops and liquids
containing solid particles or bubbles. In such ¯ows, discrete particles, i.e., drops or bubbles constitute a disperse
phase, whereas the carrier liquid or gas represents a continuum or continuous phase. The disperse phase can move
somewhat differently from the continuous phase and the
motion of both phases can be very complicated, especially
in turbulent ¯ows. Examples include spray or coal combustion, ¯uidized beds, powder transport and mixing,
atmospheric ¯ows, and cavitating ¯ows.
It is dif®cult to simulate these practical ¯ows directly,
even on the most powerful supercomputers. Therefore, for
better understanding and easier prediction or optimization of such ¯ows, simple yet accurate models are needed,
where a given numerical model has to be tested using
Received: 20 September 2000/Accepted: 2 July 2001
Published online: 29 November 2001
D. A. Khalitov (&), E. K. Longmire
Department of Aerospace Engineering and Mechanics
University of Minnesota, 107 Akerman Hall
110 Union St. S.E., Minneapolis, MN 55455, USA
e-mail: khalitov@aem.umn.edu
The authors gratefully acknowledge support from the National
Science Foundation (CTS 945-7014) and from the University of
Minnesota Graduate School.
experimental data of an appropriate type. For example,
simultaneous velocity ®eld measurements in both phases
are needed for testing Eulerian-Eulerian two-¯uid models.
The two most common methods used for velocity ®eld
measurements are particle image velocimetry (PIV) and
particle-tracking velocimetry (PTV). Since these two
methods employ similar imaging techniques, we will frequently refer to both of them as `PIV'. A review of PIV in
single-phase ¯ows can be found, for example, in Adrian
(1991). In digital PIV (most common), every image is
represented and analyzed as a rectangular array of pixels.
Basics of digital PIV are discussed in detail in Westerweel
(1993, 1997).
For simultaneous two-phase PIV, particle-laden or
bubbly ¯ows are typically seeded with tracers whose size is
signi®cantly smaller than the size of the dispersed phase
elements (bubbles, solid particles, or drops). To acquire
the PIV data, a ¯ow is illuminated by a pulsed light sheet
and recorded by a ®lm, CCD, or video camera. In the
images, dispersed elements and tracers appear as bright
spots. Knowing the time delay between the pulses and
analyzing the displacements of the bright spots, one may
compute planar instantaneous velocity vector ®elds. Because of differences in size and surface properties, the
optical signals from small tracers and larger dispersed
phase elements exhibit various differences. These differences persist in the resulting PIV images, allowing one
to discriminate between the phases and thus to employ
a single instrument to measure the continuous and
dispersed phase velocity ®elds simultaneously.
To date, researchers have developed and applied several
types of methods to separate phases in PIV images. These
methods are categorized by differences in color, image
intensity, spot size, spatial frequency, spot shape, and
correlation peak properties. Each method is described
below.
1. Color. Typically, in this method, the tracers carry
¯uorescent dye that emits light at a wavelength (color)
different from that of the illuminating light sheet (Liu and
Adrian 1992, Sridhar et al. 1991). Thus, both phases scatter
light, but only tracers ¯uoresce. To distinguish between
the scattering and ¯uorescing colors, one may use either
®lters and two synchronized monochrome cameras or one
color camera. In a more complex color separation technique (Towers et al. 1999), the dispersed phase also ¯uoresces but at a different wavelength, so that the continuous
and dispersed phase data can be extracted independently,
introducing minimal noise to each other. The color techniques can be relatively expensive because, in addition to
requiring ¯uorescent particles and possibly more powerful
lasers, they require either two monochrome cameras or a
color camera instead of the single monochrome camera
typically used for PIV.
2. Image intensity. Sakakibara et al. (1996) adjusted
photometric parameters so that all tracer pixels would not
exceed 70% of the maximum intensity level. Thus, every
pixel brighter than that would be associated with the dispersed (solid) phase. In this study, the residual gray pixels,
or coronas around the solids were a major source of noise
for the continuum (gas) measurements.
3. Spot size. This method employs image thresholding
with subsequent discrimination by white-spot area, such
that dispersed particles appear larger in the images than
tracers. This simple method was used by Chen and Fan
(1992), Hassan et al. (1992), Hassan et al. (1998), Suzuki
et al. (1999), and Paris and Eaton (1999). In addition, Gui
et al. (1997), Merzkirch et al. (1997), and Lindken and
Merzkirch (1999) applied masking techniques, but used
thresholding and size discrimination to determine the
digital masks. With any of the above techniques, the images are binarized, so that every pixel value above a prescribed intensity level is set to maximum and every pixel
below this level is set to zero. Then, connected regions of
bright pixels are determined and sized, using a recursive
connectivity algorithm. For one or both phases, spots
within certain area ranges are identi®ed as either tracers or
dispersed particles, and spots whose areas are outside of
these ranges are rejected. Hassan et al. (1992) pointed out
a problem of having a grey `corona' around bright bubbles
and solved this problem by local thresholding. They determined that the optimal threshold function would be
1/r2, where r is the distance from the particle center. These
variable thresholds were applied in order to eliminate
coronas while preserving a high percentage of tracers.
4. Spatial frequency. Kiger and Pan (1999) used a spatial
median ®lter that eliminates tracer particles by treating
them as high-frequency noise. Then, the tracer images
were examined separately by subtracting the dispersed
phase images from the originals.
5. Spot shape. This method is based on applying more
complicated spatial ®lters to either extract or eliminate
spots exhibiting certain image patterns. Kiger (1998) noted
that solid particles with diameter ~300lm had a unique
scattering/re¯ection pattern that appears in PIV images as
a bright spot with two intensity peaks. Using a convolution
algorithm, he extracted regions conforming to this pattern,
identifying them as solid particles. In the work by Oakley
et al. (1997), re¯ection patterns from individual large
bubbles formed two distinct bright spots in PIV images,
whereas tracers appeared as single dots. Combining the
median ®lter with the convolution algorithm, Kiger and
Pan (2000) obtained high-quality simultaneous PIV
measurements along with the error analysis.
6. Correlation peak properties. This method requires a
signi®cant velocity difference between the two phases at a
given location. Delnoij et al. (1999) distinguished between
tracer and bubble correlation peaks in a bubble column
using some a-priori knowledge of liquid and gas velocities.
Rottenkolber et al. (1999) ran a cross-correlation algorithm on raw PIV images of a fuel spray, identi®ed
interrogation spots containing double peaks, and separated the phases based on the resulting height and width of
these peaks. There are no universal criteria on how to
choose the cutoff heights and widths because correlation
peaks are in¯uenced by many parameters, and, as Rottenkolber et al. (1999) noted, ``comprehensive studies on
the in¯uence of these parameters on the correlation peak
properties have yet to be performed''.
A major dif®culty in all separation methods other than
color is the noise that each phase introduces to the other.
In particular, in the vicinity of the dispersed elements, the
noise that affects tracers becomes stronger, thus making
simultaneous measurements in these regions less reliable
(see the discussion of `coronas' by Hassan et al. 1992).
Other factors that make the methods described above inapplicable to or inappropriate for the present work are
discussed below.
The present work is part of a larger project that investigates interactions between solid particles and turbulence
in a fully-developed channel ¯ow of air. To quantify these
interactions, joint quantities such as slip velocities and
gas-particle covariances must be measured. To measure
these joint quantities, gas velocities must be determined
very close to the solid particles, where simultaneous velocity measurements are typically noisy. The separation
used in the present work must be robust to this and other
sources of noise. Further application of the present work
to two-phase turbulence modeling requires a very large
number of velocity ®elds to be acquired and processed in
order to compute reliable ¯ow statistics. The large volumes
of data required suggest the need for a conceptually simple
and numerically ef®cient image pre-processing algorithm.
In addition, the experiment must be conducted over a
range of wall normal positions, particle sizes, and mass
loads. Thus, the phase discrimination algorithm must be
robust to changes in the ¯ow regime, particle size, and
concentration. All of these requirements imposed limitations on the applicability of the existing techniques.
Color separation techniques were not used because of
the high potential cost associated with the large quantities
of mono-disperse ¯uorescent particles required. Image
intensity and spot size (with constant threshold) techniques were rejected because of the noise from `coronas'
around solid particles. The 1/r2 local threshold (Hassan
et al. 1992) requires a much larger size difference between
discrete particles and tracers than was appropriate for our
experiment. Pattern recognition could not be used because
our relatively small 33- and 63-lm particles do not always
exhibit a distinctive scattering/re¯ection pattern. We did
not use correlation peak properties, because in a complex
turbulent ¯ow, gas and particle velocities can be nearly
identical in many locations, and the correlation peak
discrimination requires them to be signi®cantly different.
The spatial median ®lter used by Kiger and Pan (2000)
would work for identi®cation of discrete particles, but a
more sophisticated algorithm would be required for a
proper mapping of the tracer and background ®elds.
Simple subtraction of discrete particle elements in a ®eld
with varying background level can leave signatures that
later cause contamination of correlation ®elds (see Pahuja
and Longmire 1995).
253
254
The present work attempts to address two-phase PIV
images that cannot be decomposed simply into two
distinct parts, such as continuous-phase data and discretephase data. In fact, real PIV images are much more
complicated, since they typically contain reliable tracers,
reliable solids, unidenti®ed spots, low-frequency noise,
high-frequency noise, and a background.
In real images, unidenti®ed spots could be either solids
that graze the edge of the laser sheet or coagulated tracers.
Low-frequency noise could be caused by particle `coronas',
or re¯ections from walls and/or optical camera elements.
High-frequency noise could be induced by electrical signals in the camera CCD array. Background levels vary
spatially and from image to image because of local particle-scattering effects.
Our goal in implementing phase discrimination is to
extract reliable tracers and solids only while, as much as
possible, eliminating all other parts of a given image. The
subsequent sections describe a novel technique designed
to meet the requirements outlined above. Speci®cally, the
technique is designed to yield reliable (minimal data loss)
and accurate (minimal errors) velocity measurements of
both phases. The technique is relatively ef®cient computationally and performs well under a variety of ¯ow
conditions and optical settings.
2
Equipment
2.1
Channel flow facility
The PIV measurements were taken in streamwise-spanwise planes of the test section of the rectangular channel
shown in Fig. 1. The air¯ow is driven by a frequencycontrolled centrifugal blower. Solid glass beads, supplied
by a screw feeder, enter the ¯ow path upstream of the
channel. In the preliminary tests, the glass beads had
diameters ranging from 53 to 75 lm. In the error analysis
tests, two size ranges of particles were used: 55±65 and
25±35 lm, with mass-averaged mean diameters of 33 and
63 lm, respectively. The air-particle mixture enters the top
portion of the ¯ow-conditioning section through four
hoses and passes through a series of grids and honeycombs to achieve uniform pro®les in gas and particle
mean velocity as well as a uniform particle distribution
over the channel cross section of 153 ´ 15.3 mm. Two
plates, mounted on the sidewalls, trip the ¯ow to initiate
the development of turbulent boundary layers. Downstream of the trip plates, a small amount of air seeded with
glycerin droplets (about 2% of the total mass ¯ow rate)
was added to the ¯ow through two thin slits. The glycerin
droplets, which had diameter of order 1 lm, were used as
tracers for PIV measurements. This glycerin `fog' was
added below all ¯ow-conditioning devices to avoid any
agglomeration of solids on the grids. A thin layer of solids
builds up immediately below the fog injection slits and
needs to be cleaned off approximately once every hour of
continuous facility runtime.
The length of the development region of the ¯ow facility
was 100 h, where h represents the channel half-width of
7.52 mm. In the test section, the center plane velocity U0
Fig. 1. Channel ¯ow facility. h=7.52 mm. Proportions are not to
scale
was 10 m/s, and the Reynolds number based on this velocity and the channel half-width h was Re ˆ 4600. Hotwire measurements in the center plane at the downstream
end of the test section yielded a turbulence level of 4%. The
mean and RMS velocities were uniform to within 1% over
60% of the channel span. A ¯ow-monitoring system was
designed to limit any low-frequency ¯uctuations in the
bulk ¯ow rate of both gas and solid phases to less than 1%.
Independent LDV measurements over the streamwise
range of the test section yielded mean and RMS velocity
variations in the mid-plane of less than 1%. These quali®cations show that the ¯ow in the PIV measurement region is locally homogeneous, fully-developed, and steady.
Hence, the ¯ow is suitable for the computation of turbulence statistics based on a large number of instantaneous
coupled gas and particle velocity ®elds. Ultimately, the
¯ow exits to the ambient as a plane jet before it enters the
low-pressure recycle bin located 12 h below the channel.
2.2
PIV acquisition system
The PIV acquisition system includes a pair of Nd:YAG
lasers, beam combination optics, optics for light sheet
formation, a Kodak Megaplus ES-1.0 8-bit digital camera
with resolution 1008 ´ 992 pixels, a frame grabber, a fourchannel pulse generator, and a PC for image acquisition
and analysis. After passing through all of the optics, the
two laser beams form sheets that illuminate the test region
of the channel centerplane. In various tests discussed
below, two laser pairs were used: Surelite I (Continuum,
Sanata Clara, Calif.) and Ultra PIV CFR (Big Sky Lasers,
Bozeman, Mont.). The two laser systems differ in output
power, beam diameter, shape, and divergence. As a result,
the light sheets obtained from each system had different
parameters. The Continuum lasers emitted 50 mJ of energy per pulse; the laser sheet thickness and the power
density at the measurement location were estimated as
0.2 mm and 0.4 J/cm2, respectively. For the Big Sky lasers,
these parameters were 30 mJ, 0.3 mm, and 0.26 J/cm2. The
digital camera acquired pairs of images synchronously
with the laser pulses. The camera ®eld of view was
10 ´ 10 mm, which was large enough to capture critical
turbulent eddies yet small enough to yield accurate velocity measurements. The camera aperture (f-stop) was set
to 11 for both laser systems. To reduce the background
level and saturation effects, an image intensity of 48
(typical average intensity on the scale of 0 to 255) was
subtracted prior to transferring images from the camera to
the frame grabber. The images were saved to the hard disk
as TIFF ®les.
Note that the photometric parameters and seeding were
optimized speci®cally for two-phase acquisition and would
not be optimal for each of the phases separately. For
example, increasing the camera aperture would improve
the appearance of the tracers, but it would make the solid
particles appear too saturated and surrounded by strong
`coronas'. On the other hand, reducing the aperture or the
laser power would make most of the tracers disappear.
3
Image pre-processing
A section of a typical unprocessed PIV image is shown in
Fig. 2a. This section, which has an area of 256 ´ 256 pixels, represents approximately 1/16 of the full image area. It
contains images of solids (larger and brighter), and tracers
(smaller and dimmer). One can also observe horizontally
oriented pairs of small bright objects. These pairs are
caused by re¯ections from partially illuminated solids (see
Kiger and Pan 2000, Oakley et al. 1997). Since this pattern
was not dominant in the present study, it was not
employed to identify solid particles.
The following approach was used for pre-processing of
two-phase PIV images. First, since both solids and tracers
are `particles', the same concepts and algorithms can be
applied to identify any of them as an object, characterized
by several parameters. Second, these objects can be sorted
into solids, tracers, and other objects, according to their
parameters. Now we discuss how object detection and
phase discrimination procedures were implemented.
Fig. 2. Image preprocessing:
a original image, b object pixels,
c separated tracers, d separated
solids
255
3.1
Object detection
Consider a `one-dimensional' image. Both tracers and solid
particles form continuous regions (`objects'), within which
the image intensity I reaches a local maximum. If the
intensity distribution within these regions is smooth and
approximately Gaussian (see Appendix A.4 in Westerweel
1993), then each maximum can be identi®ed using the
following property of the second-order spatial derivative
256
2
Ii;j
> Ii
1;j 1 Ii‡1;j‡1
9†
Every internal pixel Ii,j satisfying Eqs. 6, 7, 8, 9
simultaneously belongs to an object associated with a local
intensity maximum. Some of these objects may represent
tracers or solid particles. All other pixels belong to the
background, and therefore they are set to a low constant
intensity. Keeping the object pixels and eliminating the
background creates images similar to Fig. 2b. To detect
and analyze all of these connected regions as objects, we
d2 …ln I†
<0 :
1† run a recursive region-growing algorithm (Pahuja and
Longmire 1995).
dx2
Typically, object pixels occupy no more than 25% of the
Points where this condition is satis®ed belong to an
object. The natural log of intensity (ln I) was used instead total image area even at the highest level of tracer seeding.
of the image intensity itself, I, for two reasons. After ®l- Thus, using object detection with second-order gradients,
tering (see Sect. 3.2), the intensity distributions of objects one can also compress PIV images. Hart (1998) used ®rstlook more Gaussian than parabolic. Also, using (ln I) as- order gradients for image compression.
signs more grayscale pixels to the objects, thus making
3.2
correlation peaks and solid-particle shapes smoother.
Eliminating high-frequency noise
Smoothing particles and correlation peaks increases the
particle size and thus reduces pixel-locking bias and ran- The object detection algorithm described above is very
dom error (see Prasad et al. 1992, Westerweel 1997). Using sensitive to high-frequency noise because it uses secondorder spatial derivatives. The derivatives amplify the imsecond-order gradients of the intensity itself remains,
portance of the noise, resulting in identi®cation of many
however, a viable alternative.
erroneous objects. To avoid this erroneous object detecFirst, we discuss how the condition on derivatives
(Eq. 1) can be applied to a discrete one-dimensional pixel tion, a low-pass spatial ®lter can be applied to each image
prior to computation of derivatives.
grid. To approximate the derivatives with ®nite differGaussian blur is one of the most common spatial ®lters
ences, three consecutive pixels are required, Ii±1, Ii, and
used
in image processing. However, since Gaussian blur
Ii+1. Then, the discrete version of Eq. 1 becomes
uses ¯oating-point values and operations, it is relatively
ln Ii 1 2 ln Ii ‡ ln Ii‡1 < 0 ;
2† slow for processing the large volumes of data needed for
the present experiment. Therefore, we used an 8-bit inteor, after simpli®cations,
ger ®ve-point blur:
2
Ii > Ii 1 Ii‡1 :
3†
Second, in two dimensions, the differential peak
condition can be written as
o2 …ln I†
<0 ;
4†
on2
where n is any direction in the plane. It can be proven that
Eq. 4 is equivalent to the local maximum criteria for a
function of two variables, adapted from Smirnov (1951):
2
2
o2 …ln I†
o2 …ln I† o2 …ln I†
o …ln I†
< 0 and
>
:
ox2
ox2
oy2
oxoy
5†
In a discrete pixel domain, Eq. 4 is more ef®cient
computationally than Eq. 5.
A 9-pixel square mask was used for computing secondorder ®nite differences. Within this mask, the second-order differences can be obtained in four directions: vertical,
horizontal, left diagonal, and right diagonal. Thus, after
simpli®cations similar to Eq. 3, four inequalities are
employed to detect object pixels.
2
Ii;j
> Ii;j 1 Ii;j‡1
6†
2
> Ii
Ii;j
1;j Ii‡1;j
7†
2
Ii;j
> Ii
1;j‡1 Ii‡1;j 1
8†
1
cIi;j ‡ Ii 1;j ‡ Ii‡1;j ‡ Ii;j 1 ‡ Ii;j‡1 † : …10†
c‡4
In Eq. 10, c is the central point weight, which typically
takes integer values from 1 (very strong blur) to 16 (weak
blur). This blur is applied to each internal pixel of a given
image and the border pixels are left intact. Since the object
detection algorithm is very sensitive to high-frequency
noise, in some cases it might be necessary to repeat the
blur operation up to eight times. Thus, the ®ve-point blur
uses two integer parameters: the central point weight c and
the number of passes np. These two parameters can be
adjusted based on the image quality and seeding density.
In earlier tests, the seeding was relatively low and images
were ®ltered with c ˆ 4 and np ˆ 4. Very noisy images
were processed with c ˆ 1 and np ˆ 7.
More recently, both seeding and ®ltering procedures
were optimized so that c ˆ 1 and np ˆ 3 based on the ratio
of total signals from solids and tracers (see Eq. 14) and on
the computational time. To eliminate any effects of userspeci®ed parameters (other than c and np) and cross-talk
between the phases, the surface integrals in Eq. 14 were
taken over all objects in raw solids-only or tracer-only
images, regardless of object brightness or size.
In general, when ®ltering is used, the ®ltered images are
employed only to locate the pixels that belong to objects.
Once the locations of object pixels are identi®ed, the actual
intensities of these pixels are taken from the original,
Iijnew ˆ
un®ltered images. Filtering also reduces the saturation
effects discussed in the next section.
3.3
Processing saturated objects
In two-phase PIV, it is very dif®cult to adjust the photometric conditions so that the signal from solids does not
saturate the CCD array of the camera. One can reduce the
amount of light absorbed by the CCD array by decreasing
either the camera aperture or the laser power, but in either
case the signal from tracers will have very small amplitude
and could be dominated by high-frequency noise.
Therefore, the camera should receive enough light to
resolve the tracers. In many cases, then, the solids will be
saturated.
Figure 3 shows that saturated pixels form a plateau at
I ˆ 255. Obviously, the pixels within the plateau do not
satisfy the local maximum condition (Eq. 1). Some less
bright neighboring pixels do not satisfy Eq. 1 either, because saturated objects are not perfectly circular. Since all
of these pixels are bright, however, we believe they belong
to some type of particle. To resolve the saturation problem, we introduced a saturation threshold. Every pixel
equal to or brighter than the saturation threshold is treated
as an object pixel, overriding Eqs. 6, 7, 8, 9.
3.4
Phase discrimination
First, all detected objects in a given image are assigned the
following parameters.
A (object area in pixels) de®nes size;
B (object average intensity) de®nes brightness
RR
object
B ˆ RR
object
IdA
dA
;
12†
xc (object weighted centroid vector) de®nes position
RR
object
xIdA
xc ˆ RR
object
dA
:
13†
Here, size and brightness are used for phase discrimination, while centroid position vectors can be used later
for particle tracking. Figure 4 is a one-dimensional illustration of size and brightness.
In the second stage of the phase discrimination process,
a number of images (on the order of 100) are analyzed to
build a size-brightness map (see Fig. 5a). This plot indicates the total amount of signal carried by all objects with
I > Isatur
11† a given combination of size and brightness. Size is always
computed as an integer number. For building the map,
In the present work, a saturation threshold of 230
brightness was rounded to the nearest integer. For the total
worked well for all test cases. Note that this threshold was signal density, we found the most effective measure to be
ZZ
introduced only to treat saturated objects. Every pixel
below this threshold must be checked against the ®niteIdA ˆ A B N ˆ size brightness number
difference conditions (Eqs. 6, 7, 8, 9).
all objects
In summary, then, the object detection procedure
includes four steps.
14†
1. If the image is noisy, apply the ®ve-point blur ®lter to
generate a new image with reduced noise, but retain the
original image.
2. If a pixel from the ®ltered image either exceeds the
saturation threshold (Eq. 11) or passes the local maximum tests (Eqs. 6, 7, 8, 9), mark its location as an object
pixel.
3. Using a recursive algorithm, create connected regions of
object pixels and mark them as objects.
4. Copy the actual intensities of the object pixels from the
original image and set the remaining pixels to a uniform
low intensity.
Contours of the logarithm of this quantity are then
plotted in the map. This map yields distinct peaks for both
solid and tracer particles.
An alternative measure of signal would be the number
density. However, the number density by itself was not
found to be useful, because a typical image acquired in a
data set contains approximately 40,000 tracers and only
10±20 glass beads. For the same reason, quantities such as
size ´ number or brightness ´ number were also found
ineffective for phase discrimination. Even with the present
parameter choice, the tracer peak height still exceeds the
solids peak height by a factor greater than 10. Also, the
Fig. 3. Object containing saturated pixels
Fig. 4. Size and brightness of an object
257
258
Fig. 5a±d. Size-brightness maps. Each map is built on 648 1 K ´ 1 K PIV images (324 pairs) ®ltered with c ˆ 1 and np ˆ 3: a true
two-phase; b arti®cial two-phase; c tracers only; d solids only
quantity (Eq. 14) was chosen because it contributes
directly to the cross-correlation peaks.
In the third stage, we analyze the size-brightness map to
set the separation limits. That is, we de®ne two nonoverlapping rectangular regions in the map, one region
containing the tracer peak and the other containing the
solids peak. These size and brightness limits are optimized
by testing preliminary single- and two-phase data sets as
described in Sect. 4. Then, every object with size and
brightness falling within the tracer rectangle is treated as a
tracer and written to a tracers-only image ®le (Fig. 2c).
Every object with size and brightness within the solids
rectangle is considered to be a solid and written to a
solids-only image ®le (Fig. 2d). All other objects are
discarded.
Thus, the phase discrimination procedure includes the
following four steps.
3. Using the size-brightness map as well as additional information (described below), determine the separation
limits, that is, the positions of tracer and solids rectangles. In general, the ®lter parameters c and np and the
saturation threshold may vary. This variation affects the
size-brightness map and thus the choice of separation
limits. Therefore, once the separation limits are set,
®ltering and thresholding options should not be
changed.
4. Using these separation limits, separate all objects into
tracers, solids, and unidenti®ed objects.
Tracers-only and solids-only images saved by the phase
discrimination routine are used for velocity measurements.
4
Validation and optimization of the separation code
1. Find size, brightness, and centroid location for each
for velocity measurements
detected object in the image set.
Attempts to extract tracers from images containing on2. Build a contour plot of total signal versus object size and ly solids (see map in Fig. 5d) reveal a signi®cant number
brightness (`size-brightness map').
of solids remnants (mainly from out-of-plane solids and
found in Shand (1996). To suppress the noise from solids,
seeding was optimized so that the seeding density is 5 to 10
times the minimum level normally required for reliable
gas-only measurements. From two-phase PIV images, we
were able to obtain gas velocity data of similar quality with
0.3 ´ 0.3 mm (or 32 ´ 32 pixels) non-overlapping interrogation areas. Figure 6a shows an instantaneous gas velocity ®eld with the global mean subtracted. The range of
applicability of the algorithm was tested by examining
images with very high loads of solids and with strong
velocity gradients, as described in Sect. 4.2. In some of
these limiting cases, the interrogation spot size needed to
be increased to 64 pixels for reliable and accurate velocity
measurements. In all tests discussed below, however, a
32 ´ 32 interrogation spot was chosen as a `unit area'.
Solids velocity ®elds v(x,y) are computed using a particle-tracking algorithm developed in our laboratory. For
each image in a given pair, solid particle centroids are
computed using Eq. 13 and stored. Then, particles from the
second image in each pair are matched with the corresponding particles from the ®rst image. This matching is
based on the range of reasonable velocities that solid particles might have. For each particle in the ®rst image, the
tracking algorithm creates a search window in the second
image, within which it searches for a matching centroid.
With the present combination of ¯ow, photometric, and
phase discrimination parameters, the search window for
63-lm particles was 8 pixels square, while solid particle
objects were at least 9 pixels in diameter, so that the
tracking routine could ®nd no more than one centroid per
window. The resulting particle velocity vectors are spaced
relatively randomly (see Fig. 6b). For smaller particles, the
time delay was reduced by almost 50% to ensure no more
than one centroid per search window.
To validate gas velocity ®elds, we used global mean and
local mean validation routines provided with AEAT Visi¯owTM. Westerweel (1993) gives a good description and
evaluation of these techniques. Examination of individual
images and vector ®elds in the current experiments shows
that any loss of gas vectors is caused primarily by a local
absence of tracers. Absence of tracers can have two possible causes: the presence of solid particles or insuf®cient
seeding. A solid-particle object originally residing in a
given interrogation area is removed and replaced with
uniform background as a result of phase discrimination.
Therefore, if an interrogation area is small, a signi®cant
portion of it may lack tracers. One may compensate for the
loss of tracers either by signi®cantly increasing the seeding
density or by using larger interrogation areas. Taking
either of these approaches, we managed to keep the valid
data yield for gas velocity vectors above 98%. A solids
vector is treated as invalid if at least one of the surrounding four gas vectors is invalid or missing. Solids
vectors falling outside the grid for gas are excluded from
the analysis. This validation scheme for solids was chosen
because the four neighboring gas vectors are employed to
quantify gas-particle interaction.
Sometimes, with high loads of solids and very dense
Fig. 6. a Gas and b particle velocity ®elds resulting from the same
tracer seeding, we observed dark spots containing very few
image in the channel centerplane. Re ˆ 4600, u'/U ˆ 4%,
tracers. Possibly, solid particles between the laser sheet
dp ˆ 60lm, e ˆ 0.0022%. Global mean velocity has been
and the camera obscure the light scattered from tracers,
subtracted from the gas ®eld
solids coronas). These remnants act as a source of noise
for the gas velocity measurements. In Fig. 2d, one can see
that a tracer residing very close to the bottom left solid
gets attached to the solid, thus affecting the centroid location, and, possibly, the measured velocity of the particle.
As will be shown below, however, these sources of noise do
not generate any systematic bias in PIV cross-correlation
or tracking measurements. The objective of the present
tests was to evaluate and improve the quality (that is, both
reliability and accuracy) of velocity measurements. In the
present measurements, a data set is considered reliable if
the valid data yield in gas velocity is above 98%. A twophase data set is considered accurate if the object detection and phase discrimination do not introduce an RMS
error in gas velocity greater than 0.1 pixels. The concepts
of reliability and accuracy will be further discussed in this
section, along with the validation methods and error estimates.
Gas velocities u(x,y) are obtained from tracer ®les using
a commercial program, AEAT Visi¯owTM (Pittsburgh, Pa.),
based on a two-frame cross-correlation algorithm. The
most relevant description of AEAT Visi¯owTM can be
259
thus causing the dark spots. Such spots were not observed
in tracer-only images.
When the interrogation spot size was set to 64 or
128 pixels, the locations of any spurious (or missing)
vectors did not appear correlated with the particle locations because the typical particle diameter (10±12 pixels)
was signi®cantly smaller than the interrogation spot size.
However, with 32-pixel interrogation spots, the few
spurious or missing gas vectors occur mostly in the
vicinity of solid particles.
260
ages and vector ®elds, and, in some cases, image and ¯ow
statistics. In the tests discussed here, the maximum size
limit for solids was 256 pixels, because larger sizes allowed
irregularly shaped objects (caused by merged scattering
patterns from two solids) or very large `stars' (possibly
because of clustering). The minimum-brightness limit for
solids was set no lower because otherwise it would include
broken-up large and dim objects. Extending the minimum-size limit for solids would result in less reliable
tracking because, for the solids that appear small, there
could be more than one centroid per search window. Reducing the dimensions of the solids rectangle slightly
would bring no adverse effects other than some loss of
reliable solids.
In a test for inter-phase noise, three sets of measurements were used: tracers-only, solids-only, and solids plus
tracers. Each single-phase set contained 320 vector ®elds.
To match the experimental conditions for all three sets, the
volumetric gas ¯ow rates through the main channel as well
as through the fog injection slits were maintained at
constant values, regardless of the presence of fog or particles. The ®rst two data sets were, in fact, the same as in
the previously described single-phase tests. In both particle-laden sets, the diameter range of the glass beads was
53±75 lm, and the solids volume fraction e was 0.0022%.
At this volumetric load, and in the centerplane location, we
did not expect or observe any signi®cant modi®cation of
gas velocity statistics by particles.
All three data sets were processed using object detection
and phase discrimination. The separation rectangles were
chosen as described above. The separated tracer images
from the tracer-only and solids-tracer data sets were
processed with cross-correlation, and the resulting velocity
PDFs are shown in Fig. 7 as solid and dashed lines,
respectively. These PDFs agree very well, which demonstrates that the noise from solids does not bias gas velocity
measurements. Figure 7 also shows a good agreement
between the solids velocity PDFs from the solids-only and
two-phase data sets.
4.1
Preliminary tests
To optimize the separation limits and to test the performance of the phase discrimination code in the absence of
inter-phase noise, measurements were performed in ¯ow
containing solids only and tracers only. Size-brightness
maps and probability density functions (PDFs) for the
streamwise velocity component were computed in both
cases. In all preliminary tests, the Continuum lasers were
used. In measurements involving tracers, the seeding
density was low (nine tracers per 32 ´ 32 spot), and
therefore the interrogation window size was set to
128 ´ 128 pixels with 75% overlap.
For ¯ow with tracers only, we compared velocity PDFs
for tracer-only data obtained from raw images with those
obtained from processed `separated' tracers, and found
excellent agreement. The size-brightness map from the
processed tracer-only ®les was used to set size and
brightness limits for this and subsequent two-phase measurements. The tracer rectangle was set to include most of
the distribution of objects found in tracer-only images (see
Fig. 5c). The upper brightness limit for tracers left out the
brightest tracers, which could appear very similar to solids
(such as the bright pairs mentioned in the beginning of
Sect. 3). The upper size and lower brightness limits were
also set to minimize overlap with small and dim objects
identi®ed from solids-only maps (see Fig. 5d).
The separation code was run also on solids-only images.
The size and brightness limits for solids were chosen to
include as many solids as possible, while avoiding any
overlap with the tracer limits. Speci®cally, the smallest
solid was set larger than the largest tracer and the darkest
solid was brighter than the brightest tracer (see Fig. 5d and
also the next paragraph). Due to remnants originally
attached to solids, the phase separation code detected a
signi®cant number of objects within the tracer limits. To
estimate the contribution of these `tracers' to cross-correlation peaks, we analyzed the total signal, de®ned by
Eq. 14. Comparing solids-only and tracers-only sizebrightness maps, we found that the signal from these
`tracers' is approximately 1/100 of the real tracer signal.
Cross-correlation analysis of the resulting `tracer' images
yielded a few `valid' velocity vectors, and the magnitudes
of these vectors were similar to those expected for solids.
This result suggests that, in a very small number of cases,
these remnants can potentially cause `bad' vectors or bias
in gas velocity ®elds.
In general, size-brightness maps were not the only
criteria used to choose separation limits. To ®nalize the
separation limits, one also has to examine individual im- Fig. 7. Probability density plots for streamwise velocity
4.2
Error estimates with artificial two-phase
PIV images
To estimate bias and random errors caused by the separation algorithm, particle size and loading were varied
arti®cially by overlapping one or more solids-only images
with individual tracer-only images. The arti®cial images
were then employed to determine the effect of object size,
brightness and number, interrogation spot size, and
correlation peak strength on data quality and error mag-
nitude. Brightness and size of an object in pixels depend
on the actual particle diameter and on the laser power. The
number of objects per unit area follows from the actual
number density as well as the laser sheet thickness. The
shapes of correlation peaks depend on the size, brightness,
and number of tracers, as well as laser sheet thickness,
time delay, velocities of gas volumes crossing the sheet,
and gas velocity gradients.
To generate arti®cial images, individual images with
intensities I1(x, y) and I2(x, y) were overlapped as
261
Fig. 8. Generating arti®cial twophase PIV images: a tracer-only
source image; b solids-only
source image; c arti®cial twophase image; d true two-phase
image at matched parameters.
Objects extracted from e arti®cial and f true images
Iovr …x; y† ˆ max‰I1 …x; y†; I2 …x; y†Š :
262
15†
If I1(x, y) and I2(x, y) represent independent raw images containing only solids, this overlap increases the
effective number density of solids. If one of the source
images contains only tracers (Fig. 8a) and the other only
solids (Fig. 8b), then an arti®cial two-phase PIV image is
generated (Fig. 8c). In contrast to the arti®cial image, a
real image (Fig. 8d) has a background that is less uniform. Solids behind the laser sheet re¯ect the light scattered by other solids and tracers. This re¯ection possibly
causes local increases in background intensity. Similarly,
dark spots in the background may result from solids in
front of the sheet obscuring tracers. This complex interaction between illuminated tracers and solids does not
take place in the arti®cial images. Nevertheless, during
object identi®cation, any non-uniformities in the background are removed, and objects obtained from arti®cial
(Fig. 8e) and real (Fig. 8f) images look very similar. A
comparison of size-brightness maps resulting from true
(Fig. 5a) and arti®cial (Fig. 5b) images shows that scattering interactions between solids and illuminated tracers
result in a larger number of objects that fall outside of the
solid and tracer rectangles. The solids and tracer peaks
resulting from arti®cial images, however, match well with
those from real two-phase images for all parameter
variations used in the present tests. Thus, the arti®cial
images appear appropriate for the purpose of error
estimates.
Figures 5b and 5d show a comparison in terms of size
and brightness of solid objects from solids-only images
versus solid objects extracted from arti®cial two-phase
images based on the same solids-only image set. The differences in the size and brightness of objects falling in and
near the solids rectangle suggest that in arti®cial or real
PIV images, the centroids of solids may be in¯uenced by
the presence of tracers, thus altering solids velocities. At
the same time, solids on the edge of the sheet and scattering patterns around solids may affect the gas velocity
measurements.
To estimate the error introduced by merging and separation to the velocity of each phase, the following method
was implemented. First, two original single-phase PIV
image pairs are selected: one containing only tracers and
the other containing only solids (the latter could be an
overlay of several solids-only pairs). Then, using appropriate separation limits, tracers are extracted from traceronly image data, and analyzed with a cross-correlation
routine to obtain the `unperturbed' gas velocity ®eld
usep(x, y). Similarly, solids velocities vsep(x, y) are computed from properly separated original solids-only images
by tracking. Then, the original tracer and solids images are
overlaid using Eq. 15. The resulting arti®cial two-phase
images are separated into tracers and solids with the same
c
Fig. 9. Error analysis based on arti®cial two-phase PIV. Gas
velocity ®elds computed from tracer images separated from
a source tracer-only images and b arti®cial two-phase images.
c Point-by-point differences between a and b with locations of
particles represented by hollow circles. d Solids velocity ®eld. The
bottom left corner of all ®elds shown corresponds to Fig. 15c
limits and analyzed to obtain gas u2ph(x, y) and solids v2ph
(x, y) velocities. The fraction of `bad' gas vectors in
arti®cial two-phase ®elds u2ph can be higher than that in
the original single-phase ®elds usep. In addition, due to
differences in size and brightness (i.e., as in Fig. 5b, d),
some solids vectors that appear in v2ph do not appear in
vsep and vice versa. Nevertheless, for gas and solids vectors
whose (x, y) positions matched within one pixel, point-bypoint differences were computed as
Du…x; y† ˆ u2ph …x; y†
usep …x; y† ;
16†
Dv…x; y† ˆ v2ph …x; y†
vsep …x; y† :
17†
Sample ®elds of usep, u2ph, Du and v2ph are shown in
Fig. 9a±d, respectively. In Fig. 9c, no obvious correlation
is apparent between particle location and the magnitude of
the locally computed error in gas velocity Du(x,y).
As an additional check, differences were computed for
gas velocities obtained from unprocessed uraw(x,y) and
separated usep(x,y) tracer-only images
Dusep …x; y† ˆ uraw …x; y†
usep …x; y†
18†
and also for gas velocities interpolated to particle locations
from four surrounding vectors on the grid using a bilinear
scheme
~2ph …x; y†
D~
u…x; y† ˆ u
~sep …x; y† ;
u
19†
only images), interrogation spot size (32 ´ 32 and
64 ´ 64 pixels), and correlation peak height for tracers. To
maintain statistical independence of gas data, interrogation areas were not overlapped. To compute the average
solid size, the total area occupied by reliable solids was
divided by their total number. The 120-pixel and 43-pixel
solids image sets were obtained from solid particles sized
from 55±65 lm, and 25±35 lm, respectively. The 30-pixel
objects result from 25±35-lm solid particles imaged at
reduced laser power. The average brightness was computed similar to Eq. 12 where the integration was performed over all reliable solids in the images (that is, total
signal divided by total area). The average brightness of
solids in the present tests depends on their average size.
Thus, the brightness levels of 165, 180 and 205 correspond
to the average sizes of 30, 43 and 120 pixels, respectively.
The correlation peak height as an independent parameter has dimensions of size ´ brightness2 ´ number. The
mean cross-correlation peak height Hxcorr, was varied by
examining two measurement locations: the centerplane
(y+=210, Hxcorr ˆ 8.9 ´ 105) and a position very close to
the wall (y+ ˆ 14, Hxcorr ˆ 8.3 ´ 104) where the wall
partially obscured the converging laser sheet (the Big Sky
lasers were used in this test). The tracers thus appeared
dimmer close to the wall. Also, larger gas RMS velocities
normal to the plane and strong out-of-plane gas velocity
gradients near the wall served to reduce correlation peak
heights. The interrogation area size did not have any
predictable or signi®cant effect on the correlation peak
height. A full distribution of peak heights in the studied
cases is shown in Fig. 10. Throughout the ¯ow, the correlation peak height varies by a factor of more than 100,
and, possibly, so does the signal-to-noise ratio for gas data.
In real ¯ows, particles are not typically distributed
uniformly and might even exhibit strong preferential
concentration (see Eaton and Fessler 1994). Therefore,
where tilde stands for interpolated quantities. Interpolated
vectors were validated in the same manner as solids vectors,
i.e., based on the validation status of the four neighboring
grid vectors and rejecting any vectors falling outside the
regular grid. The differences in Eqs. 16, 17, 18, 19 and their
squares were averaged over a number of homogeneous ®elds
and within each ®eld to compute mean and RMS errors.
For all test cases described below, it was found that the
mean values of both components of Du, D~
u, Dusep and Dv do
not correlate with the values or directions of the mean slip
velocity and do not exceed 0.04 pixels even for the most
extreme cases tested. (In the range of cases, the mean slip
velocity varied from 1 to 10 pixels). Thus, the separation
introduces no systematic bias into velocity measurements
in either phase. Furthermore, the PDFs of these differences
for various cases show that they appear to be normally
distributed. It was also found that the streamwise RMS error
is typically slightly larger than the spanwise, and therefore
only the streamwise RMS error will be quoted here.
To verify that object detection and separation in traceronly images does not introduce any signi®cant random
errors, the RMS of Dusep was examined. For the streamwise
component of Dusep, computed with 32-pixel interrogation
areas, the RMS error was 0.048 pixels, which is one-half of
the subpixel uncertainty in ®tting correlation peaks. (According to Westerweel 1993, the uncertainty in locating
correlation peaks in a 32-pixel spot with Gaussian ®t is
0.1 pixels.) Using 64-pixel interrogation areas reduces the
RMS error to 0.037 pixels.
To estimate RMS errors, valid data yields, and the range
of applicability of the method to two-phase data, the following four parameters were varied independently: average solid object size (areas of 30, 43 and 120 pixels), solid Fig. 10. Distribution of correlation peak heights near the wall
object number density (by overlapping up to 128 solids- (y+ ˆ 14) and at the centerplane (y+ ˆ 210)
263
264
Fig. 11. RMS error (in pixels) and valid data dropout conditionally averaged over sets of interrogation spots, depending on
the number of valid solids in each interrogation spot: a with
64-pixel spots (the percentage of bad vectors was always zero);
b with 32-pixel spots. Average solid size was 43 pixels and the
average number of solids per 32 ´ 32 spot was 2.34
before performing any global estimates, it was necessary to
analyze the effect of local number density of solids on the
data quality. To perform this analysis, the RMS error and
the fraction of unvalidated vectors were averaged conditionally over subsets of vectors whose interrogation areas
contain a given number of solids centroids. To generate
arti®cial images for this test, 64 images containing 43-pixel
particles were overlapped with each individual tracer-only
image, and the resulting image pairs were analyzed. The
average number density of solids was 2.34 particles per
spot. This set of parameters allowed us to generate a suf®cient number of interrogation spots with up to four solids
per 32-pixel spot, yet kept the total error and the percentage of bad vectors reasonably low. Cross-correlation
analysis with 32- and 64-pixel interrogation areas was
performed on each separated tracer image. Point-by-point
differences were computed using Eq. 16 and conditionally
averaged to determine the RMS error and the valid data
yield as a function of number of solids per spot. The results for 64- and 32-pixel spots are plotted in Fig. 11a and
b, respectively. The probabilities of detecting a 64-pixel
spot with more than 12 solids or a 32-pixel spot with more
than 4 solids were below 0.5%, and therefore such cases
were not considered. For both interrogation area sizes, the
RMS error does not seem to depend on the local number
density of solids (see Fig. 11), except when there are no
solids in a 64-pixel spot. With 64-pixel spots, all vectors
were validated in this test; with 32-pixel spots, however,
the fraction of unvalidated vectors increases with the
number of particles. Note, that the presence of solids
eliminates some tracers. For example, four 43-pixel solids,
taken out of a given 32 ´ 32 interrogation spot and replaced with uniform background, occupy, on average, 17%
of the interrogation spot area. This fact, along with observation of individual vector ®elds, suggests that the
dropout of valid gas vectors occurs primarily due to the
local lack of tracers. On the contrary, the RMS error does
not seem to vary with the local number density, and thus it
is expected to depend on some global parameters associated with distributed solids remnants and noise.
For both reliability and accuracy estimates, global parameters are more practical than local. To see the effect of
various global factors on the valid data yield and the RMS
error, a series of tests was performed. Two tracer-only
(taken at the channel centerplane and close to the wall)
and three solids-only image sets (with average solids sizes
of 30, 43 and 120 pixels) were selected for these tests. Each
data set contained 128 image pairs. All solids image sets
were acquired at the centerplane and contained from 1,200
to 1,600 reliable solids. To double the solids number
density, each solids-only image set was split into two
subsets of equal size, and the corresponding images from
the two subsets were overlapped using Eq. 15. Then, this
operation was repeated up to seven times, until all 128
image pairs were overlapped into one. Thus, for each
particle size, a total of eight solids-only image sets with
varying number density were generated. Then, each solidsonly image set was overlapped with the corresponding
number of tracer-only images from the centerplane and
the wall, separated, and analyzed.
Due to the strong velocity gradients and dimmer tracers,
almost all near-wall gas velocity ®elds resulted in signi®cant
loss of vectors and RMS errors, and therefore such ®elds
were excluded from this study. Thus, a total of 48 centerplane and 2 wall cases were considered for the analysis of
gas data. For each case, the following quantities were
computed as discussed above: the fraction of bad vectors
for gas and solids, the RMS error for solids streamwise
velocities, and the RMS error for gas streamwise velocities
on the square grid and at interpolated locations.
The results are presented in Figs. 12, 13 and 14. In these
®gures, different symbols correspond to different average
sizes for reliable solids. For example, `30' in the legend
means a set of images containing solid objects with the
average size of 30 pixels. The line types in Figs. 12 and 13
correspond with different interrogation spot sizes and
whether the quantity was averaged over regularly spaced
or interpolated gas vectors.
The effect of solids number density, de®ned as the
number of solids per 32-pixel interrogation spot, on valid
data yield is shown in Fig. 12. Note that 64-pixel interrogation spots in the channel centerplane yielded gas vector
Fig. 12. Fraction of `bad' gas velocity vectors versus solids number density for three solid sizes, two wall positions, and various
processing parameters. Solid line ± 64 ´ 64 spots, rectangular grid;
dotted line ± 64 ´ 64 spots, interpolated; dashed line ± 32 ´ 32
spots, rectangular grid; no line ± 32 ´ 32 spots, interpolated.
Symbols in the legend indicate average particle size and channel
location. The horizontal line shows a 2% cutoff for bad data
Fig. 13. RMS error in gas velocity versus a solids number density
and b solid-to-tracer signal ratio. Solid line ± 64 ´ 64 spots,
rectangular grid; dotted line ± 64 ´ 64 spots, interpolated; dashed
line ± 32 ´ 32 spots, rectangular grid; no line ± 32 ´ 32 spots,
interpolated. Symbols in the legend indicate average particle size
and channel location. The horizontal line shows a 0.1-pixel uncertainty, typical for ®tting cross-correlation peaks
planations. First, as shown in Fig. 11b and discussed
above, the effect of solids on the valid data yield is local.
Therefore, the gas vectors used for interpolation in the
vicinity of solids are more likely to be lost. Another reason,
signi®cant at higher number densities, is that one unvalidated gas vector causes the dropout of all interpolated
vectors in the four neighboring interrogation areas.
The effect of number density on the RMS error in gas
velocity is plotted in Fig. 13a for the three particle sizes
and two wall locations. In this ®gure, four RMS errors
corresponding with the different grid parameters are
plotted for each particle size and number density. First, the
interpolated gas velocities have slightly larger RMS errors
than those on the regular grid. Second, the use of 64-pixel
interrogation spots resulted in smaller errors than the use
of 32-pixel spots because we are effectively averaging
velocities over larger areas.
With increasing global concentration of solids, the RMS
error in cross-correlation tends to increase signi®cantly
(see Fig. 13a). Note that within a given data set, the RMS
error is not affected by local variations of concentration of
solids (see Fig. 11). This error does not show any systematic trend with varying particle size and increases with
decreasing correlation peak height. These facts suggest
that the major contribution to the RMS error in gas velocity does not come just from reliable solids. It comes
from all objects recognized in solids-only images, such as
solids remnants and out-of-plane solids, and most probably from high-frequency noise that can be seen in Fig. 5d
as a strong peak composed of objects smaller and darker
than tracers. These `junk' objects are scattered uniformly
across the entire image and do not seem to be correlated
with `reliable' particle locations.
Figure 14 shows the RMS error in solids velocities,
which does not seem to depend on the concentration of
solids, except for very small particles at low concentrations. The two major factors affecting the RMS error for
tracking were solid size and tracer brightness. Larger
solids and dimmer tracer particles yield smaller RMS
error. With dim tracers, the error becomes smaller than
0.1 pixels and independent of the solid size or number
density. The increase in RMS error with increasing tracer
brightness corresponds with the idea that tracers that
become attached to solids during object identi®cation can
cause small but random shifts in centroid location.
Since the number density of solids seems to affect the
RMS error in gas velocities globally but not locally, we
attempted to ®nd a universal global parameter to properly
describe the behavior of the RMS error. We tried several
combinations and solid-to-tracer signal ratio (STSR)
worked the best, where
dropout only after overlapping 128 solids-only images.
Therefore, the centerplane data with 64-pixel spots is not
shown here. In those cases, the solids number densities
were 1.47, 3.72, and 1.09 solids per 32-pixel spot for 30-,
43-, and 120-pixel solids, respectively. The total area occupied by reliable solids exceeded 12.5% of the total image
area; yet less than 1% of gas data was lost for each particle
size.
RR
RR
Three key trends can be observed from Fig. 12. First,
IS dA IT dA
the loss of gas data is more signi®cant close to the wall due
all objects in S
all objects in T
RR
to the reduced cross-correlation peak height discussed
STSR ˆ
Hxcorr Nvec dA
above. Second, in the plot, the largest solids introduce the
all objects in T
largest data loss. This is expected because larger solids
shield more tracers within a given interrogation area. The
AS BS NS BT
ˆ
:
20†
other two particle types do not indicate any clear effect of
Hxcorr
solids size on the valid data yield. Third, it is clear that the
loss of interpolated vectors is consistently higher than that
Here, the integration is performed over all objects
of regularly spaced gas vectors. This result has two exfound in the solids-only (subscript S) or tracer-only
265
266
Fig. 14. RMS error in solids velocity versus solids number density. Solid line ± centerplane; dashed line ± wall. Symbols in the
legend indicate average particle size
(subscript T) image sets, and Nvec is the number of nonoverlapping 32-pixel interrogation spots per image.
Thus, AS is the average size of objects in solids-only
images, BS is their average brightness, NS is the number of
such objects per 32-pixel spot (all objects, not just reliable
solids). BT is the average brightness of tracers, and Hxcorr is
the average height of the correlation peaks, where both are
based on the tracers extracted from tracer-only images.
The STSR combination was used to estimate the RMS error
in gas velocity measurements as shown in Fig. 13b. In this
®gure, the data collapse fairly well for all particle sizes,
concentrations and correlation peak heights tested. The
major differences among the curves in Fig. 13b occur due
to the varying interrogation spot size and interpolation.
The errors computed with like grid parameters still do not
collapse completely for different particle sizes. Varying
particle size introduces a variation in RMS error of
approximately 50%, but this variation is not systematic.
Note that when STSR<1.0, the RMS error in u1 is less than
0.1 pixels (typical uncertainty for cross-correlation) in all
cases.
4.3
Range of applicability of the algorithm
To establish a range of parameters within which the separation code can be applied successfully, one needs to
specify performance criteria, i.e., limitations on the RMS
error and on the valid data dropout. Then, the range of
parameters can be obtained from Figs. 12, 13, 14. In our
case, measurements of correlated gas-particle motion in
turbulent channel ¯ow require second-order statistics
computed from large numbers of locally homogeneous
®elds. For this type of measurement, a high percentage of
valid velocity vectors is important but not too critical.
Therefore, we use a cutoff of 98%. Second-order statistics
require high accuracy in each sample, and a cutoff for gas
RMS velocity error of 0.1 pixels is reasonable. This is already a signi®cant part (10%) of the centerplane streamwise RMS velocity in our ¯ow. These cutoff values are
shown as dashed horizontal lines in Figs. 12 and 13. At this
point, we did not impose any restrictions on RMS error for
tracking, which is typically larger than that in crosscorrelation.
With this set of performance criteria, an image set is
considered as `very high quality' if it can be reliably and
accurately processed with 32 ´ 32 interrogation areas.
Such images require the number of solids per spot to be no
more than 1.0 for 30- and 43-pixel solids and no more than
0.2 for 120-pixel solids. In terms of solid-to-tracer signal
ratio, STSR<1.0. In real ¯ow with the present acquisition
parameters, it corresponds to data away from the wall with
0.014% volume fraction of particles with mean diameters
of 25, 33, or 63 lm.
An image set is considered `acceptable' if it can meet the
same performance criteria with 64-pixel interrogation
spots. Samples of `acceptable' images are shown in Fig. 15
for the maximum possible number density of each solid
particle size and channel location. Note that the local
concentration test (Fig. 11) was performed at the set of
parameters corresponding to Fig. 15b. Also, a comparison
of Fig. 15c and d demonstrates the importance of correlation peak height in obtaining data of acceptable quality.
5
Concluding Remarks
The validation tests show that the two-parameter phase
discrimination method works well for the purpose of simultaneous gas and solid velocity ®eld measurements. A
simple conceptual design and numerically ef®cient software implementation make the algorithm suitable for
processing large amounts of data, a necessity for computation of reliable statistics in many two-phase ¯ow regimes. Five-point blur and saturation threshold add-ons
support processing of noisy and saturated images, thus
making the algorithm applicable to a variety of photometric and ¯ow conditions.
In the most recent practical measurements in particleladen channel ¯ow, the particle volume load was increased
up to 0.0045%, which was the ¯ow rate allowed by the
particle feeder. Up to this load, the valid data yield was
above 98% and the RMS error was estimated to be less
than 0.1 pixels for gas and 0.25 pixels for solids velocity
measurements. Tests with the arti®cial two-phase images
indicate that the volume loading can be increased up to
0.014% for reliable data under these conditions. The algorithm works well with 25- (simulated), 33- and 63-lm
particles, as long as the particle scattering pattern yields a
local maximum or saturation at its center. In the near-wall
region, where RMS velocities and gradients are high and
illumination is low, the range of applicability of the algorithm is much less. This restriction close to the wall is
directly related to the reduced correlation peak quality.
The overall phase discrimination method is ¯exible,
effective and robust because of the following key design
concepts. First, the core object pixel detection steps
(Eqs. 6, 7, 8, 9) do not require any input parameters
because they are based on the ®nite-difference criteria
for a local maximum. Thus, all objects are detected in
the same manner, whether they are large or small, bright
or dim. Second, with this object detection approach, the
size and brightness parameters are computed indepen-
267
Fig. 15. Sample images on the
edge of applicability limits for
phase discrimination: a A ˆ
30 pixels, 1.5 solids per 32 ´ 32
spot, Hxcorr ˆ 8.9 ´ 105; b
A ˆ 43 pixels, 2.34 solids per
32 ´ 32 spot, Hxcorr ˆ 8.9 ´ 105;
c A ˆ 120 pixels, 1.05 solids
per 32 ´ 32 spot, Hxcorr ˆ
8.9 ´ 105; d A ˆ 120 pixels,
0.03 solids per 32 ´ 32 spot,
Hxcorr ˆ 8.3 ´ 104
dently. The use of two independent parameters (instead
of size or brightness only) results in a more effective and
¯exible phase separation. Indeed, in Fig. 5a, separation
by size only would include all large and dim objects to
the left of the solids rectangle (most probably, broken-up
out-of-focus solids) as `reliable solids', most likely introducing noise to the solids velocity measurements.
Likewise, small and bright objects to the right of the
tracer rectangle would corrupt the gas velocity measurements because, in fact, most of these objects are
remnants from solids. Phase discrimination based on two
parameters eliminates many such objects from the resulting image ®les. The object identi®cation and separation algorithms can also be applied to other types of
¯ows. For example, they were applied in liquid-liquid
¯ows with surface tension, where one of the two liquids
was marked with ¯uorescent dye (Longmire et al. 2001)
to eliminate non-uniformities in background intensity
(caused by absence or presence of dye) and to eliminate
agglomerated tracer particles.
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