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OCR for page 65
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Frontiers in Experimental Techniques
Joseph Katz (The Johns Hopkins University, USA)
INTRODUCTION
This paper discusses several recent developments in
experimental techniques in fluid mechanics and their
applications in problems that are relevant to Naval
Hydrodynamics. We are not presumptuous to cover
all the recent advances. That would require at several
books (e.g. Smits and Lim, 2000; Raffel et al., 1998~.
Thus, this paper is confined to specific technologies,
and is not free of the personal perspective of the
author. Second, the sample data presented here has
been obtained by many collaborators, graduate
students, posdocs and colleagues. It is not practical to
include all of them as co-authors, and I have no
choice but to list their names in the
acknowledgement.
First and foremost, the advances of computer
technology and consequently, the emergence of
digital image acquisition, have led to the ever-
increasing dominance of Particle Image Velocimetry
(PIV). Early contributions to the development of this
technique are summarized in Adrian (1991~. During
the 1990's the use of PIV became wide spread and
this technology is now available commercially in a
variety of forms. PIV had enabled us to examine
instantaneous two-dimensional flow structures, and
with increasing computer power, also obtain the
turbulence statistics. Subsequently, using two
cameras focusing on the same plane from different
angles, stereo PIV enables us to measure all three
velocity components in the sample area (e.g. Prasad,
20004.
Clearly, the simplicity and flexibility of 2-D and
stereo PIV are the primary reason that they are
overtaking/replacing all other velocity measurement
techniques, especially in liquids. As demonstrated in
this paper, PIV has already been implemented in our
group for measuring the complex flow structure
within multistage turbomachines, and for measuring
the flow and turbulence structure in the bottom
boundary layer of the coastal ocean. Full scale PIV
measurements of flows around helicopter rotor have
been performed by Raffel et al. (2001), and around a
car by Wendt and Furll (2001~. However, at the
present time PIV cannot provide the combined spatial
and temporal resolution of hot wire measurements in
air. A few specialized LDV systems also have higher
spatial resolution. The gap will diminish with time, as
computer and imaging technologies improves. The
current digital cameras, containing typically 2kx2k
pixels, limit the spatial resolution to the order of 1%
of the total image size. The temporal resolution is
limited by the currently available data acquisition
technologies. Digital cameras recording 1000 frames
per second and resolution of lkxlk are already
available commercially. However, since the resulting
acquisition rate, 1 GB/s, is beyond the present range
of computer busses, the period of data acquisition is
short and requires internal specialized storage
capacity. There is no doubt however, that this
limitation is temporary.
Unlike the wide-spread use of planar velocimetry,
there have been very few successful applications of
methods for measuring the three dimensional velocity
distribution in a finite volume. Holographic PIV
(HPIV) is the only technique that has successfully
measured the instantaneous 3-D velocity distribution
within a sample volume (e.g. Barnhart et al., 1994;
Meng and Hussain, 1995; Zhang et al., 1997~. The
primary difficulty in implementing HPIV is the
complex optical setup. We have already implemented
HPIV to generate instantaneous distributions with
130x130x130 velocity vectors (Tao et al., 2002), and
recent developments enabled us to increase the
particle concentration to more than 200 per mm3 and
400x400x400 vectors (Sheng et al., 2002~. Defocused
image velocimetry (Pereira and Gharib, 2002) has
successfully measured the 3-D trajectory of
particles/bubbles in a large volume. This technique is
considerably simpler than HPIV, but is limited to a
substantially lower particle concentration.
PIV MEASUREMENTS IN TURBOMACHINES
There have already been numerous applications of
PIV to flows within turbomachines, including
centrifugal pumps (Dong et al., 1992, 1997, Sinha et
al., 2000a, b, 2001; Akin and Rockwell, 1994a, b),
upstream and downstream of propellers, (e.g. Yoon
OCR for page 66
and Lee, 2002), as well as within and around
compressor blades (e.g. Sanders et al., 1999;
Goginenietel., 19973.
Most applications of PIV in turbomachines
suffer from limitations in optical access to the region
of interest. The difficulties occur in part due to the
presence of complex, multiple blades and blade rows.
In addition, reflection of the laser sheet from
boundaries overwhelms the particle traces, which
severely reduce the quality of boundary layer data.
The latter problem has been resolved in liquid flows
by using fluorescent particle as tracers. The different
(higher) wavelength of fluorescence can be separated
from the illuminating laser sheet by inserting a filter
in front of the camera, including the reflections from
boundaries (e.g. Sinha et al., 2000a, b, 2002~.
Overcoming the optical obstruction problem is a
more complicated problem, and has resulted in
partially obstructed views/data on the flow structure
(Sanders et al., 1999~. However, addressing
turbulence modeling issues, and examining the
complex wake-blade and wake-wake interactions
within turbomachines require complete views.
To overcome the optical access problem we have
constructed a facility that utilizes transparent blades
and contains liquid that has the same optical index of
refraction as the blades. The fluid is a concentrated
solution, 62%- 64% by weight, of Nat in water. This
fluid has a specific gravity of 1.8 and a kinematic
viscosity of l.lx10-6 m2/s, i.e. very close to that of
water. Consequently, the blades become almost
invisible, allowing the laser sheet to pass through
them undisturbed, and do not obstruct the field of
view. There is also very little reflection when the
laser sheet penetrates the blades. Information related
to use and maintenance of the Nat solution can be
found in Uzol et al. (2002a). As illustrated in Figure
1, the test facility consists of a two-stage axial
turbomachine, and the experiments are performed
within the second stage. Two setups with different
blade geometries, with the characteristics shown in
Figure 2 have been tested to date.
Test Setup No. 1 has 4 blade rows, forming two very
similar stages. The rotors blades have a chordlength
of 50 mm, span of 44.5 mm, thickness of 7.62 mm
and camber varying from 2.54 mm at the hub to 1.98
mm at the tip. The Reynolds number based on the tip
speed and rotor chordlength is 3.7x105 at 500 rpm,
the speed of the present tests. The stators blades have
chordlength of 73.2 mm, span of 44.5 mm, thickness
of 11 mm and camber of 6.22 mm. Test Setup No. 2
has the same 1St stage, but the 2n~ stage consists of a a
stator followed by a rotor. A honeycomb occupies the
entire gap between the two stator-rows. The purpose
of this honeycomb is to reduce the effect of large-
scale turbulence generated at the upstream blade
rows, and align the flow in the axial direction,
consistent with the orientation of the 1St stage stator.
The ultimate purpose of this arrangement is to study
the stability of swirling wakes. The system is driven
by a 25 HP rim-driven motor, which is connected
directly to the 1St stage rotor, preventing the need for
Transparen s
Transparent Rotor Or ~ Stage Rotor
~~ .
~,,,,~,,,=
(a)
Laser
sheet
(b)
Window Motor 25 HP
Transparent 1 stagestator
Transparent
Rater
Honeycomb
No. of stoics
No. of rotor blades
No. of stator blades _
Hu~to tip ratio
R2-S: anal gapIRotor =~1 chord
S1-R2 ~1 gapJRotor anal chord
Rotor pitc~to-chord ratio (kinsman)
Stator pitch-to-chord redo (~ruckspan)
Rotor chord (mm)
Stator chord (rmn)
Rotor and SteLor span (mm)
Motor 25 HP
Test SetuD
_
Ne. 1 No. 2
2
12
~17
1.92~ ~
~1.95 ~~
~1 .34~
0.66
73.2
. ~1.471
. bUA
1.34
. ~~ ~0 97
.
~0
_ 44.S
Second Stage of:
Test Setup 1
Stator (S2) Rotor (R2)
Test Setuo 2
Rotor (R2) Stator (S2)
Figure 1: The axial turbomachine (a) Test setup No.
1; (b) Test setup No. 2; (c) Geometrical parameters
for Test Setups No. 1 and No. 2.
a stator followed by a rotor. A honeycomb occupies
the entire gap between the two stator-rows. The
OCR for page 67
purpose of this honeycomb is to reduce the effect of
large scale turbulence generated at the upstream
blade rows, and align the flow in the axial direction,
consistent with the orientation of the 1St stage stator.
The ultimate purpose of this arrangement is to study
the stability of swirling wakes. The system is driven
by a 25 HP rim-driven motor, which is connected
directly to the 1St stage rotor, preventing the need for
a long shaft. The two rotors are connected by a
common shaft and supported by precision bearings.
A shaft encoder and a control system are used for
synchronizing our PIV system with the rotor phase.
Further details can be found in Uzol et al. (2002a, b)
and Chow et al. (2002~.
Optical access is provided by a window that
extends from upstream of the rotor, covers the entire
2n~ stage and extends to the far wake downstream of
the stator (Figures 1 and 2~. An additional
transparent insert enables us to insert a probe
containing the laser-sheet optics. Consequently, we
can illuminate any desired plane with a laser sheet
from the hub to the tip of the blades, including the
tip-gap. The interrogated planes can be parallel or
normal to the axis of the turbomachine. The corner
window also provides us with an optical access to the
interior of the rotor and the stator, which is essential
for future, 3-D, HPIV measurements.
u J
Insert Sheet ~
~ r Camera
PIV optics
Platform
Figure 2: Optical access to the test section and the
PIV system.
The light source of the PIV system is a dual-head Nd-
YAG laser whose beam is expanded to generate a 1
mm thick light sheet. The flow is seeded using 20%
silver coated, hollow glass, spherical particles, which
have a mean diameter of 13,um and an average
specific gravity of 1.6, i.e. slightly below that of the
working fluid. The images are recorded by a
2048x2048 pixels2, Kodak ES4.0 digital camera. The
laser and the camera are synchronized with the
orientation of the rotor using a shaft encoder that
feeds a signal to a controller containing adjustable
delay generators. Consequently, we can acquire data
at any desired rotor phase.
Typically, the sample area is 50x50 mm2, and as a
result several (five) data sets at different axial
locations with sufficient overlap have been recorded
to cover the entire stage. Measurements of wake and
boundary layer structures have been obtained at
higher magnification, a total sample area of 15x15
cm, and vector spacing of 120 ~m. Data analysis
includes image enhancement and cross-correlation
analysis. Details can be found in Uzol et al. (2002a).
The uncertainty in mean displacement in each
interrogation window is about 0.3 pixels, provided
the window contains at least 5-10 particle pairs. For
the typical displacement between exposures of 20
pixels, the resulting uncertainty in instantaneous
velocity is about 1.5%. Slip due to the difference
between the specific gravity of the particle (1.6) and
that of the fluid (1.8) may cause an error of less than
0.2%, i.e. much less than other contributors (Sridhar
andKatz,1995).
We have already recorded and process substantial
amount of data, covering the entire second stages,
and results have been presented in several
publications (Oguz et al., 2002a, b; Chow et al.,
2002~. The measurements have enables us to examine
and quantify complex flow phenomena associated
with blade-wake and wake-wake interactions. Phase-
averaged data has been obtained at 10 rotor phases,
every three degrees of blade orientation, which cover
an entire rotor blade passage of 30 . For each
condition (phase and location) at least one hundred
instantaneous realizations have been recorded. For
selected cases we record 1000 images in order to
obtain converged statistics on the turbulence. The
turbulence parameters are determined from ensemble
averaging of data at the same phase.
A detailed discussion on the flow structure within
these turbomachines is beyond the scope of this
paper. However, a few examples are selected to
illustrate the flow complexity, and the ability of PIV
measurements in the index matched facility to resolve
them. Figure 3 shows velocity and turbulent kinetic
energy distributions at three phases, positioned to
match the relative orientation of the blades. Clearly
and not surprisingly, the phase averaged velocity
distributions and turbulence are highly non uniform,
and the entire domain contains a lattice of interacting
wakes. The wakes are dissected by the blades but
their segments can be identified far downstream of
their origins.
OCR for page 68
Matching all the appropriate rotor phases relative to
the stator enables us to construct the entire flow field
around the rotor blade in the rotor frame of reference,
including its inlet and its wake. Figure 4 shows a
sample distributions of phase-averaged velocity, flow
angle and turbulent kinetic energy. The flow field is
dominated by the interaction with the 1St stage stator
and rotor wakes. In the sample shown, a stator wake,
characterized by high k and low flow angle, is just
starting to impinge on the rotor blade. The inclined
region with elevated turbulent kinetic energy just
above this stator wake is the 1St stage rotor wake.
Another segmented wake can be identified, one part
on the pressure side of the blade and the other near
the trailing edge on the suction side. The
discontinuity in wake trajectory is caused by the
differences in velocities on the suction and pressure
sides of the blade. Note also the low momentum zone
accompanied by (mostly) high (negative) flow angle
on the pressure side of the rotor blade. This region
coincides with the intersection of the 1St stage stator
and rotor wakes, illustrating the impact of upstream
blades on the flow around the blade.
The interaction of the stator wake segments with the
2n~ stage rotor wakes cause phase-dependent
meandering of the rotor wake, evident for example,
in the upper rotor wake. The non-uniformities in the
horizontal velocity distributions, which are a direct
result of the "discontinuities" in the trajectories of the
stator wake, also shear the rotor wake. As illustrated
in Figure 5, this shearing creates a kink in the
lVl/utip l
0.00 0.07 0.13 0.20 0.27 0.33 0.40 OA7 0.53 0.60
_ - .
.
1 ~ ~ _
1 idol .
0.4 ~ ~ l ~
. ~ ~
: 1 !
. 1 ~ 1
0.3
n
-0 1
-0.2
l_
_
]_
3_
__
_I
I_
_@
3~
4~_
trajectory of the rotor wake, characterized by
concentrated vorticity and high turbulence levels. We
define these regions as "turbulent hot spots."
Although the wakes diffuse, hot spots persist far
downstream of their origins. In fact, every region of
wake intersection has an elevated turbulence level
(e.g. Figure 4~.
The few examples shown here demonstrate the ability
of PIV in the index-matched facility to elucidate the
complex flow structure in multi-stage turbomachines.
Further results, including turbulent spectra, estimates
of dissipation rates, high magnification details of
wake-boundary layer interactions, distributions of
Reynolds and deterministic stresses, effects of wake-
blade and wake-wake interactions on the
performance of the turbomachine can be found in
Oguz et al. (2002a, b) and Chow et al. (2002~.
OCEANOGRAPHIC APPLICATION OF PIV
The simplicity of PIV, on one hand, and the wealth of
data that it provides makes it an attractive option for
large-scale and field applications. In problems
relevant to Naval hydrodynamics PIV has been used
for measuring the structure of breaking bow waves
(Dong et al., 1997; Roth et al., 1999), as well as the
flow and turbulence in spilling breakers and in the
wake behind ships (e.g. Gui et al., 2001). In these
examples, the images were recorded in towing tanks
k / U2tip x 105
0.00 0.45 0.65 0.86 0.91 1.08 1.67 2.78 3.89 5.00
_!
ma_
11_
ZEST
0.75 o.5
xJ Ls
-
0.25 o 0.75 o.5
x ~ Ls
Figure 3: Matched sets of phase averaged absolute velocity (|V|/UIjp, left side) and turbulent kinetic energy (k, right
side) constructed from data obtained in several phases. Arrow shows the rotor direction.
OCR for page 69
|Vl / Utjp k / U2tjp x 10~ aR (degrees)
_nnn nss nR4 nFs n7' n7.R n7s nR.R n~R 1 1n
0.45
0.4
0.35
0.3
~n
0.25
0.2
0.15
0.1
0.05
O
~ .
-
.
_
_
_
_
_
_
_
_
_
_
_
_
__
_
_
_
r ~ ~ r - - l_
nnnnnnn4Rn7nnnnnsE 1lR2En~nn
Hn nn 7n 27 -~9 77 -ER 12 -~ 62 27 En
0.3 0.2 0.1 0 0.3 0.2 0.1 0 0.3 0.2 0.1 0
xJLs xILs xJLs
(a) (b) (c)
Figure 4: (a) Sample phase averaged velocity in the rotor frame of reference; (b) Turbulent kinetic energy (c) Phase
averaged flow angle in the rotor frame of reference around the rotor blade.
(1Js)
300.00
251.02
213.54
1 65.31
1 1 6.33
87.89
73.61
52.45
43.04
30.15
14.43 -1 5
4.42 ~
-6.12 ~-20
-27.43 ~
- 0.69 >,,-25
-55.1 0
79 b9 -30
-96.70
-1 28.57
-1 65.31
-202.04
-251 .02
3nn nn
15
1n
o
-10
-40
-50
_ ~ ~ . :~
1. ~ ~:: ~':~'l~:~-~-.~:. ~ 1 1 ~ 1 1 1 1 1
30 20 10 0
x (m m)
o
-10
-35
-40
-45
-50
~_
~_
. 1 1 1 ~ I ~ I,,,, 1
30 20 10 0
x~mm)
k (m2ls2)
· 027
~ .
0.24
~3 0.21
0.18
~1 0.15
0.12
0.09
a 006
_
0.03
0.00
Figure 5: Vorticity and turbulent kinetic energy in the near field of the rotor wake obtained by combining high
magnification data sets (lSxlS mm2 each) in different areas. Location: mid-span; number of vector maps for each
area: 1000.
OCR for page 70
using submerged cameras. Over the last decade, we
have developed and deployed a submersible PIV
system for measuring the flow structure and
turbulence in the bottom boundary layer of the
coastal ocean. Several generations of this system
have been described in Bertuccioli et al. (1999),
Doron et al. (2001) and Nimmo-Smith et al. (2002a,
b). The present version of the system is illustrated in
Figure 6.
Predictions of the ocean dynamics, sediment
transport, pollutant dispersal and biological processes
require knowledge on the characteristics of
turbulence in the bottom boundary layer. Modeling of
the turbulence requires data for
development/validation of closure models.
Consequently our goal has been to measure the
Reynolds stresses (free of wave contamination),
velocity profile, dissipation rate, production,
buoyancy flux and turbulent spectra in the coastal
bottom boundary layer, and relate them to
oceanographic parameters that represent the local
environment (e.g. waves, currents, stratification,
bottom topography). Due to potential future
applications of LES for modeling oceanic flows, we
have also examined the dynamics of sub-grid scale
(SOS) stresses and SGS energy flux. Several field
trips to acquire data have already taken place along
the Atlantic coast.
A schematic of the submerged components of the
oceanic PIV system is shown in Figure 6a, and the
platform is shown in Figure 6b. The laser (a pulsed
dye laser generating pairs of 2 Us pulses) is located
on the ship and the light is transmitted through
optical fibers to submerged probes. Images are
acquired using two, 2k x 2k CCD cameras. Each
camera and associated light sheet can be aligned
independently, in the same or different planes, near
each other or apart. The data is recorded on mass data
acquisition systems (one for each camera), allowing
continuous sampling for many hours. The
submersible components of the PIV system are
mounted on a seabed platform, which can be rotated
to align the sample areas with the mean flow
direction, and extend vertically to sample at different
elevations. The platform is a 5-stage telescopic
hydraulic cylinder, with a vertical range of 9.75m.
The system also contains a series of instruments or
characterizing the local environment, including a
CTD, transmissometer, dissolved oxygen sensor,
precision pressure transducer (for sensing surface
waves), clinometer, compass and video-microscope
for sampling the particle distributions at high
magnification.
Fiber Optic
Laser Probe \~'
\ ,,,--~
Video ~ f
Direction
Vane
/ Mounting Point
. -
..~ :..:
Light Sheet
Sample Area
~1
EXTENDED
(Height 12.5m)
~ ^
r: ~ ~ ~
4~ r
Camera (x2) /'
Light Sheet tx2)
Smallest Moving
_ Stage: 1 3cm Dia.
1
_ 5-Stage Double-
—ActingTelescopic
Hydraulic Cylinder
=
~r~
Largest Moving
Stage: 25cm Dia.
RETRACTED
(Height 2.75m)
~3
l
_ ~ 1
_ i 1U n I
Li ~ ~~ I
Weighted Tripod Base (2m Dia.)
Figure 6. The oceanic PIV system.
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Representative terms from entire chapter:
boundary layer
In Nimmo-Smith et al. (2002b) we select and
compare several data sets obtained at different depth
to represent conditions of relatively high,
intermediate and weak mean flows. They also
represent substantially different turbulent Reynolds
numbers. Table 1 summarizes the selected data
series. To characterize the mean flow and amplitude
of surface waves, we average the velocity over the
vector map to obtain the instantaneous average
velocity componen_ (U and W). The mean current is
characterized by U and W. the overall average
(over all distributions), whereas URMS is the RMS
values, representing mostly the effect of surface
waves but also turbulence at scales larger than the
instantaneous distributions. The data of Runs A and
B were obtained at the mouth of the Delaware Bay, at
a mean near the bottom velocity of 38 cm s with little
wave motion. Runs C to F were obtained of-shore,
where the current is moderate to weak, but the region
is exposed to oceanic swell. For Runs C and D the
amplitude of the wave induced velocity is of the same
magnitude as the mean flow. For Runs E and F. the
mean current is very low, namely the flow consists
almost entirely of wave-induced motion. Data were
collected continuously for periods of 20 min. at 2-3.3
Hz, and at elevations up to 8.5 m above the seabed.
Here we use data obtained at mean elevations (vector
map center) of 0.55-2.5 m above the bottom.
Figure 7 presents mean, one-dimensional energy
spectra of u (E11) and w (
One can characterize the turbulence using the Taylor
micro-scale Reynolds number, Red ~ u'7 /v,
ZU#u'(l5v/~/2. To estimate ~ and w' without
being contaminated by waves one can use the second
order structure function, a method introduced by
Trowbridge (22), and implemented using PIV data in
Nimmo-Smith et al. (2002a, b). Averaged values of
u' and w' and the corresponding Rex are also
presented in Table 1. In Runs A and B Rem, is in the
300-400 range. However, Rex of the New Jersey
coast are 68-83 at moderate flow, and 14-27 when the
mean current is weak. Since Runs C-F represent
typical calm weather conditions in coastal water, the
results indicate that turbulence in the coastal bottom
boundary layer in calm weather has a very low _~0-~ .
Reynolds number. The moderate and low Rem, cases
fall in the range where assumptions of universality of ~
the energy spectrum are invalid (Pope, 2000~. ~s
up ~n~'`
PIV data can also be used for evaluating models of
the sub-grid scale (SOS) stresses, and for estimating
the SGS dissipation (or energy flux) for Large Eddy
Simulations (LES) (Liu et al., 1994, Tao et al., 2002~.
In LES the Navier Stokes Equations are filtered
spatially at a scale ~ and the resulting SGS stresses,
{iSGS=UiUi-UiUi ("~" indicates spatial filtering)
must be modelled (see example in Figure 8~.
Associated with this stress is the SGS dissipation
~ ~
rate, ESG = _~`S~Gssii' Si; = 0.5(3Ui/ik j + ~Uj/3xi),
which represents transfer of energy from the resolved
to subgrid scales. Consequently, attempts to model
the SGS stresses frequently focus on reproducing the
correct levels of BSG. Unlike viscous dissipation,
ESG can be both positive and negative. A positive
U = 12.4 cm/s, W = -0.2 cm/s
60
45
4n
104
,0-it _
t,
10-6 _
10~8 .
10
A\
2r
10 1X 1000
[~,,1
10
a~
10 1X IWO _ __
3
10 100 l00o
100
k1 (radium)
:1~- \,
1000 100 1000
Figure 7. Spatial energy spectra. Solid lines: E/l(kl9,
Dashed lines: 3/4E33(kl). Inset figures are spectra
of ~ Y sky Eii(k~) . a - f correspond to Runs A - F.
value indicates flux of energy from large to small
scales whereas a negative value indicates
"backscatter" of energy from small to large scales.
Reviews are available in Lesieur and Metais (1996),
Piomelli (1999) and Meneveau and Katz (2000~.
When the filter is in the inertial range of isotropic,
homogeneous turbulence, the mean SSG is (almost)
equal to the viscous dissipation rate. However,
-15 -10 -5 0 5 10 15
X (cm)
Figure 8: Instantaneous distributions of: a. Sample velocity distribution, NJ coast, 2001; b. The same velocity field
filtered at A=86; and c. The corresponding distributions of tl3, contoured at intervals of Sx10-6 m2/s2. Negative values
are shaded gray.
Piomelli et al., (1991) shows that near the wall of
channel flows, the mean BSG iS small and even
negative.
Evaluation of turbulence models requires data on the
SGS energy flux, estimated as
2 ~ ~ ~ ~ ~ 33 533 t! IS33—{33 S} ~ + 1 2[ ~ 3 S! 3 ~
Measured averaged values of ESG are presented in
Table 2 for three filter sizes, a=4, 8 and 16 vector
spacings (d, Table 1). At high flow (A-B) ESG iS of
the same order as ED, whereas in the moderate and
weak mean flow conditions, the SGS dissipation Is
more than an order of magnitude lower than SD,
decreasing to negligible levels as the flow
diminishes. Considering that cases C-F represent
typical calm weather conditions in coastal waters, the
results bear significant implications for applications
of LES to coastal flows. Further details, including
detailed evaluation of typically used SGS stress
models are presented in Nimmo-Smith et al. (2002b).
Clearly, PIV can be applied to characterize large-
scale flows and in difficult field conditions. The same
technology with appropriate adjustments can be used
for studying boundary layers on full-scale models.
3-D VELOCITY MEASUREMENTS USING HPIV
Stereo-PIV systems, capable of measuring the all
three velocity components in a plane are already
available commercially and used extensively.
However, as noted in the introduction, HPIV is the
only technique that can measure the 3-D velocity
distribution in a finite volume.
Several HPIV systems have been implemented over
the years. Barnhart et al (1994) introduced a phase-
conjugate off-axis recording system, and were the
first to use it as a 3-D velocity measurement
technique. Meng and Hussain (1995) proposed a
simplified in-line recording and off-axis viewing
method, which combines the simplicity of in-line
recording, and the high signal-to-noise ratio of off-
axis holography. Since in-line holography involves a
reference beam passing through the sample volume,
the particle concentration is limited, limiting the
spatial resolution of the measurement. Zhang et al.
(1997) and subsequently Tao et al. (2000, 2002)
increased the measurement accuracy and data density
using (see Figure 9) near-forward scattering, high-
pass filtering, off-axis reference beams and two
simultaneous, orthogonal views of the same flow
field. The two views are essential for overcoming the
inherent "depth of focus" problem of holography, i.e.,
the substantially larger measurement uncertainty,
typically in the 200~m - 1.5mm range, along the
depth direction (the light propagation direction),
compared to about 10mm in the other two directions.
This method was used for measuring the flow within
a square duct provided the first set of spatially
resolved, 3-D instantaneous velocity distributions
that were used as a research tool. The resulting maps
containing 130x130x130 vectors were used to study
geometric and scaling relationship of SGS stresses
and their models in a high Reynolds number
turbulent flow Tao et al. (2000, 2002~.
Another approach, introduced by Pu and Meng
(1999), consisted of a wide-angle side-scattering, off-
axis HPIV system, and promised to achieve both high
resolution and accuracy. Although their 90° side-
scattering is substantially weaker than near-forward
scattering, the wider scattering angle (larger
numerical aperture) reduces but does not eliminate
the depth-of-focus problem. In the Zhang et al.
( 1997) approach (Figure 9) this problem is
circumvented, at the cost of added complexity, by
recording two orthogonal views of the same flow
field. Furthermore, they require four windows, an
arrangement that is rarely available in typical test
facilities. Sheng et al. (2002) recently resolved this
constraint by introducing the "Single Beam Two
Views" (lB2V) HPIV system.
M
M
B2E
M B3
M~ ~
VOLUME ~=7
.
L
B1
M
t-
/ LL
R / R
~F ~
R [B.C. ~ FILM DRIVE
~ R4/
'Yll
FILM DRIVE [~
B ~ Beam splitter
B.C. t Beam collimator
H.F. ~ High pass filter
L ~ Lens
M: Mirror
R; Relay lens
Figure 9: The HPIV setup of Zhang et al. (1997).
It consists of recording two perpendicular off-
axis holograms.
The principles of the Sheng et al. (2002) approach are
sketched in Figure 10. In the recording phase, a
mirror is inserted in the flow field and as a result each
particle is illuminated in two different directions.
The first beam (Ray 1) illuminates the particle before
it is refelcted by the mirror. The second beam (Ray 2)
is reflected by the mirror first, and then illuminates
the particle. Consequently, two spatially separated
particle images, one being the "real image" (solid
lines); and the other being the "mirror image" (dotted
lines) are recorded on the same hologram. During
reconstruction both views are reconstructed
simultaneously but at a different locations in space.
Due to the depth of focus problem, both views are
elongated along the direction of the optical axis of the
reconstructed wave. However, since the two views
are perpendicular to each other, exact information on
the location of the particle can be obtained by
combining the data provided by these views. Figure
10 also shows the optical setup for recording (solid
lines) and reconstructing (dashed lines) the
holograms.
The single-beam two-views method has several
advantages. First, since the mirror is placed inside the
facility, the test facility requires only one window
instead of four. Second, having to record only one
hologram requires considerably fewer optical
components compared to the Zhang et al. (1997)
setup. However, the required window is larger and
the sample volume has a triangular shape. Third and
most important, the known 3-D coordinates of the
particles enable us to quadruple the spatial resolution
of the velocity distributions, and significantly
increase the accuracy in velocity measurements. A
reconstructed flow field containing more than 200
particles/mm3 enables us to calculate the 3-D velocity
distribution using an interrogation volume of
220x154x250 ~m, and a vector spacing of half this
distance.
To obtain the 3-D velocity vectors from the two
different holographic images, Zhang et al. (1997) and
Tao et al. (2001, 2002) scan the reconstructed field,
record 2-D slices of particle traces and use 2-D PIV
techniques to compute the velocity. The 3-D vector
field is obtained by combining the two 3-D
distributions of two velocity components. Due to the
depth of focus effect, each 2-D section through the
reconstructed field contains traces of particles that are
located within about 1 mm from this plane.
Consequently, the velocity is effectively low-pass
filtered in the depth (axial) direction. In the lB2V
approach, data processing consists of two steps. The
first, determines the 3-D location of particle
centroids, and the second, calculates the 3-D velocity
vectors using the known particle locations. The
measured centroids are used for trimming the
elongated particle traces in the original scanned
Ax
(Recording Phase)
ax
~ s ~
OR
SH: Shutter
PBS: Polarized Beam Splitter
VBE: Variable Beam Expander
PH: Pinhole
RLA: Relay Lens Assembly
L1: Plano-Concave Lens (f=1")
L2: Plano-Convex Lens (f=4")
L3: Plano-Convex Lens (f=1.5m)
L4: Plano-Convex Lens (f=10")
L5: Plano-Convex Lens (fed")
L6: Doublet Relay Lens (f=10")
M1: 3" Mirror
M2: 3" Mirror
Domed line:
Reconstruction Optics Setup
1: Reconstructed First View
2: Reconstructed Second View
~ Mirror
,,
RB: Reference Beam
1 : Particle of 1st view
1' : Mirrored view
2 : Particle of 2nd view
(b)
/ L6\ A>
/ <'
I \
_, ~ L6
1 1 ~z
Reconstructed I I
Mirror Overlap
do, ~ Region
.1 COD
Camera
Figure 10: a. Placing an inclined mirror causes
illumination of the same particle in perpendicular
directions; b. The two views during reconstruction;
c. Optical setup of a single beam two views HPIV
system.
images. The velocity is calculated from the trimmed
traces.
Sample cross sections of an elongated particle trace
are presented in Figure 11. In subsequent calculation,
each 3-D particle trace is replaced by a cylinder, least
square fitted through the measured centers of the 2-D
traces, and a mean radius, which is equal to the mean
particle diameter. The original and mirror views
generate two perpendicular fitted cylinders for each
particle. The two views are matched, and the centroid
of the particle is positioned at the center of the line
defined by the shortest distance between the two
traces. Once the centroid is determined, the particle
traces are erased form all scanned planes whose
distance from the calculated centroid location
exceeds a prescribed distance. In the examples
shown, the reconstructed field is scanned every 250
~m, and particles with centroids located more than
~125 Em from the scanned plane that is closest to the
centroid are erased. The resulting effect on an
interrogation window is illustrated in Figure 12.
Repeating this procedure for all the particles
effectively eliminates the adverse, low-pass filtering
effect of the elongated traces. Then, 2-D PIV analysis
is performed on the trimmed images, and by
combining the data from the two perpendicular
views, one obtains the 3-D vector for each
interrogation volume (220x 1 54x250 ,um3~.
As discussed in Sheng et al. (2002), the uncertainty
depends on accurate determination of the mirror
orientation, along with the typical uncertainties
associated with PIV. Experiments show that the
uncertainty in determining the particle centroid is
about 7 ~m, sufficient for trimming the elongated
traces. Velocity measurements in the wake behind
rising bubbles are used for determining the accuracy
of the 3-D velocity distributions. The analysis is
performed using an interrogation window of 220x 154
,um, with 50% overlap between windows. To check
the accuracy of our measurement, one can examine
how well the results satisfy the continuity equation.
Following Zhang et al. (1997), one can calculate the
normalized divergence,
_ _, ( /x + /Y + Liz) 3
~ ( ~/X )2 + ( By ) + ~ a W/z )
where the "over bar" denotes spatial averaging of the
velocity using a 3-D box filter over a certain length
scale. The average of ~ over an entire sample
volume varies from zero, when the continuity
equation is satisfied at every point, to 1.0 for random
data. Figure 12 shows the cumulative distributions of
or using the lB2V approach and compares them to
the data of Zhang et al. (1997~. Clearly, trimming the
elongated traces improves the data substantially. In
fact, at the both percentile, the present car is five times
smaller.
The results in Sheng et al. (2002) demonstrate that
HPIV can be implemented in a facility with one
window and with a reduced number/complexity of
optical elements Furthermore, with a vector spacing
of 125 ~m, it is possible to obtain 3-D velocity
distributions containing 400x400x400 vectors in a
sample volume of 50x50xS0 mm. At this resolution,
HPIV is a unique tool for characterizing complex, 3-
. .
-
E
-
~,
I
~ to 9'. ~
~ Hi , ,,
i.
In.
- i.,
~.~
.. ~ ,.,'.~i7.4
1 an'"' 4~ ~'' 478 29~ ~
Any 10.9~ me-' 48 Z x
-10~
14~
Figure 11: a. Line fitting through the centroid of
particle traces; b. matched perpendicular
elongated particle tracers determine the centroid
location; c. Original and filtered interrogation
window.
D turbulent flows. Recently, we have also developed
the technology for in-line, digital HPIV (Malkiel et
al., 2002~. This technique provides a simpler tool for
3-D velocity measurements, but at a lower resolution,
and a smaller sample volume.
SUMMARY AND CONCLUDING COMMENTS
This paper provides two examples demonstrating that
2-D PIV can be implemented for probing a wide
variety of complex flows. Stereo-PIV enables
1
0.8
0.6
1~
-
I_ ~
~ i nil ~~
Lit/' ~
_ ~
: -,
0.4
_
0.2
· 0~25=n
· U.
· 11an
~ Lynn
—~—B.93mm Zhang et al.
—~— ,.~'r~n Zhang et al.
O 1 1 1
0 0.2
0.4 0.6 0.8 1
Figure 12: Cumulative distributions of car
obtained with the lB2V HPIV system (Sheng et
al., 2002), compared to the data of Zhang et al.
(1997~.
measurements of all three velocity measurements in a
plane. These techniques are simple to implement, and
their present limitations are caused by constraints of
the present computer technology. These limitations
will diminish as higher resolution cameras and faster
data transfer rates become available. Cameras with
resolution of Skx5k (currently available, but not as
"cross-correlation," interline transfer systems) and
10kx10k will enable us to increase the size of vector
maps to 300x300 and 600x600 vectors, respectively.
Acquisition rates of several KHz (1 KHz cameras
with limited resolution and acquisition time are
already available) will enable us to examine unsteady
flows. Such technologies are already around the
corner.
Seeding is also an issue, especially in high-speed,
compressible gas flows. Advancements are still
needed in molecular tagging and associated/required
camera sensitivity to address these issues (see Smits
and Lim, 2000 for background). Global Doppler
Velocimetry (e.g. Roehle and Willert, 2001; Reinath,
2001), which measures the velocity from the
frequency (Doppler) shift at every point/pixel, is also
a promising technology that would substantially
increase the resolution limits. However, this
technique presently suffers from technical
limitations, mostly in the resolution of the frequency
shift.
HPIV is presently the only technique that can
measure the 3-D velocity distribution in a finite
volume. Holographic films have a resolution that is
more than an order of magnitude higher than that of
any digital recording medium. This resolution is
essential for resolving the fringe spacing of off-axis
holograms. As a result, reconstructed images can be
scanned at a resolution that is substantially higher
than that of typical digital cameras. For example, in
Tao et al. (2002), each plane is converted to 10kx10k
image, and in Sheng et al. (2002), the corresponding
equivalent resolution is 20kx20k. This higher
resolution enables us to obtain 400x400x400 vectors.
However, the optical setup of HPIV is considerably
more complex than 2-D PIV, limiting its range of
applications. Nevertheless, HPIV is the only tool that
be used for measuring/examining the structure of
high Reynolds number turbulence. As we gain
experience in implementing this technique, its range
of application will expand. Digital HPIV would serve
as an intermediate method, providing data at a lower
resolution and a smaller sample volume, but the
technology is considerably simpler to implement.
ACKNOWLEDGEMENT
The material presented in this paper is a result of
experiments performed by numerous post-does and
graduate students, as well as collaboration with
several colleagues. The measurements in
turbomachines have been performed by Oguz Uzol
and Yi-Chih Chow. The oceanic measurements have
been performed by Alex Nimmo-Smith, and he has
worked together with P. Atsavaprani, Luksa Luznik
and Weihong Zhu. The earlier HPIV measurements
have been performed by Z. Zhang and Bo Tao, and
the recent lB2V HPIV system has been developed by
Jian Sheng and Ed Malkiel. My colleagues, C.
Meneveau and T. Osborn have also been critical for
the success of these projects. The turbomachinery
work has been funded by ONR and AFOSR, the
oceanic PIV measurements have been funded by
ONR and NSF, and development of the HPIV system
has been funded by ONR and NSF.
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DISCUSSION
L.P. Purtell
Office of Naval Research, USA
What is your estimate of uncertainty for the
"three-image" PIV approach to pressure
measurement?
AUTHOR'S REPLY
The technology and data analysis procedures for
determining the unsteady pressure distribution
from the material acceleration is presently being
developed. Inherently, the uncertainty depends
on these procedures. Thus, at this stage we
cannot provide a quantitative response to this
question. However, the uncertainty is adversely
affected by having to subtract two large
quantities (velocities) with similar magnitudes.
Thus, even with sub-pixel accuracies in velocity,
the relative uncertainty in acceleration can
become substantial. Overcoming this problem
requires us to circumvent the phase of
determining the velocity. For example, PIV is
based on cross-correlation of two images, and
finding the correlation peak. To overcome the
uncertainty in finding the correlation peak, one
can directly cross-correlate the two cross-
correlation maps (associated with the two
velocities being compared), and determine the
acceleration directly from the "cross-correlated
correlation." Similarly, other sources of
uncertainty must by carefully assessed and
minimized (if possible), including issues related
to spatial resolution, effect of viscosity, etc. Our
current effort to develop the new pressure
measurement technique includes a detailed
uncertainty analysis.
