Simultaneous Measurement of All the Three Components of Vorticity
Vectors by Using a Dual-plane Stereoscopic PIV System
Tetsuo SAGA1), Hui HU1), Toshio KOBAYASHI1),
Nubuyuki TANIGUCHI1), Masashi YASUKI2) and Taizo HIGASHIYAMA3)
1. Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan
2. Industrial Instruments Department, SEIKA CORPORATION, 1-5-3 Koraku, Bunkyo-ku, Tokyo Japan
3. Fluid Measuring Instrument Division, KANOMAX JAPAN, INC., 3-18-20 Nishishinjyuku, Tokyo160, Japan
E-mail: saga@.iis.u-tokyo.ac.jp or huhui@cc.iis.u-tokyo.ac.jp
Abstract
The technical basis and system set-up of a dual-plane stereoscopic PIV system, which can obtain the flow velocity (all
three components) fields at two spatially separated planes simultaneously, was described in the present paper. The
simultaneous measurements were achieved by using two sets of double-pulsed Nd:Yag lasers with other optics to
illuminate the objective fluid flow with two orthogonally linearly polarized laser sheets at two spatially separated
planes. The scattering lights from the two illuminating laser sheets with orthogonal linear polarization were separated
by using polarizing beam splitter cubes, then recorded by high-resolution CCD cameras. Unlike conventional twodimensional PIV systems or single-plane stereoscopic PIV systems, which can just get one-component of vorticity
vectors, the present dual-plane stereoscopic PIV system can provide all the three components of the vorticity vectors
and various auto-correlation and cross-correlation coefficients of flow variables instantaneously and simultaneously.
The present dual-plane stereoscopic PIV system was applied to measure an air jet mixing flow exhausted from a lobed
nozzle to demonstrate its feasibility. In order to evaluate the measurement accuracy of the present dual-plane
stereoscopic PIV system, the measurement results of the present dual-plane stereoscopic PIV system were compared
with the simultaneous measurement results of a LDV system. It was found that both the instantaneous data and
ensemble-averaged values of the stereoscopic PIV measurement results and the LDV measurement results agree with
each other well. For the ensemble-averaged values of the out-of plane velocity component at comparison points, the
differences between the stereoscopic PIV and LDV measurement results were found to be less than 2%.
Key words: Stereoscopic PIV technique, Simultaneous measurement of the all three components of velocity and
vorticity vectors, The measurement of auto-correlation and cross-correlation coefficients of flow
variables, Polarization separation of laser beams, Lobed jet mixing flow.
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c. Instantaneous streamwise vorticity field
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Figure 6. Typical simultaneous measurement results of the Dual-plane Stereoscopic PIV system
1
Introduction
As a non-intrusive whole field measuring technique, Particle Imaging Velocimetry (PIV) can offer many advantages
for the study of fluid mechanics over other conventional experimental techniques like Laser Doppler Velocimetry
(LDV) or Hot Wire Anemometer (FWA). For example, PIV can reveal the global structures in a two-dimensional or
three-dimensional flow field instantaneously and quantitatively without disturbing the flow, which are very useful and
necessary for the research of flow mechanism, in particular for the study of unsteady flow and complex flow
phenomena.
The "classical" PIV technique, which uses a single camera oriented orthogonally to the illuminated plane, is just a twodimensional velocity measurement technique. It is only capable of recording the two dimensional projections of the
three-dimensional velocity on the plane of the laser sheet, i.e the out-of-plane velocity component is lost, while the inplane components are affected by an unrecoverable error due to the perspective transformation errors (Prasad and
Adrian 1993). For highly three-dimensional flows, this can lead to substantial measurement error of the local flow
velocity vectors.
Recent advances in PIV technique have been directed towards obtaining the all three-components of fluid velocity
vectors in a plane or in a volume simultaneously to allow the application of PIV technique to more complex flow
phenomena. Several three-dimensional PIV methods or techniques had been developed successfully in the recent years,
which include Holographic PIV (HPIV) method (Barnhart et al. 1994, Zhang et al., 1997), three-dimensional ParticleTracking Velocimetry (3D-PTV) method (Nishio et al., 1989) and Stereoscopic PIV (SPIV) method to be discussed in
the present study.
Holographic PIV (HPIV) utilizes holography technique to do PIV recording, which enables the measurement of three
components of velocity vectors throughout a volume of fluid flow. Of the existing three-dimensional PIV methods,
HPIV is capable of the highest measurement precision and spatial resolution. However, HPIV is also the most complex
and requires a significant investment in equipment and the development of advanced data processing techniques. The
continuous efforts and developments still need to make the HPIV technique to be a practical tool for the fluid flow
diagnostics.
3D-PTV technique always uses three cameras to record the positions of the tracer particles in a measurement volume
from three different view directions (Nishio et al. 1989 and Suzuki et al. 1999). Through three-dimensional image
reconstruction, the locations of the tracer particles in the measurement volume are determined. By using particletracking operation, the three dimensional displacements of the tracer particles in the measurement volume are
calculated. However, particle-tracking method provides velocity vectors that are randomly distributed in space.
Furthermore, the spatial resolution of particle tracking is low and always just less than 1,000 instantaneous velocity
vectors over the whole measurement volume can be got simultaneously by using common used CCD cameras (Suzuki,
1999). So, the small-scale vortices and turbulent structures in the flow field always can not be identified successfully
from the 3-D PTV results due to its poor spatial resolution.
Stereoscopic PIV technique is a most straightforward and easy accomplished method for the velocity three
components measurement in the illuminating laser sheet plane. It always uses two cameras at different view axis or
offset distance to do stereoscopic image recording. By doing the view reconciliation, the corresponding image segments
in the two views are matched to get three components of the flow velocity vectors. Compared with 3-D PTV method
mentioned above, the stereoscopic PIV measurement results have much higher spatial resolution. The measurement
results of a stereoscopic PIV system always can provide several thousand vectors in the illuminated plane, which is as
the same as conventional 2-D PIV measurement results.
However, the conventional stereoscopic PIV measurement results within one single plane often yields not enough
information to answer the fluid governing equations (such as Navier-Stokes equations) that summarized our fluidmechanical knowledge. In the meanwhile, for most of the vortex flows like jet mixing flows, vorticity vector (all three
components) field is another very important quantity to evaluate the evolution and interaction of various vortices and
the coherent structures in the vortex flows besides the velocity vector. In the statistical theory of turbulence, the spatial
and temporal correlation terms of the fluid variables like velocity together with the spectrums of the fluctuations are
very important for the development of turbulence models. Such information about the fluid flows always can not be
obtained from the conventional stereoscopic PIV measurement results, which were obtained at one single plane of the
objective fluid flow.
In the present paper, the development of a dual-plane stereoscopic PIV system will be described, which can obtain
the velocity (all three components) and vorticity (all three components) vector fields of fluid flows at two spatial
separated planes simultaneously and instantaneously. By adjusting the gap between the two illuminating laser sheets
or/and the time interval between the two plane measurements, the distributions of various spatial or/and temporal
correlation coefficients of flow variables can also be obtained from the measurement results of the present dual-plane
stereoscopic PIV system.
The present dual-plane stereoscopic PIV system was applied to conduct measurement in an air jet flow exhausted
from a lobed nozzle to demonstrate its feasibility. The evolution and interaction of the various vortices in the lobed jet
mixing flow was visualized quantitatively. In order to evaluate the measurement accuracy level of the dual-plane
stereoscopic PIV system, the quantitative comparison of the measurement results of the present dual-plane stereoscopic
PIV system with the simultaneous measurement results of a LDV system had also been conducted in the present study.
2
The technical basis and system set-up of the dual-plane stereoscopic PIV system
It is obvious that the key point for the simultaneous stereoscopic PIV measurements at two spatially separated planes
is to record the images of tracer particles in each illuminated plane separately. Since the two measured planes are
illuminated simultaneously, without any special arrangement, the scattering lights from the two illuminated planes will
be incident upon the same image recording camera simultaneously, which will blur the particle images and make the
simultaneous measurement to be impossible.
In order to separate one scattering light from the other, two kinds of methods can be used, which is named as color
separation method and polarization direction separation method. If the two measured planes are illuminated by using
laser sheets with different color (wavelength), the scattering lights from the two illuminating laser sheets can be
separated successfully by using different optical filters, which are transmissible for one light and are not transmissible
for the other. The polarization direction separation method is the method to illuminate the flow field by using laser
sheets with orthogonal linear polarization directions. By using polarizing beam splitters, the scattering lights from the
two illuminating laser sheets with orthogonal linear polarization directions can also be separated.
In the color separation method, it always needs to use two kinds of lasers to generate laser beams with different
wavelength or to make some optical arrangement modifications inside the laser head to generate different harmonic
light of the same laser to illuminate the objective flow field. Compared with the color separation method, polarization
direction separation method has the advantage of simple optical arrangement, which can be achieved easily by installing
some optics outside the laser head. As the same as Kahler and Kompenhans (1999), the polarized direction separation
method was used in the present study to do the simultaneous stereoscopic PIV measurement at two spatially separated
planes.
Mir r or 15
La ser sh eets
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laser tube
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mirror
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cylinder lens
half wave plate
polarizer
a. Schematic setup of the illumination system
b. Photograph of the illumination system
Figure 1.The schematic diagram and photograph of the illumination system
Illumination system
Unlike Kahler and Kompenhans(1999), who used four independent lasers to set up a four pulsed laser system, two sets
of widely used double-plused Nd:YAG lasers (New Wave, 50mJ/pulse) with optics were used in the present study to set
up the illumination system of the present dual-plane stereoscopic PIV system. A schematic diagram and photograph of
the illumination system are shown on Figure 1. In order to indicate the linear polarization direction changing of the laser
beams clearly, the optical arrangement inside the heads of the two double-pulsed Nd:YAG laser sets is also shown in the
figure.
Each of the two double-pulsed Nd:YAG laser (New Wave Laser) set is composed of two laser tubes with various
3
optics installed in a laser head unit. The wavelength of the laser beams from the laser tube 1,2,3 and 4 is 1064nm
(invisible infrared light), and the linear polarization direction of the laser beams is vertical (V). The vertically polarized
laser beams from laser tube 2 and laser tube 4 are turn into horizontally polarized laser beams (H) by passing half-wave
plate 5a and 5b shown in the Figure 1. Then, they are combined with the vertically polarized laser beams from laser
tube 1 and 3 through Polarizers 7a and 7b. The horizontally polarized laser beams (P-polarized lights) pass through the
Polarizers 7a and 7b. While, the vertically polarized light (S-polarized lights) from laser tube 1 and 3 reflected by mirror
6a and 6b to be incident upon the Plolarizers 7a and 7b at the Brewster angle. The combined P-polarized beams and Spolarized beams pass through half wave plates 8a and 8b, then go into SHG (Second Harmonic Generator) cells for
polarization direction and wavelength adjustments. The laser beams out of the SHG cells have the wavelength of the
532nm (the second harmonic light of the fundamental wavelength 1064nm). The linear polarization direction of all the
laser beams out of the SHG cells are vertical again. Reflected by mirror sets of 9a-10a and 9b-10b, the output laser
beams from the double-pulsed Nd:YAG laser set A and B have same linear polarization direction, which is vertical. The
wavelength of the laser beams has also been changed from 1064nm (invisible infrared light) to 532 nm (green light).
The vertically polarized laser beams from the double-pulsed Nd:YAG laser set B are turn into horizontally polarized
lights (P-polarized lights) by passing the half wave plate 11 before they are combined with the laser beams from the
double-pulsed Nd:YAG laser set A. The horizontal polarized laser beams ( P-polarized lights) transmit through the
Polarizer cube 13. While, the vertical polarized lights (S-polarized lights) from the double-pulsed Nd:YAG laser set A
are reflected by the Polarizer cube 13. By adjusting the angular and the location of the mirror 12, the laser beams from
the laser set A and laser set B can be co-line or not. Passing through the cylindrical lens 14 and reflected by mirror 15,
the laser beams are changed into two paralleling laser sheets with orthogonal linear polarization to illuminate the
studied flow field at two spatially separated planes or overlapped at one plane.
Horizontally polarized laser sheet (P-polarized lights) Vertically polarized laser sheet (S-polarized lights)
To la ser syst em
Sch iem flu g con dit ion
0
Syn ch ron izer
Len s pla n e
Mir r or 25
250
Mir r or
Im a ge pla n e
Ca m er a 1
Ca m er a 3
Ca m er a 2
Pola r izin g bea m
Ca m er a 4
split t er cu bes
a. Schematic setup of the image recording system
b. Photograph of the image recording system
Figure 2. The schematic diagrams and photograph of the image recording system
Image recording system
In order to capture the PIV images simultaneously at two measurement planes illuminated by the above laser sheets
with orthogonal linear polarization, two pairs of high-resolution cross-correlation CCD cameras (1k by 1k, TSI
PIVCAM 10-30) were used in the present study to do stereoscopic PIV image recording. The two pairs of the crosscorrelation cameras were settled on an optical table with a pair of polarizing beam splitter cubes and two high
reflectivity mirrors installed in front of the cameras to separate the scattering lights from the two illuminating laser
sheets with orthogonal linear polarization.
For the stereoscopic image recording, two basic approaches are commonly used, which are lens translation method and
angular displacement method. In the lens translation method, the image recording cameras are placed side by side with
the image plane parallel to the object plane. While in the angular displacement method, the recording cameras view the
same region of interest from an angle and the image planes are rotated with respect to the object plane. The detailed
discussion about the two arrangement methods can be found in Willert (1997), Bjorkquist (1998), Poser et al.(1999) and
Aikislar et al. (1999). The work described here takes advantage of angular displacement method with scheimpflug
condition (Prasad and Jensen, 1995) to obtain focused particle images everywhere in the image plane. The schematic
diagram and the photograph of the image recording system for the present dual-plane stereoscopic PIV system are
shown on the Figure 2.
The illuminating laser sheets with orthogonal linear polarization are scattered by the tracer particles seeded in the
objective fluid flow. The scattering lights from the horizontally polarized laser sheet (P-polarized lights) will pass
straight through the polarizing beam-splitter cubes to be detected by cameras 3 and 4. The scattering lights from the
vertically polarized laser sheet (S-polarized lights) will emerge from the polarizing beam splitter cubes at the right
angles to the incident lights. Before entering the lens of the cameras 1 and 2, the S-polarized lights emerging from the
polarizing beam splitter cubes are reflected by two mirrors to achieve the identical orientation of the image planes for
the two camera pairs. Such arrangement may simplify the matching of the four observation views and save CPU time
4
for the PIV image processing. In order to improve the image quality, the surface of each polarizing beam splitter cube in
which no lights scattered by tracer particles and needed for PIV image recording enters or leaves is covered by light
absorbing material, which is as the same as Kahler and Kompenhans (1999).
Synchronizer and host computer
The above illumination system and image recording system are connected with a host computer via a synchronizer
system (Figure 2), which controls the timing of laser illumination and PIV image acquisition. The two double pulsed
Nd:YAG laser sets and the image recording camera pairs can be programmed to operate simultaneously or separately
with desired time intervals.
The host computer is composed of two high-speed CPU (750mHZ, Pentium III CPU), colossal image memory and
Hard disk (2GB RAM, Hard Disk 200GB). It can acquire the continuous stereoscopic PIV image pairs up to 250 frames
every time at the framing frequency of 15 Hz.
Calibration procedure and image process
Since the angular displacement method was used in the present study to do stereoscopic image recording, the
magnification factors between the image planes and object plane are variable due to the perspective distortion. In order
to determine the local magnification factors, a calibration procedure needs to be conducted to obtain the mapping
functions between the image planes and object planes.
Following the work of Soloff et al. (1997), an in-situ calibration procedure was conducted in the present study. The insitu calibration procedure involved the acquisition of several images of a calibration target plate, say a Cartesian grid of
small dots, across the thickness of the laser sheets. Then, these images were used to determine the magnification
matrices of the image recording cameras. This technique, which determines the mapping function between the image
planes and object planes mathematically (Hill et al. 1999), therefore, takes into account the various distorting influences
between illuminated objective planes and the CCD arrays of the image recording cameras. With the mapping function
determined by this method, the stereoscopic displacement fields obtained during the experiment are readily recombined
into three-dimensional velocity vector fields (Bjorkquist, 1998).
To accomplish this in the present study, a target plate (100mm by 100mm) with 100 µm diameter dots spaced at
interval of 2.5 mm was used for the in-situ calibration. The front surface of the target plate was aligned with the center
of the laser sheet and then calibration images were obtained at three locations across the depth of the laser sheets. The
space interval between these locations was 0.5mm for the present study.
The mapping function used in the present study was taken to be a multi-dimensional polynomial, which is fourth order
for the directions paralleling the laser plane and second order for the direction normal to the laser plane, and expressed
as:
F ( x, y, z ) = a 0 + a1 x + a 2 y + a3 z + a 4 x 2 + a5 xy + a6 y 2 + a7 xz + a8 yz
+ a9 z 2 + a10 z 3 + a11 x 2 y + a12 xy 2 + a13 y 3 + a14 x 2 z + a15 xyz
+ a16 y 2 z + a17 xz 2 + a18 yz 2 + a19 x 4 + a 20 x 3 y + a 21 x 2 z 2
(1)
+ a 22 x 1 y 3 + a 23 y 4 + a 24 x 3 z + a 25 x 2 yz + a 26 xy 2 z
+ a 27 y 3 z + a 28 x 2 z 2 + a 29 xyz 2 + a30 y 2 z 2
Where the 31 coefficients a0 to a31 were determined from the calibration images by using the least square method
(Watanabe et al. 1989). The x, y directions are in the plane parallel to the laser sheet plane, while, z direction is normal
to the laser sheet plane.
The two-dimensional particle image displacements in every image planes were calculated separately by using a
Hierarchical Recursive PIV (HR-PIV) software developed in our research laboratory. The Hierarchical Recursive PIV
software is based on the hierarchical recursive processes of normal spatial correlation operation with offsetting of the
displacement estimated by the former iteration step and hierarchical reduction of the interrogation window size and
search distance in the next iteration step (Hu et al. 2000a). The multiple-correlation validation technique (Hart, 1998)
and sub-pixel interpolation treatment (Hu et al., 1998) had also been incorporated in the software. Compared with
conventional cross-correlation based PIV image processing method, the Hierarchical Recursive PIV method has the
advantages in the spurious vector suppression and spatial resolution improvement of the PIV results.
Finally, by using the mapping functions defined in equation (1) and the two-dimensional displacements in the four
stereoscopic image planes, the three components of the velocity vectors in the objective planes were reconstructed,
which is similar to the work of Bjorkquist (1998).
Lobed Jet Mixing Flow and Experiment Apparatus
In order to demonstrate its feasibility, the present dual-plane stereoscopic PIV system was used to conduct
measurement in an air jet mixing flow exhausted from a lobed nozzle. A lobed nozzle, which consists of a splitter plate
with convoluted trailing edge, had been considered to be a very promising fluid mechanic device for efficient mixing
of two co-flow streams with different velocity, temperature and/or spices (McCormick and Bennett 1994, and Belovich
and Samimy 1997). It has been paid great attention by many researchers in recent years, and has also been widely
5
applied to the aerospace engineering. For examples, for some commercial aero-engines, lobed nozzles/mixers had been
used to reduce take-off jet noise and Specific Fuel Consumption (SFC) (Preze et al. 1994). In order to reduce the
infrared radiation signals of the military aircraft to improve their survivability in the modern war, lobed nozzles had
also been used to enhance the mixing process of the high temperature and high-speed gas plume from aero-engine with
ambient cold air (Hu et al. 1999). More recently, lobed nozzles had also emerged as attractive approaches for
enhancing mixing between fuel and air in combustion chambers to improve the efficiency of combustion and reduce
the formation of pollutants (Smith et al. 1997).
The interaction of the streamwise vortices generated by lobed nozzles and spanwise vortices rolled up due to the
Kelvin-Helmholtz instability had been suggested to pay a important role for the mixing enhancement in lobed mixing
flows (McCormich and Bennett 1994, and Belovich and Samimy 1997). However, most of the previous researches
about lobed mixing flows were conducted by using Pitot probes, Laser Doppler Velocimetry (LDV) or Hot film
Anemometer (HFA). The quantitative whole-field velocity and vorticity (all three components) distributions in lobed
mixing flows had never been obtained due to the limitation of those conventional measurement techniques. The
measurement results obtained by the present dual-plane stereoscopic PIV system are expect to be the first to visualize
these vortex structures quantitatively and instantaneously.
Figure 3(a) shows the geometry parameters of the lobed nozzle used in the present study. The lobed nozzle has six
lobes. The width of each lobes is 6mm and the height of each lobe is 15mm (H=15mm). The inner and outer penetration
angles of the lobed structures are about 220 and 140 respectively. The diameters of the lobed nozzles is D=40mm.
Figure 3(b) shows the jet flow experimental rig used in the present study. The air jet was supplied by a centrifugal
compressor. A cylindrical plenum chamber with honeycomb structure in it was used to settling the airflow. Through a
convergent connection (convergent ratio is about 50:1), the airflow is exhausted from the test nozzle. All the jet supply
apparatus were installed on a two-dimensional translation mechanism so that the distance between the exit plane of the
lobed nozzle and the illuminating laser sheets can be changed by operating the two-dimensional translation mechanism.
The illumination system and image recording system are fixed during the experiment, the measurements for the
different cross planes of the lobed jet mixing flow were achieved by changing the positions of the lobed nozzle.
Therefore, all the measurements at different cross planes can be conducted just by doing the in-situ calibration
procedure one time.
The velocity of the air jet exhausting from the test nozzle can be adjusted. In the present study, the jet velocity (U0)
were set at about 20m/s. The Reynolds Number of the jet flow, based on the lobed nozzle diameter (D) and the jet
velocity is about 60,000. The thickness of the illuminating laser sheets is about 2.0mm, and the time interval between
the two laser pulsed illumination of each double pulsed Nd:YAG laser set was 30 µs .
X
Lobe trough
Lobe peak
Lobe side
D=40mm
Lobe height
Y
Z
a. the test lobed nozzle
Centrifugal compressor
Test nozzle
Cylindrical
Convergent connection
plenum chamber
Two-dimensional translation mechanism
b.air jet experimental rig
Figure 4. The the lobed nozzle and air jet experimental rig
6
A seeding generator, which is composed by an air compressor and several Laskin nozzles (Melling, 1997), was used to
generate DEHS (Di-2-EthlHexyl-Sebact) droplets as tracer particles in the jet mixing flow. The diameter of the DEHS
droplets is about 1 µm . The DESH droplets out of the seeding generator are divided into two streams; one is used to
seed the core jet flow and another for the ambient air seeding.
Experimental results and discussions
1. The separation result of the scattering lights from the two orthogonally linearly polarized laser sheets
Since the separation result of the scattering lights from the two illuminating laser sheets with orthogonal linear
polarization is directly related to the possibility of the simultaneous measurements and the measurement accuracy. A
test had been conducted in the present study to check the separation result of the scattering lights from the two
illuminating laser sheets with orthogonal linear polarization. The double-pulsed Nd:YAG laser set A and B were
controlled to fire separately, and the four CCD cameras acquired the same particle images simultaneously. When the
double-pulsed Nd:YAG laser set A was controlled to fire, the flow field was illuminated by a horizontally polarized
laser sheet (S-polarized lights). The simultaneous images detected by the four CCD cameras are shown on Figure 4.
While, when the double-pulsed Nd:YAG laser set B was controlled to fire, the flow field was illuminated by a vertically
polarized light sheet (P-polarized lights). The simultaneous particle images detected by the four CCD cameras are
shown on Figure 5.
From the comparison of the simultaneous images shown on Figure 4 and Figure 5, it can be seen that the scattering
lights from the illuminating laser sheets with orthogonal linear polarization can be separated successfully by using the
optical arrangement described in the present paper. The separation ratios of the scattering lights, which is defined as the
power ratio of the horizontal polarized lights (P-lights) transmitted through the polarizing beam splitters cube to the part
reflected by the polarized interface of the polarizer cubes or the power ratio of the horizontal polarized lights (S-lights)
reflected from the polarizer cubes to the part transmitted through the polarizer cubes, was measured by using a laser
power meter. The values are found to be about 100:1.
a. camera 1
b. camera 2
c. camera 3
d. camera 4
Figure 4. The simultaneous images acquired by the four cameras when the objective flow field was illuminated by a
vertically polarized laser sheet (S-polarized light)
a. camera 1
b. camera 2
c. camera 3
d. camera 4
Figure 5. The simultaneous images acquired by the four cameras when the objective flow field was illuminated by a
horizontally polarized laser sheet (S-polarized light)
2. The simultaneous measurement at two spatially separated planes
As described previously, by adjusting the location or angle of the Mirror in front of the double-pulsed laser set A
(Figure 1), the gap between the two paralleling laser sheets can be changed. Typical instantaneous measurement results
obtained by the present dual-plane stereoscopic PIV system at cross planes of the lobed jet mixing flow were shown on
Figure 6 and Figure 7 with the gap between the two illuminating laser sheets being 2mm.
7
From the measurement results shown on Figure 6, it can be seen that the instantaneous velocity distribution of the
lobed jet was found to have the same shape as the lobed nozzle geometry at the exit of the lobed nozzle (Z=10mm).
Based on the two simultaneous velocity fields, all the three components of the instantaneous vorticity vectors were
calculated according the following equations:
D ∂w ∂v
(
− )
U 0 ∂y ∂z
D ∂u ∂w
ϖy =
( − )
U 0 ∂z ∂x
D ∂v ∂u
ϖz =
( − )
U 0 ∂x ∂y
ϖx =
(2)
(3)
(4)
Where D is the diameter of the lobed nozzle, and U0 is the velocity of the jet flow at the test nozzle inlet. While, u,v
and w are the instantaneous velocity in X, Y and Z directions (Figure 3).
The instantaneous distributions of the voticity vector three components at Z=10mm cross plane of the lobed jet flow
were shown on Fig.6(c) and Fig.6(d) and Fig.6(e). It should be noted that a conventional one-plane stereoscopic PIV
systems just can provide one component distribution of the vorticity vectors (Z-component, with its direction normal to
the laser sheet plane) instantaneously.
For the various vortices in the lobed jet mixing flow, the six pairs of large-scale streamwise vortices generated by the
special trailing edge of the lobed nozzle can be seen clearly in the instantaneous streamwise vorticity distribution shown
on Fig. 6(e). The x-component and y-component of the vorticity vectors were used to calculate the in-plane vorticity
strength distribution (Fig.6(f)), which can indicate the behaviors of the spanwise Kelvin-Helmholtz vortices in the lobed
jet mixing flow. It can be seen that the shape of the spanwise vortex ring at the lobed nozzle exit has the same geometry
as the trailing edge of the lobed nozzle as it is expected.
The lobed jet mixing flow was found to be much more turbulent at downstream (Z=40mm, Fig. 7). Instead of the six
pairs of the large-scale streamwise vortices shown clearly at the exit plane of the lobed nozzle (Fig. 6(e)), many smallscale streamwise vortices were found to appear in the lobed jet mixing flow at this cross plane (Fig. 7(e)). The big
spanwise vortex ring (in-plane vortex ring shown on Fig. 6(f)) was also found to begin to break down into many
disconnected vortical tubes (Fig. 7(f)).
The ensemble-averaged results based on the 200 frames of the instantaneous measurement results at Z=40mm cross
plane of the lobed jet mixing flow were shown on Figure 8. Fig. 8(a) and Fig.8(b) show the ensemble-averaged velocity
distribution (U, V and W) and turbulent kinetic energy (k) distribution, which is calculated by using following
equations:
1 N
1 N
1 N
(5)
U = å u t ; V = å vt
W = å wt
N t =1
N t =1
N t =1
1
((r.m.s (u ' )) 2 + ( r.m.s (v' )) 2 + (r.m.s ( w' ) 2 )
2
1 1 N
1 N
1 N
= ( å (u t − U ) 2 + å (vt − V ) 2 + å ( wt − W ) 2 )
2 N t =1
N t =1
N t =1
k=
(6)
Where u’, v’ and w’ are turbulent velocity in X, Y and Z direction, and N=200 is frame number.
The ensemble-averaged in-plane vorticity strength and streamwise vorticity were also shown on Figure 8(c) and
Figure 8(d). It should be noted the maximum magnitudes of the ensemble-averaged vorticity (both streamwise vorticity
and in-plane (spanwise) vorticity distribution) are much smaller than that of the instantaneous values due to the
extensive mixing in the lobed jet mixing flow. In the meanwhile, the pinched-off shape of the spanwise vortex tube
suggested by McCormick and Bennett (1994) can also be found from the Fig.8(c). More detailed discussions about the
evolution and interaction of the various vortices in the lobed jet mixing flow can be available at Hu et al. (2000b).
It was well known that the cross-correlation coefficients of various flow variables are very meaningful in statistical
turbulence theory for turbulence fundamental study. Such values always can not be obtained by using conventional
stereoscopic PIV systems, which just provide measurement result at a single plane. The ensemble-averaged crosscorrelation coefficients of turbulent velocity vectors and streamwise vorticity at Z=40mm cross plane of the lobed jet
mixing flow were shown on Figure 8(e) and Figure 8(f). These cross-correlation coefficients are defined as:
Cross − R(u ' , v ' , w' ) =
=
1
N
t=N
1
N
t =100
å (u' ( x, y,40, t ) • u ' ( x, y,42, t ) + v' ( x, y,40, t ) • v' ( x, y,42, t ) + w' ( x, y,40, t ) • w' ( x, y,42, t ))
t
((u ( x, y,40, t ) − U ( x, y,40)) • (u ( x, y ,42, t ) − U ( x, y ,42))
å + (v( x, y,40, t ) − V ( x, y,40)) • (v( x, y,42, t ) − V ( x, y,42))
t
(7)
)
+ ( w( x, y,40, t ) − W ( x, y,40)) • ( w( x, y ,42, t ) − W ( x, y ,42))
1 t=N
(8)
åϖ z ( x, y,40, t ) • ϖ z ( x, y,42, t )
N t =1
By changing the gap between the two illuminating laser sheets, the spectrum profiles of the cross-correlation
Cross − R(ϖ z ) =
8
coefficients of these flow variables can be obtained.
20 m/s
20 m/s
Y
Y
20
20
Z
X
Y mm
X
0
0
-20
-20
-30
-30
-20
-20
-10
-10
0
0
a. Instantaneous result at Z=10mm plane
34
10
7
56
7 2
109
98 10
11
2 1
2
3
4
7
9
1 7
9 1820
45 6
3 3 7
65
2
9
11
4
8
1101
9
10
34
0
18
7
65
8
7
8
10
5
6
5
1
10
Y mm
56
76 2
5
6
8
5
6
7
10
7
7
45
180 76
89 11
11
7
6
6
8
78
4
9
7
11.00
9.00
7.00
5.00
3.00
1.00
-1.00
-3.00
-5.00
-7.00
-9.00
-11.00
6
-30
-40
-40
-25
0
25
50
-25
0
X mm
30
4
2
3
1
74
7
65
2
9
3
1
8
26
9
6
3
4
3
3
4
5
3
3
5 1
73
1
9 794
8 1 11
5 3 7
12
5
3
6
13
2
1
2
56 7 4
2
-20
3
4
-10
-30
4
6
4
3
2
74 8
4 6
7
4
2
-20
5
4
13 7
2
35 74
7
4 513
4
115
5
2
0
2
4
4 3
2
5.00
3.00
1.00
-1.00
-3.00
-5.00
6
4
3
3
5
-10
6
5
4
3
2
1
5
4
5
4
Y mm
4
181
106
53
4
5
9
3
23
54
3
4
6
3
2
3
10
vorticity distribution
(Z-component)
The strength of
in-plane vorticity
9
8
13 6
2
2
4
4
2
3
5
5
4
4
20
4 65
4 3 64
2
5 7
2
5
4
13
3
65
4
5 3
6
2
6
8 7 13
5
9
8163 7 1 3 2
4
2
5
3
10
50
d. instantaneous vorticity field (Y-component)
30
20
25
X mm
c. Instantaneous vorticity field (X-component)
Y mm
8
7
7
5
43 6
9
6
56
7
-20
12
11
10
9
8
7
6
5
4
3
2
1
7
190
5
11 0
12111
6
53 2
1
4
5
6
-10
89 7
8
34
56
56
6
vorticity distribution
(Y-component)
7
11
76
5
7
6
4
7 8 109
10 6
9 78 54
35 4
5
3
6
4
7
0
6
4
78
8
896
10
7
10
11.00
9.00
7.00
5.00
3.00
1.00
-1.00
-3.00
-5.00
-7.00
-9.00
-11.00
76
7
3
5
7
10
9
12
11
10
9
8
7
6
5
4
3
2
1
6
4
9 8
10
6
78
6 7
7
5
9 10
7
-30
3
9
12
11
7
65
79
1908
1 2
87 11
-10
-20
2
61
8711
12
11
98
7
6
435 12
9
0
6
5
2
583
8
10
7
65
4
4
7
4 31
6 5
4
2
53
9
6
1
42
4
20
vorticity distribution
(X-component)
7
6
5 3
8
9 7
10
4
6
3
57 6
30
5
6
3
6
4
20
Y mm
b. the simultaneous velocity field at Z=12mm cross plane
6
30
0
Y mm
Z
13
12
11
10
9
8
7
6
5
4
3
2
1
15.0
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
-30
-40
-40
-25
0
25
50
-40
X mm
-20
0
20
40
X mm
e. Instantaneous vorticity field (Z-component)
f. the strength of in-plane vorticity distribution
Figure 6. The instantaneous measurement results of the Dual-plane Stereoscopic PIV system at
Z =10mm and Z=12mm cross planes of the lobed jet mixing flow.
9
20 m/s
20 m/s
Y
Y
20
20
Z
0
X
Y mm
X
0
-20
-20
-30
-30
-20
-20
-10
-10
0
0
a. Instantaneous velocity field at Z=40mm plane
6
5
5
67
8
7
6
6
4
5
6
8
6
7
6
3 2
6
6
6
7
7
8
7
6
7
6
-30
6
7
6
7
8
7
Y mm
6
6
10
8
78
6
6
3
6
7
7
5
-40
-40
0
20
40
-40
-20
0
X mm
3
1
5
1
1
1
5
5
4
3
5
3
56
6
31
15.0
13.0
11.0
9.0
7.0
5.0
3.0
5
5
4
1
13
11
9
7
5
3
1
1
-20
1
-30
3
5
4
4
1
1
1
1
1
-10
1
5
5
5
Y mm
4
3
4
5
13
4
5
-20
1
1
5
6
5
6
3
1
1
5
1
5
0
5
5
6
4
7.0
5.0
3.0
1.0
-1.0
-3.0
-5.0
-7.0
1
35
5
6
8
7
6
5
4
3
2
1
The strength of
in-plane vorticity
3
23
-10
4 1
4
4
6
3
5
2
0
3
11
10
1 3
4
6
3
Vorticity distribution
(Z-component)
5
3
4
2
43
4
10
1
1
20
3
5
4
4
4
5
5
1
3
55
6
20
40
d. instantaneous vorticity field (Y-component)
30
1
c. Instantaneous vorticity field (X-component)
30
20
X mm
5 3
-20
13
-40
Y mm
7
6
6
7
6
8
5
11.0
9.0
7.0
5.0
3.0
1.0
-1.0
-3.0
-5.0
-7.0
-9.0
-11.0
9
8
8 9
7
8
5
8
7
9
7
-20
6
7
5
6
8
7
12
11
10
9
8
7
6
5
4
3
2
1
8
7
5
6
7
-10
5
6
4
Vorticity distribution
(Y-component)
7
-20
0
6
6
7
6
5
7
4
7
7
9
6
7
11.0
9.0
7.0
5.0
3.0
1.0
-1.0
-3.0
-5.0
-7.0
-9.0
-11.0
67
6
7
7
6
12
11
10
9
8
7
6
5
4
3
2
1
5
5
7
4
5
6
4
-10
-30
6
8
6
6
7
10
7
5
6
5
7
Vorticity distribution
(X-component)
7
8
7
8
7
10
9
6
20
6
7
5
6
5
7
5
6
7
5
7
8
7
0
7
30
20
Y mm
b. the simultaneous velocity field at Z=42mm plane
6
30
7
Y mm
Z
3
-30
4
3
-40
3
-40
-40
-20
0
20
40
-40
X mm
-20
0
20
40
X mm
e. Instantaneous vorticity field (Z-component)
f. the strength of in-plane vorticity distribution.
Figure 7. The instantaneous measurement results of the Dual-plane Stereoscopic PIV system at Z =40mm and Z=42mm
cross planes of the lobed jet mixing flow.
10
40
40
1
3
30
3
2
2
3
2
a. ensemble-averaged velocity distribution
4
-20
0
3
20
40
60
b. ensemble-averaged turbulent kinetic energy distribution
40
2
7
5
5
7
1
5
0
7
5
-30
5
20
40
-40
-40
60
-20
0
20
60
d. ensemble-averaged streamwise vorticity distribution
40
2
5
3
1
2
2
20
24
46
3
-30
1
23
1
2
0
3
3
2
1
2
2
2
Y mm
2
1
1 2
3
5
4
1
4
4
1 5
7
1
-20
3
1
5
4
1
1
2
3
-10
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
1
2
1
31
4
5
1
2
1
9
8
7
6
5
4
3
2
1
3 42
1
1
4
5
1
2
-20
1
-30
1
1
-20
0
2
2
2
4
4
9
15
3
5
3
6
4
1
10
8.50
7.50
6.50
5.50
4.50
3.50
2.50
1.50
cross-correlation values
of streawise vorticity
2
-10
53
3 1
8
7
6
5
4
3
2
1
2
5
2
4
1
2
1
1
3
4
2 3
2
3 3
5
2
4
5
13
cross-correlation values
of turbulent velocity vectors
1 2
3
2
5
20
4
2
2
3
6
2
3
2
3 2
2
20
1
1
42
2
3
30
1 2
12
1
3
1
1
30
1
40
-40
-40
40
X mm
c. ensemble-averaged in-plane vorticity strength distribution
0
6
4
X mm
10
3.00
2.33
1.67
1.00
0.33
-0.33
-1.00
-1.67
-2.33
-3.00
7
3
5
3
8
69
5
2
1
7
24
5
5
6
4
1
3
4
5
3 1
5
Y mm
-20
6
1
3
5
5
6
31
1
-20
10
9
8
7
6
5
4
3
2
1
5
65
4
7
0
2
1
4
5 6
4
5
2
8
4
3
5
-10
4
2
7
ensemble-averaged streamwise
vorticity distribution
6
6
1
7 5132
8
2
-30
5
10
5.00
4.75
4.50
4.25
4.00
3.75
3.50
3.25
3.00
2.75
2.50
5
32
1
3
4
7
2
1
3
2
11
10
9
8
7
6
5
4
3
2
1
6
3
41
3
1 42
2
3
-40
-40
2
6
4
-20
4
1
6
8
1
1
2
-10
ensemble-averaged in-plane
vorticity strength distribution
1
3
8
1
6
4
2
5
3 1
4
5 7 11 9
63
2
20
3
2
7
5
6
4
21
4
4
30
4
2
2
20
10
3
28
1
65 4
1
6
1
4
35 7
2
8
6
30
Y mm
1
2
X mm
40
Y mm
3
2
-40
-40
60
2
4
2
-30
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
21
X mm
0
3
1
8
7
6
5
4
3
2
1
2
3
1
1
5
3
4
4
4
12 1
5
2
Y mm
Y mm
4
1
40
6
4
6
20
4
6
-10
-20
2
0
2
3
1
3
3
-20
0
1
3
-40
-40
3
1
Turbulent kinetic energy
2
-30
4
5
10
3
-20
4
4 3
4
-10
1
5
5 4
0
2
20
2
10
2
1
2
W m/s
18.0
17.0
16.0
15.0
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
20
2
10 m/s
2
30
1
40
-40
-40
60
X mm
-20
0
20
40
60
X mm
e. cross-correlation coefficeints of turbulent velocity vectors
f. cross-correlation coefficeints of streamwise vorticity
Figure 8. The ensemble-averaged values of the dual-plane steroscopic PIV measurement results
at Z=40mm cross plane of the lobed mixing flow
The auto-correlation coefficients measurement with two illuminating laser sheets overlapped at a same plane
The temporal resolution of conventional PIV systems is limited to the framing rate of the cameras used for PIV image
recording. Such limitation is much more serious for the PIV systems with high-resolution digital cameras. For example,
the frame rate of a 1K by 1K pixel camera is always about 15Hz and much lower for the cameras with higher resolution.
Therefore, a conventional PIV system is typically insufficient to record time sequences in rapidly evolving or turbulent
flows. Therefore, only time-averaged quantities, such as the mean velocity and Reynolds stress, can be obtained to
characterize the flow unsteadiness.
11
30
30
10 m/s
20
20
W m/s
20.00
18.00
16.00
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0
-10
0
-10
-20
-20
-30
-30
0
20
40
-40
-20
0
20
X mm
5
5
4
4
75
4
5
3
4
20
2
1
5
1
3
4
3
2
1
1
3
2
1
2
2
6
3
3
3
Y mm
1
2
1
3
1
2
4
1
2
2
1
53
2
1
3
1
3
1
1
43
1
1
2
3
2 2
1
2
1
1
2
3
4
1
2
Y mm
2
6
5
4
3
2
1
12.00
10.00
8.00
6.00
4.00
2.00
1
-30
-40
1
2
1
1
1
3
2
3
3
1
2
1
3
4
1
-30
3
1
-10
-20
3
1
3
1
2
0
2
2
1
1
2
1
2
1
-20
3
1
3 2
2
12
-10
32
3 3
2
1
4
2
1
1 4
auto-correlation distribution
of streamwise vorticity field
3 1
2
10
13.00
11.00
9.00
7.00
5.00
3.00
2
4
1
2
0
2
3
6
5
4
3
2
1
4
2
3
1 2
40
2
2
2
1
2
1
2 3
5
1
3
20
3
2
10
1
auto-correlation distribution
of turbulent velocity field
1
2
1
3
2
2
3
53
1
1
1
34
6
2
3
Y mm
5
5
5
3
3
4
6
7
0
d. streamwsie vorticity distribution at time t=T0+0.1ms
1
2
2
4
X mm
30
20
6
5
5
-20
40
c. streamwsie vorticity distribution at time t=T0
2
7.0
5.0
3.0
1.0
-1.0
-3.0
-5.0
-7.0
5
20
8
7
6
5
4
3
2
1
5
4
X mm
30
4
4
1
5
5
3
4
4
4
5
5
5
5
4
5
5
6
5 4
5
5
4
1
54
5
3
4
5
3
6
4
4
4
4
0
3
5
45
5
4
4
-20
5
4
3 4
5
3
5
-30
-20
5
4
6
4
3
5
5
4
3
-10
5
5
4
5
5
2 4
3
0
5
2
4
-30
-40
streamwise vorticity
4
5
43
3
4
6
3
Y mm
5
4
3
4
5
4
5
5
7.0
5.0
3.0
1.0
-1.0
-3.0
-5.0
-7.0
4
4
5
4
5
5
4
5
4
4
6
4
6
4
4
5
4
5
5 6
5
4
8
7
6
5
4
3
2
1
56
10
3
5
5
-10
-20
4
4
2
4
5
6
4
5
4
5
5 4
3
streamwise vorticity
4
3
0
5
4
4
4
5
5
20
4
4
43
4
10
4
3
5
3
5
2
20
6
64
30
5
5
3
4
4
4
45
6
30
b. instantaneous velocity field at time t=T0+0.1ms
5
2
5
a. instantaneous velocity field at time t=T0
2
40
X mm
4
-20
4
-40
W m/s
20.00
18.00
16.00
14.00
12.00
10.00
8.00
6.00
4.00
2.00
10
Y mm
10
Y mm
10 m/s
3
1
1
-40
-20
0
20
40
60
X mm
-20
0
20
40
60
X mm
e. auto-correlation coefficents of the turbulent velocity vectors
f. auto-correlation coefficents of the streamwsie vorticity
Figure 9. The measurement results of the Dual-plane Stereoscopic PIV system at same cross plane (Z=40mm plane) of
the lobed jet mixing flow with 0.1ms delay between the two measurements
The limitation of the slow framing rate of image recording camera can be over-passed by the present dual-plane
stereoscopic PIV system. By adjusting the two illuminating laser sheets overlapped at the same plane, the flow field can
be measured synchronously at variable separation times up to µs order. The temporal auto-correlation functions of the
flow variables (such as velocity and vorticity) can be obtained by measuring the velocity field at time t and t+ τ , where
τ is varied to any delay amount. Figure 9(a) and 9(b) show the instantaneous measurement results of the present dualplane stereoscopic PIV system at the same cross plane (Z=40mm) of the lobed jet mixing flow with the time delay ( τ )
12
between two measurements being 100 µs . The streamwise vorticity fields derived from the two instantaneous velocity
fields are given on Fig 9(c) and Fig. 9(d).
Following the definition of Lourenco et al.(1998), the ensemble-averaged auto-correlation coefficient of the flow
variable X is calculated by using following equation:
1 N −1
(9)
Auto − R( X ) = å X n ( x, y , z, t ) • X n ( x, y, z , t + τ )
N n =0
Where N is the repeated number of the individual measurement, and N=200 in the present paper.
The auto-correlation values of the flow field parameters (such as velocity and vorticity) are the functions of the
variable lag τ . The ensemble-averaged auto-correlation coefficient of the turbulent velocity vectors and the streamwise
vorticity were shown on the Fig. 9(e) and Fig.9 (f) with τ =100 µs . By changing the time delay between the two
measurements, the auto-correlation spectrum of these flow variables can be obtained.
The comparison of the simultaneous measurement results of the present dual-plane stereoscopic PIV system with
LDV measurement results
For the accuracy evaluation of a stereoscopic PIV system, Lawson and Wu (1997a,b) introduced a geometric error
model for the error analysis of stereoscopic PIV systems based on the parallel projection assumption. The effect of
system parameters like the position and view angle of the image recording cameras on the error ratio of stereoscopic
PIV results, which was defined as the ratio of the out-of-plane velocity component to the in-plane component, was
discussed theoretically. Bjorkquist (1998) measured the parallel translation movement of a rigid body and get a
conclusion of that the absolute measurement error of his stereoscopic PIV measurement is less than 0.3%. However,
since the movements in fluid flow include not only parallel translation but also rotation and shear. So, the result just
based on the parallel translation measurement of a rigid body is not sufficient for the accuracy evaluation of a
stereoscopic PIV system for fluid flow measurement. Hill et al. (1999) compared the ensemble-averaged values of their
stereoscopic PIV measurement results in a cylindrical Couette flow with theoretical predictions and reported that the
differences between their stereoscopic PIV measurement results and theoretical values is less than 1%. Abe et al.
(1999) evaluated their stereoscopic PIV system by the comparison of the stereoscopic PIV measurement results with a
conventional 2-D PIV system.
In the present paper, the measurement results of the present dual-plane stereoscopic PIV system were compared with
the simultaneous measurement results of a LDV system. Both the instantaneous data and ensemble-averaged values of
the stereoscopic PIV measurement and LDV measurement were compared quantitatively to evaluate the accuracy level
of the present dual-plane stereoscopic PIV system.
The LDV system used in the present study is a two dimensional system, which was composed by an Argon Laser
(1.5W), a LDV optical unit (TSI TRCF2), a signal processing system (TSI IFA750) and a Synchronizer Control System
(TSI Datalink DL4). In order to achieve the simultaneous measurement as the dual-plane stereoscopic PIV system, the
synchronizer of the LDV system was connected with the synchronizer system of the present dual-plane stereoscopic
PIV system. The pulsed signals generated by the stereoscopic PIV synchronizer system, which were used to trigger the
illumination system and image recording system for stereoscopic PIV measurement, were also output to the
synchronizer of the LDV system for LDV measurement.
Two pairs of the laser beams (green and blue beams) were used to conduct the LDV measurements. The wavelength
of the green beams of the LDV system is 545.5and 488nm for the blue beams. In order to avoid the effect of the LDV
laser beams on the image recording of the dual-plane stereoscopic PIV system, sharp bend pass filters (only 532nm
pass) were installed in the heads of the CCD cameras of the dual-plane stereoscopic PIV system.
Before conducting the quantitative comparison of the stereoscopic PIV measurement results with LDV simultaneous
measurement results, both the spatial-resolution and temporal-resolution of the two systems should be discussed firstly.
Since the stereoscopic PIV system and the LDV system were operated in simultaneous measurement mode, which was
controlled the synchronizer system of the stereoscopic PIV system, the temporal-resolution of the LDV measurement
and stereoscopic PIV measurement is assumed to be same. As mentioned above, the thickness of the illuminating laser
sheets of the present dual-plane stereoscopic PIV system is about 2.0mm and 32 by 32 pixel interrogation windows
were used to conduct cross-correlation PIV image processing. The image resolution captured by image recording
cameras is about 80 µm / pixel . So, the spatial resolution of the present stereoscopic PIV measurement is about
2.5mm × 2.5mm × 2.0mm. The spatial-resolution of a LDV system is closely related with the diameter of the laser
beams for the LDV measurement. For the present LDV system, the spatial-resolution is about 65.3 µm (laser beam
diameter and also volume diameter) × 0.68mm (volume length).
The spatial resolution difference between the stereoscopic PIV system and the LDV system may result in the
differences between the stereoscopic PIV measurement results and LDV measurement results since the cut-off scale of
the turbulent motion is different. However, the effect of the spatial resolution difference between the stereoscopic PIV
system and LDV system is consider to be negligible in the present study since the comparison points are selected on the
center line of the lobed jet flow (point A(0,0,20) and point B(0,0,40)).
Two steps of the comparison test had been conducted in the present paper. Firstly, only one of the double-pulsed
Nd:YAG laser sets was controlled to fire, the dual-plane stereoscopic PIV system works as a conventional single-plane
13
stereoscopic PIV system. The instantaneous values of the simultaneous measurements from the dual-plane stereoscopic
PIV system and the LDV system were shown on Figure 10(a). Then, both of the double pulsed laser sets were
controlled to fire simultaneously, the comparison of the simultaneous measurement results were shown on Figure 10(b).
Based on the 200 instantaneous data of the simultaneous measurements, the ensemble-averaged values and deviation of
the out-of-plane velocity component were listed on Table 1.
It can be seen that, the simultaneous measurement results of the stereoscopic PIV system and LDV system agree with
each other well for both of the instantaneous data and ensemble-averaged values. For the ensemble-averaged values of
the out-of plane velocity component, the difference between the stereoscopic PIV measurement and LDV measurement
were found to be less than 2%. Since the scattering lights from the two orthogonally linearly polarized laser sheets were
separated successfully, the measurement accuracy of the dual-plane stereoscopic system was not affected by the
simultaneous illumination of the two laser sheets.
20
Velocity (m/s)
15
V-SPIV
W-SPIV
W-LDV
V-LDV
10
5
0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
-5
time (s)
a. One laser sheet on and the other off
20
Velocity (m/s)
15
V-SPIV
10
W-SPIV
W-LDV
V-LDV
5
0
0.00
-5
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
time (s)
b. Two laser sheets illuminate the flow field simultaneously
Figure 10. The instantaneous data of the simultaneous measurement results at comparison point B (0,0,40) obtained by
the dual-plane stereoscopic PIV system and the LDV system
Table 1: The comparison of the ensemble-averaged values of the steroscopic PIV measurement results with LDV results
Stereoscopic PIV measurement
LDV measurement results
Results
Deviation of the
EnsembleDeviation of
EnsembleWSPIV –WLDV
out-of-plane
averaged
the out-ofaveraged
velocity
out-of-plane
plane velocity
out-of-plane
component
Velocity
component
Velocity
STD(W)
W (m/s)
STD(W)
W(m/s)
Point A
17.271
0.600
16.973
0.640
0.298
(0,0,20)
(1.7%)
One laser sheet on
the other off
Point B
17.220
0.889
16.930
0.844
0.290
(0,0,40)
(1.7%)
Point A
17.126
0.581
16.904
0.509
0.222
Two laser sheets
(0,0,20)
(1.3%)
on simultaneously
Point B
17.213
1.006
16.864
0.856
0.349
(0,0,40)
(2.0%)
14
Summary and Conclusions
The technical basis and system set-up of a dual-plane stereoscopic PIV system, which can provide flow velocity (all
three components) fields at two spatially separated planes simultaneously, were described in the present paper. The
simultaneous measurement were achieved by using two orthogonally linearly polarized laser sheets to illuminate the
fluid flow at two spatially separated planes simultaneously. The scattering lights from the two illuminating laser sheets
with orthogonal linear polarization were recorded separately by high-resolution CCD cameras with polarizing beam
splitter cubes. Unlike conventional single-plane PIV systems, which just can obtain the one-component of the vorticity
vectors instantaneously, the present dual-plane stereoscopic PIV system can provide all three components of the
vorticity vectors and various auto-correlation and cross-correlation coefficients of flow variables instantaneously and
simultaneously.
The present dual-plane stereoscopic PIV system was used to conduct measurement in an air jet flow exhausted from a
lobed nozzle to demonstrate its feasibility. The evolution and interaction of the various vortices in the lobed jet mixing
flow were visualized quantitatively and instantaneously from the measurement results of the present dual-plane
stereoscopic PIV system.
In order to evaluate its measurement accuracy, the measurement results of the present dual-plane stereoscopic PIV
system were compared with the simultaneous measurement results of a LDV system. It was found that both the
instantaneous data and ensemble-averaged values of the simultaneous measurement results agree with each other well.
For the ensemble-averaged values of the out-of plane velocity component at comparison points, the difference between
the stereoscopic PIV and LDV measurement results is found to be less than 2%.
Acknowledgements
The authors wish to thank Mr. S. Segawa of Institute of Industrial Science, University of Tokyo for their helps in
conducting the present study.
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