Experiments in Fluids 31 (2001) 277±293 Ó Springer-Verlag 2001
Dual-plane stereoscopic particle image velocimetry: system set-up
and its application on a lobed jet mixing flow
H. Hu, T. Saga, T. Kobayashi, N. Taniguchi, M. Yasuki
Abstract The technical basis and system set-up of a dualplane stereoscopic particle image velocimetry (PIV)
system, which can obtain the ¯ow velocity (all three components) ®elds at two spatially separated planes simultaneously, is summarized. The simultaneous measurements
were achieved by using two sets of double-pulsed Nd:Yag
lasers with additional optics to illuminate the objective
¯uid ¯ow with two orthogonally linearly polarized laser
sheets at two spatially separated planes, as proposed by
Kaehler and Kompenhans in 1999. The light scattered by
the tracer particles illuminated by laser sheets with orthogonal linear polarization were separated by using polarizing beam-splitter cubes, then recorded by high-resolution
CCD cameras. A three-dimensional in-situ calibration
procedure was used to determine the relationships between
the 2-D image planes and three-dimensional object ®elds
for both position mapping and velocity three-component
reconstruction. Unlike conventional two-component PIV
systems or single-plane stereoscopic PIV systems, which
can only 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 coef®cients of ¯ow
variables instantaneously and simultaneously. The present
dual-plane stereoscopic PIV system was applied to measure an air jet mixing ¯ow exhausted from a lobed nozzle.
Various vortex structures in the lobed jet mixing ¯ow were
revealed quantitatively and instantaneously. In order to
evaluate the measurement accuracy of the present dualplane stereoscopic PIV system, the measurement results
were compared with the simultaneous measurement results of a laser Doppler velocimetry (LDV) system. It was
found that both the instantaneous data and ensembleaveraged values of the stereoscopic PIV measurement
results and the LDV measurement results agree 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%.
1
Introduction
As a non-intrusive whole ¯ow ®eld measuring technique,
particle imaging velocimetry (PIV) has matured from a
developmental stage to a reliable ¯ow velocity ®eld measuring method in the past two decades. At its current
stage, the application of the PIV technique touches upon
almost all ¯uids-related ®elds, ranging from the fundamental ¯uid mechanical study of shear ¯ow and turbulent
transition to the engineering ®eld of turbo-machinery,
automobile and aircraft designing.
The ``classical'' PIV technique is a two-component, twodimensional (2C-2D) measuring technique, which is only
capable of obtaining two components of the ¯ow velocity
vector in the plane of illuminating laser sheet. The out-ofplane component of the velocity vector is lost, while the inplane components are affected by an unrecoverable error
due to the perspective transformation (Prasad and Adrian
Received: 18 April 2000/Accepted: 2 February 2001
1993).
Recent advances in the PIV technique have been diH. Hu (&)1, T. Saga, T. Kobayashi, N. Taniguchi
rected towards obtaining all three-components of ¯uid
Institute of Industrial Science, University of Tokyo
Roppongi 7-22-1, Minato-Ku, Tokyo 106-8558, Japan
velocity vectors in a plane or in a volume simultaneously
e-mail: huhui@egr.msu.edu
to allow the application of the PIV technique to more
complex ¯ow phenomena. Several advanced PIV methods
M. Yasuki
or techniques have been developed successfully in recent
Industrial Instruments Department, Seika Corporation
years, which include the 3C-3D PIV techniques such as the
1-5-3 Koraku, Bunkyo-ku, Tokyo, Japan
holographic PIV (HPIV) method and three-dimensional
1
(3-D) particle tracking velocimetry (3D-PTV) method, and
Present address:
Turbulent Mixing and Unsteady Aerodynamics Laboratory
3C-2D PIV technique such as the stereoscopic PIV (SPIV)
A22, Research Complex Engineering
method used in the present study.
Michigan State University, East Lansing, MI 48824, USA
HPIV (Barnhart et al. 1994; Zhang et al. 1997) utilizes
the holography technique for PIV recording, which enThe authors wish to thank Mr. T. Higashiyama of Kanomax Corp. ables the measurement of three components of velocity
vectors throughout a volume of ¯uid ¯ow. Of the existing
and Mr. S. Segawa of the Institute of Industrial Science,
3-D PIV methods, holography is capable of the highest
University of Tokyo, for their help in conducting the present
study.
measurement precision (Willert 1997). However, HPIV
277
278
is also the most complex and requires a signi®cant
investment in equipment and the development of advanced data-processing techniques. Continuing efforts and
development are still needed to make the HPIV technique
to be a practical PIV technique for ¯uid ¯ow diagnostics.
The 3D-PTV technique (Nishino et al. 1989; Virant &
Dracos 1997; Suzuki 1999) always uses three cameras to
record the positions of the tracer particles in the
measurement volume from three different observation
directions. Through 3-D image reconstruction, the locations of the tracer particles in the measurement volume are
determined. By using particle-tracking operation, the 3-D
displacements of the tracer particles are calculated. However, the particle-tracking method provides velocity vectors that are randomly distributed in space. Furthermore,
most of the particle tracking algorithms rely on the assumption that nearest neighboring images belong to the
same particles, and this is not valid if the particle image
density becomes too high. So, the particle tracking methods are normally limited to relatively low particle image
density. Hence, it always provides poor spatial resolution
and the small-scale vortices and turbulent structures in the
¯ow ®eld cannot always be identi®ed successfully from the
3-D PTV results due to their poor spatial resolution.
The stereoscopic PIV technique is a most straightforward and easily accomplished method for the measurement of the three velocity components in the illuminating
laser sheet plane. It always uses two cameras at different
view axes or offset distance to carry out stereoscopic image
recording. By performing the view reconstruction, the
corresponding image segments in the two views are matched to get three components of the ¯ow velocity vectors.
Compared with the 3-D PTV method mentioned previously, the stereoscopic PIV measurement results have
much higher in-plane spatial resolution, which can provide several thousand vectors in one plane similar to the
conventional 2-D PIV measurement results.
The time-resolved velocity ®eld of the PIV measurement results together with its derivatives can help us to
understand the physics of ¯ows. However, the conventional stereoscopic PIV measurement results within one
single plane often do not yield enough information to
determine all velocity-based terms in the ¯uid governing
equations (such as Navier±Stokes equations) that summarize our ¯uid-mechanical knowledge (Kaehler and
Kompenhans 1999). For most vortex ¯ows, such as jet
mixing ¯ows, the vorticity vector (all three components)
®eld is a very important quantity for evaluating the evolution and interaction of various vortices and the coherent
structures in vortex ¯ows, besides the velocity ®elds. In the
statistical theory of turbulence, the spatial and temporal
correlation terms of ¯uid variables such as velocity, together with the spectra of the ¯uctuations, are very important for the development of turbulence models. Such
information about the ¯uid ¯ows cannot always be obtained from the conventional stereoscopic PIV measurement results, which were obtained only at one single plane
of the objective ¯uid ¯ow.
In the present paper, the technical basis and system
set-up of a dual-plane stereoscopic PIV system will be
described, which can obtain the velocity (all three com-
ponents) and the vorticity (all three components) ®elds of
the ¯uid ¯ows at two spatially separated planes simultaneously and instantaneously. By adjusting the gap between
the two illuminating laser sheets or/and the time interval
between the light pulses properly, the distributions of
various spatial or/and temporal correlation coef®cients of
¯ow variables can also be obtained from the measurement
results of the present dual-plane stereoscopic PIV system.
It should be mentioned that the present study uses the
same polarization direction separation method as Kaehler
and Kompenhans (1999) used to perform the scattered
light separation. The optical arrangement of the illumination system and stereoscopic PIV image recording
system of the present dual-plane stereoscopic PIV are also
quite similar to the so-called ``multiple-plane stereo PIV
system'' developed by Kaehler and Kompenhans (1999).
In contrast to the 2-D calibration method used by Kaehler
and Kompenhans (1999), a general 3-D in-situ calibration
procedure (Soloff et al. 1997) was used in the present
study to determine the relationships between the 3-D
objective ®elds and the two-dimensional (2-D) image
planes. For the 2-D calibration used by Kaehler and
Kompenhans (1999), mapping functions are sought only
to relate each 2-D image planes to the 2-D objective
plane. For the velocity three-component reconstruction,
the recording geometric quantities, such as separation
between lenses, objective distance, the angular orientation
of the camera axis to the object plane and so on, are still
required as inputs explicitly in the reconstruction equations (Willert 1997). It should be noted that these quantities pertaining to the recording geometry may be
dif®cult to measure accurately and may introduce errors.
Furthermore, if recording is accomplished through a
liquid±air interface, the reconstruction equations will
need to be modi®ed to account for the refraction at the
interface. The 3-D in-situ calibration method used in the
present study can incorporate all the parameters of system geometry and optical arrangement automatically and
do not need any explicit input for both position mapping
and velocity three-component reconstruction.
The present dual-plane stereoscopic PIV system was
applied to conduct measurements in an air jet ¯ow exhausted from a lobed nozzle to demonstrate its feasibility.
The evolution and interaction of various vortices in the
lobed jet mixing ¯ow were revealed quantitatively and
instantaneously from the measurement results. In order to
evaluate the measurement accuracy level of the dual-plane
stereoscopic PIV system, quantitative comparison of the
measurement results of the present dual-plane stereoscopic PIV system with the simultaneous measurement
results of a laser Doppler velocimetry (LDV) system was
also conducted in the present study.
2
The technical basis and system set-up
of the dual-plane stereoscopic PIV system
2.1
The methods for the scattered light separation
It is obvious that the key point for the simultaneous
stereoscopic PIV measurements at two spatially separated
planes is to record the tracer particle images in each illuminated plane separately. Since the two measured planes
are illuminated simultaneously, without any special arrangement, the scattered light from the two illuminated
planes will be incident upon the same image recording
camera simultaneously, which will blur the particle images
and make simultaneous measurement impossible.
In order to separate the scattered light into different
components, two methods can be used, which are referred
to as the color separation method and the polarization
direction separation method. If the two measured planes
are illuminated by using laser sheets with different colors
(wavelengths), the scattered light of particles in the two
laser light sheets can be separated successfully by using
optical ®lters, which is transmissible for the desired color
(wavelength). The polarization direction separation
method is the method of illuminating the ¯ow ®eld by
using laser sheets with orthogonal linear polarization directions. By using polarizing beam splitters, the scattered
light from the tracer particles in the two laser light sheets
can also be separated.
In the color separation method, two kinds of lasers are
always required to generate laser beams with different
wavelengths or to make some optical arrangement modi®cations inside the laser head to generate different harmonic light from the same laser (such as a Nd:YAG laser)
to illuminate the objective ¯ow ®eld. It should be noted
that using different harmonic light from the same Nd:YAG
laser always results in energy loss. Compared with the
color separation method, the polarization direction separation method has the advantage of simple optical
arrangement, which can be achieved easily by installing
some optics outside the laser head. The polarized direction
separation method was used in the present study, as in
Kaehler and Kompenhans (1999), to perform the simultaneous stereoscopic PIV measurement at two spatially
separated planes.
2.2
Illumination system
Two sets of widely used double-pulsed Nd:YAG lasers
(New Wave, 50 mJ/pulse) with additional 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 in Fig. 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
®gure.
Each of the two double-pulsed Nd:YAG laser sets is
composed of two laser tubes with various optics installed
in a laser head unit. The wavelength of the laser beams
from laser tubes 1, 2, 3 and 4 is 1,064 nm (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 halfwave plate 5a and 5b shown in the Fig. 1. Then they are
combined with the vertically polarized laser beams from
laser tubes 1 and 3 through polarizers 7a and 7b. The
horizontally polarized laser beams (P-polarized light) pass
through polarizers 7a and 7b. While the vertically polarized light (S-polarized light) from laser tubes 1 and 3 is
re¯ected by mirrors 6a and 6b to be incident upon
polarizers 7a and 7b at the Brewster angle. The combined
beams pass through half-wave plates 8a and 8b, then go
into second harmonic generator (SHG) cells for polarization direction and wavelength adjustments. The laser
beams out of the SHG cells have a wavelength of 532 nm
(the second harmonic light of the fundamental wavelength
1,064 nm) and identical linear polarization direction
(vertical direction).
The vertically polarized laser beams from the doublepulsed Nd:YAG laser set B are turned into horizontally
polarized light (P-polarized light) by passing 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 light) transmit
through the polarizer cube 13, while the vertical polarized
light (S-polarized light) from the double-pulsed Nd:YAG
laser set A is re¯ected by polarizer cube 13. By adjusting
the angle and/or the location of mirror 12, the laser beams
from laser set A and laser set B can be overlapped or not.
Passing through cylindrical lens 14 and re¯ected by mirror
15, the laser beams are expanded into two paralleling laser
sheets with orthogonal linear polarization to illuminate the
studied ¯ow ®eld at two spatially separated planes or
overlapped at one plane.
2.3
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 highresolution cross-correlation CCD cameras (1K ´ 1K, TSI
PIVCAM 10-30) were used in the present study to perform
stereoscopic PIV image recording. The two pairs of crosscorrelation cameras were settled on an optical table with a
pair of polarizing beam-splitter cubes and two high-re¯ectivity mirrors installed in front of the cameras to separate the scattered light from the two illuminating laser
sheets with orthogonal linear polarization.
For the stereoscopic image recording, two basic approaches ± the lens translation method and the angular
displacement method ± are commonly used. 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. 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 in the present paper takes
advantage of the angular displacement method with the
Scheimp¯ug condition (Prasad and Jensen 1995) to obtain
focused particle images everywhere in the image plane.
The distances between the illuminating laser sheets and
image recording planes of the CCD camera are about
650 mm, and the angles between the view axials of the
cameras are about 50°. The schematic diagram and the
279
280
Fig. 1. a The schematic diagram of the
illumination system. b Photograph of the
illumination system
photograph of the image recording system for the present
dual-plane stereoscopic PIV system are shown in Fig. 2.
The illuminating laser sheets with orthogonal linear
polarization are scattered by the tracer particles seeded
in the objective ¯uid ¯ow. The scattered light from the
horizontally polarized laser sheet (P-polarized light) will
pass straight through the polarizing beam-splitter cubes
and is detected by cameras 3 and 4. The scattered light
from the vertically polarized laser sheet (S-polarized light)
will emerge from the polarizing beam-splitter cubes at
right angles to the incident direction. Before entering the
lens of the cameras 1 and 2, the S-polarized light emerging
from the polarizing beam-splitter cubes is re¯ected by two
mirrors to achieve the identical orientation in all four
image planes. Such an arrangement may simplify the
matching of the four observation views and may save CPU
281
Fig. 2. a The schematic diagram of the
image recording system. b Photograph of
the image recording system
time for the PIV image processing. In order to improve the
image quality, the surface of each polarizing beam-splitter
cube in which no light scattered by tracer particles and
needed for PIV image recording enters or leaves is covered
by light absorbing material.
The host computer is composed of two high-speed CPU
(450 MHz, Pentium III CPU), image memory (1 Gb RAM)
and hard disk (100 Gb). It can acquire the continuous
stereoscopic PIV image pairs up to 250 frames at a framing
frequency of 15 Hz.
2.4
Synchronizer and host computer
The above illumination system and image recording
system are connected with a host computer via a
synchronizer system (Fig. 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.
2.5
Calibration procedure and image process
Since the angular displacement method was used in the
present study to do stereoscopic image recording, the
magni®cation factors between the image planes and object
plane are variable due to the perspective distortion. In
order to determine the local magni®cation factors, a calibration procedure needs to be conducted to obtain the
mapping functions between the image planes and object
¯ow ®elds.
282
Kaehler and Kompenhans (1999) and Kaehler (2000)
used a 2-D calibration-based reconstruction method suggested by Willert (1997) to get the mapping function between the image plane and object plane in their ``multiple
plane stereo PIV system''. As summarized by Prasad
(2000), the 2-D calibration method can do position mapping between the image planes and the object plane
without requiring any knowledge of the recording
geometry. However, for the ®nal step of the velocity threecomponent reconstruction, the system geometric parameters, such as separation between lenses, objective
distance, the angular orientation of the camera axis to the
object plane and so on, are required as explicit inputs in
the reconstruction equations given in Willert (1997).
However, the quantities pertaining to the recording geometry may be dif®cult to measure accurately, and could
introduce errors. Furthermore, if recording is accomplished through a liquid±air interface, the reconstruction
equations may need to be modi®ed to account for refraction at the interface.
Following the work of Soloff et al. (1997), a 3-D calibration procedure was conducted in the present study. The
3-D calibration procedure involved the acquisition of images of a calibration target plate, say a Cartesian grid of
small dots, not only at one location as in the 2-D calibration method, but at several locations across the thickness of the laser sheets. Then these images were used to
determine the magni®cation matrices of the image recording cameras. This technique, which determines the
mapping functions between the 2-D image planes and 3-D
object ®elds mathematically, therefore takes into account
the various distorting in¯uences between the test section
and the CCD arrays of the image recording cameras. Since
the 3-D in-situ calibration method can incorporate all the
parameters of system geometry and optical arrangement
automatically, it does not need any explicit input for
both position mapping and velocity three-component
reconstruction.
The general relationship between the 3-D object ®elds
(x, y, z) and the 2-D image recording planes (X(1), Y(1))
and (X(2), Y(2)) is assumed to be described by a general
mapping function:
where
c†
rF†i;j ˆ
c†
oFi
c†
ˆ Fi;j
oxj
where i ˆ 1, 2 and j ˆ 1, 2, 3. Then,
1 0
0
1
1†
1†
1†
1†
F1;1 F1;2 F1;3 0
DX
1
1
C B
B
1†
1†
1† C Dx1
B
1† C
B
C
F
F
F
B DX2 C B 2;1
2;2
2;3 C@
A
Cˆ
B
2†
2†
2† C Dx2
B DX …2† C B
F
F
F
@
A
1;1
1;2
1;3
@ 1 A
Dx3
2†
2†
2†
2†
F2;1 F2;2 F2;3
DX
4†
5†
2
The required 3-D displacements are determined from
this ®nal expression. It should be noted that the above
expression provides four equations for three unknowns,
which can be solved by using a least-squares approach
(Soloff et al. 1997).
To accomplish this in the present study, a target plate
(100 mm ´ 100 mm) with 100-lm-diameter dots spaced
at intervals 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
0.5 mm for the present study.
The mapping function used in the present study was
taken to be a multidimensional polynomial, which is
fourth order for the directions paralleling the laser sheet
plane and second order for the direction normal to the
laser sheet plane, and expressed as:
F…x; y; z†
ˆ a0 ‡ a1 x ‡ a2 y ‡ a3 z ‡ a4 x2 ‡ a5 xy ‡ a6 y2 ‡ a7 xz
‡ a8 yz ‡ a9 z2 ‡ a10 x3 ‡ a11 x2 y ‡ a12 xy2 ‡ a13 y3
‡ a14 x2 z ‡ a15 xyz ‡ a16 y2 z ‡ a17 xz2 ‡ a18 yz2
‡ a19 x4 ‡ a20 x3 y ‡ a21 x2 z2 ‡ a22 x1 y3 ‡ a23 y4
‡ a24 x3 z ‡ a25 x2 yz ‡ a26 xy2 z ‡ a27 y3 z ‡ a28 x2 z2
‡ a29 xyz2 ‡ a30 y2 z2
6†
The 31 coef®cients a0 to a31 were determined from the
calibration images by using the least squares method
(Watanabe et al. 1989). The x, y directions are in the plane
where c ˆ 1,2 for the left and right image recording
parallel to the laser sheet plane, while the z direction is
camera, and i ˆ 1,2,3 for the x, y, z directions in the
normal
to the laser sheet plane.
objective ®eld.
The
2-D
particle image displacements in every image
The particle image displacement in each image
planes
were
calculated separately by using a hierarchical
recording planes can be given by
recursive PIV (HR-PIV) software (Hu et al. 2000b) develDX …c† ˆ F …c† …x ‡ Dx† F …c† …x†
2† oped by our research laboratory. The HR-PIV software is
based on the hierarchical recursive processes of normal
Performing a Taylor series expansion of above equation spatial correlation operation with offsetting of the disand volume averaging over the interrogation cell, the ®rst- placement estimated by the former iteration step and hiorder relationship between an image plane displacement erarchical reduction of the interrogation window size and
c†
on camera c, DXi and object plane displacement, Dxj can search distance in the next iteration step. The multiplecorrelation validation technique (Hart 1998) and sub-pixel
be expressed as
interpolation with 2-D Gaussian ®t curve (Hu et al. 1998)
have also been incorporated in the software. Compared
c†
c†
DXi  rFi;j …x†Dxj
3† with the conventional cross-correlation based PIV image
X …c† ˆ F …c† …xi †
1†
processing method, the hierarchical recursive PIV method
has the advantages in spurious vector suppression and
spatial resolution improvement of the PIV results.
Finally, by using the mapping functions de®ned in
Eq. (6) and the 2-D displacements in the two image planes,
the three components of the velocity vectors in the objective planes were reconstructed by solving the equations
given in Eq. (5).
3
Lobed jet mixing flow and experimental apparatus
In order to demonstrate its feasibility, the present dualplane stereoscopic PIV system was used to conduct measurement in an air jet mixing ¯ow exhausted from a lobed
nozzle. A lobed nozzle, which consists of a splitter plate
with convoluted trailing edge, is considered to be a very
promising ¯uid mechanic device for ef®cient mixing of
two co-¯ow streams with different velocity, temperature
and/or species (McCormick and Bennett 1994; Belovich
and Samimy 1997). Lobed nozzles have been given a great
deal of attention by many researchers in recent years, and
have also been widely applied to aerospace engineering.
For example, for some commercial aero-engines, lobed
nozzles have been used to reduce both take-off jet noise
and speci®c fuel consumption (SFC) (Presz et al. 1994). In
order to reduce the infrared radiation signals of the military aircraft, lobed nozzles have also been used to enhance
the mixing process of the high temperature and highspeed gas plume from aero-engines with ambient cold air
(Hu et al. 1999). More recently, lobed nozzles have also
emerged as attractive approaches for enhancing mixing
between fuel and air in combustion chambers to improve
the ef®ciency 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 has been suggested to pay
a important role in mixing enhancement in lobed mixing ¯ows (McCormich and Bennett 1994; Belovich and
Samimy 1997). However, most of the previous work on
lobed mixing ¯ows was conducted using pitot probes, LDV
or a hot ®lm anemometer (HFA). Due to the limitation of
those conventional measurement techniques, the quantitative whole-®eld velocity and vorticity distributions in
lobed mixing ¯ows have never been obtained until the
recent work of the authors (Hu et al. 2000a, c).
In the earlier work of the authors (Hu et al. 2000a, c),
both planar laser induced ¯uorescence (LIF) and PIV
techniques were used to study lobed jet mixing ¯ows in a
water channel. By using the directly perceived LIF ¯ow
visualization images and quantitative velocity, vorticity
and turbulence intensity distributions of PIV measurement results, the evolution and interaction characteristics
of the various vortical and turbulent structures in the
lobed jet mixing ¯ows were discussed.
Since the PIV measurement results reported in the
earlier work of the authors was obtained by using a conventional 2-D PIV system, it only provided the two components of the velocity vectors in the plane of the laser
sheet and one component of the vorticity vector normal to
Fig. 3. a The test lobed nozzle used
in the present study. b Experimental rig
used in the present study
283
284
the laser sheet plane. The measurement results obtained by
the present dual-plane stereoscopic PIV system are likely
to be the ®rst to provide all three components of the velocity and vorticity ®elds of the lobed jet mixing ¯ows
instantaneously and simultaneously.
Figure 3a shows the geometry parameters of the lobed
nozzle used in the present study. The lobed nozzle has six
lobes. The width of each lobe is 6 mm and the height of
each lobe is 15 mm (H ˆ 15 mm). The inner and outer
penetration angles of the lobed structures are about 22°
and 14° respectively. The diameter D of the lobed nozzles
is 40 mm.
Figure 3b shows the jet ¯ow experimental rig used in
the present study. The air jet was supplied by a centrifugal compressor. A cylindrical plenum chamber with
honeycomb structures in it was used for settling the
air¯ow. Through a convergent connection (convergent
ratio is about 50:1), the air¯ow is exhausted from the test
nozzle. All the jet supply apparatus was installed on a 2D translation mechanism so that the distance between the
exit plane of the lobed nozzle and the illuminating laser
sheets could be changed by operating the 2-D translation
mechanism. The illumination system and image recording system were ®xed during the experiment. The measurements for the different cross planes of the lobed jet
mixing ¯ow were achieved by changing the positions of
the lobed nozzle. Therefore, all the measurements can be
conducted by doing the in-situ calibration procedure
only once.
The velocity of the air jet exhausting from the test
nozzle was adjustable. In the present study, the jet velocity (U0) was set at about 20 m/s. The Reynolds number of the jet ¯ow, based on the lobed nozzle diameter
(D) and the jet velocity was about 60,000. The thickness
of the illuminating laser sheets was about 2.0 mm, and
the time interval between the two laser pulsed illumination of each double pulsed Nd:YAG laser set was settled
as 30 ls.
A seeding generator, which is composed by an air
compressor and several Laskin nozzles (Melling 1997), was
used to generate 1-lm DEHS (di-2-ethlhexyl-sebact)
droplets as tracer particles in the jet mixing ¯ow. The
seeding DEHS droplet ¯ow from the seeding generator
were divided into two streams; one is used to seed the core
jet ¯ow and another for the ambient air seeding.
Fig. 4a±d. The simultaneous images acquired by the four cameras when the ¯ow ®eld was illuminated by using a vertically
polarized laser sheet (S-polarized light): a camera 1; b camera 2;
c camera 3; d camera 4
4
Experimental results and discussions
4.1
The separation result of the scattered light from
the two orthogonally linearly polarized laser sheets
Since the separation result of the scattered light from the
two illuminating laser sheets with orthogonal linear polarization is directly related to the possibility of the simultaneous measurements and the measurement accuracy
of the simultaneous measurement results, a test was conducted in the present study to check the separation result
of the scattered light from the two illuminating laser sheets
with orthogonal linear polarization. In order to show the
separation results more clearly, only the core jet ¯ow was
Fig. 5a±d. The simultaneous images acquired by the four cameras when the ¯ow ®eld was illuminated by using a horizontally
polarized laser sheet (P-polarized light): a camera 1; b camera 2;
c camera 3; d camera 4
seeded with DEHS droplets. The double-pulsed Nd:YAG
laser sets A and B were controlled to ®re separately, and
the four CCD cameras acquired the same particle images
simultaneously. When the double-pulsed Nd:YAG laser set
A was controlled to ®re, the ¯ow ®eld was illuminated by a
the special trailing edge of the lobed nozzle can be seen
clearly in the instantaneous streamwise vorticity distribution shown in Fig. 6e. The x and y components of the
vorticity vectors were used to calculate the in-plane vorticity strength distribution (Fig. 6f), which can indicate the
behaviors of the spanwise vortices in the lobed jet mixing
¯ow. 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.
The lobed jet mixing ¯ow was found to be much more
turbulent further downstream (Z ˆ 40 mm, Fig. 7). Instead of the six pairs of large-scale streamwise vortices
shown clearly at the exit plane of the lobed nozzle
(Fig. 6e), many small-scale streamwise vortices were
found to appear in the lobed jet mixing ¯ow at this cross
plane (Fig. 7e). The big spanwise vortex ring (in-plane
vortex ring shown in Fig. 6f) was also found to begin to
break down into many disconnected vortical tubes
(Fig. 7f).
The ensemble-averaged results based on the 200 frames
of instantaneous measurement results of the lobed jet
mixing ¯ow at Z ˆ 40 mm cross plane are shown in
Figure 8a, and Fig. 8b shows the ensemble-averaged ve4.2
locity distribution (U, V and W) and turbulent kinetic
The simultaneous measurement at two spatially
energy (k) distribution, which is calculated by using folseparated planes
As described previously, by adjusting the location or angle lowing equations:
of the mirror in front of the double-pulsed laser set A
N
N
N
1X
1X
1X
(Fig. 1), the gap between the two paralleling laser sheets
Uˆ
ut ; V ˆ
vt ; W ˆ
wt …10†
can be changed. Typical instantaneous measurement reN tˆ1
N tˆ1
N tˆ1
sults obtained by the present dual-plane stereoscopic PIV
1
system at cross planes of the lobed jet mixing ¯ow are
k ˆ ‰…rms…u0 †Š2 ‡ ‰rms…v0 †Š2 ‡ ‰rms…w0 †2 Š
2"
shown in Figs. 6 and 7, with a gap between the centers of
N
N
the two illuminating laser light sheets of 2 mm.
1 1X
1X
ut U†2 ‡
vt V†2
ˆ
From the measurement results shown in Fig. 6, it can be
2
N
N
tˆ1
tˆ1
seen that the instantaneous velocity distribution of the
#
lobed jet was found to have the same shape as the lobed
N
X
1
nozzle geometry at the exit of the lobed nozzle
11†
‡
wt W†2
N tˆ1
(Z ˆ 10 mm). Based on the two simultaneous velocity
®elds, all three components of the instantaneous vorticity
where u¢, v¢ and w¢ are turbulent velocities in the X, Y and
vectors were calculated using the following equations:
Z directions, and N ˆ 200 is the frame number.
D ow ov
The ensemble-averaged in-plane vorticity strength and
7†
-x ˆ
streamwise vorticity are also shown in Fig. 8c and d. It
U0 oy oz
should be noted the maximum magnitudes of the ensemD ou ow
8† ble-averaged vorticity [both streamwise vorticity and in-y ˆ
U0 oz ox
plane (spanwise) vorticity distribution] are much smaller
than that of the instantaneous values due to the extensive
D ov ou
9† mixing in the lobed jet mixing ¯ow. Meanwhile, the pin-z ˆ
U0 ox oy
ched-off shape of the spanwise vortex tube suggested by
where D is the diameter of the lobed nozzle, and U0 is the McCormick and Bennett (1994) can also be found from
velocity of the jet ¯ow at the test nozzle inlet, while, u, v Fig. 8c.
and w are the instantaneous velocity in the X, Y and Z
It is well known that the cross-correlation coef®cients of
directions (Fig. 3).
various ¯ow variables are very meaningful in statistical
The instantaneous distributions of the three vorticity
turbulence theory. Such values cannot be obtained by
vector components at Z ˆ 10 mm cross plane of the lobed using conventional stereoscopic PIV systems, which projet ¯ow are shown in Fig. 6c±e. It should be noted that
vide measurement results only at a single plane. The enconventional 2-D PIV systems and one-plane stereoscopic semble-averaged cross-correlation coef®cients of turbulent
PIV systems only can provide the normal component
velocity vectors and streamwise vorticity at the
distribution of the vorticity vectors (-z ) instantaneously. Z ˆ 40 mm cross plane of the lobed jet mixing ¯ow are
For the various vortices in the lobed jet mixing ¯ow, the shown in Fig. 8e and f. These cross-correlation coef®cients
six pairs of large-scale streamwise vortices generated by are de®ned as:
vertically polarized laser sheet (S-polarized light). The simultaneous images detected by the four CCD cameras are
shown in Fig. 4. When the double-pulsed Nd:YAG laser set
B was controlled to ®re, the ¯ow ®eld was illuminated by a
horizontally polarized light sheet (P-polarized light). The
simultaneous particle images detected by the four CCD
cameras are shown in Fig. 5.
From the comparison of the simultaneous images
shown in Figs. 4 and 5, it can be seen that the scattered
light 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 ratio of the scattered light, which is de®ned
as the power ratio of the horizontally polarized light
(P-light) transmitted through the polarizing beam-splitter
cube to the part re¯ected by the polarized interface of the
polarizer cubes or the power ratio of the vertically polarized light (S-light) re¯ected from the polarizer cubes to the
part transmitted through the polarizer cubes, was measured by using a laser power meter. The value is found to
be about 100:1.
285
286
Fig. 6a±f. The typical instantaneous measurement results of the
dual-plane stereoscopic PIV system at the Z ˆ 10 mm and
Z ˆ 12 mm cross planes of the lobed jet mixing ¯ow: a instantaneous result at Z ˆ 10 mm cross plane; b simultaneous velocity
®eld at Z ˆ 12 mm cross plane; c instantaneous vorticity ®eld
(X component); d instantaneous vorticity ®eld (Y component);
e instantaneous vorticity ®eld (Z component); f strength of
in-plane vorticity distribution
287
Fig. 7a±f. The typical instantaneous measurement results of the
dual-plane stereoscopic PIV system at Z ˆ 40 mm and
Z ˆ 42 mm cross planes of the lobed jet mixing ¯ow: a instantaneous velocity ®eld at Z ˆ 40 mm cross plane; b simultaneous
velocity ®eld at Z ˆ 42 mm cross plane; c instantaneous vorticity
®eld (X component); d instantaneous vorticity ®eld (Y component); e instantaneous vorticity ®eld (Z component); f strength of
in-plane vorticity distribution
288
Fig. 8a±f. The ensemble-averaged values of the dual-plane
stereoscopic PIV measurement results at Z ˆ 40 mm cross plane
of the lobed mixing ¯ow: a ensemble-averaged velocity distribution; b ensemble-averaged turbulent kinetic energy distribution;
c ensemble-averaged in-plane vorticity strength distribution;
d ensemble-averaged streamwise vorticity distribution; e crosscorrelation coef®cients of turbulent velocity vectors; f crosscorrelation of streamwise vorticity
R…u0 ; v0 ; w0 †
tˆN
1X
ˆ
f‰u0 …x; y; 40; t† u0 …x; y; 42; t†Š ‡ ‰v0 …x; y; 40; t† v0 …x; y; 42; t†Š ‡ ‰w0 …x; y; 40; t† w0 …x; y; 42; t†Šg
N t
8
9
‰u…x;
y;
40;
t†
U…x;
y;
40†Š
‰u…x;
y;
42;
t†
U…x;
y;
42†Š
>
>
tˆN <
=
1X
‡‰v…x; y; 40; t† V…x; y; 40†Š ‰v…x; y; 42; t† V…x; y; 42†Š
ˆ
12†
>
N t >
:
;
‡‰w…x; y; 40; t† W…x; y; 40†Š ‰w…x; y; 42; t† W…x; y; 42†Š
Cross
Cross
R…-z † ˆ
tˆN
1X
-z …x; y; 40; t† -z …x; y; 42; t†
N tˆ1
13†
By changing the gap between the two illuminating laser
sheets, the spectrum pro®les of the cross-correlation
coef®cients of these ¯ow variables can be obtained.
4.3
The auto-correlation coefficient measurement with two
illuminating laser sheets overlapped at the same plane
The temporal resolution of conventional PIV systems is
limited to the framing rate of the cameras used for PIV
image recording. This limitation is much more serious for
the PIV systems with high-resolution digital cameras. For
example, the frame rate of a 1K ´ 1K-pixel camera is always about 15 Hz and much lower for the cameras with
higher resolution. A conventional PIV system is typically
insuf®cient to record time sequences in rapidly evolving or
turbulent ¯ows. Therefore, only time-averaged quantities,
such as the mean velocity and Reynolds stress, can be
obtained to characterize the ¯ow unsteadiness.
In order to improve the temporal resolution of the PIV
results, several techniques have been proposed in recent
years (Lecordier and Trinite 1999; Whybrew et al. 1999;
Zhang 1999). The dual-plane stereoscopic PIV system
described in the present paper provides a new method of
overcoming the limitation of the slow framing rate of the
image recording camera to improve the temporal resolution of the PIV results. By adjusting the two illuminating
laser sheets to overlap at the same plane, the ¯ow ®eld can
be measured synchronously at variable separation times up
to microsecond order. The temporal auto-correlation
functions of the ¯ow variables (such as velocity and
vorticity) can be obtained by measuring the velocity ®eld at
time t and t + s, where s is varied to any delay amount.
Figure 9a and b shows the instantaneous measurement
results of the present dual-plane stereoscopic PIV system at
the same cross plane (Z ˆ 40 mm) of the lobed jet mixing
¯ow, with a time delay (s) between two measurements of
100 ls. The streamwise vorticity ®elds derived from the
two instantaneous velocity ®elds are given in Fig. 9c and d.
Following the de®nition of Lourenco et al. (1998), the
ensemble-averaged auto-correlation coef®cient of the ¯ow
variable X is calculated by using following equation:
N 1
1X
Auto R…X† ˆ
Xn …x; y; z; t† Xn …x; y; z; t ‡ s†
N nˆ0
14†
where N is the repeated number of the individual measurement, and N ˆ 200 in the present paper.
The auto-correlation values of the ¯ow ®eld parameters
(such as velocity and vorticity) are the functions of the
variable lag s. The ensemble-averaged auto-correlation
coef®cient of the turbulent velocity vectors and the
streamwise vorticity are shown in Fig. 9e andf with
s ˆ 100 ls. By changing the time delay between the two
measurements, the auto-correlation spectrum of these ¯ow
variables can be obtained.
4.4
The comparison of the simultaneous measurement
results of the present dual-plane stereoscopic
PIV system with LDV measurement results
For the accurate 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 such as the position and view angle of
the image recording cameras on the error ratio of stereoscopic PIV results, which was de®ned as the ratio of the
out-of-plane velocity component to the in-plane component, was discussed theoretically. Bjorkquist (1998) discussed the measurement accuracy of his stereoscopic PIV
system by measuring the parallel translation movement of
a rigid body. It should be noted that, since the movements
in ¯uid ¯ow include not only parallel translation but also
rotation and shear motion, the discussion based only on
the parallel translation measurement of a rigid body is not
suf®cient for the accurate evaluation of a stereoscopic PIV
system for ¯uid ¯ow measurement. Hill et al. (1999)
compared the ensemble-averaged values of their stereoscopic PIV measurement results in a cylindrical Couette
¯ow with theoretical predictions and reported that the
differences between their stereoscopic PIV measurement
results and theoretical values is less than 1%. Abe et al.
(2000) evaluated their stereoscopic PIV system by comparing the stereoscopic PIV measurement results with a
conventional 2-D PIV system.
In the present paper, the measurement results of the
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 2-D
system, composed of an argon laser (1.5 W), a LDV optical
289
290
Fig. 9a±f. The measurement results of the dual-plane stereoscopic PIV system at same cross plane (Z ˆ 40 mm plane) of
the lobed jet mixing ¯ow with 0.1 ms delay between the two
measurements: a instantaneous velocity ®eld at time t ˆ T0;
b instantaneous velocity ®eld at time t ˆ T0 + 0.1 ms; c stream-
wise vorticity distribution at time t ˆ T0; d streamwise vorticity
distribution at time t ˆ T0 + 0.1 ms; e auto-correlation coef®cients of turbulent velocity vectors; f auto-correlation coef®cients
of streamwise vorticity
Fig. 10. The schematic set-up for the LDV and dual-plane
stereoscopic PIV simultaneous measurement
unit (TSI TRCF2), a signal processing system (TSI IFA750)
and a synchronizer control system (TSI Datalink DL4). In
order to achieve the simultaneous measurement with the
dual-plane stereoscopic PIV system, the synchronizer of
the LDV system was connected to 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.
Figure 10 shows the system set-up for the LDV and dualplane stereoscopic PIV simultaneous measurement schematically.
Two pairs of laser beams (green and blue beams) were
used to conduct the LDV measurements. The wavelength
of the green beams of the LDV system is 488 nm and of the
blue beams 545.5 nm. In order to avoid the effect of the
LDV laser beams on the image recording of the dual-plane
stereoscopic PIV system, sharp band pass ®lters (only
532 nm 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. Since the stereoscopic PIV system and the LDV
system were operated in simultaneous measurement
mode, which was controlled by the synchronizer system of
the stereoscopic PIV system, the temporal resolution of the
LDV measurement and stereoscopic PIV measurement is
the same. As mentioned above, the thickness of the illuminating laser sheets of the present dual-plane stereoscopic PIV system is about 2.0 mm and 32 ´ 32-pixel
interrogation windows were used to conduct cross-correlation PIV image processing. The image resolution captured by the image recording cameras is about 80 lm/
pixel. So, the spatial resolution of the present stereoscopic
PIV measurement is about 2.5 mm ´ 2.5 mm ´ 2.0 mm.
The spatial-resolution of a LDV system is closely related to
the diameter of the laser beams for the LDV measurement.
For the present LDV system, the spatial-resolution is about
65.3 lm (laser beam diameter and also volume diameter) ´ 0.68 mm (volume length).
The spatial resolution difference between the stereoscopic PIV system and the LDV system may result in
Fig. 11a, b. 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: a one laser sheet on
and the other off; b two laser sheets illuminate the ¯ow ®eld simultaneously
291
Table 1. The comparison of the ensemble-averaged values of the stereoscopic PIV measurement results with LDV results
Stereoscopic PIV measurement results
LDV measurement results
Ensemble-averaged
out-of-plane
velocity
W (m/s)
Deviation of the
out-of-plane
velocity
component
STD (W)
Ensembleaveraged out-ofplane velocity
W (m/s)
Deviation of
the out-of-plane
velocity
component
STD (W)
WSPIV±WLDV
One laser sheet on
the other off
Point A
(0,0,20)
Point B
(0,0,40)
17.271
0.600
16.973
0.640
0.298 (1.7%)
17.220
0.889
16.930
0.844
0.290 (1.7%)
Two laser sheets
on simultaneously
Point A
(0,0,20)
Point B
(0,0,40)
17.126
0.581
16.904
0.509
0.222 (1.3%)
17.213
1.006
16.864
0.856
0.349 (2.0%)
292
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 centerline of the lobed jet ¯ow
[point A(0,0,20) and point B(0,0,40)].
Two steps of the comparison test were conducted in the
present paper. First, only one of the double-pulsed
Nd:YAG laser sets was controlled to ®re; the dual-plane
stereoscopic PIV system works as a conventional singleplane stereoscopic PIV system. The instantaneous values
of the simultaneous measurements from the dual-plane
stereoscopic PIV system and the LDV system are shown in
Fig. 11a. Then, both of the double pulsed laser sets were
controlled to ®re simultaneously; the comparison of the
simultaneous measurement results is shown in Fig. 11b.
Based on the 200 instantaneous data of the simultaneous
measurements, the ensemble-averaged values and
deviation of the out-of-plane velocity component are listed
in Table 1.
It can be seen that, the simultaneous measurement results
of the stereoscopic PIV system and LDV system agree well
with each other for both 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 was found to be less than 2%. Since the scattered
light from the two orthogonally linearly polarized laser
sheets was separated successfully, the measurement accuracy of the dual-plane stereoscopic system was not affected
by the simultaneous illumination of the two laser sheets.
laser sheets to illuminate the ¯uid ¯ow at two spatially
separated planes simultaneously. The scattered light
from the illuminated particles with orthogonal linear
polarization was recorded separately by high-resolution
CCD cameras with polarizing beam-splitter cubes.
Unlike conventional single-plane PIV systems, which can
only obtain 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 coef®cients of ¯ow variables instantaneously and
simultaneously.
The present dual-plane stereoscopic PIV system was
used to conduct measurement in an air jet ¯ow exhausted
from a lobed nozzle to demonstrate its feasibility. The
evolution and interaction of the various vortices in the
lobed jet mixing ¯ow 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 well with
each other. 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 was found to be less than 2%.
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