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Simultaneous Measurement of All the Three Components of VorticityVectors 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, Japan2. Industrial Instruments Department, SEIKA CORPORATION, 1-5-3 Koraku, Bunkyo-ku, Tokyo Japan3. Fluid Measuring Instrument Division, KANOMAX JAPAN, INC., 3-18-20 Nishishinjyuku, Tokyo160, JapanE-mail: [email protected] or [email protected]
Abstract The technical basis and system set-up of a dual-plane stereoscopic PIV system, which can obtain the flow velocity (allthree components) fields at two spatially separated planes simultaneously, was described in the present paper. Thesimultaneous measurements were achieved by using two sets of double-pulsed Nd:Yag lasers with other optics toilluminate the objective fluid flow with two orthogonally linearly polarized laser sheets at two spatially separatedplanes. The scattering lights from the two illuminating laser sheets with orthogonal linear polarization were separatedby using polarizing beam splitter cubes, then recorded by high-resolution CCD cameras. Unlike conventional two-dimensional PIV systems or single-plane stereoscopic PIV systems, which can just get one-component of vorticityvectors, the present dual-plane stereoscopic PIV system can provide all the three components of the vorticity vectorsand 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 lobednozzle to demonstrate its feasibility. In order to evaluate the measurement accuracy of the present dual-planestereoscopic PIV system, the measurement results of the present dual-plane stereoscopic PIV system were comparedwith the simultaneous measurement results of a LDV system. It was found that both the instantaneous data andensemble-averaged values of the stereoscopic PIV measurement results and the LDV measurement results agree witheach other well. For the ensemble-averaged values of the out-of plane velocity component at comparison points, thedifferences 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 flowvariables, Polarization separation of laser beams, Lobed jet mixing flow.
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c. Instantaneous streamwise vorticity field d. instantaneous in-plane vorticity distributionFigure 6. Typical simultaneous measurement results of the Dual-plane Stereoscopic PIV system
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Introduction As a non-intrusive whole field measuring technique, Particle Imaging Velocimetry (PIV) can offer many advantagesfor 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 orthree-dimensional flow field instantaneously and quantitatively without disturbing the flow, which are very useful andnecessary for the research of flow mechanism, in particular for the study of unsteady flow and complex flowphenomena. The "classical" PIV technique, which uses a single camera oriented orthogonally to the illuminated plane, is just a two-dimensional velocity measurement technique. It is only capable of recording the two dimensional projections of thethree-dimensional velocity on the plane of the laser sheet, i.e the out-of-plane velocity component is lost, while the in-plane components are affected by an unrecoverable error due to the perspective transformation errors (Prasad andAdrian 1993). For highly three-dimensional flows, this can lead to substantial measurement error of the local flowvelocity vectors. Recent advances in PIV technique have been directed towards obtaining the all three-components of fluid velocityvectors in a plane or in a volume simultaneously to allow the application of PIV technique to more complex flowphenomena. 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 Particle-Tracking Velocimetry (3D-PTV) method (Nishio et al., 1989) and Stereoscopic PIV (SPIV) method to be discussed inthe present study. Holographic PIV (HPIV) utilizes holography technique to do PIV recording, which enables the measurement of threecomponents 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 complexand requires a significant investment in equipment and the development of advanced data processing techniques. Thecontinuous efforts and developments still need to make the HPIV technique to be a practical tool for the fluid flowdiagnostics. 3D-PTV technique always uses three cameras to record the positions of the tracer particles in a measurement volumefrom three different view directions (Nishio et al. 1989 and Suzuki et al. 1999). Through three-dimensional imagereconstruction, the locations of the tracer particles in the measurement volume are determined. By using particle-tracking operation, the three dimensional displacements of the tracer particles in the measurement volume arecalculated. 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 velocityvectors 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 successfullyfrom 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 threecomponents measurement in the illuminating laser sheet plane. It always uses two cameras at different view axis oroffset distance to do stereoscopic image recording. By doing the view reconciliation, the corresponding image segmentsin the two views are matched to get three components of the flow velocity vectors. Compared with 3-D PTV methodmentioned above, the stereoscopic PIV measurement results have much higher spatial resolution. The measurementresults of a stereoscopic PIV system always can provide several thousand vectors in the illuminated plane, which is asthe same as conventional 2-D PIV measurement results. However, the conventional stereoscopic PIV measurement results within one single plane often yields not enoughinformation to answer the fluid governing equations (such as Navier-Stokes equations) that summarized our fluid-mechanical knowledge. In the meanwhile, for most of the vortex flows like jet mixing flows, vorticity vector (all threecomponents) field is another very important quantity to evaluate the evolution and interaction of various vortices andthe coherent structures in the vortex flows besides the velocity vector. In the statistical theory of turbulence, the spatialand temporal correlation terms of the fluid variables like velocity together with the spectrums of the fluctuations arevery important for the development of turbulence models. Such information about the fluid flows always can not beobtained from the conventional stereoscopic PIV measurement results, which were obtained at one single plane of theobjective fluid flow.
In the present paper, the development of a dual-plane stereoscopic PIV system will be described, which can obtainthe velocity (all three components) and vorticity (all three components) vector fields of fluid flows at two spatialseparated planes simultaneously and instantaneously. By adjusting the gap between the two illuminating laser sheetsor/and the time interval between the two plane measurements, the distributions of various spatial or/and temporalcorrelation coefficients of flow variables can also be obtained from the measurement results of the present dual-planestereoscopic PIV system.
The present dual-plane stereoscopic PIV system was applied to conduct measurement in an air jet flow exhaustedfrom a lobed nozzle to demonstrate its feasibility. The evolution and interaction of the various vortices in the lobed jetmixing flow was visualized quantitatively. In order to evaluate the measurement accuracy level of the dual-planestereoscopic PIV system, the quantitative comparison of the measurement results of the present dual-plane stereoscopicPIV system with the simultaneous measurement results of a LDV system had also been conducted in the present study.
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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 planesis to record the images of tracer particles in each illuminated plane separately. Since the two measured planes areilluminated simultaneously, without any special arrangement, the scattering lights from the two illuminated planes willbe incident upon the same image recording camera simultaneously, which will blur the particle images and make thesimultaneous 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 colorseparation method and polarization direction separation method. If the two measured planes are illuminated by usinglaser sheets with different color (wavelength), the scattering lights from the two illuminating laser sheets can beseparated successfully by using different optical filters, which are transmissible for one light and are not transmissiblefor the other. The polarization direction separation method is the method to illuminate the flow field by using lasersheets with orthogonal linear polarization directions. By using polarizing beam splitters, the scattering lights from thetwo 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 differentwavelength or to make some optical arrangement modifications inside the laser head to generate different harmoniclight of the same laser to illuminate the objective flow field. Compared with the color separation method, polarizationdirection separation method has the advantage of simple optical arrangement, which can be achieved easily by installingsome optics outside the laser head. As the same as Kahler and Kompenhans (1999), the polarized direction separationmethod was used in the present study to do the simultaneous stereoscopic PIV measurement at two spatially separatedplanes.
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a. Schematic setup of the illumination system b. Photograph of the illumination systemFigure 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 setsof widely used double-plused Nd:YAG lasers (New Wave, 50mJ/pulse) with optics were used in the present study to setup the illumination system of the present dual-plane stereoscopic PIV system. A schematic diagram and photograph ofthe illumination system are shown on Figure 1. In order to indicate the linear polarization direction changing of the laserbeams clearly, the optical arrangement inside the heads of the two double-pulsed Nd:YAG laser sets is also shown in thefigure. Each of the two double-pulsed Nd:YAG laser (New Wave Laser) set is composed of two laser tubes with various
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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 polarizedlaser beams from laser tube 2 and laser tube 4 are turn into horizontally polarized laser beams (H) by passing half-waveplate 5a and 5b shown in the Figure 1. Then, they are combined with the vertically polarized laser beams from lasertube 1 and 3 through Polarizers 7a and 7b. The horizontally polarized laser beams (P-polarized lights) pass through thePolarizers 7a and 7b. While, the vertically polarized light (S-polarized lights) from laser tube 1 and 3 reflected by mirror6a and 6b to be incident upon the Plolarizers 7a and 7b at the Brewster angle. The combined P-polarized beams and S-polarized beams pass through half wave plates 8a and 8b, then go into SHG (Second Harmonic Generator) cells forpolarization direction and wavelength adjustments. The laser beams out of the SHG cells have the wavelength of the532nm (the second harmonic light of the fundamental wavelength 1064nm). The linear polarization direction of all thelaser beams out of the SHG cells are vertical again. Reflected by mirror sets of 9a-10a and 9b-10b, the output laserbeams from the double-pulsed Nd:YAG laser set A and B have same linear polarization direction, which is vertical. Thewavelength 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 polarizedlights (P-polarized lights) by passing the half wave plate 11 before they are combined with the laser beams from thedouble-pulsed Nd:YAG laser set A. The horizontal polarized laser beams ( P-polarized lights) transmit through thePolarizer cube 13. While, the vertical polarized lights (S-polarized lights) from the double-pulsed Nd:YAG laser set Aare reflected by the Polarizer cube 13. By adjusting the angular and the location of the mirror 12, the laser beams fromthe 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 thestudied flow field at two spatially separated planes or overlapped at one plane.
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a. Schematic setup of the image recording system b. Photograph of the image recording systemFigure 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 sheetswith orthogonal linear polarization, two pairs of high-resolution cross-correlation CCD cameras (1k by 1k, TSIPIVCAM 10-30) were used in the present study to do stereoscopic PIV image recording. The two pairs of the cross-correlation cameras were settled on an optical table with a pair of polarizing beam splitter cubes and two highreflectivity mirrors installed in front of the cameras to separate the scattering lights from the two illuminating lasersheets with orthogonal linear polarization. For the stereoscopic image recording, two basic approaches are commonly used, which are lens translation method andangular displacement method. In the lens translation method, the image recording cameras are placed side by side withthe image plane parallel to the object plane. While in the angular displacement method, the recording cameras view thesame region of interest from an angle and the image planes are rotated with respect to the object plane. The detaileddiscussion about the two arrangement methods can be found in Willert (1997), Bjorkquist (1998), Poser et al.(1999) andAikislar et al. (1999). The work described here takes advantage of angular displacement method with scheimpflugcondition (Prasad and Jensen, 1995) to obtain focused particle images everywhere in the image plane. The schematicdiagram and the photograph of the image recording system for the present dual-plane stereoscopic PIV system areshown on the Figure 2.
The illuminating laser sheets with orthogonal linear polarization are scattered by the tracer particles seeded in theobjective fluid flow. The scattering lights from the horizontally polarized laser sheet (P-polarized lights) will passstraight through the polarizing beam-splitter cubes to be detected by cameras 3 and 4. The scattering lights from thevertically polarized laser sheet (S-polarized lights) will emerge from the polarizing beam splitter cubes at the rightangles to the incident lights. Before entering the lens of the cameras 1 and 2, the S-polarized lights emerging from thepolarizing beam splitter cubes are reflected by two mirrors to achieve the identical orientation of the image planes forthe two camera pairs. Such arrangement may simplify the matching of the four observation views and save CPU time
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for the PIV image processing. In order to improve the image quality, the surface of each polarizing beam splitter cube inwhich no lights scattered by tracer particles and needed for PIV image recording enters or leaves is covered by lightabsorbing material, which is as the same as Kahler and Kompenhans (1999).
Synchronizer and host computerThe 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 pulsedNd:YAG laser sets and the image recording camera pairs can be programmed to operate simultaneously or separatelywith desired time intervals.
The host computer is composed of two high-speed CPU (750mHZ, Pentium III CPU), colossal image memory andHard disk (2GB RAM, Hard Disk 200GB). It can acquire the continuous stereoscopic PIV image pairs up to 250 framesevery 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, themagnification factors between the image planes and object plane are variable due to the perspective distortion. In orderto determine the local magnification factors, a calibration procedure needs to be conducted to obtain the mappingfunctions 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 in-situ calibration procedure involved the acquisition of several images of a calibration target plate, say a Cartesian grid ofsmall dots, across the thickness of the laser sheets. Then, these images were used to determine the magnificationmatrices of the image recording cameras. This technique, which determines the mapping function between the imageplanes and object planes mathematically (Hill et al. 1999), therefore, takes into account the various distorting influencesbetween illuminated objective planes and the CCD arrays of the image recording cameras. With the mapping functiondetermined by this method, the stereoscopic displacement fields obtained during the experiment are readily recombinedinto three-dimensional velocity vector fields (Bjorkquist, 1998). To accomplish this in the present study, a target plate (100mm by 100mm) with 100 mµ diameter dots spaced atinterval of 2.5 mm was used for the in-situ calibration. The front surface of the target plate was aligned with the centerof the laser sheet and then calibration images were obtained at three locations across the depth of the laser sheets. Thespace 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 orderfor the directions paralleling the laser plane and second order for the direction normal to the laser plane, and expressedas:
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zxayxaxayzaxzazyaxyzazxayaxyayxazazayzaxzayaxyaxazayaxaazyxF
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(1)
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 normalto the laser sheet plane. The two-dimensional particle image displacements in every image planes were calculated separately by using aHierarchical Recursive PIV (HR-PIV) software developed in our research laboratory. The Hierarchical Recursive PIVsoftware is based on the hierarchical recursive processes of normal spatial correlation operation with offsetting of thedisplacement estimated by the former iteration step and hierarchical reduction of the interrogation window size andsearch 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 withconventional cross-correlation based PIV image processing method, the Hierarchical Recursive PIV method has theadvantages 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 fourstereoscopic 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 conductmeasurement in an air jet mixing flow exhausted from a lobed nozzle. A lobed nozzle, which consists of a splitter platewith convoluted trailing edge, had been considered to be a very promising fluid mechanic device for efficient mixingof two co-flow streams with different velocity, temperature and/or spices (McCormick and Bennett 1994, and Belovichand Samimy 1997). It has been paid great attention by many researchers in recent years, and has also been widely
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applied to the aerospace engineering. For examples, for some commercial aero-engines, lobed nozzles/mixers had beenused to reduce take-off jet noise and Specific Fuel Consumption (SFC) (Preze et al. 1994). In order to reduce theinfrared radiation signals of the military aircraft to improve their survivability in the modern war, lobed nozzles hadalso been used to enhance the mixing process of the high temperature and high-speed gas plume from aero-engine withambient cold air (Hu et al. 1999). More recently, lobed nozzles had also emerged as attractive approaches forenhancing mixing between fuel and air in combustion chambers to improve the efficiency of combustion and reducethe formation of pollutants (Smith et al. 1997). The interaction of the streamwise vortices generated by lobed nozzles and spanwise vortices rolled up due to theKelvin-Helmholtz instability had been suggested to pay a important role for the mixing enhancement in lobed mixingflows (McCormich and Bennett 1994, and Belovich and Samimy 1997). However, most of the previous researchesabout lobed mixing flows were conducted by using Pitot probes, Laser Doppler Velocimetry (LDV) or Hot filmAnemometer (HFA). The quantitative whole-field velocity and vorticity (all three components) distributions in lobedmixing flows had never been obtained due to the limitation of those conventional measurement techniques. Themeasurement results obtained by the present dual-plane stereoscopic PIV system are expect to be the first to visualizethese 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 sixlobes. The width of each lobes is 6mm and the height of each lobe is 15mm (H=15mm). The inner and outer penetrationangles 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 centrifugalcompressor. A cylindrical plenum chamber with honeycomb structure in it was used to settling the airflow. Through aconvergent connection (convergent ratio is about 50:1), the airflow is exhausted from the test nozzle. All the jet supplyapparatus were installed on a two-dimensional translation mechanism so that the distance between the exit plane of thelobed 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 thedifferent 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 calibrationprocedure 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 jetvelocity is about 60,000. The thickness of the illuminating laser sheets is about 2.0mm, and the time interval betweenthe two laser pulsed illumination of each double pulsed Nd:YAG laser set was 30 sµ .
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b.air jet experimental rigFigure 4. The the lobed nozzle and air jet experimental rig
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A seeding generator, which is composed by an air compressor and several Laskin nozzles (Melling, 1997), was used togenerate DEHS (Di-2-EthlHexyl-Sebact) droplets as tracer particles in the jet mixing flow. The diameter of the DEHSdroplets is about 1 mµ . The DESH droplets out of the seeding generator are divided into two streams; one is used toseed the core jet flow and another for the ambient air seeding.
Experimental results and discussions1. 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 linearpolarization is directly related to the possibility of the simultaneous measurements and the measurement accuracy. Atest had been conducted in the present study to check the separation result of the scattering lights from the twoilluminating laser sheets with orthogonal linear polarization. The double-pulsed Nd:YAG laser set A and B werecontrolled to fire separately, and the four CCD cameras acquired the same particle images simultaneously. When thedouble-pulsed Nd:YAG laser set A was controlled to fire, the flow field was illuminated by a horizontally polarizedlaser 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 verticallypolarized light sheet (P-polarized lights). The simultaneous particle images detected by the four CCD cameras areshown on Figure 5. From the comparison of the simultaneous images shown on Figure 4 and Figure 5, it can be seen that the scatteringlights from the illuminating laser sheets with orthogonal linear polarization can be separated successfully by using theoptical arrangement described in the present paper. The separation ratios of the scattering lights, which is defined as thepower ratio of the horizontal polarized lights (P-lights) transmitted through the polarizing beam splitters cube to the partreflected 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 laserpower 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 avertically 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 ahorizontally 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 resultsobtained by the present dual-plane stereoscopic PIV system at cross planes of the lobed jet mixing flow were shown onFigure 6 and Figure 7 with the gap between the two illuminating laser sheets being 2mm.
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From the measurement results shown on Figure 6, it can be seen that the instantaneous velocity distribution of thelobed 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 werecalculated according the following equations:
)(0 z
vyw
UD
x ∂∂−
∂∂=ϖ (2)
)(0 x
wzu
UD
y ∂∂−
∂∂=ϖ (3)
)(0 y
uxv
UD
z ∂∂−
∂∂=ϖ (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,vand 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 flowwere shown on Fig.6(c) and Fig.6(d) and Fig.6(e). It should be noted that a conventional one-plane stereoscopic PIVsystems just can provide one component distribution of the vorticity vectors (Z-component, with its direction normal tothe laser sheet plane) instantaneously. For the various vortices in the lobed jet mixing flow, the six pairs of large-scale streamwise vortices generated by thespecial trailing edge of the lobed nozzle can be seen clearly in the instantaneous streamwise vorticity distribution shownon Fig. 6(e). The x-component and y-component of the vorticity vectors were used to calculate the in-plane vorticitystrength distribution (Fig.6(f)), which can indicate the behaviors of the spanwise Kelvin-Helmholtz vortices in the lobedjet mixing flow. It can be seen that the shape of the spanwise vortex ring at the lobed nozzle exit has the same geometryas 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 sixpairs of the large-scale streamwise vortices shown clearly at the exit plane of the lobed nozzle (Fig. 6(e)), many small-scale streamwise vortices were found to appear in the lobed jet mixing flow at this cross plane (Fig. 7(e)). The bigspanwise vortex ring (in-plane vortex ring shown on Fig. 6(f)) was also found to begin to break down into manydisconnected vortical tubes (Fig. 7(f)). The ensemble-averaged results based on the 200 frames of the instantaneous measurement results at Z=40mm crossplane of the lobed jet mixing flow were shown on Figure 8. Fig. 8(a) and Fig.8(b) show the ensemble-averaged velocitydistribution (U, V and W) and turbulent kinetic energy (k) distribution, which is calculated by using followingequations:
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���===
(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) andFigure 8(d). It should be noted the maximum magnitudes of the ensemble-averaged vorticity (both streamwise vorticityand in-plane (spanwise) vorticity distribution) are much smaller than that of the instantaneous values due to theextensive mixing in the lobed jet mixing flow. In the meanwhile, the pinched-off shape of the spanwise vortex tubesuggested by McCormick and Bennett (1994) can also be found from the Fig.8(c). More detailed discussions about theevolution 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 statisticalturbulence theory for turbulence fundamental study. Such values always can not be obtained by using conventionalstereoscopic PIV systems, which just provide measurement result at a single plane. The ensemble-averaged cross-correlation coefficients of turbulent velocity vectors and streamwise vorticity at Z=40mm cross plane of the lobed jetmixing flow were shown on Figure 8(e) and Figure 8(f). These cross-correlation coefficients are defined as:
)))42,,(),42,,(())40,,(),40,,((
))42,,(),42,,(())40,,(),40,,(())42,,(),42,,(())40,,(),40,,(((
1
)),42,,('),40,,('),42,,('),40,,('),42,,('),40,,('(1)',','(
100
�
�
=
=
−•−+−•−+−•−
=
•+•+•=−
t
t
Nt
t
yxWtyxwyxWtyxwyxVtyxvyxVtyxvyxUtyxuyxUtyxu
N
tyxwtyxwtyxvtyxvtyxutyxuN
wvuRCross (7)
�=
=
•=−Nt
tzzz tyxtyx
NRCross
1),42,,(),40,,(1)( ϖϖϖ (8)
By changing the gap between the two illuminating laser sheets, the spectrum profiles of the cross-correlation
9
coefficients of these flow variables can be obtained.
-30-20
-100
-20
0
20
Ym
m
X
Y
Z
20 m/s
-30-20
-100
-20
0
20
Ym
m
X
Y
Z
20 m/s
a. Instantaneous result at Z=10mm plane b. the simultaneous velocity field at Z=12mm cross plane
1 1
1
1
22
2 2
2
3
33
3 3
3
3
3
3
4
44
4
4 444
4
44 4
4
5
5 5
5
5
5
555
5
5 5 5
5
5
5
6
6 6
6
6
6
6
66
6
6 6
6
6
6
6
66
6
7
7
7 7
7
7
7
77
7
7 7
7
7 7
7
7
7
7 7
7
7
8 8
88 8
8
8
8
88
88
8
8
8
9 9
9 9
9
9
9 9 9 99
9
9
1010
10 10
10
10 10 10
10
11 11
11 1111
1112
1212 12
X mm
Ym
m
-25 0 25 50
-40
-30
-20
-10
0
10
20
30
12 11.0011 9.0010 7.009 5.008 3.007 1.006 -1.005 -3.004 -5.003 -7.002 -9.001 -11.00
vorticity distribution(X-component)
1
12
2
22
2
3
3
3 3 3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
5
55
5
5
5
5
55
5
5
5
5 5
5
5
5
6
6 6
6 6
6
6
6
6
6
6
6
66
6
6
6
6
6
6
6
66
66
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
77
7
8
8
8
8
8
8
8
8
8
8
8
88
9
99
99
9
9
9
9
9
9
10
10 1010
10
10 10
10 10
10 10
10
11
11
11
1111
11
12
12
X mm
Ym
m
-25 0 25 50
-40
-30
-20
-10
0
10
20
30
12 11.0011 9.0010 7.009 5.008 3.007 1.006 -1.005 -3.004 -5.003 -7.002 -9.001 -11.00
vorticity distribution(Y-component)
c. Instantaneous vorticity field (X-component) d. instantaneous vorticity field (Y-component)
2
2
2
2
2
22 2
33
3
3
3
3
33
3
3
3
33
3
3
3
3
3
4 4
4
4
4
4
4 4
4
4
44
4
4
4
4
4 4
4
55
5
5
5 5 5
5
5
5
5
6
6
6
X mm
Ym
m
-25 0 25 50
-40
-30
-20
-10
0
10
20
30
6 5.005 3.004 1.003 -1.002 -3.001 -5.00
vorticity distribution(Z-component)
1
1
1
1
1
1
1
1
1
1
1 1
1
1
12
2
2
2 2
2
22
2
2
2
2
3
2
2
2
3
3
3
3
3
3
3
3
3
3
33
3
3
3
34
4
4
4
4
4
4
4
44
44
4
4
4
4
5
5
5
55 5
5
5
5
5
5
5
5 5
6
6
6 67
6
6
6
6
6
6
5 6
6
7
7
7
6
7
7
7
7
7
7
7
6
7
7
8
8
7
8
8
88 8
9
9
99
9
9
9
10
11
11
11
X mm
Ym
m
-40 -20 0 20 40
-40
-30
-20
-10
0
10
20
30
13 15.012 14.011 13.010 12.09 11.08 10.07 9.06 8.05 7.04 6.03 5.02 4.01 3.0
The strength ofin-plane vorticity
e. Instantaneous vorticity field (Z-component) f. the strength of in-plane vorticity distributionFigure 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.
10
-30-20
-100
-20
0
20
Ym
m
X
Y
Z
20 m/s
-30-20
-100
-20
0
20
Ym
m
X
Y
Z
20 m/s
a. Instantaneous velocity field at Z=40mm plane b. the simultaneous velocity field at Z=42mm plane
3
4
4 5
5
5
5
5
5
5
5
5
6
66 6
6
6
6
6 6
6
6
6
6
6
6
66
6 6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7 7
7
7
7 7
7
7
7
8 8
8
8
8
8
8
8
9 99 10
X mm
Ym
m
-40 -20 0 20 40
-40
-30
-20
-10
0
10
20
30
12 11.011 9.010 7.09 5.08 3.07 1.06 -1.05 -3.04 -5.03 -7.02 -9.01 -11.0
Vorticity distribution(X-component)
234
4 4
5
5 5
5
5
55
5
5
5
6 66
6
6
6
66
6
6
6
6 6
6
6
66
6
6
6
66
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
77
7
7
7
7
8
8
8
8
8
8
8
8
8
9
9
X mm
Ym
m
-40 -20 0 20 40
-40
-30
-20
-10
0
10
20
30
12 11.011 9.010 7.09 5.08 3.07 1.06 -1.05 -3.04 -5.03 -7.02 -9.01 -11.0
Vorticity distribution(Y-component)
c. Instantaneous vorticity field (X-component) d. instantaneous vorticity field (Y-component)
2
2
2
3
3
3
3
4
4
4
4
4
4
4
44 4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5 55
5
5
5
5
5
5
66
6
6
66
6
6 6
X mm
Ym
m
-40 -20 0 20 40
-40
-30
-20
-10
0
10
20
30
8 7.07 5.06 3.05 1.04 -1.03 -3.02 -5.01 -7.0
Vorticity distribution(Z-component)
1
1
1
11
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
11
1
1
13
3
3
3
3 3
3
33
333
33
3
3
3 33
3
5 5
55 5
5
5
5
4
5
X mm
Ym
m
-40 -20 0 20 40
-40
-30
-20
-10
0
10
20
30
13 15.011 13.09 11.07 9.05 7.03 5.01 3.0
The strength ofin-plane vorticity
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.
11
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
W m/s18.017.016.015.014.013.012.011.010.0
9.08.07.06.05.04.03.02.0
10 m/s
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2 2
2
3
3
3
3
3
33
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
44
4
4
4
4
55 5
5
5
66 6
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
8 10.007 9.006 8.005 7.004 6.003 5.002 4.001 3.00
Turbulent kinetic energy
a. ensemble-averaged velocity distribution b. ensemble-averaged turbulent kinetic energy distribution
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1 1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
22
2
3
3
3
3
3
3
3
3 3
3
3
23
33
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
55
5
5
5
5 5
5
5
6
6
6
6
6
6 6
77
7
7
7
7 7
8
8
8
8
8
8
9 9
8
11
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
11 5.0010 4.759 4.508 4.257 4.006 3.755 3.504 3.253 3.002 2.751 2.50
ensemble-averaged in-planevorticity strength distribution
3
3
3
4
4
4
4
4
4
5 5 5
5
5
5
55
5
5
5
5
5
5
5
5
5
6
66
6
6
66
6
66
6
7
7
7
7
7
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
10 3.009 2.338 1.677 1.006 0.335 -0.334 -1.003 -1.672 -2.331 -3.00
ensemble-averaged streamwisevorticity distribution
c. ensemble-averaged in-plane vorticity strength distribution d. ensemble-averaged streamwise vorticity distribution
1
1
1
11
1
1
1
1
1
1
11 1
1
1
1
1
1
2
2
2
2
22 2
2
2
2
2 2
2
2
2
2
2
2
2
2
2
33
33
3
3
3
3
3
3
3
3
3
44
4
4
4
4
4
4
5
5
5
5
5
5
6
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
8 8.507 7.506 6.505 5.504 4.503 3.502 2.501 1.50
cross-correlation valuesof turbulent velocity vectors
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2 2
2
2
2
22
2
2
2 2
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4 4
4
4
4
4
5
5
5 5 5
5 5
6
6
7
9
X mm
Ym
m
-40 -20 0 20 40 60-40
-30
-20
-10
0
10
20
30
40
9 5.008 4.507 4.006 3.505 3.004 2.503 2.002 1.501 1.00
cross-correlation valuesof streawise vorticity
e. cross-correlation coefficeints of turbulent velocity vectors f. cross-correlation coefficeints of streamwise vorticityFigure 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 imagerecording. 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 turbulentflows. Therefore, only time-averaged quantities, such as the mean velocity and Reynolds stress, can be obtained tocharacterize the flow unsteadiness.
12
X mm
Ym
m
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
W m/s20.0018.0016.0014.0012.0010.00
8.006.004.002.00
10 m/s
X mm
Ym
m
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
W m/s20.0018.0016.0014.0012.0010.00
8.006.004.002.00
10 m/s
a. instantaneous velocity field at time t=T0 b. instantaneous velocity field at time t=T0+0.1ms
12 2
2
2
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
444
4
4 4
4
4
44
44
4
4
4
4
4 4
4
444 4
4
4
4
4
4 4
4
4
5
5
5
5
5 5
5
555
5
5
5
5 555
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
66
6
6
66
6
6
6
X mm
Ym
m
-40 -20 0 20 40
-30
-20
-10
0
10
20
30
8 7.07 5.06 3.05 1.04 -1.03 -3.02 -5.01 -7.0
streamwise vorticity
1
2
2
2
3
3
3
3
3
3
3
3
3
33
3 3
3
44
4
4 4
4
4 4
4
4
4
4
4 4
4 4
4
4
4
44
4
4
4
4
4
44
4
4
4
4
4
4
4
4
5
55
5
5
5
5 5
5
5
5
5
5
5
55
5
5
5
5
5
5
5
55
5
5
5
5
5
5
5
5
5
6
6
6
6 6
6
7
7
X mm
Ym
m
-20 0 20 40
-30
-20
-10
0
10
20
30
8 7.07 5.06 3.05 1.04 -1.03 -3.02 -5.01 -7.0
streamwise vorticity
c. streamwsie vorticity distribution at time t=T0 d. streamwsie vorticity distribution at time t=T0+0.1ms
1
1
1
1
1 1
1
1
1 1
11
1
1
1 1
11 1
1
1
1
1
2 2
2
2
2
2
2
2 2
2
2
22
2
2
22
2
2
2
2 2
2
33
3
3
3
3
3
3
3
3
3 3
3
334
4
4
4
X mm
Ym
m
-20 0 20 40 60-40
-30
-20
-10
0
10
20
30
6 13.005 11.004 9.003 7.002 5.001 3.00
auto-correlation distributionof turbulent velocity field
1
11
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
12
2
22
2
2
2
2 2
2 2 2
2
2
2
2
2
2
2
2
2
2
2 2
22
3 3
3
3
3
3
3
3
33
3
3
3
3
3 3
3
3
3
4
4
4
4 4
3
4
5
5
5
5
6
X mm
Ym
m
-20 0 20 40 60-40
-30
-20
-10
0
10
20
30
6 12.005 10.004 8.003 6.002 4.001 2.00
auto-correlation distributionof streamwise vorticity field
e. auto-correlation coefficents of the turbulent velocity vectors f. auto-correlation coefficents of the streamwsie vorticityFigure 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-planestereoscopic PIV system. By adjusting the two illuminating laser sheets overlapped at the same plane, the flow field canbe measured synchronously at variable separation times up to sµ order. The temporal auto-correlation functions of theflow variables (such as velocity and vorticity) can be obtained by measuring the velocity field at time t and t+τ , whereτ is varied to any delay amount. Figure 9(a) and 9(b) show the instantaneous measurement results of the present dual-plane stereoscopic PIV system at the same cross plane (Z=40mm) of the lobed jet mixing flow with the time delay (τ )
13
between two measurements being 100 sµ . The streamwise vorticity fields derived from the two instantaneous velocityfields 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 flowvariable X is calculated by using following equation:
�−
=
+•=−1
0
),,,(),,,(1)(N
nnn tzyxXtzyxX
NXRAuto τ (9)
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 thevariable lag τ . The ensemble-averaged auto-correlation coefficient of the turbulent velocity vectors and the streamwisevorticity were shown on the Fig. 9(e) and Fig.9 (f) with τ =100 sµ . By changing the time delay between the twomeasurements, 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 withLDV measurement results For the accuracy evaluation of a stereoscopic PIV system, Lawson and Wu (1997a,b) introduced a geometric errormodel for the error analysis of stereoscopic PIV systems based on the parallel projection assumption. The effect ofsystem parameters like the position and view angle of the image recording cameras on the error ratio of stereoscopicPIV results, which was defined as the ratio of the out-of-plane velocity component to the in-plane component, wasdiscussed theoretically. Bjorkquist (1998) measured the parallel translation movement of a rigid body and get aconclusion 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 justbased on the parallel translation measurement of a rigid body is not sufficient for the accuracy evaluation of astereoscopic PIV system for fluid flow measurement. Hill et al. (1999) compared the ensemble-averaged values of theirstereoscopic PIV measurement results in a cylindrical Couette flow with theoretical predictions and reported that thedifferences 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 aconventional 2-D PIV system. In the present paper, the measurement results of the present dual-plane stereoscopic PIV system were compared withthe simultaneous measurement results of a LDV system. Both the instantaneous data and ensemble-averaged values ofthe stereoscopic PIV measurement and LDV measurement were compared quantitatively to evaluate the accuracy levelof 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, thesynchronizer of the LDV system was connected with the synchronizer system of the present dual-plane stereoscopicPIV system. The pulsed signals generated by the stereoscopic PIV synchronizer system, which were used to trigger theillumination system and image recording system for stereoscopic PIV measurement, were also output to thesynchronizer 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 wavelengthof the green beams of the LDV system is 545.5and 488nm for the blue beams. In order to avoid the effect of the LDVlaser beams on the image recording of the dual-plane stereoscopic PIV system, sharp bend pass filters (only 532nmpass) 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 simultaneousmeasurement 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 wascontrolled the synchronizer system of the stereoscopic PIV system, the temporal-resolution of the LDV measurementand stereoscopic PIV measurement is assumed to be same. As mentioned above, the thickness of the illuminating lasersheets of the present dual-plane stereoscopic PIV system is about 2.0mm and 32 by 32 pixel interrogation windowswere used to conduct cross-correlation PIV image processing. The image resolution captured by image recordingcameras is about 80 pixelm /µ . So, the spatial resolution of the present stereoscopic PIV measurement is about2.5mm×2.5mm×2.0mm. The spatial-resolution of a LDV system is closely related with the diameter of the laserbeams for the LDV measurement. For the present LDV system, the spatial-resolution is about 65.3 mµ (laser beamdiameter and also volume diameter)×0.68mm (volume length). The spatial resolution difference between the stereoscopic PIV system and the LDV system may result in thedifferences between the stereoscopic PIV measurement results and LDV measurement results since the cut-off scale ofthe turbulent motion is different. However, the effect of the spatial resolution difference between the stereoscopic PIVsystem and LDV system is consider to be negligible in the present study since the comparison points are selected on thecenter 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-pulsedNd:YAG laser sets was controlled to fire, the dual-plane stereoscopic PIV system works as a conventional single-plane
14
stereoscopic PIV system. The instantaneous values of the simultaneous measurements from the dual-plane stereoscopicPIV system and the LDV system were shown on Figure 10(a). Then, both of the double pulsed laser sets werecontrolled 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 ofthe 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 witheach other well for both of the instantaneous data and ensemble-averaged values. For the ensemble-averaged values ofthe out-of plane velocity component, the difference between the stereoscopic PIV measurement and LDV measurementwere found to be less than 2%. Since the scattering lights from the two orthogonally linearly polarized laser sheets wereseparated successfully, the measurement accuracy of the dual-plane stereoscopic system was not affected by thesimultaneous illumination of the two laser sheets.
-5
0
5
10
15
20
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
time (s)
Vel
ocity
(m/s
) V-SPIV W-SPIV W-LDV V-LDV
a. One laser sheet on and the other off
-5
0
5
10
15
20
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
time (s)
Vel
ocity
(m/s
)
V-SPIV W-SPIV W-LDV V-LDV
b. Two laser sheets illuminate the flow field simultaneouslyFigure 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 resultsStereoscopic PIV measurement
ResultsLDV measurement results
Ensemble-averaged
out-of-planeVelocityW(m/s)
Deviation ofthe out-of-
plane velocitycomponentSTD(W)
Ensemble-averaged
out-of-planeVelocityW (m/s)
Deviation of theout-of-plane
velocitycomponentSTD(W)
WSPIV –WLDV
Point A(0,0,20)
17.271 0.600 16.973 0.640 0.298(1.7%)One laser sheet on
the other off Point B(0,0,40)
17.220 0.889 16.930 0.844 0.290(1.7%)
Point A (0,0,20)
17.126 0.581 16.904 0.509 0.222(1.3%)Two laser sheets
on simultaneously Point B (0,0,40)
17.213 1.006 16.864 0.856 0.349(2.0%)
15
Summary and Conclusions The technical basis and system set-up of a dual-plane stereoscopic PIV system, which can provide flow velocity (allthree components) fields at two spatially separated planes simultaneously, were described in the present paper. Thesimultaneous measurement were achieved by using two orthogonally linearly polarized laser sheets to illuminate thefluid flow at two spatially separated planes simultaneously. The scattering lights from the two illuminating laser sheetswith orthogonal linear polarization were recorded separately by high-resolution CCD cameras with polarizing beamsplitter cubes. Unlike conventional single-plane PIV systems, which just can obtain the one-component of the vorticityvectors instantaneously, the present dual-plane stereoscopic PIV system can provide all three components of thevorticity vectors and various auto-correlation and cross-correlation coefficients of flow variables instantaneously andsimultaneously. The present dual-plane stereoscopic PIV system was used to conduct measurement in an air jet flow exhausted from alobed nozzle to demonstrate its feasibility. The evolution and interaction of the various vortices in the lobed jet mixingflow were visualized quantitatively and instantaneously from the measurement results of the present dual-planestereoscopic PIV system. In order to evaluate its measurement accuracy, the measurement results of the present dual-plane stereoscopic PIVsystem were compared with the simultaneous measurement results of a LDV system. It was found that both theinstantaneous 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 betweenthe 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 inconducting the present study.
ReferencesAbe M., Longmire E. K., Hishida K. and Maeda M., (1999), A comparison of 2D and 3D Measurements in an
Oblique Jet. Proceedings of The 3rd International Workshop on PIV, Santa Barbara, U.S.A, Sep.16-18, 1999.Adrian R. J., (1991), Particle-image Technique for Experiment Fluid Mechanics, Ann. Rev. Fluid Mech. 261-304.Aikislar M. B., Lourenco L. and Krothapalli A., (1999), 3-D PIV Measurements of a Supersonic Jet, Proceedings of
The 3rd International Workshop on PIV, Santa Barbara, U.S.A, Sep.16-18, 1999.Barnhart, D. H., Adrian, R. J. and Papen G. C., (1994), “Phase-conjugate Holographic System for High-resolution
Particle Image Velocimetry”, Applied. Optics, 33-33, pp7159-7170Bjorkquist D. C., (1998), Design and Calibration of a stereoscopic PIV System, Proceedings of the ninth International
Symposium on Application of Laser Techniques in Fluid Mechanics, Lisbon, Portugal, .Belovich V. M. and Samimy M. (l997), Mixing Process in a Coaxial Geometry with a Central Lobed Mixing Nozzle.
AIAA Journal�Vol.35, No.5�PP838-84l.Hart. D. P. (1998), “The Elimination of Correlation Error in PIV processing”, Proceedings of 9th International
Symposium on Application of Laser to Fluid Mechanics, Lisbon.Hill D.F., Sharp K.V. and Adrian R. J., (1999), The implementation of Distortion Compensated Stereoscopic PIV,
Proceedings of The 3rd International Workshop on PIV, Santa Barbara, U.S.A, Sep.16-18, 1999Hu H., Saga. T., Kobayashi T., Taniguchi N. and Okamoto K., (1998), Evaluation the Cross-Correlation Method by
Using PIV Standard Image. Journal of Visualization, Vol.1, No.1, pp87-94Hu H., Kobayashi T., Taniguchi N., Liu H. and Wu S., (1999), Research on The Rectangular Lobed Exhaust
Ejector/Mixer Systems, Transactions of Japan Society of Aeronautics and Space Science. Vol.41 No.134, pp187-194.
Hu H., Saga T., Kobayashi T., Taniguchi N. and Segawa S., (2000a) “The Spatial Resolution Improvement of PIVResult by Using Hierarchical Recursive Operation”, to be published on the Journal of Visualization, No.3 Vol. 3,2000
Hu H., Saga T., Kobayashi T. and Taniguchi N., (2000b), Stereoscopic PIV Measurement on the Lobed Jet MixingFlows, Proceedings of the Tenth International symposium on Application of Laser Techniques to FluidMechanics, July 10-13, Lisbon.
Kahler C. J. and Kompenhans J. (1999), Multiple Plane Stereo PIV: Technical Realization and Fluid-MechanicalSignificance, Proceedings of The 3rd International Workshop on PIV, Santa Barbara, U.S.A, Sep.16-18, 1999.
Lawson N.J., and Wu J. (1997a), Three Dimensional Particle Image Velocimentry: Error Anlaysis of StereoscopicTechniques. Measurement Science Technology, Vol. 8, pp894-900.
Lawson N.J., and Wu J. (1997b), Three Dimensional Particle Image Velocimentry: Experimental Error Analysis of aDigital Angular Stereoscopic System. Measurement Science Technology Vol. 8, pp1455-1464.
Lourenco L. M., Alkislar M. B. and Sen R. (1998), Measurement of Velocity Field Spectra by Means of PIV,Proceedings of the ninth International Symposium on Application of Laser Techniques in Fluid Mechanics,Lisbon, Portugal. July 13 to16, 1998
16
Melling A. (1997), Tracer Particles and Seeding for Particle image Velocimetry, Measurement Science and Technology,Vol.8, pp1406-1416.
McCormick D.C. and Bennett J.C.Jr. (l994) Vortical and Turbulent Structure of a Lobed Mixer Free ShearLayer”AIAA Journal, Vol.32, No.9. pp1852-1859.
Nishio, K., Kasagi N., and Hirata, M., (1989) Three dimensional Particle Tracking Velocimetry Based on AutomatedDigital Image Processing, tarn. ASME, J. Fluid Eng., Vol. 111 pp384-391
Poser J. D. and Riethmuller M. L. (1999), Translation Stereoscopic Digital PIV Applied to a Turbulent Jet,Proceedings of The 3rd International Workshop on PIV, Santa Barbara, U.S.A, Sep.16-18, 1999.
Prasad A. K. and Adrian R. J., (1993), Stereoscopic Particle Image Velocimetry Applied to Fluid Flows, Experimentsin Flows, Vol.15, pp49-60.
Prasad A. K. and Jensen K, (1995), Scheimpflug Stereocamera for Particle Image Velocimetry in Liquid Flows,Applied Optics, Vol.34, 7092-7099
Presz, Jr. W. M., Reynolds, G. and McCormick, D., (1994), Thrust Augmentation Using Mixer-Ejector-DiffuserSystems. AIAA Paper 94-0020.
Smith L.L, Majamak A.J., Lam I.T. Delabroy O.,Karagozian A.R., Marble F.E. and Smith, O. I., (l997) MixingEnhancement in a Lobed Injector. Phys. Fluids, Vol.9�No.3�PP667-678
Soloff S. M., Adrian R. J. and Liu Z. C. (1997), Distortion Compensation for Generalized Stereoscopic Particle ImageVelocimetry, Measurement Science and Technology, Vol.8 pp1441-1454.
Suzuki Y. (1999), Three-dimensional Particle Tracking Velocimetry”, The textbook of the seminar about three-dimensional PIV technique, VSJ-PIV-S2. (ISBN4-906497-21-9), pp79-96, Yokohama, Japan (In Japanese)
Watanabe Z., Natori M. and Okkuni Z. (1989), Fortran 77 Software for Numerical Computation, MARUZENPublication, ISBN4-621-03424-3 C3055 (In Japanese)
Willert C. (1997), Stereoscopic Digital Particle Image Velocimetr for Application in Wind Tunnel Flows. MeasurementScience and Technology, Vol.8 pp1465-1479.
Zhang, J., Tao, B. and Katz, J., (1997) "Turbulent flow measurement in a square duct with hybrid holographic PIV,"Experiments in Fluids, vol. 23, 373-381.