q 11 Camera

Figure 2 - Top view of system with mirrors and camera.

from the jet centerline to the bottom flat surface was main- tained at 5.0 cm.

The adjustable overflow device at C and the fixed over- flow device at A constituted an accurate, easy, simple, and controllable combination to allow the control of the flow down to very small velocities necessary to obtain a jet Reynolds number of 200. This was especially critical for water, the fluid of choice, plus the small amount of MgSO, needed to provide a neutral buoyant fluid to match the density of the polystyrene micro carrier spheres used as flow markers.

Figure 2 shows a top view of the experimental system with the mirrors and camera in position. The details of the PTV data acquisition system to make the measurements of the flow velocity vectors have been described elsewhere [Guezennec and Kiritsis (1990), Choi et al. (1992), Kent et al. (1993, Guezennec et al. (1994)l. In these references, time resolved velocity vector measurements were not of concern. Their goal was to obtain ensemble averaged results. Five frames would be obtained over 1/6 s; the images were then processed and velocity vectors extracted which could take a minute or more of time; the entire pro- cedure was repeated until enough vectors had been obtained for a reliable ensemble average to be established. The pro- cedure was fully automated with the final output being a three-dimensional representation (both data and visuals) of the flow field. In contrast, the experiments reported here were first recorded on SVHS video tape as an interim step. The subsequent image processing and analysis were then done without the time gaps of the previous work. Once the data was on tape and could be replayed, the analysis was also fully automated. Figure 3, shows a flow chart for our system and the steps undertaken in this research.

The size of the imaged field of view was 10 cm x 10 cm for both views that were obtained side by side as a video image. This is equivalent to three pixels corresponding to 1 mm of actual size for our imaging system. Each view cov- ered the entire flow field. The number of non-zero velocity vectors obtained ranged from a few dozen to more than a thousand per frame. The number depends on the seeding particle concentration and the Reynolds number of the flow. The particle concentration effect is obvious. The Reynolds number effect comes from the video framing rate being con- stant. At a higher Reynolds number, the convection of par- ticles into and out of the system is much greater resulting in more tracks per frame. Below a Reynolds number of 200, the non-zero velocity vectors per frame were too low. In

Grabbing and Digitization Final Images are -256’ at 60 Hr I

U U Image Preprocessing (on Grabber Board)

Average Image as Background Remove Background

Stretch Images

U U PTV Analysis (PC-based)

2-D Particle Locations, Particle Tracking. 3-D Stereo Matching, AGW Validation, 3-D Position and Velocity at Randomly Identified Spatial

Locations in the Flow Volume II

4

u Post Processing (PC-based)

AGW Interpolation of Velocity Vectors onto Regular Grid. Vorticity Calculation, 3D Drawing and Displaying, etc.

U Ensemble Averaging

A statistically stationary turbulent flow has no dependence on time ( 9 min at Re = 200). The instantaneous data at low Reynolds number flow was

not high enough for interpolation of velocities onto a meaningful three dimensional regular grid.

U Data Visualization and Analysis

Illustrate, pose, surface and animate data in both 3-D and 2-D. even with very large data sets. Explore data from many different perspectives and sections so

that all the patterns and relationships in the data can be seen and gain deepcr understanding.

Figure 3 - Flow chart for the data analysis.

water, these velocities were very low indeed, the maximum of the long time average velocity being about 0.14 c d s . For lower Reynolds numbers, one should switch to a higher vis- cosity fluid that would provide a higher velocity than for the same Reynolds number using water. Of course, any such a change would necessitate readjustment to maintain the parti- cles neutrally buoyant. Rather than undertake these additional steps, the present work was limited to Reynolds numbers above 200. The upper limit was dictated by the video fram- ing rate to be discussed later.

FLUID AND PARTICLES USED IN THE STUDY

The fluid always was tap water doctored with MgSO, to provide a density that would just match the density of the polystyrene micro carrier beads obtained from SoHill Corporation of Ann Arbor, Michigan. These beads were around 150 pm in diameter and had a density of 1.04. The doped water had exactly the same density at the ambient laboratory temperature. This was judged by visual observa- tions that the beads did not gather at the top or bottom of a beaker, but remained distributed throughout the volume. The micro carrier particles had a very uniform density that simplified the density matching.

EXPERIMENTAL PROCEDURE

The procedure was very simple. The desired balanced flow in the system was obtained by the overflow control device described in Figure 1. This was done without the

m THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 76, JUNE, 1998

flow marker beads present. Once the flow was established and maintained for a period of time, the bypass lines were opened and the rotameters were closed. At this point, the flow markers were mixed into the system at the recirculat- ing tank at the bottom (D). The flow was maintained for another period of time to ensure that the markers were well distributed before the data acquisition was started. The data acquisition was used to record adequate time on SVHS video tape. The data analysis was automated and done after all the experiments were completed.

Concepts for analysis and three-dimensional data analysis

Having previously established that the PTV system could provide full-field, time-resolved, velocity vector informa- tion, the present challenge was how to present and interpret the massive data set for the opposed jet system. There are some bounds for the system that must be established first. The opposed jet system was a low jet Reynolds number water flow, with some MgSO, added to make the particles neutrally buoyant. To obtain long-time, statistical average information, several minutes of data are needed. To estab- lish the data needed for such an average, we started by ana- lyzing fixed time sequences of the data. We generated an ensemble average for the first 2 rnin and repeated this for subsequent time segments (2 min) over the experimental data set. The result was a series of 2 min average pictures. There were clear local differences between each picture; thus, a 2 min average was not adequate to obtain average velocities. We judged this on the local characteristics of the plots rather than overall statistics that would themselves be averages. The analysis was then repeated with 4 min seg- ments. This time, there was little difference between subse- quent pictures. To insure that the average was stable we finally settled upon 9 min of data to represent the longtime average. 9 min of data represents 16200 frames studied at a Reynolds number of 200. The data analysis from the video was fully automated by having the SVHS recorder under control of the PC computer used. Thus, using a 9 min seg- ment was not a problem and the data analysis was done automatically at night. For 9 rnin of data, nearly half a mil- lion data vectors were obtained. This averaged to about 30 non-zero vectors per frame in the central jet region at the 30 Hz rate used in the analysis here. The data were also avail- able at a 60-Hz rate, but an alternate and more complex data reduction analysis would have to be used. Since the results were adequate at the 30 Hz rate, we elected to use this.

The second bound is the minimum number of vectors needed to be able to follow the flow in time. To establish this, we started with 2 min of data and worked down from there. A single frame, which had about 30 non-zero vectors in the central jet region, was clearly too few to provide a pic- ture of the flow field. The minimum that gave a smooth con- tinuous picture contained at least 200 non-zero vectors. The data present in this paper are for both a 1/4 s (- 225 non-zero vectors) and a 2 s average (- 1800 non-zero vectors). This is only for the jet Reynolds number of 200. At higher veloci- ties, more vectors per frame are available. The long-time average results are an average of nearly half a million vec- tors. This is equivalent to over 50 vectors at each nodal point in the full field (total of 213 nodal points).

All of the results reported herein are experimental. They look like computational results, but they are not. The repre-

sentations of the data base we have used could well be applied to computational results also.

Data visualization, analysis, and discussion

Obtaining and displaying three-dimensional, full-field, time-resolved velocity vectors have been a challenge for fluid dynamics researchers. A part of this study has been to develop means of visualization of such fields for the opposed jet reactor configuration. Although certainly not the last of such efforts, it does represent a new avenue for us. We would like to use color representations, but due to the limitation imposed by the printed page this is not possible. Thus, in this paper the figures are in greyscale levels and not moving. However, the same figures, in full color, can be found at the URL (Zhao and Brodkey, 1998) used to supple- ment the material shown here. Many of these are dynamic representations. In addition, we are developing simple means for true three-dimensional, stereoscopic visualization.

Color is often used as an essential element of the two- dimensional representations of the three-dimensional flow fields. Gray tone substitution, as done here, is always possi- ble. The human, eye-mind combination can extract more from color than a gray-scale representation. However, when color is not available, grey level must be used. For this, the velocities have been divided into several regions and each region is assigned a different grey level from black to light grey. In addition, the length of the line is proportional to the magnitude of the velocity.

The representations that we have developed are a result of many months of viewing to see how we can effectively con- vey the information contained therein. Our final selection was to give the viewer color examples (both static and dynamic) of our results that have been brought together on our URL (Zhao and Brodkey, 1998). In that posted material, we use both color and dynamic multi-representational views. The dynamic views are provided by animated GIF (Graphic Interchange Format) files.

ENSEMBLE AVERAGED VELOCITY FIELD AT A JET REYNOLDS NUMBER OF 200

Figure 4 is the 9 min average picture of the flow field, shown in grey level as a three-dimensional drawing with the outline of the vessel and jets superimposed. The high inlet jet velocities are darker. Color coded versions can by found at the URL (Zhao and Brodkey, 1998). On the average, the flow looks regular. The dividing velocity surfaces between the jets are clearly visible. The flow does have a longtime average that can be statistically defined that parallels the often cited picture for a standard turbine (Rushton) in a mix- ing vessel. However, just as for the mixing vessel, the flow is anything but steady. As will be shown later, even at the laminar flow inlet velocity associated with a jet Reynolds number of 200, there are large scale variations and motions of the jets in the flow field. With the software available, the three-dimensional view can be rotated and a film clip can be made of the rotation in space. However, doing much else with the representation shown in Figure 4 is difficult. It is just simply too complex for ease of interpretation.

We have found that layering the velocity from the high- to-low levels in turn can give a useful dynamic picture of the flow field. We prefer to do this as a loop, so that the dynamic picture can be embedded in our mind. Figure 5 shows the

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Figure 4 - Longtime, 9 min, averaged velocity field at a jet Reynolds number of 200 (see Zhao and Brodkey, 1998 for color).

first two levels of velocity vectors (the highest two levels of magnitude) to illustrate this idea. These are the ensemble averaged velocity vectors (as 3-D vectors with grey scale and length proportional to the magnitude of the vector) plot- ted on the grid locations. The URL citation is “3-D, time- averaged, layered velocity shown in 3-D”, which shows the entire sequence of velocities from the highest to the lowest added in turn. In this procedure we leave the first or highest level of velocity in the graph and subsequently add the next lower level of velocity. The final picture of this sequence is Figure 4. We have also used an alternate representation that substitutes each lower velocity in turn. This we have called “3-D, time-averaged, substitution velocity shown in 3-D”. In this representation, the highest to the lowest velocity are shown in turn, rather than layered one upon the next. We choose not to illustrate that here, but it is on the Web site. The procedure used for these two representations, allowed one to select any sequence of velocity levels, in any order, and dynamically show them for further analysis. These illus- trated cases are at a Reynolds number of 200 where the inlet velocity profile is parabolic; however, due to the jet motion or flapping, the jet appears flattened in these long time ensembled averages.

THREE-DIMENSIONAL VELOCITY DISTRIBUTION ON GRID PLANES

Once one feels comfortable with the representation used above, a series of quasi-planar representations can convey more information in a clearer manner. We call the three planes of the flow: horizontal (xy), jet (yz), and lateral (xz) as shown in the sketch in Figure 6. The three-dimensional velocity vectors are shown on these two-dimensional cuts, which can be scanned across the geometry to provide spatial dynamic pictures of the flow field. There are two kinds of dynamic pictures that we have generated. The first is a sim- ple time sequence on a fixed plane as a function of time. The second, the one referred to here, is a scan across the geom- etry for the long time average results. Figures 7-1 a-c shows three frames, each from one dynamic representation. The first two are the 1 lth of the 21 planes and the third is the 14* plane. These are the three-dimensional velocity vectors that originate from the points (212) on a two-dimensional plane. They are not an orthographic projection onto a plane. As such, they show directions and give more information than

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Figure 5 - Three-dimensional, time-averaged, layered velocity field (see Zhao and Brodkey, 1998 for color).

Figure 6 - Sketch of flow planes in the system where xy is the horizontal, yz is the jet, and xz is the lateral planes.

a projection could. To illustrate the difference, Figure 7-2 a, is the same grid plane as Figure 7-1 c, but as a two-dimen- sional orthographic projection. Figure 7-2 b shows the side view of the velocity vectors. Clearly, Figure 7-1 c gives a better feel for the flow and uses only one figure. The URL citation for the horizontal clip is “3-D velocity vectors, xy or horizontal plane shown as slices”. The corresponding clips for the other plans are also on the URL.

Besides the velocity information, we can show contours of dependent functions as a contour projection on a wall and/or as a surface map of the dependent function. Such functions could be the amplitude of the velocity vector given by A = (u2 + v2 + w ~ ) ~ ’ ~ , a particular component of the vorticity, an estimate of the kinetic energy, a measure of the energy dissipation function, or any other scalar function. Figure 8 shows one frame from such a dynamic representa- tion of the three-dimensional velocity vectors on a horizon- tal plane. The contours of the z-vorticity component are pro- jected on the top and the same vorticity component is also presented as a continuous surface map at the jet plane. The

540 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 76, JUNE, I998

Section: 11

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Y [mm] unit (0.1 mm/s)

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Section: 14

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Figure 7-1 - Three-dimensional, time-averaged velocity vectors in the a) horizontal (xy), b) jet (yz), and c) lateral (xz) planes (see Zhao and Brodkey, 1998 for color).

X [mml

URL citation is “3-D velocity vectors, xy (horizontal plane), with contours and surface map of the z-vorticity shown as slices”. By this means, one may directly observe the distrib- ution in both direction and magnitude of the vorticity com- ponent by looking at the vorticity surface. For example, a

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Figure 7-2 - Two-dimensional projections of the time-averaged velocity vectors in the a) lateral (xz) and b) jet (yz) planes (see Zhao and Brodkey, 1998 for color).

high hill represents a strong plus or counter clockwise (CCW) vorticity and a deep valley represents a strong neg- ative or clockwise (CW) vorticity. Still other similar clips have been and are being developed and will be put on the Web location as available. For example, there are clips that show the same velocity vector information but with the con- tours being the magnitude of the velocity vector or the tur- bulent kinetic energy.

The picture of the average flow at this lowest Reynolds number is one of two jets that collide forming an interface along the central plane between the jets. The flow from this interface pancakes outward toward the wall and then folds back forming vortex regions of high positive or negative vorticity, depending on the sense of rotation of the vortex (CW or CCW). This is the conventionally steady structure observed by Wood et al. (1991) for Reynolds numbers below 150. They noted that above the value of Re = 150, a stable interface was not observed. The results being reported here for the flow at a Reynolds number of 200 were only steady on the average. The time-dependency will by discussed shortly. However, the average picture at this low Reynolds numbers does not look much different that the steady picture observed by Wood et al. at lower Reynolds numbers.

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 76, JUNE, 1998 54 I

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Y [mm] unit (0.1 mm/s) 50 -50 x [mml

Figure 8 - Three-dimensional, time-averaged velocity vectors in the horizontal (xy) plane with contours and surface map of z-vorticity at a jet Reynolds number of 200 (see Zhao and Brodkey, 1998 for color and for dynamic representation).

INJECTED PARTICLE PATHS

Since the flow in such a mixer is complex, following single particle movement (or groups of particles) is also useful to help determine the flow structure. This is the parallel to experimental dye injection at one or more points in the flow. Such representations are not new and have been used by others when the velocity field was established by numerical calculations. There is, however, a major difference between such computational results and real experiments. In real experiments, the dye is injected on a continuous basis into the tlow field. If the flow field is unsteady, then the paths will reflect this time-dependent nature of the flow. If the flow field is steady, then the paths will always be repro- ducible in the time domain.

At the Reynolds number of 200, the flow is unsteady, but we want to visualize what the flow would be like, if it were steady at this Reynolds number. Clearly, this cannot be accomplished experimentally, since the flow is simply not steady. What we have done here is to use the time-averaged velocity field from experiments and performed calculations to establish neutrally buoyant particle paths that would be observed if we had a field that was steady in time. For exam- ple, Figure 9 shows several calculated particle paths for the ensemble averaged velocity field of Figure 4. The average vortex structures are clearly seen. However, it is very impor- tant not to forget that this is the averaged flow field and such vortex motions may or may not exist in the real flow field, which is unsteady. In the next section on the time-resolved results, similar calculations could be made, although they would be much more complex with a varying velocity field in both space and time.

TIME-RESOLVED, FULL-FIELD FLOW AT A JET REYNOLDS NUMBER OF 200

Often, ensemble averaged results are not an adequate data base for important problems that depend more on the dynamics of the flow than the statistical average character- istics. For example, problems that involve chemical reac- tions and the associated selectivity to final products are sen- sitive to the localized dynamical characteristics of the flow.

501

.--= 50

Figure 9 - Particle paths determined from the flow field as given in Figure 4 (see Zhao and Brodkey, 1998 for color).

When two components react, they react on a molecular basis. Although dynamics are the hardest to represent on the static pages, Figure 10 is an attempt to show a bit of the dynamic nature of the flow. The top row of three pictures is 2 s time average segments that cover a total of 6 s. The lower series of six pictures, each of 1/4 s average, cover exactly the same time period. The arrows show the progres- sion and only every 4th picture is shown. A far better repre- sentation of these two sequences can be observed on the HomePage as "1/4 s average period of velocity at the center- plane view of the jet (yz ) shown as a time sequence". The 2 s average periods are "two s average period of velocity at the center-plane view of the jet ( y z ) shown as a time sequence". In viewing either sequence, one can sense the unsteadiness that exists in the flow that averages out to that shown i n Figure 4. According to the observations of Wood et al. (1990), the flow at the Reynolds number of 150 is not stable. The jet oscillates from side to side and when an interface forms, it is not a central pancake structure, but rather a con- voluted surface in space.

Denshchikov et al. (1983) have experimentally studied a 2-D jet and correlated the oscillations in such jets. Sandell et al. (1 985) have reported a similar type experiment, but with the jet inclined at 30" to the diameter. At a jet Reynolds number of 250, the frequency is reported as 0.16 Hz. For the work of Sandell et al. (1983, the correlation of Denshchikov et al. over predicts the frequency by a factor of nearly 5 (0.75 Hz). It is not clear that the oscillations are the same, but they should be similar. For the geometry of our system, the correlation from Denshchikov et al. predicts a frequency of 0.28 Hz at the jet Reynolds number of 200. This should be a reasonable estimate for the frequency for our system. The correlation of Denshchikov et al. (1983) was for direct- ly opposed jets like ours, in contrast to the 30" inclination used in Sandell et al. (1985). Since, the 1/4 s (or 4 Hz) data set was taken at more than 14 times the estimated experi- mental frequency, there should be no problem with resolv- ing the oscillation by using a Nyquist criterion. Although not reported here, we obtained similar results with data aver- ages taken at 1/2 s and 1 s, which support the adequacy of the measurements and satisfy the Nyquist criterion.

542 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 76, JUNE. I998

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Y I"", " l m m l x ,I","( 1 lmml l l m m l I imm1

Figure 10 - Dynamics of the flow for 2-second averages and 1/4 second averages at a jet Reynolds number of 200 (see Zhao and Brodkey, 1998 for color and for dynamic representation).

SOME RESULTS AT HIGHER JET REYNOLDS NUMBERS

With the present limitations of using only the 30 Hz data rate, the video data can be analyzed up to a jet Reynolds number of 4000. An electronic shutter at 1/500 s was used. The full 60 Hz data (that has not been studied yet) should be good to the highest Reynolds number used of 5000. The lim- itation at higher velocities is that the images of the flow markers are moving too fast and form streaks. As an alter- nate to the higher video rates, a higher shutter speed ( up to 1/32000 s) could be used to insure sharp images that are not streaks. However, considerable additional light would be required because of either shorter exposure times or higher speeds. In the earlier efforts, where ensembled average analysis was the goal, the cameras were synchronized with a stroboscopic light and shutter speed was not a factor.

We have reduced a limited segment of the jet Reynolds number of 4000 data. Figure 11 is the parallel to Figure 4 for this data set and represent a time-average of a 1/2 min. Simple linear estimates, based on velocity and the time needed at a Reynolds number of 200, suggest that we need a 1/4 min to obtain the average. However, we have not com- pleted the full analysis for this Reynolds number (by run- ning long time segments) as we did for the lower case and cannot be certain that these figures represent true time aver-

ages. Figure 12 is the parallel to Figure 8 and shows the velocity vectors near the center plane of the jet and the con- tours and surface map of the z-vorticity on that plane. The differences in the flow patterns are dramatic. The flow at the Reynolds number of 200 is, on the average, what one would anticipate. The 20 fold increase in velocity through the jet changes the entire pattern. There is a much larger overall circulation pattern upwards along the walls as can be easier seen in the dynamic representations in the URL. Clearly, this flow is fluid dynamically rich and will require much more detailed study. It is also clear that averaging removed most of the fine details involved in the opposing jet interactions.

In contrast to the jet Reynolds number of 200 data where 114 s was needed to obtain a reasonable average, the higher Reynolds number of 4000 produced on the average 560 non- zero vectors per frame at the 30 Hz rate. This is very close to a linear estimate from the lower velocity results; i.e., 30 vectors at Re = 200 - 600 vectors at Re = 4000. For a jet Reynolds number of 4000 an estimate of the jet oscillation frequency from Denshchikov et al. (1985) is 5.7 Hz. Their data covered up to a jet Reynolds number of 4800; thus, the estimate should be reasonable for our work. Our sampling frequency of 30 Hz is over 5 times the jet oscillation and again satisfies the Nyquist frequency criteria. Furthermore,

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Figure 1 1 - Longtime, three-minute, averaged velocity field at a jet Reynolds number of 4000 (see Zhao and Brodkey, 1998 for color).

Figure 12 -Three-dimensional, time-averaged velocity vectors in the horizontal (xy) plane with con tours and surface map of z-vorticity at a jet Reynolds number of 4000 (see Zhao and Brodkey, 1998 for color and for dynamic representation).

L I lmml X m m l v lmml l l rnrnl vimm1 Xlrnrnl

Figure 13 - Dynamics of the flow for 2-second averages and 1/4 second averages at a jet Reynolds number of 4000 (see Zhao and Brodkey, 1998 for color and for dynamic representation).

the average of 560 non-zero vectors per frame provided well-smoothed results in each frame.

Finally, in Figure 13, we provided a short segment of the time-dependent information to parallel that given in Figure 10,

again the differences between the frames are dramatic. Showing the results at the 30 Hz data rate would be diffi- cult. Thus, we choose to match the times used in Figure 10. Of course, at this time-resolution, the higher frequency

544 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 76, JUNE, 1998

components of the oscillations are averaged out and cannot be observed. Having the two time scales the same does allow direct comparison between the two figures.

Conclusions

There are several important conclusions that immediately come to mind.

Our experimental PTV system can provide large scale details of a full-field, time-resolved, vector velocity field and its depended measures. The cost of such a system is nominal: however. there has been an investment in time

Denshchikov, V. A,, V. N. Kondrat’ev, A. N. Romashov and V. M. Chubarov, “Auto-Oscillations of Planar Colliding Jetu”, lzve5tiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaia 3, 148-1 50 (1983).

Fernandes, R. L. J., A. Sobiesiak and A. Pollard, “Opposed Round Jets Issuing into a Small Aspect Ratio Channel Cross Flow”, Exp. Thermal & Fluid Sci., 13, 374-394 (1996).

Givi, P., J. I. Ramos and W. A. Sirignano, “Turbulent Reacting Concentric Jets: Comparison Between PDF and Moment Calculations”, Prog. In Astro. And Aero. 95, 384-418; 1985, J. Non- Equilib. Thermodyn. 10, 75 (1985).

Guezennec, Y. G. and N. Kiritsis, “Statistical Investigation of Errors in Particle Image Velocimetry”, Exp. in Fluids 10,

associated with the data analysis. Such measurements can- 138-146 (1990). not be obtained by computational fluid dynamics (CFD) means. However, direct numerical simulation (DNS) could be used at the expense of considerable computer time. - Opposed jet mixers generate large scale, three-dimensional, unsteady motions, even at a jet Reynolds number of 200. Flat, two-dimensional paper printed in black and white

GUeZenneC, y . G. , R. s. Brodkey, N. Trigui and J. c. Kent, “Algorithms for Fully Automated Three-Dimensional Particle Tracking Velocimetry”, Exps. in Fluids 17, 209-219 (1994).

Kent, J. c,, N, Trigui, w,-c, Choi, y. G . Guezennec and R, s, Brodkey “Photogrammetric Calibration for Improved Three- Dimensional Particle Tracking Velocimetry (3-D PTV)”, Proc. SPIE 2005.400 (1993). . . .

does not permit adequate representa tions of the resulting velocity and dependent parameter fields. More complex and dynamic representation can be used to unfold the story of the trow. For now, the Internet can be used to overcome this limitation. Three-dimensional, dynamic movie type representations can recover much of the lost information. For such information, we suggest the reader visit the Internet location (Zhao and Brodkey, 1998) for color and for dynamic representations. A further step of improvement would be the development of true 3-D stereoscopic viewing to visualize such data fields.

Acknowledgements

The authors would like to acknowledge the National Science Foundation that provided a joint grant between Rutgers University (Professor Fernando Muzzio) and The Ohio State University. Throughout the course of this work, our colleagues at Ohio State (Mr. 1. Jung, Dr. S. Haam, Professor Yann Guezennec) have been most helpful and supportive. We also thank the reviewers, who suggested references that allowed analysis of the frequency of oscillation and the justification of the data analysis in the time domain.

References

Atkinson, K. N., Z. A. Khan and J. H. Whitelaw, “Experimental Investigation of Opposed Jets Discharging Normally into a Cross-Stream”, J. Fluid Mech. 115,493-504 (1982).

Brodkey, R. S. and H. C. Hershey, “Transport Phenomena, A Unified Approach”, McGraw-Hill Book Co. New York, NY ( 1988).

Choi, W.-C., Y. G. Guezennec and R. S. Brodkey, “In Situ Calibration and Stereo Matching for 3-D Particle Image Velocimetry”, Bull. Am. Phys. SOC. 37, 1791 (1992).

Cooper, D., D. C. Jackson, B. E. Launder and G. X. Liao, “Impinging Jet Studies for Turbulence Model Assessment-I. Flow-Field Experiments”, lnt. J. Heat & Mass Trans. 36,

Craft, T. J., L. J. W. Graham and B. E. Launder, “New wall-reflec- tion model applied to the turbulent impinging jet”, AIAA Journal 30, 2970-2972 (1 992).

Craft, T. J., L. J. W. Graham and B. E. Launder, “Impinging Jet Studies for Turbulence Model Assessment - 11. An Examination of the Performance of Four Turbulence Models”, Int. J. Heat & Mass Trans. 36, 2685-2697 (1993).

2675-2684 ( I 993).

Li, K. T. and H. L. Toor, “Turbulent Reactive Mixing With a Series-Parallel Reaction Effect of Mixing on Yield”, AIChE J.

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Manuscript received October 27, 1997; revised manuscript received March 16, 1998; accepted for publication April 27, 1998.

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