This manuscript was prepared for review for a special issue of IE&C in honor of its editor, Bob Seader.  A full review was not possible without the Web links; thus, this manuscript, as a preview copy (with links), was provided for reviewers. The paper has now been published:

"On Representation of Complex Turbulent Flows:Representation of large data fields on the Internet" (2000),Ind. Eng.Chem. Res., 39, 1743-1746.

This version of the manuscript has not been revised to match the final published paper. The present manuscript uses the same links an the published version; thus, it can be used to view the color and animated versions of the graphics which are not available with the original.

On Representation of Complex Turbulent Flows

Representation of large data fields on the Internet

Abstract

Full-field, time-resolved, velocity vector information is often needed for the analysis of fluid process problems. However, the reporting and analysis of such information are not simple. Publishers place a premium price on authors who use color. The use of a series of pictures to represent variation with time is poor at best. It would be advantageous to be able to provide a more thorough presentation by using color, stereoscopic viewing,and dynamic representations. The only present solution is to reference Internet locations for such representations or use dynamic links in the online journals currently available. The present paper discusses such efforts that we have used for an experimental database that provides full-field,time-resolved velocity vector information for an opposed jet reactor configuration.The key driving force is simplicity and cost of representation. The same procedures would apply for results from direct numerical simulations (DNS).The flow system used here is a simple gravity driven, opposed jet flow where the two jets interact with each other in the central region of a cylindrical volume. For data acquisition, a series of mirrors, a square chamber around the volume, and SVHS Video recording were used.
 

Introduction

With today's technology, the presentation of dynamic stereograms in full color on computers is not an issue, if cost is not an issue. The real question is how do you convey to others, the readers of journals, dynamic color data, when they do not have specialized equipment. Thus, this note will not deal with advanced techniques. We will consider means that are low cost. For example the use of paper stereo (red-blue) glasses as recently supplied with National Geographic for an article with stereoscopic pictures from the Land Rover on Mars. One aside, the progress of technology and the parallel reduction in cost will within the not too distant future make dynamic stereoscopic viewing an important part of PC systems, just as voice and video have been introduced. There is, however, a price to pay. Older systems are usually inadequate. They can be extremely slow or will simply crash when the newer software (such as Java) is downloaded.

There are three simplistic stereo procedures available. In addition,the three can be combined to enhance the stereo visualization.

• An often used, non-stereo, procedure is to use planar scanning of the data set. This technique provides a sequence of slices that are moved across the field. We have previously used this in our work on the opposed jet flow system (Zhao and Brodkey, 1998). One example would be the velocity vectors on horizontal slices that move from the top to the bottom of the vessel. This procedure requires the viewer to build the three dimensional nature of the system.
• Stereograms using the patented SpaceSpex system for viewing color pictures.Scene and color information is transmitted through a light yellow filter over the left eye. The stereo coding is transmitted through a dark blue filter over the right eye.
• Stereograms using gray level representation. All information is transmitted through both the red and blue filters. The stereo coding is transmitted by using red and blue to represent the two views needed. A color rendition is limited to brown/gray level, which is ideal of the rocks on Mars.
• Stereograms without glasses. Information can be in full color and is transmitted by using graphic perspective representations and dynamic motion of the view. However, the trade off is that longer observation times are often necessary for the viewer to see the stereo effect. In addition, many observers cannot see the pictures in three dimensions.
• Combinations and variations of the above techniques can be used to enhance the stereo effect.

Conclusions and our Final Assessment

Rather than build the story in the logical progression of the research effort, we will provide the results first and then offer the advantages and disadvantages of the alternate systems and combinations considered.

There is no question that systems that used special liquid crystal glasses and special video cards that can interface with the glasses, can provide superb stereo viewing. However, this is at the expense of hundreds of dollars.All the low-cost systems, considered here, are at best a compromise. The glasses cost nothing to a dollar or so and the dynamic technique only requires that you observe the images.

The technique that requires no glasses is the simplest for the reader to use. It is more complex for the author since it requires both color and dynamic movement to obtain the stereo image. There are two aspects to the dynamics. One is the inherent dynamic motion of the flow that is being investigated. The second is the need for motion of the field being viewed in order to see stereo. We will call this latter 'dynamic visualization.'

Stereograms using gray level representation is second best for the type of data fields we have. The levels of velocity are given by gray level and/or the length of the vectors. The stereo information is transmitted through both the red and blue filters. Our assessment is that it is satisfactory to observe the field in stereo, but using gray scale to establish magnitude of the vectors is a disadvantage. We have also combined the gray level presentation with dynamic visualization to improved the observation. However,this did not enhance it enough to make it worthwhile when compared to dynamic visualization in color alone.

Stereograms in color using the patented SpaceSpex system was the least desirable even when coupled with dynamic visualization. The SpaceSpex system is excellent when used for viewing natural pictures such as people and places. It does have limitations associated with representation of blue colors as these are also used for the stereo information. However, for simple colored lines that represent velocity vectors it is not as satisfactory even when the dynamic motion is added.
 

The Opposed Jet Data Base

The opposed jet system is shown in Figure 1. The link shows the picture in color. Further details can be found in Zhao and Brodkey (1998), which is supplemented by information given in Brodkey (1999a). In this URL, the table at the end provides a link that leads to our 'current notices.' In the right-hand column, in the table at the end of this page, further links lead to specific discussions and examples to be cited here. In each case,the URL will be given.

Figure 1 The Flow System
 

Dynamic Visualization to Capture Stereo

At Ohio State there are many seminars for the faculty and students to choose from. One long-term series is run by the Department of Optometry and covers all aspects of the visual sciences. Several have been on stereoscopic visualization in the human eye system. On one occasion, a seminar on stereoscopic perception was to be given by Jim Todd of cognitive sciences. Unfortunately,he did not have his slides, a postdoc had them in England. Thus, instead of the planned topic he talked about a topic for which he had slides. He discussed how one could perceive three dimensionality, if the 3-D perspective view was oscillated back-and-forth (see Todd, 1982, 1995; Todd et al.,1988; Todd and Bressan, 1990; and Norman and Todd, 1993). They used simple stick figures to illustrate the effect and presented the results of statistically testing the procedure on a number of observers. We have generated a similar dynamic representation and present it as a series. The basic stick figure is shown in perspective in Figure 2. The figure consists of the three lines that connect points 1 to 4. In the animations, the stick shape is fixed and the viewer's observation point is changed. The link shows the picture in color.

Figure 2 The Stick Figure
 
 

The first dynamic representation (Zhao & Brodkey, 1999b1) is for only a 6-degree change in observation using 1 degree intervals.The second (Zhao & Brodkey, 1999b2) and third (Zhao & Brodkey, 1999b3) use only 3 or 4 figures to represent an 18-degree change in observation. The final representation uses 1 degree intervals for the entire 18-degree change in viewing (Zhao & Brodkey, 1999b4).This last figure is also shown in monochrome (Zhao & Brodkey, 1999b5).To us, with prolong observation, the effect was dramatic and we undertook the present work to see if such a simple procedure would allow three dimensional observation of a dense velocity vector field. Our continued used of stereoscopic visualization in our work no doubt helped to prepare us for rapid perception of the 3-dimensional form from the moving shapes in these pictures. It is certainly not clear if we are seeing the picture in stereo or if the combination of perspective and overlay is helping our mind sort out the three-dimensionality. In any event, the enhancement was enough for us to investigate the process further. We wanted to compared these dynamic visualization results with the simple procedures of using stereo glasses to separate the information for the left and right eyes. The major question for us was would we be able to discern the 3-dimensional flow field in a densely packed view (21³ vectors) as compared to the simple stick figures.

Figure 3 shows one frame from the gray-scale, time-averaged, opposed jet data set at an inlet Reynolds numbers of 200. The link shows the figure in color. The flow is unstable above a Reynolds number of 125 or so. Shown is the longtime average of nearly a half a million vectors measured over a 9 minute period. The grid used for the averaging is 21³. This is the time-averaged structure of an unsteady flow. The URL for this dynamic representation for back and forth rotation in color is given in Zhao and Brodkey (1999c).The view where the scene is both rotated and pitched is given in Zhao and Brodkey (1999d).

Figure 3 The Three-dimensional Flow Field, Time Averaged Over Nine Minutes at a Reynolds Number of 200

The flow is in reality time varying and not steady as implied in Figure 3. The URL for the dynamic representation of the time varying flow can be seen in Zhao and Brodkey (1999e).Here, 1/4 second average periods of the velocity in the same volume are shown as a time sequence. Only the central plane between the jets is shown.The animated sequence is at Re = 200. The sequence follows at the 1/4 second rate between views for a period of 8 sec. and then repeats. A new sequence that shows the entire volume, rather than only the central plane, was generated(1999f). In this test, the field was not moved to provide dynamic visualization. In this view it is not really possible to judge depth. There is too much information provided. In Zhao and Brodkey(1999g), the dynamic visualization was added.We have synchronized the 'dynamic visualization' time cycle to the same 8 seconds. Thus, the time sequence starts over when the view is at it initial position; i.e., once each cycle. Although stereo is apparent, it is not at the level that is desired. Todd (1999) has indicated that transparent images are difficult to observe when using dynamics to provide the stereo content.

For flow visualization in fluid dynamics, the velocity vector field is often less important than the fluid particle motions that can map out in time the flow field in time. Zhao and Brodkey (1999h)have provided a simple dynamic representation of what a few particle paths might be in the opposed jet system. Here they followed the particles computationally and updated the velocity field every 1/4 second. Zhao and Brodkey (1999i1,1999i2)have at the same time provided a slow oscillation of the visual field to provide a better stereo viewing.
 

Representations of the Same Data Using the Alternate Methods

The stereo representation using gray scale can be found at Zhao and Brodkey (1999j). Here the left image has 6 degrees separation (human viewing) and the right has 10 degrees. The left image is easier to fuse; thus, we used 6 degrees in all our subsequent work with this technique. Directions for making this stereogram are available(Zhao and Brodkey, 1999k). However, gray level does not have adequate contrast. One enhancement is to use black vectors on white and length alone to indicate the magnitude. This is shown by Zhao and Brodkey (1999m). Still another enhancement of the stereo view is to observe the stereograms dynamically as shown in Zhao and Brodkey (1999n). In none of these cases is the stereoscopic visualization better than the color dynamic representations. Thus, we do not recommend this approach for further study for this type of data field.

The SpaceSpex system is much like the gray level effort, but can provide color. In general, for the type of data field to be viewed here, the system was not as good as the other techniques. This first URL is a stereogram using the full data field. The data field was too dense to obtain a good stereogram. The view was improved in the second URL by reducing the number of vectors from 21³ to 10³. These results can be seen at Zhao and Brodkey (1999p1)(1999p2).Finally, the SpaceSpex view technique can be combined with dynamic visualization as shown at Zhao and Brodkey (1999q). Again,the use of dynamic visualization alone without glasses was better.
 
 

Summary

Of the simplistic three-dimensional data representations, the use of perspective and dynamic visualization is both the simplest and does provide improved visualization of complex data sets over that obtained by using static or scanning representations. Further enhancements obtained by using stereo viewing with glasses does not provided enough added improvement to justify the additional effort needed. Higher level, liquid crystal glass systems should be tested; especially as the price of these systems becomes competitive.

References

Brodkey, R.S. (1999a) http://www.che.eng.ohio-state.edu/~brodkey/fluids.html

Todd, J.T. (1982) Visual Information About Rigid and Nonrigid Motions:A Geometric Analysis. J. of Experimental Psychology, 8, 238-252.

Todd, J.T., Akerstrom, R.A., Reichel, F.D. and Hayes, W. (1988) Apparent rotation in three-dimensional space: Effects of temporal, spatial, and structural factors. Perception & Psychophysics, 43, 179-188.

Todd, J.T., and Bressan, P. (1990). The perception of 3-dimensional affine structure from minimal apparent motion sequences. Perception& Psychophysics,48, 419-430.

Norman, J.F., and Todd, J.T. (1993) The Perceptual analysis of structure from motion for rotating objects undergoing affine stretching transformations.Perception& Psychophysics, 53, 279-291.

Todd, J.T. (1995) The Visual Perception of Tree-Dimensional structure from Motion, Perception of Space and Motion, Chapter 6, Academic Press, Inc., 201-226.

Todd, J.T. (1999). Personal communication.

Zhao, Y. and Brodkey, R.S. (1998) Averaged and Time-Resolved, Full-Field(Three-Dimensional), Measurements of Unsteady opposed Jets. Can. J.of Chem. Engr., 76, 536-545.

Zhao, Y. and Brodkey, R.S. (1999b1) anns1999n1.html

Zhao, Y. and Brodkey, R.S. (1999b2) anns1999n2.html

Zhao, Y. and Brodkey, R.S. (1999b3) anns1999n3.html

Zhao, Y. and Brodkey, R.S. (1999b4)anns1999n4.html

Zhao, Y. and Brodkey, R.S. (1999b5)anns1999n5.html

Zhao, Y. and Brodkey, R.S. (1999c) dynstr1.html

Zhao, Y. and Brodkey, R.S. (1999d) dynstr2.html

Zhao, Y. and Brodkey, R.S. (1999e) http://www.che.eng.ohio-state.edu/~brodkey/RES_OJ/ann7.html

Zhao, Y. and Brodkey, R.S. (1999f) anns1999e.html

Zhao, Y. and Brodkey, R.S. (1999g) anns1999s.html

Zhao, Y. and Brodkey, R.S. (1999h) http://www.che.eng.ohio-state.edu/~brodkey/RES_OJ/ann12.html

Zhao, Y. and Brodkey, R.S. (1999i1) anns1999i1.html

Zhao, Y. and Brodkey, R.S. (1999i2) anns1999i2.html

Zhao, Y. and Brodkey, R.S. (1999j) stereogray.html

Zhao, Y. and Brodkey, R.S. (1999k) stereorb.html

Zhao, Y. and Brodkey, R.S. (1999m) stereowhiteblack.html

Zhao, Y. and Brodkey, R.S. (1999n) dynstr3.html

Zhao, Y. and Brodkey, R.S. (1999p) stereo2.html and stereo3.html

Zhao, Y. and Brodkey, R.S. (1999q) dynstr5.html