Particle Imaging Velocimetry Standard Images

Transient Three-dimensional Images

Okamoto, K.*1 and Oki, M.*2

*1 Nuclear Engineering Research Laboratory, University of Tokyo, Tokai-mura, Ibaraki, 319-1188, Japan. E-mail: okamoto@tokai.t.u-tokyo.ac.jp

*2 School of High-Technology for Human Welfare, Tokai University, 317 Nishino, Numazu-shi, Shizuoka 410-0395, Japan.

Abstract : The Visualization Society of Japan started a project for PIV standardization and popularization in 1996. The objectives of this project are to popularize the complicated PIV system, and to be a standard tool for the measurement of flow field. The PIV-STD developed the PIV standard images to provide the evaluation tool for the PIV techniques. The new images were based on the transient three-dimensional motion. The developed PIV standard images are distributed using the Internet (http://www.vsj.or.jp/piv), and can be accessed around the world through the Internet. They can be applied for the performance investigation of any PIV techniques. Comparing with the traditional measurement technique, e.g., Laser Doppler Velocimeter and Hot Wire Anemometer, the whole field measurement is a great advantage to investigate the flow field. (10 to 15 lines)

Keywords : Visualization, PIV, Standard, Internet, Popularization. (about 5 items)

1. Introduction The Particle Imaging Velocimetry (PIV) is a quantitative velocity measurement technique, with visualizing the flow field by small tracer particles and with analyzing the visualized digital images. The PIV can measure the whole two-dimensional or three-dimensional flow field simultaneously without disturbing the flow field. Comparing with the traditional measurement technique, e.g., Laser Doppler Velocimeter and Hot Wire Anemometer, the whole field measurement is a great advantage to investigate the flow field.

Lots of PIV techniques had been developed and applied to various flow fields. The techniques include Cross-correlation technique (e.g., Adrian, 1991), Four-step particle tracking technique (e.g., Kobayashi et al., 1989), and so on. The developers analyzed the effectiveness of their PIV techniques using their own evaluation. There are no standard evaluation tools for investigating these PIV techniques, resulting in the no standard PIV techniques. Therefore, the users should determine the selection of the appropriate PIV technique without any useful information. When the users could get the velocity distribution using some PIV technique, there also were no standard evaluation tools for the measured velocity data. In order to get the accuracy information of there measured data, they have to evaluate the data by their-selves. Also, the PIV system needs lots of know-how,

because the PIV system contains many steps, i.e., test section fabrication, visualization, image capture, image analysis, particle tracking, and evaluation of accuracy.

The current status of the PIV technique is far from the popularization or generalization technique. To popularize the PIV technique for practical use, the PIV standards and the PIV guide tools should be settled. With using the PIV standards, any user can easily apply the PIV technique onto their target flow field with the accuracy information.

2. Standard Images

2.1 Computer Graphics

With considering the camera location and orientation vector, the global coordinate has been transformed to the camera coordinate system with a simple linear transformation. Then, the particle projection (X, Y) on the camera is calculated with considering the refraction at the vessel wall. To determine the refracted light path, the light path length between camera focus and particle is set to be minimum. In this study, one or three cameras are used to capture the flow field with the particles.

The image size is fixed to be 256x256 pixels. One pixel has 256 intensity levels (8bit). The particle image is generated with writing the particle onto the image. The intensity at the location (X,Y) in the image caused by the scatter from the particle (xp, yp, zp) whose projection is (Xp, Yp), is

Fig. 1 Experimental setup for the verification test (This figure is only sample.) expressed as follows,

+=

SYYXX

IYXI pp2

)()(exp),(

22

0 (1)

2.2 Example of Standard Images

The PIV standard images are distributed with using the Internet. The URL of the images is http://www.vsj.or.jp/piv/. This address is the same with that of the two-dimensional standard images. The animations of the standard images are also shown. Anybody can download the standard image file through anonymous FTP or HTML. The distribution of the standard images is easily achieved with using the Internet. Anybody can access the PIV standard images from the world. The animation of the PIV standard images is also helpful to understand the characteristics of the images.

Table 1 summarizes the standard 3D PIV images. Six standard Images are provided on the internet. In #351 and #352, a cylindrical laser light volume illumination is used. The each series contain the 144 serial images (720ms) with transient three-dimensional flow field. The flow field is the same with that of #301. Three cameras are settled on the horizontal plane. Center camera (#1) is located on the z axis, i.e., perpendicular to x-y plane. The vessel wall is also settled on parallel to the x-y plane. So, camera #1 has small refraction effects. While, left and right cameras (#0,#2) are set with the angle of 30 degree to z axis. Because of the refraction, the particle images are distorted. The refraction index in the water and wall is 1.33. The #371 and #377 are illuminated by cylindrical laser light. In #371, the camera locations are almost the same with #351, however, they have disturbances. These disturbances simulate the uncertainty of the camera setup. The camera

(a) Ratio image of RhB (b) Ratio image of PtTFPP

Fig. 2 Example of standard images (This figure is only sample.)

Table 1 Specifications of standard images Image# Number of

particles Refraction

index Comments

#301 3000 1.00 Two-dimensional flow #302 500 1.00 Two-dimensional flow #351 2000 1.33 Wall refraction was taken into account #352 300 1.33 Wall refraction was taken into account #355 500 1.33 Camera locations were unknown #357 500 1.33 Cameras were set under the bottom. Complex bottom view

has inclined horizontally and vertically. In #377, the flow field near the wall impingement is viewed from bottom. The three cameras are settled on the corner of triangle. The refraction index in the water and wall is 1.33. Because the flow field at the impingement is highly turbulent, interesting particle motions are visualized. The reconstruction of three-dimensional particle position will be difficult. This image is a challenging problem.

The images with grid point particles are provided to calculate the camera position correctly. Also, the accurate particle three-dimensional position and projection point on the images are also provided as a text file. In order to calculate the particle three-dimensional positions, reconstruction procedure from the three camera images are needed. These standard images are used to calibrate the three-dimensional reconstruction algorithm. In the standard images, three-dimensional particle position and

velocity distributions are also distributed. All of the recorded particles had its own ID number. Since the particle positions are written on the file with the ID, it is very easy to track the actual particle movement.

3. Application of Standard Images

3.1 Transient Velocity Tracking

To clarify the effectiveness of the transient three-dimensional Standard images, the #301 is analyzed, using the two-dimensional cross-correlation technique (Adrian, 1991) and Spring Model technique (Okamoto et al., 1995). Figure 2 shows the comparison between the correct velocity distribution and reconstructed velocity distributions. In the cross-correlation, the interrogation region is 16 x 16 and the search area is 20 x 20. The sub-pixel accuracy is achieved with interpolating the cross-correlation function in the 2nd order polynomial. In the spring model

Fig. 3 Pressure field on the surface of a delta wing (This figure is only sample.)

technique, the particle centroids are calculated from the image, with using the Laplace filtering and binarization. The maximum number of the particle in one cluster is 18, and search area is 10 pixels. Since the number of particles in the image is relatively large, the cross-correlation technique gives a better result. Also, the images contain no noise, therefore, there are almost no erroneous vectors. The spring model can track the individual particles with relatively high accuracy.

4. Conclusion The standard images which aim to establish an evaluation code of PIV were proposed. The standard images have been developed based on the calculated velocity field by means of three-dimensional LES.

The transient and three-dimensional motions are taking into account in the standard images. To generate the images, the wall refraction at the vessel surface is considered. The effectiveness of the present standard images is

demonstrated with using the cross-correlation and spring model technique.

References

Adrian, R. J., Particle-imaging techniques for experimental fluid mechanics, Ann. Rev. Fluid Mech., 23 (1991), 261-268. Haridi, S., Numerical data visualization method, to appear in Journal of Visualization, 2004. Kobayashi, T., Saga, T., Segawa, S. and Knada, H., Development of a Real-Time Velocity Measurement System for

Two-Dimensional Flow Fields Using a Digital Image Processing Technique, Trans. of JSME, 55-509, B (1989), 107-112. Massey, B. S., Mechanics of Fluids (Sixth edition), (1991), 123, Chapman & Hall, London. Okamoto, K., Hassan, Y. A. and Schmidl, W. D., New Tracking Algorithm for Particle Image Velocimetry, Experiment in

Fluids, 19-5 (1995), 342-347. Warren, Y. and Smith, I., Visualization of Medical Images, Journal of Visualization, 7-1(1996), 37-58. Yamanouchi, K. and Furukawa, K., Visualization using Tracer Method, Proceedings of the Fifth International Symposium on

Visualization (Tokyo), (1996-5), 582-591, IOS Press and Ohmsha.

Author Profile Koji Okamoto: He received his M.Sc.(Eng) in Nuclear Engineering in 1985 from University of Tokyo. He also received his Ph.D. in Nuclear Engineering in 1992 from University of Tokyo. He worked in Department of Nuclear Engineering, Texas A & M University as a visiting associate professor in 1994. He works in Nuclear Engineering Research Laboratory, University of Tokyo as an associate professor since 1993. His research interests are Quantitative Visualization, PIV, Holographic PIV Flow Induced Vibration and Thermal-hydraulics in Nuclear Power Plant. (within 100 words with a color photograph (3x2.5cm) of the author) Makoto Oki: He received his M.Sc.(Eng.) degree in Mechanical Engineering in 1976 from Tokai University and his Ph.D. in Mechanical Engineering in 2000 from the same university. After obtaining M. Sc. he worked as a system engineer at Japan Advanced Numerical Analysis, Inc.. He then became an assistant professor of Tokai University, and currently is an associate professor. His current research interests are computational fluid dynamics, computer graphics and internet application. (within 100 words with a color photograph (3x2.5cm) of the author)