Particle path based tomographic image velocimetry

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 2-4, 2013

Particle path based tomographic image velocimetry

1

Department of Information Systems Engineering, Osaka Sangyo University, Daito-shi, Osaka, Japan ohmi@ise.osaka-sandai.ac.jp

2

Graduate School of Osaka Sangyo University, Daito-shi, Osaka, Japan ABSTRACT

Particle path based image velocimetry has been developed for 3D volumetric velocity measurement of fluid flows. The proposed method is basically based on the tomographic reconstruction of 3D particle paths by using multiple camera views of long exposure particle images. Particle path based image velocimetry was popular in the early days of 2D PIV but went out of use rapidly because of its inherent issues like intersection of particle paths and directional ambiguity. But in the present work, this technique is further exploited by using new techniques based on the tomographic reconstruction of 3D particle paths. The velocity recovery results of this new approach are compared to those of the conventional 3D tomographic particle tracking velocimetry using two instantaneous particle images at different instants.

INTRODUCTION

Particle path visualization is an old established technique for visualizing 2D velocity of fluid flows [1]. This technique was also actively used in the early days of particle image velocimetry [2]-[3] but fell out of use rather rapidly because of the appearance of high resolution digital video cameras and high power pulse lasers. Particle path based velocimetry had also inherent issues such as intersection of particle paths and directional ambiguity. But the new trend of using the tomographic reconstruction technique in 3D particle image velocimetry seems to revive the possibility of particle path based velocimetry because of two reasons.

The first reason is that the intersection of particle paths on the camera recorded image does not largely affect the tomographic reconstruction of 3D particle paths. It is true that if the particle paths intersect on the camera recorded image, every intersection point may become a source of ghost particle image in the reconstruction. But these point-wise ghost particle images are expected to be easily discriminated from the particle path images in the voxel space because they are considerably different from a viewpoint of morphology. The second reason is that the tomographic PIV or PTV using instantaneous (point-wise) particle images often suffers from appearance of ghost particles due to inevitable intersection of line of sights in the voxel space. Needless to say, these ghost particles give rise to serious errors in the recovery of velocity vectors in the case of PTV [4] rather than in PIV. From such a background, in the present work, a new image velocimetry technique based on the tomographic reconstruction of 3D particle path has been developed.

One issue to be addressed in the revival of the particle path based image velocimetry is the directional ambiguity of the recovered velocity vectors. But this issue was once a point of keen interest in the early days of 2D particle path velocimetry as well as in the later days of 2D auto correlation based PIV. So there are a lot of counter measures proposed from which we can select one or two which are adapted to the current technology of image recording and processing. In the present study, the authors have “virtually” tried a simple parallel shift recording method according to which all the reconstructed vectors are considered to have positive x or y components. In fact, the parallel shift system is not installed in the image recording system of the present experiment but the generated flows, as it happens, can be regarded fully uni-directional in x or y direction.

VELOCITY MEASUREMENT BY PARTICLE PATH IMAGES

In the resent work, the tomographic reconstruction of particle path images is performed by using both synthetic and ex-perimental particle images. The synthetic image used is the 3D PIV standard image of the Visualization Society of Japan [5], from which the tomographic reconstruction is performed on the first and second frame particle images viewed by three cameras with different viewing angles (30º apart from each other). Since the original images of the PIV standard image are all instantaneous particle images, in the present work, the two time step images are overlapped for each camera view and every particle point is manually connected with its appropriate partner by using commercial photo retouch software. For comparison of particle path based velocimetry result with the conventional tomographic PTV result based on instantaneous particle images, the original point-wise images are also used to reconstruct the instantaneous particle location at two time steps. Then the particle coordinates determined by the tomographic reconstruction are paired be-tween the two time steps and thereby the distribution of 3D velocity vectors is obtained. For this particle pairing process,

the SOM (self-organized maps) particle tracking algorithm [6] is used. This algorithm is considered especially advan-tageous to detect and filter out loss-of-pair particles.

The second experimental image comes from the actual experiment of a 3D swirling flow in a rectangular water tank (170x110x190 mm3) as depicted in Figure 1. The swirling flow is generated by a magnetic stirrer with speed control installed under the water tank. The seeding particles (100 m diameter) are illuminated by a 10 mm thick laser light sheet and their images are recorded by 4 CCD cameras with different viewing angles (from top, bottom, left and right). In order to intensify the expanded and collimated laser light sheet, a vertical mirror is placed at the opposite end of the water tank. The exposure time of the 4 synchronized cameras is set at 1/50 sec for the mean flow velocity of about 8 mm/s. The camera calibration is carried out by using a matrix dot calibration plate which is placed at three different depth positions in the water tank. The calibration model used here is a basic DLT model because all the CCD cameras record images through a telecentric lens.

The tomographic reconstruction is performed by using different size of voxel grids between the synthetic and ex-perimental particle images. In the case of the PIV standard image, the voxel space is composed of 180x130x20 grids with 0.02 mm voxel spacing, while in the case of the swirling flow experiment, the voxel space is composed of 400x400x40 grids with 0.05 mm voxel spacing. The reconstruction algorithm is always the basic MART. In order to recover the velocity from the 3D reconstructed particle paths, the reconstructed voxel intensity is first binarized by using the dynamic threshold binarization algorithm [7]. Then the length and gradient of each particle path are quantified through linear least squares fitting and thereby the location and three components of velocity vectors are determined. As a post processing of the binarization step, an opening procedure (composed of dilation and erosion) is performed to fill up the path gaps due to the particle intensity fluctuation during the exposure time. As described in the previous section, the direction of the reconstructed vectors is determined by imposing a simple assumption on one of the measured velocity components.

Figure 1 Tomographic reconstruction of a synthetic particle point image and SOM particle pairing result

RESULTS OF EXPERIMENT

Figures 2 and 3 are comparative velocity recovery results derived from the same synthetic particle images using the same tomographic reconstruction technique. More precisely, Figure 2 shows one of the recorded particle point images (a), distribution of reconstructed 3D particle points in the voxel grid space (b) and the result of time-differential particle paring (c). Obvious decrease of number of particle points between the results (b) and (c) is mainly due to a slightly severe validation algorithm [6] used to detect ghost particles during the reconstruction. On the other hand, Figure 3 shows one of the recorded particle path images (a), distribution of reconstructed 3D particle paths in the voxel grid space (b) and the resulting 3D vector plots (c). From these two comparative results, one can presume that the particle path based tomo-graphic velocimetry is more advantageous for recovering 3D velocity vectors without the effect of ghost particles.

The second example comes from actual experimental image recorded by 4 CCD cameras viewing a weakly swirling flow in a rectangular water tank (170x110x190 mm3) with a 10 mm thick laser sheet. Figure 4 shows the four recorded particle path images (a), distribution of reconstructed 3D particle paths in the voxel grid space (b) and the resulting 3D vector plots (c). A certain amount of the particle streak spots can be observed along the depth direction border of the laser sheet. They are probably due to the reflection of illuminated particles on the glass water tank surface through which the particle streak images are recorded.

Argon‐ion laser  Mirrors  Concave and collimator lenses  Cameras with telecentric lens  Glass water tank Control PC  Function generator  Laser flux  Slit Mirror 

(a) Original instantaneous particle images recorded by 3 cameras (first time step only)

(b) Reconstructed particle images at two instants (c) SOM particle pairing result Figure 2 Tomographic reconstruction of a synthetic particle point image and SOM particle pairing result

(a) Original particle streak images recorded by 3 cameras

(b) Reconstructed path images (c) 3D velocity profile Figure 3 Tomographic reconstruction of a synthetic particle path image

(a) Four synchronized path images recorded by left, top, right and bottom cameras (from left to right)

(b) Reconstructed path images (c) 3D velocity profile Figure 4 Tomographic reconstruction of an experimental particle path image

REFERENCES

[1] Prandtl L and Tietjens OG “Applied Hydro- and Aeromechanics” McGraw-Hill (1934)

[2] Imaichi K and Ohmi K "Numerical Processing of Flow-Visualization Images --- Measurement of Two-dimensional Vortex Flow" Journal of Fluid Mechanics 129 (1983) pp.283-311

[3] Imaichi K and Ohmi K "Quantitative Flow Analysis Aided by Image Processing of Flow Visualization Images" Flow Visualization III, Hemisphere (1985) pp.365-369

[4] Joshi B.and Ohmi K “Particles detection scheme for tomographic particle tracking velocimetry” Proc. 16th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics (2012) #1.5.4

[5] Okamoto K, Nishio S, Kobayashi T, Saga T and Takehara K "Evaluation of the 3D-PIV Standard Images (PIV-STD Project)" Journal of Visualization 3 (2000) pp.115-124

[6] Ohmi K “SOM-Based Particle Matching Algorithm for 3-D Particle Tracking Velocimetry” Applied Mathematics and Computation 205 (2008) pp.890-898