3.3 Particle Image Velocimetry
3.3.3 Image processing and data post-processing
Figure 3-12 shows an image pair captured in a horizontal plane 3.5 cm above the ground and for vanes angle of 10˚. The bright strip in these images is due to the reflection inside the chamber. The captured images were processed using the TSI software to extract vector maps. Cross-correlations were performed between interrogation windows (64 by 64 pixels) in the first image and search regions (128 by 128 pixels) in the second image. Using a 50% overlap of interrogation windows, the nominal resolution of the velocity field is increased to 32 by 32 pixels. Spurious vectors were identified and removed using global and local filtering and then replaced by local median vectors. The total number of spurious vectors in each map did not exceed 1% of the total vectors. In the next step, MATLAB (R2008b) was used to analyze the data. Pixel displacements were converted to velocities (m/s) using the calibration ratio (m/pixel) and time interval values (μs). Figure 3-13 displays instantaneous velocity field obtained from the horizontal plane
measurement 3.5 cm above the ground and for three vane angles. It is observed that as the vane angle (and consequently the swirl ratio) increases, the vortex core expands. Also, a
two-celled vortex is observed at θ=30˚ which implies that the drowned vortex jump has
occurred and the flow regime is fully turbulent. This conclusion is further investigated and confirmed through flow visualizations and surface static pressure measurements [5].
a) b)
In order to compute the time and azimuthally averaged velocities, the center of the vortex was located in each vector map. In these calculations, it was assumed that the vortex is axisymmetric and therefore there is no velocity variation with azimuth. Assuming that the vortex center is always at the geometric center of the simulator, radial and tangential velocities were averaged over time and azimuth.
a) b) X (m) Y (m ) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 X (m) Y (m ) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
c)
Figure 3-13: Instantaneous horizontal velocity vector maps obtained from PIV measurements at z=3.5 cm for a) θ=10˚, b) θ=20˚ and c) θ=30˚.
Detecting the center of the vortex was one of the most challenging parts of the data analysis. There are several methods for identifying the core of a vortex (line-based) as well as the region of a vortex (region-based). In general, the region-based algorithms are easier to apply and computationally less expensive when compared to the line-based
methods. In this work a novel approach, proposed by Jiang et al. [6] in 2002, was
implemented. This point-based algorithm is based on the concept from Sperner’s lemma [7]. This method was selected for vortex detection due to its simplicity and efficiency compared to other existing methods. The following steps explain the vortex detection process applied to each vector maps:
1. Direction ranges: equally spaced direction ranges were defined for each vector.
Figure 3-14 displays three (A, B, C) and four (A, B, C and D) equally-spaced direction ranges defined for two-dimensional cases.
X (m) Y (m ) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
a) b)
Figure 3-14: a) three and b) four equally-spaced direction ranges – image from [6].
2. Labeling: using the direction ranges, vectors were labeled based on the direction
they point at. This method states that if a fully labeled triangular cell (square cell in case of using four direction ranges) exists, then the direction spanning property is satisfied. The direction spanning property means each vector at the vertex of a cell point is in a unique direction range. Therefore, a grid point which its
neighbors satisfy the direction-spanning property is within the core region [6]. Figure 3-15 shows vectors in a 2D grid labeled using three and four direction ranges. It is seen that, for this sample of the vector map, the four direction ranges perform more accurately in detecting the vortex core region. Considering the complexity of the flow in the current work, labeling was done using four direction ranges.
3. Checking grid points: Once labeling was complete, the immediate neighbors of
each grid point were checked for direction spanning property. If satisfied, that grid point was identified as being within the core region.
The accuracy of the algorithm was evaluated through visual investigations of vortex center in several vector fields. Note that for two-celled vortex structures, the center of the vortex with stronger circulation was selected as the center of the parent vortex.
a) b)
Figure 3-15: Core region detection for a 2D vortex using a) three and b) four direction ranges – image from [6].
The guidelines provided by Cowen and Monismith [8] and Prasad [9] were followed to determine the uncertainties in velocity measurements using PIV. A maximum error of 7.2% is estimated for velocity measurements in horizontal planes. The uncertainty analysis details can be found in Appendix D.
References
[1] Snyder, W. H., and LumIey, J. L., 1971, "Some Measurements of Particle Velocity
Autocorrelation Functions in a Turbulent Flow," J. Fluid Mech., 48pp. 41-71.
[2] Loth, E., 2000, "Numerical Approaches for Motion of Dispersed Particles, Droplets,
and Bubbles," Progress in Energy and Combustion Science, 26pp. 161-223.
[3] Hamburg, M., 1970, "Statistical analysis for decision making," Harcourt, Brace and World, .
[4] Adrian, R. J., 1991, "Particle-Imaging Techniques for Experimental Fluid
Mechanics," Annual Review of Fluid Mechanics, 23(1) pp. 261-304.
[5] Refan, M., and Hangan, H., 2013, "The Flow Field Characteristics in the Model WindEEE Dome," Unpublished Results.
[6] Jiang, M., Machiraju, R., and Thompson, D., 2002, "A novel approach to vortex core region detection," Joint EUROGRAPHICS - IEEE TCVG Symposium on Visualization, D. Ebert, P. Brunet and I. Navazo, eds. The Eurographics Association, pp. 217-225.
[7] Cohen, D. I. A., 1967, "On the Sperner Lemma," J. Combinatorial Theory, 2pp. 585-
587.
[8] Cowen, E. A., Monismith, S. G., Cowen, E. A., 1997, "A Hybrid Digital Particle
Tracking Velocimetry Technique," Experiments in Fluids, 22(3) pp. 199-211.
[9] Prasad, A. K., Adrian, R. J., Landreth, C. C., 1992, "Effect of Resolution on the Speed and Accuracy of Particle Image Velocimetry Interrogation," Experiments in