Experimental test case – swirling jet

The performances on a real test case are assessed by using the database of a tomographic PIV experiment performed in the Jet Tomography Facility (JTF) of TU Delft by Ianiro et al (2011). The flow field of a swirling jet at and swirl number equal to 0.4 (see Ianiro & Cardone 2012 for definition) is investigated by using three Imager Pro HS 4M cameras observing the light scattered by polyamide particles dispersed in an octagonal water tank ( height, diameter). The light source is a Quantronix Darwin-Duo Nd:YLF laser, allowing at 1kHz. Nikon objectives with and set to 32 are used; the optical magnification is approximately , with an average resolution of about . The particle image density is about , resulting in a source density of 0.34. More details on the experimental apparatus can be found in Violato & Scarano (2011).

A volume self-calibration (Wieneke 2008) is executed to reduce the calibration error; 5 MART iterations reconstruct the light intensity distribution in the volume, discretized in voxels (i.e. a cube of for each side). Both the operations are performed by the Davis 7.4 software.

The structure of the interrogation algorithm is summarized in Tab. 5.4-5.5 for the cross-correlation with top hat moving average, and with the aid of a Blackman weighting window (in both cases the dense predictor is averaged over a voxels window). Since the flow field to be measured is challenging, different combinations of solutions are tested: block FFT in the refinement part of the process, and direct correlations in the final iterations (BFFT+DC); only direct correlation (DC) or block FFT (BFFT) during all the process, except for the predictor estimation. Generally speaking, one can choose between BFFT and DC for the different stages of the process. As shown in Tab. 5.4-5.5, it is proposed to use different solutions for the refinement steps and for the final iterations or the same solution for both the stages of the process. The initial part of the process is further accelerated by binning the distributions to be interrogated by a factor of 4 in the first two steps, and of 2 in the third one.

Step Binning factor IV size [vox] Effective IV size [vox] Overlap CC evaluation method Processing time for the standard FFT approach [s] 1 4x 163 ₆₄3 _{1.3k 0% FFT-Based 2.6} 2 4x 163 ₆₄3 _{12.2k 50% Method 1 20.9} 3 2x 323 ₆₄3 _{103.8k 75% Method 1 178.8} 4 1x 483 ₄₈3 _{250k 75% Method 1 238} 5 1x 483 ₄₈3 _{250k 75% Method 2 239} 6 1x 483 ₄₈3 _{250k 75% Method 2 239}

Table 5.4 Processing algorithm: in the refinement section the CC evaluation method can be different

from that of the iterations on the final grid.

Step Binning factor IV size [vox] Effective IV size [vox] Nvect Overlap CC evaluation method Processing time for the standard FFT approach with weighting windows [s] 1 4x 243 ₉₆3 _{1.3k 33% FFT-Based 44} 2 4x 243 ₉₆3 _{12.2k 67% Method 1 317} 3 2x 483 ₉₆3 _{103.8k 83% Method 1 2662} 4 1x 723 ₇₂3 _{250k 83% Method 1 2348} 5 1x 723 ₇₂3 _{250k 83% Method 2 2349} 6 1x 723 ₇₂3 _{250k 83% Method 2} 2349

Table 5.5 Processing algorithm in the case of adoption of a Blackman weighting window in the cross-

correlation step: in the refinement section the CC evaluation method can be different from that of the iterations on the final grid.

The results in terms of reduction of processing time are reported step by step in Fig. 5.11a. Binning the distributions by a factor of 4 provides an acceleration of about 63 times of the predictor estimation; the second step is even faster when BFFT is employed, while direct correlation is slowed down by a relevant percentage of non-direct correlations to be performed (see Fig. 5.11b). The obtained speed-up

Chapter 5 – Efficient 3D PIV interrogation algorithms

Fig. 5.11 Top hat moving average approach: a) Speed-up for each step as a function of the processing

steps; b) percentage of non-direct correlations.

Fig. 5.13 Examples of profiles of the streamwise velocity component along the crosswise direction.

decreases in the refinement part as the binning factor is reduced up to unity. In the final iterations acceleration is recovered thanks to the results convergence on the final grid, reducing the percentage of non-direct correlations to be executed with the aid of FFT. In this sense, BFFT performs better than direct correlation thanks to a wider search area for the correlation peak. The overall speed-up is about 4.9, 6.6 and 11.8 times for DC, BFFT+DC and BFFT, respectively.

On the other hand, one should consider the accuracy and reliability of the results. The instantaneous vorticity fields reported in Fig. 5.12 testify that BFFT provides noisier results because of artefacts derived from the imposed periodicity on small IV, while DC on the final correction steps provides better convergence to slightly smoother results. However, the standard deviation of the difference between the two velocity field is rather small (0.07 pixels and 0.09 pixels for the u and v component, respectively).

An improvement in spatial resolution can be obtained adopting a Blackman weighting window in the cross-correlation step (see Fig. 5.12c). Of course, this increases the computational cost since more terms have to be computed to obtain the cross-correlation coefficients. However, if compared to the standard process based on FFT, the interrogation is executed 1.3 times faster with the approach BFFT+DC, with much better results. Considering that an "equivalent standard process", based on FFT weighted with a Blackman weighting window (Fig. 5.12d) is executed 10 times slower than the standard process with top hap filtering, this involves an acceleration of 13 times of the process BFFT+DC with respect to the respective standard one, with roughly the same results. The comparison between Fig. 5.12c and 5.12d points out that the proposed algorithm does not lead to a reduction of the accuracy; on the contrary, when DC is used in the last iterations of the process, the results are not affected by the artefacts due to the imposed periodicity when using the FFT. In these two last cases, the standard deviation of

Chapter 5 – Efficient 3D PIV interrogation algorithms

the difference between the two velocity field is slightly larger than the previous comparison (0.09 pixel and 0.12 pixel for the and component, respectively), but still within the expected measurement accuracy.

In Fig. 5.13 the profiles of the streamwise velocity component along a straight line parallel to the x axis are reported for the same velocity fields illustrated in Fig. 5.12. The chosen profile placed is not exactly corresponding to the diameter of the nozzle, so that the modulation effects are clearly highlighted using peaks with different intensity and width. As expected, the process with windowing enables to have an improvement in the spatial resolution, being the profiles less affected by modulation issues.