## Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation

## Abstract

Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier–Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Furthermore, our algorithm, which we term Fourier–Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to ±180° of angular misalignment, compared to 6–8° for traditional correlations, and dilation/compression factors of 0.5–2.0, compared to 0.9–1.1 for a single iteration of traditional correlations.

- Authors:

- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Purdue Univ., West Lafayette, IN (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1239292

- Report Number(s):
- LA-UR-14-28188

Journal ID: ISSN 0957-0233

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Measurement Science and Technology

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 3; Journal ID: ISSN 0957-0233

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; 47 OTHER INSTRUMENTATION

### Citation Formats

```
Giarra, Matthew N., Charonko, John J., and Vlachos, Pavlos P. Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation. United States: N. p., 2015.
Web. doi:10.1088/0957-0233/26/3/035301.
```

```
Giarra, Matthew N., Charonko, John J., & Vlachos, Pavlos P. Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation. United States. doi:10.1088/0957-0233/26/3/035301.
```

```
Giarra, Matthew N., Charonko, John J., and Vlachos, Pavlos P. Thu .
"Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation". United States. doi:10.1088/0957-0233/26/3/035301. https://www.osti.gov/servlets/purl/1239292.
```

```
@article{osti_1239292,
```

title = {Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation},

author = {Giarra, Matthew N. and Charonko, John J. and Vlachos, Pavlos P.},

abstractNote = {Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier–Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Furthermore, our algorithm, which we term Fourier–Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to ±180° of angular misalignment, compared to 6–8° for traditional correlations, and dilation/compression factors of 0.5–2.0, compared to 0.9–1.1 for a single iteration of traditional correlations.},

doi = {10.1088/0957-0233/26/3/035301},

journal = {Measurement Science and Technology},

number = 3,

volume = 26,

place = {United States},

year = {2015},

month = {2}

}

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