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An image feature consolidation technique (IFCT) to capture multi-range droplet size distributions in atomizing liquid sheets

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Abstract

Atomization of an attenuating liquid sheet beyond the breakup point is visualized by shadow imaging. Of interest is the transitional region where the disintegration of the liquid sheet into a spray occurs. This region is characterized by the coexistence of fine droplets and large unbroken ligaments. The large range of size of the droplets, relative to the unbroken ligaments, exacerbates the out-of-focus and resolution issues which are inherent in the optical imaging of sprays. To rectify these, two shadowgrams with different depths of field (DOF) and resolutions are obtained at each area of interest within the spray, using two different optical setups: finer droplets are observed in the shadowgram with shallow DOF and high resolution; and larger particles, mostly unbroken ligaments, are clearly captured in the shadowgram with deep DOF. Then, an image analysis technique is used to extract the spray features visible in each shadowgram, and the data obtained from the two shadowgrams are consolidated into one histogram representing the nearly complete range of droplet sizes within the spray. This Image Feature Consolidation Technique (IFCT) and the resulting droplet size distribution are found to be useful for applications involving developing sprays.

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Acknowledgements

The authors thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and UofT Dean’s Catalyst Professorship for funding this research.

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Authors and Affiliations

  1. Process Metallurgy Research Lab, Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, ON, M5S 3E4, Canada

    Ali Asgarian, Ziwei Yang, Ziqi Tang & Kinnor Chattopadhyay

  2. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    Ali Asgarian, Markus Bussmann & Kinnor Chattopadhyay

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  1. Ali Asgarian
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  2. Ziwei Yang
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  3. Ziqi Tang
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  4. Markus Bussmann
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  5. Kinnor Chattopadhyay
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Correspondence to Kinnor Chattopadhyay.

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Appendix A: DOF calculation

Appendix A: DOF calculation

Depth-of-field (DOF) is calculated as follows (Greenleaf 1950):

$$ DOF = D_{f} - D_{n} , $$
(21)

where \( D_{f} \) and \( D_{n} \) are the far and near distances for acceptable sharpness (mm), respectively, calculated as follows:

$$ D_{n} = \frac{{s\left( {H - f} \right)}}{H + s - 2f} $$
(22)
$$ D_{f} = \frac{{s\left( {H - f} \right)}}{H - s} $$
(23)

\( H \) is the hyperfocal distance (mm) defined as:

$$ H = \left( {\frac{{f^{2} }}{Nc}} \right) $$
(24)

and f, N, c, and s are focal length (mm), aperture f-number, circle of confusion (mm), and focus distance or distance to subject (mm), respectively.

For OS1, which is the commercial setup, the DOF for the specific settings used in this study is provided by the vendor:

$$ {{DOF}}_{{OS}1} = 900\,\upmu {\rm m}. $$

Independent checking is not possible as more detailed information is not available.

For OS2, the following parameters are used: \( f = 100\,{\rm mm}, N = 19, c = 0.011\,{\rm mm}, {\rm and} \, s = 440\,{\rm mm} \), which yields

$$ {{DOF}}_{{OS}2} = 6254\,{\rm mm}. $$

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Asgarian, A., Yang, Z., Tang, Z. et al. An image feature consolidation technique (IFCT) to capture multi-range droplet size distributions in atomizing liquid sheets. Exp Fluids 61, 14 (2020). https://doi.org/10.1007/s00348-019-2847-6

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  • DOI: https://doi.org/10.1007/s00348-019-2847-6

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