Weber-number scaling and the distance dependence of drop size in full-cone pressure-swirl sprays
Abstract
A pressure-swirl nozzle converts the feed pressure into a swirling conical sheet that breaks into ligaments and then into drops. The size of the drops governs the deposition and drift of agricultural sprays, the capture of airborne dust and the combustion efficiency of fuel injectors. The standard tool for measuring the drop size is laser diffraction, which returns a spatial, concentration-weighted distribution at the beam station. However, the dependence of the measured drop size on the nozzle-to-beam distance has not been quantified alongside a Weber-number scaling, so prefactors reported at different distances cannot be compared on an equal footing. To this end, we measure the drop-size distribution of two full-cone pressure-swirl nozzles by laser diffraction at a range of distances, pressures and orientations, together with high-speed imaging of the sheet breakup. We find that the volume-median diameter Dv50 decreases with the measurement distance L as Dv50 ∼ L−0.18 beyond the drop-formation region. A joint fit over both nozzles gives Dv50/d0 ∼ We−0.31 (L/d0)−0.21, where d0 is the orifice diameter and We the Weber number, which separates the pressure and distance effects. At a fixed distance the two nozzles collapse onto the We−1/3 scaling of Kooij et al. (2018), and the measured distance dependence may account for part of the offset between our near-field prefactor and the far-field value. Thus, a drop size obtained by laser diffraction is meaningful only when the measurement distance is reported with it, and a spray should be characterized at the actual distance between the nozzle and its target.
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BibTeX
@misc{jemaa2026webernumber,
title = {{Weber-number scaling and the distance dependence of drop size in full-cone pressure-swirl sprays}},
author = {Bilal Ben Jemaa and Vincent He and Marko Trifunović and Daniel Duke and Rishabh V. More},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20650},
eprint = {2610.20650},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20650},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weber-number scaling and the distance dependence of drop size in full-cone pressure-swirl sprays
AU - Bilal Ben Jemaa
AU - Vincent He
AU - Marko Trifunović
AU - Daniel Duke
AU - Rishabh V. More
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.20650
UR - https://arxiv.org/abs/2610.20650
AB - A pressure-swirl nozzle converts the feed pressure into a swirling conical sheet that breaks into ligaments and then into drops. The size of the drops governs the deposition and drift of agricultural sprays, the capture of airborne dust and the combustion efficiency of fuel injectors. The standard tool for measuring the drop size is laser diffraction, which returns a spatial, concentration-weighted distribution at the beam station. However, the dependence of the measured drop size on the nozzle-to-beam distance has not been quantified alongside a Weber-number scaling, so prefactors reported at different distances cannot be compared on an equal footing. To this end, we measure the drop-size distribution of two full-cone pressure-swirl nozzles by laser diffraction at a range of distances, pressures and orientations, together with high-speed imaging of the sheet breakup. We find that the volume-median diameter D_v50 decreases with the measurement distance L as D_v50 ∼ L^−0.18 beyond the drop-formation region. A joint fit over both nozzles gives D_v50/d_0 ∼ We^−0.31 (L/d_0)^−0.21, where d_0 is the orifice diameter and We the Weber number, which separates the pressure and distance effects. At a fixed distance the two nozzles collapse onto the We^−1/3 scaling of Kooij et al. (2018), and the measured distance dependence may account for part of the offset between our near-field prefactor and the far-field value. Thus, a drop size obtained by laser diffraction is meaningful only when the measurement distance is reported with it, and a spray should be characterized at the actual distance between the nozzle and its target.
ER -