# Matching the Liquid Atomization Model to Experimental Data Obtained from Selected Nozzles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}> 0.95). The model, which was generated on the basis of experimental data, will facilitate control of the operation and degree of wear of nozzles, which will contribute to ensuring uniform spraying.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment Description

- the height of the nozzles above the groove table, 500 mm;
- liquid pressure, 0.3 MPa.

#### 2.2. Development of A New Model of Liquid Amount Distribution

#### 2.3. Statistical Analysis

## 3. Results

## 4. Discussion

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Jobbágy, J.; Dančanin, P.; Krištof, K.; Maga, J.; Slaný, V. Evaluation of the Quality of Irrigation Machinery by Monitoring Changes in the Coefficients of Uniformity and Non-Uniformity of Irrigation. Agronomy
**2021**, 11, 1499. [Google Scholar] [CrossRef] - Krawczuk, A.; Parafiniuk, S.; Przywara, A.; Huyghebaert, B.; Rabier, F.; Limbourg, Q.; Mostade, O.; Kocira, S. Technical Parameters of Biostimulant Spraying a Determinant of Biometric Traits and Yield of Soybean Seeds. Agric. Eng.
**2021**, 25, 171–179. [Google Scholar] [CrossRef] - Chen, C.; Li, S.; Wu, X.; Wang, Y.; Kang, F. Analysis of Droplet Size Uniformity and Selection of Spray Parameters Based on the Biological Optimum Particle Size Theory. Environ. Res.
**2022**, 204, 112076. [Google Scholar] [CrossRef] - Forney, S.H.; Luck, J.D.; Kocher, M.F.; Pitla, S.K. Laboratory and Full Boom-Based Investigation of Nozzle Setup Error Effects on Flow, Pressure, and Spray Pattern Distribution. Appl. Eng. Agric.
**2017**, 33, 641–653. [Google Scholar] [CrossRef] [Green Version] - Griesang, F.; Spadoni, A.B.D.; Urah Ferreira, P.H.; da Costa Ferreira, M. Effect of Working Pressure and Spacing of Nozzles on the Quality of Spraying Distribution. Crop Prot.
**2022**, 151, 105818. [Google Scholar] [CrossRef] - Višacki, V.; Sedlar, A.; Bugarin, R.; Turan, J.; Burg, P. Effect of Pressure on the Uniformity of Nozzles Transverse Distribution and Mathematical Model Development. Acta Univ. Agric. Silvic. Mendel. Brun.
**2017**, 65, 563–568. [Google Scholar] [CrossRef] [Green Version] - Lipiński, A.J.; Lipiński, S.; Burg, P.; Sobotka, S.M. Influence of the Instability of the Field Crop Sprayer Boom on the Spraying Uniformity. J. Agric. Food Res.
**2022**, 10, 100432. [Google Scholar] [CrossRef] - Cui, L.F.; Xue, X.Y.; Ding, S.M.; Le, F.X. Development of a DSP-Based Electronic Control System for the Active Spray Boom Suspension. Comput. Electron. Agric.
**2019**, 166, 105024. [Google Scholar] [CrossRef] - Li, S.; Wang, W. Adaptive Backstepping Robust Control of Nonlinear Spray Boom System. J. Adv. Agric. Technol.
**2019**, 6, 246–252. [Google Scholar] [CrossRef] - Çetin, N.; Sağlam, C.; Demir, B. Determination of Spray Angle and Flow Uniformity of Spray Nozzles with Image Processing Operations. J. Anim. Plant Sci.
**2019**, 29, 1603–1615. [Google Scholar] - Sayinci, B.; Demir, B.; Açik, N. Comparison of Spray Nozzles in Terms of Spray Coverage and Drop Distribution Uniformity at Low Volume. Turk. J. Agric. For.
**2020**, 44, 262–270. [Google Scholar] [CrossRef] - Parafiniuk, S. Conversion of Test Results Obtained for Single Spray Nozzles to Identify the Working Parameters of the Sprayer Boom; Libropolis: Lublin, Poland, 2013. [Google Scholar]
- Lodwik, D.; Pietrzyk, J.; Malesa, W. Analysis of Volume Distribution and Evaluation of the Spraying Spectrum in Terms of Spraying Quality. Appl. Sci.
**2020**, 10, 2395. [Google Scholar] [CrossRef] [Green Version] - Shirwal, S.; Veerangouda, M.; Palled, V.; Shilendra, S.; Hosamani, A.; Krishnamurthy, D. Studies on Operational Parameters of Different Spray Nozzles. Int. J. Curr. Microbiol. Appl. Sci.
**2020**, 9, 1267–1281. [Google Scholar] [CrossRef] - Nowakowski, T.; Ośko, M. Mathematical Model of Cross-Distribution Non-Uniformity for Twin Flat Nozzle. Ann. Warsaw Univ. Life Sci.—SGGW—Agric.
**2017**, 69, 5–12. [Google Scholar] [CrossRef] - Liao, J.; Hewitt, A.J.; Wang, P.; Luo, X.; Zang, Y.; Zhou, Z.; Lan, Y.; O’donnell, C. Development of Droplet Characteristics Prediction Models for Air Induction Nozzles Based on Wind Tunnel Tests. Int. J. Agric. Biol. Eng.
**2019**, 12, 1–6. [Google Scholar] [CrossRef] - Wawrzosek, J.; Parafiniuk, S. Optimization of the Opening Shape in Slot Spray Nozzles in a Field Boom Sprayer. Sustainability
**2021**, 13, 3291. [Google Scholar] [CrossRef] - Wawrzosek, J.; Parafiniuk, S. The Use of the Permutation Algorithm for Suboptimising the Position of Used Nozzles on the Field Sprayer Boom. Appl. Sci.
**2022**, 12, 4359. [Google Scholar] [CrossRef] - Oqielat, M.N.; Turner, I.W.; Belward, J.A.; McCue, S.W. Modelling Water Droplet Movement on a Leaf Surface. Math. Comput. Simul.
**2011**, 81, 1553–1571. [Google Scholar] [CrossRef] [Green Version] - Cieniawska, B.; Pentos, K. Average Degree of Coverage and Coverage Unevenness Coefficient as Parameters for Spraying Quality Assessment. Agriculture
**2021**, 11, 151. [Google Scholar] [CrossRef] - Musiu, E.M.; Qi, L.; Wu, Y. Evaluation of Droplets Size Distribution and Velocity Pattern Using Computational Fluid Dynamics Modelling. Comput. Electron. Agric.
**2019**, 164, 104886. [Google Scholar] [CrossRef] - Duga, A.T.; Delele, M.A.; Ruysen, K.; Dekeyser, D.; Nuyttens, D.; Bylemans, D.; Nicolai, B.M.; Verboven, P. Development and Validation of a 3D CFD Model of Drift and Its Application to Air-Assisted Orchard Sprayers. Biosyst. Eng.
**2017**, 154, 62–75. [Google Scholar] [CrossRef] - Wang, J.; Liang, Q.; Zeng, T.; Zhang, X.; Fu, W.; Lan, Y. Drift Potential Characteristics of a Flat Fan Nozzle: A Numerical and Experimental Study. Appl. Sci.
**2022**, 12, 6092. [Google Scholar] [CrossRef] - Renaudo, C.A.; Yommi, A.; Slaboch, G.; Bucalá, V.; Bertin, D.E. Prediction of droplet size distributions from a pre-orifice nozzle using the Maximum Entropy Principle. Chem. Eng. Res. Des.
**2022**, 185, 198–209. [Google Scholar] [CrossRef] - Tomantschger, K.; Petrović, D.V.; Radojević, R.L.; Tadić, V. Mathematical Method for Droplet Size Distribution of Agricultural Nozzles. Teh. Vjesn.
**2021**, 28, 1749–1754. [Google Scholar] [CrossRef] - De Cock, N.; Massinon, M.; Salah, S.O.T.; Lebeau, F. Investigation on Optimal Spray Properties for Ground Based Agricultural Applications Using Deposition and Retention Models. Biosyst. Eng.
**2017**, 162, 99–111. [Google Scholar] [CrossRef] [Green Version] - Kaizzi, K.C.; Mohammed, M.B.; Nouri, M. Fertilizer Use Optimization: Principles and Approach. In Fertilizer Use Optimization in Sub-Saharan Africa; CABI: Wallingford, UK, 2017. [Google Scholar] [CrossRef]
- Fytilis, K.; Kontogeorgos, A.; Michailidis, A.; Semos, A. Crop structure optimisation for maximising yield within environmental constraints in a rural area. Int. J. Sustain. Agric. Manag. Inform.
**2022**, 8, 200–217. [Google Scholar] [CrossRef] - Echiegu, E.A.; Ede, N.C.; Ezenne, G.I. Optimization of Blaney-Morin-Nigeria (BMN) Model for Estimating Evapotranspiration in Enugu, Nigeria. Afr. J. Agric. Res.
**2016**, 11, 1842–1848. [Google Scholar] [CrossRef] [Green Version] - Angaleeswari, M.; Ravikumar, V. Estimating Evapotranspiration Parameters by Inverse Modelling and Non-Linear Optimization. Agric. Water Manag.
**2019**, 223, 105681. [Google Scholar] - ISO 16122-2; Agricultural and Forestry Machinery—Inspection of Sprayers in Use—Part 2: Horizontal Boom Sprayers. International Organization for Standardization: Geneva, Switzerland, 2015; p. 18.
- ISO 5682-1; Equipment for Crop Protection—Spraying Equipment—Part 1: Test Methods for Sprayer Nozzles. International Organization for Standardization (ISO): Geneva, Switzerland, 2017.
- Post, S.L.; Hewitt, A.J. Flat-Fan Spray Atomization Model. Trans. ASABE
**2018**, 61, 1249–1256. [Google Scholar] [CrossRef] [Green Version] - Ferguson, J.C.; O’Donnell, C.C.; Chauhan, B.S.; Adkins, S.W.; Kruger, G.R.; Wang, R.; Urach Ferreira, P.H.; Hewitt, A.J. Determining the Uniformity and Consistency of Droplet Size across Spray Drift Reducing Nozzles in a Wind Tunnel. Crop Prot.
**2015**, 76, 1–6. [Google Scholar] [CrossRef] - Griesang, F.; Decaro, R.A.; Santos, R.T.S.; Vechia, J.F.D.; Santos, C.A.M.; Ferreira, M. Droplet size and uniformity influence on the qualitative and quantitative parameters of agricultural spray. Asp. Appl. Biol.
**2018**, 137, 217–222. [Google Scholar] - Butts, T.R.; Luck, J.D.; Fritz, B.K.; Hoffmann, W.C.; Kruger, G.R. Evaluation of Spray Pattern Uniformity Using Three Unique Analyses as Impacted by Nozzle, Pressure, and Pulse-Width Modulation Duty Cycle. Pest Manag. Sci.
**2019**, 75, 1875–1886. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Li, L.; Chen, L.; Zhang, R.; Tang, Q.; Yi, T.; Liu, B.; Deng, W. Spray Drift Characteristics of Pulse-Width Modulation Sprays in Wind Tunnel. Int. J. Agric. Biol. Eng.
**2022**, 15, 7–15. [Google Scholar] [CrossRef] - Fabula, J.; Sharda, A.; Luck, J.D.; Brokesh, E. Nozzle Pressure Uniformity and Expected Droplet Size of a Pulse Width Modulation (PWM) Spray Technology. Comput. Electron. Agric.
**2021**, 190, 106388. [Google Scholar] [CrossRef]

**Figure 6.**Spray fallout distribution for the nozzle (CV = 1.490%; CV = 10.000%)—acceptable deviation ranges.

Name of Nozzle | Name of Manufacturer | Type of Nozzle | Flow Rate [L·min^{−1}] | Size of Nozzle | Spray Angle |
---|---|---|---|---|---|

XR | TeeJet, Spraying Systems Co. | Standard | 0.8 | 02 | 110° |

EŻK | MMAT Poland | Air-induction | 0.99 | 025 | 110° |

RSMM | MMAT Poland | Standard | 1.18 | 03 | 110° |

AZMM | MMAT Poland | Anti-drift | 1.18 | 03 | 110° |

IDK | Lechler GMBH | Air-induction | 1.58 | 04 | 120° |

XR | EŻK | RSMM | AZMM | IDK | |
---|---|---|---|---|---|

R | 0.957 | 0.953 | 0.978 | 0.983 | 0.964 |

R^{2} | 0.915 | 0.908 | 0.956 | 0.966 | 0.930 |

a | b | p | q | |
---|---|---|---|---|

CV = 1.490% | 0.127 | 0.100 | 2.000 | 1.800 |

CV = 10.000% | 0.104 | 0.129 | 2.000 | 1.799 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cieniawska, B.; Parafiniuk, S.; Kluza, P.A.; Otachel, Z.
Matching the Liquid Atomization Model to Experimental Data Obtained from Selected Nozzles. *Appl. Sci.* **2023**, *13*, 4433.
https://doi.org/10.3390/app13074433

**AMA Style**

Cieniawska B, Parafiniuk S, Kluza PA, Otachel Z.
Matching the Liquid Atomization Model to Experimental Data Obtained from Selected Nozzles. *Applied Sciences*. 2023; 13(7):4433.
https://doi.org/10.3390/app13074433

**Chicago/Turabian Style**

Cieniawska, Beata, Stanisław Parafiniuk, Paweł A. Kluza, and Zdzisław Otachel.
2023. "Matching the Liquid Atomization Model to Experimental Data Obtained from Selected Nozzles" *Applied Sciences* 13, no. 7: 4433.
https://doi.org/10.3390/app13074433