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A coupled atomization-spray drift model as online support tool for boom spray applications

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Abstract

The effectiveness of agrochemical products strongly depends on the capability of the atomized droplets to reach the target site in the desired amount. Spray drift is the movement of droplets downwind of the target area, and its minimization is a growing concern to ensure operator health, protect the environment, achieve efficient crop protection and transform the spraying of phytosanitary products into a sustainable activity. In this contribution, a coupled atomization-spray drift model suitable for different types of nozzles is developed and validated against experimental data. Particularly, the article focuses on providing a simple simulation tool, based on a minimum number of input data that are easily accessable to predict the ground deposition spray drift of a nozzle. It was found that the atomized droplets size distribution can be accurately predicted just as a function of the median volumetric diameter, which was successfully estimated as a function of spray pressure, nozzle nominal flowrate and spray angle (commonly known data). Besides, the proposed model, based on bivariate probability density functions, is able to accurately represent different physical phenomena using a low number of calculations. Its implementation is possible using low-resource computing systems as required for sprayer on-board software tools.

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Abbreviations

\({a}_{ul}\) :

Parameter defined in Eq. 10 (–)

\({A}_{n}\) :

Nozzle orifice area (m2)

\(C\) :

Displacement of deposited droplets respect to \({x}_{0}\) (m)

\({C}_{PH}\) :

Nozzle constant (m)

\({C}_{d}\) :

Discharge coefficient (–)

\(d\) :

Droplet diameter (m)

\({d}_{0}\) :

Atomized droplet diameter (m)

\({d}_{crit}\) :

Critical droplet diameter (m)

\({d}_{dep}\) :

Deposited droplet diameter (m)

\({d}_{max}\) :

Maximum diameter of atomized droplets (m)

\({d}_{min}\) :

Minimum initial diameter of a droplet that reaches the soil surface (m)

\({D}_{V10}\) :

Diameter where ten percent of the atomized droplets volume distribution has a smaller particle size (m)

\({D}_{V50}\) :

Diameter where fifty percent of the atomized droplets volume distribution has a smaller particle size (m)

\({D}_{V90}\) :

Diameter where ninety percent of the atomized droplets volume distribution has a smaller particle size (m)

\({f}_{{x}_{0}}\) :

Volume distribution pattern of atomized droplets (1/m)

\({f}_{d,{x}_{dep}}\) :

Density function of droplets with respect to the initial diameter and deposition distance (1/m)

\({f}_{d}\) :

Density function of the atomized spray (1/m)

\({f}_{dep}\) :

Density function of droplets with respect to the deposition distance (1/m)

\({f}_{d\alpha }\) :

Bi-variate probability distribution (1/m rad)

\({f}_{\alpha }\) :

Droplet trajectory angle distribution function (1/rad)

\({F}_{d}\) :

Cumulative function of the atomized spray (–)

\(F\) :

Desired applied dose (m3/m2)

\(g\) :

Gravity acceleration constant (m/s2)

\(H\) :

Nozzle height (m)

\(k\) :

Constant defined in Eq. 23 (s/m2)

\(Oh\) :

Ohnesorge number (–)

\(P\) :

Atomization pressure (Pa)

\({P}_{ref}\) :

Atomization pressure for which the nominal flowrate is specified (270 kPa for ISO 10625:2018 compliant nozzles) (Pa)

\(Q\) :

Nozzle volumetric flowrate (m3/s)

\(RH\) :

Relative humidity (%)

\(t\) :

Time (s)

\({t}_{dep}\) :

Deposition time of droplets (s)

\({t}_{resp}\) :

Response time of a droplet (s)

\(T\) :

Wet bulb temperature (K)

\({T}_{bh}\) :

Dry bulb temperature (K)

\(\overline{U }\) :

Representative wind speed of the total atomized droplets population (m/s)

\(U\) :

Wind speed (m/s)

\({U}_{0}\) :

Wind speed at the nozzle height \(H\) (m/s)

\({v}_{A}\) :

Sprayer forward speed (m/s)

\({v}_{T}\) :

Terminal velocity (m/s)

\(w\) :

Nominal spray width of a nozzle

\(x\) :

Spatial downwind coordinate (m)

\({x}_{0}\) :

Spatial position of the volume distribution pattern (m)

\(Y\) :

Spray drift (–)

\(z\) :

Vertical co-ordinate (m)

\(\alpha\) :

Initial path angle of a drop (rad)

\(\gamma\) :

Wind speed constant (–)

\(\delta\) :

Nominal density function of droplets with respect to the deposition distance (1/m)

\(\Delta T\) :

Difference between dry and wet bulb temperatures (K)

\(\epsilon\) :

Roughness of the terrain (m)

\({\mu }_{g}\) :

Air viscosity (Pa s)

\(\theta\) :

Spray angle (rad)

\({\rho }_{d}\) :

Droplet density (kg/m3)

\({\rho }_{g}\) :

Air density (kg/m3)

\(\sigma\) :

Surface tension (N/m)

\({\sigma }_{{\mathrm{H}}_{2}\mathrm{O}}\) :

Water surface tension (N/m)

\({\sigma }_{s}\) :

Standard deviation of \({f}_{{x}_{0}}\) (m)

\({\sigma }_{ul}\) :

Parameter defined in Eq. 9 (–)

\(\Psi\) :

Nozzle parameter \(\left({\upmu}\text{m}{\left(\frac{{\mathrm{m}}^{3}}{\mathrm{s}}\right)}^{-\frac{1}{3}}{\left(\mathrm{Pa}\right)}^\frac{1}{3}{\left(^\circ \right)}^\frac{2}{3}\right)\)

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Acknowledgements

The authors gratefully acknowledge the financial support by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), the Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT) and the Universidad Nacional del Sur (UNS) from Argentina.

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Authors and Affiliations

  1. Departamento de Ingeniería Química, Universidad Nacional del Sur (UNS), Bahía Blanca, Argentina

    Carlos A. Renaudo, Diego E. Bertin & Verónica Bucalá

  2. Planta Piloto de Ingeniería Química – PLAPIQUI (UNS-CONICET), Bahía Blanca, Argentina

    Carlos A. Renaudo, Diego E. Bertin & Verónica Bucalá

Authors
  1. Carlos A. Renaudo
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  2. Diego E. Bertin
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  3. Verónica Bucalá
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Correspondence to Carlos A. Renaudo.

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Renaudo, C.A., Bertin, D.E. & Bucalá, V. A coupled atomization-spray drift model as online support tool for boom spray applications. Precision Agric 23, 2345–2371 (2022). https://doi.org/10.1007/s11119-022-09923-1

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  • DOI: https://doi.org/10.1007/s11119-022-09923-1

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