# Numerical Modelling of the Multiphase Flow in an Agricultural Hollow Cone Nozzle
## 1 Introduction
A hybrid model combining both approaches was employed in [27] to investigate liquid spray from spill-return atomizers. The DPM method was also used by [PERSON] et al. [28] to simulate the droplet behavior generated by an atomizer mounted on an agricultural unmanned aerial vehicle (UAV). The influence of rotor-induced downwash during UAV spraying operations was analyzed using CFD in [29]. The DPM method can also be coupled with VOF to capture the behavior of pesticide spray droplets upon impacting a leaf surface [30]. This problem can also be investigated using the standalone VOF approach [31]. The numerical approach is readily used by researchers involved in the analysis of agricultural nozzles. [PERSON] et al. [32] presented a numerical study of two-phase flow in an induction nozzle with water and air for agricultural applications. The conducted simulation analysis was verified using experimental data. Studies have shown that the interaction between air and water at a molecular level at the orifice exit leads to the formation of a strong shear layer intensified with an increase in the inlet pressure. It was observed that in the sprayer under consideration, regulating the ratio of inlet air to the supplied liquid is crucial to ensure that the generated microbubbles meet the design criteria. A similar two-phase nozzle design for agricultural applications was analyzed in study [33]. In that work, CFD software (FLUENT and CFX solvers) was employed to simulate the airflow field, and experimental verification was performed. The reported relative deviation in air velocity between the measured and simulated values was less than 10%, indicating the reliability of the numerical results. Another example of simulation studies on a two-phase sprayer designed for mixing fertilizer with water is presented in the study [34]. [PERSON] et al. [35] studied the distribution of slotted agricultural sprayers for different operating pressures using CFD. The simulation method can also be used for broader analyses of spraying efficiency. An example is the study of the deposition characteristics of droplets applied under different conditions from an agricultural drone-octocopter [36]. Computational fluid dynamics has been widely applied in agricultural spraying research to analyze various aspects of nozzle performance and spray dynamics. Studies have explored pulsating liquid jets in spray nozzles [37] and investigated the impact of mesh type on spray properties [38]. CFD modeling has also been utilized to analyze flat-fan sprays in crossflow [39], predict droplet drift from aerial applications [40], and simulate the operation of air-assisted sprayers [41, 42]. Furthermore, CFD models have proven valuable in predicting pesticide flow in orchards and assessing spray drift [43], considering the influence of plant geometry [44] and fan-induced airflow on droplet trajectories [45]. This study presents a numerical analysis of liquid flow from a selected nozzle designed for applications in orchards and vineyards. This component is equipped with a factory-installed insert responsible for swirling the liquid jet passing through the outlet orifice. The aim of the study was to quantitatively and qualitatively evaluate the liquid flow process through the investigated nozzle for a selected liquid inlet operating pressure.