# Numerical Modelling of the Multiphase Flow in an Agricultural Hollow Cone Nozzle
## 2 Research Object and Methodology  
The ALBUZ ATR 80 nozzle (ALBUZ, Evreux, France), designed for use in orchards and vineyards, was selected for the study. It is a vortex nozzle with a hollow cone pattern. The recommended plant protection products for application with this model are fungicides and insecticides. The cone angle of the sprayed jet is 80\({}^{\circ}\) at a pressure of 5 bar or higher. The nozzle enables the production of droplets with a volume median diameter (VMD) of less than 130 \(\upmu\)m. As a result of the liquid spraying, a hollow cone jet with fine droplets is formed. The spray nozzle consists of three main components, as shown in Figure 1. Inside the plastic body, there is a ceramic vortex insert with two channels that enable liquid flow. It is pressed against the body by a stem with a ceramic tip connected to a plastic disc. The disc features three holes with an elongated, oval (bean-shaped) design. This nozzle design is characterized by a lack of geometric symmetry. Therefore, three-dimensional (spatial) numerical calculations had to be carried out. All components were made with a high degree of precision, down to hundredths of a millimeter. This design ensures precise and reliable nozzle operation at high pressures while maintaining high durability. The manufacturer's recommended operating pressure range is 3-20 bar. Figure 1: Components of the actual nozzle subjected to modeling: (**a**) top view; (**b**) bottom view (1—body, 2—stem with disc, 3—vortex insert). In order to prepare an accurate computer model of the nozzle, selected surfaces of the actual geometry were scanned. The optical profilometer used for this was the FRT MicroProf 100 (Fries Research & Technology GmbH, Bergisch Gladbach, Germany), which makes it possible to measure the profile and surface roughness, flatness, and other parameters related to the profile and cross-section of the surface under examination using a non-contact optical method (Figure 2). The device enables vertical axis measurements up to 500 \(\upmu\)m with an accuracy of 6 nm and up to 3 mm with an accuracy of 110 nm. The scanning conducted makes it possible to create 3D surface maps and 2D cross-sections (Figure 3). The resulting point cloud was used to create a solid model in Catia V5-6R2021 software (Dassault Systemes, Velizy-Villacoublay, France). The points were imported into the Digitized Shape Editor module. This allowed the linear dimensions to be accurately mapped onto the sketch, and then a series of solid operations to be performed. Based on the nozzle geometry created in the form of a solid model (Figure 5), work began on the flow model. For this purpose, the geometry was imported into Ansys 2024 software (Ansys, Inc., Canonsburg, PA, United States), where a computational domain was created (Figure 6), and a three-dimensional mesh was generated. The domain was in the form of a cylinder, on the base of which a sprayer was placed. The inlet area was the surface of the inlet to the modeled nozzle. The entire cylindrical surface of the computational domain and the bottom and top bases were defined as pressure outlets. The developed mesh consisted of tetrahedral and hexahedral elements, comprising a total of 1,313,911 nodes and 4,783,050 elements. In areas with small cross-sections, element densification was applied. In addition, a boundary layer was created on the walls, using Inflation with Smooth Transition. The mesh size was determined by a mesh convergence study. The number of mesh elements was gradually increased, and the average velocity on the control surface passing through the nozzle outlet was observed (Figure 7c). A difference of 0.6% was noted between the adopted mesh and the previous one in terms of size. This value was considered satisfactory, and the final calculations were performed using the largest mesh among those analyzed. The tests showed that the number of elements  
Figure 4: (**a**) An example of a surface profile and (**b**) a point cloud obtained for one of the components of the examined nozzle.