Based on the computational fluid dynamics (CFD) theory, this paper proposes a film formation model and a numerical simulation method that can be used in thickness prediction of airless spraying robots. The spraying flow field and the film formation process in the airless spraying process were simulated by the Eulerian–Eulerian approach, and the airless spraying film formation model including the paint expansion model and the wall hitting model was established. To verify the correctness of the model, numerical simulations of static spraying and dynamic spraying were carried out on the plane and arc surfaces. The simulation results showed that the width of the spraying flow field on the far wall increased linearly with the longitudinal distance in the major-axis direction. The busbar spraying on the outer surface of the arc surface showed the similar characteristics to the plane in the major-axis direction. Besides, the annular spraying was similar to the plane spraying in the minor-axis direction, but the inner surface spraying was completely opposite. When spraying the outer surface, the film thickness increased with the increase of the inner diameter but was smaller than that of the plane spraying, while the inner surface spraying was completely opposite. In the spraying experiment, the plane dynamic spraying and the arc plane inner and outer surface translation spraying were selected for verification. The experimental results were in good agreement with the simulation results, indicating that the film formation model of airless spraying established in this paper is basically correct. As a result, this model can be used for thickness prediction of spraying robots.

Near-nozzle atomization characteristics in air-assisted spraying were investigated through a novel 3D transient model integrating Volume-of-Fluid and Large Eddy Simulation (VOF-DPM) methods, with experimental validation of droplet distributions (Malvern analyzer) and coating thickness profiles. Key findings reveal that (1) the spray field stabilizes within 30 mm downstream, achieving 80% atomization efficiency (droplets ≤ 100 μm) at 27.5 mm axial distance; (2) radial momentum originates dually from fan-shaped airflow (max 595 m/s) and transverse motion induced by central atomizing air entrainment—a previously unreported mechanism; (3) paint loading delays flow stabilization to 2.5 ms (vs. 0.7 ms for gas-only flow) while reducing peak axial velocity by 18%–22% due to gas–liquid momentum exchange; (4) auxiliary and fan airflows synergistically constrain dispersion, forming elliptical sprays with characteristic cone angles of 61.7° (short axis) and 99.1° (long axis). Significantly, surface tension plays a dual role in inhibiting droplet atomization while promoting ligament pinch-off at 8.1 mm breakup length. These results provide the first quantitative characterization of gas–liquid interactions in near-nozzle regions, enabling precise parameter control for enhanced coating uniformity on complex surfaces.

When painting complex surfaces, such as large-curvature surfaces, poor coating quality is often obtained, which may be caused by lack of an appropriate atomization model, insufficient understanding of atomization mechanisms and laws, and improper painting parameters. This paper presents a numerical model of paint atomization of air spraying using the volume-of-fluid method and large eddy simulation. The interface capture and the turbulent flow were mainly considered in the model: the former was tracked by the volume-of-fluid method and the latter was predicted by the large eddy simulation. After the computational domain being meshed by the staggered-grid method, the governing equations were discretized by the finite volume method and were solved by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) Consistent algorithm. The results of numerical simulations show that the characteristics of atomization flow field, such as velocity variation, pressure distribution, and paint volume fraction are in agreement with the regularities of atomization. Moreover, the primary and secondary atomization phenomena can be clearly observed: as soon as the paint issues from the nozzle, the paint flow begins to distort and the paint fragments continuously eject from the main paint flow and then these paint fragments distort and disintegrate into smaller elements. A comparison with the experimental data from the literature proves that the model of the whole atomization process of air spray is effective. The model is suitable for simulating the whole atomization process and easy to obtain initial conditions, which can be applied to set the appropriate painting parameters and study paint atomization mechanisms and laws in depth.

The paper proposes a sliding mesh model-based method to conduct a dynamic painting simulation for an arc connecting surface. In order to meet the requirements for using a sliding mesh model, the computational domain was designed with three parts—a stationary part, a translational part and a rotational part. The film-forming model based on the Euler–Euler model and the conservation equation for a sliding mesh model were established. The dynamic painting of arc connecting surface with the angles of 60, 90 and 120 degrees under the nozzle speed of 100 mm/s were simulated. It was found that the thickness on the arc surface section was larger than those on the plane sections, and through an analysis of the vector distribution, the reason for this was that more paint would be deposited on the arc surface section than on the plane sections due to the concavity of the arc surface. The results obtained from the simulation were in a reasonable agreement with the experimental results, which indicates the proposed method would be effective and applicable in simulating a dynamic painting process.

The modeling of the paint atomization process is a barrier in computational fluid dynamics numerical simulation for the whole process of air spraying, and seriously restricts robot intelligent spray gun trajectory planning and the improvement of coating quality. Consequently, a multi-scale paint atomization model based on the hybrid Euler–Lagrange method was established in this paper, which included a large liquid micelle motion model, a particle motion model, and a turbulence flow model. The Euler method was adopted to capture the gas–liquid interface in the atomization flow field to describe the deformation and motion of large liquid micelles. The identification and transformation mechanisms of large liquid micelles and small particles were constructed by the particle motion model, and the motion of small droplets generated by paint atomization was tracked by the Lagrange method. The turbulence motion of the fluid in the process of paint atomization was described by a two-equation turbulence model. The model calculation method consisting of a finite-volume model, an adaptive hexcore mesh technique and a pressure-based coupled algorithm was established. The multi-scale atomization model was solved and model validation was carried out, which included mesh independence verification and model reliability analysis. The numerical simulation results predicted the atomization flow field parameters, paint atomization shapes, and the changing process from paint to liquid droplets, which was consistent with the experimental data. As a result, the established multi-scale atomization model in this paper is reliable for studying the paint atomization process of air spraying.

Painting a V-shaped surface, which is widely found in various facilities and equipment, often results in poor coating quality, which may be caused by an insufficient understanding of film-forming characteristics and mechanism. In this study, computational fluid dynamic (CFD) simulations were carried out for in-depth research on the film-forming characteristics and mechanism of painting V-shaped surfaces. The mathematical model of film formation was established with the Euler–Euler method, and the unstructured grids and adaptive-mesh refinement were adopted to discretize the computational domain. By solving the model, the coating thickness distribution law and flow-field characteristics of spraying a V-shaped surface were obtained. When painting a V-shaped surface with an angle less than 180°, the coating thickness distribution appeared as two peaks, instead of the single peak that appeared when painting a flat wall. As the V-shaped angle decreased, the coating thickness became thinner. The peak position gradually shifted to both sides, and the thickness distribution became wider. Analysis of the spray flow-field characteristics revealed the thickness distribution mechanism, by whichthe geometric characteristics of the V-shaped surface changed the near-wall distribution of the flow field. When the V-shaped angle decreased, the pressure peak at the center of the V-shaped surface and the eccentric pressure peaks that formed on both sides increased. The near-wall paint fluid was confined between the central pressure peak and the off-center pressure peak, resulting in paint droplets depositing between the pressure peaks and double-peak distribution of the coating thickness forming on the V-shaped surface. The spraying experiments verified the correctness of the numerical simulations, film-forming characteristics, and corresponding mechanism, which are of great significance for efficient and high-quality spraying on V-shaped surfaces.