Guichun Yang

The breakup process of near-field jets in airless spraying directly determines the initial droplet size distribution and macroscopic spray pattern, making it a critical factor af-fecting coating quality. This study establishes a numerical model for near-field atomi-zation based on computational fluid dynamics, coupling the VOF interface capturing method with the SST k-ω turbulence model. The model’s accuracy is validated through mass flow rate experiments and high-speed imaging. By incorporating instability theory, expressions for the characteristic lengths of Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities—including viscous corrections—are derived, revealing the competitive mechanisms among surface tension, viscous forces, and inertial forces during interface destabilization. Results show that the axial velocity along the center-line exhibits a segmented behavior characterized by “sharp acceleration—gradual decay—high-frequency oscillation,” while volume fraction and velocity display strong spatial phase coupling. Both core length and breakup length significantly decrease with increasing spray pressure but increase linearly with viscosity, leading to empirical formulas for characteristic lengths (with fitting errors < 15%). Power-law scaling analysis further indicates that the KH stage is dominated by surface peeling, with characteristic length sensitive to pressure, viscosity, and surface tension; whereas the RT stage is primarily governed by bulk breakup, where the characteristic length shows relative independence from pressure and is mainly controlled by viscosity and surface tension. The ratio of the two characteristic lengths ranges approximately between 4 and 6, providing theoretical guidance for optimizing airless spraying process parameters.

To address the challenge of uneven coating deposition during air-assisted robotic spraying on horn-shaped surfaces, a gas–liquid coupled numerical model was developed using the Euler–Euler multi-phase flow approach and subsequently validated through experimentation. Two dynamic spray trajectories—axial spraying and circumferential spraying—were designed to examine the influence of spraying strategy, horn angle (ranging from 45° to 135°), spray distance, and spraying speed on film-forming characteristics. The results demonstrate that the features of the horn alter the near-wall flow field due to wall confinement effects, leading to spray splitting and kinetic energy attenuation with pronounced anisotropy. Specifically, stronger geometric constraints are observed along the minor axis, while weaker constraints are noted along the major axis. Axial spraying requires approximately 60% less time than circumferential spraying and results in more uniform coatings, thereby establishing it as the preferred strategy. In axial spraying, film thickness increases steadily with horn angle, with a 147.7% increase from 45° to 135°. Circumferential spraying achieves the best uniformity at angles of 67.5° to 90° due to geometric and temporal influences. Film thickness decreases with spraying speed following a power-law relationship (h ∝ 1/v). Pearson correlation shows moderate links between film thickness and horn angle (r = 0.466), spraying speed (r = −0.347), and spray distance (r = −0.325), with an ideal spray distance of 190–210 mm. The study highlights the anisotropic effects of horn features on spray flow, offering quantitative insights for precise robotic spraying of complex surfaces.

To address the challenge of uneven coating deposition during air-assisted robotic spraying on horn-shaped surfaces, a gas–liquid coupled numerical model based on the Euler-Euler multiphase flow approach was developed and experimentally validated. Two dynamic spray trajectories (axial spraying and circumferential spraying) were designed to investigate the effects of spraying strategy, horn angle (45°–135°), spray distance, and spraying speed on film-forming characteristics. Results indicate that horn features alter the near-wall flow field through wall confinement effects, causing spray splitting and kinetic energy attenuation with significant anisotropy—stronger geometric constraints along the minor axis and weaker along the major axis. Axial spraying requires approximately 60% less time than circumferential spraying and yields more uniform coatings, making it the preferred strategy. During axial spraying, the central film thickness increases monotonically with horn angle (up to 147.7% over 45°–135°), while circumferential spraying achieves optimal uniformity at 67.5°–90° governed by competing geometric and temporal effects. The film thickness approximately follows a power-law decay with spraying speed (h ∝ 1/v). Pearson correlation analysis identifies horn angle as the primary variable controlling film thickness (r = 0.466), followed by spraying speed (r = −0.347) and spray distance (r = −0.325), with an optimal spray distance of 190–210 mm recommended. This study reveals the anisotropic regulation mechanism of horn features on the spray flow field and provides quantitative guidance for precise robotic spraying of complex-curved components.

Taking arc-shaped bent pipes as the subject of study, a three-dimensional dynamic spraying numerical model based on Euler–Euler approach and a wall film formation model was developed through numerical simulation and experimental validation. The effects of geometric parameters, such as the bending radius and pipe diameter, on the distribution of coating thickness were systematically investigated. Numerical simulations were used to reproduce the motion of gas–liquid two-phase flow and the evolution of spray film formation, and the reliability of the model was verified experimentally. The results indicate that the film thickness distribution for axial spraying exhibits good stability, whereas circumferential spraying shows significant position dependence due to differences in local curvature and the angle of incidence. In addition, increased curvature in convex areas reduces the peak film thickness and widens the spray pattern, while concave areas enhance localized deposition, resulting in a narrower distribution of the coating. Spray coating experiments conducted on flat and bent pipe confirmed that the film thickness distribution trends and peak locations predicted by the model were in good agreement with the experimental results. This study provides a theoretical basis and practical guidance for spray trajectory planning and film thickness control in complex curved components.

Cavitation flow within airless spray nozzles critically influences both atomization quality and nozzle longevity. However, its highly transient and multiphase-coupled nature poses significant challenges to the predictive accuracy of turbulence models. To improve numerical simulation fidelity, this study develops an improved dynamic Wall-Adapting Local Eddy-viscosity (WALE) subgrid-scale model for Large Eddy Simulation (LES). Building on the standard WALE formulation, the model incorporates a dynamic coefficient determined via the Germano identity and a least-squares approach, which enables it to adaptively capture the turbulence modulation effects induced by cavitation. Coupled with a Volume of Fluid (VOF) multiphase flow method, this framework is employed to systematically simulate the complex internal nozzle flow under varying spray pressures, coating viscosities, and surface tensions. Results indicate that the improved dynamic WALE model increases numerical stability by approximately 15% compared with the standard model. The internal flow can be partitioned into three regions: a potential-flow acceleration region, a cavitation-induced fluctuation region, and an outlet formation region. Within the cavitation-induced fluctuation region near the wall, cavitation generates a local double-peaked velocity profile and pronounced pressure pulsations. Cavitation intensity increases approximately linearly with spray pressure but decreases with increasing viscosity and surface tension. Both the discharge coefficient and velocity coefficient decrease linearly with increasing cavitation number, indicating that moderate cavitation can enhance instantaneous throughput by altering the flow-field structure. Finally, outflow mass-flow experiments validate the numerical model’s reliability: the improved dynamic WALE model achieves prediction errors ranging from 0.47% to 11.91%, substantially outperforming the standard WALE model, which has errors ranging from 1.27% to 21.10%.

Frequency spectrum correction of noisy real sinusoidal signals has garnered widespread attention in numerous fields. This paper proposes a spectrum correction method for noisy real signals based on the interior point (IP) approach, transforming the spectrum correction problem into an unconstrained optimization problem. By adopting a peak detection method to determine the peaks on both sides of the true spectral peak, which serve as the upper and lower bounds for the IP approach solution, precise estimates of the amplitude, frequency, and phase of the single-frequency signal are obtained, thereby achieving frequency spectrum correction. Simulation results indicate that this method exhibits lower computational cost and higher efficiency for real sinusoidal signals. Compared with other frequency spectrum correction methods, it demonstrates superior accuracy.

This paper focuses on key engineering issues, particularly the overall turbulent transport of paint spray and coating film distribution characteristics, in the process of airless spraying film formation. By deeply considering the geometric features of spherical surfaces and their impact on the near-wall region of the flow field, an airless spraying film formation model consisting of the Eulerian multiphase model, the realizable k–ε turbulence model, and the Eulerian Wall Film model was established. Through numerical simulations of static spraying on the inner and outer walls of spherical surfaces with different radii, the influence of geometric features on the spray flow field and film formation characteristics on spherical surfaces was investigated. Subsequently, based on numerical simulations of dynamic spraying on different nozzle trajectories, the film formation characteristics were analyzed, and the optimal spray trajectory planning method was determined. Additionally, this study examined the coating distribution characteristics during dynamic spraying on spherical surfaces with varying geometric dimensions. Finally, a kind of chlorinated rubber anti-corrosion primer was chosen to carry out spraying experiments, which validated that the airless spray coating model and the corresponding numerical simulation methods established in this paper were reasonable and feasible for investigating the film formation characteristics on spherical surfaces. This work is expected to further promote the application of airless spray techniques in machinery, automotive, shipbuilding, and aviation industries.