A tunable surface tension pseudopotential lattice Boltzmann method (LBM) with an axisymmetric boundary is applied to study a droplet splashing on a thin film. Our work focused on the crown behavior influenced by the different parameters, including the Reynolds number, Weber number, liquid film thickness, and gravity acceleration. In addition, the total kinetic energy of the crown is proposed to explain the evolution of the crown shape from the perspective of energy. Based on the achieved results, it is found that the crown radius changes with time are unaffected by these parameters and consistent with the power-law in previous studies. However, the height of the crown and the satellite droplet formation process are affected by the referred parameters. Besides, it is found that the energy consumption during the collapse process and splash angle are two key factors affecting the height of the crown. There is a threshold liquid film thickness with the maximum height of the crown, which is between 0.2 and 0.25 times the droplet radius. This study shows that the proposed LBM pseudopotential model is a robust and effective tool for the study of the droplet splashing on the thin film and has the potential to predict the droplet splashing phenomena in the presence of complex boundaries.

Many researchers have studied the energy dissipation characteristics of two-jet collisions in air, but few have studied the related spatial rainfall distribution characteristics. In this paper, in combination with a model experiment and theoretical study, the spatial distributions of rainfall intensity of two-jet collisions, with different collision angles and flow ratios, are systematically studied. The experimental results indicated that a larger collision angle corresponds to a larger rainfall intensity distribution. The dimensionless maximum rainfall intensity sharply decreased with the flow ratio, while the maximum rainfall intensity slightly increased when the flow ratio was greater than 1.0. A theoretical equation to compute the location of maximum rainfall intensity is presented. The range of rainfall intensity distribution sharply increased with the flow ratio. When the flow ratio was greater than 1.0, the range of longitudinal distribution slightly increased, whereas the lateral distribution remained unchanged or slowly decreased. A formula to calculate the boundary lines of the x-axis is proposed.

Energy dissipation is one of the most important factors in choosing stepped spillways. However, very few studies have investigated energy dissipation with different horizontal face angles. In this paper, the realizable k-ε turbulent model was used to study the flow field, energy dissipation rates and turbulent kinetic energy and its dissipation rate for different stepped spillways with five horizontal face angles in the skimming flow regions. Results showed that the field and direction of the flow were changed by the horizontal face angles of the stepped spillway, which produced some unique characteristics and thus caused better energy dissipation. The fluctuation of free water surface will be larger with increasing horizontal face angles and the energy dissipation rate decreases with an increasing unit discharge and increases for the enlargement of the horizontal face angles. This conclusion could provide a reference for the relevant research of V shaped stepped spillways.

Pressure flow generally exists in water conservancy projects and pipelines. The flow boundary of the contraction section faces a potential risk of cavitation erosion under high velocity. However, there is a lack of effective methods to suppress cavitation in engineering practices with pressure flow, posing a challenge to the operational safety of discharge structures and pipeline devices. The purpose of this paper was to realize the application of air entrainment in a plug-type contraction section of pressure flow. It was found that a single air vent and a low air flow rate could achieve complete vena contracta aeration. The pressure profiles of the vena contracta were investigated, and the results showed that the pressure distribution allowed the entrained air to diffuse laterally and convectively. Finally, we proposed a fitting algorithm to predict the air concentration in the vena contracta. These conclusions are of great significance for improving the safety and cavitation resistance of the contraction section of pressure flow.