This article investigates the volume change law of trapped fluid in the meshing process and the flow characteristics of external gear pumps under the following two cases: the pump design with and without relief groove. In this study, a mathematical modeling of gear pairs is deduced based on the meshing theory and a complete set of mathematical equations of tooth profile, and the flow rate equation is derived based on law of conservation of mass across the changing boundaries of a control volume. During the process, the function of the pump displacement is established, which is formed by two parts: tooth space volume and trapped volume. In addition, using a control volume approach, the trapped volume and flow rate characteristics of the pump under different design parameters of gears are discussed. The results show that the curve of trapped volume is similar to a parabola and the pump designed with a large number of teeth, module, and pressure angle easily obtained good flow rate characteristics under the same condition, which have a great benefit for designing the relief grooves and external gear pumps.

In the tight sandstone oil production stage, the migration of particles will not only block the oil path and throat, but also block the wellbore and damage the equipment. Based on the theory of non-Newtonian fluid, hydrodynamics, the extended Derjaguin Landau Verwey Overbeek (DLVO) theory and the JKR (the model of Johnson–Kendall–Roberts) contact theory, the mathematical model and quantitative analysis of the critical condition of the particle separation from the surface due to the influence of oil flow in the fracture environment are presented in this paper. A theoretical model with pressure gradient as the core parameter and particle size, crack size and various contact forces as variables is established. By adding the formula of non-Newtonian fluid and taking the consistency coefficient and fluidity index as the contrast relation, the change rule of particle migration under the influence of non-Newtonian fluid is obtained. Effective prevention and control measures for the purpose of effectively preventing particle migration are also put forward. The results show that with the increase in the fluidity index, the pressure gradient decreases obviously; with the increase in the consistency coefficient, the pressure gradient increases obviously; and with the increase in particle size, the pressure gradient first decreases and then increases, thus creating a U-shaped curve. The lowest pressure gradient exists under the fixed condition.

The movement of the gas–liquid interface caused by the movement of the bubble position will have an impact on the starting conditions for particle migration. This article quantifies the influence of moving bubbles on the starting conditions of particle migration in non-Newtonian fluids, and it aims to better understand the influence of bubbles moving in non-Newtonian fluids on particle migration to achieve more effective control. First, the forces and moments acting on the particles are analyzed; then, fluid dynamics, non-Newtonian fluid mechanics, extended DLVO (Derjaguin Landau Verwey Overbeek theory), surface tension, and friction are applied on the combined effects of particle migration. Then, we reasonably predict the influence of gas–liquid interface movement on particle migration in non-Newtonian fluids. The theoretical results show that the movement of the gas–liquid interface in non-Newtonian fluids will increase the separation force acting on the particles, which will lead to particle migration. Second, we carry out the particle migration experiment of moving bubbles in non-Newtonian fluid. Experiments show that when the solid–liquid two-phase flow is originally stable, particle migration occurs after the bubble movement is added. This phenomenon shows that the non-Newtonian fluid with bubble motion has stronger particle migration ability. Although there are some errors, the experimental results basically support the theoretical data.

Efficient oil–water separation of produced fluids from high water-cut oilfields requires significant improvement in hydrocyclone separation performance. In this work, computational fluid dynamics simulations were applied to analyze the influence of integrating gas flotation with hydrocyclone separation. To describe the internal flow behavior and the distribution of oil droplets in gas-assisted operation, the Mixture multiphase model together with the Realizable k - ε turbulence model was utilized. Based on a conventional liquid-liquid hydrocyclone, a porous medium region was incorporated into the large cone section to represent microporous walls for microbubble injection, thereby achieving the coupling of flotation and hydrocyclone separation. The results show that gas injection enhanced the separation efficiency from 83.56 % to 95.96 %. Moreover, microbubble size exhibited a pronounced influence on separation performance: smaller bubbles facilitated better oil-water separation. The optimal performance was obtained with an air bubble diameter of 5 μm, where the separation efficiency reached 97.73 %.

The processing and assembly of umbrella ribs in umbrella manufacturing still rely on manual labor due to the specific nature of umbrella production. If parts could be fed and riveted in a fixed orientation during this process, it would improve production efficiency. This paper proposes a vibration feeder designed for the orienting and conveying of umbrella rib parts. In this paper, a 3D model of the vibratory feeder was created using SOLIDWORKS, and modal analysis was performed using ANSYS software. Through modal analysis, the first eight modes of the feeder were obtained, determining its natural frequencies and mode shapes under these vibrational modes, which provide a basis for studying the feeder.