Since it is low in cost and low in toxicity and has good biodegradability, gas-liquid-foam three-phase flow has been widely used in industrial fire protection. Due to the different characteristics of gas, liquid, and foam, liquid precipitation is liable to occur under static conditions, resulting in unstable performance of the mixture. To improve fire extinguishing efficiency, it is of great significance to study the separation process of gas-liquid-foam. In the present study, the effects of the surface tension (range from 0.04 to 0.07) and initial liquid volume fraction (range from 0.2 to 0.5) on the gas-liquid-foam separation process are investigated with the numerical tool Fluent. The liquid volume fraction is mainly influenced by two inverse effects: (a) the transformation of liquid into foam, and (b) the liquid drainage and bursting of foam. In the separation process, the volume fraction of small foam decreases monotonically while the volume fraction of medium and large foam increases slightly. Since the volume fraction of small foam is much greater than medium and large foam and its bursting process is dominant, the liquid volume fraction presents a monotonic increasing trend. The volume of the separated liquid increases almost linearly with time at various surface tensions and initial volume fractions, and the increase rate is about 0.004. In the range of the surface tension examined, the separation process is insensitive to the surface tension, resulting in almost the same drainage time. On the other hand, the separation process depends on the initial liquid volume fraction non-monotonically; namely, when the initial volume fraction is small, with the increase of the initial volume fraction, the liquid is more easily separated from the mixture, and when the initial volume fraction is over a critical value (about 0.4), the separation process is decelerated.

The flow in the square cavity with internal obstacles exists widely; thus, investigating the effect of the existence of the obstacles on the flow and the motion of the solid particles is important. To understand, predict, and control the motion of the solid particles, the motion of a neutrally buoyant circular particle in a lid-driven square cavity with an internal circular obstacle is studied with the lattice Boltzmann method, where the effects of the obstacle size, obstacle location, initial position of the circular particle, and Reynolds number are investigated. Under the effect of the obstacle, the flow and the motion of the particle are quite different. Especially, under some cases, no limit cycle is observed, and the particle is captured by the secondary vortex at the lower layer of the square cavity, which is insensitive to the initial position of the circular particle. The effect of the Reynolds number on the motion of the particle is significant, with the increase in the Reynolds number, and the motion of the particle is different obviously. At low Reynolds numbers, the motion of the particle is confined by the primary vortex, which moves along the limit cycle at the upper layer of the square cavity. With the increase in the Reynolds number, the effect of the inertia of the particle becomes stronger, and the particle moves from the primary vortex to the secondary vortex until it is captured by the secondary vortex. At relatively high Reynolds numbers, the primary vortex develops, and the particle is confined by the primary vortex again, forming another limit cycle.

Understanding, predicting and controlling the motion of the solid particles became active research topics, like debris flows, sand storms, transport of volcanic ash, coal combustion, drug delivery and steel making. Thus, the motion of a neutrally buoyant elliptical particle in a double-lid-driven square cavity is studied with the lattice Boltzmann method, where the effects of the initial position, Reynolds number and aspect ratio are studied. The square cavity is divided into two parts by the two primary vortexes, and the motion of the elliptical particle is determined by the interaction of the two primary vortexes. The limit cycle is sensitive to the initial position of the elliptical particle, namely, placing the elliptical particle at different positions initially, the motion of the elliptical particle exhibits different modes. Especially, the elliptical particle is apt to cross the horizontal centerline of the square cavity at moderate Reynolds numbers. The effect of the Reynolds number on the motion of the elliptical particle is significant, with the increase of the Reynolds number, the effects of the two primary vortexes on the motion of the elliptical particle are different, which affects the trajectory of the elliptical particle fundamentally. With the increase of the aspect ratio, the elliptical particle becomes flatter, the hydrodynamic force and torque acting on the elliptical particle become unbalanced and the elliptical particle no longer moves along the 8-like limit cycle.