Numerical simulation of the horizontal rotating cylinder and the air entrainment near the free surface

The flow around a cylinder near a free surface contains many physical phenomena and mechanisms, especially when the cylinder is moving. In this paper, the two-dimensional flow of a rotating cylinder near the free surface is simulated. The dynamic behavior of the rotating cylinder and the flow characteristics such as force coefficient, vortex structure, and air entrainment under different depth ratios, Fr numbers, and rotation ratios are discussed. In such problems, the rotational motion is rarely mentioned. The two-phase model is the sharp volume of the fluid method based on the two-dimensional incompressible Navier–Stokes equation. Combined with the spatially adaptive four-octree grid, the gas–liquid interface is reconstructed with the high-density ratio (ρwater/ρair = 816). The results show that, at α ≤ 2.0, the combined effect of the free surface and the rotation causes the wake vortex to produce a positive upper and negative lower distribution, which is contrary to the single condition. For the rotating cylinder, the existence of a free surface leads to the stable vortex layer at a low rotation ratio (α = 1.0), which only occurs at the high rotation ratio (2 < α < 4.2) without free surface. For the force coefficients, the simultaneous existence of the free surface and the rotation obviously changes the value and periodicity of the coefficients, which is different from the single condition. As for the air entrainment, it can be divided into two categories within the selected parameters: vortex entrainment caused by the parallel free surface and wake jet entrainment. In the latter model, the entailed bubbles have a wider distribution in space due to the influence of shedding vortices.