A numerical study on free-fall of a torus with initial inclination angle at low Reynolds numbers

In this study, the sedimentation of a torus is studied numerically over a range of Reynolds number spanning 10 ≤ ReT ≤ 90. The three-dimensional governing equations are solved using the fluid–structure interaction version of the SVD-GFD method on a hybrid Cartesian-cum-meshless grid. The torus has a fixed aspect ratio AR = 2, and is set to fall along the negative x direction at an initial inclination angle θ0, in the range of 0 ≤ θ0 ≤ 80°. The flow behavior induced by the falling torus is characterized by the far field vortex sheet and the near field recirculation zone. At a given ReT, the flow reaches the same terminal state and the torus maintains the same final state, orientation and terminal velocity, regardless of θ0. The torus initially experiences a zigzag motion (along the x and z directions) in the global frame and the pitch motion in its body frame, which are more obvious at larger ReT and θ0. The offset of the torus centroid in the z direction between the initial and terminal states increases with increasing ReT and θ0 because of the θ0 effect. The falling time (Tf) for the torus traveling along the same distance in the x direction decreases with increasing θ0 when ReT ≤ 50. However, when ReT > 50, Tf initially increases and then decreases with increasing θ0, with the maximum Tf occurring at θ0 ≈ 60°. A lift-like force is generated in the positive x direction due to the translational torus motion in the z direction, which originates from the pressure. This force is most pronounced at θ0 ≈ 60° for ReT > 50, which thus significantly decelerates the falling speed of the torus and increases Tf.