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

Abstract In this study, the sedimentation of a torus is studied numerically over a range of Reynolds number spanning 10 ≤ Re T ≤ 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 θ 0 , in the range of 0 ≤ θ 0 ≤ 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 Re T , the flow reaches the same terminal state and the torus maintains the same final state, orientation and terminal velocity, regardless of θ 0 . 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 Re T and θ 0 . The offset of the torus centroid in the z direction between the initial and terminal states increases with increasing Re T and θ 0 because of the θ 0 effect. The falling time ( T f ) for the torus traveling along the same distance in the x direction decreases with increasing θ 0 when Re T ≤ 50. However, when Re T > 50, T f initially increases and then decreases with increasing θ 0 , with the maximum T f occurring at θ 0 ≈ 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 θ 0 ≈ 60° for Re T > 50, which thus significantly decelerates the falling speed of the torus and increases T f .