Flow past three identical circular cylinders is numerically investigated using the immersed boundary method. The cylinders are arranged in an equilateral-triangle configuration with one cylinder placed upstream and the other two side-by-side downstream. The focus is on the effect of the spacing ratio $L/D(=1.0{-}6.0)$ , Reynolds number $Re(=50{-}300)$ and three-dimensionality on the flow structures, hydrodynamic forces and Strouhal numbers, where $L$ is the cylinder centre-to-centre spacing and $D$ is the cylinder diameter. The fluid dynamics involved is highly sensitive to both $Re$ and $L/D$ , leading to nine distinct flow structures, namely single bluff-body flow, deflected flow, flip-flopping flow, steady symmetric flow, steady asymmetric flow, hybrid flow, anti-phase flow, in-phase flow and fully developed in-phase co-shedding flow. The time-mean drag and lift of each cylinder are more sensitive to $L/D$ than $Re$ while fluctuating forces are less sensitive to $L/D$ than $Re$ . The three-dimensionality of the flow affects the development of the wake patterns, changing the $L/D$ ranges of different flow structures. A diagram of flow regimes, together with the contours of hydrodynamic forces, in the $Re-L/D$ space, is given, providing physical insights into the complex interactions of the three cylinders.

In this paper, the entrainment and movement of coarse particles on the bed of an open channel is numerically investigated. Rather than model the sediment transport using a concentration concept, this study treats the sediment as individual particles and investigates the interaction between turbulent coherent structures and particle entrainment. The applied methodology is a combination of the direct numerical simulation of turbulent flow, the combined finite-discrete element modeling of particle motion and collision, and the immersed boundary method for the fluid-solid interaction. In this study, flow over a water-worked rough-bed consisting of 2-3 layers of densely packed spheres is adopted and the Shields function is 0.065 which is just above the entrainment threshold to give a bed-load regime. Numerical results for turbulent flow, sediment entrainment statistics, hydrodynamic forces acting on the particles, and the interaction between turbulence coherent structures and particle entrainment are presented. It is shown that the presence of entrained particles significantly modifies the mean velocity and turbulence quantity profiles in the vicinity of a rough-bed and that the instantaneous lift force can be larger than a particle's submerged weight in a narrow region above the effective bed location, although the mean lift force is always smaller than the submerged weight. This, from a hydrodynamic point of view, presents strong evidence for a close cause-and-effect relationship between coherent structures and sediment entrainment. Furthermore, instantaneous numerical results on particle entrainment and the surrounding turbulent flow are reported which show a strong correlation between sediment entrainment and sweep events and the underlying mechanisms are discussed.

This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of two to three layers of densely packed spheres. The Shields function is 0.065 which is just above the sediment entrainment threshold to give a bed-load regime. The applied methodology is a combination of three technologies, i.e., the direct numerical simulation of turbulent flow; the combined finite-discrete element modeling of the deformation, movement, and collision of the particles; and the immersed boundary method for the fluid-solid interaction. It is shown that the presence of entrained particles significantly modifies the flow profiles of velocity, turbulent intensities, and shear stresses in the vicinity of a rough bed. The quasi-streamwise-aligned streaky structures are not observed in the near-wall region and the particles scatter on the rough bed owing to their large size. However, in the outer flow region, the turbulent coherent structures recover due to the weakening rough-bed effects and particle interferences. First- and second-order statistical features of particle translational and angular velocities, together with sediment concentration and volumetric flux density profiles, are presented. Several key parameters of the particle saltation trajectory are calculated and agree closely with published experimental data. Time histories of the hydrodynamic forces exerted upon a typical saltating particle, together with those of the particle's coordinates and velocities, are presented. A strong correlation is shown between the abruptly decreasing streamwise velocity and increasing vertical velocity at collision which indicates that the continuous saltation of large-grain-size particles is controlled by collision parameters such as particle incident angle, local bed packing arrangement, and particle density, etc.