“…In recent years, the interface-resolved direct numerical simulation methods have been used to probe the mechanisms in the interactions between the turbulence and the finite-size particles, in which the interface between the particles and fluids is resolved and all turbulent structures are resolved with the direct numerical simulation method. Such methods have been applied to the simulations of particle-laden isotropic homogeneous flows (e.g., Ten Cate et al, 16 Lucci et al, 17 Gao et al, 18 and Cisse et al 19 ), pipe flow, 20 vertical channel flows, 21,22 and horizontal channel flows (e.g., Pan and Banerjee, 23 Shao et al, 24 Kidanemariam et al, 25 Do-Quang et al, 26 Picano et al, 27 Wang et al 28 ), as well as the interactions between the turbulence and a fixed particle (e.g., Bagchi and Balachandar, 29 Burton and Eaton, 30 Naso and Prosperetti 31 ). The aim of the present work is to investigate the effects of the finite-size neutrally buoyant particles on the turbulent flows in a square duct with the interface-resolved DNS method, focusing on the mean and root-mean-square velocities and in particular the mean secondary flow.…”