A modified drag coefficient model for calculating the terminal settling velocity and horizontal diffusion distance of...

Deep-sea mining inevitably produces plumes, which will pose a serious threat to the marine environment with the continuous movement and diffusion of plumes along with ocean currents. The terminal settling velocity (w_t) of irregular particles is one of the crucial factors for determining the plumes' diffusion range. It is generally calculated by drag coefficient (C_D), while most existing C_D models only consider single shape characteristic parameter or have a smaller range of Reynolds number (Re). In this study, a new shape factor (γ) of irregular particles is proposed by considering the thickness (one-dimension), the projected area (two-dimension), and the surface area (three-dimension) of irregular particles as well as their coupling effect to establish a modified C_D model for calculating the w_t. A modified Gaussian plume model is proposed to predict the horizontal diffusion distance of the plume particles by considering the settling velocity and diffusion effect of irregular particles. Research results show that the w_t increases nearly linearly, with a gradually decreased slope and slightly then greatly with the increasing of γ, d_p (diameter) and ρ_p (density), respectively. The modified C_D model is verified to be more valid with a wider application range (Re < 3×10⁵) than five existing C_D models by the test results. The larger the ρ_p or d_p, the larger the w_t and thus the smaller the S_h. This study could provide a theoretical basis for calculating the plume diffusion range to further study the impact of deep-sea mining on the ocean environment.