Body interaction effects on mean drag forces for an infinite array of cylindrical cruciform shapes with normal inflow

The move of aquaculture farms to open ocean areas poses great challenges to aquaculture farming technologies and operations due to the harsh offshore wave and current conditions. Understanding the drag and lift responses of netted aquaculture structures is key for accurately predicting nonlinear sea loads and seakeeping responses. Our particular interest is understanding the drag force on a single net element idealized as a cylindrical cruciform, with and without a canonical knot, to better inform turbulent viscous drag forces on the full netted aquaculture cages. We use high-resolution 3D direct numerical simulation of a cylindrical cruciform shape with doubly periodic conditions and constant normal inflow to study the body interaction effects on the mean drag forces on the net element. The numerical method uses Boundary Data Immersion Method (BDIM) to solve the incompressible Navier-Stokes equations. We analyze the mean drag forces of the individual net element for a large range of cylinder diameter-to-length (d/l) ratios (or the net solidity) for cruciforms with and without spherical knots at the center at two different Reynolds numbers. For small d/l, we show that the presence of the second cylinder in a cruciform arrangement produces a drag coefficient less than that of a single cylinder in infinite domain. We identify the d/l above which where body interaction effects become important to the mean drag force. By analyzing the pressure coefficient on the net element at different locations, we establish that the body interaction effect, similar to solid blockage effect in tunnel experiments, is the relevant influence on the drag coefficient as opposed to wake blockage. Finally, we show that the overall presence of the knot, below a certain knot diameter, reduces the overall drag on the net element and that the above results are independent of a cylinder-diameter-based Reynolds number.