Will sailing in formation reduce energy consumption? Numerical prediction of resistance for ships in different formation configurations

• Discussion on the question of whether sailing in specific formation configurations can reduce resistance, and thus, reduce energy consumption. • Numerical predictions of resistance for ships in three common geometric configurations. • The relation between resistance, relative distance, and Froude number. • Energy-saving configurations with different speeds that can be used as the foundation of a novel waterborne transportation system design based on formation sailing. In nature, emergent collective behaviors suggest that the followers would obtain energy benefit from positive interaction with the leader’s wake by certain configurations. This article answers the question about the motivation of formation control research -- “will sailing in formation reduce energy consumption”. We carried out a series of numerical analyses on the relationship between resistance and formation configurations using the Reynolds Averaged Navier-Stokes (RANS) method in combination with the Shear Stress Transport (SST) k - ω turbulence model. At the first stage, verification and four-separate-distance benchmark cases are conducted to test grid discretization and numerical methods. Then, parametric studies are performed at various longitudinal offsets and transverse separations in tandem, parallel, and triangle formations. The numerical results indicate that specific formation configurations could bring resistance reduction and achieve energy benefit from the perspective of the whole convoy and the individual ship. Discussions on the resistance, energy consumption, and formation configuration are provided, respectively. Five energy consumption regions are established based on the resistance variations under different formation configurations. In terms of energy preservation, tandem formation is the optimal fleet configuration, followed by the triangle and parallel formation. Besides, for better maneuverability, specific longitudinal distances and lateral gaps are given to eliminate the additional lateral force and yaw moment caused by the ship-ship interaction.