Numerical investigation of resistance reduction mechanisms and scale effects in tandem ship formation

Abstract

Ship formation offers a strategic approach for resistance reduction in sustainable maritime transportation, whereas the underlying physical mechanisms and their scale dependencies remain insufficiently understood. In the present research, a URANS-based framework integrated with resistance decomposition was constructed to investigate two-ship tandem configurations, where the SST k–ω and VOF models were adopted. After evaluating the characteristics of resistance components across varying speeds, systematic numerical simulations were performed and analyzed across a range of geometric scales and various longitudinal spacings. The results indicate that the formation effects are primarily manifested on the trailing ship. Specifically, viscous resistance reduction is governed by the wake-shadowing effect, yet this benefit diminishes with increasing Reynolds number. In contrast, pressure resistance variation is governed by wave interference and remains kinematically scale-independent under Froude similarity. These findings elucidate the underlying physics and scale effects, providing a mechanistic basis for interpreting full-scale tandem-ship resistance trends and guiding engineering-oriented formation design.