Unsteady hydrodynamics and energy loss during the water-exit process of a delta wing

Abstract

Delta-wing layout is a promising design in trans-medium vehicles. However, its water-exit process involves complex interactions among three-dimensional vortex evolution, free-surface deformation, and hydrodynamic loading, leading to flow and loading characteristics that differ from those commonly reported for canonical blunt bodies. In this study, high-fidelity computational fluid dynamics simulations are conducted to investigate the water-exit dynamics of a neutrally buoyant three-dimensional delta wing. The evolution of vortex structures, free-surface deformation, hydrodynamic loads, and moment characteristics is analyzed over a range of initial velocities. Unlike blunt bodies, for which flow separation may occur over an extended and geometry-dependent region, the sharp leading-edge corners of the delta wing promote concentrated flow separation and coherent tip vortices, resulting in a distinct wake topology and subsequent vortex evolution. As the wake develops, progressive deformation and asymmetric evolution of the vortex system lead to increasingly asymmetric three-dimensional vortex structures, producing an imbalance in hydrodynamic loading and resulting in pronounced roll and yaw moments even when the wing motion is constrained to a single vertical degree of freedom. The results suggest that, if rotational degrees of freedom are released, the vortex-induced moment imbalance may lead to wing deflection and trajectory instability. Meanwhile, the free surface undergoes strongly nonlinear deformation accompanied by pronounced wave radiation, with most of the wave energy propagating in the spanwise direction. The energy analysis reveals that hydrodynamic dissipation dominates the kinetic energy loss during the submerged stage, while free-surface effects become increasingly important during emergence. These findings provide new insight into the coupled evolution of vortex structures, free-surface deformation, and hydrodynamic loads during the water-exit process of finite-span lifting surfaces and highlight the potential importance of vortex-induced moment imbalance for the stability and control of trans-medium vehicles.