Free-Surface Effects on the Evolution of a Marine Propeller's Wake

The present paper analyses the vortical structures in the wake of a naval propeller operating underneath a free surface using detached-eddy simulation. We investigate the flow topology for several loading conditions and compare it with analogous observations behind a propeller operating in open water. We show that the wake topology is similar to that observed in open water only for low-loading conditions. For mild blade loading, the free surface's presence seems to stabilize the flow. On the contrary, for high blade loading, the mutual interaction between the vortex system and the free surface leads to vortex breakdown that over-shadows the multiple pairing mechanisms observed in open-water conditions.The structure of propeller wakes received great attention in the past (Kerwin, 1986) and in recent years (Felli et al., 2011; Muscari et al., 2013; Di Mascio et al., 2014a; Muscari et al., 2017a; Magionesi et al., 2018) because the evolution of the main vortical structures that emanate from the blade tips and the hub is tightly related to vibrations, noise and aerodynamic/hydrodynamic performances. The wake of a rotor has a very complex topology, with several vortical systems with various shapes and strengths. Three main structures are generally present: tip vortices, blade vortex sheets and hub vortex. For each blade, the tip vortex and the blade vortex sheet correspond to the trailing vortex system of a wing, whose local strength is proportional to the radial variation of blade circulation. Since the most significant circulation variation appears at the blade end, vorticity is markedly higher at the tip than in the rest of the blade vortex sheet, with a distinguishable concentrated tip vortex. The hub vortex system is a well-defined streamwise structure, where the vorticity is equal in strength and opposite in orientation to the sum of blade vortex systems (in a simplified portrait of inviscid flow plus horseshoe vortices, it consists of the sum of each horseshoe vortex for the blades). In a more realistic picture of a viscous fluid, the blade vortex sheet also carries the vorticity generated in the boundary layer that detaches at the trailing edge. Moreover, horseshoe vortices are also present at each blade root. All these structures interact during downstream convection in a peculiar way that depends on the blade load (i.e. local incidence). For some loading conditions, the regular vortex system becomes unstable. These basic mechanisms were largely studied for the four-bladed E779A marine propeller by means of flow visualizations (Felli et al., 2011) and further corroborated by numerical simulations (Muscari et al., 2013; Ahmed et al., 2020; Wang et al., 2021a,b). The tip vortex is the first to experience helical instabilities associated with self- and coil-to-coil interaction due to self-induction. These perturbations propagate along the vortex tube and cause transverse oscillations of the cores. Further downstream, due to the weakening of the blade vortex sheet, the tip and hub vortices are no longer linked and evolve independently as separate structures, giving rise to destabilization process (Okulov and Sørensen, 2007). In facts, in the absence of the blade sheet (that damps tip vortex oscillations), the interactions between consecutive tip vortices are strengthened, giving rise to long-wave instabilities and promoting the merging of two adjacent tip vortices. Reduced- order analysis using proper orthogonal decomposition and dynamic mode decomposition of detached-eddy simulations proved that the merging process consists of a sequence of modes with an asymmetric evolution of the coupled tip vortices at the periphery of the slipstream (Magionesi et al., 2018). Consequently, the hub vortex experiences transverse oscillations that amplify downstream, driving a low-frequency precession motion of the outer structures. These mechanisms amplify vortex stretching and tilting, with complete redistribution of the vorticity that leads to the complete loss of coherence in the wake and transition to almost homogeneous turbulence. Experimental observations and numerical simulations show that all vortex pairing mechanisms and instabilities move upstream when the blade load increases; this happens because the distance between tip vortices decreases, thus increasing the mutual interaction.