Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller

Abstract

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.