Modal analysis of tip vortex cavitation with an insight on how vortex roll-up enhances its instability

Abstract

The instability mechanism of tip vortex cavitation (TVC) is investigated in the present paper, which is found to be significantly influenced by the roll-up of secondary vortices. The three-dimensional proper orthogonal decomposition (3D-POD) analysis is utilized to identify the coherent structures around the TVC, and a modal turbulence transport theory is introduced to further measure the modal contribution to the TVC instability. According to the dynamic evolution of coherent structure identified by the 3D-POD analysis, the fluctuating component is gradually introduced into the tip vortex together with the roll-up of secondary vortices. Moreover, the dynamic evolution of coherent structure is always accompanied by a significant distribution of modal turbulence kinetic energy (TKE), implying that the TVC instability is promoted along with the merging of secondary vortices into the tip vortex. A deeper understanding is gained with the assistance of the modal turbulence transport theory. It is found that the modal Reynolds stress introduced by the vortex roll-up is the trigger for the local TVC instability, because it can significantly enhance the energy input from mean flow to fluctuating flow.