PIV Snapshot Clustering Reveals the Dual Deterministic and Chaotic Nature of Propeller Wakes at Macro- and Micro-Scales

Abstract

This study investigates the underlying mechanisms governing the evolution of tip vortices in the far field of a naval propeller wake. To achieve this, a novel approach utilizing data clustering applied to particle image velocimetry snapshots is employed. The clustering of data is carried out using the k-means algorithm, with the optimal number of clusters determined by evaluating two metrics: the within-cluster sum of squares and the average silhouette. The clustering of phase-locked propeller wake data is focused on the vorticity associated with the regions containing tip vortices. Additionally, techniques such as proper orthogonal decomposition, t-distributed stochastic neighbor embedding, and kernel density estimation are employed to visually represent the data clusters in a two-dimensional space, facilitating their assessment and subsequent discussion. This paper shows how the application of data clustering enables a comprehensive understanding of the complex mechanisms driving the dynamics of propeller wake vortices in both the transitional and far fields. Specifically, it reveals the dual nature of the propeller wake flow, characterized by deterministic and chaotic behavior at macro- and micro-scales.

Keywords

• snapshot clustering
• <i>k</i>-means
• proper orthogonal decomposition
• principal component analysis
• <i>t</i>-distributed stochastic neighbor embedding
• propeller wake