Analysis of Hydrofoil Cavitation using Proper Orthogonal Decomposition

Cavitation is the change of phase from liquid to vapor when the pressure falls below the saturation pressure. For marine propellers, occurrence of cavitation is accepted on modern designs. However, there is a need to keep cavitation under control, because its extent can influence propeller efficiency, as well as lead to undesired phenomena such as increased noise and erosion. To understand the dynamics of cavitation, researchers often focus on cavitation on simpler geometries, such as hydrofoils. In this work, the test case consists on a two dimensional NACA0015 hydrofoil. It was studied by many authors both numerically (Arndt et al. (2000)) and experimentally (Ganesh and Ceccio(2016)). The results from a viscous flow simulation are considered here; the scope is to gain additional insight into cavitation dynamics in a regime of cavity shedding, by applying a Proper Orthogonal Decomposition (POD) technique. POD is used for analysis of experimental data or CFD results and relies on the approximation of the flow field by a linear combination of basis functions which are representative of flow structures. It is often applied to distinguish coherent structures from turbulent fluctuations (Chen et al.(2012)) or to detect specific flow features (Minelli et al.(2016)). POD was also applied to experimental observation of hydrofoil cavitation, Prothin et al.(2016), where the authors analyzed the variations of grey-scale level in high-speed video frames. This paper provides a description of the numerical setup and the basic theoretical background for POD in section 2. The flow dynamics predicted by the CFD code are shortly discussed in section 3.1. More extensively, Section 3.2 is dedicated to the outcome of orthogonal decomposition for two scalar fields: the vapor volume fraction and the pressure coefficient.