Mode decomposition methods for the analysis of cavitating flows in turbomachinery

The present work is aimed at the characterization of the cavitating flow regimes by applying the coupled POD/DMD technique to the vapor volume fraction field. The proposed approach provided an improved spatio-temporal-frequency description of the flow, based on the detection of the most energetic flow structures with information about their shape and size, and their decomposition into wave patterns oscillating with specific frequency and decay rate. The novel technique was applied to numerical results concerning the bubble cavitation and the supercavitation regimes of 2D water flows around a NACA hydrofoil at ambient temperature. Numerical simulations were performed by using a homogenous mixture model equipped with an extended Schnerr-Sauer cavitation model, in combination with a Volume of Fluid (VOF) interface tracking method. The proposed approached provided a better characterization of the unsteady cavitating flow, and allowed for a deeper insight about the dynamics of the vapor cavity, especially in cases involving the more chaotic regime of supercavitation. In particular, POD results figured out the most energetic coherent vapor structures associated to each cavitation regime: the first mode highlighted the main sheet cavity which grew on the hydrofoil up to detached, the second mode pointed out the cavitating/condensating doublet structures and the third mode figured out the smaller structures owning less energy but a higher frequency content. DMD modes performed a decomposition of the coherent structures detected by means of the POD analysis, into a subset of vapor pattern periodically evolving with a single frequency and a characteristic decay rate. Furthermore, results showed that the supercavitating flow structures owned characteristic frequencies which ranged from 5 to 26 Hz, while the less intensive bubble cavitation regime was characterized by frequencies ranging from 15 to 42 Hz.