Characterization of unsteady cavitating flow regimes around a hydrofoil, based on an extended Schnerr–Sauer model coupled with a nucleation model

The present work is aimed at the numerical spatio-temporal characterization of the unsteady cavitating flow structures on a hydrofoil by means of Proper Orthogonal Decomposition (POD) and Fast Fourier Transform (FFT) techniques. Three different cavitation regimes have been investigated: bubble cavitation, cloud cavitation and supercavitation. The homogeneous mixture approach has been used, in combination with an extended Schnerr–Sauer cavitation model. The accuracy of the numerical predictions has been improved by means of the implementation of a Density Correction Model of the turbulent viscosity, and a simplified Population Balance Modeling (PBM) which solved the spatial distribution and the temporal evolution of the nuclei. In particular, the PBM has led to a reduction of the intensity of the evaporation inside the vapor cavities and a consequent condensation enhancement at the cavity closure and in the wake downstream. This phenomenon mainly impacted on the vapor cavity dynamics during supercavition by facilitating the formation of the re-entrant jet and the vapor cavity detachment. Also, during supercavitation the nuclei density nb exhibited maximum variations of about 35.6% with respect to the inlet nuclei density. As the cavitation number increased, both the intensity and the extension of oscillations significantly reduced, and in bubble cavitation regime nb fluctuated at amplitudes of about 10% of the inlet nuclei density. The characterization of the cavitation regimes revealed that the bubble cavitation regime had a more stable and periodic dynamics highlighted by a higher hydrodynamic efficiency and a reduced root mean square of the lift force. The cloud cavitation and the supercavitation exhibited a more violent bubble detachment which caused stronger oscillations of the vapor cavity as well as the pressure upstream. This was retrieved in an increase of the average drag coefficient of about the 38% due to the presence of vapor cloud transported downstream, which promoted the surge of the flow. The vorticity analysis underlined that the formation of the re-entrant jet and the bubble detachment were promoted by the baroclinic vorticity, while the dilatation vorticity drove the dynamics of the detached clouds, governed by the phase change phenomena. The FFT analysis of the dynamics of the vapor cavity and the pressure upstream led to the detection of the most representative frequencies and Strouhal numbers of each cavitation regimes, in particular (fs=16.6Hz, St=0.355) for bubble cavitation, (fs=10.74Hz, St=0.358) for cloud cavitation, and (fs=8.79Hz, St=0.300) during supercavitation. The POD analysis allowed for the detection of the most relevant cavitating structures, in relation to the vapor cavity fluctuations and their frequency content. Furthermore, the FFT analysis of the temporal eigenfunctions demonstrated that the first POD mode of the liquid volume fraction described the overall unsteady behavior previously detected. Instead, high order POD modes revealed frequency values well above the overall ones of the main flow previously detected.