Vapor concentration and bimodal distributions of turbulent fluctuations in cavitating flow around a hydrofoil

Abstract

The article presents results of a statistical analysis of the original PIV data for the cavitating flow around the 2D symmetric hydrofoil mimicking a guide vane of a Francis turbine which were previously reported in Timoshevskiy et al. (2020). We employ the procedure of statistical vector filtration (Heinz et al., 2004) to eliminate vector outliers from the measured velocity fields, which allows us to retrieve genuine spatial distributions of higher-order statistical moments of velocity fluctuations, and the method of vapor phase detection (Pervunin et al., 2021) to extract time-averaged fields of vapor in the cavitating flow. The spatial distributions of the probability of vapor phase occurrence allowed us to unambiguously distinguish the extension of the flow area occupied by the dispersed phase (cavitation) together with the time-averaged concentration of the vapor phase in the three characteristic regimes of the cavitating flow as well as different features of cavitation evolution, including the location and length of an attached cavity and the place of detachments of cloud cavities in the case of unsteady cloud cavitation. The development of cavitation is also reflected in the fields of higher-order statistical moments of turbulent fluctuations by the example of coefficients of asymmetry and excess. With a transition to unsteady cloud cavitation, the distribution of velocity fluctuations transforms, taking a nonequilibrium shape, with an increase in magnitudes of the asymmetry and excess coefficients over a significant flow area. In a region of the attached cavity, around the place of formation of vapor clouds and downstream, where the cloud cavities are carried away by the flow, the distribution of velocity fluctuations becomes bimodal. Through visual inspection of the raw PIV images, realizations related to two characteristic phases of the cavity oscillation cycle were extracted, providing quasi-phase-averaged data. As a result, the bimodal shape of the distributions in certain areas of the unsteady cavitating flow was demonstrated to be most probably linked with periodic detachments and downstream advection of the vapor clouds as the predominant fundamental process determining the flow structure and dynamics.