Data-driven spatiotemporal analysis of cloud cavitation by means of spectral proper orthogonal decomposition

Abstract

The global dynamics of cloud cavitation are not always obvious; cloud cavitation may exhibit chaotic, multimodal and intermittent behaviour, where dominant flow structures are hidden to the naked eye. To address this, spectral proper orthogonal decomposition (SPOD) is applied, a method that can continuously transition between proper orthogonal decomposition (POD) and discrete Fourier transformation (DFT)/dynamic mode decomposition (DMD). This provides the opportunity to break down the complex dynamics of interacting and transient processes into interpretable modal bases. Experiments were conducted in a high-speed cavitation tunnel using a two-dimensional NACA 0015 hydrofoil at a fixed Reynolds number of \(8 \times 10^5\) and an incidence of \(12^\circ\) for varying cavitation numbers. The cavitation was recorded using a synchronised dual-camera set-up with simultaneously captured pressure signals. Shockwave-driven and re-entrant flow-driven cloud shedding is identified, as well as the transition regime in between, exhibiting more complex behaviour. The transition from shockwave-driven to re-entrant flow-driven cloud cavitation is smooth, with shockwaves becoming more dominant as the cavitation number decreases. SPOD modes allow for a frequency and amplitude variation, which successfully decomposes the data into the dominant modes, whereas classical modal decomposition methods such as POD and DMD do not provide interpretable decompositions. SPOD grants access to a transient analysis of the data via the SPOD time coefficients. We validate the SPOD results using space–time plots and power spectral density (PSD) of the pressure signals, being in good agreement with the SPOD spatial modes and time coefficients. The complex time coefficients give access to instantaneous mode frequencies and allow calculating a standard deviation of the frequency modulation of the modes. The findings provide a deep insight into the spatial and temporal behaviour of cloud cavitation and support the understanding of its physics.