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 * 105, and an incidence of 12° for varying cavitation numbers. The cavitation was recorded using a synchronised dual-camera setup with simultaneously captured pressure signals. Shockwave-driven and re-entrant flow-driven cloud shedding are identified, as well as the transition regime in between, exhibiting more complex behaviour. 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.