Application of Data Analysis Methods to Complex Flows with Gas-Liquid Phase Change

Cavitation is a complex hydrodynamic phenomenon that occurs when the local pressure in a liquid drops below the saturation vapor pressure, resulting in the phase transition of the liquid into vapor. This process was characterized by intricate three-dimensional flow structures and highly unsteady, violent dynamics. For applications such as hydraulic machinery, ship propulsion, and hydraulic engineering, cavitation often induces detrimental effects, and has significant impact on performance and reliability in engineering systems. In order to investigate the structure of non-constant cavitation flow field, this paper adopted the experimental method of image particle velocimetry PIV-LIF, which used a high-speed camera to photograph the cavitation flow from the side of the experimental section and followed the liquid flow by fluorescent tracer particles, so as to measure the cavitation velocity field. Using the high-resolution velocity field and grayscale snapshot data, the dynamic mode decomposition (DMD) was carried out to analyze the structure of the non-constant cavitation flow field. The DMD method can effectively decompose the flow field into several modes and identify the dominant mode for analysis. Based on the DMD method, the decomposition of the cavitated flow field has the characteristics of a single mode frequency and growth rate, which is more advantageous in the analysis of cavitated periodic flow. By analyzing the main modes that account for higher energy and performing modal reconstruction, it is found that all these modes contain certain characteristics of vacuole motion, which are related to the structure of the re-entrant jet and the accompanying vortex in the flow field, and the main evolution frequency of the vacuole is consistent with the vortex shedding frequency. The results of the flow field characteristics of each mode show that the first-order mode of the cavitation flow corresponds to a frequency of 0, which represents the average flow field; the second-order mode corresponds to a frequency of about the vacuole shedding frequency, which reveals that the vacuole grows and sheds periodically at the leading edge of the occurrence; the third-order mode corresponds to a frequency about twice that of the second-order mode, which reveals the fusion behavior of two large-scale vortices behind the hydrofoil; the fourth-order mode corresponds to a frequency about three times higher than the second-order mode, which characterizes the fusion behavior of some small-scale vortices in the flow field. Finally, the modal decomposition analysis of the cavitation flow field with different cavitation numbers was carried out, and it is found that the vortex structure of the shedding vacuole increases with decreasing cavitation number, and the second-order mode frequency decreases with decreasing cavitation number.