An entropy measure-based study on flow pattern of gas–liquid two-phase flow in a U-Tube

U-tubes are widely applied in gas–liquid two-phase transportation in chemical engineering. The diverse flow patterns within these tubes significantly affect the pressure loss, heat transfer efficiency, and even the fluid-induced vibration amplitude of the tubes. This study explores the complex flow pattern features in a U-tube in a vertical plane and focuses on recognizing them. For the acquisition and classification of flow patterns, a Computational Fluid Dynamics (CFD) model for gas–liquid two-phase flow is first established, and its quantitative calculation error is ensured to be less than 5%. Then, the spatiotemporal evolution characteristics of flow patterns is analyzed. The real-time pressure drop response is chosen as the representation signal, and its nonlinear features in the time and frequency domain under different flow patterns are explored. A nonlinear time series is constructed by extracting a segment from the real-time pressure drop data, and six entropy measures are applied to analyze and identify them. Finally, the sensitivity of entropy measures to both the time series lengths and the tested sections are evaluated. Results show that there are six typical flow patterns in a U-tube. According to most entropy measures, the bubble flow has the highest complexity; however, the plug flow presents the lowest complexity. In the U-bend, pressure drop signals for the bubble and annular flows show random fluctuations within a specific range, in contrast to the marked periodicity in plug flow signals, while wavy and slug flows exhibit intermittent peak values. Including the upstream and downstream straight pipes in the analysis, rather than focusing solely on the U-bend, significantly increases the complexity of the stratified, plug, and slug flows. Fuzzy entropy is an effective tool for identifying the six flow patterns, demonstrating good resilience to variations in the length of the data series. This characteristic makes it highly useful for real-time identification of flow patterns in the U-bend sections of non-transparent U-tubes, offering considerable potential in chemical equipment.