Fractal feature map construction and validation for the gas-solid two-phase flow

Feature maps have shown significant potential in gas-solid two-phase flow research. However, traditional feature maps, such as chaotic attractors and recurrence plots, suffer from issues like dependence on subjective parameter selection or structural folding. This study proposes a novel method for constructing a fractal feature map of the gas-solid two-phase flow that effectively captures its fractal properties. Using phase space reconstruction, the electrostatic signal is transformed into a phase space trajectory, and then an inter-point distance matrix is calculated to generate the map. This map exhibits a unique texture structure composed of horizontal and vertical stripes, with a construction process that is nearly independent of parameter selection and free from structural folding. To validate the effectiveness of the fractal feature map, this study simultaneously employs detrended fluctuation analysis (DFA) to examine from a time perspective, and a new method based on the power-law relationship between periodic intensity and spatial scale to examine from a spatial perspective. Results show that the power-law curves obtained from both methods exhibit consistent trends, revealing the fractal properties of gas-solid two-phase flow and confirming the effectiveness of the fractal feature map in capturing such dynamics. This map provides a new tool for flow feature visualization, offering a new perspective for analyzing the behavior of gas-solid two-phase flow, and provides a reference for future exploration of combining deep learning techniques with fractal feature maps to enhance flow pattern recognition and prediction capabilities.