Structural Velocity Measurement of Gas–Liquid Slug Flow Based on EMD of Continuous Wave Ultrasonic Doppler

Gas-liquid slug flow widely exists in many industrial processes. The structural velocities of slug flow are important for fluid mechanics modeling, scientific researches, and process assurance. To measure the structural velocities of slug flow nonintrusively, a continuous wave ultrasonic Doppler sensor and a conductance sensor are combined to obtain the Doppler shift signal and water holdup, respectively. Due to the intense fluctuation of phase fraction and velocity, the scatters in different regions of the slug flow produce different Doppler shifts. Therefore, the Doppler signal is a signal with multiscale fluctuations containing structural information of slug flow. To extract the structural velocities, the Doppler shift signal was decomposed into several intrinsic mode functions (IMFs) by the empirical mode decomposition, and the main IMFs that reflect the essential characteristics of the signal were determined by cross correlation method. By combining water holdup signal, the short-time Fourier transform (STFT) was applied to the main IMFs to determine the correlation between the specific main IMFs and the structure of a slug unit. Finally, the velocities of the liquid slug nose, the liquid slug, and the liquid film were extracted from the STFT results. To validate the proposed model, theoretical structural velocities were calculated based on Dukler's model, and the results showed good agreement with the extracted velocities with the average relative difference of 3.34%. For further validation, the total volume flow rate was calculated using a quadratic threshold method. Compared with the reference total volume flow rate, the mean absolute percentage error was 3.53%.