Ultrasonic Attenuation Model of Gas Holdup in Polydisperse Gas–Liquid Two-Phase Bubbly Flows

The measurement of gas holdup in polydisperse gas–liquid bubbly flows presents significant challenges due to complex interfacial dynamics and variable bubble size distributions that critically influence ultrasonic attenuation characteristics. This study develops an improved ultrasonic attenuation model that systematically accounts for bubble size distribution effects to achieve accurate gas holdup prediction. The research integrates ultrasonic attenuation measurements obtained using 2.25-MHz probes with high-speed imaging-based bubble size characterization through a custom fluid sampler. By employing maximum likelihood estimation, we establish robust statistical correlations between ultrasonic attenuation patterns and bubble size distributions, leading to the development of an equivalent cross section scattering model specifically designed for polydisperse systems. Comprehensive experimental validation demonstrates the model’s superior performance compared to conventional MCBL, Qian, and Stravs-Ren average models, with an absolute average percentage deviation (AAPD) of 3.6%. The proposed approach offers a significant advancement in multiphase flow measurement by enabling noninvasive determination of both gas holdup and bubble size distribution characteristics.