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    Experimental constraints for population balance modeling in the bubbly-nonbubbly transition region of cavitating flows

    Hao Zhang1, Mingjin Wen1, Yunqiao Liu1,*, Benlong Wang1, and Xinming Du2

    • *Contact author: yunqiaoliu@sjtu.edu.cn

    Phys. Rev. Fluids 11, 114301 – Published 3 November, 2026

    DOI: https://doi.org/10.1103/fkwm-d8t3

    Abstract

    The bubbly-nonbubbly transition region characterizes the edge of cavitation and involves active dynamics of dispersed vapor bubbles. Experimental data in this region are essential for developing numerical models that bridge dispersed bubbles and macroscopic vapor cavities, with the population balance model being a representative example. In this study we perform point-by-point measurements of cavitating flow around a twisted hydrofoil using an optical probe system, obtaining local void fraction, bubble size, and velocity. The void-fraction and streamwise bubble-velocity profiles both exhibit self-similar behavior. The void-fraction profile is well fitted by a Gaussian function, which closely resembles the Gaussian form of the vertical gradient of the streamwise bubble velocity. This gradient arises from the error-function distribution of the bubble-velocity profile. The similarity between these two Gaussian profiles suggests a connection between high vapor concentration and strong shear in the bubble-velocity field. Nevertheless, their characteristic widths reveal distinct spreading scales. This scale separation gives an effective bubble-momentum-based Schmidt number of Sceff≈1.63, indicating that bubble-velocity recovery extends over a broader region than vapor-concentration spreading. The bubble size distributions exhibit distinct characteristics depending on the local flow conditions: the inner region features high void fraction and strong shear, and the outer region shows low void fraction and weak shear. The typical −4/3 scaling for small bubbles is observed in both regions, whereas the −10/3 power law scaling is observed only in the outer region, where the flow approaches isotropic turbulence. Within the strong shear region, large bubbles are abundant and thus the size distribution exhibits a flatter slope. This finding suggests that the choice of a presumed distribution function in population-balance modeling should be region-dependent within the cavitation zone. The experimental data further demonstrate that bubble velocities are strongly size-dependent and vary across different flow regions, offering a potential basis for modeling the slip velocity of bubbles that do not strictly follow the liquid phase. Overall, this study provides experimental constraints for closing the population balance model, which governs the transport and diffusion of dispersed vapor bubbles in cavitating flows.

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