Dispersed vapor bubbles are the dominant rheology in cloud cavitation, and their size distribution is directly associated with cavitation noise and erosion. However, the numerical resolution of large numbers of dispersed bubbles remains a challenge. In this work, we establish a new cavitation model based on the population balance equation (PBE) that can predict the size distribution and spatiotemporal evolution of bubbles within cloud cavitation under different cavitation numbers. An expression for the phase transition source term without empirical parameters is derived based on the bubble size distribution (BSD) function, enabling the coupling of mass transfer in the governing equations with the PBE cavitation model. The cavitation model is solved alongside the Eulerian homogeneous mixture flow. The mass transfer between water and vapor, and the bubble coalescence and breakup under turbulent flows, are modeled to determine the BSD. The numerical model is carefully validated through comparisons with experimental results for cavitation flows on a wedge-shaped flat plate, and good agreement is achieved with respect to the pressure distribution, void fraction, and BSD. This confirms that our proposed cavitation model can accurately predict the void fraction and BSD within the cloud cavitation region.
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