Two-phase flow modelling by an error-corrected population balance model

Abstract

High-velocity aerated flow is a common phenomenon in spillways. Its accurate modelling is challenging, mainly due to the lack of realistic physics in the conventional two-phase models. To this end, this study establishes a population balance model (PBM) approach to account for the evolutionary process of air bubbles. The air-water flow in a stepped chute is examined. The model performance is evaluated by statistical metrics: correlation coefficient (CC), root mean squared error (RMSE), and mean absolute error (MAE). Compared with conventional models, the PBM generates improved air-water predictions. However, the flow parameters are still underestimated, particularly in areas with intense air-water interactions. For further development, an error-corrected PBM (EPBM) is proposed by incorporating machine learning (ML) techniques into the PBM. Compared with the PBM, the EPBM leads to a mean augmentation in velocity prediction by 19.8% for the CC, 73.0% for the RMSE, and 77.1% for the MAE. The gains in air concentration estimation are 2.0%, 67.6% and 73.5%, respectively. The EPBM generates the most accurate results, with 99.6% and 89.6% of the velocity and air concentration predictions within a 20% relative error range. The main contributions are establishing a PBM for air-water flows and developing an error-corrected PBM using ML.