Abstract

The liquid film flow rate or droplet flow rate in annular flow is determined by a parameter known as the entrainment fraction. Conventional empirical correlations are commonly employed for predicting the entrainment fraction; however, their applicability is often restricted to specific operating conditions and working fluids. Recently, a few machine learning (ML) models have been developed to achieve better accuracy in entrainment fraction prediction. However, these models are completely data-driven, meaning they are good for prediction in the interpolated domain, but exhibit limited generalization capability in the extrapolated domain. To address this limitation, a physics-informed machine learning-aided framework (PIMLAF), combining physics-based correlations and ML models—Random Forest (RF) and Artificial Neural Network (ANN)—is proposed to predict the entrainment fraction in gas–liquid annular flow across both interpolated and extrapolated domains. The dataset comprises 1515 data points, with 80% for training and 20% for testing. Initially, predictions are obtained using physics-based correlations, followed by training the ML model on the residuals (the difference between experimental and correlation-predicted values) to capture the unaccounted physical behavior. The final prediction is obtained by combining the outputs of the correlation and ML model. Model performance was evaluated using Mean Absolute Percentage Error (MAPE) , relative Root Mean Square Error (rRMSE) , and the Coefficient of Determination (R2) across test, unseen, and extrapolated datasets. Among the developed models, the PIMLAF, combining the RF model with the Cioncolini and Thome correlation, demonstrated the best predictive performance in the extrapolated domain while maintaining good accuracy in both the test and unseen datasets.

Department(s)

Nuclear Engineering and Radiation Science

Publication Status

Full Text Access

Keywords and Phrases

Annular flow; Artificial neural network (ANN); Entrainment fraction (RF); Machine learning (ML); Physics-informed machine learning; Random Forest (RF)

International Standard Serial Number (ISSN)

1359-4311

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Elsevier, All rights reserved.

Publication Date

01 Jun 2026

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