A new paradigm in critical flow analysis: Combining Buckingham Pi theorem with neural network for improved predictions in microchannels

Abstract

Critical flow phenomena are prevalent in many chemical engineering processes, such as microchannel heat exchangers, nuclear safety analysis, jet pump modeling, and industrial systems utilizing subcooled or two-phase pressurized fluids. Understanding the impact of various physical parameters on critical flow and accurately predicting critical flow mass flux is essential in these processes. This article collects extensive experimental data on subcooled water two-phase critical flow and supplements it with additional experimental data from actual micro-cracked channels, constructing a comprehensive benchmark database. The database covers an inlet pressure range of 1.82–16.29 MPa, an inlet subcooling range of 0.3–119.35 K, and a microchannel hydraulic diameter range of 0.09–2.2 mm. By integrating the classical Buckingham Pi theorem with a data-driven active subspace method, the dominant dimensionless numbers in subcooled water two-phase critical flow were identified, addressing some limitations of the Buckingham Pi theorem by ranking the influences of these dimensionless numbers. Based on these dominant dimensionless numbers, the impact of physical quantities on two-phase critical flow was accurately identified, leading to a concise predictive correlation for critical flow mass flux with a mean absolute percentage error of 20.3 % across 1071 experimental data points, outperforming commonly used critical flow models. Furthermore, leveraging the dominant dimensionless numbers improved existing model results, enhancing the Henry-Fauske model’s overall prediction accuracy from a mean absolute percentage error of 47.6 % to 17.8 %. This study outlines a promising path for discovering physical characteristics and mechanisms in data-driven critical flow, facilitating a deeper understanding of critical flow phenomena.