Modeling interfacial area concentration in bubbly flow

Accurate mass, momentum, and energy transfer predictions through gas and liquid interfaces are critical in simulating gas–liquid two-phase flow dynamics. Since the interfacial transfer rates depend on the interfacial area concentration (IAC), it is essential to model the IAC accurately for robust two-phase flow analyses. The inverse of the IAC characterizes bubble characteristic length, and thus, the IAC is related to the bubble Sauter mean diameter (SMD). This study proposed a method to use neural networks for systematically developing a one-dimensional SMD correlation, i.e., an IAC correlation for forced convective and bubble columns. First, an extensive literature survey provided 799 data points, consisting of 590 data points in forced convective bubbly flows and 209 in bubble columns. The neural networks were applied to 799 data points to determine the maximum attainable prediction accuracy of the hypothetical SMD correlations. Target mean absolute percentage errors (MAPEs) of 21.2% for IAC and 15.6% for SMD were established. The neural network could identify three critical non-dimensional parameters: liquid fraction, bubble Reynolds number, and viscosity number, enabling the development of the SMD correlation. With void fraction (VF) predicted by the drift-flux correlation, the SMD correlation could be converted to the IAC correlation, i.e., IAC = 6×VF/SMD. The newly developed SMD and IAC correlations demonstrated reliable predictive capabilities. For forced convective bubbly flows, MAPEs were 19.5% for IAC and 16.1% for SMD. For bubble columns, MAPEs were 45.6% for IAC and 26.9% for SMD. Across all of the datasets, the correlation achieved MAPEs of 26.3% for IAC and 19.0% for SMD. The developed correlations were successfully applied to a wide range of flow conditions: channel geometries (medium-to-large circular pipes, rectangular ducts, rod bundles, and annuli); flow directions (upward, downward, and horizontal); gas–liquid systems (air–water, nitrogen–water, and oxygen–sodium sulfite solution); hydraulic diameters (9.0 to 304 mm); and pressures (0.10 to 2.0 MPa).