Bubble coalescence and breakup model evaluation and development for two-phase bubbly flows

Abstract

The performance of thermal-hydraulics analysis codes heavily depends on the reliable models developed for interfacial transfer terms in the two-fluid model. This requires the accurate modeling of the interfacial area concentration (IAC). The interfacial area transport equation (IATE) developed from the population balance equation is one of the promising ways to be able to dynamically describe the IAC evolutions in the two-phase flows. A lot of efforts have been made to develop the IATE and its bubble coalescence and breakup models in the past two decades. The one-group IATE with its bubble coalescence and breakup models serves as an important and promising model to predict the IAC behaviors in the bubbly flows now. This paper made an extensive survey on the recent theoretical and experimental researches on the IATE and collected the available 8 sets of bubble coalescence and breakup models and the latest experimental databases measured with the up-to-date measuring techniques. The 8 sets of bubble coalescence and breakup models are originally developed to model the bubble evolution in bubbly flows and the small bubble evolution in the flows beyond bubbly flow. The collected data covers the bubbly flows taken the vertical pipes with the diameter ranging from 0.0508 m to 0.200 m and the height-to-diameter ratio ranging from 4 to 113. To confirm the reliability of the 8 sets of bubble coalescence and breakup models, this paper systematically compared and evaluated them with the collected experimental data in the 1D one-group IATE numerical calculations. Although the bubble coalescence and breakup models of Sun et al. (2004, Modeling of bubble coalescence and disintegration in confined upward two-phase flow. Nucl. Eng. Des. 230, 3–26) and Hibiki and Ishii (2000, One-group interfacial area transport of bubbly flows in vertical round tubes. Int. J. Heat Mass Transfer 43, 2711–2726) were found to show the best and second-best predicting performance for the collected latest experimental databases of bubbly flows with data-number-averaging mean absolute relative errors of 33.5% and 61.7% respectively, their relative errors are not satisfactory. Hibiki and Ishii (2000, One-group interfacial area transport of bubbly flows in vertical round tubes. Int. J. Heat Mass Transfer 43, 2711–2726) model only consisting of the contributions of the bubble random collision coalescence and turbulent impact breakup mechanisms can reasonably predict the IAC experimental data in the bubbly flows with high-liquid flow-rate flow conditions and significantly overpredict the IAC experimental data in the bubbly flows with low-liquid flow-rate flow conditions. To further improve the performance of the 1D one-group IATE, this paper has developed a bubble coalescence and breakup model by greatly improving the model of Hibiki and Ishii (2000, One-group interfacial area transport of bubbly flows in vertical round tubes. Int. J. Heat Mass Transfer 43, 2711–2726) with the addition of the contribution of the wake entrainment bubble coalescence mechanism which prevails in low-liquid flow-rate bubbly flows and optimized the adjustable coefficients of the 3 major constitutive models with the collected latest experimental databases of bubbly flows. The data-number-averaging mean absolute relative error of the newly-proposed bubble coalescence and breakup model is accordingly improved to be 17.1% in the predictions of the collected latest experimental databases of bubbly flows.