An Interfacial Area Transport Modeling for Two-phase Flow in Small and Large Circular Pipes

Abstract

With the rapid development of the advanced two-phase flow experimental technologies, more experimental databases with extended measurement ranges have been established to support the two-phase flow model development. The advantage of the Two Fluid model in modeling the complex two-phase flow phenomena over the mixture models stands out. One key aspect in the Two Fluid model development is the accurate modeling of the interfacial area between phases, which is strongly related to the interfacial mass, momentum, and energy transfer. As a closure relation of interfacial area concentration (interfacial area per unit volume) for the Two Fluid model, the Interfacial Area Transport Equation (IATE) provides dynamic predictions on the interfacial area change. It substantially solves the shortcoming of using flow-regime-dependent empirical correlations that can introduce numerical discontinuities between flow regimes. The IATE has been extensively developed over the past twenty-five years. Many studies targeted on improving its prediction capability by developing bubble interaction source terms based on their experimental data. The existing models are usually based on medium and large flow channels, yet the models may not be physically fit the small flow channels. The major reason is that the wall effect can have a larger influence on the two-phase flow in a small flow channel, as the surface area to volume ratio greatly increases. Therefore, the primary objectives of this study are to physically investigate the wall effect on two-phase flow and develop a generalized IATE by extending the application range of existing IATE from large and medium flow channels to small flow channel.To achieve the objective, this study established a rigorous database of air-water two-phase flows in a small diameter pipe with its inner diameter of 12.7 mm, focusing on the bubbly-to-slug transition regime. The experimental analysis was performed on the pipe wall effect on the interfacial characteristics, based on the current experimental database and the existing experimental database collected on vertical pipes of different sizes. It is observed that 1) the pipe wall effect can alter the non-uniform radial two-phase distribution; 2) the bubbly-to-slug flow regime transition in a small diameter pipe happens in a smaller void fraction than in a large diameter pipe; 3) the bubble coalescence phenomenon can be more dominant for small pipe flow, and an intensive intergroup transfer can happen for the two-group interfacial area transport in two-phase flows. As the interfacial area transport is directly related to the two-phase geometrical configuration, the two-phase geometrical parameters, void fraction and relative bubble size, are identified as the key parameters for modeling.In the modeling of IATE source terms, the high geometrical scalability of the model is realized by properly including the wall effect into the modeling consideration. The following major improvements on the existing models are: 1) the inertia subrange assumption on the turbulent-driven interaction is properly improved; 2) the bubble-induced turbulent-driven interactions such as wake entrainment is revised by considering the wall effect on the wake region. In summary, models of bubble interaction due to random collision, wake entrainment, turbulent impact, and shearing-off are revised based on the existing studies on the IATE source terms development. The newly proposed interfacial area transport models are evaluated against an experimental database with 112 test conditions in total from a wide range of experimental pipe diameters from 12.7 mm to 304.8 mm. The new models can accurately capture the drastic intergroup transfer of void fraction and interfacial area concentration between two groups in transition flows. Overall, the relative error of void fraction and interfacial area concentration comparing with the experimental data are within ±15\\% and ±10\\%, respectively.