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<div>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. </div><div><br></div><div>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. </div><div>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.</div><div><br></div><div>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. </div><div>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.</div><div><br></div><div>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.</div>

<p>To fully realize the advantages of the two-fluid model, the interfacial area concentration (IAC) should be properly given by a constitutive model. The conventional flow-regime-based IAC correlations intrinsically cannot predict the dynamic flow structure change and would introduce a discontinuity and numerical instability to system codes. As a promising alternative, the interfacial area transport equation (IATE) is developed to model the interface structure mechanistically. Progress has been achieved for IATE modeling in bubbly, slug, and churn-turbulent flow during the past two decades. Aiming at a comprehensive flow structure predictor for all flow regimes, further development in two directions is highly desirable. First is extending the current experiment and modeling capability from churn-turbulent to annular flow. In this study, an advanced four-sensor droplet capable conductivity probe (DCCP-4) is developed to capture all interfaces in churn-turbulent and annular flow, including liquid film, liquid droplet, gas core, and gas bubble. A first of a kind experimental database in churn-turbulent, annular, and wispy annular flow with two-dimensional spatial distributions is established, which provides the experimental basis for the multi-field two-phase flow model development. The measured parameters include local time-averaged volume faction, IAC, and velocity for various fields of annular flow. In addition, a new constitutive model to quantify the interfacial area between the gas core and liquid film of annular flow is developed, which fills the last theoretical gap of interfacial area modeling. The other important direction is improving the current IATE model to fulfill the dynamic prediction of developing flow, especially the bubbly to slug transition flow. Vertical-upward air-water two-phase flow experiments are performed. The state-of-the-art IATE model is evaluated against the newly collected data at bubbly and slug flow, and the result shows unsatisfactory performance in predicting the developing flow with intensive bubble coalescence. A new bubble coalescence model is derived by using the log-normal bubble size distribution, which significantly improves the model prediction capability.</p>

<p>To improve the prediction of two-phase local structure and heat transfer in subcooled boiling flow, the wall nucleation phenomenon was studied to accurately model the wall source term in the interfacial area transport equation (IATE) for the use with the two-fluid model. The existing experimental datasets and modeling works of departure diameter, departure frequency and active nucleation site density were comprehensively reviewed. Since these parameters are coupled in the bubble ebullition cycles, simultaneous measurements of departure diameter, departure frequency and active nucleation site density were performed in a vertical annular test section. The ranges of the existing experimental database were extended to high pressure and high heat flux conditions. The stochastic characteristics of the departure diameter and departure frequency measured from a single nucleation site and over multiple nucleation sites were investigated. Significant variations between different nucleation sites were observed. A parametric study of departure diameter, departure frequency and nucleation site density were conducted at varying system pressure, heat flux, flow rate and subcooling conditions. The existing models of these parameters were evaluated with the experimental dataset of the existing and the present works. Significant discrepancies were observed between model predictions and experimental data, which indicates that the mechanism of nucleate boiling is not fully understood. The heat flux partitioning model was also evaluated. The results show that the heat flux at high pressure or low flow rate conditions was significantly underestimated. This may suggest that major heat transfer mechanisms are missing in the heat flux partitioning model.</p>

<p>  </p> <p>The study of two-phase flow in different orientations can allow for greater understanding of the fundamentals of two-phase flow dynamics. While a large amount of work has been performed for vertical flows and recent work has been done for horizontal flows, limited research has been done studying inclined upward two-phase flows between those two orientations. Studying two-phase flows at various inclinations is important for developing physical models and simulations of two-phase flow systems and understanding the changes between what is observed for symmetric vertical flows and asymmetric horizontal flows. The present work seeks to systematically characterize the effects of inclination on adiabatic concurrent air-water two-phase flows in straight pipes. An experimental database is established for local and global two-phase flow parameters in a novel inclinable 25.4 mm inner diameter test facility using four-sensor conductivity probes, high speed video capabilities, a ring-type impedance meter, a pressure transducer, and a gamma densitometer. Rotatable measurement ports are employed to allow for local conductivity probe measurements across the flow profile to capture asymmetric parameter distributions during experiments without stopping the flow. Some of the major effects of inclination are investigated, including the effects on flow regime transition, bubble distribution, frictional pressure loss, and relative motion between the two phases. Flow visualization and machine-learning methods are employed to identify the transitions between flow regimes for inclined orientations, and these transitions are compared against existing theoretical flow regime transition criteria proposed in literature. The theoretical transitions in literature agree well with both methods for vertical flow, but additional work is necessary for angles between 0 degrees and 60 degrees. The effect of inclination on two-phase frictional pressure drop is explored, and a novel adaption of the Lockhart-Martinelli pressure drop correlation is proposed, which is able to predict the pressure drop for the conditions investigated with an absolute percent difference of 2.6%. To explore the relationships between orientation, void fraction, and relative motion, one-dimensional drift flux analyses are performed for the data at each angle investigated. It is observed that the relative velocity between phases decreases as the angle is reduced, with a relative velocity near zero at some intermediate angles and a negative relative velocity for near-horizontal orientations.  Existing modeling capabilities that have been developed for vertical and horizontal flows are evaluated based on the local two-phase parameters collected at multiple orientations. The performance of the one-dimensional interfacial area transport equation for vertical and horizontal flows is tested against experimental data and a novel model for horizontal and inclined-upward bubbly flows is proposed. Finally, an evaluation of existing momentum transfer relations is performed for the two-fluid model using three-dimensional computational fluid dynamics tools for horizontal and inclined. The prediction of the void fraction distribution and gas velocity profiles are compared against experimental data, and improvements to the lift force model are identified based on changes in the relative velocity between phases. </p>