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Following Part (I) of the current study, which presents the experimental results of the elbow effects on two-phase flow parameters in bubbly flow, Part (II) develops models and correlations to predict the evolution of these parameters across and downstream of 90° vertical-upward and vertical-downward elbows. To quantify the length requires for the effects of the elbows to dissipate (or the dissipation length), the strength of elbows is defined as the variance of the local void fraction distribution. The axial development of the elbow-strength is modeled by an exponential function of the axial development length based on the experimental data. Then, the dissipation length of the elbow is determined by characterizing the evolution of the elbow-strength parameter. The elbow-strength parameter is also used to correlate the void-weighted bubble velocity and covariance terms in the interfacial area transport equation (IATE). The two-phase pressure drop across vertical elbows is modeled with a modified Lockhart-Martinelli correlation which considers the additional pressure drop induced by elbows. To evaluate the above developed models and correlations, they are implemented into the IATE applicable to the elbow-influenced region. The established IATE together with the available IATE of different flow orientations in straight channels are implemented to predict the interfacial area transport from the vertical-upward to horizontal to vertical-downward two-phase flow across elbows. It is found that the interfacial area concentration predictions are in good agreement with the experimental data with an average absolute percent difference of ±6% throughout the test section. The individual contributions to the interfacial area concentration transport due to each source and sink term in the IATE are discussed, demonstrating that the models and correlations developed for the two-phase flow parameters in elbow regions are reliable.

This study performs experimental investigation on two-phase bubbly flow through 90° vertical elbows going from vertical-upward to horizontal and horizontal to vertical-downward orientations. The elbows have an inner diameter of 50.8 mm and a radius of curvature of 152.4 mm. A detailed database for local and global two-phase flow parameters in different flow orientations and across vertical elbows is established with a state-of-the-art four-sensor conductivity probe, a pressure transducer, and a high-speed video camera. The evolution of void fraction, interfacial area concentration, bubble velocity, and two-phase pressure drop along the axial development length in different orientations and across elbows are presented. It is observed that elbows create secondary flow and cause redistribution of the bubbles, which significantly affect the development of two-phase flow parameters. The effects occur across the elbows and remain for a significant length downstream. The effects on the void fraction distribution downstream of the elbow are discussed in detail for both elbow orientations. Characteristic differences in the elbow effects due to the elbow orientation are observed. For the vertical-upward elbow, a similar trend in the evolution of the void fraction distribution is observed for all flow conditions investigated while two different trends are observed downstream of the vertical-downward elbow. It is found that the effects of the vertical-downward elbow dissipate faster than that of the vertical-upward elbow. The elbow effects on interfacial area concentration, bubble velocity, and two-phase pressure drop are also discussed. The evolution of the interfacial area concentration is similar to that of the void fraction evolution in the straight pipe sections. However, it increases significantly across both elbows due to the promotion of the bubble breakup induced by the secondary flow. The void-weighted area-averaged bubble velocity is subject to significant changes across and immediately downstream of the elbows due to the redistribution of the bubbles. Additionally, the two-phase pressure gradients across the vertical-upward and vertical-downward elbows are approximately 1.5 and 2 times of that in the straight pipe sections.

The current work investigates the plug-to-slug transition in horizontal air–water two-phase flow in small (38.1 mm) and large (101.6 mm) diameter pipes. An extensive database is established to study the local interfacial structure in plug-to-slug transition flow. Detailed measurements across the flow area are performed for nine and six test conditions in small and large pipes, respectively, at three different axial locations downstream of the inlet using the local four-sensor conductivity probe. The effects of jg, jf, development length and pipe size are investigated. It is found that the number of small bubbles in the liquid plug/slug increases significantly in plug-to-slug transition with increasing jg, which are generated by the strong shear between the gas slug and liquid film. Due to the relative motion, these small bubbles either coalesce with the nose of the following plug/slug bubble, or slide between the plug/slug bubble and the wall, and then travel around the pipe circumference to reside beneath the large bubbles. This explains the large number of small bubbles observed at the top of the liquid film for the conditions at high gas flow rates. In the process of traveling downwards, some of the small bubbles coalesce with the slug bubbles. It is also found that increasing jg or jf decreases the size of the small bubbles. While shearing-off is believed to dominate as jg increases, turbulent-impact is enhanced as jf increases due to the increasing turbulence level in the liquid phase. Increasing jg, development length, or decreasing jf slightly increases the depths of the plug/slug bubbles; however, significant growth of plug/slug bubbles is observed in the axial direction. For the same condition, the contribution from large bubbles to total void fraction increases as pipe size increases, while the distribution of total void fraction is similar. The size of both small and large bubbles is found to be larger in the large diameter pipe. Due to the current bubble injection mechanism, small bubbles are generated at the inlet; they coalesce into large bubbles as the flow develops. The large bubble is found to accelerate as it grows along the axial direction, which can lead to a decreasing void fraction although pressure keeps decreasing.

Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. Mechanistic modeling of the interfacial area concentration entirely relies on accurate local flow measurements over extensive flow conditions and channel geometries. From this point of view, accurate measurements of flow parameters such as void fraction, interfacial area concentration, and interfacial velocity were performed by a multi-sensor probe at three axial locations as well as seven radial locations in vertical downward bubbly flows using a 25.4 mm-diameter pipe. In the experiment, the superficial liquid velocity and the void fraction ranged from −1.25 to −3.11 m/s and from 1.61% to 21.0%, respectively.

In view of the great importance to two-fluid model, structure of downward bubbly flows in vertical pipes has been discussed intensively based on available data sets of local flow parameters including extensive air–water data sets recently measured by the authors. In this study, an approximate radial phase distribution pattern map has been proposed based on available data sets, and radial profiles of local flow parameters such as void fraction, interfacial area concentration, interfacial velocity, and bubble Sauter mean diameter have been discussed in detail. The one-dimensional drift-flux model for a downward two-phase flow and the correlation of the interfacial area concentration have been compared with the downward flow data. The correlations applicable to the predictions of one-dimensional void fraction and interfacial area concentration for a downward bubbly flow have been recommended by the comparison.

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for downward two-phase flows. The constitutive equation that specifies the distribution parameter in the downward flow has been derived by taking into account the effect of the downward mixture volumetric flux on the phase distribution. It was assumed that the constitutive equation for the drift velocity developed by Ishii for a vertical upward churn-turbulent flow determined the drift velocity for the downward flow over all of flow regimes. To evaluate the drift-flux model with newly developed constitutive equations, area-averaged void fraction measurement has been extensively performed by employing an impedance void meter for an adiabatic vertical co-current downward air–water two-phase flow in 25.4-mm and 50.8-mm inner diameter round tubes. The newly developed drift-flux model has been validated by 462 data sets obtained in the present study and literatures under various experimental conditions. These data sets cover extensive experimental conditions such as flow system (air–water and steam–water), channel diameter (16–102.3 mm), pressure (0.1–1.5 MPa), and mixture volumetric flux (−0.45 to −24.6 m/s). An excellent agreement has been obtained between the newly developed drift-flux model and the data within an average relative deviation of ±15.4%.

The interfacial area transport equation dynamically models two-phase flow regime transitions and predicts continuous changes of the interfacial area concentration along the flow field. It replaces the flow regime-dependent correlations for the interfacial area concentration in thermal-hydraulic system analysis. In the present study, detailed formulation of the interfacial area transport equation is presented along with its evaluation results based on the detailed benchmark experiments. In view of model evaluation, the equation is simplified into one-dimensional steady state one-group interfacial area transport equation. The prediction made by model agrees well with the experimental data obtained in round pipes of various diameters. The framework for the two-group transport equation and the necessary constitutive relations are also presented in view of bubble transport of various sizes and shapes.

The objective of the present study is to develop a miniaturized four-sensor conductivity probe, applicable to a wide range of two-phase flows to obtain the time-averaged local two-phase flow parameters of various types of bubbles. Experimental data acquired by the probe are categorized into two groups in view of two-group interfacial area transport: namely spherical/distorted bubbles as Group 1 and cap/Taylor bubbles as Group 2. Benchmark experiment employing the image analysis method is performed. The results from the benchmark experiment assess both the measurement principle and signal processing scheme of the newly developed four-sensor conductivity probe method.

In the two-fluid model, interfacial concentration is one of the important parameters. The objective of this study is to develop an interfacial area equation with the source and sink terms being properly modeled. For bubble coalescence, the random collisions between bubbles due to turbulence, and the wake entrainment process due to the relative motions of the bubbles, were included. For bubble breakup, the impact of turbulent eddies is considered. Compared with measured axial distributions of the interfacial area concentration under various flow conditions, the adjustable parameters in the source/sink terms were obtained for the simplified one-dimensional transport equation.