Two-Group Drift-Flux Model for Dispersed Gas-Liquid Flow in Large-Diameter Pipes

Interfacial Heat and Mass Transfer Are Prevalent in Industrial Processes. the Interfacial Transfer Rate Can Be Obtained by the Product of their Fluxes and Interfacial Area Concentration (IAC) Calculated by the Interfacial Area Transport Equation (IATE). Bubbles Show Different Behavior According to their Sizes. Hence, Bubbles Are Classified into Two Groups. Consequently, Two-Group IATE is Required Causing to Use of Two Gas Momentum Equations Leading to More Complexity. the Present Study Suggests a New Reliable Two-Group Drift-Flux Modeling to Reduce the Two Gas Momentum Equations to One Gas Mixture Momentum Equation for Gas-Liquid Flow in Large-Diameter Pipes. the Model is Developed based on the Drift-Flux Model Concept and Experimental Data. Group-One and Group-Two Distribution Parameters and Drift Velocities Are Validated through Experimental Data. the Results Show that the Proposed Two-Group Drift-Flux Model Can Support the Concept of Drift Velocity from the Bubbly to Beyond the Bubbly Flow and Consistency between the One-Group and Two-Group Drift-Flux Models. Moreover, Steam-Water Data Are Used to Validate the Applicability of the Model in Steam-Water Flows Condition. the Developed Two-Group Drift-Flux Model is Indispensable for Reducing the Two Gas Momentum Equations to One Gas Mixture Momentum Equation When Two-Group IATE is Implemented into Thermal-Hydraulic Codes to Improve the Prediction Accuracy of IAC

On the use of area-averaged void fraction and local bubble chord length entropies as two- phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 mm and 50.8 mm pipes have been calculated. The measured conditions cover ranges from 0.13 m/s to 5 m/s in the superficial liquid velocity jf and ranges from 0.01 m/s to 25 m/s in the superficial gas velocity jg. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions

Bubble Lift-off Size in Forced Convective Subcooled Boiling Flow

Forced convective subcooled boiling flow experiments were conducted in a BWR-scaled vertical upward annular channel. Water was used as the testing fluid, and the tests were performed at atmospheric pressure. A high-speed digital video camera was applied to capture the dynamics of the bubble nucleation process. Bubble lift-off diameters were obtained from the images for a total of 91 test conditions. A force balance analysis of a growing bubble was performed to predict the bubble lift-off size. The dimensionless form of the bubble lift-off diameter was formulated to be a function of Jacob number and Prandtl number. The proposed model agreed well with the experimental data within the averaged relative deviation of ±35.2 %

DEFEM Method and Its Application in Pebble Flows

Based on the concept of embedded discrete elements (EDEs), the discrete element-embedded finite element model (DEFEM) is extended in this work. The new method can be used to calculate the motion and stress variation of particles. This work discusses its application in granular flow simulation for particle motions with small deformations. The updated Lagrangian finite element method is used to obtain the coupling solution of the internal stress and the overall motion of particles in the DEFEM. The computation of deformation displacement is based on the concepts of displacement decomposition (translational and rotational motions and deformation displacement). The deformation displacement is the difference between particles and template particles [rigid body, using the discrete element method (DEM) to calculate translational and rotational displacements]. It is used to calculate the dynamic stress distribution of particles and the internal force of the node. Therefore, it has a wide scope of application (for example, it can be extended to non-spherical particles). The software validation proves the accuracy of this method. The application of the DEFEM in the accumulation process of particles is given. The motion characteristics and deformation of particles are discussed, and the stress distribution and force chain structure in particle accumulation are obtained

Interfacial Area Transport of Vertical Upward Bubbly Two-Phase Flow in an Annulus

In relation to the development of the interfacial area transport equation in a subcooled boiling flow, the one-dimensional interfacial area transport equation was evaluated by the data taken in the hydrodynamic separate effect tests without phase change for an adiabatic air-water bubbly flow in a vertical annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Twenty data sets consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s were used for the evaluation of the one-dimensional interfacial area transport equation. The one-dimensional interfacial area transport equation agreed with the data with an average relative deviation of ±8.96 %. Sensitivity analysis was also performed to investigate the effect of the initial bubble size on the interfacial area transport. It was shown that the dominant mechanism of the interfacial area transport was strongly dependent of the initial bubble size

Local Flow Measurements of Vertical Upward Bubbly Flow in an Annulus

Local measurements of flow parameters were performed for vertical upward bubbly flows in an annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Double-sensor conductivity probe was used for measuring void fraction, interfacial area concentration, and interfacial velocity, and Laser Doppler anemometer was utilized for measuring liquid velocity and turbulence intensity. A total of 20 data sets for void fraction, interfacial area concentration, and interfacial velocity were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. A total of 8 data sets for liquid velocity and turbulence intensity were acquired consisting of five void fractions, about 0.050, and 0.10, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter namely interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment using the annulus

Modeling of Bubble-Layer Thickness for Formulation of One-Dimensional Interfacial Area Transport Equation in Subcooled Boiling Two-Phase Flow

In relation to the formulation of one-dimensional interfacial area transport equation in a subcooled boiling flow, the bubble-layer thickness model was introduced to avoid many covariances in cross-sectional averaged interfacial area transport equation in the subcooled boiling flow. The one-dimensional interfacial area transport equation in the subcooled boiling flow was formulated by partitioning a flow region into two regions; boiling two-phase (bubble-layer) region and liquid single-phase region. The bubble-layer thickness model assuming the square void peak in the bubble-layer region was developed to predict the bubble-layer thickness of the subcooled boiling flow. The obtained model was evaluated by void fraction profile measured in an internally heated annulus. It was shown that the bubble-layer thickness model could be applied to predict the bubble-layer thickness as well as the void fraction profile. In addition, the constitutive equation for the distribution parameter of the boiling flow in the internally heated annulus, which was used for formulating the bubble-layer thickness model, was developed based on the measured data. The model developed in this study will eventually be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flows

Formulation of one-dimensional interfacial area transport equation in subcooled boiling flow

In relation to the formulation of one-dimensional interfacial area transport equation in a subcooled boiling flow, the bubble-layer thickness model was introduced to avoid many covariances in crosssectional averaged interfacial area transport equation in the subcooled boiling flow. The one dimensional interfacial area transport equation in the subcooled boiling flow was formulated by partitioning a flow region into two regions; boiling two-phase (bubble-layer) region and liquid singlephase region. The bubble-layer thickness model assuming the square void peak in the bubble-layer region was developed to predict the bubble-layer thickness of the subcooled boiling flow. The obtained model was evaluated by void fraction profile measured in an internally heated annulus. It was shown that the bubble-layer thickness model could be applied to predict the bubble-layer thickness as well as the void fraction profile. In addition, the constitutive equation for the distribution parameter of the boiling flow in the internally heated annulus, which was used for formulating the bubble-layer thickness model, was developed based on the measured data. The model developed in this study will eventually be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flows