One-dimensional drift-flux model for two-phase flow in a large diameter pipe

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 vertical upward two-phase flow in a large diameter pipe. One of the important flow characteristics in a large diameter pipe is a liquid recirculation induced at low mixture volumetric flux. Since the liquid recirculation may affect the liquid velocity profile and promote the formation of cap or slug bubbles, the distribution parameter and the drift velocity in a large diameter pipe can be quite different from those in a small diameter pipe where the liquid recirculation may not be significant. A flow regime at a test section inlet may also affect the liquid recirculation pattern, resulting in the inlet-flow-regime dependent distribution parameter and drift velocity. Based on the above detailed discussions, two types of inlet-flow-regime dependent drift-flux correlations have been developed for two-phase flow in a large diameter pipe at low mixture volumetric flux. A comparison of the newly developed correlations with various data at low mixture volumetric flux shows a satisfactory agreement. As the drift-flux correlations in a large diameter pipe at high mixture volumetric flux, the drift-flux correlations developed by Kataoka-Ishii, and Ishii have been recommended for cap bubbly flow, and churn and annular flows, respectively, based on the comparisons of the correlations with existing experimental data.     

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

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 kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equations that specify the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, the shear stresses, the interfacial momentum transfer and the wall friction, since these macroscopic effects govern the relative velocity between phases. A comparison of the models with existing experimental data shows a satisfactory agreement.     

Drift-flux model for downward two-phase flow

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%.     

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 eight data sets for liquid velocity and turbulence intensity were acquired consisting of two 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.     

Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, and interfacial velocity of vertical upward bubbly flows in an annulus with the hydraulic equivalent diameter of 19.1 mm were measured by the double-sensor conductivity probe. A total of 20 data 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. The obtained data will be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flow systems.     

Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. 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.     

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.     

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, or 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 on the initial bubble size.     

Numerical and experimental investigation of two-phase flow in an electrochemical cell

In this study, a two-phase mathematical model is adapted to study void fraction distribution, flow field and characteristics of electrolysis process. The model involves transport equations for both liquid and gaseous phases. An experimental set-up is established to collect data to validate and improve the mathematical model. The void fraction is determined from measurement of resistivity changes in the system due to the presence of bubbles. It is observed that there is a good agreement between the numerical results and the experimental data.     

Internal flow structure description of slug flow-pattern in a horizontal pipe

Utility of the hot-film anemometry technique in describing the internal flow structure of a horizontal slug flow-pattern is discussed within the scope of intermittent nature of slug flow. It is shown that a single probe can be used for identifying the gas and liquid phases and for differentiating the large elongated bubble group from the small bubbles present in the liquid slug. Analyzing the nature of voltage signals, a signal processing scheme is developed for measurements of time-averaged void fractions of small and large bubbles as well as for the measurements of local mean axial velocity and turbulent intensity in the liquid phase. Some results of local measurements of time-averaged void fractions of small and large bubble groups, axial mean velocity and turbulent intensity are presented at relatively low and high gas and liquid flows for a horizontal slug flow-pattern in a 50.3 mm i.d. pipe.     

Two-phase air-water flow in micro-channels: An investigation of the viscosity models for pressure drop prediction

Adiabatic two-phase air-water flow is experimentally studied in this work. Two channels, made of fused silica, with different diameters of 0.53 and 0.15 mm are used as test sections. The void fraction data for both tubes are obtained by image analysis. For the larger channel, the void fraction is found to be a linear relationship with the volumetric quality. In the case of the smaller one, however, the non-linear void fraction is obtained. The measured frictional pressure drop data are compared with the predictions regarding the homogeneous flow assumption. Several well-known two-phase viscosity models are subsequently evaluated for applicability to micro-channels.     

Numerical investigation of boiling flow of nitrogen in a vertical tube using the two-fluid model

The two-fluid model has been extensively used in modeling boiling flow of water, however, there are few equivalent studies of boiling flow of cryogenic liquids. In the present study, the two-fluid model which is basically included in the CFX code was modified by incorporating new closure correlations, then boiling flow of liquid nitrogen in a vertical tube was numerically simulated using the basic model and the modified model, respectively. Comparison with experimental data shows that the modified model is satisfactorily improved in accuracy. This study demonstrated that the following parameters and models are important for accurate prediction: the lift force, the bubble diameter distribution and the active site density, among which, the active site density has the most significant effect.     

速度滑移条件下气体-微颗粒两相流动数值模拟研究

基于欧拉-拉格朗日方法构建了气体-微颗粒两相流动数值计算模型,采用考虑速度滑移的拖曳力系数关联式以研究微颗粒表面动量非平衡效应。在此基础上,分析速度滑移、斯托克斯数(St)对微颗粒在受限空间中运动轨迹的影响规律。研究结果表明:速度滑移对颗粒运动轨迹影响明显,其运动过程明显滞后于常规颗粒运动;St较小时,颗粒能及时响应流场变化,可较好地跟随流体运动,随St增大,颗粒运动受自身惯性影响愈加明显。     

Entropy generation in a micropolar fluid past an inclined channel with velocity slip and heat flux conditions: Variation parameter method

An investigation is carried out on the analysis of entropy on the flow of non-Newtonian fluid, in particular, micropolar fluid past an inclined channel. To enhance the fluid properties, velocity and thermal slip conditions are taken into consideration. At the outset, the novelty of the present investigation lies on the analysis of entropy generation that occurs due to the temperature differences between the media. The governing nonlinear equations are transformed to nonlinear ODE by the use of suitable transformed nondimensional variables. Furthermore, the motivation for the study is the solution of these governing equations using the semi-analytical technique, namely, the variation parameter method. The behavior of the flow phenomena is characterized by the contributing parameters, in particular, the Bejan number, on the entropy are displayed via graphs and tables and elaborated in Section 5. The results reveal that the microrotation profile exhibited its dual character with an augmentation of the inclined angle, and both the coupling parameter and the Reynolds number are favorable in resisting entropy.     

A droplet size dependent multiphase mixture model for two phase flow in PEMFCs

A droplet size dependent multiphase mixture model is developed in this paper, and the droplet size in the gas channel can be considered as a parameter in this multiphase mixture model, which includes the effect of gas diffusion layer (GDL) properties and the gas drag function and cannot be considered in the commonly used multiphase mixture model in the references. The three-dimensional two phase and non-isothermal simulation of the PEMFCs with a straight flow field is performed. The effect of droplet size on the liquid remove, the effect of liquid water on the heat transfer and the effect of gas flow pattern on the heat and mass transfer are mainly investigated. The simulation results show that the large droplet is hard to be dragged by the gas, so it produces large water saturation. The results of the heat transfer show that the liquid water hinders the heat transfer in the GDL and catalyst layer, so it produces the large relative high temperature area, and there are large temperature difference and water saturation in the PEMFCs operated with coflow pattern compared with counter flow pattern.     

受热工况截面平均空泡率对漂移流模型分布参数C0的影响分析

空泡率是汽液两相流动的基本参数之一.在计算空泡率的众多模型中,Zuer-Findlay漂移流模型目前应用最为广泛.根据受热工况下局部界面参数径向分布特性实验研究结果,并通过对现有实验数据的处理,分析了受热工况下垂直上升两相流漂移流模型分布参数C0随截面平均空泡率的变化规律.证实了从过冷沸腾泡状流到饱和沸腾弹状流工况,随着空泡率的增加,分布参数C0从一个小于1的值增加到1.0～1.2.     

Correlation analysis on the SGS velocity between phases in an isotropic gas-particle two-phase flow with FDF model

Correlation of the SGS (sub-grid scale) velocity between the two phases in an isotropic gas-particle two-phase flow was numerically investigated with FDF model. The results show the SGS gas velocity seen by the particles varies with the relative velocities between particle phase and gas phase. The relative velocity between the two phases produces the effect of the anisotropic turbulence on the particles. The variation of Stokes number influences the magnitude of the interaction between the two phases.     

Mathematical modelling of two-phase flow in a vertical well considering paraffin deposits and external heat exchange

Processes, occurring during exploration of gas-oil wells in frozen rock are simulated. A system of differential equations, describing hydro and thermal dynamics of an ascending two-phase flow of a hydrocarbon system in a vertical channel taking into account phase transitions and structure of a flow is developed. Kinetics of paraffin deposits on internal walls of an elevating column of a well are considered. The effect of the heat exchange of a well within frozen rock is developed using differential equations that describe the evolution of the radius of thermal influence of the well and the radius of the melting zone. We conclude with numerical research of some preventive ways of dealing with paraffin deposits.     

Effect of void fraction models on the two-phase friction factor of R134a during condensation in vertical downward flow in a smooth tube

The void fraction of R134a condensing inside a vertical smooth tube is experimentally investigated in this study. The vertical test section is a 0.5 m long countercurrent flow double tube heat exchanger with refrigerant flowing down the inner tube and cooling water flowing upward in the annulus. The inner tube is made from smooth copper tubing and has an 8.1 mm inner diameter. The test runs are done at an average saturated condensing temperature of 40 °C. The average qualities are between 0.8 and 0.99 while the mass fluxes are 300 kg m^− 2s^− 1 and the heat fluxes are between 22 and 39.8 kW m^− 2. The void fractions are indirectly determined using relevant measured data together with various void fraction models and correlations reported in the open literature. The friction factors obtained from various void fraction models and correlations are compared with each other and also with those determined from graphical information provided by Bergelin et al. The effect of void fraction alteration on the momentum pressure drop is also presented.