Modeling of droplet entrainment phenomena at a quench front

The phenomena of droplet entrainment at a quench front is of practical importance as a clear understanding of the underlying mechanisms required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. The present study proposes a model for droplet entrainment at a quench front that is based on the best-understood physics related to the Lagrangian quenching phenomenon characteristic to light water reactor (LWR) safety analysis. The model is based on a film boundary layer and stability analysis that attempts to match the characteristic time and length scales of the entrainment phenomenon. This model has been developed such that direct implementation can be made into any two-phase flow simulation code with a three-field (continuous liquid, droplet, and vapor) flow model. Comparisons with integrated transient test data independent of those used for model development have been performed to verify the applicability of the proposed model for the prediction of the entrainment rate of liquid droplets at a quench front under typical reflood conditions envisioned in LWRs.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

垂直上升气液环状流流动参数的数值计算

提出了一个新的气核-液膜耦合模型来求解垂直上升气液环状流在充分发展段的流动参数.本模型考虑了液膜、气核以及它们之间的相互影响和作用.模型中基本的气核区域和液膜区域的质量和动量方程由Fluent6.3.26进行求解,而液滴方程以及相界面上的夹带和沉积作用通过用户自定义接口函数UDF(User Defined Functi...     

Downwards co-current annular flow

This paper summarizes a study of the characteristics of downwards annular two-phase flow. The measurements reported are of film thickness, wave velocity and frequency, local pressure fluctuations, pressure gradient and liquid entrainment. The most important new feature of the work is the use of continuous data recording with either on-line or off-line statistical analysis. Experiments were carried out with air-water flows in tubes of 3.18 and 3.82 cm bore. It is shown that the interfacial characteristics of the flow may require at least 5 m for full development at some flow rates and most measurements were carried out with an entrance region of this length. It is also shown that the pressure fluctuations, characteristic of this two-phase flow regime, are primarily due to pressure surges caused by disturbance waves in the system passing through the exit device. A new regime map is proposed, based on experimental evidence, in which several distinctive types of interfacial behaviour are noted.     

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the frictional pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model from normal gravity to reduced gravity conditions. A comparison of the newly developed flow regime transition criteria model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71 and 9.81 m/s² corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly–slug and slug–annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of droplet entrainment, higher superficial gas velocity was obtained at higher gravity level.     

Study of two-phase flows in reduced gravity using ground based experiments

Experimental studies have been carried out to support the development of a framework of the two-fluid model along with an interfacial area transport equation applicable to reduced gravity two-phase flows. The experimental study simulates the reduced gravity condition in ground based facilities by using two immiscible liquids of similar density namely, water as the continuous phase and Therminol 59^® as the dispersed phase. We have acquired a total of eleven data sets in the bubbly flow and bubbly to slug flow transition regimes. These flow conditions have area-averaged void (volume) fractions ranging from 3 to 30% and channel Reynolds number for the continuous phase between 2,900 and 8,800. Flow visualization has been performed and a flow regime map developed which is compared with relevant bubbly to slug flow regime transition criteria. The comparison shows that the transition boundary is well predicted by the criterion based on critical void fraction. The value of the critical void fraction at transition was experimentally determined to be approximately 25%. In addition, important two-phase flow local parameters, including the void fraction, interfacial area concentration, droplet number frequency and droplet velocity, have been acquired at two axial locations using state-of-the-art multi-sensor conductivity probe. The radial profiles and axial development of the two-phase flow parameters show that the coalescence mechanism is enhanced by either increasing the continuous or dispersed phase Reynolds number. Evidence of turbulence induced particle interaction mechanism is highlighted. The data presented in this paper clearly show the marked differences in terms of bubble (droplet) size, phase distribution and phase interaction in two-phase flow between normal and reduced gravity conditions.     

Research on heat transfer of two-phase dispersed flow in narrow annular channel

Narrow channel heat transfer technique is a new developing heat transfer technique in recent years. As the temperature of droplet, steam and wall are decided by forced convection heat transfer between the steam and the wall, between the droplet and the wall, between the steam and the droplet and radiation heat transfer, which makes heat transfer mechanism of dispersed flow be difficultly interpretative. Dispersed flow in narrow annular channel is analyzed in the paper, investigating the influence of all kinds of heat transfer processes on dispersed flow, building annular channel dispersed flow model using thermodynamic non-equilibrium model. Calculation results show heat transfer is mainly controlled by heat transfer process between steam and wall. When temperature is low, radiation can be ignored on heat transfer coefficient calculation. The calculation of model can provide a reference for engineering application of steam generator, refrigeration system and so on.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.     

Two-phase two-component interface drag coefficients in separated phase flows

This work examines the behavior of the interface friction factor or drag coefficient as a means for extending the modeling of separated two-phase flows through the separate consideration of each phase. The model development of this work builds primarily upon the work of Carofano & McManus (1969), Wallis (1970) and Smith (1968). A one-dimensional flow model was developed for the case of vertical upward annular fiow of an air-water mixture with droplet entrainment. The model was developed for the investigation of accelerating flows in a nozzle but is utilized in this study for the investigation of momentum transport occurring in non-accelerating flows. This study presents experimental data showing the behaviour of the flow pressure drop occurring at various flow qualities and gas velocities. Also presented are empirical results for values of the air-water interface drag coefficient as a function of flow quality and gas core Reynolds number. The drag coefficient variation is compared to a previous correlation developed by Wallis 1969).     

Modeling transient churn-annular flows in a long vertical tube

This work investigates the transient behavior of high gas fraction gas-liquid flows in vertical pipes (annular and churn flows). Hyperbolic balance equations for mass, momentum and entropy are written for the gas and liquid, which is split between a continuous film and droplets entrained in the gas core. Closure relationships to calculate the wall and interfacial friction and the rates of droplet entrainment and deposition were obtained from the literature. A finite-difference solution algorithm based on a coefficient matrix splitting method was implemented to deal with sharp variations in the spatial and temporal domains, such as pressure and phase holdup waves. The model results were compared with steady-state experimental data from eight different sources, totaling more than 1500 data points for pressure gradient, liquid film flow rate and void/core fraction. The absolute average deviation between the model and the data was 17% for the pressure gradient and 5.8% for the void fraction. A comparison of the model results with fully transient air-water data generated in a 49-mm ID, 42-m long vertical pipe is also presented. The experimental results consist of two outlet pressure-induced and two inlet mass flow rate-induced transient tests. Two main transient parameters are compared, namely the local void fraction and the pressure difference between selected points along the test section and the outlet (taken as a reference). The comparisons between the experiments and the numerical model indicate that the model was capable of describing the transient annular to churn flow transition with absolute average deviations of 14.5% and 7.9% for the pressure difference and void fraction, respectively.     

Numerical simulation of annular two-phase flow considering the four involved mass transfers

In the present study, a numerical model is developed for simulation of annular two-phase flow considering bubbly flow regime in the liquid film along with the four involved mechanisms of mass transfer those are evaporation, entrainment, deposition and condensation. In the numerical approach, liquid film accompanied by fine nucleated bubbles are simulated with innovative model named suction model, the whole domain containing liquid film and the vapor core is simulated by volume of fluid model. While the vapor and the entrained droplets are treated as homogeneous flow. The interface between the liquid and the vapor is traced by level set formulation. The model is then validated by experimental models of Lee & Lee and Stevanovic et al. and shows a good precision such that it predicts the experimental results of Stevanivic et al. Better than their own numerical model. This issue is due to the least possible simplifying assumptions along with considering the effect of boiling in liquid film and all mechanisms of mass transfer in the fluid flow.     

The effect of orifices on the liquid distribution in annular two-phase flow

The effect of using orifices to disrupt the water film in air-water annular two-phase flow has been studied experimentally in a vertical tube by measuring the wall film flowrate at various distances upstream and downstream of several different sizes of orifice. The orifices cause a temporary reduction in the downstream water film flowrate, which returns to its equilibrium value further downstream. The experimental results have been used, together with those of other investigators, to compare the effects of orifices to those of swirl tapes, and further to compare the processes of entrainment and deposition within annular two-phase flow.     

Non equilibrium gas-liquid flows in variable cross section ducts

The behaviour of two-phase high velocity flows in variable cross section ducts was investigated using a one-dimensional numerical model developed for the study of the annular flow configuration. Heat, mass, and momentum transfer between the phases during the flow were considered. The validation of the calculation procedure was made with some experimental data for the air-water couple, while the main application concerned the evaluation of momentum transfer from an expanding gas to an entrained liquid stream in droplet form. A liquid metal-gas flow was considered to simulate the process taking place in a plant where electrical power is generated by a liquid metal flowing in a magnetic field (MHD). The effectiveness of energy and momentum transfer between the liquid and the gas phase during the expansion was evaluated and the influence of nozzles with different convergence angles was investigated.     

Visualization of flow boiling of liquid nitrogen in a vertical mini-tube

The flow boiling patterns of liquid nitrogen in a vertical mini-tube with an inner diameter of 1.931 mm are visualized with a high-speed digital camera. The superficial gas and liquid velocities are in the ranges of 0.01–26.5 m/s and 0.01–1.2 m/s, respectively. Four typical flow patterns, namely, bubbly, slug, churn and annular flow are observed. Some interesting scenes about the entrainment and liquid droplet deposition in the churn and annular flow, and the flow reversal with the indication of negative pressure drop, are also presented. Based on the visualization, the two-phase flow regime maps are obtained. Compared with the flow regime maps for gas–water flow in tubes with similar hydraulic diameters, the region of slug flow in the present study reduces significantly. Correspondingly, the transition boundary from the bubbly flow to slug flow shifts to higher superficial gas velocity, and that of churn to annular flow moves to lower superficial gas velocity. Moreover, time-averaged void fraction is calculated by quantitative image-digitizing technique and compared with various prediction models. Finally, three kinds of oscillations with long-period and large-amplitude are found, possible explanation for the oscillations is given by comparing the instantaneous flow images with the data of pressure, mass flux and temperature recorded synchronously.     

A two-phase, two-component model for vertical upward gas-liquid annular flow

In this paper, a new two-fluid two-component computational fluid dynamics (CFD) model is developed to simulate vertical upward two-phase annular flow. The two-phase VOF scheme is utilized to model the roll wave flow, and the gas core is described by a two-component phase consisting of liquid droplets and gas phase. The entrainment and deposition processes are taken into account by source terms of the governing equations. Unlike the previous models, the newly developed model includes the effect of liquid roll waves directly determined from the CFD code, which is able to provide more detailed and, the most important, more self-standing information for both the gas core flow and the film flow as well as their interactions. Predicted results are compared with experimental data, and a good agreement is achieved.     

Benchmarking of the one-dimensional one-group interfacial area transport equation for reduced-gravity bubbly flows

In order to properly design and safely operate two-phase flow systems, especially those deployed on future space missions, it is necessary to have accurate predictive capabilities. The application of a novel predictive method, the interfacial area transport equation (IATE), to dynamically predict the change of interfacial area concentration for reduced-gravity two-phase flows is described in this paper. Fluid particle interaction mechanisms such as coalescence and breakup that are present in reduced-gravity two-phase flows have been studied experimentally as reported in a previous paper by the current authors [Vasavada et al., 2007]. These mechanisms represent the source and sink terms in the IATE and their mechanistic models are benchmarked using experimental data obtained in a 25 mm inner diameter ground-based test section wherein reduced-gravity conditions were simulated. The comparison of the predictions from the model against experimental data shows good agreement. It has been found that, in contrast to the hypothesis extended in the literature, the wake entrainment based coalescence mechanism is present in reduced-gravity two-phase flows and in some cases is more important than coalescence due to random collision. Physics based arguments are extended to support this conclusion.     

Modeling Kinetic Interphase Mass Transfer for Two-Phase Flow in Porous Media Including Fluid–Fluid Interfacial Area

Interphase mass transfer in porous media takes place across fluid–fluid interfaces. At the field scale, this is almost always a kinetic process and its rate is highly dependent on the amount of fluid–fluid interfacial area. Having no means to determine the interfacial area, modelers usually either neglect kinetics of mass transfer and assume local equilibrium between phases or they estimate interfacial area using lumped parameter approaches (in DNAPL pool dissolution) or a dual domain approach (for air sparging). However, none of these approaches include a physical determination of interfacial area or accounts for its role for interphase mass transfer. In this work, we propose a new formulation of two-phase flow with interphase mass transfer, which is based on thermodynamic principles. This approach comprises a mass balance for each component in each phase and a mass balance for specific interfacial area. The system is closed by a relationship among capillary pressure, interfacial area, and saturation. We compare our approach to an equilibrium model by showing simulation results for an air–water system. We show that the new approach is capable of modeling kinetic interphase mass exchange for a two-phase system and that mass transfer correlates with the specific interfacial area. By non-dimensionalization of the equations and variation of Peclet and Damköhler number, we make statements about when kinetic interphase mass transfer has to be taken into account by using the new physically based kinetic approach and when the equilibrium model is a reasonable simplification.     

Frictional pressure drop during vapour–liquid flow in minichannels: Modelling and experimental evaluation

Condensation in minichannels is widely used in air-cooled condensers for the automotive and air-conditioning industry, in heat pipes and other applications for system thermal control. The knowledge of pressure drops in such small channels is important in order to optimize heat transfer surfaces. This paper presents a model for calculation of the frictional pressure gradient during condensation or adiabatic liquid–gas flow inside minichannels with different surface roughness. In order to account for the effects of surface roughness, new experimental frictional pressure gradient data associated to single-phase flow and adiabatic two-phase flow of R134a inside a single horizontal mini tube with rough wall has been used in the modelling. It is a Friedel (1979) [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: Proceedings of the European Two-Phase Flow Group Meeting, Ispra, Paper E2] based model and it takes into account mass velocity, vapor quality, fluid properties, reduced pressure, tube diameter, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, it has been built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and mist flow are here predicted. However, the suggested procedure is extended to the intermittent flow in minichannels and it is also applied with success to horizontal macro tubes.