Droplet entrainment correlation in vertical upward co-current annular two-phase flow

Upward annular two-phase flow in a vertical tube is characterized by the presence of liquid film on the tube wall and entrained droplet laden gas phase flowing through the tube core. Entrainment fraction in annular flow is defined as a fraction of the total liquid flow flowing in the form of droplets through the central gas core. Its prediction is important for the estimation of pressure drop and dryout in annular flow. In the following study, measurements of entrainment fraction have been obtained in vertical upward co-current air–water annular flow covering wide ranges of pressure and flow conditions. Comparison of the experimental data with the existing entrainment fraction prediction correlations revealed their inadequacies in simulating the trends observed under high flow and high pressure conditions. Furthermore, several correlations available in the literature are implicit and require iterative calculations.Analysis of the experimental data showed that the non-dimensional numbers, Weber number (We = ρ_gj_g²D/σ(Δρ/ρ_g)^1/4) and liquid phase Reynolds number (Re_f = ρ_fj_fD/μ_f), successfully collapse the data. In view of this, simple, explicit correlation was developed based on these non-dimensional numbers for the prediction of entrainment fraction. The new correlation successfully predicted the trends under the high flow and high pressure conditions observed in the current experimental data and the data available in open literature. However, in order to use the proposed correlation it is necessary to predict the maximum possible entrainment fraction (or limiting entrainment fraction). In the current analysis, an experimental data based correlation was used for this purpose. However, a better model or correlation is necessary for the maximum possible entrainment fraction. A theoretical discussion on the mechanism and modeling of the maximum possible entrainment fraction condition is presented.     

Void fraction and flow regime in adiabatic upward two-phase flow in large diameter vertical pipes

In pipes with very large diameters, slug bubbles cannot exist. For this reason, the characteristics of two-phase flow in large pipes are much different than those in small pipes. Knowledge of these characteristics is essential for the prediction of the flow in new nuclear reactor designs which include a large chimney to promote natural circulation. Two of the key parameters in the prediction of the flow are the void fraction and flow regime. Void fraction measurements were made in a vertical tube with diameter of 0.15 m and length of 4.4 m. Superficial gas and liquid velocities ranged from 0.1 to 5.1 m/s and from 0.01 to 2.0 m/s, respectively. The measured void fractions ranged from 0.02 to 0.83. Electrical impedance void meters at four axial locations were used to measure the void fraction. This data was verified through comparison with previous data sets and models. The temporal variation in the void fraction signal was used to characterize the flow regime through use of the Cumulative Probability Density Function (CPDF). The CPDF of the signal was used with a Kohonen Self-Organized Map (SOM) to classify the flow regimes at each measurement port. The three flow regimes used were termed bubbly, cap-bubbly, and churn flow. The resulting flow regime maps matched well with the maps developed previously through other methods. Further, the flow regime maps matched well with the criteria which were proposed based on Mishima and Ishii's (1984) criteria.     

垂直上升矩形流道内气液两相流流型图的数值模拟

两相流流型在分析换热、流动不稳定性以及临界热流密度方面具有基础性作用.本文基于VOF(Volume of Fluid)多相流模型,对垂直上升矩形流道内气液两相流动进行数值模拟,表观气速0.1～110 m/s,表观液速0.1～3.2 m/s.得到了流道内气液两相流的主要流型:泡状流、弹状流、搅混流和环状流,分析了流道内截面含气率分布与流型的对应关系,以及截面含气率与气液两相流容积含气率的关系;分析了各种流型下的压降分布特性,并绘制了基于气液表观动能通量的不同流量下气液两相流的流型图,直观的表示出各种流型的分布区域及各流型间的流型转换边界,与已发表文献的实验结果对比符合较好.     

The mechanism of bubble non-homogeneous distribution in two-phase shear flow

For the first time, the double peaks of void fraction radial profiles are presented and analyzed by the bubble deposition model. It was found that bubbles segregation according to their size is an important phenomenon which contributes to bubble non-homogeneous distribution in vertical upward two-phase shear flow.     

A self-standing two-fluid CFD model for vertical upward two-phase annular flow

In this paper, a new two-fluid CFD (computational fluid dynamics) model is proposed to simulate the vertical upward two-phase annular flow. This model solves the basic mass and momentum equations for the gas core region flow and the liquid film flow, where the basic governing equations are accounted for by the commercial CFD package Fluent6.3.26^®. The liquid droplet flow and the interfacial inter-phase effects are accounted for by the programmable interface of Fluent, UDF (user defined function). Unlike previous models, the present model includes the effect of liquid roll waves directly determined from the CFD code. It is able to provide more detailed and, the most important, self-standing information for both the gas core flow and the film flow as well as the inner tube wall situations.     

Model evaluation of two-group interfacial area transport equation for confined upward flow

The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined upward flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flows. The two-group IATE is evaluated in steady-state, one-dimensional (1D) form. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes.     

Flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels

In relation to the cooling system of high performance microelectronics, a high power research reactor with plate type fuels and plasma facing components of a fusion reactor, study of two-phase flow in a narrow rectangular channel has been paid considerable attention, recently. For the two-fluid model, direct geometrical parameters such as the void fraction should be used in flow-regime criteria. From this point of view, flow-regime transition criteria for vertical upward flows in narrow rectangular channels have been developed considering the mechanisms of flow-regime transitions. The basic concept of the present modeling followed the Mishima and Ishii model for vertical upward two-phase flows in round tubes. Newly developed criteria have been compared with the existing experimental data for air–water flows in narrow rectangular channels with the gaps of 0.3–17 mm. The present criteria showed satisfactory agreements with those data. Further comparisons with data for steam–water in a rectangular channel at relatively high system pressures have been made. The results confirmed that the present flow-regime transition criteria could be applied over wide ranges of parameters as well as to boiling flow.     

Modeling and measurement of interfacial area concentration in two-phase flow

This paper presents experimental and modeling approaches in characterizing interfacial structures in gas-liquid two-phase flow. For the modeling of the interfacial structure characterization, the interfacial area transport equation proposed earlier has been studied to provide a dynamic and mechanistic prediction tool for two-phase flow analysis. A state-of-the-art four-sensor conductivity probe technique has been developed to obtain detailed local interfacial structure information in a wide range of flow regimes spanning from bubbly to churn-turbulent flows. Newly obtained interfacial area data in 8 × 8 rod-bundle test section are also presented. This paper also reviews available models of the interfacial area sink and source terms and existing databases. The interfacial area transport equation has been benchmarked using condensation bubbly flow data.     

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.     

Influence of a flow obstacle on the occurrence of burnout in boiling two-phase upward flow within a vertical annular channel

When a flow obstruction such as a cylindrical spacer is set in a boiling two-phase flow within an annular channel, the inner tube of which is used as a heater, the temperature on the surface of the heating tube is severely affected by its existence. In some cases, the cylindrical spacer has a cooling effect, and in the other cases it causes the dryout of the cooling water film on the heating surface resulting in the burnout of the heating tube.In the present paper, we have focused our attention on the influence of a flow obstacle on the occurrence of burnout of the heating tube in boiling two-phase flow.The results are summarized as follows:

(1)When the heat flux approaches the burnout condition, the wall temperature on the heating tube fluctuates with a large amplitude. And once the wall temperature exceeds the Leidenfrost temperature, the burnout occurs without exception.

(2)The trigger of dryout of the water film which causes the burnout is not the nucleate boiling but the evaporation of the base film between disturbance waves.

(3)The burnout never occurs at the downstream side of the spacer. This is because the dryout area downstream of the spacer is rewetted easily by the disturbance waves.

     

On the occurrence of burnout downstream of a flow obstacle in boiling two-phase upward flow within a vertical annular channel

If a flow obstacle, such as a spacer is placed in a boiling two-phase flow within a channel, the temperature on the surface of the heating tube is severely affected by the existence of the spacer. Under certain conditions, a spacer has a cooling effect, and under other conditions, the spacer causes dryout of the cooling water film on the heating surface. The burnout mechanism, which always occurs upstream of a spacer, however, remains unclear.In a previous paper [Fukano, T., Mori, S., Akamatsu, S., Baba, A., 2002. Relation between temperature fluctuation of a heating surface and generation of drypatch caused by a cylindrical spacer in a vertical boiling two-phase upward flow in a narrow annular channel. Nucl. Eng. Des. 217, 81–90], we reported that the disturbance wave has a significant effect on dryout and burnout occurrence and that a spacer greatly affects the behavior of the liquid film downstream of the spacer.In the present study, we examined in detail the influences of a spacer on the heat transfer and film thickness characteristics downstream of the spacer by considering the result in steam–water and air–water systems. The main results are summarized as follows:

(1) The spacer averages the liquid film in the disturbance wave flow. As a result, dryout tends not to occur downstream of the spacer. This means that large temperature increases do not occur there. However, traces of disturbance waves remain, even if the disturbance waves are averaged by the spacer.

(2) There is a high probability that the location at which burnout occurs is upstream of the downstream spacer, irrespective of the spacer spacing.

(3) The newly proposed burnout occurrence model can explain the phenomena that burnout does occur upstream of the downstream spacer, even if the liquid film thickness t_F m is approximately the same before and behind the spacer.

Modeling and analysis of hydrodynamic instabilities in two-phase flow using two-fluid model

Because of the practical importance of two-phase flow instabilities, especially in boiling water nuclear reactor technology, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics of marginally-stable/unstable boiling systems. The purpose of this paper is to present an integrated methodology for the analysis of flow-induced instabilities in boiling channels and systems. The major novel aspects of the proposed approach are: (a) it is based on the combined frequency-domain and time-domain methods, the former used to quantify stability margins and to determine the onset of instability conditions, the latter to study the nonlinear system response outside the stability boundaries identified using the nearly-exact results of the frequency-domain analysis; (b) the two-fluid model of two-phase flow has been used for the first time to analytically derive the boiling channel transfer functions for the parallel-channel and channel-to-channel instability modes. In this way, the major characteristics of a boiling system, including the onset-of-instability conditions, can be readily evaluated by using the qualitative frequency-domain approach, whereas the explicit time-domain integration is performed, if necessary, only for the operating conditions that have already been identified as unstable. Both methods use the same physical two-fluid model that, in one case, is linearized and used to derive a rigorous analytical solution in the complex domain, and, in the other case, is solved numerically using an algorithm developed especially for this purpose. The results using both methods have been compared against each other and extensively tested. The testing and validation of the new model included comparisons of the predicted steady-state distributions of major parameters and of the transient channel response against experimental data.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

Characteristics and behavior of the interfacial wave on the liquid film in a vertically upward air-water two-phase annular flow

The behavior of individual interfacial waves on liquid film in vertically upward air-water annular flows has been visualized, observed and analyzed by a pigment luminance method(PLM) which was calibrated with a fiber-optic liquid film sensor. By means of this technique, we distinguished three different types of interfacial waves, i.e. the ripple wave, the ring wave and the disturbance wave. Furthermore we measured the characteristics of these three different kinds of waves, and in particular those of the disturbance wave: i.e. its propagation velocity, its frequency in passing and the distance between two adjacent waves, and then obtained the dependency of these characteristics on the air and water volumetric fluxes j_g and j_l. These results agreed well with the results obtained by other investigators, using an electric needle contact method. A probable mechanism of the occurrence of the ring and the disturbance waves was posited.     

Sensitivity analysis of bubble size and probe geometry on the measurements of interfacial area concentration in gas-liquid two-phase flow

Interfacial area concentration measurement is quite important in gas-liquid two-phase flow. To determine the accuracy of measurement of the interfacial area using electrical resistivity probes, numerical simulations of a passing bubble through sensors are carried out. The two-sensors method, the four-sensors method and the correlative method are tested and the effects of sensor spacing, bubble diameter and hitting angle of the bubbles on the accuracy of each measurement method are investigated. The results indicated that the two-sensors method is insensitive to the ratio between sensor spacing and bubble diameter, and hitting angle. It overestimates the interfacial area for small hitting angles while it gives a reasonable accuracy for smaller bubbles and large hitting angles. The four-sensors method gives accurate interfacial area measurements particularly for the larger bubble diameters and smaller hitting angles, while for smaller bubbles and larger hitting angles, the escape probability of bubbles through the sensors becomes large and the accuracy becomes worse. The correlative method gives an overall accuracy for interfacial area measurement. Particularly, it gives accurate measurements for larger bubbles and larger hitting angles while for smaller hitting angles, the spatial dependence of the correlation functions affects the accuracy.     

Numerical simulation of lateral phase distribution in turbulent upward bubbly two-phase flows

New constitutive models for the interfacial forces acting on bubbles were developed for accurately predicting the lateral phase distribution in turbulent bubbly two-phase flow in vertical channels. Several experimental measurements have revealed that the lateral void profile in bubbly two-phase flow varies from the void peaking near the wall to the almost flat distributions as the liquid velocity increases. However, within the authors' knowledge, the effect of liquid velocity on the void profile has not been successfully predicted by the existing models; this would indicate the strong limitation of the existing multidimensional two-phase flow models. In view of these, the validity of the present constitutive models was tested in varied conditions of the liquid velocity as well as the bubble size. Since several assumptions were required in the models mainly due to the insufficient knowledge of the bubble motion, further improvements should still be needed. Nevertheless, the predicted lateral phase distributions were found to be in reasonably good agreement with available experimental data. It is hence expected that the present constitutive models can effectively be used in the practical applications and also be the base of the more sophisticated ones.     

Flooding and flow reversal of two-phase annular flow

The flooding and flow reversal conditions of two-phase annular flow are mathematically defined in terms of a characteristic function representing a force balance. Sufficiently below the flooding point in counter-current flow, the interface is smooth and the characteristic equation reduces to the Nusselt relationship. Just below the flooding point and above the flow reversal point in cocurrent flow, the interface is “wavy”, so that the interfacial shear effect plays an important role. The theoretical analysis is compared with experimental results by others. It is suggested that the various length effects which have been experimentally observed may be accounted for by the spatial variation of the droplet entrainment.     

Modeling of bubble shape in horizontal and inclined tubes

An experimental and theoretical study on the bubble shape of intermittent flow in the horizontal and inclined pipes has been carried out. The experiment results show that the bubble shape depends on the Froude number, bubble length and pipe inclination. The bubble with staircase pattern tail is observed at low Froude numbers, which is corresponding to plug flow. A model for the prediction of the bubble shape in horizontal and inclined pipes is proposed. The model is able to predict the bubble shape, flow pattern transition between plug and slug flow regimes as well as nose-tail inversion phenomenon observed in the downwardly inclined pipe. Validation shows the model can well predict the bubble shapes in horizontal and inclined pipes. The model discloses that the transition between plug and slug flow regimes occurs within a region. The Froude number range for plug flow regime in the downwardly inclined pipe is much wider than that in the horizontal or upwardly inclined pipe. The assumption of fully developed liquid film under the long bubbles tends to under-estimate the liquid fraction in this part of the slug structure, especially, for the intermittent flow in the upwardly inclined pipe with high Froude numbers.     

Modeling of the coalescence of gas pores during annealing

The kinetics of the coalescence of gas bubbles under the conditions of high-temperature annealing is modeled. The case where the growth of gas pores is controlled by thermal dissolution of gas atoms from bubbles is examined. The modeling is performed by solving the basic kinetic equation numerically. The numerical calculations are compared with the results of an analytical model which describes the asymptotic behavior of the gas pores. The time characteristics of the process which are obtained in this work are at variance with the results of the analytical model. The discrepancies found are discussed.