Void fraction in vertical gas-liquid slug flow: Influence of liquid slug content

In this study we develop a model for computing the mean void fraction and the liquid slug void fraction in vertical upward gas-liquid intermittent flow. A new model for the rate of gas entrained from the Taylor bubble to the liquid slug is formulated. It uses the work done by the pressure force at the rear of the Taylor bubble. Then an iterative approach is employed for equating the gas entrainment flux and the gas flux obtained via conservation equations. Model predictions are compared with experimental data. The developed iterative method is found to provide reasonable quantitative predictions of the entrainment flux and of the void fraction at low and moderate liquid slug void fraction conditions. However, with an increased liquid slug void fraction experimental data indicate that the flow in the liquid slug transits to churn-heterogeneous bubbly flow thus gas entrainment flux tends to zero. Considering this effect in the iterative model significantly improved the predictions for large liquid slug void fraction conditions.     

The role of surface tension in microgravity slug flow

In the analysis of slug flow under gravity conditions surface tension is usually neglected. The liquid slug is treated as a homogeneous mixture and the liquid film adjacent to the wall, in the Taylor bubble zone behind the slug, is treated using the one-dimensional approach (channel flow theory). Although the use of the one-dimensional approach is not accurate, especially close to the bubble cap, it is considered as a valid approximation and it yields reasonable results for the modeling of pressure drop, bubble length and void fraction in slug flow. Since for the case of microgravity flow, surface tension is expected to be a dominant force that should not be overlooked, one may be tempted to use the same procedure for the analysis of slug flow under microgravity conditions with the surface tension included (this can be done also for non-microgravity conditions). In this work, it is shown that the inclusion of the surface tension in the one-dimensional approach for the film analysis leads to erroneous and unacceptable results near the bubble cap that cannot be used even as an approximation. It is also shown that far away from the cap the solution with and without the surface tension is practically the same. Thus, a simplified model for slug flow in microgravity is suggested that assumes a spherical shape of the bubbles at the nose that is matched with the conventional one-dimensional viscous solution far downstream. In this procedure the effect of surface tension at the nose is in fact taken into account indirectly by the imposition of a spherical cap. That is, the assumption that the bubble nose behaves similar to the behavior of small size bubbles that are controlled by surface tension.     

矩形截面螺旋通道内气液两相流局部含气率分布实验研究

应用电导探针测量技术,对矩形截面螺旋通道内气液两相流局部含气率进行实验研究。在不同的气相折算速度下,应用电导探针测量了弹状流弹单元的长度,并与可视化方法进行对比,验证了电导探针的可靠性,并为信号处理选择合适的阈值。分别在泡状流、弹状流及环状流三种流型的条件下,分析了气相与液相折算速度对局部含气率分布的影响。实验结果发现,螺旋通道气液两相局部含气率呈非对称的抛物线形分布,这种非对称性受流型和液相折算速度的影响。     

Investigating the effect of pressure on a vertical two-phase upward flow with a high viscosity liquid

This article presents void fraction and pressure gradient data for sulfur hexafluoride (SF₆) with gas densities of 28 and 45 kg/m³ and oil (with viscosity 35 times that for water) in a 127 mm diameter pipe. The superficial velocities of gas ranged from 0.1 to 3 m/s and those for liquid from 0.1 to 1 m/s, respectively. Measurements of void fraction data were recorded using a capacitance wire mesh sensor (WMS) system, which permits the 3D visualization of the flow patterns. All the data were obtained with a data acquisition frequency of 1,000 Hz. A differential pressure transducer was used to measure the pressure drops along the length of the pipe. The WMS provide time and cross-sectionally resolved data on void fraction and from an analysis of its output, flow patterns were identified using the characteristic signatures of probability density function (PDF) plot of time series of void fraction. The PDF plots showed the single peak shapes associated with bubbly and churn flows but not the twin-peaked shape usually seen in slug flows. This confirms previous work in larger diameter pipes but with less viscous liquids. For the bubble and churn flows investigated, the pressure gradient was observed to decrease with an increase in gas superficial velocity. Nevertheless, there was an insignificant observed effect of pressure on void fraction below certain transitional flow rates, the effect however became significant beyond these values. In the present work, wisps appear to be smaller, which might be due to the different fluid properties of the working fluids employed. In addition, wisps are easily revealed as long as there is a transition between churn and annular flows regardless of the pressure. Experimental data on void fraction and pressure gradient are compared against existing data. Reasonably good agreements were observed from the results of the comparison.     

基于MUSIG模型的低温流体过冷沸腾数值模拟

在低温泡状流中,鉴于液相中离散的气泡尺寸大小不一,文中将MUSIG模型应用于低温流体过冷沸腾计算中。通过模拟液氮在竖直圆管内过冷流动沸腾过程,对各尺寸组气泡的分布、轴向空泡份额的分布规律及流动不稳定性进行了分析。计算结果表明:各尺寸组气泡在壁面和中心区呈现不同的分布规律;平均空泡份额沿轴向呈非线性递增变化;由于流型的转变,管内压降将出现突变。     

Experimental investigation of cocurrent two-phase flow in a vertical rectangular channel

New time averaged data of two-phase flow in bubbly and slug regimes are presented. A modified dual spherical tipped optical fiber probe is used to measure local void fractions, gas velocity and bubble sizes. Hot film anemometry was used to measure the local mean liquid velocity axially. The void fraction, gas and liquid velocities values were presented as averages over the long and short dimensions respectively. Also core values of these variables are presented along the smaller dimension of 12.7 mm, near the plane of symmetry of the longer dimension, to show the most general trend of the different bubbly and slug flow runs. Bubble sizes obtained experimentally were compared with predictive models applied to circular geometries and were found to have a reasonable agreement. It was also interesting to find that local void fractions measured using hot film anemometers were comparable to those found by optical fiber probes. Frequencies of interfacial passage of bubbles and slugs are presented which show rather flat profiles across the channel. It is hoped that these data can be further used in predictive two-phase two-fluid models in the future. Lastly of interest is the fact that slip values near the boundaries were shown to be less than 1.0 for some cases in bubbly flow similar to those observed in circular geometries.     

On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group average bubble number density (ABND) model for handling the bubble size distribution of gas-liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. [1998. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41, 1103-1112], Hibiki and Ishii [2002. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45, 2351-2372] and Yao and Morel [2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47, 307-328] are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff [1993a. Structure of air-water bubbly flow in a vertical pipe—I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36, 1049-1060; 1993b. Structure of air-water bubbly flow in a vertical pipe—II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36, 1061-1072] and Hibiki et al. [2001. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44, 1869-1888]. In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas-liquid bubbly flows, the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models’ capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherical shape and allowed to move freely in bubbly flow regime.     

Two‐Phase Bubbly Flow Structure in Large‐Diameter Vertical Pipes

The two‐phase flow structure of an air‐water, bubbly, upward flow in a 20 cm diameter pipe is presented with particular emphasis on the local interfacial area concentration. The radial distribution of void fraction, bubble velocity, bubble size, bubble frequency, and interfacial area concentration were measured using a local dual‐optical probe. The experimental results showed that the saddle‐type distribution of void fraction and interfacial area concentration, which are common for bubbly flow in small diameter pipes, only appeared in the present experiments under conditions of very low area‐averaged void fraction (<?> < 0.04). The values for the interfacial area concentration were higher in large diameter pipes when compared with data obtained under the same flow conditions in small pipes. The area‐averaged void fraction data were correlated using the drift‐flux model.     

Ideality analysis and general laws of bubble swarm microflow for large-scale gas-liquid microreaction processes

The flow ideality of bubbly microflow remains unclear even though it is vital for the design of microreactors, especially the ideality of bubble swarm microflow for large-scale gas-liquid microreaction processes. This work is the first time to report the ideality analysis of the microbubble swarm in a relatively large microchannel. The bubble swarm microflow has undergone two conditions: quasi-homogeneous plug flow and liquid phase/gas-liquid quasi-homogeneous phase two-phase laminar flow. Both the deviations of void fraction and bubble velocity from the ideal plug flow can divide into two parts, and the two transition points simultaneously happen at the velocity ratio of 1.25. There exists a critical capillary number to maintain the quasi-homogeneous plug flow, which could be regarded as the general laws for the design of gas-liquid microreactors. Finally, a novel model is developed to predict the bubble velocity. This work could be very helpful for the large-scale gas-liquid microreactors design.     

用改进ECT技术测定油气两相流中空泡分数的测量研究

To measure the void fraction online in oil-gas pipeline, an improved electrical capacitance tomography (ECT) system has been designed. The capacitance sensor with new structure has twelve internal electrodes and overcomes the influence of the pipe wall. The data collection system is improved by using high performance IC (integrated circuit). Static tests of bubble flow, stratified flow and annular flow regime are carried out. Measurements are taken on bubble flow, stratified flow and slug flow. Results show that the new ECT system performs well on void fraction measurement of bubble flow and stratified flow, but the error of measurement for slug flow is more than 10%.     

Experimentally‐based constitutive relations for co‐current gas‐liquid flow in randomly packed beds

Experimental Observations on average pulse velocity and frequency in concurrent gas‐liquid (down) flow through randomly packed beds are used to extract constitutive relations for the gas‐liquid interaction and mean curvature terms that appear in a recently proposed volume‐averaged two‐fluid model for bubbly flow. The proposed closures lead to a reasonably quantitative prediction of the average pressure drop and liquid saturation under bubbly flow conditions and in the near pulse regime. In addition, the proposed closures provide realistic estimates for the location of the bubble‐to‐pulse transition in microgravity and in 1g down‐flow and predict the disappearance of the bubbly flow pattern at low liquid fluxes in 1g down‐flow. © 2016 American Institute of Chemical Engineers AIChE J, 63: 812–822, 2017     

Destabilisation of homogeneous bubbly flow in an annular gap bubble column

Experimental results are presented to show that there are very significant differences in the mean gas void fractions measured in an open tube and a annular gap bubble column, when operated at the same gas superficial velocity, using a porous sparger. Measurements were carried out in a vertical 0.102 m internal diameter column, with a range of concentric inner tubes to form an annular gap, giving diameter ratios from 0.25 to 0.69; gas superficial velocities in the range 0.014–0.200 m/s were investigated. The mean gas void fraction decreases with increasing ratio of the inner to outer diameter of the annular gap column and the transition to heterogeneous flow occurs at lower gas superficial velocities and lower void fractions. Two reasons are proposed and validated by experimental investigations: (1) the presence of the inner tube causes large bubbles to form near the sparger, which destabilise the homogeneous bubbly flow and reduce the mean void fraction; this was confirmed by deliberately injecting large bubbles into a homogeneous dispersion of smaller bubbles, and (2) the shape of the void fraction profiles changes with gap geometry and this affects the distribution parameter in the drift‐flux model. Both of these effects serve to reduce the mean gas void fraction in an annular gap bubble column compared to an open tube at the same gas superficial velocity.     

Tomographic imaging of counter-current bubbly flow by wire mesh tomography

The objective of this work is to investigate characteristics of counter-current bubbly flow in a circular pipe with an inner diameter of 50 mm by using wire mesh tomography (WMT). The accuracy of WMT on void fraction measurement is also clarified by comparing the result with a non-intrusive optical method. The accuracy is within ±10%. Local void fractions of many flow conditions are reported. Local void fraction profile affected by superficial liquid velocity and bubble size is shown and discussed. Furthermore, intrusive effects, including bubble break-up and bubble deceleration, are also investigated. Bubbles passing a transparent wire mesh sensor (WMS) are investigated by the optical method. It is shown that bubbles are broken and decelerated by wires of the sensor. It can be concluded that the bubble break-up rate increase with increasing of bubble velocity. However, the bubble deceleration is not depending on the bubble velocity.     

Hydrodynamic characteristics of gas-liquid slug flow in a downward inclined pipe

Gas-liquid slug flow in a downward inclined pipe was studied experimentally by employing a wire-mesh sensor that enables quantitative measurements of the cross-sectional void fraction distribution. Processing of the wire-mesh sensor data was applied to carry out a statistical analysis of characteristic parameters of downward slug flow, such as bubble and liquid slug length distributions, as well as to determine the ensemble-averaged shapes of the bubble nose, liquid film and bubble tail. It was found that the pipe inclination affects mainly the bubble length, while variation in the gas flow rate affects both bubble and slug length. The bubble nose shape is more sensitive to the flow conditions than the bubble tail. The 3D structure of an elongated bubble in downward slug flow was reconstructed from the wire-mesh sensor data.     

气液两相垂直管流中弹状流型数学模型

本文对气液两相垂直管流的弹状流型的流动机理进行了分析,建立了数学模型。模型的特点是采用了以弹状气泡速度运动的相对座标系,在弹状气泡周围下落液膜流动、液体段空隙率计算和压降计算等方面部提出了新的观点。在两种管径中用空气-水系统进行了实验以验证模型,与一些其他作者的实验数据和理论模型也进行了比较,结果都表明这个机理模型计算的弹状流型的各种流体力学参数值与实验值吻合良好,也优于其他作者提出的模型。     

Void fraction measurement and calculation model of vertical upward co-current air–water slug flow

The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air–water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^-1 and gas superficial velocity ranging from 0.049 to 0.65 m·s^-1. A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness C_δ and nose shape C_Z^* were proposed to calculate α_TB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate α_LS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.     

矩形小通道内气液两相流垂直向上流动特性

以氮气和水为实验介质,利用高速摄像机对水力直径为1.15 mm的矩形小通道内的气液两相垂直向上流动特性进行可视化研究,依次得到泡状流、弹状流、搅拌流和环状流4种典型的流型图像。针对小通道内气泡之间相互无遮掩性的优势,运用图像处理技术对流型图像分形增强,检测气泡边缘并填充后根据提出的气相体积模型,得到两相流动的含气率。结合实验数据,根据分液相Reynolds数把流动分为层流区、过渡区和紊流区,并对Chisholm关系式进行修正,结果表明：修正后的压降模型能较好地预测本文实验结果。     

A CONTRIBUTION TO THE MATHEMATICAL MODELING OF BUBBLY/SLUG FLOW REGIME TRANSITION

A new mathematical modeling approach has been applied to the analysis of bubbly vapor/liquid flows. In particular, an integro-differential equation has been formulated which describes the bubble size distribution function. Various moments of this equation yield important two-phase flow parameters, such as the bubble number density, the mean bubble radius, and the interfacial area density. The steady-state distribution function has been numerically evaluated and an approximate analytical solution has been constructed. It was found that the model appears to be inherently capable of predicting the bubble to slug flow regime transition.     

PREDICTION OF VOID FRACTION AND VELOCITY PROFILES OF BUBBLY FLOWS IN VERTICAL PIPES

Adopting a similar approach to Beyerlein et al. (1985), void fraction distributions in turbulent two-phase bubbly air/water upflows and downflows in vertical pipes were analyzed using a simple transport model which was based on the assumptions that the lateral shear-induced lift force acting on bubbles (Thomas et al., 1983) is balanced by bubble dispersion, and that bubbles in the flow are conserved i.e. no bubble breakup or coalescence occurs. The model shows the importance of considering the lateral lift force experienced by bubbles as they move relative to the liquid phase in a non-uniform velocity field. This force causes the bubbles to accumulate near the wall forming a high concentration for upward flow, while the concentration increases toward the centre of the pipe for downward flow. The eddy diffusivity, as widely used in calculation of single-phase flow, can be extended to include the effect of pseudo-turbulence (Lance and Balaille, 1991) due to bubbles, and thus can be linked with the bubble dispersion coefficient. It is also demonstrated that the transverse or radial pressure gradient induced by the Reynolds stress exerts a lateral force on the bubbles, and thus affects their distribution in the flow. A comparison of the model predictions with experimental data from Serizawa et al. (1975) for upflows and Wang et al. (1987) for both upflows and downflows shows that our model predicts void fraction peaking near the wall for upflows and coring at the centre-line for downflows. Compared with similar investigations (e.g., Drew and Lahey, 1982; Lopez de Bertodano et al., 1990) of the same problem, our model approach appears to be simpler and more suitable for engineering calculations.     

CFD modeling and validation for two-phase medium viscosity oil-air flow in horizontal pipes

This study presents the results of a Computational Fluid Dynamics (CFD) simulation of two-phase medium viscosity oil-air flow in a 50.8?mm internal diameter horizontal pipe. Void fraction and pressure gradient predictions were validated using experimental data for four different oil viscosities (0.039, 0.06, 0.108 and 0.166?Pa s) and different flow rates varying from 0.1 to 2.9?m/s for the gas phase and from 0.01 to 2.95?m/s for the liquid phase, where four flow patterns were predicted (stratified, dispersed bubble, bubble elongated and slug flow). The obtained results of void fraction and pressure gradient presented a mean relative error of 30.04 and 21.38%, respectively. Furthermore, the CFD results were compared against 66 empirical correlations and predictions from OLGA. It was found that between the three studied methods (CFD, OLGA and empirical correlations) the CFD model outperformed the other two methods regarding the predicted flow patterns, pressure gradients and void fractions on most cases.