垂直上升圆管内等温泡状流的数值模拟

介绍了描述等温状态下垂直气泡流流动的总体平衡方法(population balanceapproach). 将平均气泡数密度控制方程引入到双流体模型中实现总体平衡. 介绍了描述气泡聚并与破裂机制的Yao和Morel理论模型以及Hibiki等人的实验方法. 利用商业计算流体力学软件ANSYSCFX10, 对圆管特定位置上的5个基本变量:气含率、气泡平均直径、相间表面积浓度以及气体和液体速度沿半径分布进行了模拟计算. 预测结果与实验数据的比较表明,预测结果和实测数据之间有很好的一致性.      

Bubbly jets in stagnant water

Air–water bubbly jets are studied experimentally in a relatively large water tank with a gas volume fraction, C_o, of up to 80% and nozzle Reynolds number, Re, ranging from 3500 to 17,700. Measurements of bubble properties and mean axial water velocity are obtained and two groups of experiments are identified, one with relatively uniform bubble sizes and another with large and irregular bubbles. For the first group, dimensionless relationships are obtained to describe bubble properties and mean liquid flow structure as functions of C_o and Re. Measurements of bubble slip velocity and estimates of the drag coefficient are also provided and compared to those for isolated bubbles from the literature. The study confirms the importance of bubble interactions to the dynamics of bubbly flows. Bubble breakup processes are also investigated for bubbly jets. It was found that a nozzle Reynolds number larger than 8000 is needed to cause breakup of larger bubbles into smaller bubbles and to produce a more uniform bubble size distribution. Moreover, the Weber number based on the mean water velocity appears to be a better criteria than the Weber number based on the bubble slip velocity to describe the onset of bubble breakup away from the nozzle, which occurs at a Weber number larger than 25.     

Bubbly-to-cap bubbly flow transition in a long-26 m vertical large diameter pipe at low liquid flow rate

The concurrent upward two-phase flow of air and water in a long vertical large diameter pipe with an inner diameter (D) of 200 mm and a height (z) of 26 m (z/D = 130) was investigated experimentally at low superficial liquid velocities from 0.05009 to 0.3121 m/s and the superficial gas velocities from 0.01779 to 0.5069 m/s. The resultant void fractions range from 0.03579 to 0.4059. According to the observations using a high speed video camera, the flow regimes of bubbly, developing cap bubbly and fully-developed cap bubbly flows prevailed in the flows. The developing cap bubbly flow appeared as a flow regime transition from bubbly to fully-developed cap bubble flow in the vertical large diameter pipe. The developing cap bubbly flow changes gradually and lasts for a long time period and a wide axial region in the flow direction, in contrast to a sudden transition from bubbly to slug flows in a small diameter pipe. The analysis in this study showed that the flow regime transition depends not only on the void fraction but also on the axial distance in the flow and the pipe diameter. The axial flow development brings about the transition to happen in a lower void fraction flow and the increase of pipe diameter causes the transition to happen in a higher void fraction flow. The measured void fraction showed an N-shaped axial changing manner that the void fraction increases monotonously with axial position in the bubbly flow, decreases non-monotonously with axial position in the developing cap bubbly flow, and increases monotonously again with axial position in the fully-developed cap bubbly flow. The temporary void fraction decrease phenomenon in the transition region from bubbly to cap bubbly flow can be attributed to the formation of medium to large cap bubbles and their gradual growth into the maximum size of cap bubble and/or cluster of large cap bubbles in the developing cap bubbly flow. In order to predict the N-shaped axial void fraction changing behaviors in the flow regime transition from bubbly to cap bubbly flow, the existing 12 drift flux correlation sets for large diameter pipes are reviewed and their predictabilities are studied against the present experimental data. Although some drift flux correlation sets, such as those of Clark and Flemmer (1986) and Hibiki and Ishii (2003), can predict the present experimental data with reasonable average relative deviations, no drift flux correlation set for distribution parameter and drift velocity can give a reliable prediction for the observed N-shaped axial void fraction changing behaviors in the region from bubbly to cap bubbly flow in a vertical large diameter pipe.     

Interfacial area concentration in gas–liquid bubbly to churn flow regimes in large diameter pipes

This study performed a survey on existing correlations for interfacial area concentration (IAC) prediction and collected an IAC experimental database of two-phase flows taken under various flow conditions in large diameter pipes. Although some of these existing correlations were developed by partly using the IAC databases taken in the low-void-fraction two-phase flows in large diameter pipes, no correlation can satisfactorily predict the IAC in the two-phase flows changing from bubbly, cap bubbly to churn flow in the collected database of large diameter pipes. So this study presented a systematic way to predict the IAC for the bubbly-to-churn flows in large diameter pipes by categorizing bubbles into two groups (group 1: spherical or distorted bubble, group 2: cap bubble). A correlation was developed to predict the group 1 void fraction by using the void fraction for all bubble. The group 1 bubble IAC and bubble diameter were modeled by using the key parameters such as group 1 void fraction and bubble Reynolds number based on the analysis of Hibiki and Ishii (2001, 2002) using one-dimensional bubble number density and interfacial area transport equations. The correlations of IAC and bubble diameter for group 2 cap bubbles were developed by taking into account the characteristics of the representative bubbles among the group 2 bubbles and the comparison between a newly-derived drift velocity correlation for large diameter pipes and the existing drift velocity correlation of Kataoka and Ishii (1987) for large diameter pipes. The predictions from the newly-developed two-group IAC correlation were compared with the collected experimental data in gas–liquid bubbly to churn flow regimes in large diameter pipes and their mean absolute relative deviations were obtained to be 28.1%, 54.4% and 29.6% for group 1, group 2 and all bubbles respectively.     

Turbulence kinetic energy budget in bubbly flows in a vertical duct

Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate experimental data are required for quantitative validation of the ε equation.     

Lagrangian tracking of bubbles interacting with pin-fins in a microchannel

This paper presents new image analysis algorithms to measure the trajectories of breaking and coalescing bubbles in microscale bubbly flows. Image analysis of high-speed movies provides information on bubble dynamics and bubble interaction including bubble coalescence and breakage events. Individual bubbles that overlap in the image are recognized with a presented breakline method. The breakline method discriminates the overlapping bubbles with lines based on the bubble perimeter curvature analysis. Coalescence and breakage events are automatically recognized, and the path lines of bubbles travelling through the field of view are analyzed. The functionality of the algorithms was examined in bubbly flow in a microchannel encompassing two pin-fins in tandem.     

A numerical scheme for Euler–Lagrange simulation of bubbly flows in complex systems

An Eulerian–Lagrangian approach is developed for the simulation of turbulent bubbly flows in complex systems. The liquid phase is treated as a continuum and the Navier–Stokes equations are solved in an unstructured grid, finite volume framework for turbulent flows. The dynamics of the disperse phase is modeled in a Lagrangian frame and includes models for the motion of each individual bubble, bubble size variations due to the local pressure changes, and interactions among the bubbles and with boundaries. The bubble growth/collapse is modeled by the Rayleigh–Plesset (RP) equation. Three modeling approaches are considered: (a) one‐way coupling, where the influence of the bubble on the fluid flow is neglected, (b) two‐way coupling, where the momentum‐exchange between the fluid and the bubbles is modeled, and (c) volumetric coupling, where the volumetric displacement of the fluid by the bubble motion and the momentum‐exchange are modeled. A novel adaptive time‐stepping scheme based on stability‐analysis of the non‐linear bubble dynamics equations is developed. The numerical approach is verified for various single bubble test cases to show second‐order accuracy. Interactions of multiple bubbles with vortical flows are simulated to study the effectiveness of the volumetric coupling approach in predicting the flow features observed experimentally. Finally, the numerical approach is used to perform a large‐eddy simulation in two configurations: (i) flow over a cavity to predict small‐scale cavitation and inception and (ii) a rising dense bubble plume in a stationary water column. The results show good predictive capability of the numerical algorithm in capturing complex flow features. Copyright © 2010 John Wiley & Sons, Ltd.     

A novel fuzzy-logic based method for determination of individual bubble velocity and size from dual-plane ultrafast X-ray tomography data of two-phase flow

Ultrafast X-ray tomography enables non-invasive imaging of gas-liquid flows with high spatial and temporal resolution. While it is relatively straightforward to extract e.g. gas fraction profiles from cross-sectional tomographic images, the extraction of bubble and gas-liquid interface information requires advanced image processing techniques. Thereby it is an important necessity to transform the temporal scale in the scanned sequences into a corresponding length scale for obtaining correct volumetric information. For bubbly flows this means that the velocity of the dispersed phase, e.g. the gas bubbles, has to be determined from dual-plane scans. A common and widely applied method to obtain gas phase velocities is cross-correlating the image sequences of the two scanning planes. This gives an averaged velocity for each position in the cross-section. In the present work, a new method is introduced, which determines the velocity of individual gas bubbles. This new method is termed as “bubble twinning method”, because it tries to identify twin-bubbles in both scanning planes. The developed algorithm compares essential bubble parameters, that is, volume, position and residence time in the slice, by applying a fuzzy-logic based membership function approach. The algorithm was tested for bubbly flow as well as slug flow conditions. Results are compared with established theoretical predictions as well as the cross-correlation method.     

Bubble effect on Kelvin-Helmholtz instability

We derive boundary conditions at interfaces (contact discontinuities) for a class of Lagrangian models describing, in particular, bubbly flows. We use these conditions to study the Kelvin-Helmholtz instability that develops in the flow of two superposed layers of a pure incompressible fluid and a fluid containing gas bubbles, co-flowing with different velocities. We show that the presence of bubbles in one layer stabilizes the flow in some intervals of wavelengths.Received: 8 October 2002, Accepted: 5 May 2003PACS: 47.20.Ma, 47.55.Dz, 47.55.Kf Correspondence to: S.L. Gavrilyuk     

Development of a robust image processing technique for bubbly flow measurement in a narrow rectangular channel

This paper presents a robust image processing technique for bubbly flow measurement over a wide range of void fractions. The proposed algorithm combines geometrical, optical and topological information recorded with high speed cameras to separate and reconstruct the overlapping bubbles. The common difficulties such as overlapping, irregular bubble shape, surface deformation and large clustering in digital image processing are solved by combining different information based on a preset decision table and flow chart. Test with synthetic bubble images is performed to evaluate the reliability of the algorithm and quantify the uncertainty of the data. The result shows that the proposed algorithm can accurately measure bubbly flows with void fraction up to 18% for large bubbles. Four runs of bubbly flow images in a 30 mm  ×  10 mm rectangular channel are then recorded by three high speed cameras. The area-averaged void fraction of these test runs range from 2.4% to 9.1%. The axial and lateral distributions of bubble number density are obtained by the present algorithm for studying the characteristics of these flows.     

One-group interfacial area transport equation and its sink and source terms in narrow rectangular channel

The characteristics of two-phase flow in a narrow rectangular channel are expected to be different from those in other channel geometries, because of the significant restriction of the bubble shape which, consequently, may affect the heat removal by boiling under various operating conditions. The objective of this study is to develop an interfacial area transport equation with the sink and source terms being properly modeled for the gas–liquid two-phase flow in a narrow rectangular channel. By taking into account the crushed characteristics of the bubbles a new one-group interfacial area transport equation was derived for the two-phase flow in a narrow rectangular channel. The random collisions between bubbles and the impacts of turbulent eddies with bubbles were modeled for the bubble coalescence and breakup respectively in the two-phase flow in a narrow rectangular channel. The newly-developed one-group interfacial area transport equation with the derived sink and source terms was evaluated by using the area-averaged flow parameters of vertical upwardly-moving adiabatic air–water two-phase flows measured in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm. The flow conditions of the data set covered spherical bubbly, crushed pancake bubbly, crushed cap-bubbly and crushed slug flow regimes and their superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. Good agreement with the average relative deviation of 9.98% was obtained between the predicted and measured interfacial area concentrations in this study.     

Order and disorder in particle–liquid flows in a pipe

The spherical expanded polystyrene particle–oil two-phase flow in a vertical pipe was used to simulate the dispersed phase distribution in laminar bubbly flows. A three-dimensional particle image tracking technique was used to track the particles in the flow to study the ordered structure of dispersed phase distribution and its transition to disorder. The ordered structures behaved as particle strings aligned in the flow direction as induced by the flow shear. The structures were quite durable in high liquid velocity flows and dispersed gradually as the liquid velocity decreased. In lower velocity flows, the particles tended to form clusters in the horizontal direction, as predicted by potential theory for spherical bubbles rising in a quiescent inviscid liquid and as observed in experiments on non-shear bubbly water flows.     

Numerical simulation of circulation in gas-liquid column reactors: isothermal, bubbly, laminar flow

The gas-liquid flow inside a circular, isothermal column reactor with a vertical axis has been studied using numerical simulations. The flow is assumed to be in the laminar, bubbly flow regime which is characterized by a suspension of discrete air bubbles in a continuous liquid phase such as glycerol water. The mathematical formulation is based on the conservation of mass and momentum principle for the liquid phase. The gas velocity distribution is calculated via an empirically prescribed relative velocity as a function of void fraction. The interface viscous drag forces are prescribed empirically. For some cases a profile shape is assumed for the void ratio distribution. The influence of various profile shapes is investigated. The results are compared with those where the void ratio distribution is calculated from the conservation of mass equation. The mathematical model has been implemented by modifying a readily available computer code for single-phase newtonian fluid flows. The numerical discretization is based on a finite volume approach. The predictions show a good agreement with measurements. The circulation pattern seems not to be so sensitive to the actual shape of the void fraction profiles, but the inlet distribution of it is important. A significantly different flow pattern results when the void fraction distribution is calculated from the transport equation, as compared to those with a priori prescribed profiles. When the void fraction is uniformly distributed over the whole distributor plate, no circulation is observed. Calculations also show that even the two-phase systems with a few discrete bubbles can be simulated successfully by a continuum model.     

Vertical stability of bubble chain: Multiscale approach

Linear stability is investigated of a uniform chain of equal spherical gas bubbles rising vertically in unbounded stagnant liquid at Reynolds number Re = 50–200 and bubble spacing s > 2.6 bubble radii. The equilibrium bubble positions are questioned for their stability with respect to small displacements in the vertical direction, parallel to the chain motion. The transverse displacements are not considered, and the chain is assumed to be laterally stable. The bubbles are subjected to three kinds of forces: buoyant, viscous, inviscid. The viscous and inviscid forces have both pairwise (local) and distant (nonlocal) components. The pairwise forces are expressed by the leading-order formulas known from the literature. The distant forces are expressed as a linear superposition of the pairwise forces taken over several farther neighbours. The stability problem is addressed on three different length scales corresponding to: discrete chain (microscale), continuous chain (mesoscale), bubbly chain flow (macroscale). The relevant governing equations are derived for each scale. The microscale equations are a set of ODE’s, the Newton force laws for the individual discrete bubbles. The mesoscale equation is a PDE for bubbles continuously distributed along a line, obtained by taking the continuum limit of the microscale equations. The macroscale equations are two PDEs, the mass and momentum conservation equations, for an ensemble of noninteracting mesoscale chains rising in parallel. This transparent two-step process (micro → meso → macro) is an alternative to the usual one-step averaging, in obtaining the macroscale equations from microscale information. Here, the scale-up methodology is demonstrated for 1D motion of bubbles, but it can be used for behaviour of 2D and 3D lattices of bubbles, drops, and solids.It is found that the uniform equilibrium spacing results from a balance between the attractive and repulsive forces. On all three length scales, the equilibrium is stabilized by the viscous drag force, and destabilized by the viscous shielding force (shielding instability). The inviscid forces are stability neutral and generate conservative oscillations and concentration waves. The stability region in the parameter plane s − Re is determined for each length scale. The stable region is relatively small on the microscale, larger on the mesoscale, and shrinks to zero on the macroscale where the bubbly chain flow is inherently unstable.The shielding instability is expected to occur typically in intermediate Re flows where the vertical bubble interactions dominate over the horizontal interactions. This new kind of instability is studied here in a great detail, likely for the first time. Its relation to the elasticity properties of bubbly suspension on different length scales is discussed too. The shielding force takes the form of a negative bulk modulus of elasticity of the bubbly mixture.     

Two-phase damping and interface surface area in tubes with vertical internal flow

Two-phase flow is common in the nuclear industry. It is a potential source of vibration in piping systems. In this paper, two-phase damping in the bubbly flow regime is related to the interface surface area and, therefore, to flow configuration. Experiments were performed with a vertical tube clamped at both ends. First, gas bubbles of controlled geometry were simulated with glass spheres let to settle in stagnant water. Second, air was injected in stagnant alcohol to generate a uniform and measurable bubble flow. In both cases, the two-phase damping ratio is correlated to the number of bubbles (or spheres). Two-phase damping is directly related to the interface surface area, based on a spherical bubble model. Further experiments were carried out on tubes with internal two-phase air–water flows. A strong dependence of two-phase damping on flow parameters in the bubbly flow regime is observed. A series of photographs attests to the fact that two-phase damping in bubbly flow increases for a larger number of bubbles, and for smaller bubbles. It is highest immediately prior to the transition from bubbly flow to slug or churn flow regimes. Beyond the transition, damping decreases. It is also shown that two-phase damping increases with the tube diameter.     

Characterization of diabatic two-phase flows in microchannels: Flow parameter results for R-134a in a 0.5 mm channel

An optical measurement method for two-phase flow pattern characterization in microtubes has been utilized to determine the frequency of bubbles generated in a microevaporator, the coalescence rates of these bubbles and their length distribution as well as their mean velocity. The tests were run in a 0.5 mm glass channel using saturated R-134a at 30 °C (7.7 bar). The optical technique uses two laser diodes and photodiodes to measure these parameters and to also identify the flow regimes and their transitions. Four flow patterns (bubbly flow, slug flow, semi-annular flow and annular flow) with their transitions were detected and observed also by high speed video. It was also possible to characterize bubble coalescence rates, which were observed here to be an important phenomena controlling the flow pattern transition in microchannels. Two types of coalescence occurred depending on the presence of small bubbles or not. The two-phase flow pattern transitions observed did not compare well to a leading macroscale flow map for refrigerants nor to a microscale map for air–water flows. Time averaged cross-sectional void fractions were also calculated indirectly from the mean two-phase vapor velocities and compared reasonably well to homogeneous values.     

On the numerical study of bubbly flow created by ventilated cavity in vertical pipe

The dispersion of bubbles into a down-liquid flow in a vertical pipe is investigated. At low flow rates, the intended design of a swarm of discrete bubbles is achieved. At high flow rates, a ventilated cavity is nonetheless formed, which is attached close to the gas sparger. Behind this ventilated cavity, three different flow regimes characterize the complex bubbly flow field downstream of the down-liquid flow: vortex region with high void fraction, transitional region and pipe flow region. In this study, a numerical model that solved the entire development of the gas–liquid flow including the extended single-phase liquid region upstream to the wall-jet and recirculating-vortex zones in order to allow a more realistic determination of the boundary conditions of the down-liquid flow was adopted. Coupling with the Eulerian–Eulerian two-fluid model to solve the respective gas and liquid phases, a population balance model was also applied to predict the bubble size distribution in the wake right below the cavity base as well as further downstream in the transitional and fully-developed pipe flow regions. The numerical model was evaluated by comparing the numerical results against the data derived from theoretical, numerical and experimental approaches. Prediction of the Sauter mean bubble diameter distributions by the population balance approach at different axial locations confirmed the dominance of breakage due to the high turbulent intensity below the ventilated cavity which led to the generation of small gas bubbles at high void fraction. Further downstream, the coalescence effect dominated leading to merging of the small bubbles to form bigger bubbles.     

On two-phase flow patterns and transition criteria in aqueous methanol and CO2 mixtures in adiabatic,rectangular microchannels

This paper presents flow map investigations of adiabatic two-phase flow in square cross-sectioned, 200 μm deep microchannels fabricated in silicon, employing laser induced fluorescence microscopy. The influence of surface tension and nozzle geometry on the flow pattern transition was investigated using two nozzle widths (orifices of 30 μm and 50 μm, respectively) and methanol–water solutions with CO₂ as the gas phase. It was found and quantified that smaller nozzle geometries and smaller liquid surface tension promote the propagation of capillary gas bubbles at lower superficial gas and liquid velocities. Within the measurement domain of superficial gas (0.01–0.625 m/s) and liquid (0.0005–0.5000 m/s) velocities, we observed dispersed bubbly, regularly ordered bubbly, wedging, slug and annular flows, thus extending the experimental knowledge base to smaller superficial liquid velocities by almost two orders of magnitude. With the help of the flow maps presented herein, we were able to characterize the observed regularly ordered bubbly flow as the transition regime between dispersed bubbly and wedging flow. The results of the present investigation are of direct relevance to the operation of small-scale direct methanol fuel cells.     

Comparison of results from DNS of bubbly flows with a two-fluid model for two-dimensional laminar flows

Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compared with predictions of a two-fluid model for steady-state flow. The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as downflow. In all cases the results agree reasonably well, even though the simulated void fraction is considerably higher than what is assumed in the derivation of the model. The results do, however, suggest a need to understand the lift and the wall repulsion force on bubbles better, particularly in dense flows.