群体平衡模型对复杂气液泡状流数值模拟

引言 气液泡状流广泛出现于航空航天、石油化工、核工程技术等领域,且多为复杂湍流泡状流.在工程领域中,准确预测这种复杂泡状流的含气率、气一液速度、气泡直径等参数对工业设备安全与优化分析十分重要.     

Population balance modelling for bubbly flows with heat and mass transfer

Population balance equations combined with a three-dimensional two-fluid model are employed to predict bubbly flows with the presence of heat and mass transfer processes. Subcooled boiling flow belongs to this specific category of bubbly flows is considered. The MUSIG (MUltiple-SIze-Group) model implemented in CFX4.4 is further developed to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements near the test channel exit is made for the radial distribution of the bubble Sauter diameter, void fraction, interfacial area concentration and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison was also performed against existing boiling model in CFX4.4 and the modified model developed in our previous work (Int. J. Heat Mass Transfer 45 (2002) 1197). Good agreement is better achieved with the local radial bubble Sauter diameter, void fraction, interfacial area concentration and liquid velocity profiles against measurements using the newly formulated MUSIG boiling model over the simpler boiling models. However, significant weakness of the model is still evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the model by the consideration of additional momentum equations or an algebraic slip model to account for bubble separation.     

Gas–liquid flows in medium and large vertical pipes

Gas–liquid bubbly flows with wide range of bubble sizes are commonly encountered in many industrial gas–liquid flow systems. To assess the performances of two population balance approaches – Average Bubble Number Density (ABND) and Inhomogeneous MUlti-SIze-Group (MUSIG) models – in tracking the changes of gas volume fraction and bubble size distribution under complex flow conditions, numerical studies have been performed to validate predictions from both models against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. These experiments have been strategically chosen because of flow conditions yielding opposite trend of bubble size evolution, which provided the means of carrying out a thorough examination of existing bubble coalescence and break-up kernels. In general, predictions of both models were in good agreement with experimental data. The encouraging results demonstrated the capability of both models in capturing the dynamical changes of bubbles size due to bubble interactions and the transition from “wall peak” to “core peak” gas volume fraction profiles caused by the presence of small and large bubbles. Predictions of the inhomogeneous MUSIG model appeared marginally superior to those of ABND model. Nevertheless, through the comparison of axial gas volume fraction and Sauter mean bubble diameter profiles, ABND model may be considered an alternative approach for industrial applications of gas–liquid flow systems.     

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.     

Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces

Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, C_S, as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737-1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965-2000] to account for the bubble-induced turbulence in the k-ε model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with C_S=0.08 and 0.10 agree well with the measurements. When C_S is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio (H/D=3 and H/D=6), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results.     

Interfacial area concentration in boiling bubbly flow systems

The interfacial area, which describes available area for the interfacial transfer of mass, momentum and energy, is a crucial parameter in a two-fluid model formulation. From this point of view, this study performed (i) extensive survey on existing models and correlations developed for boiling bubbly flows, (ii) extensive survey on existing interfacial area database for boiling bubbly flows, (iii) formulation of the physical model based on bubble number density transport equation, (iv) simplification of the model to identify the dominant parameters governing the interfacial area, and (v) finalization of the model based on the collected extensive data and development of the interfacial area correlation. The developed correlation of the interfacial area concentration agreed with 569 adiabatic flow data and 343 boiling flow data within averaged relative deviations of ±21.1% and ±31.0%, respectively.     

On the prediction of the phase distribution of bubbly flow in a horizontal pipe

Horizontal bubbly flow is widely encountered in various industrial systems because of its ability to provide large interfacial areas for heat and mass transfer. Nonetheless, this particular flow orientation has received less attention when compared to vertical bubbly flow. Owing to the strong influence due to buoyancy, the migration of dispersed bubbles towards the top wall of the horizontal pipe generally causes a highly asymmetrical internal phase distributions, which are not experienced in vertical bubbly flow. In this study, the internal phase distribution of air-water bubbly flow in a long horizontal pipe with an inner diameter of 50.3 mm has been predicted using the population balance model based on direct quadrature method of moments (DQMOM) and multiple-size group (MUSIG) model. The predicted local radial distributions of gas void fraction, liquid velocity and interfacial area concentration have been validated against the experimental data of Kocamustafaogullari and Huang (1994). In general, satisfactory agreements between predicted and measured results were achieved. The numerical results indicated that the gas void fraction and interfacial area concentration have a unique internal structure with a prevailing maximum peak near the top wall of the pipe due to buoyancy effect.     

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。     

Spatial Evolution of CO2-Contaminated Water Bubble Flows in a Vertical Pipe

Experiments on CO₂-water bubble flows in a vertical pipe were carried out for clean water, an aqueous NaCl solution, and an aqueous NaCl solution with 1-octanol to obtain databases of spatial evolutions of the flows with the impurities. Mass transfer correlations for bubbles in these liquids were implemented into a one-way bubble tracking method. Numerical predictions of the spatial evolution, e.g., transition from a bubbly to a slug flow, depending on the impurities agreed well with the experiments.     

绝热层流泡状流运动的双流体模型

绝热层流泡状流是泡状流研究中的一个基础范例 .目前描述绝热层流泡状流常采用的双流体模型由于相间作用考虑欠缺而适用性差 .本文结合理论和实验研究结果导出了描述壁面“排斥”作用的表达式 ,并建立了一个封闭的双流体模型 .模型预测值和实验值的比较表明 ,由于相间作用的合理考虑 ,扩大了该模型的适用范围     

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.     

Interfacial area density in bubbly flow

The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.     

The split of vertical two-phase flow at a small diameter T-junction

Measurements and observations of the phase split occurring at a small diameter vertical T-junction are reported. Time varying, void fraction data obtained using ring-type conductance probes have been analysed to yield valuable information regarding the effect of the junction on flow behaviour. It is shown through comparisons with the work of Stacey et al. [2000. The split of annular two-phase flow at a small diameter T-junction. International Journal of Multiphase Flow 26, 845-856] in a horizontal T-junction of a similar size that the orientation of the junction has no influence on the flow split. This behaviour is attributed to the absence of flooding and is corroborated by our high-speed images. Subsequently, better prediction of the phase split is obtained when the model of Azzopardi [1988. Measurements and observations of the split of annular flow at a vertical T-junction. International Journal of Multiphase Flow 14, 701-710] is modified to account for the absence of flooding. Regarding flow transitions, the methods by Barnea et al. [1983. Flow pattern in horizontal and vertical two-phase flow in small diameter pipes. The Canadian Journal of Chemical Engineering 61, 617-620] and Omebere-Iyari et al. [2005. Flow patterns for gas/liquid flow in small diameter tubes. Ninth UK National Heat Transfer Conference, Manchester, UK, 5-6 September] are found to give good predictions of the exit flow patterns in the horizontal side arm and vertical run arm, respectively.     

竖直环形通道内液氮流动沸腾的数值模拟

在多尺寸组模型的基础上,从加热壁面上脱离汽泡的受力分析人手,对液氮过冷流动沸腾模型进行了修正.将新模型应用于环形通道内液氮过冷流动沸腾的数值模拟,同时为了比较,采用基于Kirichenko,Fritz汽泡脱离直径公式的多尺寸组模型对同一管道内液氮过冷流动进行了数值模拟.结果表明:结合脱离汽泡受力分析模型的多尺寸组模型可...     

Local Measurement of Gas-Liquid Bubbly Flow with a Double-Sensor Probe

A double-sensor probe was used to measure local interfacial parameters of a gas-liquid bubbly flow in a horizontal tube. The parameters included void fraction, interfacial concentration, bubble size distribution, bubble frequency and bubble interface velocity. The authors paid special attention to the probe design and construction for minimizing measurement errors. Measures were also taken in the design of sensor ends for preventing corrosions in the flow. This is an effort to improve the current double-sensor probe technique to meet the ever-increasing needs to local varameter measurements in gas-liquid two-phase flows.     

基于MUSIG模型的竖直圆管内液氮过冷沸腾数值模拟研究(英文)

Multiple size group （MUSIG） model combined with a threedimensional twofluid model were em ployed to predict subcooled boiling flow of liquid nitrogen in a vertical upward tube. Based on the mechanism of boiling heat transfer, some important bubble model parameters were amended to be applicable to the modeling of liquid nitrogen. The distribution of different discrete bubble classes was demonstrated numerically and the distribu tion patterns of void fraction in the wallheated tube were analyzed. It was found that the average void fraction in creases nonlinearly along the axial direction with wall heat flux and it decreases with inlet mass flow rate and sub cooled temperature. The local void fraction exhibited a Ushape distribution in the radial direction. The partition of the wall heat flux along the tube was obtained. The results showed that heat flux consumed on evaporation is the leading part of surface heat transfer at the rear region of subcooled boiling. The turning point in the pressure drop curve reflects the instability of bubbly flow. Good agreement was achieved on the local heat transfer coefficient aalnst experimental measurements, which demonstrated the accuracy of the numerical model.     

AN EXPERIMENTAL STUDY OF DISPERSED LIQUID/LIQUID TWO-PHASE UPFLOW IN A PIPE

This paper presents experimental data for dispersed liquid/liquid upflows. Water was the continuous phase and mineral oil was the dispersed droplet phase. For this flow regime reduced gravity bubbly flow phenomena was simulated because the mineral oil and water had almost the same density. The mean velocity and turbulence fields, the size distributions of the oil droplets, the volume fraction, and interfacial area density distribution were measured using fiber optic Laser Doppler Anemometer (LDA) and phase Doppler Anemometer (PDA) systems. Significantly, the results presented in this paper are similar to those for bubbly air/water flows in microgravity conditions (Kamp el at., 1995).     

Flow structure of gas-liquid two-phase flow in an annulus

The flow structure of gas-liquid two-phase flow in vertical annulus channel has been investigated. The inner and outer diameters of the annular channel were 19.1 and 38.1 mm, respectively. The total height of the test section was 4.37 m. Nineteen inlet flow conditions were selected, which cover bubbly, cap-slug, and churn-turbulent flows. The local flow parameters, such as void fraction, interfacial area concentration (IAC), and bubble interface velocity, were measured at nine radial positions within the gap of the annulus at z/D_h=230 of the test section. The flow regimes of the flow conditions, which were based on visual observations, were compared with several flow regime maps. In addition, the local measurements were used to calculate distribution parameter, C₀ in drift-flux model, and area-averaged IAC. A new correlation of C₀ was proposed based on the experimentally obtained C₀ values. This correlation was tested in the drift-flux model successfully along with Ishii's drift velocity correlations. The area-averaged IAC values were compared with the most widely used models. The advantages and drawbacks of these models were highlighted.     

Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures

Two-dimensional axisymmetric Eulerian/Eulerian simulations of two-phase (gas/liquid) transient flow were performed using a multiphase flow algorithm based on the finite-volume method. These numerical simulations cover laboratory scale bubble columns of different diameters, operated over a range of superficial gas velocities ranging from the bubbly to the churn turbulent regime. The bubble population balance equation (BPBE) is implemented in the two-fluid model that accounts for the drag force and employs the modified k-ε turbulence model in the liquid phase. Several available bubble breakup and coalescence closures are tested. Quantitative agreements between the experimental data and simulations are obtained for the time-averaged axial liquid velocity profiles, as well as for the kinetic energy profiles, only when model predicted breakup rate is increased by a factor of ten to match the coalescence rate. The calculated time-averaged gas holdup profiles deviate in shape from the measured ones and suggest that full three-dimensional simulation is needed. Implementation of BPBE leads to better agreement with data, especially in the churn-turbulent flow regime, compared to the simulation based on an estimated constant mean bubble diameter. Differences in the predicted interfacial area density, with and without BPBE implementation, are significant. The choice of bubble breakup and coalescence closure does not have a significant impact on the simulated results as long as the magnitude of breakup is increased tenfold.     

TRANSPORT OF GAS-LIQUID FLOWS THROUGH VERTICAL COLUMNS

Applicability of a theoretical model, based on the fundamental governing equations of fluid motion is investigated to predict two-phase bubbly air-water flow structure through vertical columns. The model predictions are compared to experimental data for a wide range of flow parameters. The relative importance of various modes of interfacial momentum transfer, under different flow conditions, is also examined. It is found that correct estimation of the interfacial momentum transfer is necessary for agreement between the predictions and experimental data. The present study shows that the flow structure for air-water flows through vertical columns depends on the inlet flow conditions. This model predicts the experimentally observed trends well. In most cases the experimental data of local liquid velocity and gas volume fraction agree well with the calculated values.