Model Development for Bubble Turbulent Diffusion and Bubble Diameter in Large Vertical Pipes

Multi-dimensional analyses have been expected recently with expanding computation resources for gas-liquid two- phase flow analyses of advanced nuclear systems such as passive safety systems and natural-circulation-type reactors. However, the applicability of previous constitutive equations for multi-dimensional analyses has not been fully investigated especially for the effects of flow path scale because the equations have been assessed for small-scale experiments. In this study, we analyzed the scale effects by the multi-dimensional two-fluid model code using data in 38 mm and 200 mm diameter pipes. We clarified a key-parameter to model the scale effects and developed models for the effects on phase distribution. The scale effects can be classified by the relative relationship between bubble diameter d_b and turbulent length scale l_T . Bubble-induced turbulence is increased under that d_b is smaller than l_T and bubble coalescence is predominated rather than breakup under that l_T is about three times larger than d_b and under higher void fraction. Based on these findings, we established new models for bubble turbulent diffusion and bubble diameter. The applicability was promising through assessments against the 38 mm and 200 mm pipes under different flow rates and against databases for 60 mm, 100 mm and 480 mm pipes.     

倾斜管内上升泡状流界面参数分布特性实验研究

采用双头光纤探针对倾斜圆管内空气-水两相泡状流界面参数分布特性进行了实验研究,包括局部空泡份额、气泡通过频率、界面面积浓度及气泡当量直径径向分布特性。实验段内径为50 mm,液相表观速度为0.144 m/s,气相表观速度为0~0.054 m/s。结果表明倾斜管内向上泡状流气泡明显向上壁面聚集。局部界面浓度、空泡份额及气泡通过频率径向分布相似。倾斜条件下局部界面参数分布下壁面附近峰值相对于竖直状态被削弱甚至消失,上壁面附近峰值被加强,中间区域从下壁面往上逐渐增大,且随倾斜角度的增加变化更加剧烈。气泡等价直径随径向位置、气相速度及倾斜角度的不同无明显变化,气泡聚合和破碎现象较少发生。通过气泡受力分析解释了倾斜对泡状流局部界面参数分布的影响机理。     

Characteristics of Cocurrent Two-Phase Downflow in Tubes

An experimental study was made in a cocurrent downflow for air-water system in tube on flow pattern, void fraction and pressure drop. In addition to wetted wall flow which is a distinguished feature in downflow, the same kinds of flow patterns as in up-flow were observed. They were represented on the flow map of downflow with the same variables as those of upflow. The flow maps showed that gas phase is relatively hard to exist in the form of bubble in the cocurrent downflow.

General correlations of the void fraction and the pressure drop in a cocurrent down-flow were obtained by applying the following equations which have been established in upflow, i.e. α/(1-α)(1-Kα)=β/(1-β) for void fraction and φl=(1.α)- ^z for pressure drop. The determined values of K and Z by using the experimental results in the present study and other experimental works in cocurrent downflow wereK=2.0–0.4/β for β≤0.2, K=-0.25+1.250 for β≥0.2 and Z=0.90.

Comparisons between the predicted values by the presented correlations and experimental data showed satisfactory agreement.     

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.     

Flow Behavior and Phase Distribution in Two-Phase Flow around Inverted U-Bend

Experimental results are presented on the flow behavior, phase distribution, average void fraction and slip ratio in air-water two-phase mixture flowing through an inverted U-bend. The curved test section of transparent acrylic resin tubing with 24 mm I. D. was used, comprising a riser, an inverted U-bend with radius of 96 mm, and a downcomer. From the visual observation, a flow map was derived, which indicates the relation between the flow patterns and velocities. Distributions of local void fraction along a diameter lying in the central plane of the bend and over the whole cross section of bend tube were measured, and those distribution mechanisms were explained by the effect of centrifugal and gravitational forces. The average void fraction around the bend was obtained by numerical integration of the measured local void fraction, and the slip ratio was calculated using the average void fraction.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part II: numerical simulation

Numerical simulations of bubbly flows in a four by four rod bundle are carried out using a multi-fluid model to examine effects of the numerical treatment of phase distribution and drag model. The transport equations of bubble number density and void fraction are used as the continuity equation of the gas phase. Two drag models are tested: one of them accounts for the bubble deformation (aspect ratio), whereas the other does not. The rod diameter, the rod pitch and the hydraulic diameter of the rod bundle are 10, 12.5 and 9.1 mm, respectively. The gas and liquid volume fluxes are J_G = 0.06 m/s and J_L = 0.9 and 1.5 m/s, respectively. The bubble diameter ranges from 1 to 5 mm. Comparisons between the numerical and measured data show that (1) the restriction on bubble lateral motion due to the presence of rods can be taken into account by using the transport equation of bubble number density, whereas that of the void fraction cannot deal with the restriction and causes large errors in the distribution of void fraction and (2) the reduction in the bubble-relative velocity near the wall is predictable by using the drag model accounting for the bubble deformation effect.     

Local two-phase flow measurements using sensor techniques

Radial profiles of various local parameters in bubbly two-phase flow were obtained. Measurements of the local void fraction, the local interfacial area concentration, the bubble interfacial velocity and Sauter mean diameter were made using the double sensor probe method. At the same locations, local liquid velocity and turbulence intensity measurements were made using a hotfilm anemometer. Data was taken at three different axial locations (L/D=2, L/D=32 and L/D=62) along a 3.24 m test section with an inner diameter of 0.0508 m. In comparison to previous data sets, the following data is more complete in the sense that both interfacial area measurements are combined with one of the local driving forces for interfacial transfer, namely the liquid turbulent diffusion. There have been few, if any, studies done combining local liquid turbulence and the local interfacial area concentration. The data taken will eventually be applied to the closure relations required by the one-dimensional, time-averaged interfacial area transport equation.     

中压沸腾工况相径向分布实验研究

采用高温高压单探头光学探针．在中压沸腾工况下进行了局部空泡率与汽泡频率径向分布特性实验研究,并根据探针信号对两相流流型进行了识别,分析了中压沸腾工况下空泡率径向分布与流型的关系。研究结果表明：随热平衡含汽率增加,整个直径方向上空泡率分布从近U形向鞍形和弧形发展;汽泡频率则以近U形分布为主;泡状流工况下,空泡率呈U形或近壁区显著高于中心区的鞍形分布,弹状流工况下,中心区空泡率略低于近壁区。整个直径上空泡率呈弧形分布。     

Development of ATR Type Steam Separator Performance Analysis Code and Its Validation, (I)

The purpose of the study is to develop a method for predicting steam carryunder which is one of the important characteristics of a steam separator. Bubbles returning to the liquid surface and trapped by the re-circulating flow are calculated by tracking the behavior of bubbles moving in liquid bulk where velocity and temperature distributions have been calculated beforehand in conjunction with the Monte-Carlo method. Regarding the statistics of bubbles, a survey of references and visual tests have been conducted. To validate this method, several tests to measure bubble behavior under air/water conditions at atmospheric pressure and high temperature and pressure ranging 3~7 MPa have been conducted with a full-scale steam separator.

As a result, the developed method predicted with good precision the carryunder ratio obtained by the full-scale tests under the condition that carried-under void fraction was less than 20%, but underestimated carryunder ratio in the ATR “Fugen” reactor in which steam drum water level was shallow and average void fraction in water bulk was high. This method has a characteristic that carryunder ratio is underestimated in the case that void fraction is more than 20%.     

竖直圆管内泡状流界面参数分布特性

采用双头光纤探针对内径为50 mm竖直圆管内空气-水两相泡状流界面参数径向分布特性进行了实验研究。气液两相表观速度变化范围分别为0.004～0.05 m/s和0.071～0.283 m/s。结果表明,竖直管内向上泡状流局部界面面积浓度（IAC）、空泡份额及气泡频率径向分布相类似,即气相流速较低时管道中间很大范围内以上3个局部界面参数几乎恒定,近壁区迅速下降到较低值;随气相流速的增加,局部界面参数在管道中心出现峰值。本实验中气泡聚合与破碎现象较少发生,索特平均直径沿径向近似均匀分布,且随气液两相流速变化很小。通过气泡横向受力解释了局部界面参数分布的影响机理。     

Upward air–water bubbly flow characteristics in a vertical square duct

In nuclear engineering fields, gas–liquid bubbly flows exist in channels with various shape and size cross-sections. Although many experiments have been carried out especially in circular pipes, those in a noncircular duct are very limited. To contribute to the development of gas–liquid bubbly flow model for a noncircular duct, detail measurements for the air–water bubbly flow in a square duct (side length: 0.136 m) were carried out by an X-type hot-film anemometry and a multi-sensor optical probe. Local flow parameters of the void fraction, bubble diameter, bubble frequency, axial liquid velocity and turbulent kinetic energy were measured in 11 two-phase flow conditions. These flow conditions covered bubbly flow with the area-averaged void fraction ranging from 0.069 to 0.172. A pronounced corner peak of the void fraction was observed in a quarter square area of a measuring cross-section. Due to a high bubble concentration in the corner, the maximum values of both axial liquid velocity and turbulent kinetic energy intensity were located in the corner region. It was pointed out that an effect of the corner on accumulating bubble in the corner region changed the distributions of axial liquid velocity and turbulent kinetic energy intensity significantly.     

Mitigation Technologies for Damage Induced by Pressure Waves in High-Power Mercury Spallation Neutron Sources (III)—Consideration of the Effect of Microbubbles on Pressure Wave Propagation through a Water Test—

The effects of microbubbles dispersed in a liquid on a high-rising-rate pressure wave were experimentally investigated with water. Intense, high-rising-rate pressure waves with a rise time of about 1.5 ms were produced by a spark discharge in water, and gas microbubbles were produced by two different bubble generators. Particular attention was focused on the attenuation effect of microbubbles on propagating pressure waves. The dependence of the attenuation effect on the radius and void fraction of the microbubbles was carefully examined. It was found that when the microbubbles are sufficiently small (e.g., about 50 μm in peak radius), the amplitude of wall vibration induced by the spark-induced pressure wave is dramatically decreased with an increase in void fraction. The present study provides strong experimental evidence that microbubbles can act as a strong absorber for high-rising-rate pressure waves as recently predicted numerically.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.     

水平管泡状流液相速度分布与相分布

用热膜探针测量了内径为 3 5mm的水平管泡状流中的液流速度 ,同时用双头电导探针测量了有关的相界面参数 ,结果表明 ,局部液流平均速度在靠管道下部的分布与单相液流的分布类似 ,在靠管道上部突然减小 ;局部液流平均速度在靠管道下部随气流折算速度的增加而增加 ,在靠管道上部则随气流折算速度的增加而减小 ;局部含气率和气泡频率随气流折算速度的增加而增大 ,在靠近管道上壁处有一峰值 ,其分布规律随液流速度的增加而趋向均匀     

Numerical study of a bubble plume generated by bubble entrainment from an impinging jet

The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k–? model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX.According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface.A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.     

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s⁻¹, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s⁻¹. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.     

On the modelling of bubbly flow in vertical pipes

To qualify CFD codes for two-phase flows, they have to be equipped with constitutive models standing for the interaction between the gaseous and the liquid phases. In case of bubbly flow this particularly concerns the forces acting on the bubbles and bubble coalescence and break-up. Applying a two fluid approach, besides the drag forces describing the momentum exchange in flow direction, the non-drag forces acting perpendicular to the flow direction play an important role for the development of the flow structure. Gas–liquid flow in vertical pipes is a very good object for studying the corresponding phenomena. Here, the bubbles move under clear boundary conditions, resulting in a shear field of nearly constant structure where the bubbles rise for a comparatively long time. The evolution of the flow within the pipe depends on a very complex interaction between bubble forces and bubble coalescence and break-up, e.g. the lift-force, which strongly influences the radial distribution of the bubbles, changes its sign depending on the bubble diameter. The consequence is the radial separation of small and large bubbles. Neglecting this phenomenon, models are not able to describe the correct flow structure. Extensive experiments measuring the radial gas volume fraction distribution, the bubble size distribution and the radial residence of bubbles dependent on their size were determined for different distances from the gas injection. Basing on these experiments the applicability and the limits for the simulation of bubble flow with current CFD-codes are demonstrated, using the simulation of vertical pipe flow with CFX-4 as an example. Using a simplified model focusing particularly on the radial phenomena described above, parametric studies were conducted. They give an indication for necessary improvements of the codes. Finally a possible way for the improvement of the CFD-codes is shown.     

Influence or Void and Flow Regime on Liquid Metal MHD Induction Generator Using Two-Phase Flow

In the present paper, the performance characteristics of a liquid metal MHD induction converter operated with two-phase mixture flow are treated experimentally and analytically in comparison with those with single-phase liquid flow as working fluid.

The experiments were performed with a flat-linear channel induction converter, through which NaK-N₂ two-phase mixture was made to flow at a velocity ranging 5–30m/sec, with a void fraction 0–50%.

Data were taken over the following range of non-dimensional parameters:

• Reynolds number: 3.3x10⁴–2.0x10⁵ (for liquid flow alone)

• Hartmann number: 12 (with magnetic field in r.m.s. and slip S = 1)

• Baroczy's property index: 0.0031–0.023 (for two-phase flow)

The electrical power output of the experimental generator showed a sudden decrease near 20% void fraction, which was attributed to change in the flow pattern, while the generator efficiency did not show such an abrupt drop, but decreased gradually with increase of the void fraction.

Coupling the electro-magnetic equations with the power law distribution for both fluid velocity and void fraction proposed by Bankoff, we have obtained numerically the performance characteristics of the liquid metal MHD induction converter operated with two-phase flow, which provided a quite satisfactory clarification of the results obtained experimentally.     

Characteristics of Counter current Gas-Liquid Two-Phase Flow in Vertical Tubes

Investigations into the flow pattern and the void fraction for countercurrent air-water flow in vertical tubes of diameter D = 40 and 80 mm were reported. The flow maps were presented and showed slug flow regime occupied larger portion on them. The void fraction was measured by the quick-closing valve technique, in bubbly and slug flow regime.

The void fraction data available in the literatures as well as present work for counter- current flow in vertical tubes were correlated in terms of dimensionless groups. The experimental results of the present work were also compared with the drift flux model.     

竖直窄矩形通道内弹状流液弹中分区特性研究

弹状流的液弹部分受气弹尾部影响,其水力特性参数沿流动方向存在分区的不一致性。本文对竖直窄矩形通道中弹状流液弹内参数的分布特性进行了研究。结果表明：液弹内气泡在近壁面附近所受径向力较为平衡,气泡频率较大;随着远离气弹尾部,管道中间气泡频率逐渐增大。根据气泡频率波动变化将液弹分为3个区域,尾流区占液弹长度的40%～45%,过渡区占10%～15%,主流区占40%～50%。尾流区和主流区内,空泡份额呈“三峰型”分布;随着气相流速的增加,尾流区内近壁面处峰值逐渐增大,管道中间峰值逐渐下降,但主流区内情况相反。气泡直径随气相流速的增大而变大,且液弹内气泡聚合和破碎现象较少。