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.     

Geometric effects of 90-degree Elbow in the development of interfacial structures in horizontal bubbly flow

Present study investigates the geometric effects of flow obstruction on the distribution of local two-phase flow parameters and their transport characteristics in horizontal bubbly flow. The round glass tubes of 50.3 mm in inner diameter are employed as test sections, along which a 90-degree Elbow is located at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions are examined within the air–water bubbly flow regime. The detailed local two-phase flow parameters are acquired by the double-sensor conductivity probe at four different axial locations. The effect of elbow is found to be evident in both the distribution of local parameters and their development. The elbow clearly promotes bubble interactions resulting in significant changes in interfacial area concentration. It is also found that the elbow-effect propagates to be more significant further downstream (L/D = 250) than immediate downstream (L/D = 225) of the elbow. Furthermore, it is shown that the elbow induces significant oscillations in the flow in both vertical and horizontal directions of the tube cross-section. Characteristic geometric effects due to the existence of elbow are also shown clearly in the transport of one-dimensional interfacial area concentration and void fraction along the flow.     

Horizontal bubbly flow with elbow restrictions: Interfacial area transport modeling

The present study develops an interfacial area transport equation applicable to an air-water horizontal bubbly flow, along which two types of horizontal elbows are installed as flow restrictions. Two sets of experiments are performed in a round glass tube of 50.3 mm inner diameter. Along the test section, a 90-degree elbow is installed at L/D = 206.6 from the two-phase mixture inlet and then a 45-degree elbow is installed at L/D = 353.5. In total, 15 different flow conditions in the bubbly flow regime for each of the two flow restriction experiments are studied. Detailed local two-phase flow parameters are acquired by a double-sensor conductivity probe at four different axial locations in the 90-degree experiment and three different axial locations in the 45-degree experiment. The effect of the elbows is found to be evident in the distribution of local parameters as well as in the development of interfacial structures. It is clear that the elbows make an effect on the bubble interactions resulting in significant changes to both the void fraction and interfacial area concentration. In the present analysis, the interfacial area transport equation is developed in one-dimensional form via area averaging. In the averaging process, characteristic non-uniform distributions of the flow parameters in horizontal two-phase flow are treated mathematically through a distribution parameter. The mechanistic models for the major bubble interaction phenomena developed in vertical flow analysis are employed in the present study. Furthermore, the change in pressure due to the minor loss of an elbow is taken into consideration by using a newly developed correlation analogous to Lockhart and Martinelli's. In total, 105 area-averaged data points are employed to benchmark the present model. The present model predicts the data relatively well with an average percent difference of approximately ±20%.     

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.     

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。     

Local measurement of bubbly flow in helically coiled tubes using double-sensor conductivity probe

ABSTRACT

The two-phase flow in helically coiled tubes (HCTs) is rather important in many industries, such as the heat exchange facility in nuclear power plant. In this work, a double-sensor conductivity probe was used to study the air/water bubbly flow in HCTs. The cross-sectional distribution profile of the interfacial parameters (void fraction, interfacial area concentration, bubble size, etc.) of air–water bubbly flow were systematically studied. Through carefully processing the raw data collected by the double-sensor conductivity probe, the distribution of the void fraction, interfacial area concentration, the bubbles number frequency over the cross-section are demonstrated, as well as the bubble velocities and sizes vertically in the dense region. Some statistical parameters of cross-sectional-averaged quantities, coefficients of variation, and bubble aggregation core coordinates are defined to quantitatively describe the distribution characteristics of interfacial parameters. The measured data are helpful for improving the understanding of two-phase flow characteristics in HCTs.     

Measurement and modeling of average void fraction, bubble size and interfacial area

The local void fraction, bubble size and interfacial area concentration for co-current air-water bubbly flow through a horizontal pipe of 50.3 mm internal diameter were investigated experimentally using the double-sensor resistivity probe method. The local and area-averaged void fractions and interfacial area concentrations were analyzed as a function of liquid and gas flow rates. These parameters were found to increase systematically with decreasing liquid flow and increasing gas flow. However, variations with the liquid flow were not as significant as with the gas flow. A consistent variation of the gas phase drift velocity and distribution parameter with the liquid flow rate was observed. It was demonstrated that presentation of the average void fraction in terms of flowing volumetric concentration was more appropriate for horizontal bubbly flow. Several bubble break-up mechanisms were discussed. It was concluded that average pressure fluctuations generated by the turbulent liquid fluctuations acting across a bubble diameter are the only mechanism which causes distortion of a bubble. Based on this force and the competing surface tension force, a theoretical model was developed for mean bubble size and interfacial area concentration. The theoretically predicted mean bubble size and interfacial area concentration were found to agree reasonably well with those measured by the double-sensor resistivity method.     

Measurement of interfacial area concentration in subcooled liquid-vapour flow

In two-fluid modelling, accurate prediction of the interfacial transport of mass, momentum and energy is required. Experiments were carried out to obtain a database for the development of interfacial transport models, or correlations, for subcooled water-steam flow in vertical conduits. The experimental data of interest included the interfacial area concentration, interfacial condensation heat transfer and bubble relative velocity. This paper focuses on the interfacial area concentration. The interfacial area concentration was obtained by measuring the distributions of bubble volume and surface area as well as the area-averaged void fraction at various axial locations in subcooled water-steam condensing vertical upward flow under low flow rate and low pressure conditions. The bubble size and surface area were determined using high-speed photography and digital image processing techniques. The area-averaged void fraction was measured by a single-beam gamma densitometer. The results were compared with existing correlations, which were developed on the basis of data obtained for air-water adiabatic flows. Poor agreement between the present data and the existing correlations was obtained. Accordingly, new correlations suitable for subcooled liquid-vapour bubbly flow are proposed.     

竖直圆管中泡状流含汽率径向分布的统计测量方法

为了研究竖直圆管中高含汽率泡状流的含汽率径向分布,设计了一种测量含汽率径向分布的方法.该方法通过统计投影视图中的像素信息得到泡状流的投影含汽率,根据汽泡投影重叠概率计算出截面含汽率在投影面上的边缘分布;再基于竖直圆管中含汽率分布轴对称的假设,使用改进的傅里叶级数展开方法求解Abel逆变换,计算出含汽率沿圆管径向的分布.为验证该方法的有效性,测量了较低含汽率时的泡状流径向含汽率,并与匹配方法的测量结果进行比较.实验结果表明:此方法能得到高含汽率或含汽率近壁分布等其他方法难以测量的含汽率分布.     

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.     

基于竖直圆管空气-水两相流实验的相间曳力模型研究

研究两相流相间阻力特性对系统程序关键本构模型封闭具有重要意义。本文基于竖直圆管开展了空气-水两相流实验,采用四探头电导探针对空泡份额、气泡弦长和界面面积浓度等气泡参数的径向分布进行了测量。结果表明空泡份额和气泡弦长呈现“核峰型”分布,而界面面积浓度并没有表现出随流速的单调关系。进一步开发了泡状流和弹状流的相间曳力模型,考虑了液相表观流速与管径对气泡尺寸分布的影响,建立了临界韦伯数与不同液相流速的关系。计算得到的空泡份额和界面面积浓度与实验数据整体符合较好,验证了模型的可靠性,为两相流相间阻力特性研究提供参考意义。     

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。     

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.     

螺旋直径对螺旋管泡状流截面分布特性的影响

研究了不同螺旋直径螺旋管中泡状流的相界面参数（空泡份额、相界面浓度、气泡尺寸等）的截面分布特性。通过图像法标定了电导探针的测试精度,并通过合理地处理双头电导探针,得到了螺旋管中泡状流的空泡份额、相界面浓度和气泡数量频率的定量分布云图。为进一步量化地描述相界面参数的分布特征,采用统计方法定义了截面平均参数、相界面离散系数和气泡平均聚集坐标来表征其特性。实验结果表明,随着管道旋转直径的增大,气泡截面平均空泡份额有所下降,分布范围缩小,平均聚集坐标向上方和外侧移动,气泡尺寸整体上有所下降。     

Numerical study of the influence of the internal structure of a horizontal bubbly flow on the average void fraction

This paper presents the results of a numerical experiment aimed to study the influence of the void fraction profile on integral flow characteristics of horizontal bubbly flows. To perform this analysis, a particular model which reflects better both the effect of non-uniform flow and concentration profiles as well as the effect of the local relative velocity between the phases than the well known drift flux model, was used. The relative phase velocity has been estimated by considering the movement of a single bubble in a liquid flow having a non-uniform velocity distribution. The analysis has shown that, in the case of strongly gravity-skewed local void fraction profiles, the volumetric flow quality β can be smaller than the average void fraction 〈α〉. This 〈α〉-β relationship is conditioned by the fact that the corresponding distribution parameter is less than 1, while the void fraction weighted average relative velocity of the gas phase is negative.     

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。     

On the stability of a one-dimensional two-fluid model

An analysis on the stability of the governing differential equations for area averaged one-dimensional two-fluid model is presented. The momentum flux parameters for gas and liquid are introduced to incorporate the effect of void fraction profiles and velocity profiles. The stability of the governing differential equations is determined in terms of gas and liquid momentum flux parameters. It is shown that the two-fluid model is well posed with certain restrictions on the liquid and gas momentum flux parameters. Simplified flow configurations for bubbly flow, slug flow, and annular flow are constructed to test the validity of proposed stability criteria. The momentum flux parameters are calculated for these flow configurations by assuming a power-law profile for both velocity and void fraction. Existing correlation for volumetric distribution parameter C_o is used. By employing simplified velocity profiles, the void fraction profile is determined from C_o correlation. It is found that the void fraction is wall-peaked at low void fraction and it becomes center-peaked as the void fraction increases. A simplified annular flow is also constructed. With these flow configurations, the momentum flux parameters are determined. It is shown that the calculated momentum flux parameters are located in the stable region above the analytically determined stability boundary. The analyses results indicate that the use of momentum flux parameter is promising, since they reflect flow structure and help to stabilize the governing differential equations.     

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     

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit, (III)

The authors have developed a new measurement system which consisted of an Ultrasonic Velocity Profile Monitor (UVP) and a Video Data Processing Unit (VDP) in order to clarify the two-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for two-dimensional two-phase flow. In the present paper, the proposed measurement system is applied to fully developed bubbly cocurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. In addition, the two-phase multiplier profile of turbulence intensity, which was defined as a ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow, were examined. Next, these flow characteristics were compared with those in bubbly countercurrent flows reported in our previous paper. Finally, concerning the drift flux model, the distribution parameter and drift velocity were obtained directly from both bubble and water velocity profiles and void fraction profiles, and their results were compared with those in bubbly countercurrent flows.     

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors.This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX.The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.