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.     

Measurement of Liquid Turbulent Structure in Bubbly Flow at Low Void Fraction Using Ultrasonic Doppler Method

Microscopic structure in bubbly flows has been a topic of interest in the study of fluid dynamics. In the present paper, the ultrasonic Doppler method was applied to the measurement of bubbly. The experiments were carried out for an air-water dispersed bubbly flow in a 20 mm × 100 mm vertical rectangular channel having a void fraction smaller than 3%. Two ultrasonic transducers were installed on the outer surface of the test section with a contact angle of 45^° off the vertical axis, one facing upward and the other facing downward. By applying statistical methods to the two directional velocity profiles, Reynolds stress profiles were calculated. Furthermore, to clarify the wake effect induced by the leading bubbles, the velocity profiles were divided into two types of data. The first one is for all of the liquid data and the other is the data which did not include the wake effect. For Re_m ≥1,593, it was observed that the bubbles suppressed the liquid turbulence. Furthermore, comparing with the Reynolds stress profiles in bubbly flow, it was found that Reynolds stress profiles varied with the amount of bubbles present in the flow and the effect of wake causes turbulence in the liquid.     

Modified two-fluid model for the two-group interfacial area transport equation

This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model.     

Effect of Gas Introduction on Temperature Distribution for Tube Flow with Internal Heat Sources

An experimental study has been conducted to investigate the effect of gas introduction on the heat transfer characteristics for turbulent flow of a heat generating liquid in an adiabatic tube 20 mm in inside diameter. Heat generation within the fluid was brought about by passing an alternating current through the working fluid, which was an aqueous solution of sodium chloride mixed with air bubbles. The superficial liquid Reynolds number ranged 3,700–11,000. The quality was varied from 2.6×10^?5 to 3.3×l0^?3. Measurements were made of the temperature distributions in the fluid as well as on the tube wall. The experimental results were compared with theoretical analyses.

In bubbly flow; the introduction of air into liquid brought forth a flat temperature distribution due to a considerable increase of turbulence and a saddle-shaped void distribution, which had a maximum near the tube wall. In slug flow, however, the void distribution changed to a dome-shaped profile with a maximum at the tube center and the rate of heat generation was higher near the wall than in the center region, resulting in a steep temperature distribution.     

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。     

Two-group interfacial area transport in vertical air-water flow: I. Mechanistic model

The prediction of the dynamical evolution of interfacial area concentration is one of the most challenging tasks in two-fluid model application. This paper is focused on developing theoretical models for interfacial area source and sink terms for a two-group interfacial area transport equation. Mechanistic models of major fluid particle interaction phenomena involving two bubble groups are proposed, including the shearing-off of small bubbles from slug/cap bubbles, the wake entrainment of spherical/distorted bubble group into slug/cap bubble group, the wake acceleration and coalescence between slug/cap bubbles, and the breakup of slug/cap bubbles due to turbulent eddy impacts. The existing one-group interaction terms are extended in considering the generation of cap bubbles, as well as different parametric dependences when these terms are applied to the slug flow regime. The complete set of modeling equations is closed and continuously covers the bubbly flow, slug flow, and churn-turbulent flow regimes. Prediction of the interfacial area concentration evolution using a one-dimensional two-group transport equation and evaluation with experimental results are described in a companion paper.     

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.     

Pressure wave propagation in air-water bubbly and slug flow

Related to nuclear reactor safety problems, such as the loss of coolant accident caused by some small crevasses in nuclear reactor, choked flows after postulated breaks of hot and cold legs of pressurized water reactors and the boiling flow instability in parallel channels, the characteristics of pressure wave propagation were investigated experimentally for the air-water bubbly and slug two-phase flow in a vertical pipe. Pressure wave was generated from the small pressure disturbance by the up-and-down movement of piston in the test section. Air void fraction was up to 0.7 and superficial liquid velocity was up to 1.5 m/s as experimental conditions. The experimental results show that the pressure wave propagation velocity in bubbly flow decreases acutely with the increase of air void fraction from 0 to 0.05. In slug flow, it is constant when the air void fraction is less than 0.5 but increases gradually when the void fraction increases beyond 0.5. The attenuation coefficient of pressure wave increases with the increase of air void fraction in bubbly flow. The dependency of pressure wave propagation velocity on angle frequency ω in air-water flow shows the dispersion characteristic. The propagation velocity and attenuation coefficient increases gradually with the increase of angle frequency. However, the increase vanishes slowly as the angle frequency reaches 250 Hz in bubbly flow. The propagation of pressure wave in bubbly flow is independent of the superficial velocity of fluids in the range of experiment.     

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.     

Modeling of bubble coalescence and disintegration in confined upward two-phase flow

This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas–liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas–liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equation in the confined flow. These models include both intra-group and inter-group bubble interactions.     

Nuclear magnetic resonance: A new tool for the validation of multiphase multidimensional CFD codes

Turbulent transport models and data in bubbly flows are briefly reviewed since they play an important role in the modeling of boiling flows in forced convection. Shortcomings of earlier measurements of the eddy diffusivity by NMR (Lemonnier and Leblond, 2007b) are analyzed and a new procedure is presented which is now consistent with the procedure of Gatenby and Gore (1994) developed for single-phase turbulent flow characterization. The newly estimated eddy diffusivity agrees now with that previously obtained by Serizawa et al. (1975b) with a thermal method and that of the model of Sato and Sadatomi (1981). This procedure also provides the liquid velocity fluctuation RMS and the Lagrangian correlation time of velocity fluctuations. In addition, the same NMR technique provides also the area-averaged liquid velocity and void fraction. Bubbly flow data up to transition to slug flow are provided which also agree with existing drift-flux models (Ishii and Hibiki, 2006). It is finally discussed how the NMR method can be extended to local measurements and may provide a fully non-intrusive diagnostic in two-phase flows and which is not limited to bubbly flow.     

Numerical simulation of lateral phase distribution in turbulent upward bubbly two-phase flows

New constitutive models for the interfacial forces acting on bubbles were developed for accurately predicting the lateral phase distribution in turbulent bubbly two-phase flow in vertical channels. Several experimental measurements have revealed that the lateral void profile in bubbly two-phase flow varies from the void peaking near the wall to the almost flat distributions as the liquid velocity increases. However, within the authors' knowledge, the effect of liquid velocity on the void profile has not been successfully predicted by the existing models; this would indicate the strong limitation of the existing multidimensional two-phase flow models. In view of these, the validity of the present constitutive models was tested in varied conditions of the liquid velocity as well as the bubble size. Since several assumptions were required in the models mainly due to the insufficient knowledge of the bubble motion, further improvements should still be needed. Nevertheless, the predicted lateral phase distributions were found to be in reasonably good agreement with available experimental data. It is hence expected that the present constitutive models can effectively be used in the practical applications and also be the base of the more sophisticated ones.     

用热膜测速仪测量水平管内气液泡状流的液相速度和紊流结构

对热膜测速仪应用于气液两相泡状流中的测量方法进行了研究。提出了一套全新的相鉴别技术，用此方法对水平管内的气液两相泡状流的液相速度和紊流强度进行了测量。并对液相水质及温度对测量结果的影响进行了探讨。实验结果表明．在水平管泡状流中．靠管道下部液流速度和紊流强度分布与单相液流的分布差别不大；管道上部较多的气泡使两相液流速度明显低于单相液流速度，增强了紊流强度；使紊流强度分布在r／R=0．5附近有一峰值。     

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

The authors have developed a measurement system which is composed of an ultrasonic velocity profile monitor and a video data processing unit in order to clarify its multi-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for multi-dimensional two-phase flow. In this paper, the measurement system was applied for bubbly countercurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. Next, turbulence intensity in a continuous liquid phase was defined as a standard deviation of velocity fluctuation, and the two-phase multiplier profile of turbulence intensity in the channel was clarified as a ratio of the standard deviation of flow fluctuation in a bubbly countercurrent flow to that in a water single phase flow. Finally, the distribution parameter and drift velocity used in the drift flux model for bubbly countercurrent flows were calculated from the obtained velocity profiles of both phases and void fraction profile, and were compared with the correlation proposed for bubbly countercurrent flows.     

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。     

Internal structure and interfacial velocity development for bubbly two-phase flow

This paper describes an experimental study of the internal structure of air-water flowing horizontally. The double-sensor resistivity probe technique was applied for measurements of local interfacial parameters, including void fraction, interfacial area concentration, bubble size distributions, bubble passing frequency and bubble interface velocity. Bubbly flow patterns at several flow conditions were examined at three axial locations, L/D = 25, 148 and 253, in which the first measurement represents the entrance region where the flow develops, and the second and third may represent near fully developed bubbly flow patterns. The experimental results are presented in three-dimensional perspective plots of the interfacial parameters over the cross-section. These multi-dimensional presentations showed that the local values of the void fraction, interfacial area concentration and bubble passing frequency were nearly constant over the cross-section at L/D = 25, with slight local peaking close to the channel wall. Although similar local peakings were observed at the second and third locations, the internal flow structure segregation due to buoyancy appeared to be very strong in the axial direction. A simple comparison of profiles of the interfacial parameters at the three locations indicated that the flow pattern development was a continuous process. Finally, it was shown that the so-called “fully developed” bubbly two-phase flow pattern cannot be established in a horizontal pipe and that there was no strong correspondence between void fraction and interface velocity profiles.     

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.     

Experimental Study on Gas Carry-Under in Liquid Down Flow from a Two-Phase Mixture

The gas carry-under characteristics in liquid down flow from a two-phase mixture flow have been studied for various flow parameters, based on experiments with a small scale air- water system simulating the concept of a natural circulation BWR with no separators. For high void fraction in the riser, as the liquid superficial velocity jf increased to 0.17 m/s, the void fraction in the lower part of the downcomer αd increased sharply due to the descent of comparatively large bubbles (diameter: about 4–6mm). In the region of jf> 0.17m/s, on increasing jf, the void fraction αd increased until it reached a maximum value at jf.3. For liquid descending velocities higher than 0.3 m/s, αd became almost constant and the level of the mixture above the riser had little effect on the void fraction ad due to the phase separation of the large bubbles formed by bubble coalescence in the upper part of the downcomer. The void fraction αd increased as the void fraction αr increased until bubble coalescence occurred in the upper part of the downcomer, and αd became constant and independent of αr after the occurrence of bubble coalescence. Under the conditions of high void fractions in the riser, 0.4<αr<0.64 (upper limit of the tests), and high liquid descending velocities in the down-comer, 0.3 m/s<jf.<0.4 m/s (upper limit of the tests), the void fraction αd was represented by a dimensionless number (G = η⁴ g/σ³ pf) and by the upper limit of void fractions in bubbly flow, αd=0.3.     

竖直窄矩形通道内空气-水两相流中气弹运动速度研究

以空气和水为工质,应用高速摄像仪,对竖直窄矩形通道(3.25 mm×40 mm)内气液两相弹状流进行了可视化实验研究。气、液相表观速度分别为0.1~2.51 m/s和0.16~2.62 m/s,工作压力为常压。实验中发现窄矩形通道内弹状流与圆管中存在较大差别,气弹多发生变形,高液相流速时变形更为严重。窄边液膜含气量较高,在高液相流速时窄边液膜不下落,宽边液膜中含有由气弹头部进入和气弹尾部进入的气泡。气弹速度受气弹头部形状和宽度影响较大,受气弹长度影响较小。气弹速度可由Ishii & Jones-Zuber模型计算,但在低液相折算速度时偏差较大,其主要原因为漂移速度计算值较实验值偏小。     

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.