Scaling of damping induced by bubbly flow across tubes

The damping of tubes subjected to two-phase air–water bubbly cross-flow is investigated with the use of an experimental database from several authors. A new definition of damping in stagnant flow is proposed using an extrapolation of the measured values at low dimensionless flow velocities. This approach yields values of damping substantially lower than those currently defined in the literature. They are found to vary continuously with void fraction, within the bubbly flow regime. These data are used to compare several models of the equivalent viscosity of a two-phase mixture. The effect of the flow velocity is then analysed up to fluidelastic instability. It is observed that, using scaling factors based on the characteristics of the liquid phase, fluidelastic effects of bubbly flows are closely related to those known in single-phase flows.     

微重力气/液两相泡状流的摩擦压降

针对微重力条件下气／液两相泡状流动特征,建立了其摩擦压降的半理论模型：ｆＴＰ＝ＡＲｅ＾－１ＴＰ,并利用献报道的微重力实验数据,确定了模型参数Ａ的数值。     

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

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.     

水平管道气固两相分层流动过程的研究

以空气作为输送动力、粉煤灰及玻璃微珠作为输送物料,对气力输送管道中气固两相流的流动特性进行了系统的试验研究.对管路系统的特性、操作条件、物料和气体的性质等影响气固两相流压力损失的主要因素进行了探讨.并在实验的基础上对两相流动的沉积速度、经济速度进行了确定.同时在对粉体受力分析的基础上建立了分层流动的物理及数学模型,通过对比数学模型计算值与试验值得出该数学模型具有一定的计算精度,能够用于指导分层流动的研究及应用.     

Investigation on two-phase flow-induced vibrations of a piping structure with an elbow

The dynamic behaviors of a horizontal piping structure with an elbow due to the two-phase flow excitation are experimentally investigated. The effects of flow patterns and superficial velocities on the pressure pulsations and vibration responses are evaluated in detail. A strong partition coupling algorithm is used to calculate the flow-induced vibration (FIV) responses of the pipe, and the theoretical values agree well with the experimental results. It is found that the lateral and axial vibration responses of the bend pipe are related to the momentum flux of the two-phase flow, and the vibration amplitudes of the pipe increase with an increase in the liquid mass flux. The vertical vibration responses are strongly affected by the flow pattern, and the maximum response occurs in the transition region from the slug flow to the bubbly flow. Moreover, the standard deviation (STD) amplitudes of the pipe vibration in three directions increase with an increase in the gas flux for both the slug and bubbly flows. The blockage of liquid slugs at the elbow section is found to strengthen the vibration amplitude of the bend pipe, and the water-blocking phenomenon disappears as the superficial gas velocity increases.     

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.     

An experimental study on developing air-water two-phase flow along a large vertical pipe: effect of air injection method

The flow structure in a developing air-water two-phase flow was investigated experimentally along a large vertical pipe (inner diameter, D_h: 0.48 m, ratio of length of flow path L to D_h: about 4.2). Two air injection methods (porous sinter injection and nozzle injection) were adopted to realize an extremely different flow structure in the developing region. The flow rate condition in the test section was as follows: superficial air velocity: 0.02–0.87 m/s (at atmospheric pressure) and superficial water velocity: 0.01–0.2 0.01–0.2 m/s, which covers the range of bubbly to slug flow in a small-scale pipe (D_h about 0.05 m).

No air slugs occupying the flow path were recognized in this experiment regardless of the air injection methods even under the condition where slug flow is realized in the small-scale pipe. In the lower half of the test section, the axial distribution of sectional differential pressure and the radial distribution of local void fraction showed peculiar distributions depending on the air injection methods. However, in the upper half of the test section, the effects of the air injection methods are small in respect of the shapes of the differential pressure distribution and the phase distribution. The comparison of sectional void fraction near the top of the test section with Kataoka's correlation indicated that the distribution parameter of the drift-flux model should be modeled including the effect of D_h and the bubble size distribution is affected by the air injection methods. The bubble size distribution is considered to be affected also by L/D_h based on comparison of results with Hills' correlation.     

Degassing of water-solved gases in thin pipings during fast pressure drops

 A one-dimensional model is presented, which describes the transient two-phase flow in thin pipes during fast pressure drops and degassing by use of Eulerian and Lagrangian systems. The reduction in dimension is obtained by introduction of a geometry model for bubbly and slug flow regimes. The complete model includes the transient two-phase flow, bubble formation and bubble growth. The flow model predicts rising velocities of bubbles and plugs in arbitrary inclined highly accurate pipes. The mass transfer (diffusion) of the dissolved phase is calculated by the bubble growth model. The quality of the model was examined by simulation of experimental series, whereby water was depressurised from the saturation pressure of the dissolved gas mixture (air), by variation of saturation pressure, pressure gradient and pipe geometry. The results of numerical simulation fit the experimental data well. Received on 17 January 2000     

Estimation of solid concentration in solid–liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study, an inverse-problem method was applied to estimate the solid concentration in a solid–liquid two-phase flow. An algebraic slip mixture model was introduced to solve the forward problem of solid–liquid convective heat transfer. The time-average conservation equations of mass, momentum, energy, as well as the volume fraction equation were computed in a computational fluid dynamics (CFD) simulation. The solid concentration in the CFD model was controlled using an external program that included the inversion iteration, and an optimal estimation was performed via experimental measurements. Experiments using a fly-ash–water mixture and sand–water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method. The estimated results were rectified using a method based on the relationship between the estimated results and estimation error; consequently, the accuracy of the corrected inversion results improved significantly. After a verification through experiments, the inverse-problem method was concluded to be feasible for predicting the solid concentration, as the estimation error of the corrected results was within 7% for all experimental samples for a solid concentration of less than 50%. The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid–liquid two-phase flow systems.     

Damping of tubes due to internal two-phase flow

Two-phase internal flow is present in many piping system components. Although two-phase damping is known to be a significant constituent of the total damping, the energy dissipation mechanisms that govern two-phase damping are not well understood. In this paper, damping of three different clamped–clamped tubes subjected to two-phase air–water internal axial flow is investigated. Experimental data are reported, showing a strong dependence of two-phase damping on void fraction, flow velocity and flow regime. Data-points plotted on two-phase flow pattern maps indicate that damping is greater in a bubbly flow regime. The two-phase damping ratio reaches a maximum value at the highest void fraction before the transition to a churn flow regime. An analytical model that relates the two-phase damping ratio to the interface surface area is proposed. The model is based on rigid spherical bubbles in cubic elementary flow volumes. The analytical results are well correlated with the experiments.     

明渠气二相流的双流体模型

从解决平均二相流基本方程的封闭问题出发,分析了水利工程中气水二相流的特点,介绍了据此提出的可用于水利工程稀疏气泡流计算的双流体模型,并对明渠气水二相流进行了算例验证。     

Shock-wave formation in flowing bubbly mixtures by steepening of compression waves

The formation and propagation of shock waves in a two-component flowing bubbly mixture has been investigated experimentally. The structure of shock waves formed by steepening of compression waves is compared with the corresponding features of shocks produced spontaneously in shock tubes. Experimentally determined values of the speed of propagation of the shock compare favorably with the Hugoniot relationship based upon a homogeneous two-phase model. The effect of the gravitational and frictional pressure gradients on the shock characteristics is also examined.     

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.     

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor

Two-phase flow measurements were carried out using a resistive void fraction meter coupled to a venturi or orifice plate. The measurement system used to estimate the liquid and gas mass flow rates was evaluated using an air–water experimental facility. Experiments included upward vertical and horizontal flow, annular, bubbly, churn and slug patterns, void fraction ranging from 2% to 85%, water flow rate up to 4000 kg/h, air flow rate up to 50 kg/h, and quality up to almost 10%. The fractional root mean square (RMS) deviation of the two-phase mass flow rate in upward vertical flow through a venturi plate is 6.8% using the correlation of Chisholm (D. Chisholm, Pressure gradients during the flow of incompressible two-phase mixtures through pipes, venturis and orifice plates, British Chemical Engineering 12 (9) (1967) 454–457). For the orifice plate, the RMS deviation of the vertical flow is 5.5% using the correlation of Zhang et al. (H.J. Zhang, W.T. Yue, Z.Y. Huang, Investigation of oil–air two-phase mass flow rate measurement using venturi and void fraction sensor, Journal of Zhejiang University Science 6A (6) (2005) 601–606). The results show that the flow direction has no significant influence on the meters in relation to the pressure drop in the experimental operation range. Quality and slip ratio analyses were also performed. The results show a mean slip ratio lower than 1.1, when bubbly and slug flow patterns are encountered for mean void fractions lower than 70%.