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.     

Monte-Carlo calculation of the calibration factors for the interfacial area concentration and the velocity of the bubbles for double sensor conductivity probe

This paper presents a study of the estimation of the correction factors for the interfacial area concentration and the bubble velocity in two phase flow measurements using the double sensor conductivity probe. Monte-Carlo calculations of these correction factors have been performed for different values of the relative distance (ΔS/D) between the tips of the conductivity probe and different values of the relative bubble velocity fluctuation parameter. Also this paper presents the Monte-Carlo calculation of the expected value of the calibration factors for bubbly flow assuming a log-normal distribution of the bubble sizes. We have computed the variation of the expected values of the calibration factors with the relative distance (ΔS/D) between the tips and the velocity fluctuation parameter. Finally, we have performed a sensitivity study of the variation of the average values of the calibration factors for bubbly flow with the geometrical standard deviation of the log-normal distribution of bubble sizes. The results of these calculations show that the total interfacial area correction factor is very close to 2, and depends very weakly on the velocity fluctuation, and the relative distance between tips. For the velocity calibration factor, the Monte-Carlo results show that for moderate values of the relative bubble velocity fluctuation parameter (H_max ≤ 0.3) and values of the relative distance between tips not too small (ΔS/D ≥ 0.2), the correction velocity factor for the bubble sensor conductivity probe is close to unity, ranging from 0.96 to 1.     

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.     

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.     

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。     

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.     

Interfacial measurements in horizontal stratified flow patterns

The interfacial characteristic parameters of horizontal stratified wavy flow patterns were experimentally investigated for a mixture of air and water two-phase flow by using the double-sensor, parallel wire conductance probe method. The experiments were conducted in a horizontal flow loop 15.4 m long consisting of Pyrex glass tubing of 50.3 mm i.d. The range of gas superficial velocities was from 0.85 to 31.67 ms⁻¹ and the liquid superficial velocities ranged from 0.014 to 0.127 ms⁻¹. Several interfacial wave patterns as described by Andritsos and Hanratty (Int. J. Multiphase Flow 13 (1987a) 583–603) were identified and their characteristic parameters such as wave height, most dominant frequency, mean propagation velocity and mean wavelength were investigated in terms of liquid and gas flow rates. The interfacial shear stress calculated from the experimental measurements was used to evaluate the most widely used interfacial shear models.     

Non-stationary outflow and rarefaction waves in flashing liquid

The outflow of high pressure liquid (in particular, water) to the atmosphere from a closed tube (of length a few metres and diameter more than a few centimetres) because of sudden destruction of one bottom is theoretically investigated. Evaporation takes places on the nucleus bubbles. The number of nuclei depends on the quality of the liquid or its purification. The process involves flashing evaporation of the liquid.There are two rarefaction waves at the initial stage. The velocity of the first wave (elastic forerunner) is sound speed in the one phase liquid and equals about 1000 m s⁻¹. After the elastic forerunner the liquid becomes superheated because the pressure drops and evaporation begins.The velocity of the second rarefaction wave is about 1–10 ms s⁻¹. There is intensive bubbly evaporation on and after the second wave. Intensity of the outflow is determined by the intensity of evaporation on the interface of the bubbles and by intensity of fragmentation of the bubbles because of their relative slip velocity in the liquid (0.1–1 m s⁻¹). The fragmentation of the bubbles significantly intensifies the evaporation because of augmentation of the bubbly interface.The degree of non-equilibrium or superheating behind the forerunner in water grows with the increasing initial temperature T₀. For T₀<530−540 K this superheating is negligible and the process may be described by an equilibrium scheme. For T₀ above 0.95T_cr≈605 K homogeneous nucleation is possible.After forerunner reflection from the closed bottom, intense evaporation is initiated near the bottom. Then the equalization of the pressure along the tube occurs (quasi-static homobaric stage).There is good correlation with experimental data.     

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

In a companion paper, mechanistic models of major fluid particle interaction phenomena involving two bubble groups have been proposed. The prediction of interfacial area concentration evolution using the one-dimensional two-group transport equation and evaluation with experimental results are performed in the paper. These evaluations are based on solid databases for a 2-inch air–water loop with sufficient information on the axial development and the radial distribution of the local parameters. Model evaluation strategies are systematically analyzed. The predictions for the interfacial area concentration evolution demonstrate satisfactory accuracy. The proposed model predicts a smooth transition across the bubbly-to-slug flow regime boundary and demonstrates mechanisms for the generation and development of the cap/slug bubble group. The two-group interfacial area transport equation covers a wide range from bubbly, slug, to churn turbulent flow regimes for adiabatic air–water upward flow in moderate diameter pipes. The generality of the interfacial transport model is also discussed.     

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.     

Evolution of interfacial area concentration in a vertical air–water flow measured by wire–mesh sensors

An application of wire–mesh sensors to obtain the interfacial area concentration in vertical pipes is presented as an alternative to the widely used multiple-tip electrical or optical fibre probes. The measuring data of a mesh sensor consists of a three-dimensional matrix of local instantaneous gas fractions measured at each crossing point of the wires and recorded as a time sequence. Bubbles are clearly distinguishable in this data matrix, since they represent regions of interconnected elements containing the gaseous phase. The method to deduce the interfacial area concentration from this data is based on a full reconstruction of the gas–liquid interface, where the interfacial area of each bubble is recovered as the sum of the surface area of all surface elements belonging to the given bubble. The new method can be applied to large bubbles with an arbitrary shape. To study the change of the interfacial area concentration along the pipe the distance between sensor and gas injection was varied. The axial development of the interfacial area density measured in the test pipe of 195.3 mm inner diameter was compared to the measurements carried out by Sun et al. [Sun, X., Smith, T., Kim, S., Ishii, M., Uhle, J., 2002. Interfacial area of bubbly flow in a relatively large diameter pipe. Exp. Thermal Fluid Sci. 27, 97–109] in a pipe of 101.6 mm diameter, which is the largest pipe for which interfacial area densities are presented in literature. An acceptable agreement was found, whereas deviations are consistent with the differences in the boundary conditions of both experiments.     

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s⁻¹, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s⁻¹ (the first range), and they become higher for the velocities higher than ≈1 m s⁻¹ (the second range). Slight dependence on a vertical position being nearly proportional to z^−1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.     

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。     

Effect of flow-induced vibration on local flow parameters of two-phase flow

A preliminary study was conducted experimentally in order to investigate the effect of flow-induced vibration on flow structure in two-phase flow. Two kinds of experiments were performed, namely ‘reference’ (no vibration) and ‘vibration’ experiments. In the reference experiment, an experimental loop was fixed tightly by three structural supports, whereas the supports were loosen a little in the vibration experiment. In the vibration experiment vibration was induced by flowing two-phase mixture in the loop. For relatively low superficial liquid velocity, flow-induced vibration promoted the bubble coalescence but liquid turbulence energy enhanced by the vibration might not be enough to break up the bubble. This leaded to the marked increase of Sauter mean diameter, and the marked decrease of interfacial area concentration. Accordingly, flow-induced vibration changed the void fraction profile from ‘wall peak’ to ‘core peak’ or ‘transition’, which increased distribution parameter in the drift-flux model. For high superficial liquid velocity, shear-induced liquid turbulence generated by two-phase flow itself might be dominant for liquid turbulence enhanced by flow-induced vibration. Therefore, the effect of flow-induced vibration on local flow parameters was not marked as compared with that for low superficial liquid velocity. Since it is anticipated that flow structure change due to flow-induced vibration would affect the interfacial area concentration, namely interfacial transfer term, further study may be needed under the condition of controlled flow-induced vibration.     

Two-group interfacial area transport in vertical air-water flow -II. Model evaluation

In a companion paper, mechanistic models of major fluid particle interaction phenomena involving two bubble groups have been proposed. The prediction of interfacial area concentration evolution using the one-dimensional two-group transport equation and evaluation with experimental results are performed in the paper. These evaluations are based on solid databases for a 2-inch air-water loop with sufficient information on the axial development and the radial distribution of the local parameters. Model evaluation strategies are systematically analyzed. The predictions for the interfacial area concentration evolution demonstrate satisfactory accuracy. The proposed model predicts a smooth transition across the bubbly-to-slug flow regime boundary and demonstrates mechanisms for the generation and development of the cap/slug bubble group. The two-group interfacial area transport equation covers a wide range from bubbly, slug, to churn turbulent flow regimes for adiabatic air-water upward flow in moderate diameter pipes. The generality of the interfacial transport model is also discussed.     

Implementation and evaluation of one-group interfacial area transport equation in TRACE

The present study implements the one-dimensional interfacial area transport equation into the TRACE code, being developed by the U.S. Nuclear Regulatory Commission. The interfacial area transport equation replaces the conventional flow regime dependent correlations and the regime transition criteria for furnishing the interfacial area concentration in the two-fluid model. This approach allows dynamic tracking of the interfacial area concentration by mechanistically modeling bubble coalescence and disintegration mechanisms. Thus, it eliminates potential artificial bifurcations or numerical oscillations stemming from the use of conventional static correlations. To implement the interfacial area transport equation, a three-field version of TRACE is utilized, which is capable of tracking both the continuous liquid and gas fields as well as a dispersed gas field. To demonstrate the feasibility of the present approach, the steady-state one-group interfacial area transport equation applicable to adiabatic air-water bubbly two-phase flow is first tested in the present study. Data obtained in 18 different flow conditions from two vertical co-current upward air-water bubbly two-phase flow experiments performed in round pipes (25.4 mm and 48.3 mm) are used to help evaluate the implementation. Results obtained from TRACE with the interfacial area transport equation (TRACE-T) and those from TRACE without the transport equation (TRACE-NT) are compared to demonstrate the enhancement in prediction accuracy. The predictions made by TRACE-T agree well with the data with an average percent difference of approximately ±8%. It is also evident from the results that while TRACE-T accounts for dynamic interaction of bubbles along the flow field, the predictions made by TRACE-NT are attributed primarily to the pressure change.     

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.     

Simulation of bubbly flow in vertical pipes by coupling Lagrangian and Eulerian models with 3D random walks models: Validation with experimental data using multi-sensor conductivity probes and Laser Doppler Anemometry

A set of two phase flow experiments for different conditions ranging from bubbly flow to cap/slug flow have been performed under isothermal concurrent upward air–water flow conditions in a vertical column of 3 m height. Special attention in these experiments was devoted to the transition from bubbly to cap/slug flow. The interfacial velocity of the bubbles and the void fraction distribution was obtained using 2 and 4 sensors conductivity probes.Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code with an Eulerian one. The first one tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, ?, z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, wall lubrication. Also we have incorporated a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. Also we have considered the deformations undergone by the bubbles when they touch the walls of the pipe and are compressed until they rebound.The velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate ? transport equations were simultaneously solved using the k, epsilon model in a (r, z) grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions.     

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.     

Countercurrent flow limitation in inclined channels with bends

The countercurrent flow limitation phenomenon in an inclined round channel connected to bends at both ends is experimentally studied. The channel inner diameter is 1.9 cm, the bend radius divided by channel diameter is 10, and the channel length divided by channel diameter is varied in the 105–315 range. Countercurrent flow rates are measured with liquid and gas superficial velocities in the 0.015–0.21 m s⁻¹ and 0.1–3.1 m s⁻¹ ranges respectively. Air and water at room temperature and atmospheric pressure are used in the experiments. The liquid injection system is a constant-head plenum, and the channel angle of inclination with respect to the vertical line is varied in the 0°–60° range. The measured liquid and gas flow rates for all the angles of inclination are correlated using Wallis' flooding correlation, with a unique value for each of the two constants in the correlation.