Area-averaged Void Research Articles

On the use of area-averaged void fraction and local bubble chord length entropies as two-phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 and 50.8-mm pipes have been calculated. The measured conditions cover ranges from 0.13 to 5 m/s in the superficial liquid velocity j f and ranges from 0.01 to 25 m/s in the superficial gas velocity j g. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions.

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.

S0802-2-2 強制対流サブクール沸騰中のボイド率発展に関する一考察(原子力システムおよび要素技術(2))

The mechanism of net vapor generation in subcooled flow boiling was investigated experimentally. The test section was a vertical rectangular channel and one side face of the test channel was heated uniformly. The test fluid was water and the system pressure was close to the atmospheric pressure. The inlet mass flux and the wall heat flux were kept constant while the inlet subcooling was changed parametrically to control the thermal equilibrium quality at the measuring section. The void fraction distribution was measured using an optical void probe and bubble behavior was observed using a high speed camera. In the present experiments, bubbles were usually lifted off the heated surface within a short period of time after the nucleation. After the lift-off, the bubbles disappeared quickly due to condensation upstream of the point of net vapor generation (PNVG). However, when the bubble coalescence took place, drastic change was observed. Since the coalesced bubbles frequently repeated the coalescence with other bubbles, typical bubble size increased discontinuously. Since the increase of the bubble size led to the decrease of the interfacial area concentration, the bubble life-time and the cross-sectional area-averaged void fraction increased significantly if the bubble coalescence took place. It was concluded that the bubble coalescence is a key phenomenon in determining the PNVG at least in the experimental condition tested in the present work.

Axial Development of Flow Regime in Adiabatic Upward Two-Phase Flow in a Vertical Annulus

This study has investigated the axial development of flow regime of adiabatic upward air-water two-phase flow in a vertical annulus. The inner and outer diameters of the annulus are 19.1 mm and 38.1 mm, respectively. The hydraulic diameter of the flow channel, DH, is 19.0 mm and the total length is 4.37 m. The flow regime map includes 72 flow conditions within a range of 0.01 m/s<⟨jg⟩<30 m/s and 0.2 m/s<⟨jf⟩<3.5 m/s, where ⟨jg⟩ and ⟨jf⟩ are, respectively, superficial gas and liquid velocities. The flow regime has been classified into four categories: bubbly, cap-slug, churn, and annular flows. In order to study the axial development of flow regime, area-averaged void fraction measurements have been performed using impedance void meters at three axial positions corresponding to z/DH=52, 149, and 230 simultaneously, where z represents the axial position. The flow regime indicator has been chosen to be statistical parameters from the probability distribution function of the area-averaged void fraction signals from the impedance meters, and self-organized neural networks have been used as the mapping system. This information has been used to analyze the axial development of flow regime as well as to check the predictions given by the existing flow regime transition models. The axial development of flow regime is quantified using the superficial gas velocity and void fraction values where the flow regime transition takes place. The predictions of the models are compared for each flow regime transition. In the current test conditions, the axial development of flow regime occurs in the bubbly to cap-slug (low superficial liquid velocities) and cap-slug to churn (high superficial liquid velocities) flow regime transition zones.

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.

Development of two-phase flow downstream of a horizontal sudden expansion

Experiments were performed to characterize the development of air–oil two-phase flow downstream of horizontal sudden expansions with area ratios of 0.0625 and 0.25. The tests were performed at oil and air superficial velocities in the range 0.02–0.756 and 0.136–3.75 m/s. In addition to the axial variation of the pressure and area-averaged void fraction, time-averaged local profiles of the void fraction, mean liquid velocity and turbulence intensity were measured downstream of the expansion using hot-film anemometry. The fully developed downstream void fraction can either increase or decrease from its upstream value, and depends on the flow pattern change across the expansion. The turbulence intensity is higher in the immediate vicinity of the sudden expansion. It then decreases with axial distance and asymptotes to an approximately constant value. The phase redistributions immediately downstream of the expansion and the developing length was found to be strongly dependent on the upstream flow pattern and the sudden expansion area ratio.

비선형 위상공간에서의 기포 분율 신호의 끌개밀도분식을 이용한 수직 상향 이상유동의 유동패턴분류

The nonlinear signals from an Impedance meter for the area average void traction in two-phase flow have been analyzed to construct a phase space trajectory. The pseudo phase space was constructed with the time delay and proper dimensions. The time delay and the embedding dimension were chosen by the average mutual information and by the false nearest neighborhood, respectively The attractor-density-map of projected states was used to produce the two dimensional probability distribution functions (2D-PDF) Since the developed 2D-PDF showed clear distinction of the flow patterns, the flow regime identification was made with three rules and with the 2D-PDF Also, the transition criteria of Mishima-Ishri agree well with the present results.

Drift-flux model for downward two-phase flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for downward two-phase flows. The constitutive equation that specifies the distribution parameter in the downward flow has been derived by taking into account the effect of the downward mixture volumetric flux on the phase distribution. It was assumed that the constitutive equation for the drift velocity developed by Ishii for a vertical upward churn-turbulent flow determined the drift velocity for the downward flow over all of flow regimes. To evaluate the drift-flux model with newly developed constitutive equations, area-averaged void fraction measurement has been extensively performed by employing an impedance void meter for an adiabatic vertical co-current downward air–water two-phase flow in 25.4-mm and 50.8-mm inner diameter round tubes. The newly developed drift-flux model has been validated by 462 data sets obtained in the present study and literatures under various experimental conditions. These data sets cover extensive experimental conditions such as flow system (air–water and steam–water), channel diameter (16–102.3 mm), pressure (0.1–1.5 MPa), and mixture volumetric flux (−0.45 to −24.6 m/s). An excellent agreement has been obtained between the newly developed drift-flux model and the data within an average relative deviation of ±15.4%.

Local liquid velocity measurements in air-water bubbly flow

Local measurements of axial liquid velocity were performed for vertical upward air-water bubbly flow in a 101.6-mm inner-diameter round pipe by using a laser Doppler anemometer (LDA) and a hot-film anemometer (HFA). The data reduction approaches for both the LDA and HFA are discussed in detail. A threshold scheme with the information of local void fraction and velocity distribution in single-phase flow was applied to the LDA to approximately discriminate liquid velocity signals from those of the bubble interface velocity. Furthermore, a formulation was given to account for the effect of the bubble relative velocity on the liquid in the front and wake regions of the bubbles. For the HFA, an amplitude threshold scheme and a slope criterion were used to extract liquid velocity information. To reduce the measurement uncertainty, the experiments were performed in flow conditions where the area-averaged void fraction was less than 20%. The experimental results showed satisfactory agreement between the liquid volumetric flow rates calculated by area integration of the local liquid velocity and void fraction measurements, and the measured value by a magnetic flow meter. Also, the area-averaged relative velocity between the gas and liquid phases obtained from the current measurements agreed well with previous research.

F112 強制対流気液二相流の微細流動構造

Microscopic structure of forced-convective air-water two-phase flow was experimentally investigated. In the experiment, setting the flowrates of water and air at several values, bubbly and slug flows were realized in a vertical circular tube of 19.7mm I.D. The holdup sensor was used to measure the time variation of instantaneous cross-sectional area-averaged void fraction about 1m downstream from the two-phase mixer. The void data were analyzed by means of the discrete Fourier transformation (DFT). The analytical results showed that the change from bubbly to slug flows are rather continuous. It was considered that the bubble clusters formed in the transition regime between bubbly and slug flows play important role in the present experiments.

Vertical two-phase flow identification using advanced instrumentation and neural networks

Most two-phase flow measurements, including void fraction measurements, depend on correct flow regime identification. There are two steps taken towards the successful identification of flow regimes: first, develop a non-intrusive instrument to demonstrate area-averaged void fluctuations and second, develop a non-linear mapping approach to perform objective identification of flow regimes. In this paper, an advanced non-intrusive impedance void-meter provides input signals to neural networks which are used to identify flow regimes. After training, both supervised and self-organizing neural network learning paradigms performed flow regime identification successfully. The methodology presented holds considerable promise for multiphase flow diagnostic and measurement applications.

Local characteristics of two-phase flow parameters in an annulus boiling channel

Local two-phase flow parameters were measured to investigate the internal flow structures of steam-water boiling flow in an annulus channel. Two kinds of measuring methods for the local two-phase flow parameters were investigated. A two-conductivity probe was used for local vapor parameters and a Pitot tube for local liquid parameters. Using these probes, the distributions of phasic velocities, interfacial area concentration (IAC) and void fraction are measured in a steam-water boiling flow. In this study, it is observed that the local void fraction is smoothly decayed out from the surface of a heating rod to the channel center in subcooled boiling without any wall void peaking, which were observed in air-water experiments. The distributions of the local IAC and bubble frequency coincide with those of the local void fraction for a given area-averaged void fraction.

Bubble Behavior and Mean Diameter in Subcooled Flow Boiling

Bubble behavior and mean bubble diameter in subcooled upward flow boiling in a vertical annular channel were investigated under low pressure and mass flux conditions. A high-speed video system was used to visualize the subcooled flow boiling phenomenon. The high-speed photographic results indicated that, contrary to the common understanding, bubbles tend to detach from the heating surface upstream of the net vapor generation point. Digital image processing technique was used to measure the mean bubble diameter along the subcooled flow boiling region. Data on the axial area-averaged void fraction distributions were also obtained using a single-beam gamma densitometer. Effects of the liquid subcooling, applied heat flux, and mass flux on the mean bubble size were investigated. A correlation for the mean bubble diameter as a function of the local subcooling, heat flux, and mass flux was obtained.

Void Fraction Measurement by the Improved Multi-Channel Impedance Void Meter

An improved multi-channel Impedance Void Meter (IVM) is developed to measure an area-averaged void fraction. It consists of a main sensor, a reference sensor and a signal processor. The sensor was designed to be flush-mounted to the inner wall of the test section to avoid the flow disturbances. Guard electrodes are used to obtain evenly distributed electrical field in a measuring volume. A reference sensor is also installed to eliminate the drift in void signal caused by the changes in electrical properties of working fluid. The signal processor with three channels is specially designed so as to minimize the inherent error due to the phase difference between channels. As an example of applications, the mean and fluctuating components of void fraction are measured for bubbly and slug flow regime, and it is shown that IVM has good dynamic resolution which is required to investigate the structural developments of bubbly flow and the propagation of void waves in a flow channel.

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.

Optimization of a one-shot gamma densitometer for measuring area-averaged void fractions of gas-liquid flows in narrow pipelines

A novel theoretical method for optimization of a gamma densitometer was applied in measuring the area-averaged void fraction in gas-liquid flows. This theory provides design criteria that are comprehensive, mechanistic, quantitative and all are obtained from first principles. Also, a computer simulation was developed to test the design criteria and the predictions were compared with experimental data in the literature. Extensive experimental validation of the optimization theory was performed. Direct in situ measurement of void fraction using differential pressure, a double-sensor resistivity probe and lucite mock-ups were compared with the optimized gamma densitometer measurements. The results demonstrated good agreement between the reference measurements and the gamma densitometer in each case. The measured void fractions for the concurrent vertical forced flow ranged from 0.02 to 0.8, and spanned the bubbly, slug and churn turbulent flow regimes in a 25.4 mm tube. The mock-up studies used lucite tubes of 12.7 mm outer diameter as substitutes for the flow field over void fractions ranging from 0.03 to 0.8.

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.

Sensitivity analysis of an impedance void meter to the void distribution in annular flow: a theoretical study

Impedance void meters are frequently used to measure the area-averaged void fraction in pipes. This is primarily for two reasons: firstly, this method is non-intrusive since the measurement can be made by electrodes flush mounted in the walls, and secondly, the signal processing equipment is simple. Impedance probes may be calibrated by using a pressure drop measurement or a quick closing valve system. In general, little attention is paid to void distribution effects. It can be proved that in annular flow, the departure from radial symmetry has a strong influence on the measured mean film thickness. This can be easily demonstrated by solving the Laplace equation for the electrical potential by simple analytical methods. When some spatial symmetry conditions are encountered, it is possible to calculate directly the conductance of the two-phase medium without a complete calculation of the potential. A solution of this problem by using the separation of variables technique is also presented. The main difficulty with this technique is the mixed nature of the boundary conditions: the boundary condition is both of Neumann and of Dirichlet type on the same coordinate curve. This formulation leads to a non-separable problem, which is solved by truncating an infinite algebraic set of linear equations. The results, although strictly valid in annular flow, may give the correct trends when applied to bubbly flow. Finally, the theory provides an error estimate and a design criterion to improve the probe reliability.

Development of a converter to change gas-liquid two-phase slug flow to bubbly flow in a vertical tube. (2nd Report. Minimum length of the bubbly-flow region and consideration of the regeneration process to slug flow).

In the previous paper, a flow pattern converter composed of five stages of porous plates was devloped. Three kinds of sintered porous plates of spherical particles were selected for the converter under fixed gas and liquid flow rates. In this paper, a diagram is proposed to predict a minimum length of the bubbly-flow region for arbitrary gas and liquid flow rates and three kinds of porous plates. A distribution of the area-averaged void fraction and fluctuation of the void fraction in the downstream of the converter were measured to improve the performance of this converter and to predict the location at which a large bubble is regenerated. This prediction includes an attempt to clarify the mechanism of transition from bubbly flow to slug flow. It was confirmed that fluctuation of the void fraction played an important role in the transition from bubbly flow to slug flow.