Local Interfacial Area Concentration Research Articles

Modeling local interfacial area concentration for adiabatic and boiling bubbly flows

Bubbly flows appear in various heat and mass transfer systems, and interfacial area concentration (IAC) is a critical geometrical parameter for the flows. The fidelity of accurately computed IACs is essential for reliable three-dimensional computational fluid dynamics analyses of bubbly flows because the IACs directly affect the interfacial force and interfacial heat and mass transfer rates. This study targeted development of a simple and robust model for predicting the local IAC under steady-state bubbly flows with and without phase change. The dependent two-phase flow parameters of the IAC were derived by considering bubble coalescence and breakup rates. The IAC transport equation simplified under steady-state conditions was used for this purpose. A simplified turbulence model was introduced to formulate the energy dissipation rate per unit mass necessary for computing the bubble coalescence and breakup rates. The prediction accuracy of the local IAC model for bubbly flow conditions with area-average void fraction values less than 10 % was estimated to be 20 % based on 803 local data collected for adiabatic air–water bubbly flows in round tubes with diameters ranging from 9.0 to 200 mm. The model was also applied to predict the local IAC data of subcooled boiling flows in heated channels with hydraulic diameters ranging from 18.5 to 22.2 mm. The test conditions covered pressures from 0.1 to 1.46 MPa. The model prediction accuracy for bubbly flow conditions with area-average void fraction values less than 10 % was estimated to be 40 % based on 155 subcooled boiling flow data.

Development of ANN structural optimization framework for data-driven prediction of local two-phase flow parameters

In this paper, a workflow of ANN-based model development for data-driven prediction of the local two-phase flow parameters has been proposed. To effectively construct an ANN-based model, a framework of ANN structural optimization was also developed based on Genetic Algorithm method and classical Trial-and-Error method. Two case studies with 638 data points of local void fraction (in subcooled boiling flow) and 3125 data points of local interfacial area concentration (in adiabatic air-water flow) of two-phase flow were investigated. The results clearly proved the effectiveness of optimization framework as well as the predictive capability of developed ANN-based models. Also, comparison results with CFD (computational fluid dynamics) showed that better agreements with experimental data can be obtained with well-trained ANN structure.

Modeling sensitivity in prediction of interfacial area concentration in boiling flow

A comprehensive review and validation of three approaches to predict interfacial area concentration in subcooled boiling flow are presented. The three methods are geometry-based semi-empirical correlations, empirical correlations, and the interfacial area transport equation (IATE). Extensive boiling experiment databases with the measurement of local interfacial area concentration and other local two-phase parameters are employed in the validation. The benchmark shows that the most suitable semi-empirical or empirical correlations chosen to predict the interfacial area concentration are different in the low void fraction region and high void fraction region. The closure model sensitivity in the IATE evaluation is analyzed for the bubble layer thickness models, point of net vapor generation (PNVG) determination approaches, and the presence of large cap and slug bubbles. The analysis of the bubble layer thickness model in IATE reveals that the model is necessary for subcooled boiling systems and the flat bubble layer thickness model is more appropriate than the triangle bubble layer thickness model. The result suggests a necessity of measuring the Point of Net Vapor Generation (PNVG) information in experiments for IATE calculation and the necessity of improvement to the PNVG models. The benchmark shows that the one-group IATE has exceptional performance in low group-2 void fraction region; while in high void fraction flows, the multi-group approach is needed to account for the different characteristics between small and large bubbles.

Simplified two-group two-fluid model for three-dimensional two-phase flow Computational Fluid Dynamics for vertical upward flow

Recent progress in nuclear thermal-hydraulics simulations has been largely focused on coupling with other computational packages, improved closure models for subcooled boiling and for bubbly flows, and the development of higher-fidelity simulation capabilities (Kulesza et al., 2016). While high-fidelity 3D simulation is important for model validation, scientific understanding, and some design calculations, it can be prohibitively expensive for system design applications or applications involving large geometries. Thus, there is also a need for practical, simplified approaches for those applications. The two-fluid model strikes a balance between detail and computational resources, but requires the accurate specification of several key constitutive models. These include (1) interfacial forces, (2) interfacial area concentration, (3) two-phase turbulence, and (4) wall and bulk boiling and condensation. In many modern CFD packages, uncertainties in the local interfacial area concentration can have strong effects on the ability to predict the other key parameters. This paper demonstrates that the drag force in 3D CFD can be formulated in much the same way as in 1D system analysis codes and that this approach can be used to formulate a model for interfacial area concentration. The method is also applied to two-group approaches to consider the difference in transport properties for different bubble size classes. This approach may open a method to calculate the interfacial forces without the need for interfacial area transport equations. This reduces the number of differential equations and avoids the modeling challenges associated with bubble breakup and coalescence kernels and the need to specify the inlet interfacial area concentration a priori. The new method is expected to decouple the effects of interfacial area uncertainty and calibrated coefficients, and should provide reasonable local bubble diameters for both group-1 and group-2 bubbles. The approaches proposed in this study are applicable to two-phase flow simulations in rather simple geometries such as upward two-phase flow in vertical channels. In view of many applications for upward two-phase flow in vertical channels, including nuclear reactor systems, the proposed methods are considered useful.

Bubble properties measurement in bubble columns: From homogeneous to heterogeneous regime

Bubble properties, such as local gas holdup, bubble frequency, bubble velocity, bubble size, and interfacial area concentration, are of great significance for the design and scale-up of bubble columns. In the present study, bubble properties in a 0.15m in diameter bubble column were measured by a dual-tip conductivity probe. A new method was proposed to establish the relationship between chord length distribution (CLD) and bubble size distribution (BSD) without the assumption of fixed bubble aspect ratio. The bubble velocity and BSD measured by the probe were validated by a high speed camera in a square column. The results indicate that considering the decreasing of bubble aspect ratio with bubble diameter is required to obtain accurate BSD from measured CLD. Furthermore, the measured bubble properties at different axial positions show that the flow development is much more rapid in the churn-turbulent regime than that in the homogeneous regime. It is also found that the bubble breakage is dominant over the bubble coalescence in the homogeneous regime due to the large bubbles generated at the perforated distributor. The measured results provide a benchmark data for validation of CFD simulation.

Gas-liquid bubbly flow structure in a vertical large-diameter square duct

An experimental study was performed on the local structure of atmospheric upward-moving air–water two-phase flow in a vertical large-diameter square duct with a cross-section of 100 mm × 100 mm and a height of 3 m by using a four-sensor probe at the axial position of z/DH = 29.2. The flow regime was simultaneously observed by a high speed camera at z/DH = 12.5. The four-sensor probe method classifying spherical and non-spherical bubbles was applied as a key measurement way to obtain local parameters such as 3-D bubble velocity vector, bubble diameter and interfacial area concentration, which are necessary for people to know the internal flow structures as well as local void fraction change. The local measurements were performed at 66 points within an octant symmetric triangular area of the cross-section, which agreed well with area-averaged void fractions from differential pressure gauges and the superficial gas velocity from air flow meters. Both the local void fraction and interfacial area concentration indicated radial core-peak and wall-peak distributions at low and high liquid flow rates respectively. Main flow component of the bubble velocity vector showed a power-law distribution shape with its center peak increasing with the liquid flow rate. The 2 components of the bubble velocity vector in the cross-section revealed that there exists a rotating secondary flow in the octant symmetric triangular area and the magnitude of the rotating secondary flow increases with the liquid flow rate. Some of constitutive correlations of drift-flux model for rectangular flow channels and large-diameter circular flow channels and interfacial area concentration correlations for small-diameter and large-diameter circular flow channels are selected and reviewed to study their predictabilities against the present experimental data. The comparison study shows that the drift-flux correlations by Hibiki and Ishii (2003) reasonably predict void fraction and the interfacial-area-concentration correlations by Hibiki and Ishii (2002) and Shen and Hibiki (2015) can be recommended for the prediction of interfacial area concentration in the bubbly flows in large-diameter square ducts.

Local flow structure beyond bubbly flow in large diameter channels

A thorough review of the available literature has revealed a significant lack of usable data regarding the transport of interfacial area in large diameter channels. This represents a concern for various industrial systems, but especially for predicting the performance of safety systems in nuclear reactor systems. In order to remedy this gap in the current experimental database a series of experiments has been performed. These experiments included the measurement of the local interfacial area concentration and other parameters using local electrical conductivity probes in pipes with diameters of 0.152m [6in.], 0.203m [8in.] and 0.304m [12in.]. Volumetric fluxes ranged up to 2m/s [6.56ft/s] for the liquid phase and 10 m/s [32.8ft/s] for the gas phase, and two nominal pressure conditions of 180kPa [26.1psia] and 280kPa [40.6psia] were included. Gas was injected as large cap bubbles in order to provide a basis for evaluating models for cap-bubbly flow at low void fractions. Measurements were performed simultaneously at three axial locations to allow the evaluation of interfacial area transport. The resulting data provides valuable insight into the flow structure and behavior in all flow regimes other than annular flow and will serve as a valuable database for the evaluation of models for predicting the transport of interfacial area across a wide variety of flow conditions and pipe sizes.

Spherical-bubble-based four-sensor probe signal processing algorithm for two-phase flow measurement

This paper describes a newly-developed complete four-sensor probe signal processing algorithm for local instantaneous 3-dimensional bubble velocity vector, local instantaneous bubble diameter, local instantaneous interfacial normal unit vector, local interfacial area concentration (IAC) in a multi-dimensional two-phase flow by utilizing the spherical bubbles in the flow. The newly-developed algorithm has opened a way for the measurement of 3-dimensional bubble velocity vector and bubble diameter with a four-sensor probe. The newly-developed algorithm also has overcome the weakness of the conventional four-sensor probe signal processing algorithm, in which the interfaces passing through the tips of the probe sensors are supposed to be planar, even in the small bubble measurement for the local IAC. The newly-developed algorithm can keep a consistency with the conventional algorithm in measuring large bubbles since the newly-developed algorithm is reduced to the conventional algorithm for the local IAC, the local instantaneous interfacial normal unit vector and the local instantaneous 3-dimensional interfacial displacement velocity vector when the bubble size becomes to be much larger than the size of the four-sensor probe and the interface of the bubble can be locally viewed as 2 tangent planes. The bubbles in practical two-phase flows are classified into spherical bubbles and non-spherical bubbles according to a newly-introduced bubble deviation coefficient from spherical shape (namely an aspheric shape factor). Based on the spherical bubbles, the newly-developed signal processing algorithm can perform the measurement for the local parameters in two-phase flows. The newly-developed signal processing algorithm was applied to the measurements in a vertical air–water multi-dimensional two-phase flow in a large-diameter pipe as an example and was checked against the other measurement methods. The comparisons were very satisfactory and showed that the newly-developed four-sensor probe signal processing algorithm can perform the local measurements for the practical multi-dimensional two-phase flow.

Local interfacial velocity measurement method using a four-sensor probe

This paper presents a theoretical foundation of the measurement methods for the instantaneous local interfacial velocity vector and the time-averaged local interfacial area concentration using a four-sensor probe for multi-dimensional two-phase flow measurements. The measurement method is derived based on a large bubble assumption that locally views the front and rear interfaces of an approaching bubble as two tangent planes. The newly-derived method provides an explicit expression for the instantaneous local interfacial velocity vector using a four-sensor probe. The derived method for the time-averaged local interfacial area concentration was found to be in the same form as that proposed by Kataoka et al. (1986) [1]. The derived method was applied to the practical two-phase flow measurements in a vertical pipe with an inner diameter of 200mm. The measured void fraction and interfacial velocity component in the axial direction were checked against the void fraction measurement using differential pressure gages and the superficial gas velocity measurement using gas flow meters, respectively. The measured interfacial velocity components in the radial and circumferential velocity components were found to be close to zero, which is in accordance with the fact that no stable flow of bubbles with certain horizontal velocity component exists in a vertical circular pipe. The measured interfacial area concentrations showed reasonable radial distributions in the pipe. The good agreements in the practical measurements suggest that the newly-derived method can reasonably measure interfacial velocity vector and interfacial area concentration in multi-dimensional two-phase flows.

Experimental study of interfacial parameter distributions in upward bubbly flow under vertical and inclined conditions

Radial distribution of interfacial parameters for air–water bubbly flow in a circular tube (i.d.50mm) was investigated experimentally under vertical and inclined conditions with the help of double optical fiber probe method, including the local Interfacial Area Concentration (IAC), bubble frequency and void fraction. The ranges of superficial gas and liquid velocities are 0.002∼0.037m/s and 0.072∼0.569m/s, respectively. The inclination angles are 5°, 15° and 30°. The core peak, wall peak, intermediate peak and transition distribution types were observed for vertical upward flow. Under inclined condition, bubbles congregate toward the upper part of the tube, resulting in the asymmetrical distributions of the local interfacial parameters. Comparing with that of vertical flow, the central broad peak leans to the upper part of the tube, and its value increases as the inclination angle increases. Accordingly, with increasing of the inclination angle, the peak near the lower wall weakens gradually, even disappears, whereas, the one near the upper wall of the tube boosts up. The interfacial parameters increase diametrically from ri/R=−0.84 to the peak location in upper part of the inclined pipe, of which higher slope is observed as the inclination angle increases. The Sauter mean diameter is influenced by the gas and liquid velocities as well as the inclination angles. The asymmetrical distributions of interfacial parameters under inclined condition are induced by the radial component of buoyancy force.

Measurement and modeling of two-phase flow parameters in scaled 8 × 8 BWR rod bundle

The behavior of reactor systems is predicted using advanced computational codes in order to determine the safety characteristics of the system during various accidents and to determine the performance characteristics of the reactor. These codes generally utilize the two-fluid model for predictions of two-phase flows, as this model is the most accurate and detailed model which is currently practical for predicting large-scale systems. One of the weaknesses of this approach however is the need to develop constitutive models for various quantities. Of specific interest are the models used in the prediction of void fraction and pressure drop across the rod bundle due to their importance in new Natural Circulation Boiling Water Reactor (NCBWR) designs, where these quantities determine the coolant flow rate through the core. To verify the performance of these models and expand the existing experimental database, data has been collected in an 8×8 rod bundle which is carefully scaled from actual BWR geometry and includes grid spacers to maintain rod spacing. While these spacer grids are ’generic’, their inclusion does provide valuable data for analysis of the effect of grid spacers on the flow. In addition to pressure drop measurements the area-averaged void fraction has been measured by impedance void meters and local conductivity probes have been used to measure the local void fraction and interfacial area concentration in the bundle subchannels. Experimental conditions covered a wide range of flow rates and void fractions up to 80%.

Geometric Effects of 45-deg Elbow in Horizontal Air-Water Bubbly Flow

The present study investigates the geometric effects of a 45-deg elbow on the development and distribution of local two-phase flow parameters in horizontal bubbly flow. A round pipe with an inner diameter of 50.3 mm is used as a test section throughout the study. The test section consists of a 90-deg elbow followed farther downstream by a 45-deg elbow. Local two-phase flow parameters and pressure measurements are made at three different axial locations, one upstream and two downstream of the 45-deg elbow. In total, 15 different flow conditions are investigated for the present analysis. At the measurement port just downstream of the 45-deg elbow, the local parameters are acquired in both the vertical and horizontal directions along the radius of the pipe cross section to capture geometric effects of the flow restriction. The local two-phase flow parameters acquired in the present study include void fraction, bubble velocity, interfacial area concentration, and Sauter mean diameter. In view of one-dimensional transport, the local void fraction and interfacial area concentration are area averaged and plotted along the axial direction. The characteristic geometric effects of the flow restrictions are clearly demonstrated in the distribution of the two-phase flow parameters and pressure, as well as their development along the flow direction. The drastic changes in the interfacial area concentration across the elbow suggest that a 45-deg elbow induces significant changes in bubble interaction mechanisms.

Population balance modeling of bubbly flows considering the hydrodynamics and thermomechanical processes

AbstractThree‐dimensional two‐fluid model and population balance equation is presented to treat the complex hydrodynamics and thermomechanical processes under various bubbly flow conditions. The class method, realized by the MUSIG model, alongside with suitable bubble coalescence and bubble breakage kernels is adopted. Homogeneous MUSIG model predictions have shown to yield good agreement against isothermal bubbly flow measurements. Subcooled boiling flow is further modeled through the use of class method with an improved wall heat partition model. Against experimental data, numerical results also showed good agreement for the local Sauter mean bubble diameter, void fraction, and interfacial area concentration profiles. Inhomogeneous MUSIG model is applied to investigate transition bubbly‐to‐slug flow. Better prediction of bubble diameter is accomplished, especially capturing separation of small and large bubbles. Weakness exists nonetheless in the interfacial forces model. Work is in progress through the consideration of swarm and cluster bubbles instead of isolated spherical bubble calibration. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Interfacial area concentration in annular two-phase flow

Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. The interfacial area concentration in annular flow and annular-mist flow is especially relevant to the transition process to the liquid film dryout, which might lead to fatal problem in the safety and efficient operation of boiling heat transfer system. However, very few experimental and theoretical studies focusing on the interfacial area concentration in annular flow region have been conducted. From this point of view, measurements of annular flow parameters such as one-dimensional interfacial area concentration of liquid film and local interfacial area concentration profile of liquid film were performed by a laser focus displacement meter at 21 axial locations in vertical upward annular two-phase flow using a 3-m-long and 11-mm-diameter pipe. The axial distances from the inlet ( z) normalized by the pipe diameter ( D) varied over z/ D = 50–250. Data were collected for preset gas and liquid flow conditions and for Reynolds numbers ranging from 31,800 to 98,300 for the gas phase and 1050 to 9430 for the liquid phase. Axial development of the one-dimensional interfacial area concentration and the non-dimensional local interfacial area concentration profile of liquid film were examined with the data obtained in the experiment. Total interfacial area concentration including liquid film and droplets was also discussed with help of the existing drift-flux model, entrainment correlation, and droplet size correlation.

Validation physique du modèle Neptune diphasique : plan de validation à adopter, programmes expérimentaux à installer et techniques associées d'instrumentation développées

The NEPTUNE Project constitutes the Thermal-Hydraulics part of a long-term joint development program for the next generation of nuclear reactors simulation tools. The physical validation of the involved modelling embedded in this new two-phase flow software platform is a crucial issue. After explaining the general validation strategy to be adopted, a four-step generic work approach has been defined; it includes: (i) a thorough analysis of the concerned industrial applications to identify the key physical phenomena involved and associated dominant basic models, (ii) an assessment of these models against the available validation pieces of information, to specify the additional validation needs and define dedicated validation plans, (iii) an inventory and assessment of existing validation data (with respect to the requirements specified in the previous step) to identify the actual needs for new validation data, (iv) the specification of the new experimental programs to be set up to provide the needed new data. This work approach has resulted in the definition of (i) the validation plan and experimental programs to be set up for the open medium 3D CFD modelling, successively in close connection with the in-PWR core DNB and PTS applications, and (ii) high priority experimental programs, with respect to porous medium multi-field and interfacial area transport, in connection with LB-LOCA application. These experimental programs will require the use of specific instrumentation to provide local characteristics of both liquid and vapor phases, such as local void fraction, local interfacial area concentration and local liquid velocity. To fulfill these needs, some measurement techniques have been developed/enhanced and assessed.

Methodological improvement of an intrusive four-sensor probe for the multi-dimensional two-phase flow measurement

This paper aimed to improve the four-sensor probe methodology for the multi-dimensional two-phase flow measurement. We theoretically derived the interfacial measurement theorem relating the local instantaneous interfacial velocity to local measurable velocities of the multi-sensor probe in the improvement. Based on this theorem, theoretical measurement methods for the local instantaneous interfacial normal direction and the local time-averaged interfacial area concentration (IAC) using the four-sensor probe were presented. An interface-pairing signal-processing scheme was proposed to identify the same interfaces from the sequential signals detected by different sensors. The practical application of the improved IAC methodology to the two-phase flow in a vertical large diameter pipe showed that the four-sensor probes (together with the interface-pairing signal-processing scheme) could effectively measure the local time-averaged IACs with high effective interface percentages not only in the one-dimensional two-phase flow but also in the multi-dimensional two-phase flow. The measurement error analysis indicated that the errors from the bubble deformation and velocity variation due to the sensor piecing were negligible if we only applied the multi-sensor probe to the two-phase flow with the bubbles having much larger size than the sensor diameter. The total error from both the escaped and missing bubbles in the void fraction and IAC measurements was estimated at about 15.75% in the two-phase flow in a pool.

An experimental study on local interfacial area concentration using a double-sensor probe

Interfacial area concentration is an important parameter in modeling the interfacial transfer terms in the two-fluid model. In this paper, the interfacial area concentration, void fraction, and bubble Sauter mean diameter for air–water bubbly flow through a vertical transparent pipe with 40 mm internal diameter was investigated experimentally using both digital high-speed camera system and a double-sensor conductivity probe. Based on the experimental data of digital high-speed camera system, the statistical models derived by different researchers for local interfacial area concentration measurement using double-sensor conductivity probe were evaluated. The results show that there are obvious differences among the values of local interfacial area concentration calculated by different statistical models even from the same probe signals. The section-averaged values of the local interfacial area concentration calculated using the statistical model by Kataoka et al. agree best with experimental data of digital high-speed camera system. Therefore, the statistical model developed by Kataoka et al. is recommended for the local measurement of interfacial area concentration using a double-sensor conductivity probe in bubbly two-phase flow. Using the verified double-sensor probe method, we carry out experiment to study the local distribution characteristic of the interfacial area concentration and void fraction in air–water bubbly flow through a vertical pipe.

Numerical simulation of improved five-sensor probe method for local interfacial area concentration measurement

Interfacial area concentration is an important parameter in the two-phase flow models which significantly affects the accuracy of the prediction. Currently, there are three probe methods to measure the interfacial area concentration, which are the double-, four- and five-sensor methods. Among them, the four- and five-sensor probe methods can be applied to various flow regimes where the shape of the bubbles is beyond a spherical shape. The five-sensor method classifies the bubble passing type through the sensors into four categories and has an independent measuring method for each category's interface by considering the bubble motion and shape. It was developed to measure the missing bubbles which bypass one or more of the rear sensors more accurately than the other methods. In general, the missing bubble has a large interfacial area concentration due to the steep shape of the interface at the position of the probe tip. Such interfaces give us rather limited information since all of the sensors do not detect the interface. Therefore, some assumptions for the interface shape are applied to the measurement method for the missing bubbles. However, for the bubbles having a high lateral velocity, there can be some measurement errors since the validity of the assumption for the missing interfaces is reduced. In this study, the measurement error is quantified and corrected with the factors related to the turbulent intensity based on numerical simulations. The corrected five-sensor method also includes a modification for the small bubbles of which the shape can be considered to be spherical. The bubble parameters related to the bubble motion and geometry are determined by the Monte Carlo approach.

Benchmarking and improvements of measurement techniques for local-time-averaged two-phase flow parameters

Accurate measurements of local time-averaged two-phase flow parameters is of fundamental importance for the evaluation of two-phase flow models as well as for the development of closure relations used in the two-fluid model. For cross-calibration purposes, we compared the measurements of local-time-averaged two-phase flow parameters using a four-sensor conductivity probe developed by the TRSL (Thermal-hydraulics and Reactor Safety Laboratory) at Purdue University, and a four-sensor optical probe developed by the CEA (French Atomic Energy Commission). A system coupling methodology was also performed in order to isolate the effects of each instrumentation's components, i.e., probe, acquisition, thresholding, and processing effects. Experimental results have shown a reasonable agreement in the local void fraction, local bubble velocity, and local interfacial area concentration measurements comparisons. However, it is shown that particular attention must be given to the sensor probe design in order to get accurate measurements.

Two‐Phase Bubbly Flow Structure in Large‐Diameter Vertical Pipes

AbstractThe two‐phase flow structure of an air‐water, bubbly, upward flow in a 20 cm diameter pipe is presented with particular emphasis on the local interfacial area concentration. The radial distribution of void fraction, bubble velocity, bubble size, bubble frequency, and interfacial area concentration were measured using a local dual‐optical probe. The experimental results showed that the saddle‐type distribution of void fraction and interfacial area concentration, which are common for bubbly flow in small diameter pipes, only appeared in the present experiments under conditions of very low area‐averaged void fraction (<ϵ> < 0.04). The values for the interfacial area concentration were higher in large diameter pipes when compared with data obtained under the same flow conditions in small pipes. The area‐averaged void fraction data were correlated using the drift‐flux model.