Drift-flux model for upward two-phase cross-flow in horizontal tube bundles

In relation to void fraction prediction of cross-flow in horizontal tube bundle of shell-tube heat exchangers, a drift-flux correlation has been developed to meet the demand on the study of two-phase flow gas and liquid velocities, two-phase pressure drop, heat transfer, flow patterns and flow induced vibrations in the shell side. Two critical parameters such as distribution parameter and drift velocity have been modeled. The distribution parameter is obtained by constant asymptotic values and taking into account the differences in channel geometry. The drift velocity is modelled depending on the density ratio and the non-dimensional viscosity number. The relationship between the channel averaged and gap mass velocity has been discussed in order to obtain the superficial gas and liquid velocities in the drift-flux correlation. The newly developed drift-flux correlation agrees well with cross-flow experimental databases of air-water, R-11 and R-113 in parallel triangular, normal square and normal triangular arrays with the mean absolute error of 1.06% and the standard deviation of 4.47%. In comparison with other existing correlations, the newly developed drift-flux correlation is superior to other studies due to the improved accuracy. In order to extend the applicability of the newly developed drift-flux correlation to void fraction of unity, an interpolation scheme has been developed. The newly developed drift-flux correlation is able to calculate the void fraction of cross-flow over a full range with different sub-channel configurations in shell-tube type heat exchangers.     

Two-group drift-flux model for closure of the modified two-fluid model

In an effort to improve the prediction of void fraction and heat transfer characteristics in two-phase systems, closure relations to the one-dimensional modified two-fluid model are addressed. The drift-flux general expression is extended to two bubble groups in order to describe the void weighted mean gas velocities of spherical/distorted (group-1) bubbles and cap/slug/churn-turbulent (group-2) bubbles. Therefore, correlations for group-1 and group-2 distribution parameters and drift velocities are proposed and evaluated with experimental data. Furthermore, the covariance in the convective flux of the one-dimensional two-fluid model is addressed and interpreted with the available database. The dataset chosen for evaluation of the two-group drift-flux general expression contains 126 total data points taken in an annulus geometry. The proposed distribution parameters show an agreement within ±4.9% and ±1.2% for group-1 and group-2 data, respectively. The overall estimation of group-1 and group-2 void weighted mean gas velocity calculated with the newly proposed two-group drift-flux general expression shows an agreement of ±11.8% and ±17.7%, respectively.     

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.     

One-dimensional interfacial area transport of vertical upward bubbly flow in narrow rectangular channel

The design and safety analysis for miniature heat exchangers, the cooling system of high performance microelectronics, research nuclear reactors, fusion reactors and the cooling system of the spallation neutron source targets requires the knowledge of the gas–liquid two-phase flow in a narrow rectangular channel. In this study, flow measurements of vertical upward air–water flows in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm were performed at seven axial locations by using the imaging processing technique. The local frictional pressure loss gradients were also measured by a differential pressure cell. In the experiment, the superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. The developing two-phase flow was characterized by the significant axial changes of the local flow parameters due to the bubble coalescence and breakup in the tested flow conditions. The existing two-phase frictional multiplier correlations such as Chisholm, 1967, Mishima et al., 1993 and Lee and Lee (2001) were verified to give a good prediction for the measured two-phase frictional multiplier. The predictions of the drift-flux model with the rectangular channel distribution parameter correlation of Ishii (1977) and several existing drift velocity correlations of Ishii, 1977, Hibiki and Ishii, 2003 and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities. The interfacial area concentration (IAC) model of Hibiki and Ishii (2002) was modified by taking the channel width as the system length scale and the modified IAC model could predict the IAC and Sauter mean diameter acceptably.     

The use of drift-flux techniques for the analysis of horizontal two-phase flows

New data is presented for horizontal air/water two-phase flow having various flow regimes. It is shown that drift-flux models are able to correlate these data and that the drift velocity, V_gj, is normally finite.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

Prediction of refrigerant void fraction in horizontal tubes using probabilistic flow regime maps

A state of the art review of two-phase void fraction models in smooth horizontal tubes is provided and a probabilistic two-phase flow regime map void fraction model is developed for refrigerants under condensation, adiabatic, and evaporation conditions in smooth, horizontal tubes. Time fraction information from a generalized probabilistic two-phase flow map is used to provide a physically based weighting of void fraction models for different flow regimes. The present model and void fraction models in the literature are compared to data from multiple sources including R11, R12, R134a, R22, R410A refrigerants, 4.26–9.58 mm diameter tubes, mass fluxes from 70 to 900 kg/m² s, and a full quality range. The present model has a mean absolute deviation of 3.5% when compared to the collected database.     

Interfacial area transport across a 90° vertical-upward elbow in air–water bubbly two-phase flow

This study develops a one-group interfacial area transport equation (IATE) for vertical-upward-to-horizontal air–water bubbly two-phase flows through a 90° elbow with a non-dimensional centerline radius of curvature of three. In order to develop the model, an extensive database is established by acquiring local two-phase flow parameters using a four-sensor conductivity probe upstream and downstream of the elbow. The data show there exist three characteristic regions in void distribution, including a bimodal-to-bimodal region, a bimodal-to-single-peaked region, and a developed horizontal flow region with void accumulated at the top of the pipe cross-section. Using the database, the preliminary dissipation length model developed by Yadav et al. (2014b) is improved by including the transition region near the exit of the elbow in addition to the dissipation region. To close the IATE model, the bubble velocity advection term and bubble interaction terms in the IATE are correlated with the parameter characterizing the “elbow-strength”. The two-phase pressure drop across the elbow is modeled using the modified Lockhart–Martinelli correlation which takes into account the minor loss effect. The closed IATE model is implemented to predict interfacial area transport in vertical-upward-to-horizontal two-phase flow. It is found that the developed model is capable of predicting interfacial area concentration with an average percent difference of less than ±6%.     

Axial development of subcooled boiling flow in an internally heated annulus

For the main purpose of database construction in order to develop the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and bubble number density were measured in boiling water bubbly flows in a vertical-upward internally heated annulus using a double-sensor conductivity probe. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. A total of 11 data sets were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s, two heat fluxes, 100 and 150 kW/m², and two inlet liquid temperatures, 95.0 and 98.0°C. The axial developments of the flow parameters were discussed based on the measured data in detail. In addition to the database construction, the measured data validated recently proposed constitutive equations for the distribution parameter, drift velocity, and bubble Sauter mean diameter, which will improve the accuracy of the drift-flux model in subcooled bubbly flow.     

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.     

Effect of gravity on axial development of bubbly flow at low liquid Reynolds number

In view of the great importance of two geometrical parameters such as void fraction and interfacial area concentration to the accurate two-phase flow analysis at microgravity conditions, axial developments of flow parameters such as void fraction, interfacial area concentration, bubble Sauter mean diameter, and bubble number density were measured in bubbly flow at microgravity and low liquid Reynolds number conditions where the gravity effect on the flow parameters were pronounced. A total of seven data sets were acquired in the flow range of the void fraction from 1.01% to 3.36% and the liquid Reynolds number from 1,400 to 4,750. The measurements were also performed in the similar flow range at normal gravity conditions. The transport mechanisms of the flow parameters are discussed in detail based on the data measured at normal and microgravity conditions, and the drift-flux model developed at microgravity conditions are compared with the measured data.An erratum to this article can be found at     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.     

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.     

Void fraction measurement of bubble and slug flow in a small channel using the multivision technique

Using the multivision technique, a new void fraction measurement method was developed for bubble and slug flow in a small channel. The multivision system was developed to obtain images of the two-phase flow in two perpendicular directions. The obtained images were processed—using image segmentation, image subtraction, Canny edge detection, binarization, and hole filling—to extract the phase boundaries and information about the bubble or slug parameters. With the extracted information, a new void fraction measurement model was developed and used to determine the void fraction of the two-phase flow. The proposed method was validated experimentally in horizontal and vertical channels with different inner diameters of 2.1, 2.9, and 4.0 mm. The proposed method of measuring the void fraction has better performance than the methods that use images acquired in only one direction, with a maximum absolute difference between the measured and reference values of less than 6%.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Prediction of void fraction for gas–liquid flow in horizontal,upward and downward inclined pipes using artificial neural network

In this work, the ability of artificial neural networks (ANNs) to predict void fraction of gas–liquid two–phase flow in horizontal and inclined pipes was investigated. For this purpose, an ANN model was designed and trained using a total of 301 experimental data points reported in the literature for inclination angles between –20° and +20°. Pipe inclination angle as well as superficial Reynolds number of gas (Re_sg) and liquid (Re_sl) were chosen as input parameters of different structures of multilayer perceptron (MLP) neural networks, while the corresponding void fraction was selected as their output parameter. A hyperbolic tangent sigmoid and a linear function were employed as transfer functions of hidden and output layers, respectively, and Levenberg–Marquardt back propagation algorithm was used to train the networks. By trial–and–error method, a three–layer network with 10 neurons in the hidden layer was achieved as optimal structure of the ANN which made it possible to predict the void fraction with a high accuracy. Mean absolute percent error (MAPE) of 1.81% and coefficient of determination (R²) of 0.9976 for training data and MAPE of 1.52% and R² value of 0.9948 for testing data were obtained. Also for all data, MAPE of 1.95% and R² value of 0.9972 were calculated, and 96% data were within ±5% error band. In addition, the accuracy of the proposed ANN model was compared with the predictions from 17 void fraction correlations available in the literature for different flow patterns and horizontal and inclined flows. For all cases, the proposed ANN model gave better performance than all of the studied correlations. The results confirm the very good capability of the ANNs to predict the void fractions of gas–liquid flow in inclined pipes, regardless of flow pattern. Finally, by performing interpolation using the trained network, the void fraction values for some other conditions were predicted.     

Friction factor improved correlations for laminar and turbulent gas–liquid flow in horizontal pipelines

We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.     

Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry

Particle tracking velocimetry (PTV) is applied to a bubbly two-phase turbulent flow in a horizontal channel at Re = 2 × 10⁴ to investigate the turbulent shear stress profile which had been altered by the presence of bubbles. Streamwise and vertical velocity components of liquid phase are obtained using a shallow focus imaging method under backlight photography. The size of bubbles injected through a porous plate in the channel ranged from 0.3 to 1.5 mm diameter, and the bubbles show a significant backward slip velocity relative to liquid flow. After bubbles and tracer particles are identified by binarizing the image, velocity of each phase and void fraction are profiled in a downstream region. The turbulent shear stress, which consists of three components in the bubbly two-phase flow, is computed by analysis of PTV data. The result shows that the fluctuation correlation between local void fraction and vertical liquid velocity provides a negative shear stress component which promotes frictional drag reduction in the bubbly two-phase layer. The paper also deals with the source of the negative shear stress considering bubble’s relative motion to liquid.     

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%.