A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes is proposed. In order to overcome the effect of flow pattern on heat transfer, a flow pattern factor (effective wetted-perimeter) is developed and introduced into our proposed correlation. To verify the correlation, local heat transfer coefficients and flow parameters were measured for air–water flow in a pipe in the horizontal position with different flow patterns. The test section was a 27.9 mm ID stainless steel pipe with a length to diameter ratio of 100. A total of 114 data points were taken by carefully coordinating the liquid and gas superficial Reynolds number combinations. The heat transfer data were measured under a uniform wall heat flux boundary condition ranging from about 3000 W/m² to 10,600 W/m². The superficial Reynolds numbers ranged from about 820 to 26,000 for water and from about 560 to 48,000 for air. These experimental data including different flow patterns were successfully correlated by the proposed general two-phase heat transfer correlation with an overall mean deviation of 5.5%, a standard deviation of 11.7%, and a deviation range of −18.3% to 37.0%. Ninety three percent (93%) of the data were predicted within ±20% deviation.     

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.     

Effects of dynamic load on flow and heat transfer of two-phase boiling water in a horizontal pipe

An experimental investigation was performed to obtain the flow and heat transfer characteristics of single-phase water flow and two-phase pipe boiling water flow under high gravity (Hi-G) in present work. The experiments were conducted on a rotating platform, and boiling two-phase flow state was obtained by means of electric heating. The data were collected specifically in the test section, which was a lucite pipe with inner diameter of 20 mm and length of 400 mm. By changing the parameters, such as rotation speed, inlet temperature, flow rate, and etc., and analyzing the fluid resistance, effective heat and heat transfer coefficient of the experimental data, the effects of dynamic load on the flow and heat transfer characteristics of single phase water and two-phase boiling water flow were investigated and obtained. The two-phase flow patterns under Hi-G condition were obtained with a video camera. The results show that the dynamic load significantly influences the flow characteristic and boiling heat transfer of the two-phase pipe flow. As the direction of the dynamic load and the flow direction are opposite, the greater the dynamic load, the higher the outlet pressure and the flow resistance, and the lower the flow rate, the void fraction, the wall inner surface temperature and the heat transfer capability. Therefore, the dynamic load will block the fluid flow, enhance heat dissipation toward the ambient environment and reduce the heat transfer to the two-phase boiling flow.     

Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (Re_L) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent Re_L and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Composite power law holdup correlations in horizontal pipes

A wide range of experimental holdup data, from different sources, are analyzed based on a theoretical model proposed in this work to evaluate the holdup in horizontal pipes. 2276 gas–liquid flow experiments in horizontal pipelines with a wide range of operational conditions and fluid properties are included in the database. The experiments are classified by mixture Reynolds number ranges and composite analytical expressions for the relationship between the liquid holdup and no-slip liquid holdup vs. the gas–liquid volumetric flow rate are obtained by fitting the data with logistic dose curves. The Reynolds number appropriate to classify the experimental data for gas–liquid flows in horizontal pipes is based on the mixture velocity and the liquid kinematic viscosity. Composite power law holdup correlations for flows sorted by flow pattern are also obtained. Error estimates for the predicted vs. measured holdup correlations together with standard deviation for each correlation are presented. The accuracy of the correlations developed in this study is compared with the accuracy of 26 previous correlations and models in the literature. Our correlations predict the liquid holdup in horizontal pipes with much greater accuracy than those presented by previous authors.     

Experimental investigation of the flow pattern,pressure drop and void fraction of two-phase flow in the corrugated gap of a plate heat exchanger

The two-phase flow in the corrugated gap created by two adjacent plates of a plate heat exchanger was investigated experimentally. One setup consisting of a transparent corrugated gap was used to visualize the two-phase flow pattern and study the local phenomena of phase distribution, pressure drop and void fraction. Saturated two-phase R365mfc and an air-water mixture were used as working fluids.In a second experimental setup, the heat transfer coefficients and the pressure drop inside an industrial plate heat exchanger during the condensation process of R134a are determined. Both experimental setups use the same type of plates, so the experimental results can be connected and a flow pattern model for the condensation in plate heat exchangers can be derived. In this work the results of the flow pattern visualization, the two-phase pressure drop in the corrugated gap and the void fraction analysis by measurement of the electrical capacity are presented. A new pressure drop correlation is derived, which takes into account different flow patterns, that appear during condensation. The mean deviation of the presented pressure drop model compared to the experimental data and data from other experimental works is 18.9%. 81.7% of the calculated pressure drop lies within ±30% compared to the experimental data.     

Two-phase flow measurements with sharp-edged orifices

This paper contains the results of a set of two-phase flow measurements of 4 different ratios of vapor to liquid density (up to 0.328) across a sharp-edged circular orifice. Test fluid was R-113. Tests were carried out upon 3 orifices whose diameter ratios were 0.312, 0.439 and 0.625. The test quality ranged from 0–100%, while the mass velocity from 917–1477 kg/m².s. On the basis of a modified separated flow model, a relationship is developed for the flow rate and quality and is compared with experimental data and 5 proposed correlations. Comparison shows this method can be used to calculate the flow rate or the quality of vapor liquid (or steam water) mixture in the range 0.00455 to 0.328 of the density ratio, and in pipe size ranging from 8 to 75 mm (β = 0.25–0.75).

The RMS error of this method is about 12% when the quality, x, ranges from 2% to 100%.     

Two-phase flow in inclined tubes with specific reference to condensation: A review

Tilting influences the flow patterns and thus the heat transfer and pressure drop during condensation in smooth tubes. However, few studies are available on diabatic two-phase flows in inclined tubes. The purpose of the present paper is to review two-phase flow in inclined tubes, with specific reference to condensation. Firstly, the paper reviews convective condensation in horizontal tubes. Secondly, an overview is given of two-phase flow in inclined tubes. Thirdly, a review is conducted on condensation in inclined tubes. It is shown for convective condensation in inclined tubes that the inclination angle influences the heat transfer coefficient. The heat transfer coefficient can be increased or decreased depending on the experimental conditions, and especially the flow pattern. Under certain conditions, an inclination angle may exist, which leads to an optimum heat transfer coefficient. Furthermore, this paper highlights the lack of experimental studies for the prediction of the inclination angle effect on the flow pattern, the heat transfer coefficient and the pressure drop in two-phase flows during phase change.     

Slip between the phases in two-phase water–oil flow in a horizontal pipe

This paper is devoted to slip phenomenon between the phases that occurs in unstable two-phase water–oil flow systems in a horizontal pipe. The emphasis is placed on the relation between the slip and the real (in situ) water fraction in a flowing mixture, as well as the substitute physical properties of the whole two-phase system. The experimental data collected throughout research served for the evaluation of the accuracy of the methods of real phase fraction in a water–oil flow system in horizontal pipes as they were referred to in the bibliography. Subsequently we have suggested the author indicate a method of determination of the fraction for two-phase liquid systems like O/W, W/O and W + O. In order to establish the specific equations, the drift-flux model has been used here.     

Flow pattern and boiling heat transfer of CO2 in horizontal small-bore tubes

Increasing attention has been focused on carbon dioxide (CO₂) heat pump system where the temperature level is rather low, while the operating pressure is rather high. In this system, the density difference between vapor and liquid becomes rather small, which significantly affects flow patterns. Low surface tension and latent heat also have significant influence on two-phase flow patterns and heat transfer. This paper describes experimental and numerical investigation on flow patterns and heat transfer characteristics of boiling flow CO₂ at high pressure in horizontal small-bore tubes ranging from 1.0 mm to 3.0 mm I.D. Even though the density difference is rather small at high pressure, phase stratification takes place, which leads to the intermittent dryout at the upper wall. So far developed discrete bubble model by the authors for vertical flows is modified so as to include horizontal flow mechanisms. The predicted flow patterns with this new model agree on the whole with the experimental observation.     

Frictional pressure drop during vapour–liquid flow in minichannels: Modelling and experimental evaluation

Condensation in minichannels is widely used in air-cooled condensers for the automotive and air-conditioning industry, in heat pipes and other applications for system thermal control. The knowledge of pressure drops in such small channels is important in order to optimize heat transfer surfaces. This paper presents a model for calculation of the frictional pressure gradient during condensation or adiabatic liquid–gas flow inside minichannels with different surface roughness. In order to account for the effects of surface roughness, new experimental frictional pressure gradient data associated to single-phase flow and adiabatic two-phase flow of R134a inside a single horizontal mini tube with rough wall has been used in the modelling. It is a Friedel (1979) [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: Proceedings of the European Two-Phase Flow Group Meeting, Ispra, Paper E2] based model and it takes into account mass velocity, vapor quality, fluid properties, reduced pressure, tube diameter, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, it has been built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and mist flow are here predicted. However, the suggested procedure is extended to the intermittent flow in minichannels and it is also applied with success to horizontal macro tubes.     

Two-phase flow patterns across triangular tube bundles for air–water upward flow

This paper presents flow pattern experimental results obtained during two-phase upward flow across a horizontal tube bundle. Experiments were performed for flows across a normal triangular tube bundle with 19 mm OD tubes and transversal pitch of 24 mm. Results were obtained for gas and liquid superficial velocities ranging from 0.13 to 10.00 m/s and 0.02 to 1.50 m/s, respectively. Flow patterns were identified subjectively based on visual observations through side windows, and objectively using the k-means clustering method based on signals of a differential pressure transducer and a capacitive sensor. Bubbles, large bubbles, dispersed bubbles, churn, intermittent and annular flow patterns were identified subjectively. The clustering method satisfactorily identified groups of data corresponding to the distinct flow patterns, which were compared with predictive methods available in the open literature. New predictive methods for transitions between flow patterns are proposed based on the flow patterns identified objectively. The proposed methods predicted accurately the data obtained in the present study as well as experimental results and flow pattern maps available in the open literature for distinct geometries.     

Probabilistic mapping of adiabatic horizontal two-phase flow by capacitance signal feature clustering

In order to better quantify two-phase flow regime transitions, a sensor is developed which measures the electric capacitance of two-phase flows. A large number of experiments are done with air–water flow in a 9 mm ID horizontal tube. Based on a multivariate analysis, the most suitable sensor signal parameters are selected for building a flow regime classifier. This classifier is based on a fuzzy c-means clustering algorithm together with a regression technique. The output of the algorithm is used to create a probabilistic flow regime map. A comparison between a visual classification based on high speed camera images and the outcome of the flow regime classifier shows a remarkable agreement. The flow regime transitions are further quantified and discussed based on the probabilistic information and the sensor signal characterization. Probabilistic mapping makes it possible to combine flow regime dependent correlations in the two-phase flow models for heat transfer and pressure drop with smooth and appropriately quantified transitions from one flow regime to another.     

Two phase flow and heat transfer characteristics of a separate-type heat pipe

Two phase flow and heat transfer characteristics of a separate-type heat pipe have been studied experimentally and theoretically. The experimental apparatus have the same geometry for the evaporator and the condenser which consist of 5-tube-banks, with working temperature ranges of 80–125°C. The experimental working fluid is dual-distilled water with corrosion-resistant agents. Heat transfer coefficients for boiling and condensation along with heat flux and working temperature are measured at different filling ratio. According to the results of the experiments, the optimized filling ratio ranges from 16 to 36%. Fitted correlations of average heat transfer coefficients of the evaporator and Nusselt numbers of the condenser at the proposed filling ratio are obtained. Two phase flow characteristics of the evaporator and the condenser as well as their influence on heat transfer are described on the basis of simplified analysis. Reasons for the pulse-boiling process remain to be studied.     

Experimental study on oil–water flow in horizontal and slightly inclined pipes

Oil–water two-phase flow experiments were conducted in a 15 m long, 8.28 cm diameter, inclinable steel pipe using mineral oil (density of 830 kg/m³ and viscosity of 7.5 mPa s) and brine (density of 1060 kg/m³ and viscosity of 0.8 mPa s). Steady-state data on flow patterns, two-phase pressure gradient and holdup were obtained over the entire range of flow rates for pipe inclinations of −5°, −2°, −1.5°, 0°, 1°, 2° and 5°. The characterization of flow patterns and identification of their boundaries was achieved via observation of recorded movies and by analysis of the relative deviation from the homogeneous behavior. A stratified wavy flow pattern with no mixing at the interface was identified in downward and upward flow. Two gamma-ray densitometers allowed for accurate measurement of the absolute in situ volumetric fraction (holdup) of each phase for all flow patterns. Extensive results of holdup and two-phase pressure gradient as a function of the superficial velocities, flow pattern and inclinations are reported. The new experimental data are compared with results of a flow pattern dependent prediction model, which uses the area-averaged steady-state two-fluid model for stratified flow and the homogeneous model for dispersed flow. Prediction accuracies for oil/water holdups and pressure gradients are presented as function of pipe inclination for all flow patterns observed. There is scope for improvement for in particular dual-continuous flow patterns.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

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.