Experimental study of convective condensation in an inclined smooth tube. Part II: Inclination effect on pressure drops and void fractions

This article is the second part of a two-part paper, dealing with an experimental study of convective condensation of R134a at a saturation temperature of 40 °C in an 8.38 mm inner diameter smooth tube in inclined orientations. The first part concentrates on the flow pattern and the heat transfer coefficients. This second part presents the pressures drops in the test condenser for different mass fluxes and different vapour qualities for the whole range of inclination angles (downwards and upwards). Pressures drops in a horizontal orientation were compared with correlations available in literature. In a vertical orientation, the experimental results were compared with pressure drop correlations associated with void fraction correlations available in literature. A good agreement was found for vertical upward flows but no correlation predicted correctly the measurements for downward flows. An apparent gravitational pressure drop and an apparent void fraction were defined in order to study the inclination effect on the flow. For upward flows, it seems as if the void fraction and the frictional pressure drop are independent of the inclination angle. Apparent void fractions were successfully compared with correlations in literature. This was not the case for downward flows. The experimental results for stratified downward flows were also successfully compared with the model of Taitel and Dukler.     

Condensation pressure drop characteristics of various refrigerants in a horizontal smooth tube

The two-phase pressure drop characteristics of the pure refrigerants R410a, R502, and R507a during condensation inside a horizontal tube-in-tube heat exchanger were investigated to determine the two-phase friction factor, the frictional pressure drop, and the total pressure drop. The two-phase friction factor and frictional pressure drop are predicted by means of an equivalent Reynolds number model. Eckels and Pate's experimental data, presented in Choi et al.'s study provided by NIST, were used in the analysis. In their experimental setup, the horizontal test section was a 3.81 m long countercurrent flow double tube heat exchanger with refrigerant flowing in the inner smooth copper tube (8.01 mm i.d.) and cooling water flowing in the annulus (13.7 mm i.d.). Their test runs were performed at saturated condensing temperatures from 38.33 °C to 51.78 °C while the mass fluxes were between 119 and 617 kg m⁻² s⁻¹ for the horizontal test section. The separated flow model was modified by ten different void fraction models and correlations, as well as six different correlations of friction factors, in order to determine the best combination for the validation of the experimental pressure drop values. Carey's friction factor was found to be the most predictive. The refrigerant side total and frictional pressure drops were determined within ± 30% using the above friction factor and the void fraction combinations of Carey, Baroczy, and Armand for R410a; and those of Carey, Spedding and Spence, and Rigot for R502 and R507a. The equivalent Reynolds number model was modified using the void fraction correlation of Rigot in order to determine the frictional condensation pressure drop and the two-phase friction factor. The effects of vapor quality and mass flux on the pressure drop are discussed in this paper. The importance of using the alternative void fraction and friction factor models and correlations for the separated flow model is also addressed.     

Experimental and numerical investigation of two-phase pressure drop in vertical cross-flow over a horizontal tube bundle

Experimental pressure drop data for vertical two-phase air–water flow across horizontal tubes is presented for gas mass fractions in the range 0.0005–0.6 and mass fluxes in the range 25–700 kg/m² s. The square in-line tube bundle had one column containing ten tubes and two columns of half tubes attached to the walls. The tubes had a diameter of 38 mm and a pitch to diameter ratio of 1.32. This data and air–water and R113 vapour–liquid data available in the literature are compared with the predictions from two kettle reboiler models, the one-dimensional model and a one-dimensional formulation of the two-fluid model. The one-dimensional model was implemented with three separate void fraction correlations and one two-phase friction multiplier correlation. The results show that the two-fluid model predicts air–water void fraction data well but R113 data poorly with pressure drop predictions for both being unsatisfactory. The one-dimensional model is shown to predict pressure drop and void fraction data reasonably well, provided a careful choice is made for the void fraction correlation.     

Correlations of two-phase frictional pressure drop and void fraction in mini-channel

Alternative correlations of two-phase friction pressure drop and void fraction are explored for mini-channels based on the separated flow model and drift-flux model. By applying the artificial neural network, dominant parameters to correlate the two-phase friction multiplier and void fraction are picked out. It is found that in mini-channels the non-dimensional Laplace constant is a main parameter to correlate the Chisholm parameter as well as the distribution parameter. Both previous correlations and the newly developed correlations are extensively evaluated with a variety of data sets collected from the literature.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.     

A generalized numerical correlation study for the determination of pressure drop during condensation and boiling of R134a inside smooth and corrugated tubes

The measured pressure drop of R134a, flowing downward and horizontally inside smooth and corrugated copper tubes, is estimated by the closed form of artificial neural network method to have a reliable empirical correlation using some dimensionless numbers. The working fluids are R134a and water flowing in the test tube and annular tube, respectively. This paper is a continuation of the authors' previous work and includes all their previous works about condensation and boiling in tubes. All data used in the present paper are obtained from the authors' previous studies. The training sets have the experimental data of convective condensation and boiling experiments including various mass fluxes and saturation temperatures of R134a. Froude number, Weber number, Bond number, Lockhart and Martinelli number, void fraction, the ratio of density to dynamic viscosity, liquid, vapor and equivalent Reynolds numbers, surface tension parameter and liquid Prandtl number are the inputs of the formula as the dimensionless numbers obtained from measured values of test section, while the output of the formula is the measured pressure drops in the analysis. A closed form of multi-layer perceptron (MLP) method of artificial neural network (ANN) is used to estimate the experimental pressure drop of R134a numerically. 1177 data points are used in the analyses of the ANN method to be able to have a single generalized empirical correlation for both condensation and boiling flows. The evaluation of the closed form of multi-layer perceptron (MLP) with two or three inputs and one hidden neuron architecture was successful predicting the measured pressure drops with their error bands being within the range of ± 30% for all used data. The proposition of empirical correlations are performed for both condensation and boiling flows separately. A single empirical correlation is able to calculate the measured pressure drop of both condensation and boiling flows together. Moreover, the dependency of output of the proposed formula from input values is examined in the study. By means of the dependency analyses, liquid Prandtl number, Butterworth's void fraction and Lockhart and Martinelli parameter are found to be the most dominant parameters among other dimensionless numbers.     

Two-Phase Flow and Heat Transfer across Horizontal Tube Bundles‐A Review

This paper presents a state-of-the-art review of two-phase flow and flow boiling across horizontal tube bundles. The review covers studies related to the dynamic aspects of two-phase flow on the shell side of staggered and in-line tube bundles for upward, downward, and side-to-side flows (i.e. the evaluation of void fraction, two-phase flow behaviors and pressure drops). Heat transfer experimental work and heat transfer prediction methods on tube bundles in cross-flow for plain, low-fin, and enhanced boiling tubes are also covered. The proposed flow pattern maps and semi-empirical correlations for predicting void fraction and frictional pressure drop are critically described. These prediction methods are generally based on experimental results for adiabatic air-water flows, and noticeable discrepancies are revealed in the results provided by them. This study reveals that before now, there were no heat transfer prediction methods that can be recommended as a general design tool. Finally, this study suggests further research focusing on the development of representative databanks and prediction methods.     

Measurement and Modeling of Void Fraction in High-Pressure Condensing Flows Through Microchannels

Void fraction measurements are obtained using high-speed video for the condensation of R404A in tubes of diameter 0.508, 1.00, and 3.00 mm. Experiments were conducted on refrigerant R404A throughout the entire condensation quality range (0.05–0.95) at varying mass fluxes (200–800 kg m^?2 s^?1) and saturation temperatures from 30 to 60°C (which correspond to the reduced pressure range 0.38–0.77). These high pressures are representative of actual operation of air-conditioning and refrigeration equipment. The influence of saturation temperature on void fraction is most pronounced in the quality range 0.25–0.75. In addition, it was found that the influence of mass flux on void fraction was negligible for all saturation temperatures and tube diameters investigated. Three void fraction models from the literature are compared with the data. Of these, the Baroczy correlation predicted the data the best, with an overall absolute average deviation of 11.2%. A new drift flux void fraction model is developed to predict void fraction for condensing flows in microchannels and compared with the R404A data and R134a void fraction data from Winkler et al. Overall, the model is able to predict 92.3% of the R404A data and 81.6% of all refrigerant data within 25%.     

Eulerian multiphase study of direct steam generation in parabolic trough with OpenFOAM

Direct steam generation (DSG) in parabolic trough solar collectors is a feasible option for economic improvement in solar thermal power generation. Three-dimensional Eulerian two-fluid simulations are performed under OpenFOAM to study the turbulent flow in the evaporation section of the parabolic trough receiver and investigate the phase change, and pressure drop of water as a heat transfer fluid. First, the model's validity has been tested by comparing the numerical results of a laboratory scale boiler with the available correlations and semi-correlations of boiling flows from the literature. Simulations agreed well with Rouhani–Axelsson correlation for horizontal tubes, with a mean relative error of less than 7.1% for all studied cases. However, despite a mean relative error of less than 13.19% compared to the experimental data in the literature, the reported pressure drop factor remains valid; overprediction remains tolerable for most engineering applications. Second, the scaling effect on the mathematical model, from laboratory to commercial-scale configuration, was tested with experimental data of the DISS test loop in Platforma Solar de Almeria, Spain. The Monte Carlo Ray Tracing method under the Tonatiuh package allowed for obtaining the nonuniform heat flux distribution. Due to the large size of the evaporation section in the DISS loop (eight collectors), each collector is considered independently in the simulations. Thus, simulations follow each other, taking the numerical results of each collector output as input data in the next collector and so on until the last. The numerical results showed an excellent agreement for the void fraction with 3.53% against the Rouhani–Axelsson correlation. Frictional pressure losses are within a 17.06% error of the Friedel correlation, in the range of previous work in the literature, and the heat loss is less than 4.69% error versus experimental correlation.     

Nusselt number and friction factor correlations for packed bed solar energy storage system having large sized elements of different shapes

In order to investigate the effect of system and operating parameters on heat transfer and pressure drop characteristics of packed bed solar energy storage system with large sized elements of storage material, an extensive experimental study has been conducted and reported in the present paper. Five different shapes of elements of storage material have been investigated. Correlations have been developed for Nusselt number and friction factor as function of Reynolds number, sphericity and void fraction. The present correlations can be used to predict the performance of the actual packed bed solar energy storage system having packing material elements of different shapes and bed porosities within the range of parameters investigated.     

Void Fraction Variations in a Fractal-Like Branching Microchannel Network

Based on predictions of lower pressure drop penalties in fractal-like branching channels compared to parallel channels, an experimental investigation of two-phase void fraction variations was performed. The flow network, mimicking flow networks found in nature, was designed with a self-similar bifurcating channel configuration and etched 150 μ m into a 38.1 mm diameter silicon disk. A Pyrex® cover was anodically bonded to the silicon disk to allow for flow visualization. The length and width scale ratios between channels on either side of a bifurcation are fixed. The channel widths range in size from 100 μ m to 400 μm over a total channel length of approximately 17 mm. Experimental results of flow boiling are presented for a heater energy input power of 66 W and an inlet water flow rate of 45 g/min at a fixed inlet fluid temperature of 88°C. High-speed, high-resolution imaging was used to visualize the flow and quantify void fraction values in several channels within a branching structure. Both time-averaged and instantaneous two-dimensional void fraction data are presented, showing a correlation between channels at the same bifurcation level and between channels at different bifurcation levels.     

Characteristics of Two-Phase Flows in a Rectangular Microchannel with a T-Junction Type Gas-Liquid Mixer

In this study, gas–liquid two-phase flows in a horizontal rectangular microchannel have been investigated. The rectangular microchannel has a hydraulic diameter of 0.235 mm, and a width and depth of 0.24 mm and 0.23 mm, respectively. A T-junction-type gas–liquid mixer was used to introduce gas and liquid in the channel. In order to know the effects of liquid properties, distilled water, ethanol, and HFE7200 were used as the test liquids, with nitrogen gas was used as the test gas. The flow pattern, the bubble length, the liquid slug length, and the bubble velocity in two-phase flow were measured with a high-speed video camera, and the void fraction was determined from the bubble velocity data and the superficial gas velocity data. In addition, the pressure drop was also measured with a calibrated differential pressure transducer. The bubble length data were compared with the calculation by the scaling law proposed by Garstecki et al. [7]. The bubble velocity data and/or the void fraction data were well correlated with the well-known drift flux model [12] with a new distribution parameter correlation developed in this study. The frictional pressure drop data were also well correlated with the Lockhart-Martinelli method with a correlation of the two-phase friction multiplier.     

Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks – Part 2. Subcooled boiling pressure drop and heat transfer

This second part of a two-part study explores the performance of a new cooling scheme in which the primary working fluid flowing through a micro-channel heat sink is indirectly cooled by a refrigeration cooling system. The objective of this part of study is to explore the pressure drop and heat transfer characteristics of the heat sink. During single-phase cooling, pressure drop decreased with increasing heat flux because of decreased liquid viscosity. However, pressure drop began increasing with increasing heat flux following bubble departure. These opposite trends produced a minimum in the variation of pressure drop with heat flux. Increasing liquid subcooling decreased two-phase pressure drop because of decreased void fraction caused by strong condensation at bubble interfaces as well as decreased likelihood of bubble coalescence. It is shown macro-channel subcooled boiling pressure drop and heat transfer correlations are unsuitable for micro-channel flows. However, two new modified correlations produced good predictions of the present heat transfer data.     

Refrigerant Condensation Flow Regimes in Enhanced Tubes and Their Effect on Heat Transfer Coefficients and Pressure Drops

Flow regimes influence the heat and mass transfer processes during two-phase flow, implying that any statistically accurate and reliable prediction of heat transfer and pressure drop during flow condensation should be based on the analysis of the prevailing flow pattern. Many correlations for heat transfer coefficient and pressure drop during flow condensation completely ignored flow regime effects and treated flows as either annular or non-stratified flow or as stratified flow. This resulted in correlations of poor accuracy and limited validity and reliability. Current heat transfer coefficient, pressure drop, and void fraction models are based on the local flow pattern, though, resulting in deviations of around 20% from experimental data. There are, however, several inconsistencies and anomalies regarding these models, which are discussed in this paper. A generalized solution methodology for two-phase flow problems still remains an elusive goal, mainly because gas-liquid flow systems combine the complexities of turbulence with those of deformable vapor-liquid interfaces. The paper focuses on the state of the art in correlating flow condensation in micro-fin tubes and proposes flow regime-based correlations of heat transfer coefficient and pressure drop for refrigerant condensation in smooth, helical micro-fin, and herringbone micro-fin tubes.     

低流速净蒸汽产生点模型预测过冷沸腾空泡率

空泡率是汽液两相流动的基本参数之一,而已有过冷沸腾空泡率计算方法研究以高质量流速为主,且大量文献报道现有空泡率模型难以适用于低流速过冷沸腾工况。本文基于低流速过冷沸腾净蒸汽产生点(NVG)理论模型,进一步建立了计算过冷沸腾空泡率的分布拟合模型。在较宽广的压力、质量流速、热流密度和流道尺寸范围内将模型计算结果与现有空泡率实验数据进行了比较,低流速工况下该模型与实验数据符合良好,表明该模型可适用于低流速过冷沸腾工况。     

A two-dimensional model of the kettle reboiler shell side thermal-hydraulics

A two-dimensional two-fluid numerical model is developed for the prediction of two-phase flow thermal-hydraulics on the shell side of the kettle reboiler. The two-phase flow around tubes in the bundle is modeled with the porous media approach. A closure law for the vapour–liquid interfacial friction is based on modified pipe two-phase flow correlations. The tube bundle flow resistance is calculated by applying to each phase stream the correlations for the pressure drop in a single phase flow across tube bundles and by taking into account the separate contribution of each phase to the total pressure drop. Physically based boundary conditions for the velocity field at the two-phase mixture swell level are stated. The system of governing equations is solved numerically with the finite volume approach for two-phase flow built in the commercial computer program. Simulations are performed for available conditions of performed physical experiments. In comparison to the previous kettle reboiler two-dimensional modeling approaches, here presented model is original regarding the applied closure laws for the interfacial friction and bundle flow resistance, as well as applied boundary conditions for the modeling of two-phase mixture free surface. Also, regarding the previous published results, here obtained numerical results are compared with the available measured data of void fraction within the tube bundle and acceptable agreement is shown.     

An experimental study on the pressure drop of nanofluids containing carbon nanotubes in a horizontal tube

This article reports an experimental study on the flow characteristics of the aqueous suspensions of carbon nanotubes (CNTs). Stable nanotube suspensions were made for pressure drop measurements by two different methods. One of them is to disperse nanotubes using a surfactant, and the other is to introduce oxygen-containing functional groups on the CNT surfaces by acid treatment. The pressure drops in a horizontal tube and viscosities of nanofluids were measured and the effects of CNT loading and different preparation methods were investigated. Viscosity measurements show that both CNT nanofluids prepared by two methods are shear thinning fluids and at the same volume fraction, the nanofluids prepared by the acid treatment have much smaller viscosity than the ones made with surfactant. Under laminar flow conditions, the friction factor of CNT nanofluids stabilized by adding surfactant is much larger than that of CNT nanofluids prepared by acid treatment, and both nanofluids show larger friction factors than distilled water. In contrast to this, under turbulent flow conditions, the friction factors of both nanofluids become similar to that of the base fluids as the flow rate increases. It is also shown that as CNT loading is increased, laminar regime of nanofluids has been extended to further higher flow rates, therefore, nanofluids could have low friction factors than pure water flows at certain range of flow rates.     

Prediction of two-phase pressure drop and void fraction in microchannels using probabilistic flow regime mapping

Probabilistic two-phase flow map pressure drop and void fraction models are developed for 6-port microchannels in order to provide a more accurate and common means of predicting void fraction and pressure drop. The models are developed for R134a, R410A, and air–water in 6-port microchannels at 10 °C saturation temperatures, qualities from 0 to 1, and mass fluxes varying from 50 to 300 kg/m² s. The probabilistic flow map models developed are found to accurately predict void fraction and pressure drop for the entire quality range and for all three fluids.     

Heat- mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe

Experimental and theoretical results on flow, heat and mass transfer characteristics for the countercurrent flow of air and water in a vertical circular pipe are compared. An experimental setup was designed and constructed. Hot water is introduced through a porous section at the upper end of a test section and flows downward as a thin liquid film on the pipe wall while the air flows countercurrently. The air and water flow rates used in this study are those before the flooding is reached. A developed mathematical model is separated into three parts: A high Reynolds number turbulence model, in which the local state of turbulence characteristics consists of the turbulent kinetic energy (k) and its dissipation rate (ϵ).The transport equations for both k and s are solved simultaneously with the momentum equation to determine the kinetic turbulence viscosity, the pressure drop, interfacial shear stress and then the friction factor at the film/core interface; Heat and mass transfer models are proposed in order to estimate the distribution of the temperature and the mass fraction of water vapor in gas core. The results from the model are compared with the present experimental ones. It can be shown from the present study that the influence of the interfacial wave phenomena is significant to the pressure loss, and the heat and mass transfer rate in the gas phase.     

水平管内油气水三相分层流截面含气率的研究

以油气水三相混合物为工质,对水平管内分层流动的平均截面含气率进行了理论与实验研究。通过对分层流动的简化动力学分析,得到了截面含气率的理论模型,计算值与实验值符合良好。结果表明：影响分层流截面含气率的因素不仅包括折算气速和折算液速,还包括油水混合物的含油率。