Experiments for liquid phase mass transfer rate in annular regime for a small vertical tube

The double film extraction technique was used to measure the deposition rate and the entrainment rate of droplets for vertical upward annular two-phase flow in a small diameter tube. The test section was a round tube of 5 mm in inside diameter, air and water were used as test fluids and the system pressure was varied within 0.14–0.76 MPa. It was shown in the present experimental conditions that the deposition rate was primarily influenced by the droplet concentration in the gas core and that the entrainment rate was correlated well with the dimensionless number denoting the ratio of interfacial shear force to surface tension force acting on the surface of liquid film. These results were consistent with available empirical correlations that were developed using the experimental data for larger diameter tubes.     

New entrainment rate correlation in annular two-phase flow applicable to wide range of flow condition

Assuming the rate of droplet entrainment is characterized by the ratio of the interfacial shear force to the surface tension force acting on the phase interface, new correlation representing the rate of droplet entrainment in annular-dispersed two-phase flow was developed. Although the correlation is based on the simple assumption, the quasi-equilibrium droplet flow rates measured in many experiments were predicted reasonably well (root mean square error of entrainment fraction was roughly halved comparing with several existing correlations). Its applicability to the non-equilibrium situation was also demonstrated by the numerical calculations using a one-dimensional three-fluid model.     

Flow boiling heat transfer in two-phase micro-channel heat sinks--I. Experimental investigation and assessment of correlation methods

This paper is the first of a two-part study concerning measurement and prediction of saturated flow boiling heat transfer in a water-cooled micro-channel heat sink. In this paper, new experimental results are discussed which provide new physical insight into the unique nature of flow boiling in narrow rectangular micro-channels. The micro-channel heat sink contained 21 parallel channels having a m cross-section. Tests were performed with deionized water over a mass velocity range of 135-402 kg/m² s, inlet temperatures of 30 and 60 °C, and an outlet pressure of 1.17 bar. Results indicate an abrupt transition to annular flow near the point of zero thermodynamic equilibrium quality, and reveal the dominant heat transfer mechanism is forced convective boiling corresponding to annular flow. Contrary to macro-channel trends, the heat transfer coefficient is shown to decrease with increasing thermodynamic equilibrium quality. This unique trend is attributed to appreciable droplet entrainment at the onset of annular flow regime development, and the increase in mass flow rate of the annular film by droplet deposition downstream. Eleven previous empirical correlations are assessed and deemed unable to predict the correct trend of heat transfer coefficient with quality because of the unique nature of flow boiling in micro-channels, and the operating conditions of water-cooled micro-channel heat sinks falling outside the recommended application range for most correlations. Part II of this study will introduce a new annular flow model as an alternative approach to heat transfer coefficient prediction for micro-channels.     

A new generalised model for liquid film cooling in rocket combustion chambers

A one dimensional analytical model of liquid film cooling in rocket combustion chambers operating at subcritical conditions is developed. The approach followed involves the selection of a control volume for mass and energy balance. The coolant evaporation rate per area is obtained from this energy balance. The present model incorporates mass transfer via entrainment by adapting suitable correlations from literature pertaining to annular flow conditions. The model predicted favourably with the experimental data available in open literature and produced superior results compared to all existing models. Results are presented for a mixed gas–water system under different conditions. Results indicate that convection dominates the heat transfer at the gas–liquid interface. Effects of gas Reynolds number, coolant inlet temperature, combustion chamber pressure, mass flow ratio of the liquid coolant to the free stream and the free stream turbulence on the liquid film length are presented in detail.     

Flow boiling heat transfer in two-phase micro-channel heat sinks--II. Annular two-phase flow model

This paper is Part II of a two-part study devoted to measurement and prediction of the saturated flow boiling heat transfer coefficient in water-cooled micro-channel heat sinks. Part I discussed the experimental findings from the study, and identified unique aspects of flow boiling in micro-channels such as abrupt transition to the annular flow regime near the point of zero thermodynamic equilibrium quality, and the decrease in heat transfer coefficient with increasing quality. The operating conditions of water-cooled micro-channels fell outside the recommended range for most prior empirical correlations. In this paper, an annular flow model is developed to predict the saturated flow boiling heat transfer coefficient. Features unique to two-phase micro-channel flow, such as laminar liquid and vapor flow, smooth interface, and strong droplet entrainment and deposition effects, are identified and incorporated into the model. The model correctly captures the unique overall trend of decreasing heat transfer coefficient with increasing vapor quality in the low vapor quality region of micro-channels. Good agreement is achieved between the model predictions and heat transfer coefficient data over broad ranges of flow rate and heat flux.     

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.     

CO2跨临界循环吸热过程换热性能理论分析

通过对两相流型和干涸现象进行分析，发现CO2在吸热沸腾过程中，环状流是主要的流型，液滴夹带和沉降是支持环状流最可能的机理。与其他制冷剂相比，CO2出现环状流以及发生干涸时的干度值要低得多。并且干涸前和干涸后的传热特点，以及关联式形式存在很大差别，应该区分对待。因此，研究能淮确描述CO2流动沸腾换热关联式，为CO2跨临界制冷循环蒸发器的优化设计提供理论依据，是非常必要的。     

Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface

Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet’s free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120 °C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet’s evaporation rate is predicted using a model based on Fick’s law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid–gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.     

Mass transfer on and within a frost layer

This paper investigates fundamental phenomena related to understanding of frost deposition and growth. The water vapor mass transfer rate from the air stream to a frost surface was tested and the results analyzed. The water vapor pressure at the frost surface was found to be supersaturated, and this phenomenon is explained using laminar concentration boundary layer analysis. A simple equation for calculating the supersaturated water vapor density at the frost surface was developed using boundary layer analysis, and it was compared to the experimental data. The comparison showed that the proposed equation for the water vapor supersaturation degree at the frost surface agrees well with the experimental data. The physical meaning of the tortuosity factor, which is related to mass diffusion within the frost layer, is mathematically explained, and published correlations were reviewed. It was found that some existing correlations are basically empirical curve fits that force agreement of the frost growth rate with the measured values. Further, these empirical curve fits do not satisfy the known physical bounds on the tortuosity factor. This deficiency further supports the existence of supersaturation at the frost surface. The effect of uncertainty in tortuosity factor on the heat transfer rate through a frost layer was quantitatively analyzed, and it was found that its uncertainty does not significantly affect the heat transfer rate through the frost layer in typical frosting conditions.     

Acoustic Wave Prediction in Flowing Steam-Water Two-Phase Mixture

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Numerical study of condensation flow regime transition in wavy microchannels

A numerical research on flow regime transition in wavy microchannels was conducted. The model was based on the volume of fluid approach and user-defined routines including interfacial mass transfer and latent heat. The observed droplet flow, annular–wavy flow, injection flow, and slug–bubbly flow were qualitatively compared against experimental data and transition lines were established. The effects of inlet vapor velocity, wall heat flux, and microchannel geometry characteristics on the annular length, occurrence frequency of injection flow, initial slug volume, and bubble detachment frequency were investigated.     

Numerical simulation of emulsified fuel spray combustion with puffing and micro-explosion

The purpose of this study was to develop numerical simulation of spray combustion of emulsified fuel with considering puffing and micro-explosion. First, a mathematical model for puffing was proposed. In the proposed puffing model, the rate of mass change of a droplet during puffing was expressed by the evaporation rate of dispersed water and the mass change rate due to fine droplets spouted from the droplet surface. The mass change rate due to fine droplets was related to the evaporation rate of the dispersed water and each liquid content. This model had only one experimental parameter. The essential feature of this model was that it was simple to apply to numerical simulation of spray combustion. First, the validity of the proposed puffing model was investigated with the experimental results for a single droplet. The calculated results for a single droplet with the experimental parameter varying from 5.0 to 10 were in good agreement with the experimental results. Moreover, numerical simulation of spray combustion of emulsified fuel was carried out. The occurrence of puffing and micro-explosion was determined by the inner droplet temperature. When micro-explosion occurred, a droplet changed to vapor rapidly. When the proposed puffing model was used in numerical simulation of spray combustion, the experimental parameter in the puffing model was determined for each droplet by random numbers within the range 5.0-10. The calculated results of spray combustion of emulsified fuel without considering puffing or micro-explosions were different from the experimental results even where combustion reactions were almost terminated. Meanwhile, the calculated results when considering puffing and micro-explosions were in good agreement with experimental results at the same location.     

Effect of pressure on entrainment flow rate in vertical upwards gas—liquid annular two-phase flow. Part I: Experimental results for system pressures from 0.3 MPa to 20 MPa

The purpose of this study is to investigate the pressure effects on the entrainment flow rates in vertical gas—liquid annular two-phase flow. The cross-sectional entrainment flow rates were measured using an isokinetic probe method. It was found that the behavior of cross-sectional entrainment flow rate profiles is divided into low- and high-pressure regions. Also, the entrainment flow rates amount to 90 percent of the total liquid flow rate under high-pressure conditions. In this study, system pressure in the closed-loop system was changed substantially from 0.3 MPa to 20 MPa at a constant fluid temperature in vertical upward flow. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(5): 267–280, 1996     

Experimental validation of a lumped model of single droplet deformation,oscillation and detachment on the GDL surface of a PEM fuel cell

Proton Exchange Membrane Fuel Cell (PEMFC) performance significantly depends on electrodes water content. Liquid water emerging from the Gas Diffusion Layer (GDL) micro-channels can form droplets, films or slugs in the Gas Flow Channel (GFC). In the regime of droplets formation, the interaction with the gas flow leads to an oscillating mechanisms that is fundamental to study the detachment from the GDL surface. In this work, a numerical model of a droplet growing on the GDL surface is developed to describe the interaction between droplet and gas flow. Therefore, a lumped force balance is enforced to determine the center of mass motion law. Oscillation frequencies during growth and at detachment are found as a function of droplet size. The model is also exploited to find the relationship between droplet critical detachment size and gas velocity. The numerical results are compared with the experimental data previously published by the authors as well as with other experimental results available in the literature. The matching between the numerical and experimental data is very good. The low computational burden and the conciseness of the proposed approach make the model suitable for applications such as control and optimization strategies development to enhance PEMFC performance. Additionally, the model can be exploited to implement monitoring and diagnostic algorithm as well.     

Flow condensation in parallel micro-channels – Part 2: Heat transfer results and correlation technique

This second part of a two-part study concerns heat transfer characteristics for FC-72 condensing along parallel, square micro-channels with a hydraulic diameter of 1 mm, which were formed in the top surface of a solid copper plate. Heat from the condensing flow was rejected to a counter flow of water through channels brazed to the underside of the copper plate. The FC-72 condensation heat transfer coefficient was highest near the channel inlet, where the annual liquid film is thinnest. The heat transfer coefficient decreased along the micro-channel because of the film thickening and eventual collapse of the annular regime. Notable heat transfer enhancement was observed for annular flow regions of the micro-channel associated with interfacial waves. Comparing the present data to predictions of previous annular condensation heat transfer correlations shows correlations intended for macro-channels generally provide better predictions than correlations intended specifically for mini/micro-channels. A new condensation heat transfer coefficient correlation is proposed for annular condensation heat transfer in mini/micro-channels. The new correlation shows excellent predictive capability based on both the present FC-72 data and a large database for mini/micro-channel flows amassed from eight previous sources.     

New model for frost growth rate

Many models have been published to predict frost growth. These may be divided into empirical and theoretical models. All prior theoretical models assume the water vapor is saturated at the interface between the air stream and frost layer. This paper provides a new theoretically based numerical model of frost deposition and growth. The present model: (1) uses supersaturated water vapor at the frost surface, which is fundamentally correct; (2) improved correlations for frost thermal conductivity; (3) uses a rationally based tortuosity factor; and (4) calculates the local frost density variation. For numerical simulation of the frost growth rate, the measured thermal conductivity was used. Frost growth rate on a cold surface was measured, and the experimental data were compared to the numerical model and agreed within 15%. The proposed supersaturation model was also compared to previous investigators’ experimental data, and it was found that the supersaturation model is superior to analytical or numerical models that assume the water vapor at the frost surface to be saturated.     

An experimental study of flow pattern and pressure drop for flow boiling inside microfinned helically coiled tube

In this paper, flow patterns and their transitions for refrigerant R134a boiling in a microfinned helically coiled tube are experimentally observed and analyzed. All the flow patterns occurred in the test can be divided into three dominant regimes, i.e., stratified-wavy flow, intermittent flow and annular flow. Experimental data are plotted in two kinds of flow maps, i.e., Taitel and Dukler flow map and mass flux versus vapor quality flow map. The transitions between various flow regimes and the differences from that in smooth straight tube have also been discussed. Martinelli parameter can be used to indicate the transition from intermittent flow to annular flow. The transition from stratified-wavy flow to annular or intermittent flow is identified in the vapor quality versus mass flux flow map. The flow regime is always in stratified-wavy flow for a mass flux less than 100 kg/m² s.The two-phase frictional pressure drop characteristics in the test tube are also experimentally studied. The two-phase frictional multiplier data can be well correlated by Lockhart–Martinelli parameter. Considering the corresponding flow regimes, i.e., stratified and annular flow, two frictional pressure drop correlations are proposed, and show a good agreement with the respective experimental data.     

Direct-contact condensation of pure steam on co-current and counter-current stratified liquid flow in a circular pipe

We carried out a set of experiments on the direct-contact condensation of atmospheric steam for subcooled water flowing co-currently and counter-currently in a circular pipe. The condensation heat transfer coefficient was evaluated both for co-current and counter-current steam–water flow cases in a horizontal circular pipe. In the current experiment the dependency of the liquid Nusselt number on the gas Reynolds number is higher in the counter-current than in the co-current experimental data. The dependency of the liquid Nusselt number on the steam Reynolds number is stronger in the rectangular channel than in the circular pipe. The overall heat transfer characteristics are better in the co-current flow than in the counter-current flow with the same injection flow rates of the steam and the water. The present co-current experimental data were used to assess four existing correlations. However, there are few reliable correlations existing to predict co-current experimental data. The comparisons of the present counter-current experimental data with the existing correlations show that Chu’s (Chu, I.C., Yu, S.O., Chun, M.H. 2000. Interfacial condensation heat transfer for counter-current steam–water stratified flow in a circular pipe, J. Korea Nucl. Soc., 32 (2), 142–156) correlation predicts the experimental data well.     

3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling

The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solid–vapor/liquid–vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid–vapor and solid–vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet’s initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.     

垂直窄缝通道内环状流沸腾传热特性

本研究基于液膜和蒸汽的质量、动量和能量方程,建立了均匀热流垂直窄缝通道内环状流沸腾传热模型,通过相关文献估算环状流起始点处液膜厚度,利用有限差分法对环状流模型方程组进行数值求解,得到沿流道环状流区域的液膜厚度,并进一步预测了局部沸腾传热系数,结果表明:环状流区域的局部沸腾传热系数随质量流量和干度的增加而增加,与Kenning关联式对比,模型预测沸腾传热系数较关联式计算值偏低。将不同工况下的226组两相环状流实验数据与模型预测结果进行对比,平均绝对误差为18.2%。