Numerical and analytical study of laminar film condensation in upward and downward vapor flows

Abstract

Laminar film condensation in upward and downward vapor flows is numerically investigated by using a sharp-interface level-set method to track the condensate film surface and accurately calculating the phase-change mass flux under the saturation temperature condition at the interface. An analytical model for steady laminar film condensation in upward as well as downward vapor flows is developed to validate the present numerical results. As the vapor velocity increases, the condensation rate is observed to decrease in upward vapor flows whereas it increases in downward vapor flows. The effects of vapor velocity and wall temperature on laminar film condensation in upward and downward vapor flows are investigated.     

Visualization on flow patterns during condensation of R410A in a vertical rectangular channel

The visualization experiments on HFC R410A condensation in a vertical rectangular channel （14.34mm hydraulic diameter, 160mm length） were investigated. The flow patterns and heat transfer coefficients of condensation in the inlet region were presented in this paper. Better heat transfer performance can be obtained in the inlet region, and flow regime transition in other regions of the channel was also observed. Condensation experiments were carried out at different mass fluxes （ from 1.6 kg/h to 5.2 kg/h） and at saturation temperature 28~ C. It was found that the flow patterns were mainly dominated by gravity at low mass fluxes. The effects of interfacial shear stress on condensate fluctuation are significant for the film condensation at higher mass flux in vertical flow, and con- sequently, the condensation heat transfer coefficient increases with the mass flux in the experimental conditions, The drop formation and growth process of condensation were also observed at considerably low refrigerant vapor flow rate.     

Condensation of vapor in the presence of non-condensable gas in condensers

This paper presents a set of differential and algebraic equations that model heat and mass transfer in condensers in which a mixture of water vapor and non-condensable gas is cooled. The model has been used to predict the condensation rate, the bulk temperatures of the coolant and the gas–vapor mixture, and the surface temperatures of the condenser wall. The predicted results for counter flow tube condensers are compared with three sets of published experimental data for system in which air is the non-condensable gas. It is found that the predicted condensation rates and coolant bulk temperatures agree very well with all the three sets of experimental data, the predicted wall temperatures agree reasonably well with the experimental results, and the agreement between the predictions and the experimental results on the bulk temperature of the air–vapor mixture is excellent for one set of the experimental data, reasonable for the second set of experimental data, but poor for the third set of experimental data. It is suggested that the poor agreement between the predicted and measured bulk temperatures of the mixture for the third set of experimental data arises from the experimental errors. The results from this study show that when modeling vapor condensation in the presence of a non-condensable gas, a simple model for the mixture channel alone may not be sufficient since neither the temperature nor the heat flux at the wall can be assumed to be constant. The results also show that the wall temperature in the coolant channel can be quite high, and careful modeling of the heat transfer in the coolant channel is needed in order to achieve good agreement between the model predictions and the experimental results.     

Numerical Simulation of Laminar Film Condensation in a Horizontal Minitube with and Without Non-Condensable Gas by the VOF Method

Based on the volume of fluid (VOF) method, a steady three-dimensional numerical simulation of laminar film condensation of water vapor in a horizontal minitube, with and without non-condensable gas, has been conducted. A user-defined function defining the phase change is interpreted and the interface temperature is correspondingly assumed to be the saturation temperature. An annular flow pattern is to be expected according to a generally accepted flow regime map. The heat-transfer coefficient increases with higher saturation temperature and a smaller temperature difference between the saturation and wall temperatures, but varies little with different mass flux and degree of superheat. The existence of a non-condensable gas will lead to the generation of a gas layer between vapor and liquid, resulting in a lower mass-transfer rate near the interface and higher vapor quality at the outlet. In consequence, the heat-transfer coefficient of condensation with a non-condensable gas drops sharply compared with that of pure vapor condensation. Meanwhile, the non-condensable gas with a smaller thermal conductivity would cause a stronger negative effect on heat flux as a result of a higher thermal resistance of heat conduction in the non-condensable gas layer.     

水平管外TFE/NMP部分膜状冷凝热、质耦合传递过程研究

通过对水平管外双组分(TFE／NMP为三氟乙醇／氮甲基吡咯烷酮)部分膜状冷凝过程特点的分析，建立起部分膜状冷凝过程中热质传递过程的物理模型。以双膜理论为基础，利用部分膜状冷凝的特点，通过对界面传质、液膜内质量平衡、界面相平衡、界面能量平衡和汽膜截面能量平衡的分析计算，得到汽相温度和界面温度分布、汽相及液相NMP质量分数分布，由此进一步计算出冷凝膜厚分布、液膜传热系数分布和热流密度的分布。计算的热流密度与相关实验作了比较，发现与实验能较好的吻合。     

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved.The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.     

Condensation heat transfer and pressure drop of refrigerant R-410A flow in a vertical plate heat exchanger

Heat transfer and associated frictional pressure drop in the condensing flow of the ozone friendly refrigerant R-410A in a vertical plate heat exchanger (PHE) are investigated experimentally in the present study. In the experiment two vertical counter flow channels are formed in the exchanger by three plates of commercial geometry with a corrugated sinusoidal shape of a chevron angle of 60°. Downflow of the condensing refrigerant R-410A in one channel releases heat to the upflow of cold water in the other channel. The effects of the refrigerant mass flux, imposed heat flux, system pressure (saturated temperature) and mean vapor quality of R-410A on the measured data are explored in detail. The results indicate that the R-410A condensation heat transfer coefficient and associated frictional pressure drop in the PHE increase almost linearly with the mean vapor quality, but the system pressure only exhibits rather slight effects. Furthermore, increases in the refrigerant mass flux and imposed heat flux result in better condensation heat transfer accompanying with a larger frictional pressure drop. Besides, the imposed heat flux exhibits stronger effects on the heat transfer coefficient and pressure drop than the refrigerant mass flux especially at low refrigerant vapor quality. The friction factor is found to be strongly influenced by the refrigerant mass flux and vapor quality, but is almost independent of the imposed heat flux and saturated pressure. Finally, an empirical correlation for the R-410A condensation heat transfer coefficient in the PHE is proposed. In addition, results for the friction factor are correlated against the Boiling number and equivalent Reynolds number of the two-phase condensing flow.     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.     

Cross Vapor Stream Effect on Falling Film Evaporation in Horizontal Tube Bundle Using R134a

The falling film evaporation of R134a with nucleate boiling outside a triangular-pitch (2-3-2-3) tube bundle is experimentally investigated, and the effects of saturation temperature, film flow rate and heat flux on heat transfer performance are studied. To study the effect of cross vapor stream on the falling film evaporation, a novel test section is designed, including the tube bundle, liquid and extra vapor distributors. The measurements without extra vapor are conducted at the saturation temperature of 6, 10 and 16°C, film Reynolds number of 220 to 2650, and heat flux of 20 to 60 kWm^?2. Cross vapor stream effect experiments are operated at three heat fluxes 20, 30, and 40 kWm^?2 and two film flow rates of 0.035 and 0.07 kgm^?1s^?1, and the vapor velocity at the smallest clearance in the tube bundle varies from 0 to 2.4 ms^?1. The results indicate that: film flow rate, heat flux and saturation temperature significantly influence the heat transfer; the cross vapor stream either promote or inhibit the falling film evaporation, depending on the tube position, film flow rate, heat flux and vapor velocity.     

Falling film evaporation of ternary mixture under three different modes of heating

This numerical study deals with heat and mass transfer by evaporation under mixed convection in three different configurations of a ternary liquid film in a vertical channel. The ternary liquid mixture water-methanol-benzene falls along the right plate of channel while the other plate is kept thermally insulated. In the first configuration, a heat flux density is applied to the wall carrying the trickle film, while in the other configurations this same amount of heat is used to preheat the liquid film or the air at the inlet of the channel. The implicit finite difference scheme is used to solve the system of equations in both liquid and vapor phases. According to this study, it was observed that the evaporation efficiency is high when the mass fraction of volatile components is high or in the preheating state of ternary film.     

Wall heat flux partitioning during subcooled forced flow film boiling of water on a vertical surface

Subcooled flow film boiling experiments were conducted on a vertical flat plate, 30.5 cm in height, and 3.175 cm wide with forced convective upflow of subcooled water at atmospheric pressure. Data have been obtained for mass fluxes ranging from 0 to 700 kg/m²s, inlet subcoolings ranging from 0 to 25 °C and wall superheats ranging from 200 to 400 °C. Correlations for wall heat transfer coefficient and wall heat flux partitioning were developed as part of this work. These correlations derive their support from simultaneous measurements of the wall heat flux, fluid temperature profiles, liquid side heat flux and interfacial wave behavior during steady state flow film boiling. A new correlation for the film collapse temperature was also deduced by considering the limiting case of heat flux to the subcooled liquid being equal to the wall heat flux. The premise of this deduction is that film collapse under subcooled conditions occurs when there is no net vapor generation. These correlations have also been compared with the data and correlations available in the literature.     

Visualization study of steam condensation in triangular microchannels

A visualization experiment is conducted to investigate the condensation of steam in a series of triangular silicon microchannels. The results indicate that droplet, annular, injection and slug-bubbly flow are the dominant flow patterns in these triangular silicon microchannels. With increased mass flow rate, or an increase in the hydraulic diameter under the same Reynolds number, the location at which the injection occurred is observed to move towards the channel outlet. The frequency of the injection increases, i.e. the flow of condensation instability is higher with increased inlet vapor Reynolds number, condensate Weber number and the prolongation of the injection location, or with a decrease in the hydraulic diameter of the channel. In addition, the wall temperature of the channel decreases along the condensation stream. The total pressure drop, the average condensation heat transfer coefficient and the average Nusselt number are observed to be larger with increased inlet vapor Reynolds number. Moreover, it is found that the condensation heat transfer is enhanced by a reduction in the channel scale.     

The effect of gravity on R410A condensing flow in horizontal circular tubes

Heat transfer characteristics of R410A condensation in horizontal tubes with the inner diameter of 3.78?mm under normal and reduced gravity are investigated numerically. The results indicate that the heat transfer coefficients increase with increasing gravitational accelerations at a lower mass flux, whereas their differences under varying gravity are insignificant at a higher mass flux. The liquid film thickness decreases with increasing gravity at the top part of the tube, whereas the average liquid film thickness is nearly the same under different gravity accelerations at the same vapor quality and mass flux. The local heat transfer coefficients increase with increasing gravity at the top of the tube and decrease with increasing gravity at the bottom. The proportion of the thin liquid film region is important for the overall heat transfer coefficients for the condensing flow. A vortex with its core lying at the bottom of the tube is observed under normal gravity because of the combined effect of gravity and the mass sink at the liquid–vapor interface, whereas the stream traces point to the liquid–vapor interfaces under zero gravity. The mass transfer rate under zero gravity is much lower than that of normal gravity.     

Conjugate film condensation and natural convection along the interface between a porous and an open space

This paper reports a theoretical investigation focusing on the interaction between film condensation and natural convection along a vertical wall separating a fluid reservoir from a fluid-saturated porous reservoir. The two reservoirs are maintained at different temperatures. The study consists of two parts: in the first part the condensation phenomenon takes place in the fluid reservoir and the natural convection phenomenon in the porous layer. In the second part, the opposite situation is considered. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer are documented for a wide range of the problem parameters. These parameters appear after boundary layer scaling of the governing equations. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized in the course of the study. Finally, the effect of the thermal resistance of the wall constituting the interface separating the two reservoirs, on the overall heat flux from the condensation side to the natural convection side is determined.     

Evaporation heat transfer and pressure drop of refrigerant R-134a in a small pipe

An experiment was carried out to investigate the characteristics of the evaporation heat transfer and pressure drop for refrigerant R-134a flowing in a horizontal small circular pipe having an inside diameter of 2.0 mm. The data are useful in designing more compact and effective evaporators for various refrigeration and air conditioning systems. The effects of the imposed wall heat flux, mass flux, vapor quality and saturation temperature of R-134a on the measured evaporation heat transfer and pressure drop were examined in detail. When compared with the data for larger pipes (D_i ≥ 8.0 mm) reported in the literature, the evaporation heat transfer coefficient for the small pipe considered here is about 30–80% higher for most situations. Moreover, we noted that in the small pipe the evaporation heat transfer coefficient is higher at a higher imposed wall heat flux except in the high vapor quality region, at a higher saturation temperature, and at a higher mass flux when the imposed heat flux is low. In addition, the measured pressure drop is higher for increases in the mass flux and imposed wall heat flux. Based on the present data, empirical correlations were proposed for the evaporation heat transfer coefficients and friction factors.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Numerical Study of Condensation Heat Transfer in Curved Square and Triangle Microchannels

Abstract

A numerical study of condensation heat transfer in curved square and triangle microchannels with various curvatures is conducted. The model is based on the volume of fluid approach and user-defined routines. The predictive accuracy of the numerical results is assessed by comparing the heat transfer coefficient with available correlation. After the validation, the effects of the mass flux and heat flux on heat transfer coefficient are analyzed in detail. Increasing mass flux could strengthen heat transfer performance, while wall heat flux has little effect on condensation heat transfer coefficient. The curved microchannels show an advantage in heat transfer enhancement comparing with the straight ones, and the enhancement performs better in curved microchannels with larger curvatures. Besides, the heat transfer performance could be enhanced in triangle microchannels in comparison with square microchannels.     

Condensation of steam in silicon microchannels

A visualization study was performed on condensation of steam in microchannels etched in a 〈100〉 silicon wafer that was bonded by a thin Pyrex glass plate from the top. The microchannels had a trapezoidal cross section with a hydraulic diameter of 75 μm. Saturated steam flowed through these parallel microchannels, whose walls were cooled by natural convection of air at room temperature. The absolute pressure of saturated steam at the inlet ranged from 127.5 kPa to 225.5 kPa, and the outlet was at atmospheric pressure at approximately 101.3 kPa with the outlet temperature of the condensate ranging from 42.8 °C to 90 °C. Stable droplet condensation was observed near the inlet of the microchannel. When the condensation process progressed along the microchannels, droplets accumulated on the wall. As the vapor core entrained and pushed the droplets, it became an intermittent flow of vapor and condensate at downstream of the microchannels. The traditional annual flow, wavy flow and dispersed flow observed during condensation in macrochannels were not observed in the microchannels. Based on a modified classical droplet condensation theory, it is predicted that the droplet condensation heat flux increases as the diameter of the microchannel is decreased. It is also predicted that the droplet condensation heat flux of saturated steam at 225.5 kPa can reach as high as 1200 W/cm² at ΔT=10 °C in a microchannel having a hydraulic diameter of 75 μm.     

An overview of the effect of lubricant on the heat transfer performance on conventional refrigerants and natural refrigerant R-744

This review provides an overview of the lubricant on the heat transfer performance, including nucleate boiling, convective boiling, shell side condensation, forced convective condensation, and gas cooling, for conventional refrigerants and natural refrigerant R-744. Various parameters affecting the heat transfer coefficient subject to lubricant, such as oil concentration, heat flux, mass flux, vapor quality, geometric configuration, saturation temperature, thermodynamic and transport properties are discussed in this overview. It appears that the effect of individual parameter on theProd. Type: FTP heat transfer coefficient may be different from studies to studies. This is associated with the complex nature of lubricant and some compound effect accompanying with the heat transport process. In this review, the authors try to summarize the general trend of the lubricant on the heat transfer coefficient, and to elaborate discrepancies of some inconsistent studies. The lubricant can, increase or impair the heat transfer performance depending on the oil concentration, surface tension, surface geometry, and the like. For the condensation, it is more well accepted that the presence of lubricant normally will impair the heat transfer performance due to deposited oil film. However, the deterioration is comparatively smaller than that in nucleate/convective boiling. For the effect of lubricant on R-744 with convective evaporation, the general behavior is in line with the convectional refrigerant. For gas cooling, the lubricant cast significant effect on heat transfer coefficient especially for a higher mass flux or at a smaller diameter tube.     

基于有限元方法的溴化锂降膜吸收传热传质的数值研究

吸收器是吸收式制冷系统的重要部件.溴化锂溶液的降膜吸收是吸收器中最常见的传质传热形式之一.通过对溴化锂溶液在降膜吸收过程中传质和传热特性的分析,使用基于有限元法的COMSOL Multiphysics软件,建立了溴化锂溶液和水蒸汽降膜吸收的物理数学模型,计算了液膜内部温度和质量分数的分布、界面处传质通量、界面处传热通量...