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.     

Turbulent film condensation in the presence of non-condensable gases over a horizontal tube

A numerical model is presented for studying turbulent film condensation in the presence of non-condensable gases over a horizontal tube. Inertia, pressure gradient are included in this analysis, and the influence of turbulence in the proposed two-phase model is considered. The numerical results demonstrate that a very small bulk concentration of non-condensable gas reduces the heat transfer coefficient and film thickness considerably. The local heat flux and film thickness increase as tube surface temperature decreases at any bulk concentration of non-condensable gas. Moreover, inlet velocity increases as film thickness decreases and heat flux increases, a numerical result in agreement with that obtained by Nusselt. Numerical results indicate that average dimensionless heat transfer coefficients are in good agreement with theoretical and experimental data.     

Forced convection condensation in the presence of noncondensables and interfacial resistance

The effect of a noncondensable gas on condensation in a forced convection laminar boundary-layer flow is explored analytically. The analysis is first carried out in general for any arbitrary flow consisting of a vapor and a noncondensable gas, and certain universal results are obtained. Solutions of the similarity differential equations are found both numerically and by an integral method. The general formulation is applied to the steam-air system, and the heat transfer with and without the noncondensable is compared for a wide range of operating conditions. The reductions in heat transfer due to the non-condensable are accentuated at low operating pressures. In general, condensation in the forced convection flow is much less sensitive than that in a gravity flow. The effect of an interfacial resistance (i.e. a temperature jump at the liquid-vapor interface) is also examined. The computed results reveal a negligible effect on the heat transfer.     

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.     

A generalized mathematical description for comparative assessment of various horizontal polar tube geometries with regard to external film condensation in presence of non-condensable gases

A generalized mathematical treatment is postulated to investigate the condensation heat transfer performance of horizontal tubes with varying geometries, with the presence of non-condensable gases in the free stream. The governing equations of mass, momentum and energy conservation in the liquid phase are solved semi-analytically, with matching constraints being imposed at the liquid–vapour interface, while the governing equations of energy and species conservation in the vapour phase are solved numerically. An air–water vapour system is considered for demonstrating the mathematical model. Special cases of the model are illustrated with the aid of elliptical and equiangular spiral geometries. It is revealed that the geometrical features of typical polar surfaces can turn out to be favourable in arresting probable drastic reductions in the condensation heat transfer rates that could be otherwise associated with the presence of non-condensable gases in the free stream. The favourable effects induced by polar surfaces become relatively more prominent, as percentage of non-condensable gases in the free stream increases. A geometrical shape function is also ascertained in this regard, which quantifies the extent of this augmentation in the heat transfer performance. In general, it is suggested that polar surfaces with higher values of the shape function over a majority of the azimuthal regime can turn out to be more desired choices for achieving enhanced rates of condensation heat transfer, provided that there are no serious manufacturability constraints.     

Theoretical investigation of stable dropwise condensation heat transfer on a horizontal tube

The heat transfer model of stable dropwise condensation for saturated vapor on a horizontal tube is developed based on previous theoretical models. Through a comprehensive analysis of all the contributing thermal resistances, the convection effect inside the droplet itself is taken into consideration in the model. For the stable dropwise condensation process in dynamic conservation, a method of double integration of heat flux through numerous inclined plates with different inclination angles is introduced to obtain the overall heat flux through the horizontal tube surface. The model can predict the variation of heat transfer of stable dropwise condensation with different contact angles outside a horizontal tube. The influences of contact angle, temperature difference, and other typical parameters on both a single droplet and the whole condensation process are discussed. The results indicate that a high contact angle can cause a size reduction of falling droplets from condensing surface and thus taking more heat away. The adsorbed condensate film adds an extra thermal resistance and its thickness plays a significant role on the dropwise condensation heat transfer.     

凝结蒸汽中加入添加剂对凝结换热影响研究

研究当凝结蒸气中含有表面添加剂时单根管外的凝结换热。在对圆管外Marangon i凝结换热过程进行了理论分析的基础上,建立了含有凝结液膜的物理模型和基于边界层方程组的数学模型,应用相似理论进行了无量纲变换。计算结果表明,添加添加剂可以诱发界面流动,从而导致了气液界面处的液膜的不稳定,在气体凝结过程中产生了自发的扰动,加强了凝结换热。     

Film condensation in presence of non-condensable gases: Interplay between variable radius of curvature and interfacial slip

A theoretical study has been executed to investigate the implications of interfacial slip in presence of non-condensable species in the bulk mixture of vapour on heat transfer characteristics in film condensation over horizontal tubes with varying radius of curvature. A polar surface comprising a segment of an equiangular spiral in the form of Rp = ae^mθ (a and m being parametric constants), generated symmetrically on a vertical chord, has been considered. We reveal that there is a substantial enhancement in the rate of condensation heat transfer due to an effective interfacial slip at the solid–liquid interface. The enhancement in condensation heat transfer due to solid–liquid interfacial slip is more pronounced in the case of vapour with non-condensable species, but less pronounced for higher values of m (a surface profile parameter).     

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。     

A Numerical Analysis of the Forced Convection Condensation of Saturated Vapor Flowing Axially Outside a Horizontal Tube

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Transition from natural to mixed convection for steam–gas flow condensing along a vertical plate

An analysis method based on two-phase boundary layer analysis has been developed to study the effects of superimposed forced convection on natural convection steam–gas flow condensing along a vertical plate. The mechanism by which superimposed forced convection enhances heat transfer is evaluated: the bulk flow blows away non-condensable gases accumulating near the interface, resulting in an elevated condensation driving force. Further, this bulk flow blowing capability may be characterized by a conventional mass transfer driving potential. Results of the new model are shown to be consistent with experimental data. Finally, a simple criterion was developed to identify transition to mixed convection from natural convection steam–gas flow.     

Non-iterative condensation modeling for steam condensation with non-condensable gas in a vertical tube

Based on a heat and mass transfer analogy, an iterative condensation model for steam condensation in the presence of a non-condensable gas in a vertical tube is proposed including the high mass transfer effect, entrance effect, and interfacial waviness effect on condensation. A non-iterative condensation model is proposed for easy engineering application using the iterative condensation model and the assumption of the same profile of the steam mass fraction as that of the gas temperature in the gas film boundary layer. It turns out that the Nusselt number for condensation heat transfer is expressed in terms of air mass fraction, Jakob number, Stanton number for mass transfer, gas mixture Reynolds number, gas Prandtl number and condensate film Nusselt number. The comparison shows that the non-iterative condensation model reasonably well predicts the experimental data of Park, Siddique, and Kuhn.     

A closed-form solution for laminar film condensation from downward pure vapour flow in vertical tubes

An analytical solution is derived for the film thickness for simplified steady-state governing equations of laminar film condensation from laminar pure vapours flowing downward in vertical tubes. This approach yields an accurate, approximate closed-form non-marching solution for the condensate film thickness. All other relevant quantities such as the heat transfer coefficient, the vapour and liquid velocity profiles, the vapour and liquid mass flow rates, the interfacial shear stress, and the pressure gradient can be easily computed in closed-form from this solution directly at any given axial location. The present solution compares very well to other analytical works that require more complicated iterative techniques with a marching solution approach.     

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.     

Condensation heat transfer enhancement in the presence of non-condensable gas using the interfacial effect of dropwise condensation

Heat transfer characteristics of dropwise condensation (DWC) were experimentally studied on a vertical plate for a variety of non-condensable gas (NCG) concentration, saturation pressure, and surface sub-cooling degree. As the heat transfer performance was dominated by the vapor diffusion process near the interface of the gas–liquid within the gas phase, the additional thermal resistance of the coating layer may not be strictly limited, a fluorocarbon coating was applied to promote dropwise condensation mode. Compared with the traditional filmwise condensation (FWC), heat and mass transfer with NCG can be enhanced with the dropwise condensation mode. In the present paper, the effect of condensate liquid resistance should not be regarded as the most vital factor to explain the results, but the vapor diffusion process. This is attributed to the liquid–vapor interfacial perturbation motion caused by coalescence and departure of condensate droplets. The results also demonstrated that the feature of droplets departure is the dominant factor for the steam–air condensation heat transfer enhancement.     

Heat transfer research on vapor‐gas mixture with condensation in a vertical tube

The convection‐condensation heat transfer of vapor‐gas mixtures in a vertical tube was studied theoretically and experimentally. The effects of the condensation of a small amount of water vapor (8 to 20%) on heat transfer in a vertical tube were discussed. Comparisons show that theoretical solutions obtained through modified film model and experimental results are in good agreement. The results show that the condensation heat transfer of a small amount of water vapor and single‐phase convection heat transfer in the vapor‐gas mixtures are of the same order of magnitude, and these two modes of heat transfer could not be neglected. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 531–539, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10055     

Condensation of organic binary mixtures flowing horizontally in a horizontal tube bundle

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for film condensation of organic binary mixtures such as ethanol-water and methanol-water. Experimental results on the average heat flux, vapor-liquid interface temperature and liquid-phase Nusselt number are compared with analytical solutions based on stagnant film theory and heat-transfer relationships for film condensation from a pure vapor. Experimental heat transfer results agree well with the analytical solutions, except that the experimental liquid-phase Nusselt numbers under conditions of low mass fraction of water are considerably higher than predicted by the analytical solutions. This high value of the liquid-phase Nusselt number is considered to be caused by dropwise condensation in the liquid phase. However, its effect on the tube bundle is not so remarkable compared with that in gravity-controlled condensation on a vertical surface. This is considered to be caused by the condensate inundation effect. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(6): 342–361, 1996     

Three-dimensional numerical simulation of non-condensables accumulation induced by steam condensation in a non-vented pipeline

A substantial increase of the concentration of non-condensable gases in the mixture with steam can occur in a non-vented pipeline due to the condensation. This phenomenon is investigated with the thermal-hydraulic and physicochemical code HELIO. The hydrogen and oxygen accumulation is simulated and analyzed for a real non-vented steam pipeline of the nuclear power plant. The results show the propagation of non-condensables concentration front, the temperature and velocity field of the steam–non-condensables mixture, and the velocity and thickness of the condensate that drains on the pipeline’s inner walls. The gas mixture temperature is verified with measurements from a full size test facility. The presented modelling approach and numerical results are unique regarding the simultaneous solution of the heat and mass transfer in the system consisting of the steam–non-condensable gases mixture and the thin liquid film on the pipe’s wall.     

Theoretical analysis of film condensation heat transfer inside vertical mini triangular channels

An analytical model is presented for predicting film condensation of vapor flowing inside a vertical mini triangular channel. The concurrent liquid-vapor two-phase flow field is divided into three zones: the thin liquid film flow on the sidewall, the condensate flow in the corners, and the vapor core flow in the center. The model takes into account the effects of capillary force induced by the free liquid film curvature variation, interfacial shear stress, interfacial thermal resistance, gravity, axial pressure gradient, and saturation temperatures. The axial variation of the cross-sectional average heat transfer coefficient of steam condensing inside an equilateral triangular channel is found to be substantially higher than that inside a round tube having the same hydraulic diameter, in particular in the entry region. This enhancement is attributed to the extremely thin liquid film on the sidewall that results from the liquid flow toward the channel corners due to surface tension. The influences of the inlet vapor flow rates, the inlet subcooling, and the channel size on the heat transfer coefficients are also examined.     

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.