Experimental and theoretical investigation of film condensation with noncondensable gas

Experimental and theoretical investigations were conducted for the film condensation with noncondensable gas in a vertical tube. Condensation experiments were performed for a steam–air mixture in a vertical tube submerged in a water pool where the heat from the condenser tube was removed through a boiling heat transfer. Degradation of the condensation with noncondensable gas was investigated. A heat and mass analogy model for the annular filmwise condensation with noncondensable gas was developed. In the steam–air mixture region, general momentum, heat and mass transport relations derived by analytic method were used with the consideration of surface suction effect. The predictions from the model were compared with the experimental data and the agreement was satisfactory.     

Effect of an interfacial shear stress on steam condensation in the presence of a noncondensable gas in a vertical tube

Experimental and analytical studies were performed to examine local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The experimental data for pure steam and steam/nitrogen mixture bypass modes were compared to study the effects of noncondensable nitrogen gas on annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm. The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen mass fraction decreased. The results obtained using steam/nitrogen mixtures with a low inlet nitrogen mass fraction were similar to those obtained using pure steam. Therefore, the effects of noncondensable gas on steam condensation were weak in the small-diameter condenser tube because of interfacial shear stress. A new correlation based on dimensionless shear stress and noncondensable gas mass fraction variables was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. A theoretical model using a heat and mass transfer analogy and simple models using four empirical correlations were developed and compared with the experimental data obtained under various experimental conditions. The predictions of the theoretical model and the simple model based on a new correlation were in good agreement with the experimental results.     

Temperatures and the condensate heat resistance in dropwise condensation of multicomponent mixtures with inert gases

The temperature variations occurring in dropwise condensation at condenser plates of a compact, polymer heat exchanger are studied using instantaneous infrared temperature field recordings. An averaging procedure in time and an assessment of extreme values is proposed and carried out. With the results, the heat resistance of the condensate is quantified. It is found that mixing and convection in the condensate, caused by coalescence and drainage of drops, reduces the condensate heat resistance by a factor 4 as compared with purely conductive heat transfer. This reduction is comparable, both in nature and in magnitude, to the effect of enhanced mixing due to turbulence in the liquid film of filmwise condensation. A second condensable species has been added to the gas mixture in order to study the contribution of Marangoni convection due to concentration gradients to the condensate heat transfer resistance. No contribution is found.     

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 Study of the Forced Convective Condensation on a Short Vertical Plate

Numerical investigation was conducted on the effects of gravity, surface tension, and wall adhesion upon condensation on a short vertical plate. The volume of fluid method was applied to model the interaction between the liquid and vapor phases and to capture the interface. The surface tension was implemented by employing the method of continuum surface force model. A modified phase-change model, derived from basic equations related to the kinetic gas theory, was proposed and verified based on the cases of Nusselt film condensation of water vapor on a vertical flat plate, the forced convection film condensation on a horizontal flat plate, and the capillary blocking due to condensation in a horizontal miniature circular tube. The predicted results showed that a laminar capillary wavy flow regime exists and the waves enhance the heat transfer of condensation on the plate. The mean film thickness increases and the heat transfer performance becomes worse with decrease of gravity. A high value of surface tension or contact angle, representing a large surface free energy difference, leads to an enhancement of heat transfer on the plate with large-amplitude waves.     

Two-phase modelling of laminar film condensation from vapour–gas mixtures in declining parallel-plate channels

A two-phase model is presented that analyzes laminar film condensation from mixtures of a vapour and a non-condensing gas in parallel-plate channels. The channel is declining (inclined downward from the horizontal) and has an isothermal cooled bottom plate and an insulated upper plate. The model uses a finite volume method to solve the complete two-phase boundary-layer equations including inertia forces, energy convection, interfacial shear, and axial pressure change. Results are presented for steam–air mixtures in terms of axial variation of film thickness and local Nusselt number for various Froude numbers, inlet Reynolds numbers, inlet gas mass fractions, and inlet temperature differences. Profiles of axial velocity, temperature, and gas mass fraction are also presented. Increasing the angle of declination (decreasing the Froude number) produces thinner, faster moving films. The change in local Nusselt number with Froude number was not as substantial as the change in film thickness. The detrimental effect of the noncondensable gas on the heat transfer rate was observed to be more pronounced at higher Froude numbers. An exact analytical solution for the liquid and mixture axial velocity profiles under end of condensation conditions is also presented and compared with the numerical results.     

Approximate equations for film condensation in the presence of non-condensable gases

Non-condensable gases greatly influence vapor condensation, resulting in a substantial reduction in the condensation heat transfer coefficient. Although extensive analytical and numerical investigations of condensation heat transfer in the presence of non-condensable gases have been done, most of the solutions are quite complicated. Based on a thermodynamics analysis, when the vapor is not close to its critical state and the mass fraction of the non-condensable gas in the main stream is less than 0.1, an equation which relates the vapor/gas-liquid interface parameters and the main stream parameters was developed in the present work. For forced convection film condensation heat transfer on the outside surface of a horizontal tube, the present equation combining with an existing analytical solution as well as a heat transfer correlation given by previous investigators, gives the heat flux and the interfacial parameters of the water vapor-air mixture. The results show that the predicted heat flux is in good agreement with experimental data available in the literature and that even a small amount of air substantially reduces the heat flux. An algebraic equation set is given to calculate free convection film condensation on a vertical flat surface, which associates the interfacial and main stream parameters, an integral solution and an analytical solution given by previous investigators. The calculated results are in good agreement with experimental data in the literature.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

新型复合防腐表面烟气对流凝结换热实验研究

烟气对流凝结换热强化和换热表面防腐是天然气热能动力设备烟气余热回收利用关键技术。不同防腐表面耐腐蚀性能不同,且换热性能也不同。采用CCD高速摄像仪,对烟气在新型复合防腐表面上的凝结形态和凝结过程进行了可视化观测和换热实验研究,采用对图像边缘提取法,获得凝结液的边缘曲线。研究表明,烟气在新型复合防腐表面上的凝结为珠状凝结,凝结液珠最大粒径为0.2～0.28 mm,与其他表面形成的膜状凝结相比,在实验范围内,珠状凝结换热可提高约7倍。为增强烟气对流凝结换热和开发烟气冷凝余热回收利用技术提供了参考和依据。     

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     

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.     

Local heat transfer measurements of steam/air mixtures in horizontal condenser tubes

Condensation of vapor/noncondensable gas mixtures in horizontal tubes is not well understood because condensate stratification and the multidimensional nature add to the complexity of the phenomena. The heat transfer and fluid flow phenomena in a horizontal condenser tube were experimentally studied, along with the heat transfer reduction effect of a noncondensable gas. The temperature gradient across the condenser tube wall was measured locally to investigate the asymmetrical heat transfer characteristics around the condenser tube periphery. The condensation heat transfer coefficients on the tube top were much greater than the values at the bottom and the noncondensable gas significantly reduced the heat transfer rate.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

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.     

混合气体管内对流凝结传热研究

研究了混合气体在垂直圆管内的对流凝结传热。利用修正的膜模型与Nusselt凝结理论建立了换热数学模型，预测了壁面温度对膜厚度和界面温度的影响，计算了凝结液膜厚度，并与报相热阻法进行比较，研究结果表明该模型更接近实验果，提出了混合气体对流凝结换热与Nusselt凝结的不同。     

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     

Numerical study of the evaporative cooling of liquid film in laminar mixed convection tube flows

A numerical study is reported to investigate the evaporative cooling of liquid film falling along a vertical tube. A marching procedure is employed for solution of the equation of mass momentum, energy and concentration in the flow. Numerical results for air-water system are presented. The effects of flow conditions on the film cooling mechanism are discussed. Results show that a better liquid film cooling is noticed for a system having a higher inlet liquid temperature T_L0, a higher gas flow Reynolds number Re or a lower liquid flow rate Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the interface.     

Laminar mixed convection heat and mass transfer in vertical rectangular ducts with film evaporation and condensation

The investigation of mixed convection heat and mass transfer in vertical ducts with film evaporation and condensation has been numerically examined in detail. This work is primarily focused on the effect of film evaporation and condensation along the wetted wall with constant temperature and concentration on the heat and mass transfer in rectangular vertical ducts. The numerical results, including the distributions of dimensionless axial velocity, temperature and concentration distributions, Nusselt number as well as Sherwood number are presented for moist air mixture system with different wall temperatures and aspect ratios of the rectangular ducts. The results show that the latent heat transport with film evaporation and condensation augments tremendously the heat transfer rate. Better heat transfer enhancement related with film evaporation is found for a system with a higher wall temperature.     

Condensation of a vapor-noncondensable gas mixture within a horizontal air-cooled tube

The equations governing the coupled heat and mass transport mechanism are derived for the condensation of a pure vapor—non condensable gas mixture within a horizontal finned tube cooled by air in cross flow. Assuming that temperatures of both the gaseous and liquid phase vary linearly in a short length tube element, where the problem is posed, a couple of equations are obtained for the exit temperatures of the streams as a function of the inlet and the interphase ones. These equations can be handled iteratively as a sub-routine of a simulation program already implemented by Urbicain and Paloschi (1). The heat transfer mechanism is governed by an overall coefficient U defined between the main gaseous stream and the cooling air, calculated from the individual resistances which operate on two different sections of the condensing film. The procedure has been succesively tested on a water vapor-carbon dioxide finned air cooled condenser and represents a generalization of the step by step program mentioned above.     

Flow Boiling in Rectangular Microchannels: 1-D Modeling of the Influence of Inlet Resistance on Flow Reversal

Pressure changes caused by the growth of confined bubbles during flow boiling in mini-/microchannels lead to transient flow reversal in the presence of inlet (upstream) compressibility. A one-dimensional (1-D) model is presented to study the effect of inlet resistance on maximum flow reversal distance, local pressure fluctuations for different initial upstream compressible volumes, channel dimension, locations of nucleation site, heat flux, and initial channel velocity for water and FC-72 at atmospheric pressure and R134a at 800 kPa. The two upstream compressibility models considered are condensable vapor in a subcooled boiling region and trapped noncondensable gas.