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.     

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.     

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.     

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.     

Transient analysis of direct contact evaporation and condensation within packed beds

Transient one-dimensional conservation equations have been developed to analyze the heat and mass transfer within direct-contact evaporators and condensers. The conservation equations are solved numerically to predict water, air/vapor mixture and packed bed temperatures and humidity ratio within the evaporator and the condenser. The heat and mass transport models account for the transient variations within the packed-bed due to time varying inlet air and water temperatures and humidity. Direct contact evaporator and condenser experimental facilities have been configured. The measured water and air/vapor mixture temperature differences agree well with those predicted using the transient model. The measured humidity difference is slightly greater than that predicted, and the maximum deviation is on the order of 20%.     

An experimental study on vapor condensation of wet flue gas in a plastic heat exchanger

An experimental system investigating condensation heat transfer of wet flue gas was set up, and the heat transfer performance of vapor‐gas mixture with vapor condensation was discussed. The experimental results of laminar flow in a plastic longitudinal spiral plate heat exchanger were obtained and are in good agreement with the modified classical film model. It is shown that the plastic air preheater can avoid acid corrosion in the low‐temperature field for the boiler using fuel containing sulfur and recover latent heat of the water vapor of the wet flue gas. Also some SO₂ was scrubbed during the vapor condensing process in the heat exchanger. © 2001 Scripta Technica, Heat Trans Asian Res, 30(7): 571–580, 2001     

A New Inundation Correlation for the Prediction of Heat Transfer in Steam Condensers

A new correlation used to account for the inundation effect on the prediction of heat transfer between steam vapor and cooling water in tube-and-shell condensers is proposed in this work. The proposed correlation is validated by comparing the predicted results with the experimental data of a steam surface condenser. A modified k–ε turbulence model for gas–liquid two-phase flows with distributed flow resistance is used in the numerical simulation. The predicted results using the proposed correlation agree better with the experimental data than those obtained using the existing correlations for inundation.     

Evaluations of Closure Correlations for the Simulation of Two-Phase Flows in Condensers

The effects of different closure correlations on numerical simulations of vapor-liquid two-phase flow and heat transfer in steam surface condensers are critically assessed in this study. A modified k-? turbulence model for two-phase flows is used in the simulation. The closure correlations are those for condensation vapor shear, interphase drag forces, non-condensable air, tube-side fluid flow, inundation, and hydraulic resistance due to the tube bundle. Numerical simulations of a steam surface condenser are carried out using different closure correlations, and the numerical results are compared with the experimental data. Recommendations are given for different closure correlations.     

A modified k–ε turbulence model for the simulation of two-phase flow and heat transfer in condensers

A modified k–ε turbulence model is developed in this study to simulate the gas–liquid two-phase flow and heat transfer in steam surface condensers. A quasi-three-dimensional algorithm is used to simulate the fluid flow and heat transfer in steam surface condensers. The numerical method is based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for non-condensable gases. The numerical simulation of an experimental steam surface condenser has been conducted using the proposed modified k–ε turbulence model. The results obtained from the proposed model agree well with the experimental results and the results also show an obvious improvement in the prediction accuracy comparing with previous results where a constant value for the turbulent viscosity was used.     

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.     

增压富氧煤燃烧烟气凝结换热的计算

针对含有少量水蒸气的增压富氧煤燃烧产生的烟气在竖直管内的对流凝结换热进行了分析研究.利用修正的膜模型与Nusselt凝结理论建立了换热数学模型,并对不同壁面温度、不同雷诺数和不同水蒸气份额下烟气的凝结换热进行了计算.结果表明:壁面温度升高时,烟气的凝结速率、换热流率和凝结液膜的厚度均减小;混合气体的雷诺数增大时,烟气的凝结速率和换热流率增大,凝结液膜的厚度减小;烟气中水蒸气的份额减小时,烟气的凝结速率和换热流率减小,凝结液膜的厚度减小不明显.     

Exergy Efficiency of Two-Phase Flow in a Shell and Tube Condenser

This study deals with a comprehensive efficiency investigation of a TEMA “E” shell and tube condenser through exergy efficiency as a potential parameter for performance assessment. Exergy analysis of condensation of pure vapor in a mixture of non-condensing gas in a TEMA “E” shell and tube condenser is presented. This analysis is used to evaluate both local exergy efficiency of the system (along the condensation path) and for the entire condenser, i.e., overall exergy efficiency. The numerical results for an industrial condenser with a steam–air mixture and cooling water as working fluids indicate significant effects of temperature differences between the cooling water and the environment on exergy efficiency. Typical predicted cooling water and condensation temperature profiles are illustrated and compared with the corresponding local exergy efficiency profiles, which reveal a direct (inverse) influence of the coolant (condensation) temperature on the exergy efficiency. Further results provide verification of the newly developed exergy efficiency correlation with a set of experimental data.     

Reflux condensation in narrow rectangular channels with perforated fins

Reflux condensation is an industrial process that aims to reduce the content of the less volatile component or to eliminate the non-condensable phase of a vapour mixture, by the means of separation. Separation consists in condensing the less volatile phase and to recover the condensate while simultaneously, the non-condensable species are recuperated at the top of the system. Compact plate-fin heat exchangers can be used in gas separation processes. The aim of this study is to test the process of reflux condensation of an air–steam mixture in the channels of a plate fin heat exchanger with a hydraulic diameter of 1.63 mm. The experimental study shows that reflux condensation occurs in specific parts of the heat exchanger, the other parts remaining dry.Moist air condensation is modelled by the film theory and the results show that the model is well adapted to simulating the heat and mass transfer.     

具有凝结的混合气体热回收装置热力计算软件的开发

对含不凝气的蒸汽冷凝传热机理进行了分析.基于面向对象和模块化编程思想,以Visual Basic 6.0为软件开发平台,同时结合Access数据库,开发了具有凝结的混合气体热回收装置热力计算软件.该软件实现了对具有凝结的混合气体热回收装置的设计计算,具有操作简单、实用性强、界面友好的优点.现场验证表明该软件具有良好的计...     

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。     

Choked flow and heat transfer of low density gas in a narrow parallel-plate channel with uniformly heating walls

The discharge and heat transfer characteristics of the continuum and slip choked gas flows through a narrow parallel-plate channel with uniform heat flux walls are studied by experimental means, numerical simulation, and analytical approximate solution. The numerical results of the discharge coefficient and the wall surface temperature distributions agree relatively well with the experimental results. The effects of the heat transfer at the walls on the discharge coefficient can be correlated with the dimensionless heat input at the walls. Three kinds of Nusselt numbers which are defined by adiabatic wall, bulk mean, and total temperatures as a reference temperature, respectively, are proposed and the effects of the viscous heating on these Nusselt numbers are clarified.     

A numerical model for ammonia–water absorption into a constrained microscale film

A one-dimensional, steady state model for absorption of ammonia vapor into a constrained microscale film is presented. A weak solution of ammonia–water flows in a microchannel into which ammonia vapor bubbles are injected in cross flow from a porous wall. A counter flowing coolant solution removes the heat generated due to absorption from the opposite wall. The 1-D, steady state species and energy transport equations are solved to yield, along the length of the channel, concentration and temperature profiles of the solution stream and the temperature profile of the coolant fluid stream. The model is validated from experimental measurements of global parameters. A parametric study of fluid and geometrical parameters based on the validated model is presented. Results show that a balance between the residence time within the absorber and the absorption time scales, by way of adjusting the mass flow rates of the vapor and weak solution, is needed to ensure complete absorption. A lower coolant inlet temperature significantly enhances absorption rate by increasing the local concentration difference between the saturation and bulk values. The absorption rate is more sensitive to the liquid–vapor interfacial area than to the heat transfer area between the solution and the coolant.     

Condensation from gas–vapour mixtures in small non-circular tubes

Careful measurements have been made during condensation of steam from steam–air mixtures flowing in a small, flattened, horizontal tube. The ranges of the relevant variables covered (inlet temperature, pressure, air mole fraction and mixture mass flow rate) were chosen to simulate those occurring in an exhaust heat-exchanger tube of a proposed fuel-cell engine. The experimental tube was cooled by water in laminar counter flow to simulate the external heat-transfer coefficient (air flowing over fins) in the application. The total heat-transfer rate was found from the mass flow rate and temperature rise of the coolant. The tube wall temperature was measured by thermocouples attached in grooves along its length. Special arrangements were made to ensure good mixing of the coolant (in laminar flow) prior to measuring the inlet and outlet temperatures. The condensate was separated using a cyclone at exit from the tube. A simple model was developed to predict local and total heat-transfer and condensation rates and local bulk vapour composition, temperature and pressure along the tube in terms of the inlet parameters and the wall temperature distribution. The measured heat-transfer and condensation rates for the tube were found to be in good agreement with the calculated values without having recourse to empirical adjustment.     

Effect of Nonuniformities in Vapor Saturation Pressure and Coolant Velocity on Noncondensable Contaminant Accumulation in Single-Pass Air-Cooled Condensers

In the present work, noncondensable contaminant accumulation in tubes of single-pass, multiple-row, cross-flow condensers is investigated. A mathematical model of condensation in such heat exchangers is proposed, which considers changes along the tubes in the saturation temperature, coolant velocity, and heat transfer effectiveness. The model equations are solved with an original algorithm. The vapor distribution, the global effectiveness of the condenser, and the pressure drop between the inlet and outlet plena are determined under different working conditions.     

Entropy generation of vapor condensation in the presence of a non-condensable gas in a shell and tube condenser

This article investigates the entropy production of condensation of a vapor in the presence of a non-condensable gas in a counter-current baffled shell and one-pass tube condenser. The non-dimensional entropy number is derived with respect to heat exchange between the bulk fluid and condensate, as well as heat exchange between the condensate and coolant. Numerical results show that heat transfer from the condensate to the coolant has a dominant role in generating entropy. For example, at an air mass flow rate of 330 kg/h, 93.4% of the total entropy generation is due to this source. The resultant profiles during the condensation process indicate that a higher air mass flow rate leads to a lower rate of entropy production. For example, as the air mass flow rate increases from 330 kg/h to 660 kg/h and 990 kg/h, the total entropy generation decreases from 976 J/s K to 904 and 857.2 J/s K, respectively. By introducing a new parameter called the condensation effectiveness, a correlation is also developed for predictions of the entropy number, and an illustrative example is presented.