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.     

Experimental Study of Condensation in a Shell and Tube Heat Exchanger in the Presence of a Noncondensable Gas

In this paper, an experimental study of the condensation of water vapor from a binary mixture of air and low‐grade steam has been depicted. The study is based upon diffusion heat transfer in the presence of high concentration of noncondensable gas. To simplify the study, experimental analysis is supported by empirical solutions. The experimental setup is custom designed for testing a new shell and tube type heat exchanger supplied by the manufacturer. Air–vapor mixture at 80 °C (max) and 20.2% relative humidity enters the heat exchanger at a mass flow rate of 480 kg/h and condenses 27 kg/h vapor using cooling water at an inlet temperature of 7 °C to 10 °C and mass flow rate of 3500 kg/h. By using the experimental data of constant inlet air mass fraction, mixture gas velocity, and different volumetric flow rate of the cold fluid, the local heat transfer coefficients are obtained. The main objective of this work is to establish an approximate value for surface area and overall heat transfer coefficient of a horizontal shell and tube condenser used in process space. Under designed working conditions, the condenser is found to work efficiently with 90% vapor condensation by mass.     

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.     

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.     

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.     

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 solution of film condensation from turbulent flow of vapor–gas mixtures in vertical tubes

A complete two-phase model is presented for film condensation from turbulent downward flow of vapor–gas mixtures in a vertical tube. The model solves the complete parabolic governing equations in both phases including a model for turbulence in each phase, with no need for additional correlation equations for interfacial heat and mass transfer. A finite volume method is used to form the discretized mean flow equations for conservation of mass, momentum, and energy. A fully coupled solution approach is used with a mesh that automatically adapts to the changing film thickness. The results of using three turbulence models involving combinations of mixing length and k–ε models in the film and mixture regions are compared. This new model is extensively compared with previous numerical and experimental studies. In the experimental comparisons, it was found that a model consisting of a k–ε turbulence model for both the film and the mixture flows produced the best agreement. Results are also presented for a parametric study of condensation from steam-air mixtures. The effects of changes to the inlet Reynolds number, the inlet gas mass fraction, and the inlet-to-wall temperature difference on the film thickness and heat transfer are presented and discussed. Local profiles of axial velocity, temperature, and gas mass fraction are also presented.     

Analysis of an air cooled ammonia–water vertical tubular absorber

This paper presents a detailed analysis of an ammonia–water vertical tubular absorber cooled by air. The absorption process takes place co-currently upward inside the tubes. The tubes are externally finned with continuous plate fins and the tube rows are arranged staggered in the direction of the air flow. The air is forced over the tube bank and circulates between the plain fins in cross flow with the ammonia–water mixture. The analysis has been carried out by means of a mathematical model developed on the basis of mass and energy balances and heat and mass transfer equations. The model takes into account separately the churn, slug and bubbly flow patterns experimentally forecasted in this type of absorption processes inside vertical tubes and considers the simultaneous heat and mass transfer processes in both liquid and vapour phases, as well as heat transfer to the cooling air. The model has been implemented in a computer program. Results based on a representative design and nominal operating conditions of an absorber for a small capacity ammonia–water absorption refrigeration system are shown. A parametric analysis was realised to investigate the influence of the design parameters and operating conditions on the absorber performance. The noteworthy results that have effect on practical design of the absorber are presented and commented.     

An Experimental Study on Latent Heat Recovery of Exhaust Wet Flue Gas

The experiment was conducted to investigate the heat transfer performance of wet flue gas in a vertical tube. The factors influencing the convective condensation of wet flue gas were experimentally investigated. The measured results indicate that the convective heat transfer of bulk flow and condensation heat transfer of vapor have significant contribution to the total heat transfer and the dominant transport mechanism is dependent upon the vapor fraction in mixture.     

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     

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.     

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.     

The Simulation of Multicomponent Mixtures Condensation in Plate Condensers

The application of plate heat exchangers for the condensation of multicomponent mixtures requires reliable, well-grounded methods of calculation. A numerical simulation using semi-empirical equations of heat and mass transfer performance along the surface of plate condensers was carried out for different multicomponent mixtures with noncondensable components. The plates with cross-corrugated patterns for plate condensers were used. The simulation was done for four different types of corrugated plates of industrially manufactured plate heat exchangers.

The results of the simulation are in a good accordance with experimental data obtained during long-time experiments for a pilot plant at the pharmaceutical factory in Kharkiv.

It is shown that the enhancement of heat and mass transfer in a plate condenser for the case of a four-component mixture gives the possibility of decreasing by 1.8–2 times the necessary heat transfer surface area comparatively with shell-and-tube unit for the same process parameters.     

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.     

Computational fluid dynamics simulations of direct contact heat and mass transfer of a multicomponent two-phase film flow in an inclined channel at sub-atmospheric pressure

A method for simultaneous heat and multicomponent mass transfer incorporated with the volume of fluid surface tracking method was developed in a two-dimensional inclined channel. The process in the channel includes direct contact condensation of hydrocarbon mixtures with and without noncondensable gas, and distillation effect is also considered. Interfacial transport was performed by a multicomponent phase change model in kinetic forms considering the assumption of thermodynamic equilibrium at the vapor–liquid or vapor/gas–liquid interface using Peng–Robinson equations. The shear-stress transport k–ω turbulence model damped near the vapor–liquid or vapor/gas–liquid interface was used. The hydrocarbon mixtures in both phases were described by five pseudo-components, and Stefan–Maxwell equations were used to describe diffusional interactions in the multicomponent system. Parametric studies were performed to investigate further the model with various boundary conditions. Simulations for a binary system were also performed for a preliminary validation. For the liquid phase, similar trends of the Sherwood numbers were found between the results by simulations and predicted by the Penetration Theory. For the vapor phase, good agreement was observed between the results by empirical correlation and simulations.     

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.     

Free convective condensation heat transfer with noncondensable gas on a vertical surface

Free convective condensation with noncondensable gas on an isothermal vertical surface is studied under the condition of thermal equilibrium. An analysis is made by use of equations of a liquid film and boundary layars adjoining the liquid film and including small droplets generated by condensation, condensable and noncondensable gases. Tha calculation is made in the range of 1–99 per cent weight fractions of condensable gas. The result shows that Nusselt number asymptotically approaches those of free convection and film condensation at both extremes, and the phenomenon treated here intermediates free convection and film condensation along a vertical plate.     

Condensation heat transfer on tubes in actual flue gas

In order to improve boiler efficiency, latent heat recovery from flue gas is a very important concept. Condensation heat transfer on horizontal stainless‐steel tubes was investigated experimentally by using an actual flue gas from a natural gas boiler. The experiment was conducted at different air ratios of the flue gas and a wide range of tube wall temperatures. The condensation pattern was similar to a dropwise condensation near the dew point. By decreasing the wall temperature, the wall region covered with a thin liquid film increased. The heat and mass transfer behavior was well predicted with the analogy correlation at the high‐wall‐temperature region. At the low‐wall‐temperature region, the total heat transfer was higher than that predicted by the analogy correlation. © 2001 Scripta Technica, Heat Trans Asian Res, 30(2): 139–151, 2001     

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.