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.     

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.     

A two-phase flow model for geothermal wells in the presence of non-condensable gas

Quantitative information on the phenomena occuring during the upward flow of a geothermal fluid in water-dominated wells is a requisite for designing the wellhead system and optimizing resource exploitation. The geothermal fluid consists, for the most part, of a two-phase mixture of water containing dissolved salts, steam and non-condensable gases. Various, closely interrelated effects must therefore be taken into consideration: pressure drop of the rising fluid; heat and mass transfer between the phases (due to evaporation and desorption); heat exchange with rock formations. Simultaneous application of the mass, energy and momentum equations results in a rather complex model that can be solved by a numerical computer program. The model described here accounts for the effects of: the presence of salts, when computing all the thermodynamic properties of the fluids, especially enthalpy, density, vapour pressure of the brine and superheated steam enthalpy; the presence of non-condensable gases, considering their deviations from ideal behaviour and their contribution to density; the heat exchange with the surrounding rock formations; variation in salt concentration along the flow-path; possible variation in pipe diameter and surface roughness with height. The simplified hypotheses adopted are: fluid flow is stationary; thermodynamic equilibrium conditions exist between the phases in each point along the well; the non-condensable gases are assumed to be CO₂; Henry's law is assumed valid and the quantity dissolved chemically is assumed negligible; the salts are assumed to be NaCl; the activity coefficients are unitary; liquid surface tension and viscosity values are assumed equal to those of pure water. Comparison of the results of the computer program and the experimental pressure and temperature profiles shows that these are in satisfactory agreement within a rather wide range of operative conditions. The noncondensable gases, even in very low concentrations, were shown to be of importance to these calculations. Once the experimental temperature and pressure profiles are known, the model will also permit calculation of the concentration of non-condensable gases. The most efficient of the two correlations used to compute pressure drop in two-phase regimes seems to be that devised by CISE^‡, which is based on global parameters not correlated to the different flow regimes.     

Interface conditions governing evaporation of stored liquids in presence of non-condensable gas

Experiments were conducted to determine the variation of interface temperatures during the storage and draining of liquid nitrogen from large containers in the presence of the non-condensable gas. A chilled layer was seen to be formed at the interface in the presence of the non-condensable gas and this layer advanced into the warm liquid at speeds higher than the characteristic speeds associated with thermal diffusion. A theoretical model was developed for the interface temperatures considering the evaporation from the stratified layer in the stored column of liquid. The predictions of the model were shown to compare well with the experimental measurements. A correlation was obtained for the interface temperatures when the proportion of the non-condensable gas was varied.     

Electric-field-induced enhancement of vapour condensation heat transfer in the presence of a non-condensable gas

This paper presents the results of an experimental investigation of heat transfer in film vapour condensation from a vapour-gas mixture on a vertical plate under the influence of an electric field. It is shown that with a gas concentration in vapour below 10% a uniform electric field should be applied, and at higher concentrations a corona discharge should be used. The heat transfer augmentation is found to be determined by the electric hydrodynamic processes just as on the surface of a condensate film in the form of a rearranging wave structure and condensate splashing, that decrease the condensate film thickness, so over the volume of the vapour-gas mixture which is stirred by condensate droplets and, to a greater extent, by the corona discharge electric wind. The effects of gas concentration in vapour, of medium pressure, temperature difference between a vapour-gas mixture and a wall, difference of potentials, electric current strength, physical properties of a liquid phase and of a vapour-gas mixture on the degree of heat transfer enhancement are investigated. A seven-fold increase of the relative heat transfer coefficient in the conditions of corona discharge effect is obtained the development of which is favoured by the maximum gas concentration and minimum temperature differences.     

Effect of electrohydrodynamic (EHD) on condensation of R-134a in presence of non-condensable gas

Effects of applying EHD and non-condensable (NC) gas contents have been experimentally studied on inter-tubular condensation of refrigerant R-134a flow. Applying of electrical field enhances condensing heat transfer coefficient (CHTC), but presence of NC gas in condensing vapour reduces this coefficient. In competition of these two effective parameters on condensation, it can be observed that at higher concentration of NC gas, the effect of electrical field on enhancement of CHTC is greatly reduced. But at lower concentration of NC gas, the effect of electrical field is more considerable, due to thickness of heat transfer boundary layer.     

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.     

Thermal analysis of plate condensers in presence of flow maldistribution

Flow maldistribution in plate heat exchangers causes deterioration of both thermal and hydraulic performance. The situation becomes more complicated for two-phase flows during condensation where uneven distribution of the liquid to the channels reduces heat transfer due to high liquid flooding. The present study evaluates the thermal performance of falling film plate condensers with flow maldistribution from port to channel considering the heat transfer coefficient inside the channels as a function of channel flow rate. A generalized mathematical model has been developed to investigate the effect of maldistribution on the thermal performance as well as the exit quality of vapor. A wide range of parametric study is presented, which shows the effects of the mass flow rate ratio of cold fluid and two-phase fluid, flow configuration, number of channels and correlation for the heat transfer coefficient. The analysis presented here also suggests an improved method for heat transfer data analysis for plate condensers.     

Simulation of binary vapor condensation in the presence of an inert gas - a sequel

Three approximate methods of calculating multicomponent mass transfer rates due to Toor-Stewart-Prober, Taylor-Smith and Burghardt-Krupickza are compared to an exact method due to Krishna-Standart. All four methods are based on a film model of mass transfer. It is shown that the three approximate methods are exact if all binary diffusion coefficients are equal $\text{and}$ the film thickness is a constant. In applications to binary vapor condensation in the presence of an inert gas, for example, where empirical methods of estimating mass tranfer coefficients must be used, it is shown that the method of Burghardt and Krupiczka is $\text{not}$ in agreement with the other methods even when the binary diffusion coefficients are all equal. The magnitude of the discrepancy is not, however, large except when the mole fraction of inert species is small.     

Condensation in gas transmission pipelines.

Several pressure and temperature reductions occur along gas transmission lines. Since the pressure and temperature conditions of the natural gas in the pipeline are often close to the dew point curve, liquid dropout can occur. Injection of hydrogen into the natural gas will change the phase envelope and thus the liquid dropout. This condensation of the heavy hydrocarbons requires continuous operational attention and a positive effect of hydrogen may affect the decision to introduce hydrogen. In this paper we report on calculations of the amount of condensate in a natural gas and in this natural gas mixed with 16.7% hydrogen. These calculations have been performed at conditions prevailing in gas transport lines. The results will be used to discuss the difference in liquid dropout in a natural gas and in a mixture with hydrogen at pressure reduction stations, at crossings under waterways, at side-branching, and at separators in the pipelines.     

不凝气对池内亚音速蒸汽直接接触凝结影响

利用VOF多相流模型和修正的热相变凝结模型对含不凝气蒸汽亚音速射入池内的直接接触凝结过程进行了数值模拟。主要研究了不同不凝气含量对蒸汽直接接触凝结过程中气羽形态、温度和压力分布的影响。研究结果表明：随着凝结的进行不凝气在气液界面处集聚成为一层不凝气层,随着不凝气含量的增加,不凝气层的厚度也增加,气羽不再呈现周期性的变化;不凝气的存在使得池内温度高温区域增大,温度分布相对均一;同时随着不凝气含量的升高,压力振荡的强度减弱,凝结形成的负压值升高。     

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.     

Mono-component fuel droplet evaporation in the presence of background fuel vapor

A simplified set of equations is examined for the problem of droplet evaporation. The equations employ the Clausius–Clapeyron (CC) boundary condition for the surface fuel-vapor, which is responsible for mathematical behaviors that include an initial condensation stage of droplet swelling followed by an evaporation stage. Numerical methods of analysis are used in conjunction with an asymptotic analysis of each of the three stages: (I) condensation; (II) transition; and (III) evaporation. Droplet evaporation in partial condensation environments is discussed.     

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).     

Film condensation in presence of non-condensable gases over horizontal tubes with progressively increasing radius of curvature in the direction of gravity

A theoretical study is executed to investigate the simultaneous influences of reduction in heat transfer rate on account of condensation in presence of non-condensables and its augmentation by the geometry of an horizontal tube surface with increasing radius of curvature in the direction of gravity. The tube surface profile considered for the present work is an equiangular spiral described in a polar form as: R = ae^mθ (a and m being parametric constants). It is observed that a very small bulk concentration (even less than 1%) of the non-condensable gas reduces considerably the heat transfer coefficient. However, there is an enhancement in heat transfer coefficient for condensation over a polar tube surface, as compared to that over a circular tube surface. This enhancement in heat transfer coefficient, with an increase in the value of m (a surface profile parameter), in presence of non-condensables is more than the corresponding proportional enhancement in the same in absence of any non-condensable species.     

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     

Co-gasification of waste wood with coal: Release of condensable and non-condensable inorganic gas species

This letter deals with the in-situ determination of important inorganic gas phase species in high temperature gasification product gas. The fuels are waste wood and German hard coal which were co-gasified at 1500 °C in lab-scale experiments. The release of the vapour species ³⁴H₂S⁺, ³⁶HCl⁺, ⁵⁶KOH⁺, ⁵⁸NaCl⁺, ⁶⁰COS⁺, ⁶⁴SO₂⁺, and ⁷⁴KCl⁺ was determined online by a Molecular Beam Mass Spectrometer. The experimentally determined data sets were compared to calculated data sets in order to distinguish the underlying release mechanisms. The release behaviour of the inorganics ³⁴H₂S⁺, ³⁶HCl⁺, ⁶⁰COS⁺, ⁶⁴SO₂⁺ and ⁵⁸NaCl⁺ cannot be attributed to simple mixing and dilution effect only. Further, it is shown that the release of these inorganics is significantly influenced by secondary reactions, e.g. competitive reaction with S and Cl.     

Evaporation in mixture of vapor and gas mixture

The evaporation problem in vapor and gas mixture is investigated by the methods of molecular-kinetic theory and fluid dynamics. Solution results are obtained for the case when investigation domain length is several thousands mean free paths of molecules. In this statement two types of evaporation problem solutions are obtained. In the first type gas is completely pushed up by vapor from the region near the evaporation interface surface. In this, “shelf” (straight step) in dependence of vapor density on coordinate takes place. In the second type such “shelf” is not formatted. Transition from one type solution to another is found.