Condensation Flux Research Articles

Experimental investigation of humidified air condensation in different rows of serpantine heat exchanger – Cooling water flow rate effect

Condensing economizers are used in the industry as they enable the acquisition of additional heat during vapor condensation. In condensing heat exchangers, water is the usual cooling agent due to its high specific heat capacity and thus efficient heat removal. Therefore, experiments of hot humid air condensation in a serpentine economizer being cooled by water were performed to reveal the effect the cooling water flow rate has on humidified air condensation in separate rows of the serpentine type economizer (with vertical tubes). The results have shown that the cooling ratio (mass flow ratio between the coolant and the humid air) had a minor effect on the distribution of the humidified air temperature along test section for inlet Reynolds number of 3000–10000. The effects on the condensation flux distribution in different rows were much stronger. The most optimal cooling ratio was determined to be 3. The results have shown that the biggest condensation efficiency is up to 35%. It was revealed that in some cases the convection was prevailing in the first rows of the economizer and this resulted in a decreased efficiency/performance of the exchanger.The obtained results from the practical point of view will provide an extended basis for the optimisation of the design of economizers for waste heat recovery in the cases of different cooling water flow rates. It could also be applied to validate computational models developed for condensation heat transfer and condensate flux numerical modelling along economizer.

Development of a laboratory complex for measuring the condensation of atmospheric water vapors

This article presents the results of an experimental study of multiphase flows focusing on the influence of convective condensation of atmospheric water vapour on heat and mass transfer. The primary emphasis is on developing a laboratory setup capable of directly measuring the condensation rate of atmospheric water vapour on a water surface. Such an approach provides the opportunity to obtain more precise and reliable data on convective condensation and its impact on the water balance under various conditions. The experimental results revealed a nonlinear relationship between the condensation rate and the moisture excess, which differs from the linear relationship described by Dalton's law. This deviation was thoroughly examined, and a linear relationship between downward molecular flows and the forces induced by differences in relative humidity concentrations in the convective layer was proposed. The estimated average values of the condensation rate obtained in the experiments were 0.017 L/m²·hour, which, according to estimations, accounts for the condensation flux of water from the atmosphere to the ocean, consistent with the precipitation-evaporation balance in the land-ocean water balance. This information helps to more accurately determine the role of convective condensation in the water balance, contributing to refining assessments of water balance components in various watersheds. The results of this study have practical significance for hydrologists, climatologists, and experts in thermohydraulics and energy engineering. The proposed approaches and methods for measuring convective condensation of atmospheric water vapour can be applicable in various engineering systems and technologies to enhance the efficiency and accuracy of water balance calculations and forecasts.

A kinetic partitioning method for simulating the condensation mass flux of organic vapors in a wide volatility range

Organic aerosols are ubiquitous, playing important roles in various atmospheric physicochemical processes such as the formation of cloud droplets and haze. Condensation of organic vapors, as a net effect of association with particles and dissociation from the condensed phase, is a fundamental process that drives the formation of organic aerosols. Kinetic models are often used to simulate the condensation fluxes of low-volatility organic vapors and aerosol growth. However, the widely used kinetic growth models usually calculate the evaporation of a certain species based on previous particulate compositions, without including the co-condensation of other species. Here we present a new kinetic partitioning method for calculating the condensation fluxes of organic vapors in a wide volatility range with low computational cost. In this method, the organic vapors are assumed to be in a quasi-steady state, but never reach real association-dissociation equilibrium during the simultaneous condensation of multiple species. We show a good consistency between the kinetic partitioning method and kinetic models in simulating particle mass fractions and condensation fluxes. Under relevant atmospheric conditions, we reveal that the kinetic partitioning method also reproduce the trend that low-volatility species are almost non-volatile while volatile organic compounds almost reach association-dissociation equilibrium, while there is a transition regime between them. This transition regime varies with atmospheric conditions, such as temperature and vapor concentrations. Compared with previous studies combining kinetic growth methods with equilibrium partitioning theories to simplify the condensation flux calculation, this method helps to improve accuracy without a significant expense of computation cost, and it can be applied in a wider range of atmospheric conditions such as in extremely cold atmospheres and polluted exhaust plumes.

Effects of Organic Surface Contamination on the Mass Accommodation Coefficient of Water: A Molecular Dynamics Study.

The mass accommodation coefficient (MAC), a parameter that quantifies the possibility of a phase change to occur at a liquid-vapor interface, can strongly affect the evaporation and condensation rates at a liquid surface. Due to the various challenges in experimental determination of the MAC, molecular dynamics (MD) simulations have been widely used to study the MAC on liquid surfaces with no impurities or contaminations. However, experimental studies show that airborne hydrocarbons from various sources can adsorb on liquid surfaces and alter the liquid surface properties. In this work, therefore, we study the effects of organic surface contamination, which is immiscible with water, on the MAC of water by equilibrium and nonequilibrium MD simulations. The equilibrium MD simulation results show that the MAC decreases almost linearly with increasing surface coverage of the organic contaminants. With the MAC determined from EMD simulations, the nonequilibrium MD simulation results show that the Schrage equation, which has been proven to be accurate in predicting the evaporation/condensation rates on clean liquid surfaces, is also accurate in predicting the condensation rate at contaminated water surfaces. The key assumption about the molecular velocity distribution in the Schrage analysis is still valid for condensing vapor molecules near contaminated water surfaces. We also find that under nonequilibrium conditions the adsorption of the water vapor molecules on the organic surface results in an adsorption vapor flux near the contaminated water surface. When the water surface is almost fully covered by the model organic contaminants, the adsorption flux dominates over the water condensation flux and leads to a false prediction of the MAC from the Schrage equation.

Coupled heat and mass transfer in shallow caves: Interactions between turbulent convection, gas radiative transfer and moisture transport

Understanding and predicting the microclimate of shallow caves is a key issue for the conservation of parietal art. In order to determine the dominant mechanisms of heat transfer in a configuration close to that of painted caves, we performed numerical simulations of a parallelepiped cavity whose dimensions and depth are of the order of 10m. This simple geometry allowed us to use a detailed model including turbulent natural convection, gas radiation, along with vapor transport and latent heat fluxes resulting from condensation and evaporation on the walls.Gas radiation increases the flow circulation in the cavity through wall–gas radiative exchanges and significantly modifies the wall radiative flux. Conversely, the wall conductive flux remains unchanged (a non trivial behavior reported in the literature about the differentially heated cavity). In the energy balance at the walls, the radiative flux overcomes the conductive flux. However, the addition of conduction and latent heat fluxes, both driven by convection, prevails over radiation in some regions of the cavity.Heat and mass fluxes are maximum in areas of the cavity roof where the distance from the ground is the shortest. Due to the asymmetry induced by the inversion of the vertical temperature gradient twice a year, net condensation resulting in limestone dissolution is expected in these areas, whereas the other regions of the cave undergo net evaporation resulting in limestone deposition. The orders of magnitude of the condensation flux (a few microns per day) and of the retreat velocity of the wall (a few tenth of a micron per year) are in line with the field data available in the literature.

Numerical investigation of water and heat recovery from flue gas by using nanoporous ceramic membrane tubes

Direct emission of high humidity flue gas results in great wastage of water and thermal energy. Ceramic membrane technology has been widely regarded as a potential technology for water and heat recovery from flue gas. This study presents numerical investigations of water and heat recovery processes from flue gas by using nanoporous ceramic membrane tubes (CMTs). A comprehensive mathematical model is developed based on the Kelvin equation, and the Hagen–Poiseuille equation is applied to calculate the bilateral pressure difference needed for continuous recovery operation. Decreasing the pore size of the separation layer of the ceramic membrane improves the capillary condensation flux but also drastically increases the required bilateral pressure difference. CMT with a pore size of 20 nm is appreciated for the studied conditions. The performances of the CMTs located in the last rows along the flow direction are limited by local low gas temperature and humidity. Twelve rows of tubes are suggested to be arranged along the gas flow direction for ceramic membrane devices with pore sizes of 20 nm and higher. A low transverse spacing obviously improves the overall water and heat recovery efficiency of the device, decreases the performance of each tube, and enhances the gas flow resistance. A transverse spacing ratio of less than 1.4 is suitable for the studied conditions. A combined arrangement by substituting the tubes located in the last rows with those of smaller pore size is a better method than using uniform tubes. The device with combined 20 and 10 nm CMTs is suggested for the studied conditions.

Nano-porous transport membrane condenser for flue gas water recovery: Modeling and parametric membrane design analysis

Water resources are becoming scarce and climate change is exacerbating the stress on traditional water supplies. Thus, it is important to identify viable solutions to resolve tensions in the water energy nexus. One example is the use of transport membrane condensers (TMCs) to recover water as well as waste heat from flue gases with the aim to improve economics and to reduce the environmental impact of the industrial sector. In this work, the authors present a detailed 1D+1D TMC model and investigate the impact of three key membrane design parameters upon the water recovery rate. Sensitivity analyses of pore radius, membrane porosity and contact angle reveal that pore radii of smaller than 10 nm can substantially improve condensation rates due to the exponential vapor pressure dependency described by the Kelvin equation. Reducing the pore radius from 15 nm to 1 nm increases water recovery by over 74% in some of the study scenarios. Additionally, a higher membrane porosity is shown to increase water condensation rates. A higher porosity increases the number of pores on the surface, and thus, the driving force for mass transport. The results show an increase in water recovery of up to 7.7% per 10% porosity increase. The contact angle, which is related to the hydrophilicity of the membrane material, influences the formation of the meniscus inside the pore. Changes in the contact angle from a flat surface (90°) to 30° are shown to have a strong impact upon the water condensation rate. Furthermore, condensation flux improvements through the above-mentioned membrane design modifications are more pronounced in environments with low mass transport driving force due to the nature of the suction effect, which is governed by diffusion and convection transport laws.

Predicting evaporation/condensation mass fluxes using a chemical kinetics framework: Pseudo-chemical potential as the activation energy

A new model for evaporation/condensation is developed using a chemical kinetics framework. The unidirectional evaporation/condensation flux is calculated by the Arrhenius equation, in which the activation energy is assumed to be the pseudo-chemical potential (PCP) barrier and the pre-factor is determined by the collision frequency of liquid/vapor atoms. The value of the PCP barrier is obtained from the equilibrium molecular dynamics (MD) simulations of a liquid–vapor coexisting argon system using umbrella sampling. Simulation results show that the PCP barrier from vapor to liquid is zero, and that from liquid to vapor is the PCP difference between the two phases. The collision frequency can be derived from the Maxwell–Boltzmann velocity distribution, which is established in vapor and liquid phases. A density expression of the model is further derived by estimating the PCP barrier with the densities of the liquid and vapor. The condensation fluxes calculated from the original and density expressions are consistent with the results from the MD simulations of argon condensation. Moreover, the density expression of the new model has been validated by comparing it with results from previous MD simulations for verification purposes.

Effect of inter-pore interference on liquid evaporation rates from nanopores by direct simulation Monte Carlo

Liquid evaporation from micro/nanoscale pores is widely encountered in cutting-edge technologies and applications. Due to its two- or three-dimensional features, the nano-porous evaporation is less understood compared to the one-dimensional evaporation of a planar liquid surface. This paper reported a novel study of the inter-pore interference effect in nano-porous evaporation, clarifying the variation in the net evaporation rate from individual nanopores when the inter-pore distance, neighboring nanopore diameter, or liquid temperature were changed. Molecular simulation results showed that the reduction in inter-pore distance could enhance the evaporation rate from nanopores by augmenting the vapor convection effect and suppressing the condensation flux. This interference effect was more pronounced at lower evaporation intensity with the evaporation flux being different by up to 25% from the one-dimensional case. The inter-pore interference was equally observed for Knudsen numbers of 0.1 and 10. Additionally, the non-uniformity in nanopore size distribution had no influence on the evaporative mass flux within the present parameter range. The non-uniformity in nanopore temperatures, however, could affect the net evaporation from individual nanopores, similarly by modulating the vapor convection magnitude in adjacent to the interface and the condensation flux. The effect of inter-pore interference is found to be essential at low evaporation intensity, which is highly relevant in industrial applications such as water evaporation under atmospheric pressure.

Study on the Precursor Signal Capturing of Unfavorable Weather: Months/Years in Advance to Ultra-Early Forecast for Hourly Transient Weather Changes during the Beijing Winter Olympics

Today, among the existing numerical weather prediction models, those detailing target classifications have been sufficiently explored; however, there are still many weather forecasting goals and needs, and research from theoretical to practical methods still needs additional study. For example, it is important to know as early as possible (months to years in advance) the forecast during a “specific large public event,” such as the hourly weather forecast for the Olympic Games. This study elaborates on the theory and methods for such ultra-early prediction of severe transient weather processes in the atmosphere. The main results of this study include (1) establishing the academic concept to capture precursor signals in modern meteorology and provide definitions; (2) establishing methods for capturing precursory signal quantification of unfavorable weather and proposing quantitative measurable thresholds; and (3) proposing the “ultra-early prediction” target task. A typical case is discussed: the meteorological conditions of the Beijing Winter Olympics, which serves as an example of social demand for weather forecasting of “special large-scale public activities,” as the case results show that the real-time observations during the Beijing Winter Olympics are consistent with the forecast and followed the precursor signal developed using the theoretical and methodological approaches in this study. The numerical quantization indicators for precursor signals include: (1) for a decrease in the height of the mixed layer hidden in the diurnal change; the precursor signal threshold is defined as a drop of more than 100 m for 3 consecutive days; (2) the signal of the δΘe displayed as a change by “negative ⟶ positive” of more than seven days in a continuous period. (3) the supersaturation (S) with thresholds reaching 6–7%, as well as the threshold <0.5 × 10−3 for saturated condensation flux signals (ξp); and (4) the hourly resolution transport index of PLAM (parameter linking air-pollution to meteorological condition) PLAM ⟶ obj remaining continuous for 48 h, with its threshold reaching more than 100.

Non-equilibrium condensation

The condensation process today requires more accurate, efficient and well-tested modeling approaches. In this article the numerical simulations of monatomic vapor condensation on its liquid phase have been carried out by applying the S-model kinetic equation, the Molecular Dynamics approach and the Moment Method. A good agreement is found between the results obtained by these three methods for monatomic gases. The Moment Method has great potential for efficient estimation of condensation fluxes by respecting the conservation of mass, momentum and energy through the Knudsen layer. This method has no analytical solution in the case of condensation, unlike the evaporation process, and the three conservation equations must be solved numerically (the Python tool is provided in Supplementary). Similar to evaporation, the nonlinear form of Schrage’s analytic expression requires information about the third parameter, additionally to two needed in the case of condensation, while linear Schrage’s formula overestimates the condensation rate for small condensation velocities and underestimates it for higher ones. We have tested our approaches by comparison with experimental data for the condensation of mercury for a wide range of Mach numbers, up to 0.85. The existence of an inverted temperature gradient has been showed numerically as well as the reason of its appearance and its evolution for different experimental conditions. The methodology for extracting the condensation coefficient based on the results of the Moment method is proposed. Obtained by this way condensation coefficients were found to be close to unity and decreasing with increasing vapor pressure and temperature.

Asymmetric Condensation Characteristics during Dropwise Condensation in the Presence of Non-condensable Gas: A Lattice Boltzmann Study.

In this work, the condensation characteristics of droplets considering the non-condensable gas with different interaction effects are numerically studied utilizing a multicomponent multiphase thermal lattice Boltzmann (LB) model, with a special focus on the asymmetric nature induced by the interaction effect. The results demonstrate that for isolated-like growth with negligible interactions, the condensation characteristics, that is, the concentration profile, the temperature distribution, and the flow pattern, are typically symmetric in nature. For the growth regime in a pattern, the droplet has to compete with its neighbors for catching vapor, which leads to an overlapping concentration profile (namely the interaction effect). The distribution of the condensation flux on the droplet surface is consequently modified, which contributes to the asymmetric flow pattern and temperature profile. The condensation characteristics for droplet growth in a pattern present an asymmetric nature. Significantly, the asymmetric condensation flux resulting from the interaction effect can induce droplet motion. The results further demonstrate that the interaction strongly depends on the droplet's spatial and size distribution, including two crucial parameters, namely the inter-distance and relative size of droplets. The asymmetric condensation characteristics are consequently dependent on the difference in the interaction intensities on both sides of the droplet. Finally, we demonstrate numerically and theoretically that the evolution of the droplet radius versus time can be suitably described by a power law; the corresponding exponent is kept at a constant of 0.50 for isolated-like growth and is strongly sensitive to the interaction effect for the growth in a pattern.

Numerical and experimental examinations of free convection condensation of steam in the presence of air over the cooled panel

In this paper, experimental and numerical investigations have been conducted to evaluate the steam condensation in the presence of air over a vertical plate for a small temperature difference between the air and a cold wall. In the paper, we describe the experimental set-up, emphasizing the conditioning and measuring equipment introduced for this research. A numerical model is also described in detail. The estimated condensation quantities agreed well with the experimental data. According to the data, simulated total condensation quantities were higher than measured total condensation amounts in all cases, ranging from 6.8 to 13.4% (average 8.9%). The condensation rate increases by 28% as the sub-cooling temperature rises from 2.1 °C to 4.4 °C. The mass fraction of water vapor in the air also induces condensation. Average condensation flux decreases 41.7% when relative humidity decreases from 74.9 to 65.4% at the same surface temperature. In the last part, an empirical correlation, which is characterized by the partial pressure difference of water vapor at the surface and out of the boundary layer conditions, was proposed to estimate the condensation flux over the vertical plate. This practical correlation is novel and can be used for various engineering applications.

A comparative evaluation of waste wood and herbaceous biomass fireside corrosion behaviours

Biomass/biomass waste (BBW) is a renewable energy source fired in combustion power plants. However, challenges associated include accelerated ‘fireside’ corrosion of heat exchangers. Fireside corrosion is fuel dependent, e.g. virgin wood fuels have lower fireside corrosion risks; as such their demand and cost is high. Waste wood fuels (WWF) and herbaceous grass biomass (HGB), generate different combustion environments, influencing heat exchanger fireside corrosion damage.This paper compares the fireside corrosion of WWF and HGB fuels to improve understanding of their attack mechanisms on T91 and 374HFG. The species generated in combustion have been investigated by thermodynamic modelling. Corrosion damage has been evaluated by high temperature corrosion furnace tests at 600 °C, employing the well-established deposit recoat method based on these evolved species. Vapour condensation fluxes have been compared for both fuel categories; corrosion rates increase with this condensation flux. Deposition fluxes from HGB fuels are higher than for WWF. For example, the average KCl deposition fluxes calculated are 1566 µg/cm2h and 295 µg/cm2h per kg fuel feed respectively, explaining the comparatively greater fireside corrosion rates experienced in power plants combusting HGB fuels. The deposit chemistries generated are also different: K-containing compounds only (for HGB fuels) versus K-, Na- and Ca-containing compounds (for WWF).Evaluation of corroded samples exposed to the different deposit chemistries show increased corrosion attack to both steels under simulated WWF firing conditions than for the HGB at matched deposit flux (100 µg/cm2h).

Numerical analysis of wave effect on steam–air condensation on a vertical surface

Steam condensation with non-condensable gas is an unavoidable problem for passive containment cooling system (PCCS) in many third generation reactors. The effects of the air mass fraction in steam–air flow and condensing wall subcooling on the steam condensation at the different gas velocities under the different types and amplitudes of solitary or sinusoidal wave walls are numerical analyzed, in the cases that the wavy film is regarded as wavy solid wall. The 41% rise of average condensation flux (ACF) of steam–air flow can be obtained in the channel with large-amplitude solitary wave wall than that of flat wall while the less variation of ACF happens in the mode with sinusoidal wave wall. The sudden expansion and contraction of flow section along the wavy wall as well as vortex generation in the channel influence local condensation flux greatly. All these results are helpful for thermal analysis of condensation in the PCCS.

Molecular simulation of steady-state evaporation and condensation of water in air

It was shown in recent experiments and molecular dynamics (MD) simulations that Schrage equation predicts evaporation and condensation rates of water in the absence of a non-condensable gas with good accuracy. However, it is not clear whether Schrage equation is still accurate or even valid for quantifying water evaporation and condensation rates in air. In this work, we carry out MD simulations to study steady-state evaporation and condensation of water at a planar water-air interface. The simulation results show that the evaporation and condensation fluxes of water in the presence of air are still in a good agreement with the predictions from Schrage equation. From Schrage equation and Stefan's law of mass diffusion, we derive an analytical expression for the effective thermal conductivity of a planar heat pipe. The analytical prediction of the dependence of effective thermal conductivity on heat pipe length and density of non-condensable gas is corroborated by our MD simulation results and recent experimental data.

Vapor mediated interaction of two condensing droplets

The present work investigates the internal flow structure of two condensing droplets of aqueous solution during interaction. Velocity of fluid inside the droplets was investigated by confocal micro-PIV technique. Simulation study has also been carried out to supplement the understanding of internal hydrodynamics inside droplets. Condensation on the droplets was carried out inside a closed chamber by generating a difference in vapor pressure between the droplet interface and a reservoir fluid surrounding the droplet in the room temperature without any cooling. Condensation on the droplet leads to spatial variation of solute concentration inside the droplet causing buoyancy driven Rayleigh convection. Fluid flow pattern inside a single condensing droplet is symmetric in nature whereas the fluid flow pattern for two condensing droplets is asymmetric in nature. The neighboring droplet influences the internal convection through vapor mediated interaction between the two condensing droplets. The condensing droplet senses the neighboring droplet from a distance without any physical contact. The asymmetric nature of the flow pattern is attributed to the modification in the distribution of condensation flux of the droplet in the presence of the neighboring droplet. The flow pattern observed for interacting droplets during condensation is opposite to that of evaporating droplets. The effect of the neighboring droplet on the internal convection of the condensing droplet reduces with increase in separation distance between the droplets.

Steam Condensation Heat Transfer During Initial Blow-Down Period of a Severe Nuclear Accident

Abstract Heat transfer coefficient (HTC) relations developed using steady-state experimental data are used for capturing the complete heat transport characteristic in a severe nuclear accident. It is important to verify the applicability of these correlation(s) at an early stage of the accident where heat transfer is transient in nature. In this paper, an experimental study is executed for this purpose. High-pressure steam (at 0.26 MPa (2.6 bar) and 0.41 MPa (4.1 bar) absolute pressure) is leaked into the closed containment initially filled with atmospheric air, and filmwise condensation is studied on an isothermally maintained vertical stainless steel test plate. During the experiment, temperature variation across the test plate at specified locations and inside the containment are recorded using the microthermocouples. The steam–air mixture composition is also examined using an online mass-spectrometry system. An inverse heat conduction (IHC) technique, validated using air-jet impingement heat transfer data, is used to estimate the time-varying condensation heat flux. It is found that the existing correlations based on the steady-state experimental data predict the transient condensation flux quite well, except in very early transient situation with a time scale of ∼20 s.

Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions

We investigated the evaporation and condensation coefficients of vapor, which represent evaporation and condensation rates of vapor molecules, under high gas pressure (high gas density) conditions in a system of a vapor/gas-liquid equilibrium state. The mixture gas is composed of condensable gas (vapor) and non-condensable gas (NC gas) molecules. We performed numerical simulations of vapor/gas–liquid equilibrium systems with the Enskog–Vlasov direct simulation Monte Carlo (EVDSMC) method. As a result of the simulations, we found that the evaporation and condensation fluxes decrease with increasing NC gas pressure, which leads to a decrease in the evaporation and condensation coefficients of vapor molecules. Especially, under extremely high gas pressure conditions, the values of these coefficients are close to zero, which means the vapor molecules cannot evaporate and condensate at the interface. Moreover, we found that the vapor molecules behave as NC gas molecules under high gas pressure conditions. We also discussed the reason why NC gas molecules interfere with evaporation and condensation of vapor molecules at the vapor/gas–liquid interface.

Numerical investigation of heat transfer in direct contact condensation of steam to subcooled water spray

The direct contact condensation heat transfer (DCCHT) of saturated steam to subcooled water spray produced by a pressure-swirl nozzle was examined by computational fluid dynamics (CFD) in which a two-dimensional (2-D) axisymmetric swirl calculation was performed to simulate the hydraulic characteristics and the temperature profile of the water spray in the sheet region. The CFD simulations were validated by the experimental results obtained in the studies under the same operational conditions. In the simulation, the kinetic theory-based Schrage model was used for condensation flux calculation, and the interfacial area density of liquid sheet was introduced to evaluate the area of the vapor-liquid interface. The numerical simulations indicated that condensation did not significantly affect the spray cone angle, the sheet thickness and the interfacial area density although it significantly affected the sheet breakup length. Additionally, when compared with traditional film-wise condensation on solid walls, heat transfer coefficient in the DCCHT was significantly higher than that in general film-wise condensation.