Droplet Growth Rate Research Articles

Effect of inlet wetness on transonic wet-steam and moist-air flows in turbomachinery

This study investigates the effect of inlet wetness on transonic wet-steam and moist-air flows through turbine and compressor cascade channels. We first simulated the transonic wet-steam flows through a Bakhtar’s turbine cascade channel under wind-tunnel conditions with inlet wetness. We then predicted the effects of inlet wetness on the moist-air flows expected through an aircraft engine and an industrial gas turbine. For this purpose, we simulated the transonic moist-air flows through a transonic compressor cascade channel while changing the inlet wetness conditions. In both wet-stream and moist-air flows, the inlet wetness was quite sensitive to the growth and evaporation rates of the water droplets, and greatly influenced the shock location. Our results for moist-air flows suggest that the temperature beyond the shock is effectively decreased by a large number density of smaller water droplets.

Numerical Simulation of Non-Equilibrium Two-Phase Wet Steam Flow through an Asymmetric Nozzle

The present study reported of the numerical investigation of a high-speed wet steam flow through an asymmetric nozzle. The spontaneous non-equilibrium homogeneous condensation of wet steam was numerically modeled based on the classical nucleation theory and droplet growth rate equation combined with the field conservations within the computational fluid dynamics (CFD) code of ANSYS Fluent 13.0. The equations describing droplet formations and interphase change were solved sequentially after solving the main flow conservation equations. The calculations were carried out assuming the flow two-dimensional, compressible, turbulent, and viscous. The SST k-ω model was used for modeling the turbulence within an unstructured mesh solver. The validation of numerical model was accomplished, and the results showed a good agreement between the numerical simulation and experimental data. The effect of spontaneous non-equilibrium condensation on the jet and shock structures was revealed, and the condensation shown a great influence on the jet structure.

Stochastic coalescence in Lagrangian cloud microphysics

Abstract. Stochasticity of the collisional growth of cloud droplets is studied using the super-droplet method (SDM) of Shima et al.(2009). Statistics are calculated from ensembles of simulations of collision–coalescence in a single well-mixed cell. The SDM is compared with direct numerical simulations and the master equation. It is argued that SDM simulations in which one computational droplet represents one real droplet are at the same level of precision as the master equation. Such simulations are used to study fluctuations in the autoconversion time, the sol–gel transition and the growth rate of lucky droplets, which is compared with a theoretical prediction. The size of the coalescence cell is found to strongly affect system behavior. In small cells, correlations in droplet sizes and droplet depletion slow down rain formation. In large cells, collisions between raindrops are more frequent and this can also slow down rain formation. The increase in the rate of collision between raindrops may be an artifact caused by assuming an overly large well-mixed volume. The highest ratio of rain water to cloud water is found in cells of intermediate sizes. Next, we use these precise simulations to determine the validity of more approximate methods: the Smoluchowski equation and the SDM with multiplicities greater than 1. In the latter, we determine how many computational droplets are necessary to correctly model the expected number and the standard deviation of the autoconversion time. The maximal size of a volume that is turbulently well mixed with respect to coalescence is estimated at Vmix = 1.5 × 10−2 cm3. The Smoluchowski equation is not valid in such small volumes. It is argued that larger volumes can be considered approximately well mixed, but such approximation needs to be supported by a comparison with fine-grid simulations that resolve droplet motion.

Mathematical Modeling And Numerical Simulation of Dropwise Condensation on an Inclined Circular Tube

Dropwise condensation can improve heat transfer process and, consequently, leads to considerable reduction in size and weight of condensers as well as improvement in the dehumidification process in many applications, especially in civil transport aircraft. It can also be used as an efficient cooling tool for electronics and electrical systems in aircraft engineering and aerospace technology. In this paper, the stable dropwise condensation on an inclined tube is mathematically analyzed. To do this, the population of small droplets is estimated by population balance theory while an empirical correlation is used for large droplets. To calculate heat transfer across each droplet, sum of temperature drops due to droplet curvature, phase change at droplet-vapor interface, conduction through the droplet and promoter layer, are equated with surface subcooling. The total heat transfer is calculated with the given droplets population and heat transfer through single droplet. Subsequently, effects of various parameters, including surface subcooling, contact angle and contact angle hysteresis on the growth rate, maximum radius of droplet, droplets population, and total heat transfer rate, are investigated. Results show that growth rate and heat flux of small droplets are much higher than those of the larger ones; hence, surface with small droplets is preferred for dropwise condensation purposes. Droplets with low contact angle and contact angle hysteresis have higher heat transfer rates. Increasing the inclination of tube improves heat transfer process to such an extent that vertical tubes have higher heat transfer rate than the horizontal ones. This fact indicates that vertical tubes must be used for designing condensers with dropwise condensation, which is quite the opposite for condensers designed based on filmwise condensation.

Controlling the Accumulation of Water at Oil-Solid Interfaces with Gradient Coating.

In this work, we demonstrate a strategy to control the accumulation of water in the oil-solid interface using a gradient coating. Gradient chemistry on glass surface is created by vapor diffusion of organosilanes, leading to a range of contact angles from 110 to 20°. Hexadecane is placed on the gradient substrate as an oil layer, forming a "water/hexadecane/gradient solid substrate" sandwich structure. During incubation, water molecules spontaneously migrate through the micrometer-thick oil layer and result in the formation of micrometer-sized water droplets at the oil-solid interface. It turns out that water droplets at more hydrophobic regions tend to be closer to a regular spherical shape, which is attributed to their higher contact angle with the hydrophobic substrate. However, along the gradient from hydrophobic to hydrophilic, the water droplets gradually form more irregular shapes, as hydrophilic surfaces pin the edges of droplets to form a distorted morphology. It indicates that more hydrophilic surfaces containing more Si-OH groups lead to a higher electrostatic interaction with water and a higher growth rate of interfacial water droplets. This work provides further insights into the mechanism of spontaneous water accumulation at oil-solid interfaces and assists in the rational design for controlling such interfacial phenomenon.

Growth Rates and Spontaneous Navigation of Condensate Droplets Through Randomly Structured Textures.

Dropwise condensation is a phenomenon of common occurrence in everyday life, the understanding and controlling of which is of great interest to applications ranging from technology to nature. Scalable superhydrophobic textures on metals are of direct relevance in improving phase change heat transport in realistic industrial applications. Here we reveal important facets of individual droplet growth rate and droplet departure during dropwise condensation on randomly structured hierarchical superhydrophobic aluminum textures, that is, surfaces with a microstructure consisting of irregular re-entrant microcavities and an overlaying nanostructure. We demonstrate that precoalescence droplet growth on such a surface can span a broad range of rates even when the condensation conditions are held constant. The fastest growth rates are observed to be more than 4 times faster as compared to the slowest growing droplets. We show that this variation in droplet growth on the hierarchical texture is primarily controlled by droplet growth dynamics on the nanostructure overlaying the microstructure and is caused by condensation-induced localized wetting nonuniformity on the nanostructure. We also show that the droplets nucleating and growing within the microcavities are able to spontaneously navigate the irregular microcavity geometry, climb the microtexture, and finally depart from the surface by coalescence-induced jumping. This self-navigation is realized by a synergistic combination of self-orienting Laplace pressure gradients induced within the droplet as it dislodges itself and moves through the texture, as well as multidroplet coalescence.

A comprehensive predictive corrosion model incorporating varying environmental gas pollutants applied to wider steel applications

A comprehensive model has been developed to predict uniform corrosion rate of structural steel under the effect of low pH conditions for example, acid rain. Acid rain is mainly caused by emissions of sulphur dioxide (SO2) which reacts with the water droplets in the atmosphere to produce acidic solution which is the primary cause of corrosion of steel structures such as bridges, high value assets, weathering of stone buildings and statues. A five-stage approach was applied to mathematically describe the model as: (i) the growth rate of air-suspended water droplets (i.e. moisture) depending on the condensation/evaporation rate, (ii) the absorption of gas phase SO2 in the droplets forming bisulfite HSO3− ions, (iii) the coalescence of these SO2 absorbed water droplets under the effects of wind speed and gravity, (iv) the deposition rate of SO2 absorbed droplets on steel substrate depending on the inclination and azimuth angles of steel surfaces and, (v) the corrosion rate of steel due to the deposition of these SO2 absorbed droplets. The incorporation of all of the above stages develops a comprehensive corrosion prediction model which includes both the electrochemical parameters and large number of physical, environmental and material parameters. Experiments were performed to analyse the corrosion rate of steel samples by exposing them to moist SO2 corrosion test. A comparative analysis between the modelled predictions and experimental results was performed to verify the reliability of the model. The predictive trends of corrosion rate of steel were also generated for various values of temperature, relative humidity and SO2 mole percentage. This research provides design solutions and guidelines against degradation due to aggressive application environments. Enhanced corrosion resistivity within large structures, installations, automotive, locomotives, aerospace and building with historic biography will aid longevity and cost savings.

Droplet formation caused by laser-induced surface-tension-driven flows in binary liquid mixtures

Experimental and numerical study of the droplet formation mechanism in thin layers of water-isopropanol mixtures under the laser heating is presented. It is shown that after the beginning of the irradiation the thermocapillary convection dominates that result in the thinning of the layer in the heated area due to the flow of liquid into the cold area. In a few seconds, the loss of isopropanol in the heated area due to evaporation become significant that produces solutocapillary convection with the opposite directed flows. As a result, a droplet appears in the laser beam and continuously grows owing to the solutocapillary liquid flow through the wetting film between the droplet and the receding layer. The experimental results indicate that an increase in the initial concentration of isopropanol in mixture leads to a decrease in the droplet growth rate at a given power of the laser beam. A numerical model of the droplet formation process is proposed. The evolution of the liquid-gas interface is modelled in the frame of lubrication theory including the dependency of surface tension on both temperature of mixture and concentration of volatile component. The model takes into account the dynamics of the vapor in the gas phase including the convective and diffusion mechanisms. A reasonable agreement between the numerical and experimental results is shown.

Impacts of the Manaus pollution plume on the microphysical properties of Amazonian warm-phase clouds in the wet season

Abstract. The remote atmosphere over the Amazon can be similar to oceanic regions in terms of aerosol conditions and cloud type formations. This is especially true during the wet season. The main aerosol-related disturbances over the Amazon have both natural sources, such as dust transport from Africa, and anthropogenic sources, such as biomass burning or urban pollution. The present work considers the impacts of the latter on the microphysical properties of warm-phase clouds by analysing observations of the interactions between the Manaus pollution plume and its surroundings, as part of the GoAmazon2014/5 Experiment. The analysed period corresponds to the wet season (specifically from February to March 2014 and corresponding to the first Intensive Operating Period (IOP1) of GoAmazon2014/5). The droplet size distributions reported are in the range 1 µm ≤ D ≤ 50 µm in order to capture the processes leading up to the precipitation formation. The wet season largely presents a clean background atmosphere characterized by frequent rain showers. As such, the contrast between background clouds and those affected by the Manaus pollution can be observed and detailed. The focus is on the characteristics of the initial microphysical properties in cumulus clouds predominantly at their early stages. The pollution-affected clouds are found to have smaller effective diameters and higher droplet number concentrations. The differences range from 10 to 40 % for the effective diameter and are as high as 1000 % for droplet concentration for the same vertical levels. The growth rates of droplets with altitude are slower for pollution-affected clouds (2.90 compared to 5.59 µm km−1), as explained by the absence of bigger droplets at the onset of cloud development. Clouds under background conditions have higher concentrations of larger droplets (> 20 µm) near the cloud base, which would contribute significantly to the growth rates through the collision–coalescence process. The overall shape of the droplet size distribution (DSD) does not appear to be predominantly determined by updraught strength, especially beyond the 20 µm range. The aerosol conditions play a major role in that case. However, the updraughts modulate the DSD concentrations and are responsible for the vertical transport of water in the cloud. The larger droplets found in background clouds are associated with weak water vapour competition and a bimodal distribution of droplet sizes in the lower levels of the cloud, which enables an earlier initiation of the collision–coalescence process. This study shows that the pollution produced by Manaus significantly affects warm-phase microphysical properties of the surrounding clouds by changing the initial DSD formation. The corresponding effects on ice-phase processes and precipitation formation will be the focus of future endeavours.

Controlled Bulk Properties of Composite Polymeric Solutions for Extensive Structural Order of Honeycomb Polysulfone Membranes.

This work provides additional insights into the identification of operating conditions necessary to overcome a current limitation to the scale-up of the breath figure method, which is regarded as an outstanding manufacturing approach for structurally ordered porous films. The major restriction concerns, indeed, uncontrolled touching droplets at the boundary. Herein, the bulk of polymeric solutions are properly managed to generate honeycomb membranes with a long-range structurally ordered texture. Water uptake and dynamics are explored as chemical environments are changed with the intent to modify the hydrophilic/hydrophobic balance and local water floatation. In this context, a model surfactant such as the polyoxyethylene sorbitan monolaurate is used in combination with alcohols at different chain length extents and a traditional polymer such as the polyethersufone. Changes in the interfacial tension and kinematic viscosity taking place in the bulk of composite solutions are explored and examined in relation to competitive droplet nucleation and growth rate. As a result, extensive structurally ordered honeycomb textures are obtained with the rising content of the surfactant while a broad range of well-sized pores is targeted as a function of the hydrophilic-hydrophobic balance and viscosity of the composite polymeric mixture. The experimental findings confirm the consistency of the approach and are expected to give propulsion to the commercially production of breath figures films shortly.

Fabrication and condensation characteristics of metallic superhydrophobic surface with hierarchical micro-nano structures

Metallic superhydrophobic surfaces have various applications in aerospace, refrigeration and other engineering fields due to their excellent water repellent characteristics. This study considers a simple but widely applicable fabrication method using a two simultaneous chemical reactions method to prepare the acid-salt mixed solutions to process the metal surfaces with surface deposition and surface etching to construct hierarchical micro-nano structures on the surface and then modify the surface with low surface-energy materials. Al-based and Cu-based superhydrophobic surfaces were fabricated using this method. The Al-based superhydrophobic surface had a water contact angle of 164° with hierarchical micro-nano structures similar to the lotus leaves. The Cu-based surface had a water contact angle of 157° with moss-like hierarchical micro-nano structures. Droplet condensation experiments were also performed on these two superhydrophobic surfaces to investigate their condensation characteristics. The results show that the Al-based superhydrophobic surface has lower droplet density, higher droplet jumping probability, slower droplet growth rate and lower surface coverage due to the more structured hierarchical structures.

Condensation on slippery asymmetric bumps.

Controlling dropwise condensation is fundamental to water-harvesting systems, desalination, thermal power generation, air conditioning, distillation towers, and numerous other applications. For any of these, it is essential to design surfaces that enable droplets to grow rapidly and to be shed as quickly as possible. However, approaches based on microscale, nanoscale or molecular-scale textures suffer from intrinsic trade-offs that make it difficult to optimize both growth and transport at once. Here we present a conceptually different design approach--based on principles derived from Namib desert beetles, cacti, and pitcher plants--that synergistically combines these aspects of condensation and substantially outperforms other synthetic surfaces. Inspired by an unconventional interpretation of the role of the beetle's bumpy surface geometry in promoting condensation, and using theoretical modelling, we show how to maximize vapour diffusion fluxat the apex of convex millimetric bumps by optimizing the radius of curvature and cross-sectional shape. Integrating this apex geometry with a widening slope, analogous to cactus spines, directly couples facilitated droplet growth with fast directional transport, by creating a free-energy profile that drives the droplet down the slope before its growth rate can decrease. This coupling is further enhanced by a slippery, pitcher-plant-inspired nanocoating that facilitates feedback between coalescence-driven growth and capillary-driven motion on the way down. Bumps that are rationally designed to integrate these mechanisms are able to grow and transport large droplets even against gravity and overcome the effect of an unfavourable temperature gradient. We further observe an unprecedented sixfold-higher exponent of growth rate, faster onset, higher steady-state turnover rate, and a greater volume of water collected compared to other surfaces. We envision that this fundamental understanding and rational design strategy can be applied to a wide range of water-harvesting and phase-change heat-transfer applications.

Simultaneous Measurement of CCN Activity and Chemical Composition of Fine-Mode Aerosols at Noto Peninsula, Japan, in Autumn 2012

Size resolved CCN activity and bulk chemical composition of atmospheric aerosols in the submicrometer size range were measured at Noto Ground-based Research Observatory (NOTOGRO), facing the Sea of Japan at the tip of Noto Peninsula, in autumn 2012. In the atmospheric measurement, the CCN efficiency spectra, where the CCN number fraction is plotted against the diameter of aerosols, were obtained for four different supersaturation (SS) conditions. The hygroscopicity parameter κ, which depends on the chemical composition of aerosols, was estimated from analysis of the CCN spectra. The CCN activation diameters of ambient aerosols were clearly larger than those of pure ammonium sulfate under all SS conditions. The bulk chemical composition derived by an aerosol chemical speciation monitor (ACSM) also indicated the significant mass fraction of organics in the submicrometer size range. The relationship between the estimated κ values and the CCN activation diameters suggests that organics contribute the aerosol mass especially in the size range of less than 100 nm. The contribution of organics observed in this study was more apparent than those of other sites in East Asia. The mass concentrations and chemical compositions of the aerosols varied with trajectory pathway, which caused large fluctuations in κ values especially at higher SS conditions. The negative correlations between organic mass fraction and the diameters of cloud droplet diameters were observed under low SS conditions (0.13% and 0.25%), suggesting that less-hygroscopic organics, that can suppress the initial growth rates of cloud droplets, were included during the periods of large organic mass concentrations.

Predicting the size of droplets produced through Laplace pressure induced snap-off.

Laplace pressure driven snap-off is a technique that is used to produce droplets for emulsions and microfluidics purposes. Previous predictions of droplet size have assumed a quasi-equilibrium low flow limit. We present a simple model to predict droplet sizes over a wide range of flow rates, demonstrating a rich landscape of droplet stability depending on droplet size and growth rate. The model accounts for the easily adjusted experimental parameters of geometry, interfacial tension, and the viscosities of both phases.

Impact of microemulsion inspired approaches on the formation and destabilisation mechanisms of triglyceride nanoemulsions.

Even after 30+ years of research, there are still few examples of physically stable transparent nanoemulsions despite their high potential to revolutionise pharmaceutical, personal care, and food products. In this study, we examine how low-energy "microemulsion inspired" (co-solvent/co-surfactant) approaches impact the formation and destabilisation mechanisms of homogenised triglyceride nanoemulsions. The addition of n-alcohol co-solvents and Span 80 co-surfactants had two effects on nanoemulsion droplet diameter; a beneficial one that reduced droplet diameter from 120 to 50 nm and a deleterious one that caused destabilisation. The decrease in nanoemulsion droplet diameter facilitated by n-alcohols is thought to arise from changes in: (i) solvent quality near the interface and (ii) interface spontaneous curvature which dramatically reduce interfacial tension. The strength of this effect was magnified by n-alcohol partitioning behaviour and their tendency to associate with the headgroup of POE surfactants. Addition of an excess of n-alcohol led to nanoemulsion destabilisation, unusually for nanoemulsions, destabilisation was not via Ostwald ripening, instead coalescence was found to be the primary destabilisation mechanism. A rapid increase in nanoemulsion droplet growth rate with increasing n-alcohol content was observed for each n-alcohol. Such rapid changes in nanoemulsion instability with composition are reminiscent of PIC/PIT emulsions in the Winsor III region, whose instability has been described to be a function of the activation energy barrier to coalescence. The microemulsion inspired approaches developed in this work highlight a new general approach to the creation of transparent nanoemulsions, and are particularly advantageous for triglyceride oils which are inherently stable against Ostwald ripening.

Retention effect of droplet departure in dropwise condensation at low steam pressure

Dropwise condensation caused by interfacial effects plays a crucial role in the thermal effciency and integration of power production. It is important to understand the effect of droplet dyanmic characteristics on heat transfer perfromace for the controlling mechanism of dropwise condensation heat transfer at low steam pressure and the development of efficient heat transfer techniques. Based on droplet departure characteristics in dropwise condensation at different steam pressures, the droplet departure retention effect at low pressure was proposed in this paper. Due to the increase of condensate viscosity at low steam pressure, the pulsation of droplet surface weakened and the contact angle hysteresis became apparent. Condensed droplets grew larger and moved more slowly in the departure process at low pressure compared to that at atmospheric pressure. Meanwhile, the droplet moved quickly downward once it grew to the departure size at atmospheric while the droplet exhibited a slow stick-slip motion although it reached the departure size at low pressures, which was called the droplet departure retention effect. In a growth cycle of condensed droplet, the heat transfer process was controlled by the droplet growth rate in small surface subcooling range. However, the droplet departure retention delayed the surface renewal reducing the effective heat transfer area in large surface subcooling range. Furthermore, droplet departure retention was introduced to explain the inherent mechanism of the nonlinear increasement of heat flux varying with surface subcooling. This work is beneficial to clear the controlling mechanisms of dropwise condensation heat transfer and offer a new avenue to further enhance heat transfer of dropwise condensation at low steam pressure.

Laser-induced capillary effect in thin layers of water-alcohol mixtures.

The effect of droplet formation in thin layers of water-alcohol mixtures upon laser heating was studied. The droplet growth in the laser beam is governed by the surface tension gradient, which induces solutocapillary flows from the periphery to the center of the heated area. This gradient arises due to the local increase in surface tension caused by the evaporation of alcohol from the heated area of the layer. The experimental results have shown that the increase in the initial concentration of water in the mixture gives rise to the increase in droplet size. However, the increase in the power of laser irradiation leads to a decrease in the droplet growth rate. A simplified one-dimensional model of droplet growth is developed. The model involves the dependence of surface tension on both the temperature and concentration of components in the mixture, as well as the evaporation and condensation of alcohol. The experimental results are compared with those obtained using numerical simulations. A reasonable agreement between experimental and numerical results was shown.

Time-averaged droplet size distribution in steady-state dropwise condensation

This work focused on the time-averaged droplet size distribution in steady-state dropwise condensation. Through theoretical analysis, we derived an expression to describe the droplet size distribution, which is a function of the surface fraction, fractal dimension, and the maximum radius of droplets. Compared with the well-known semi-empirical model by Le Fevre and Rose (1966), the present model has no empirical constant and all parameters in the model have clearly physical meaning. Computer simulations were further conducted for different initial configuration of primary droplets, growth rate of an individual droplet and time step. It was found that the simulation results corresponded well with the available experimental data. The predictions from the semi-empirical model by Le Fevre and Rose and from the present model were also compared with the simulation results and the measured data. A good agreement between them implies that both the two models are valid to be used to describe the time-averaged droplet size distribution under various conditions used in experiments and simulations.

Exploiting Microscale Roughness on Hierarchical Superhydrophobic Copper Surfaces for Enhanced Dropwise Condensation

Hierarchical micro/nanostructured super­hydrophobic surfaces are developed to control the nucleation, growth, and departure of condensate droplets on copper substrates. The microscale roughness elements on the hierarchical surface yield a 40% higher droplet growth rate and a 300% increase in cumulative droplet departure volume as compared to superhydrophobic surfaces with nanostructures alone.

Spreading behavior of a distilled water droplet on a superhydrophobic surface

The investigation of dynamic contact angle between distilled water droplet and superhydrophobic surface was conducted experimentally. To obtain the values of contact angle during spreading, shadow method was implemented. We used Schlieren method to control the droplet symmetry. The droplet was formed on the surface by syringe pump using nontraditional bottom-up methodology. The drop growth rate was varied by the syringe pump from 0.005 ml/s to 0.32 ml/s. DCA versus drop volume was obtained for different values of the drop growth rate. Some features of spreading on superhydrophobic surface were pointed out. Interestingly, that the dynamic contact angle increases during all stages previously selected for copper substrates (1 – droplet formation; 2 – spreading; 3 – formation of the equilibrium contact angle). However, at the droplet growth rate 0.005ml/s we found decrease in the contact angle. The droplet was found to take a shape close to a spherical cap in the range of the drop growth rate 0.005 ml/s – 0.16 ml/s. At higher rates (0.32 ml/s and higher) liquid splashing was observed.