Dropwise Condensation Heat Transfer Research Articles

Experimental analysis of drop-size density distribution during dropwise condensation of steam

Dropwise condensation (DWC) has attracted research interest since its first description in 1930 due to the high heat transfer coefficients that can be obtained by promoting this mechanism as compared to the case of filmwise condensation. The modelling of dropwise condensation heat transfer is complex since it must account for droplets nucleation, growth and removal: researchers proposed different methods and the first semi-empirical model was presented in 1966 by Le Fevre and Rose. Their model predicts the total heat transfer across a surface during DWC by estimating the drop-size density distribution and the heat transfer through a single droplet. The goal of the present work is to investigate the large drop-size density distribution during dropwise condensation considering different operating conditions (heat flux and surface coating). In this work, a new illumination system (torus-shaped LED) has been designed and built to allow droplets detection with diameters from millimetres down to few microns. The torus-shaped LED is used as light source for a high-speed camera coupled with microscope lens. The recorded images have been analysed by a homemade software in MATLAB® code, and the measured droplet population has been compared with the theoretical formula proposed by Le Fevre and Rose [1]. More than six million droplets have been detected and an excellent agreement with the Le Fevre and Rose theory has been found.

Analysis of Factors Affecting Dropwise Condensation Heat Transfer Based on Theoretical Model

Analysis of Factors Affecting Dropwise Condensation Heat Transfer Based on Theoretical Model

Improved modeling of heat transfer in dropwise condensation

Dropwise condensation has drawn significant attention due to its efficient heat transfer performance compared to filmwise condensation. In this paper, typical experimental data for dropwise condensation on smooth hydrophobic surfaces were collected as well as the typical available heat transfer models. The comparisons between the prediction results and the experimental data indicated that the existing models were not generally applicable to various conditions. A new model for a vertical smooth surface was developed to predict the heat transfer characteristics of dropwise condensation. The new model was based on the nucleation condensation mechanism, and the total heat transfer on the surface includes the heat through all the droplets and the heat through the surface between the droplets. For the latent heat through the droplets the effect of the contact angle was taken into consideration on the basis of the nucleation condensation mechanism. The surface area between the droplets on the surface was thought to be the bare surface, and sensible heat transferred on the bare surface and the droplets surface was viewed as forced convection heat transfer. The calculation results from the model show that, although the heat transferred by forced convection is greatly dependent on the experimental parameters, it is three orders of magnitude smaller than the latent heat through the droplets. Comparisons show that the present model has better prediction precision, with an error range of -35–20% for 87.39% of the data and an error range of -35–25% for 90.37% of the data. The findings obtained from the model suggest that the heat transfer rate and the critical nucleation radius for a single droplet and the droplet size distribution are remarkably affected by the contact angle. In fact, a smaller contact angle enhances the condensation heat transfer and increases the nucleation density. In addition, the thickness of the promoter layer weakens the condensation heat transfer and decreases the nucleation density.

Density Maximization of One-Step Electrodeposited Copper Nanocones and Dropwise Condensation Heat-Transfer Performance Evaluation.

Currently, it is still a great challenge to obtain copper-based high-efficient dropwise condensation heat transfer (CHT) interfaces via template-free electrodepositing technologies. Here, we report that the density of template-free electrodeposited copper nanocones can maximally reach 1.5 × 106/mm2 by the synergistic control of substrate surface roughness, poly(ethylene glycol) (PEG) molecular weight, and PEG concentration. After thiol modification, the densely packed copper nanocone samples can present low-adhesive superhydrophobicity and condensate microdrop self-jumping function at ambient environment. Condensation heat and mass transfer characterizations show that the CHT coefficient of copper surfaces can maximally enhance 98% for 20 °C vapor and 51% for 40 °C vapor by in situ growth of superhydrophobic densely packed copper nanocones. Although the dropwise condensation mode can change from the jumping mode to the mixed jumping and sweeping mode and the shedding-off mode along with the increase of surface subcooling and vapor temperature, the CHT performance of the nanosample is still superior to that of the contrast flat hydrophobic surface during the whole testing range of surface subcooling. As vapor temperature increases to 80 °C, the CHT performance of the nanosample is inferior to that of the contrast sample. The CHT enhancement under low-temperature vapor should be ascribed to the enhancement of small-drop mass transfer ability caused by low-adhesive superhydrophobicity nature of nanosample surfaces. Their performance degradation mainly results from increased drop-drop drag force along with the increase of surface subcooling and vapor temperature. In sharp contrast, the CHT deterioration under high-temperature vapor should be ascribed to larger drop-surface adhesion and drop-drop drag force. The former is caused by vapor penetration, whereas the latter is caused by the dramatically increased nucleation density and growth rate of condensates. These findings would help design and develop copper-based high-efficiency condensation heat transfer interfaces.

Experimental and modeling investigations of dropwise condensation out of convective humid air flow

In this work, experimental and modeling investigations of convective dropwise condensation from moist air are carried out for the mechanistic understanding of the influence of non-condensable gas. For modeling, different droplet growth models in the presence of non-condensable gas are firstly developed by treating the droplet as an isolated form. During dropwise condensation, the presence of non-condensable gas brings some specific condensation characteristics, including the interaction effect between droplets and convection mass transfer. However, those characteristics cannot be reasonably captured by the droplet growth model. In this work, the distributed point sink method and the droplet Sherwood number are used to evaluate the inter-droplet interaction and convection mass transfer, respectively. Combining those progresses, the droplet growth rate is predicted and the prediction is evaluated by the measurements. Based on the accurate prediction for the droplet condensation rate, a semi-analytical modeling method is released to predict convective dropwise condensation of moist air. It considers the latent heat by condensation and the sensible heat by forced convection. Finally, this work presents the direct comparisons of the overall heat flux measured in experiments and the prediction. Furthermore, mechanistic understanding is discussed simultaneously and conclusively. Throughout this work, we highlight the reduction (the diffusion resistance of water vapor and the inter-droplet interaction) and enhancement (convection mass transfer) factors for dropwise condensation in the presence of non-condensable gas. In addition, in the case of this work, large droplets are more beneficial for heat transfer of dropwise condensation.

Dropwise condensation on solid hydrophilic surfaces.

Droplet nucleation and condensation are ubiquitous phenomena in nature and industry. Over the past century, research has shown dropwise condensation heat transfer on nonwetting surfaces to be an order of magnitude higher than filmwise condensation heat transfer on wetting substrates. However, the necessity for nonwetting to achieve dropwise condensation is unclear. This article reports stable dropwise condensation on a smooth, solid, hydrophilic surface (θa = 38°) having low contact angle hysteresis (<3°). We show that the distribution of nano- to micro- to macroscale droplet sizes (about 100 nm to 1 mm) for coalescing droplets agrees well with the classical distribution on hydrophobic surfaces and elucidate that the wettability-governed dropwise-to-filmwise transition is mediated by the departing droplet Bond number. Our findings demonstrate that achieving stable dropwise condensation is not governed by surface intrinsic wettability, as assumed for the past eight decades, but rather, it is dictated by contact angle hysteresis.

Numerical simulation of droplet dynamics on chemically heterogeneous surfaces by lattice Boltzmann method

Purpose This paper aims to investigate spontaneous movement of single droplet on chemically heterogeneous surfaces induced by the net surface tension, using the improved three-dimensional (3D) lattice Boltzmann (LB) method. Design/methodology/approach D3Q19 Shan-Chen LB model is improved in this paper. Segmented particle distribution functions coupled with the P-R equation of state are introduced to maintain the higher accuracy and greater stability. In addition, exact difference method (EDM) is adopted to implement force term to predict the droplet deformation and dynamics. Findings The numerical results demonstrate that spontaneous movement of single droplet (=1.8 µm) along wedge-shaped tracks is driven by net surface tension. Advancing angle decreases instantaneously with time, while receding angle changes slightly first and then decreases rapidly. Wetting length is affected by vertex angle and wetting difference, whereas the final value is only dependent on the stronger wettability. Although the velocity of single droplet on wedge-shaped tracks can be increased by the larger vertex angle, it has a negative influence on the displacement. For the same wetting difference, vertex angle equal to 30º is an optimization strategy in this model. If the simulation length is extended enough, then the smaller vertex angle is beneficial for the droplet movement. In addition, a larger wetting difference is beneficial to spontaneous movement, which can speed up the droplet movement. Originality/value The proposed numerical model of droplet dynamics on chemically heterogeneous surfaces provides fundamental insights for the enhancement of drop-wise condensation heat transfer.

Dropwise condensation heat transfer enhancement on surfaces micro/nano structured by a two-step electrodeposition process

Condensation is an important regime of heat transfer which has wide applications in different industries such as power plants, heating, ventilating and air conditioning, and refrigeration. Condensation occurs in two different modes including filmwise (FWC) and dropwise (DWC) condensation. DWC occurring on hydrophobic and superhydrophobic surfaces has a much higher heat transfer capacity than FWC. Therefore, wide investigations have been done to produce DWC in recent years. Superhydrophobic surfaces have micro/nano structures with low surface energy. In this study, a two-step electrodeposition process is used to produce micro/nano structures on copper specimens. The surface energy of specimens is reduced by a self-assembled monolayer using ethanol and 1-octadecanethiol solution. The results show that there is an optimum condition for electrodeposition parameters. For example, a surface prepared by 2000 s step time has 5 times greater heat transfer than FWC while a surface with 4000 s step time has nearly the same heat transfer as FWC. The surfaces of the fabricated specimens are examined using XRD and SEM analyses. The SEM analyses of the surfaces show that there are some micro-structures on the surfaces and the surface porosities are reduced by increasing the second step electrodeposition time.

Influence of different parameters of preparing self-assembled monolayers on copper surfaces in the dropwise condensation heat transfer: an experimental study

Dropwise condensation (DWC) is one of the phase change heat transfer regimes, which due to its high capacity has received much attention from investigators. To produce DWC, it is necessary to have hydrophobic surfaces. Low surface energy coatings have been usually used to produce hydrophobic surfaces. These coatings due to their low thermal conductivities must have the minimum thickness. Therefore, self-assembled monolayers coatings like stearic acid or 1-octadecanethiol coatings (with thicknesses as high as a few nanometers) have been used in the literature. To create hydrophobic coatings by these materials, the surfaces are immersed in hydrophobic solutions with particular concentrations and in a specific time. There is not any general investigation on the effects of the time and concentration of these coatings on DWC in the literature. In this study, first, a proper apparatus for DWC experiments is designed and fabricated. Then, the effects of concentration and immersing time of the two mentioned materials on DWC phenomena have been studied. Between four coating times and solution concentrations of 1-octadecanethiol, concentration of 0.025 M at coating time of 30 min increases DWC heat transfer coefficient by about 4–7 times with respect to filmwise condensation in different subcooling temperatures. Concentration of 0.0025 M at coating time of 1 hour of stearic acid also increases the heat transfer coefficient by about 3–4 times. As well as the 1-octadecanethiol coating has a more uniform structure and higher heat transfer coefficient with respect to stearic acid coating.

Steam Condensation Enhancement by Applying Self-Assembled Monolayer (Chlorosilane) on Titanium Corrugated Tubes

It is well known that dropwise condensation enhances the condensation heat transfer coefficient significantly compared with film condensation. In the present study, dropwise condensation heat transfer characteristics on titanium corrugated tubes were investigated. Two corrugated tubes with different corrugation pitch and depth were tested at the steam pressures of 5 and 10[Formula: see text]kPa. To promote dropwise condensation, silane-based SAM was coated. For bare corrugated tubes, significant enhancement of condensation heat transfer was noted, especially for the 2.1/0.2 (corrugation pitch/corrugation depth in mm) tube. For SAM-coated tubes, the heat transfer enhancement was significant (2.61 at 5[Formula: see text]kPa and 2.45 at 10[Formula: see text]kPa) for the smooth tube. For the corrugated tubes, however, the enhancement decreased to 1.78 and 2.22 for 8.7/0.4 tube and to 1.26 and 1.52 for 2.1/0.2 tube. The present results suggest that corrugations may not be as an effective heat transfer method for dropwise condensation as it is for film condensation. This result was supported by the photos taken by mist spray, which suggested that surface tension drained condensation by corrugations is not a major heat transfer mechanism for dropwise condensation on corrugated tubes.

Modeling and Simulation of Dropwise Condensation: A Review

In this review, we present significant developments that have been made in the mathematical modeling and simulations of dropwise condensation. In dropwise condensation, vapor condenses in the form of distinct drops. Modeling of DWC involves modeling heat transfer through a single drop and applying it to a population of drops. In the first part, we discuss heat transfer through a single droplet and compare the approximate analytical solution with the results of numerical simulations. We also address the shortcomings of the analytical model. In the second part, we present methods utilized to find the drop size distribution which are coupled with a model for heat transfer through the single droplet to obtain overall dropwise condensation heat transfer rate. In particular, we discuss the population balance method and the Monte Carlo method to predict drop size distribution and heat transfer rate. We support our discussion with the results from the literature.

A phase-change thermal diode using electrostatic-induced coalescing-jumping droplets

Analogous to the electronic diode, a thermal diode is a device which allows heat to flow to a preferential direction. Compared with other thermal diodes, phase-change thermal diodes yield greater thermal rectification performance due to high latent heat. With coalescing-jumping droplets as a result of dropwise condensation and water evaporation through a vapor space in the forward mode and thermal conduction through a high thermal resistance material in the reverse mode, the thermal rectification of this phase-change thermal diode can be higher than 100. However, due to the limited jumping height of coalescing-jumping droplets, progressive flooding occurs on a non-wetting surface causing a degraded heat transfer performance. Nevertheless, an applied electric field has proved to be one of the effective methods to enhance heat transfer in water evaporation and dropwise condensation. Thus, this study aims to investigate the effects of applied electrical fields on the effective thermal conductivity and thermal rectification of a phase-change thermal diode using electrostatic-induced coalescing-jumping droplets. The thermal diode is designed, assembled and investigated experimentally. The results show that the applied electric field potentially enhances the effective thermal conductivity and thermal rectification of the phase-change thermal diode. At the applied electrical voltage of 50 V, the maximum average thermal rectification of 325 is reported. This number shows a 90% greater improvement over thermal rectification in the no-electric-field condition and is considered to be one of the highest performances of all experimental thermal diode studies.

مطالعه تجربی چگالش قطره ای بر روی سطوح آبگریز شده با استفاده از فرایند الکترونشست تک مرحله ای

Dropwise condensation occurs on hydrophobic and superhydrophobic surfaces. The rate of heat transfer depends mostly on the preparing process of hydrophobic surface. Two main features of hydrophobic surfaces are existing micro-nanostructures and their low surface energy. In this paper, a one-step electrodeposition process is used to produce the necessary micro-nanostructures on copper surfaces and a self-assembled mono-layer of 1-Octaecanethiol as surface energy reducing agent. Effects of different electrochemical cell parameters such as electrical current and time of process on the dropwisecondensation heat transfer are investigated. The heat transfer experiments are performed in a device fabricated for this purpose. The surface of the specimens is analyzed using scanning electron microscopy images and X-ray diffraction analysis. The results show that some microstructures made from copper grow on the surface. The results show that current and process time have positive effects on the dropwise condensation heat transfer. It has been seen that surfaces fabricated at low electrodeposition time (15 and 45 sec) have a worse dropwise heat transfer rate than filmwise condensation heat transfer. On the other hand, higher electrodeposition times (135 sec) give 2-4 times higher heat transfer than filmwise heattransfer in the sub-cooling range lower than 10 Kelvin.

Convective dropwise condensation heat transfer in mini-channels with biphilic surface

For dropwise condensation (DWC) in confined channels, droplets slide on surface and may spoil the nano-pillars, thus the nano-pillars structure is not suitable. Here, we provide a robust biphilic surface with polymer film as hydrophobic wettability. Mesh screen is sintered on copper surface to form welding junction array. Dipping the sintered package in a Teflon solution followed by baking technique forms a hydrophobic coating film. Hydrophilic dots are exposed by separating mesh screen from copper substrate. Condensation experiment was performed in a mini-channel with dimensions of 30.0 × 3.13 × 0.97 mm3 and pure water–vapor as the working fluid. Mass flux covered a range of 10.5–63.8 kg/m2 s. It is shown that condensation heat transfer coefficients on biphilic surface were 5.54 times of those on polished copper surface, and 1.89 times of those on hydrophobic polymer layer surface, maximally. Pressure drops are almost identical in condensers with biphilic surface and hydrophobic surface. For DWC on biphilic surface, growing droplet on hydrophilic dot attracts and merges neighboring droplets to generate directional-droplets-coalescence, explained by the Gibbs energy analysis. Higher droplet departure frequency was observed on biphilic surface than hydrophobic surface. Compared with hydrophobic surface, droplet on biphilic surface has different contact angle, covers several hydrophilic dots and reduces droplet thermal resistance. The above effects explain the heat transfer enhancement mechanism when biphilic surface is present.

Dropwise condensation heat transfer on superhydrophilic-hydrophobic network hybrid surface

Superhydrophilic-hydrophobic (SHPi-HPo) network hybrid surface was designed to investigate the condensation heat transfer using stainless steel as substrate material. The SHPi-HPo surface was comprised of superhydrophilic network grooves and hydrophobic regions. Hydrophobic (HPo) surface was prepared with fluorocarbon coating using polytetrafluoroethylene (PTFE) as the matrix resin and micro-nano silicon dioxide (SiO2) as additive to control surface roughness. Three kinds of SHPi-HPo surfaces were tested, having a grid spacing of 1.5, 2.5 and 3.5 mm and named as SHPi-HPo-1, SHPi-HPo-2 and SHPi-HPo-3, respectively. To study the effects of the wall subcooling, steam mass flux, cooling water temperature, cooling water mass flow rate and grid spacing, a series of experiments were conducted and a high speed camera was used to visualize the condensation process. The results show that SHPi-HPo surface can well control condensate droplet diameters and its condensation heat transfer performance is better than that of smooth hydrophilic (HPi) and HPo surfaces. This is attributed to SHPi-HPo surface sucking away droplets in time and limiting the growth of large condensate droplets through the superhydrophilic grooves. At wall subcooling ΔTw = 6.3 K, the heat transfer coefficient of SHPi-HPo-2 surface is 2.7 and 3.4 times that of HPi and HPo surfaces, respectively. For SHPi-HPo surface, there is optimum grid spacing between superhydrophilic grooves to enhance condensation heat transfer. Among three SHPi-HPo surfaces, the heat transfer coefficient of SHPi-HPo-2 surface has the best condensation heat transfer performance, about 0–10% higher than that of SHPi-HPo-1 surface, and at ΔTw = 9 K, the heat transfer coefficient is 1.7 times that of SHPi-HPo-3 surface.

Dropwise condensation on superhydrophobic nanostructure surface, Part I: Long-term operation and nanostructure failure

Dropwise condensation heat transfer (DWC) on superhydrophobic nanograsses surface (NGS) was investigated for long-term operation. For DWC of pure water-vapor on fresh NGS, two heat transfer regimes are identified: higher heat transfer coefficients with droplet jumping, and constant heat transfer coefficients with droplet rolling. The one-week operation not only deteriorates heat transfer performance, but also changes jumping or rolling mode to sliding mode. The condensation heat transfer coefficients are apparently decreased from first to third day, but they approach a limit value since the third day. In order to identify if the single-molecule-layer of polymer (SML) modified on nanograsses was destroyed, DWC on a smooth single-molecule-layer of polymer surface (SSML) was tested to display stable heat transfer with drop sliding for one-week operation, concluding no failure of the polymer layer. The collapse and breakage of nanograsses were observed to explain the decayed heat transfer versus time on NGS. Compared with SSML, the NGS has smaller droplet departure size but lower heat transfer coefficients, indicating positive and negative effects after introducing nanostructures. Three nanostructure failure mechanisms are proposed. This work suggests a new research field of the nanoscale fluid-wall interaction.

Droplet size distributions in dropwise condensation heat transfer: Consideration of droplet overlapping and multiple re-nucleation

Evolution and distribution of condensate droplets are the most important information in dropwise condensation. For surfaces with larger contact angles, droplet interactions and distributions become more complicated due to their three dimensional profiles. In this study, the effect of droplet overlapping and multiple re-nucleation on droplet size distribution and heat transfer are analyzed quantificationally by numerical simulations. Experimental droplet images obtained by environmental scanning electronic microscope are also presented to support the analyses. The simulated droplet size distributions show that droplet overlapping and multiple re-nucleation can improve the spatial distribution of small droplets for larger contact angle surfaces, and the difference in droplet size distributions decreases as droplet radius is increased. The distributions of larger droplets with radii larger than the critical coalescence size are also affected by the overlapping and multiple re-nucleation effect. The difference between droplet size distributions finally diminish for different contact angles when droplet radius is increased to dozens of microns and the effect of overlapping and multiple re-nucleation become less important in that size range. As contact angle is increasing, surface coverage decreases, while the number density of small droplets is greatly increased, and the overall effect leads to an improved heat transfer performance. The present simulations reveal the effect of droplet overlapping and multiple re-nucleation quantificationally from the perspective of three dimensional droplet profiles, which provide insight into the better understanding of droplet size distributions and extend the dropwise condensation theory.

Numerical Study for a Large-Volume Droplet on the Dual-Rough Surface: Apparent Contact Angle, Contact Angle Hysteresis, and Transition Barrier.

The profile, apparent contact angle (ACA), contact angle hysteresis (CAH), and wetting state transmission energy barrier (WSTEB) are important static and dynamic properties of a large-volume droplet on the hierarchical surface. Understanding them can provide us with important insights into functional surfaces and promote the application in corresponding areas. In this paper, we establish three theoretical models (models 1-3) and the corresponding numerical methods, which were obtained by the free energy minimization and the nonlinear optimization algorithm, to predict the profile, ACA, CAH, and WSTEB of a large-volume droplet on the horizontal regular dual-rough surface. In consideration of the gravity, the energy barrier on the contact circle, the dual heterogeneous structures and their roughness on the surface, the models are more universal and accurate than the previous models. It showed that the predictions of the models were in good agreement with the results from the experiment or literature. The models are promising to become novel design approaches of functional surfaces, which are frequently applied in microfluidic chips, water self-catchment system, and dropwise condensation heat transfer system.

Droplet departure modeling and a heat transfer correlation for dropwise flow condensation in hydrophobic mini-channels

Droplet nucleation, growth, coalescence, and departure control dropwise condensation heat transfer. Smaller droplets are associated with higher heat transfer coefficients due to their lower liquid thermal resistances. Unlike quiescent dropwise condensation with gravity-driven droplet departure, droplet departure sizes in flow condensation are governed by flow-droplet shear forces and droplet-solid adhesive forces. This research models droplet departure, droplet size distributions, and heat transfer through single droplets under different flow conditions. Heat transfer through single droplets includes the thermal resistances at the vapor-liquid interface, temperature depression across the curved surface, conduction in the liquid droplet, and conduction through the surface promoter (e.g., Teflon). Droplet size distributions were determined for two ranges using the population balance method and power law function for small and large droplets, respectively. Droplet departure sizes (e.g., 10–500 µm) were derived using force balances between drag forces (obtained using FLUENT) and droplet-solid adhesive forces (determined using a third-order polynomial for contact angle distribution along contact line). The analytical model was compared to experimental flow condensation heat transfer data in a Teflon AF™-coated rectangular mini-gap with hydraulic diameters of 0.95 and 1.8 mm. The correlation was compared against experiments with a steam mass flux range of 35–75 kg/m2 s and quality of 0.2–0.9. There was good agreement between the model and experimental data; without any curving fitting, the mean absolute errors of the heat transfer correlation were 9.6% and 8.8% respectively for the 0.95-mm and 1.8-mm mini-gaps.

Mathematical Model for Dropwise Condensation on a Surface With Wettability Gradient

We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.