A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation

A level-set method is presented for computation of microdroplet evaporation including not only the effects of heat and mass transfer, phase change and contact line dynamics but also the Marangoni effect, which is a key parameter affecting the internal flow of the droplet and the particle deposition pattern. A sharp-interface formulation of the Marangoni force is derived and tested for two-phase Marangoni convection in a cavity. The computed results show good convergence in both the liquid and gas regions and are in excellent agreement with the analytical solutions. The level-set formulation is applied to microdroplet evaporation on a solid surface to investigate the Marangoni effect.     

A Level-Set Method for the Direct Numerical Simulation of Particle Motion in Droplet Evaporation

A sharp-interface level-set (LS) method is presented for direct numerical simulation (DNS) of particle motion in droplet evaporation. The LS formulation for liquid–gas flows is extended to liquid–gas–solid flows by treating the moving solid region as a high-viscosity fluid phase. The evaporation effect is accurately implemented by imposing the coupled temperature and vapor fraction conditions at the interface. The LS method is tested through computations of particle sedimentation in single-phase and two-phase fluids. The DNS of particle motion in droplet evaporation demonstrates the pinning phenomena of the liquid–gas–solid contact line.     

Interfacial heat transfer during microdroplet evaporation on a laser heated surface

A comprehensive experimental and numerical investigation on water microdroplet impingement and evaporation is presented from the standpoint of phase-change cooling technologies. The study investigates microdroplet impact and evaporation on a laser heated surface, outlining the experimental and numerical conditions necessary to quantify the interfacial thermal conductance (G) of liquid-metal interfaces during two-phase flow. To do this, continuum-level numerical simulations are conducted in parallel with experimental measurements facilitating high-speed photography and in-situ time-domain thermoreflectance (TDTR). During microdroplet evaporation on laser heated Al thin-films at room temperature, an effective interfacial thermal conductance of G_eff = 6.4 ± 0.4 MW/m² is measured with TDTR. This effective interfacial thermal conductance (G_eff) is interpreted as the high-frequency (ac) interfacial heat transfer coefficient measured at the microdroplet/Al interface. Also on a laser heated surface, fractal-like condensation patterns form on the Al surface surrounding the evaporating microdroplet. This is due to the temperature gradient in the Al surface layer and cyclic vapor/air convection patterns outside the contact line. Laser heating, however, does not significantly increase the evaporation rate beyond that expected for microdroplet evaporation on isothermal Al thin-film surfaces.     

Simulation of mass transfer from an oscillating microdroplet

Mass transfer from micrometer and sub-micrometer airborne microdroplets arises in various chemical process, material science, and atmospheric phenomena, such as impinging flow reactor and unsteady pollutant diffusion, where microdroplet oscillation can substantially increase the mass transfer rate. Previous theories, however, do not adequately predict this enhancement of mass transfer, especially in the case of relatively large-amplitude oscillations. We have analyzed slow evaporation of an oscillating microdroplet having a sufficiently low vapor pressure such that it remains at the surrounding gas temperature and has a negligibly small rate of change of diameter. We solved the governing convective diffusion equation numerically to obtain the Sherwood number as a function of the system parameters. These include the oscillation frequency, the maximum velocity, and the initial microdroplet diameter. The theoretical results are compared with mass transfer data from the literature for a dodecanol microdroplet levitated in an electrodynamic balance (EDB) and oscillated by varying the dc levitation voltage and the ac amplitude and frequency. The predicted Sherwood numbers agree with the experimental results with a mean deviation of 9.2%. The analysis shows a distinct periodic change in the mass transfer rate or Sherwood number with a period that is one-half the period of oscillation of the microdroplet.     

Fringe probing of an evaporating microdroplet on a hot surface

The phenomenon of droplets impacting and evaporating on a hot surface is of interest in many areas of engineering. Quantitative measurement of these processes provides great help to reveal the physics behind. A novel technique was developed to quantitatively measure the volume evolution and contact diameter of an evaporating microdroplet on a hot surface utilizing interference fringe scattering method. In this method, fine fringes produced by the interference of two coherent laser beams was scattered by the droplet and projected onto a screen. The profile and volume of the droplet can be derived from the spatial fringe spacing on the screen. The number of total fringes measurable on the screen was used to determine the instantaneous contact diameter of the microdroplet. Validation experiments demonstrated that the measurement errors are less than ±5% and ±1% for microdroplet volume and contact diameter, respectively. By using this method, the dynamic of droplet impingement, evaporation and boiling using ethanol, pure water and water solution of a surfactant (sodium dodecyl sulfate) with impact velocity of 7.5 m/s and diameters ranged from 0.19 to 0.46 mm were investigated.     

A novel kinetically-controlled de-pinning model for evaporating water microdroplets

A numerical investigation of neutrally hydrophobic water microdroplet evaporation on a flat, isothermal surface was conducted. The axisymmetric time-dependent governing equations of continuity, momentum, energy, and species were solved using FLUENT. The numerical model includes temperature- and species-dependent thermodynamic and transport properties. The explicit volume of fluid (VOF) model with dynamic meshing and variable-time stepping was utilized. The continuum surface force (CSF), the gravitational body force, and Schrage's molecular kinetic-based evaporation model were included in the governing equations. A novel approach was used to model de-pinning by using Blake's molecular kinetic-based contact line motion theory. Experimentally, droplet evaporation data was acquired with a standard dispensing/imaging system and high-speed photography. There is good agreement between the measured and predicted dimensionless droplet profile as characterized by the droplet volume (∀_d/∀₀), dynamic contact angle (θ/θ₀), contact radius (R/R₀), and apex height (H/H₀) when the de-pinned microdroplet numerical model is used. The de-pinning time (t_d) and volume (∀_d/∀₀) are controlled by both the de-pinning parameters (K_w and λ = n^− 2) and the accommodation coefficient (ε). On the other hand, the de-pinning contact angle (θ_d/θ₀) and height (H_d/H₀) are independent of ε.     

自然环境下湿分分层土壤中热湿迁移规律的研究

建立描述存在干饱和层时的土壤热湿传递的数学模型并进行数值模拟，获得自然环境下土壤中温度、湿分分布以及水分蒸发的动态特性，分析干饱和土壤层对土壤热湿迁移及水分蒸发的影响。数值模拟获得实验支持。     

Evaporation heat transfer of falling water film on a horizontal tube bundle

A numerical simulation and experimental study were carried out for evaporation heat transfer of a falling water film on a smooth horizontal tube bundle evaporator. A laminar model and a turbulence model were respectively adopted to calculate the heat transfer coefficients of falling water film on horizontal heated tubes. The calculation zone on the heated tube was divided into the top stagnation zone and the lateral free film zone. The initial boundary conditions for the free film zone were determined from the calculated results of the stagnation zone. The modified wall function method was used for the turbulent flow. Comparisons between the experimental data and the numerical solutions by use of two flow models show that the experimental data lie between the laminar model solutions and the latter turbulence model solutions and that they are closer to the latter solutions. Finally, a simple dimensionless correction based on the numerical simulations is proposed for predicting the evaporation heat transfer of falling water film for actual engineering applications. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 42–55, 2002     

Numerical investigation of effective parameters of falling film evaporation in a vertical-tube evaporator

Wastewater treatment is one of the most effective solutions to manage the problem of water scarcity. Falling film evaporators are excellent technology in wastewater treatment plants. These wastewater evaporators provide high heat transfer, short residence time in the heating zone, and high-purity distilled water. In the present study, the mechanism of turbulent falling film evaporation in a vertical tube has been investigated. A model has been developed for symmetrical two-dimensional pure and saline water flow in a vertical tube under constant wall heat flux. The numerical simulation has been carried out by a commercial computational fluid dynamics code. The evaporation of saturated liquid film is simulated utilizing a two-phase volume of fluid method and Tanasawa phase-change model. The main objective of this study is to evaluate the effects of water salinity, liquid Reynolds number, wall heat flux, and liquid film thickness on the two-phase heat transfer coefficient and vapor volume fraction. The numerical heat transfer coefficients are compared with the obtained results by Chen's empirical correlation. With a MAPE ≤ 11%, this study proves that the numerical method is highly effective at predicting the heat transfer coefficient. Moreover, the empirical coefficient of the Tanasawa model and the minimum thickness of the falling film are determined.     

Enhanced Evaporation in a Multilayer Porous Media Under Heat Localization: A Numerical Study

Evaporation and steam generation are two of the most vital processes in industry. A new method to advance the efficiency of evaporation involves localizing heat at the water surface where the vapor escapes into the air to minimize energy loss. In this research, we numerically investigate the improvement of a novel evaporation process via solar heat localization in a porous medium. A layer of carbon foam with a combination of interconnected and dead-end pores with a high hydrophilicity surface adjacent to a layer of expanded graphite with known porosity and properties were modeled numerically using a finite volume method. The hydrophilic porous media facilitates the capillary forces for better transportation of the bulk water through the porous media to the top surface of the porous media where the absorbed solar energy is delivered to the water inside the pores for evaporation. Continuity, momentum, heat and mass transfer equations were solved in this modeling effort. The modeling results were validated with the experimental data available in the literature. The findings in this numerical study can shed light on the complex interplay between the fluid dynamics and heat and mass transfer across the porous medium, which are important for efficient evaporation processes.     

Melting of powder grains in a plasma flameFusion des grains spheriques dans un jet de plasmaSchmelzen von pulver-körnern in einer plasma-flammeПлa;влe;ниe; зio;p;e;н пo;p;o;шкa; в плa;змe;ннo;м фa;кe;лe;

A numerical method to determine the heat transfer and phase change processes of a spherical particle in a jet stream is deduced. The variations of the thermophysical properties of the particle and of the plasma with temperature are taken into account. An example of alumina particles heated in an argon-hydrogen plasma jet is given. The numerical results, compared with experimental measurements of surface temperature, particle velocity and diameter show good agreement.     

太阳辐照下湿份分层土壤中热湿传输的数值模拟

考虑温度对土壤湿分迁移的影响，建立描述存在干饱和层时的土壤热湿传递的数学模型，并就自然环境和恒定太阳辐照下两种情况进行数值模拟，获得不同环境条件下土壤中温度和湿分分布以及水分蒸发的动态特性，分析干饱和土壤层对土壤热湿迁移与水分蒸发以及温度对土壤湿分传输的影响。     

A numerical investigation on the influence of liquid properties and interfacial heat transfer during microdroplet deposition onto a glass substrate

This work investigates the impingement of a liquid microdroplet onto a glass substrate at different temperatures. A finite-element model is applied to simulate the transient fluid dynamics and heat transfer during the process. Results for impingement under both isothermal and non-isothermal conditions are presented for four liquids: isopropanol, water, dielectric fluid (FC-72) and eutectic tin–lead solder (63Sn–37Pb). The objective of the work is to select liquids for a combined numerical and experimental study involving a high resolution, laser-based interfacial temperature measurement to measure interfacial heat transfer during microdroplet deposition. Applications include spray cooling, micro-manufacturing and coating processes, and electronics packaging. The initial droplet diameter and impact velocity are 80 μm and 5 m/s, respectively. For isothermal impact, our simulations with water and isopropanol show very good agreement with experiments. The magnitude and rates of spreading for all four liquids are shown and compared. For non-isothermal impacts, the transient drop and substrate temperatures are expressed in a non-dimensional way. The influence of imperfect thermal contact at the interface between the drop and the substrate is assessed for a realistic range of interfacial Biot numbers. We discuss the coupled influence of interfacial Biot numbers and hydrodynamics on the initiation of phase change.     

Interaction of the transfer processes in semitransparent liquid droplets

The study presents the mathematical model of unsteady heat transfer in evaporating semitransparent droplets of non-isothermal initial state and the numerical research method, evaluating selective radiation absorption and its influence on the interaction of transfer processes. The relation of the transfer processes inside droplets and in their surroundings and the necessity of thorough research of these processes are substantiated. When modeling the combined energy transfer in water droplets, the evaluation of thermoconvective stability in evaporating semitransparent liquid droplets is presented; the influence of the droplet initial state on its heating and evaporation process is investigated. The influence of heat transfer peculiarities on the change of the evaporating droplet state is indicated. Main parameters, which decide the peculiarities of the interaction of unsteady transfer processes in droplets and their surroundings, are discussed. The results of the numerical research are compared to the known results of the experimental studies of water droplet temperature and evaporation rate.     

Numerical Simulation of Evaporation-Induced Particle Line Formation on a Moving Substrate

Numerical simulations are performed for evaporation-induced particle line formation on a moving substrate by solving the conservation equations of mass, momentum, energy, vapor concentration, and particle concentration in the liquid–gas phases. The liquid–gas interface and the liquid–gas–solid contact line are tracked by using a level-set method, which is modified to include the effects of contact line, phase change, and particle concentration. The numerical results for liquid evaporation and particle deposition in confined convective coating between two parallel plates showed that the substrate velocity is a key parameter determining the particle deposition pattern and the particle line formation can be controlled by varying the substrate velocity.     

微通道内气体-近壁颗粒流动传热数值模拟研究

数值模拟了微通道受限空间内气体-近璧颗粒流动与传热过程,所建模型考虑微尺度气体的可压缩与交物性特征,且在通道和颗粒壁面采用速度滑移和温度跳跃边界条件以考虑滑移区气体动量/能量非连续效应.在此基础上,计算分析了克努森数(Kn)和颗粒偏移比对颗粒表面拖曳力系数(CD)以及传热努塞尔数(Nu)的影响规律.研究结果表明:受气体...     

Numerical simulation of droplet impact and evaporation on a porous surface

Numerical simulation is performed for the evaporation of a droplet impacted on a porous surface. A level-set formulation for tracking the droplet deformation is extended to include the effects of evaporation coupled to heat and mass transfer, porosity and porous drag and capillary forces. The local volume averaged conservation equations of mass, momentum, energy and vapor fraction for the porous region are simultaneously solved with the conservation equations for the external fluid region. The computations demonstrate not only the evolution of the liquid-gas interface during the whole period of droplet penetration and evaporation in a porous medium, but also the associated flow, temperature and vapor fraction fields. The effects of impact velocity, porosity and particle size on the droplet deformation and evaporation are quantified.     

建筑屋面太阳能被动蒸发冷却研究

提出利用多孔含湿材料太阳能被动蒸发冷却建筑屋面的新方法，建立了多孔含湿材料利用太阳能被动蒸发的热质耦合传递数学模型，通过理论分析，数值计算和实验测试，揭示了热过程规律，结果表明，利用太阳能被动蒸发多孔含湿材料水分降温方法是可行的。     

Non-isothermal Evaporation of Salt Solutions on a Microstructured Surface

Heat transfer of a droplet and layer during evaporation of aqueous solutions of salts has been studied. The behavior of salt solutions on a smooth and microstructured surface is compared here. Evaporation rate of aqueous salt solutions is greater for a microstructured surface than for a smooth wall. The behavior of heat transfer coefficient α can be described by two time regimes: quasi-constant values of α and significant increase in heat transfer at a multiple decrease in the liquid layer height. Measurements made with application of the particle image velocimetry showed that the structured surface increases liquid speed inside the sessile drop. The largest value of the heat transfer coefficient α on the structured surface corresponds to water for the final stage of evaporation. For salt solutions, the heat transfer coefficient is lower than that for water in the entire period of evaporation on the structured surface. The maximal excess (20–30%) of α of the structured wall above the smooth surface corresponds to the maximal height of the liquid layer at the beginning of evaporation. With increasing time, the excess is reduced. A drop of heat transfer intensification with a decrease in the layer height relates to suppression of free convection (a multiple decrease in the average velocity in the drop).