Numerical investigation on the evaporation of droplets depositing on heated surfaces at low Weber numbers

The evaporation of water droplets, impinging with low Weber number and gently depositing on heated surfaces of stainless steel is studied numerically using a combination of fluid flow and heat transfer models. The coupled problem of heat transfer between the surrounding air, the droplet and the wall together with the liquid vaporisation from the droplet’s free surface is predicted using a modified VOF methodology accounting for phase-change and variable liquid properties. The surface cooling during droplet’s evaporation is predicted by solving simultaneously with the fluid flow and heat transfer equations, the heat conduction equation within the solid wall. The droplet’s evaporation rate is predicted using a model from the kinetic theory of gases coupled with the Spalding mass transfer model, for different initial contact angles and substrate’s temperatures, which have been varied between 20–90° and 60–100 °C, respectively. Additionally, results from a simplified and computationally less demanding simulation methodology, accounting only for the heat transfer and vaporisation processes using a time-dependent but pre-described droplet shape while neglecting fluid flow are compared with those from the full solution. The numerical results are compared against experiments for the droplet volume regression, life time and droplet shape change, showing a good agreement.     

Mechanisms of film boiling heat transfer of normally impacting spray

The heat transfer mechanisms of horizontally impacting sprays were studied experimentally. An impulse-jet liquid spray system and a solid particle spray system were used. The liquid spray system is capable of producing uniform droplets with the independent variables of droplet size, velocity, liquid flow rate, and air velocity. The horizontally impacting sprays give a lower heat transfer at film boiling than the corresponding vertically impacting spray. The film boiling heat transfer is mainly controlled by the liquid mass flux. At low liquid mass flux and low droplet Weber number, the heat transfer increases with the droplet Weber number. At high droplet Weber number or high liquid mass flux, the heat transfer is not significantly affected by the droplet Weber number.     

A numerical investigation of the evaporation process of a liquid droplet impinging onto a hot substrate

A numerical investigation of the evaporation process of n-heptane and water liquid droplets impinging onto a hot substrate is presented. Three different temperatures are investigated, covering flow regimes below and above Leidenfrost temperature. The Navier–Stokes equations expressing the flow distribution of the liquid and gas phases, coupled with the Volume of Fluid Method (VOF) for tracking the liquid–gas interface, are solved numerically using the finite volume methodology. Both two-dimensional axisymmetric and fully three-dimensional domains are utilized. An evaporation model coupled with the VOF methodology predicts the vapor blanket height between the evaporating droplet and the substrate, for cases with substrate temperature above the Leidenfrost point, and the formation of vapor bubbles in the region of nucleate boiling regime. The results are compared with available experimental data indicating the outcome of the impingement and the droplet shape during the impingement process, while additional information for the droplet evaporation rate and the temperature and vapor concentration fields is provided by the computational model.     

Discussions of transient heat transfer to a water droplet on heated surfaces under atmospheric pressure

This paper discusses the transient heat transfer to a water droplet on heated surfaces considering a surface temperature change, in the contact period when the droplet is in contact with them. The initial surface temperature ranges from the lowest limit of the nucleate boiling region to the Leidenfrost point. Attention is paid to the two parts of the contact period : the waiting period before the onset of the first bubbling and the successive boiling period after this onset. Our proposal of transient heat transfer is based on some assumptions backed up by theoretical and experimental considerations—a theory of the first bubbling by Michiyoshi and a few experimental results from our previous papers and other works.     

不同润湿性表面液滴铺展及蒸发过程的LBM数值模拟

基于格子玻尔兹曼方法（Lattice Boltzmann Method, LBM）对固着在加热基板上的液滴铺展及蒸发过程进行模拟,主要研究重力场、基板润湿性以及初始环境温度对液滴铺展及蒸发过程的影响。通过预测蒸发过程中液滴与基板的接触直径变化和液滴剩余质量变化,分析液滴形状及体积变化。研究结果发现,液滴形貌及蒸发过程受重力影响较大,重力作用下液滴铺展现象明显且蒸发加快。基板的接触角越小,液滴铺展现象越明显,其接触直径越大,蒸发越快。当环境温度与基板温度相差较大时,液滴内部出现涡流,强化换热使蒸发过程加快。     

Pattern analysis of a single droplet impinging onto a heated plate

The time scale for measuring the heat transfer phenomena, such as the Leidenfrost phenomenon, is much longer than the hydrodynamic transient period of a droplet impinging onto a heated surface. However, the Leidenfrost temperature has been long since taken as the criterion to classify characteristic regimes for not only heat transfer but also hydrodynamic impact patterns of liquid‐solid‐interface problems in the literature. The impingement phenomena of a single droplet onto a heated plate for We <200 were experimentally classified as five different characteristic patterns in this paper. They are [I] completely wet, [II] wet film boiling, [III] transition, [IV] dry rebounding, and [V] satellite dry rebounding impact patterns. The former two patterns belong to wet impact, while the latter two are dry impact. This work reveals that the hydrodynamic impact parameter does influence the classification of characteristic impact patterns, especially for the dry impact patterns. For high impact Weber numbers, the dry impact happens to the plate surface temperature much lower than the commonly believed Leidenfrost temperature due to the squeeze film effect. The evolutions that impact changes from one to another characteristic patterns are also discussed. This paper offers a systematic and reliable database for future numerical simulations. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(8): 579–594, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20089     

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.     

快速降压环境下盐水液滴蒸发过程的传热传质研究

采用VOF（Volume of Fluid）自由表面捕捉方法对盐水液滴蒸发过程中气液界面进行追踪,建立了降压环境下单个盐水液滴的蒸发模型,并通过盐水液滴蒸发的实验数据验证了此模型。通过对盐水液滴在相变过程中的形态变化以及传热传质特性的分析,研究了液滴内部温度、速度、蒸汽分布以及液滴形态等随时间的变化情况,分析了影响盐水液滴降压蒸发过程的主要因素。结果表明：在降压蒸发过程中液滴形态变化和环境中蒸汽的分布会随速度场的变化而变化;蒸发过程中初始盐组分质量浓度越大的液滴蒸发速率越缓慢,最终能达到的液滴最低中心温度越高,且液滴中心温度回升速度越慢、回升时间也越晚;液滴初始温度对蒸发速率影响较大,初始温度越高,表面蒸发速率越快,液滴中心温度回升速度越快。     

Molecular Dynamics–Continuum Hybrid Simulation for the Impingement of Droplet on a Liquid Film

A molecular dynamics–continuum hybrid method is used to study the droplet impingement process on a liquid film. The hybrid code is validated by simulating the sudden-start Couette flow and unsteady heat transfer problem. The impingement process is strongly affected by Weber number. At low Weber number, the evolution of the crown after droplet impingement is stable, while at high Weber number the secondary droplets emerge and the splash phenomenon occurs. The effect of liquid film thickness on the evolution of crown diameter is also investigated.     

Interfacial temperature measurements,high-speed visualization and finite-element simulations of droplet impact and evaporation on a solid surface

The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid–liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid–gas boundary. For cases involving evaporation, the diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. High-speed visualizations are performed to provide matching parameters for the wetting model used in the simulations. Numerical and experimental results are compared for the transient heat transfer and the fluid dynamics involved during the droplet deposition. Our results describe and explain temperature oscillations at the drop–substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.     

固着液滴蒸发研究进展及展望

固着液滴是指附着于壁面上的液滴,其蒸发行为及传热传质特性是喷雾冷却、喷墨打印等相变传热传质领域的基础问题之一。文中重点针对固着液滴蒸发过程所涉及的自身形态演变规律、气液固三相耦合传热/传质/流动特性进行了综述。结合毫微尺度固着液滴基本蒸发模式、热质传递形式、气液两相流动特征和界面输运行为,分析了液滴性质、壁面条件、气相环境条件等关键因素对固着液滴蒸发过程的内在作用机制和影响规律,提出了微纳尺度固着液滴（群）热质传递过程与机理的相关研究展望。     

正丁醇水溶液液滴的蒸发特性实验研究

自湿润流体是一种具有特殊的表面张力特性的二元流体,了解其蒸发传热特性对于揭示其强化传热机理十分重要.为了探究添加自湿润流体液滴的蒸发特性,采用液滴形状分析仪(DSA100)研究了不同温度(30、40、50、60℃)下铜底板上去离子水、正丁醇水溶液(质量分数为0.5％)液滴的蒸发特性.结果 表明:加入少量正丁醇溶液并不影...     

Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface

Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet’s free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120 °C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet’s evaporation rate is predicted using a model based on Fick’s law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid–gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.     

Energetic budget on an evaporating monodisperse droplet stream using combined optical methods: Evaluation of the convective heat transfer

Aerothermal properties in a fuel spray is a central problem in the field of the design of the combustion chambers of automotive engines, turbojets or rocket engines. Heat and mass transfer models are necessary in the predictive calculation schemes used by the motorists. Reliable experimental data must be obtained for both the validation and development of new physical models linked to heat transfer and evaporation in sprays, where aerodynamic interactions have a key role. This paper proposes an experimental study of the energetic budget of a monodisperse ethanol droplet stream, injected in the thermal boundary layer of a vertical heated plate. The droplet size reduction is measured using a light scattering technique (interferential method) in order to characterize the evaporation, as the droplet mean temperature is monitored using the two colors laser-induced fluorescence technique. The convection heat transfer coefficient and the Nusselt number are inferred from the overall energetic budget, as a function of the inter-droplet distance, characterizing the interaction regime. The results are compared to physical models combined with numerical simulations available in the literature, for moving, evaporating isolated droplets and for three droplets arrangement in linear stream.     

Flow and thermal field in sessile droplet evaporation at various environmental conditions

Sessile droplets' evaporation is a complex process that involves fluid flow coupled with heat and mass transfer. In this study, mathematical modelling of sessile droplet evaporation on hydrophobic substrates is developed and simulations are carried out on COMSOL. The model results are validated with the data available in the literature. Postvalidation, the simulation of droplet evaporation is carried out on the various substrate hydrophobicities and various environmental conditions. For these conditions, contours are plotted for temperature, velocity, and mass concentration for the droplet and moist air domain. The result shows that Marangoni convection plays a very important role in droplet evaporation. A high rate of evaporation is observed at the droplet interface at low relative humidity and a large degree of subheating. The effect of air velocity on the evaporation rate is studied, however, its effect is very marginal as compared to relative humidity and degree of subheating. The heat flux at the three-phase contact line is large for a smaller Prandtl number fluid. Overall, the evaporation rate increases with increasing the Prandtl number because it has a large value of Marangoni convection.     

Heat and mass transfer of combusting monodisperse droplets in a linear stream

Heat and mass transfer phenomena in fuel sprays is a key issue in the field of the design of the combustion chambers where the fuel is injected on a liquid form. The development and validation of new physical models related to heat transfer and evaporation in sprays requires reliable experimental data. This paper reports on an experimental study of the energy budget, i.e. internal flux, evaporation flux and convective heat flux for monodisperse combusting droplets in linear stream. The evaporation flux is characterized by the measurement of the droplet size reduction by the phase Doppler technique, and the droplet mean temperature, required for the internal and convective heat flux evaluation, is determined by two-color, laser-induced fluorescence. The Nusselt and Sherwood numbers are evaluated from the heat and mass fluxes estimation, as a function of the inter-droplet distance. The results are compared to physical models available in the literature, for moving, evaporating and isolated droplets. A correction factor of the isolated droplet model, taking into account drop-drop interaction on the Sherwood and Nusselt numbers, is proposed.     

Leidenfrost drops on micro/nanostructured surfaces

In the Leidenfrost state, the liquid drop is levitated above a hot solid surface by a vapor layer generated via evaporation from the drop. The vapor layer thermally insulates the drop from the heating surface, causing deteriorated heat transfer in a myriad of important engineering applications. Thus, it is highly desirable to suppress the Leidenfrost effect and elevate the Leidenfrost temperature. This paper presents a comprehensive review of recent literature concerning the Leidenfrost drops on micro/nanostructured surfaces with an emphasis on the enhancement of the Leidenfrost temperature. The basic physical processes of the Leidenfrost effect and the key characteristics of the Leidenfrost drops were first introduced. Then, the major findings of the influence of various micro/nanoscale surface structures on the Leidenfrost temperature were presented in detail, and the underlying enhancement mechanism for each specific surface topology was also discussed. It was concluded that multiscale hierarchical surfaces hold the best promise to significantly boost the Leidenfrost temperature by combining the advantages of both micro- and nanoscale structures.     

Advanced models of fuel droplet heating and evaporation

Recent developments in modelling the heating and evaporation of fuel droplets are reviewed, and unsolved problems are identified. It is noted that modelling transient droplet heating using steady-state correlations for the convective heat transfer coefficient can be misleading. At the initial stage of heating stationary droplets, the well known steady-state result Nu=2 leads to under prediction of the rate of heating, while at the final stage the same result leads to over prediction. The numerical analysis of droplet heating using the effective thermal conductivity model can be based on the analytical solution of the heat conduction equation inside the droplet. This approach was shown to have clear advantages compared with the approach based on the numerical solution of the same equation both from the point of view of accuracy and computer efficiency. When highly accurate calculations are not required, but CPU time economy is essential then the effect of finite thermal conductivity and re-circulation in droplets can be taken into account using the so called parabolic model. For practical applications in computation fluid dynamics (CFD) codes the simplified model for radiative heating, describing the average droplet absorption efficiency factor, appears to be the most useful both from the point of view of accuracy and CPU efficiency. Models describing the effects of multi-component droplets need to be considered when modelling realistic fuel droplet heating and evaporation. However, most of these models are still rather complicated, which limits their wide application in CFD codes. The Distillation Curve Model for multi-component droplets seems to be a reasonable compromise between accuracy and CPU efficiency. The systems of equations describing droplet heating and evaporation and autoignition of fuel vapour/air mixture in individual computational cells are stiff. Establishing hierarchy between these equations, and separate analysis of the equations for fast and slow variables may be a constructive way forward in analysing these systems.     

分子动力学方法研究纳米尺度下液滴蒸发的物理规律

采用分子动力学方法对纳米尺度下氩液滴在氩蒸气中蒸发过程进行了模拟,其中液相分子采用球形截断的Lennard-Jones势能函数描述。模拟过程首先在三维模拟空间产生准稳态平衡的液滴和周围气相环境,随后控制液滴的外界物理条件形成蒸发现象,同步记录气液两相分子坐标和动量变化,从微观信息中统计计算出相应的宏观物理信息。研究了蒸发初始液滴半径的不同研究其对液滴蒸发过程的影响,结果表明纳米尺度下液滴蒸发现象与微米以上尺度液滴蒸发现象存在差异;引入等效辐射能的概念在分子动力学方法中实现了对辐射能传递过程的模拟,证实了辐射传递能量会对纳米尺度液滴蒸发过程产生很大的影响。     

Comparative Investigation on Droplet Evaporation Models for Modeling Spray in Cross-Flow

The coupling model of flow and heat and mass transfer for gas-spray droplet two-phase flow has been developed to simulate the evaporating spray in cross-flow. The correlations used for describing the droplet evaporation and motion in convective flow have been compared. The comparisons of calculated results show that the different correlations for determining Nusselt number and Sherwood number impose a significant influence on the lifetime of droplet. The modification of Nusselt number and Sherwood number with regard to the heat and mass boundary around the droplet is of great importance, while different mixing laws for mixture properties and different drag coefficient equations only demonstrate a slight effect on the evaporation characteristics of droplet. The characteristics of spray droplets and cross-flow in terms of both evaporation and motion are obtained. The secondary flow phenomenon is observed in the simulation results and contributes to achieving a more even distribution of temperature and an improved mixing effect of the vapor and cross-flow.