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.     

A coupled level set and volume-of-fluid simulation for heat transfer of the double droplet impact on a spherical liquid film

A coupled level set and volume-of-fluid method is applied to investigate the double droplet impact on a spherical liquid film. The method focuses on the analysis of surface curvature, droplet diameter, impact velocity, double droplets vertical spacing, the thickness of the liquid film of two liquid droplets after the impact on a spherical liquid film, and the influence of flow and heat transfer characteristics. The results indicate that the average wall heat flux density of the double liquid droplet impact on a spherical liquid film is greater than that of a flat liquid film. Average wall heat transfer coefficient increases with the increase in the liquid film’s spherical curvature. When the liquid film thickness is smaller, the average wall heat flux density of the liquid film is significantly reduced by the secondary droplets generated from the liquid film. When the liquid film thickness is larger, the influence of liquid film thickness on the average wall heat flux density gradually decreases. The average wall heat flux density increases with the increase in impact velocity and the droplet diameter; it also decreases with the increase in double droplets vertical spacing.     

蒸发液滴内部非稳态流动的数值计算

在气液两相流VOF(volume of fluid,VOF)模型的基础上耦合CSF(continuum surface force,CSF)表面张力模型,建立了高温平板上的铺展液滴与高温空气中悬浮液滴蒸发过程中内部非稳态流动模型,对液滴蒸发过程中内部非稳态流动进行了研究。基于相变理论,采用用户自定义函数将流体相变模型加入非稳态流动模型中进行耦合计算,获得了高温平板上的铺展液滴与高温空气中悬浮液滴蒸发过程中的内部流动及变化过程。液滴蒸发过程中非稳态内部流动由液滴表面的温度梯度引发,Marangoni流动在液滴内部形成的时间非常短,流体从液滴表面高温区域流向低温区域。计算结果表明:高温平板上随着液滴蒸发的进行,液滴内部一直保持两个对称的涡流,Marangoni流动比较稳定;高温空气环境中随着液滴蒸发的进行,液滴内部四个涡流逐渐转变成两个对称的涡流;液滴内部温度分布因Marangoni流动加强传热而变得均匀,同时由于温度分布变得均匀,Marangoni流动被削弱。     

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。     

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.     

On the dynamics and heat transfer of bubble train in micro-channel flow boiling

The dynamics and heat transfer characteristics of flow boiling bubble train moving in a micro channel is studied numerically. The coupled level set and volume of fluid (CLSVOF) is utilized to track interface and a non-equilibrium phase change model is applied to calculate the interface temperature as well as heat flux jump. The working fluid is R134a and the wall material is aluminum. The fluid enters the channel with a constant mass flux (335 kg/m² 1 s), and the boundary wall is heated with constant heat flux (14 kW/m²). The growth of bubbles and the transition of flow regime are compared to an experimental visualization. Moreover, the bubble evaporation rate and wall heat transfer coefficient have been examined, respectively. Local heat transfer is significantly enhanced by evaporation occurring vicinity of interface of the bubbles. The local wall temperature is found to be dependent on the thickness of the liquid film between the bubble train and the wall.     

3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling

The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solid–vapor/liquid–vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid–vapor and solid–vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet’s initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.     

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...     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Modeling gas oil spray coalescence and vaporization in gas solid riser reactor

The sprayed feed droplet behavior, including coalescence and vaporization into gas–solid flow, is complex especially near the atomizer region in fluid catalytic cracking (FCC) riser reactor. A three dimensional CFD model of the riser reactor has been developed, which takes into the account three phase hydrodynamics, heat transfer and evaporation of the liquid droplets into a gas–solid flow as well as phase interactions. A hybrid Eulerian–Lagrangian approach was applied to numerically simulate the collision and vaporization of gas oil droplets in the gas–solid fluidized bed. This numerical simulation accounts the possibility of coalescence of feed spray droplets in computing the trajectories and its impact on droplet penetration in the reactor. The modeling result shows that droplet coalescence mainly occurs at the initial part of the atomizing region and where three phase flow hits the reactor wall and bounces back. The model has the ability of inspecting the effects of feed injector geometry on the overall reactor hydrodynamic and heat transfer. The CFD simulation results showed that the evaporated droplet gas caused higher local velocities of the gas and solid particles and gas–solid flow temperature reduction.     

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.     

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.     

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 transfer in a high temperature region of spray cooling interacting with liquid film flow

We present experimental results on heat transfer distribution in the high temperature region of spray cooling interacting with subcooled liquid film flow. The results show that the flow field can be divided into the interacting and film flow regions by the heat transfer distribution. In the interacting region, the heat transfer coefficient can be correlated to the liquid-film-flow heat transfer by using a heat-transfer enhancement coefficient defined as the ratio of the droplet flow rate to liquid film velocity. In the wall region, it can be predicted from the equation obtained from a previous study, which is very similar to that of turbulent heat transfer of single-phase flow. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 236–248, 1997     

重力热管内部相变及传热传质过程的数值模拟

重力热管内部包含复杂的两相流动以及相变传热过程,传统理论分析及实验手段不能直观给出其内部流动、相变、热质传递的详细信息。采用VOF(volume of fluid)多相流模型对重力热管内气液两相流动及传热进行模拟,捕捉到蒸发段气泡产生、合并、长大、上升,以及冷凝段壁面附近液滴形成、合并、下滑、汇集到液池的全过程,得到的壁温分布与实验测量值对比体现良好一致性,表明数值模拟的正确性。同时,以热阻、传热量和热效率为评价标准,研究不同充液率和倾斜角度下对重力热管运行性能的影响。结果表明:在所研究的参数范围内,随着充液率的增加,热阻逐渐减小,冷凝段传热量逐渐增大。且工质初始充注量充满蒸发段时热管性能较好;倾角对热阻的影响不明显,冷凝段传热量和热效率均随倾角增加而增长。     

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。     

The peculiarities of hot liquid droplets heating and evaporation

The change of the thermal state of a sprayed liquid droplet is calculated using the method of combined analytical and numerical research, which requires the balance of energy flows, incoming to the droplet and outgoing from it. The method evaluates unsteadiness of heat and mass transfer processes and interaction, which occurs under the influence of the Stefan’s hydrodynamic flow, radiant flow absorbed in semitransparent liquid and the Knudsen layer, which surrounds the droplets. The expedience of the thermal state’s evaluation of dispersed liquid is verified using the parameter, expressed by the ratio of liquid’s initial temperature on equilibrium evaporation temperature of droplets. As the above-mentioned parameter is less than 1, liquid is offered to be called “cold”; “warm”, as the parameter equals 1 and “hot”, as it exceeds 1. In each case the peculiarities of the thermal state change of sprayed liquid droplets are individual during an unsteady phase transformation mode. The characteristic curves, representing the change of transfer parameters, are determined for conductively heated droplets and when the Knudsen layer’s influence is neglected. These curves join together variation of the parameters of the thermal state change and phase transformation for droplets of infinitesimal set of diameters, but with the same initial liquid temperature, as the droplets evaporate in gas with constant parameters. Deviations from the characteristic curves allow evaluating the influence of more complicated boundary conditions on the interaction of transfer processes.     

Transient modeling of micro-grooved heat pipe

One-dimensional transient model for fluid flow and heat transfer is presented for a micro-grooved heat pipe of any polygonal shape utilizing a macroscopic approach. The coupled non-linear governing equations for the fluid flow, heat and mass transfer are developed based on first principles and are solved simultaneously. The transient behavior for various parameters, e.g. substrate temperature, radius of curvature, liquid velocity, etc. are studied. The effects of the groove dimensions, heat input and Q-profiles on the studied parameters have been evaluated. The steady state profiles for substrate temperature, radius of curvature, liquid velocity etc. have also been generated. The model predicted steady state substrate temperature profile is successfully compared with the experimental results from the previous study. The general nature of the model and the associated parametric study ensure the wide applicability of the model.     

Wake Flow and Heat Transfer Due to a Spherical Viscous Droplet

A numerical study on the buoyancy-assisted flow and heat transfer from a liquid spherical droplet falling in fluid medium is made. The investigation is based on the solution of the Navier-Stokes equations together with the energy equation inside and outside the droplet, along with a suitable interface condition. The governing equations for three-dimensional flow and heat transfer are solved through the pressure correction based iterative algorithm, SIMPLE. The Reynolds number for the exterior flow is considered below 300 with the Richardson number in the range 0 ≤ Ri ≤ 1.5. The form of the wake due to the viscous droplet and its influence on heat transfer and drag coefficient are analyzed for a wide range of physical parameters. It is found that by increasing the Reynolds number, the predicted rate of heat transfer is significantly increased for a liquid droplet compared to a solid sphere. The increment of viscosity of the droplet increases the drag experienced by the droplet but reduces the rate of heat transfer. An increase in Richardson number produces an increment in drag coefficient as well as in heat transfer. In order to establish a simplified model for heat transfer due to a viscous droplet, we compared our computed solutions with several empirical correlations for conjugate heat transfer and proposed a model (in absence of buoyancy). We have also investigated the validity of several empirical correlations for the drag coefficient.     

Fluid flow and heat transfer model for high-speed rotating heat pipes

A new complete model has been developed to predict the performance of high-speed rotating heat pipes with centrifugal accelerations up to 10 000 g. The flow and heat transfer in the condenser is modeled using a conventional modified Nusselt film condensation approach. The heat transfer in the evaporator has previously been modeled using a modified Nusselt film evaporation approach. It was found, however, that natural convection in the liquid film becomes more significant at higher accelerations and larger fluid loadings. A simplified evaporation model including the mixed convection is developed and coupled with the film condensation model. The predictions of the model are in reasonable agreement with existing experimental data. The effects of working fluid loading, rotational speed, and pipe geometry on the heat pipe performance are reported here.