A Level-Set Method for Analysis of Particle Motion in an Evaporating Microdroplet

A sharp-interface level-set (LS) method is presented for computing particle motion in an evaporating microdroplet. The LS formulation for incompressible two-phase flow is extended to include the effects of evaporation, mass transfer, heat transfer, and dynamic contact angles. A numerical technique for the conservation of particle concentration is incorporated into the LS method, and calculation procedures are also developed and tested for reducing the numerical errors caused in the computation of interface curvature and liquid–gas velocity jump. The improved LS method is applied to the simulation of particle distribution in microdroplet evaporation on a solid surface.     

Internal flow in evaporating droplet on heated solid surface

This work numerically studies the evaporation process of a liquid droplet on a heated solid surface using a comprehensive model. The internal flow within the evaporating liquid droplet is elucidated, while considering the effects of buoyancy force, thermocapillary force, and viscous resistance. The evaporation process is modeled by simultaneously solving the Navier–Stokes equations and energy equation for the liquid domain and the heat conduction equation for the solid domain, while assuming the liquid–vapor interface is a free surface. Three dimensionless parameters are utilized to describe the contribution of individual driving forces to internal flow. Evolutions of the thermal and internal flows during evaporation are discussed. The volume evolution and experimental data are in good agreement.     

A level-set method for ultrasound-driven bubble motion with a phase change

A level-set (LS) method is presented for computation of ultrasound-driven bubble motion including the effect of liquid and vapor compressibility as well as the effect of liquid–vapor phase change. The semi-implicit pressure correction formulation is implemented into the LS method to avoid the serous time-step restriction in low Mach number (or near incompressible) flows. The numerical results for one-dimensional compressible flows and spherical bubble motion in a periodic acoustic field show good agreement with the analytical solutions. The effects of phase change and ambient temperature on the ultrasound-driven bubble motion are quantified.     

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.     

A LEVEL SET METHOD FOR INCOMPRESSIBLE TWO-FLUID FLOWS WITH IMMERSED SOLID BOUNDARIES

ABSTRACT

A numerical method is presented for computing incompressible gas–liquid (or two-fluid) flows with immersed solid boundaries on fixed Cartesian meshes. A level set technique for tracking the gas–liquid interface is modified to treat the contact angle condition at the gas–liquid–solid interline as well as the no-slip condition at the fluid–solid interface. The no-slip condition is imposed by introducing another level set for fluid–solid phases and an effective viscosity formulation. In the immersed solid region where the level set function for gas–liquid phases is not well defined, its zero level set is calculated so that the contact angle condition should be satisfied where the three phases meet. The numerical method is validated through computations of interfacial motion subject to Taylor instability, single-fluid flow past a circular cylinder, and bubbles adhering to a cylindrical solid.     

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.     

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.     

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.     

Heat convection within evaporating droplets in strong aerodynamic interactions

The temperature field within evaporating ethanol droplets is investigated, relying on the two-color laser induced fluorescence (LIF) measurement technique and on a Direct Numerical Simulation (DNS). The configuration studied corresponds to a monodisperse droplet stream in a diffusion flame sustained by the droplet vapor. An experimental probe volume, small compared to the droplet size, is used to characterize the temperature field within the droplets, whereas DNS takes into account key aspects of the droplet heating and evaporation such as the non-uniform and transient stress, and the mass and heat transfer coefficients at the droplet surface. These investigations reveal that the frictional stresses are strongly reduced due to the small spacing between the droplets. They also show that the Marangoni effect has a significant influence on the internal motion and hence on the internal temperature field.     

Numerical Simulation of Droplet Deposition and Self-Alignment on a Microstructured Surface

Numerical simulation is performed for droplet impact and deposition on a microstructured surface. The droplet deformation is calculated by a sharp-interface level-set method which is extended to treat the immersed solid structure and the contact angle at the liquid–gas–solid interline. The computations are further carried out to investigate the droplet self-alignment behavior derived by the interfacial characteristics between the liquid-gas-solid phases, which can be used to overcome a droplet placement error and to improve the accuracy in film formation. The effects of contact angle, surface tension, and microstructure configuration on the droplet deposition are quantified.     

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.     

Three‐dimensional simulation of water droplet movement in PEM fuel cell flow channels with hydrophilic surfaces

Water management is one of the critical issues in proton exchange membrane fuel cells, and proper water management requires effective removal of liquid water generated in the cathode catalyst layer, typically in the form of droplets through cathode gas stream in the cathode flow channel. It has been reported that a hydrophilic channel sidewall with a hydrophobic membrane electrode assembly (MEA) surface would have less chance for water accumulation on the MEA surface. Therefore, a comprehensive study on the effect of surface wettability properties on water droplet movement in flow channels has been conducted numerically. In this study, the water droplet movements in a straight flow channel with a wide range of hydrophilic surface properties and effects of inlet air velocities are analyzed by using three‐dimensional computational fluid dynamics method coupled with the volume‐of‐fluid (VOF) method for liquid–gas interface tracking. The results show that the water droplet movement is greatly affected by the channel surface wettability and air flow conditions. With low contact angle, droplet motion is slow due to more liquid–wall contact area. With high air flow velocities, increasing the contact angle of the channel surface results in faster liquid water removal due to lesser liquid–wall contact area. Copyright © 2010 John Wiley & Sons, Ltd.     

Direct numerical simulations of a planar jet laden with evaporating droplets

A direct numerical simulation (DNS) study is conducted on the various aspects of phase interactions in a planar turbulent gas-jet laden with non-evaporative and evaporative liquid droplets. A compressible computational model utilizing a finite difference scheme for the carrier gas and a Lagrangian solver for the droplet phase is used to conduct the numerical experiments. The effects of droplet time constant, mass-loading and mass/momentum/energy coupling between phases on droplet and gas-jet fields are investigated. Significant changes in velocity, temperature, density and turbulence production on account of the coupling between the liquid and gas phases are observed in non-isothermal jets with evaporating droplets. Most of these changes are attributed to the density stratification in the carrier gas that is caused by droplet momentum and heat transfer.     

Nonequilibrium Molecular Dynamics Modeling Of A Fuel Nanojet In Sub/supercritical Environments: Chamber Pressure Effects On Characteristics Of The Gas–liquid Interface

Molecular dynamics simulation is conducted to microscopically study the effects of environmental pressure on the injection process of a fuel nanojet. The united-atom force field and Lennard-Jones 12-6 potential are applied, which is validated by a single liquid droplet evaporation model against experiments. A gas–liquid–gas model represented by a simulation box for single droplet evaporation and an n-heptane nanojet injected into vacuum, lowly supercritical, and highly supercritical environments are investigated. Results indicate that at lowly supercritical conditions, the gas–liquid interface has been widened, and the interface tension still exists and the phase interface is detected. Only at highly supercritical conditions does the interface becomes sufficiently wide and a continuous phase transition without a distinct phase interface prevails. The most interesting conclusion from the molecular dynamics (MD) results is that the transition of a fluid from subcritical to supercritical states does not occur instantaneously when it goes across the critical point but is a gradual process that can be completed only when the temperature and pressure are sufficiently higher than the critical values. This microscopic analysis is well in accordance with the macroscopic measurements and observations in the literature.     

Evaporation of acoustically levitated multi-component liquid droplets

A theoretical model for the evaporation of multi-component liquid droplets based on the model by Abramzon and Sirignano is presented and applied to the evaporation of acoustically levitated droplets. The liquid phase is treated as a thermodynamically real fluid, using the UNIFAC method for calculating the component activities, and the gas phase as ideal. Computational results, which consist in the droplet surface and volume, temperature and composition as functions of time, are verified by experiments carried out with single droplets evaporating in an acoustic levitator. The results are in excellent agreement, suggesting that the model correctly captures the physico-chemical phenomena in multi-component liquid droplet evaporation.     

Population balance model of heat transfer in gas–solid particulate systems

A population balance model is derived for heat transfer processes in gas–solid systems with intensive motion of particles in order to describe the temperature distribution of particulate phase. The model involves collisional particle–particle and particle–wall heat transfers, and continuous gas–particle, gas–wall and wall–liquid environment heat transfer processes. Collisional heat transfers are characterised by collision frequencies and random heat exchange parameters with general probability distributions with support [0, 1], describing the heat transfer efficiency between the colliding solid bodies. An infinite hierarchy of moment equations, describing the time evolution of moments of the temperature of particle population is derived from the population balance equation, which can be closed at any order of moments. The properties of the model and the effects of parameters are examined by numerical experiments using the second order moment equation model of a spatially homogeneous fluidized bed.     

Derivation of the conditional moment closure equations for spray combustion

In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray combustion with the CMC equations formulated for the gas phase. The CMC equations are to be viewed as an adjunct to existing methods for the modelling of the dynamics of sprays: they provide a refinement of the modelling of chemical reactions in the gas phase. The resulting CMC equations differ significantly from those already in use in the literature. They contain, of course, unclosed terms that need to be modelled. Investigation of the unclosed terms associated with evaporation at the droplet surface is well beyond the capabilities of laboratory measurement or direct numerical simulation. It is proposed that modelling of these terms be based on the well-established ‘laws’ of similarity between heat and mass transfer: an example is detailed for one example of the general modelling of the spray dynamics. Other unclosed terms are important throughout the gas phase. Models used for these terms in single-phase flows are reviewed and it is proposed that any modifications needed for these models be investigated by DNS of suitable model problems having good resolution of the flow and mixing in the inter-droplet space. It is proposed that a spray analogue of the scalar mixing layer that has been widely studied in single-phase flows be used as the model problem for such DNS studies and also for LES and RANS modelling.     

A discrete multicomponent fuel evaporation model with liquid turbulence effects

A new approach to simultaneously account for finite thermal conductivity, finite mass diffusivity and turbulence effects within atomizing multicomponent liquid fuel sprays has been developed in this study. The main contribution of this paper is to incorporate the liquid turbulence effect in modeling the boundary layer heat and mass resistance during multi-component droplet evaporation. The finite conductivity model is based on an existing two-layer film theory, where the turbulence characteristics of the droplet are used to estimate the effective thermal conductivity. The present paper extends the two-layer film theory formulation to include multi-component mass diffusivities within the droplet liquid phase. In this model four regions are considered: the interior region of the droplet, droplet-side interface, gas-side interface, and the surrounding gas phase. Approximate solutions to the quasi-steady energy and mass transfer equations were used to derive an explicit expression for the heat and mass flux from the surrounding gas to the droplet–gas interface, and within the multi-component droplet. Extension of the model to high pressures using the Peng–Robinson equation of state is also considered. The validation study was carried out for a bi-component decane/hexadecane fuel, followed by application studies of complex gasoline–ethanol blended fuels evaporating in hot gas environments.     

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.     

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。