Numerical simulation of droplet merging and chemical reaction in a porous medium

The chemical reaction between droplets merging in a porous medium is numerically investigated by solving the conservation equations of mass, momentum and chemical concentration in the internal and external regions of the porous medium. A level-set formulation for two-phase flows is extended to include the effects of porosity and mass transfer with chemical reaction. The numerical result for one-dimensional mass transfer with chemical reaction shows good agreement with the exact solution. The numerical method is applied to investigate the effects of droplet size, impact velocity and porosity on the droplet merging and the associated chemical reaction in a porous medium.     

Numerical Simulation of Liquid Film Evaporation in Circular and Square Microcavities

Numerical simulations are performed for liquid film evaporation in circular and square microcavities, which occurs frequently in ink-jet fabrication. The conservation equations of mass, momentum, energy, and mass fraction in the liquid and gas phases are solved using a sharp-interface level-set method, which is modified to include the effects of evaporation and dynamic contact angles. Three-dimensional computations for a square cavity are efficiently carried out in a reduced domain by introducing an effective mass transfer length for the truncated region. The liquid film evaporation pattern is observed to depend strongly on the dynamic contact angles and cavity geometry.     

A numerical model for transport in flat heat pipes considering wick microstructure effects

A transient, three-dimensional model for thermal transport in heat pipes and vapor chambers is developed. The Navier–Stokes equations along with the energy equation are solved numerically for the liquid and vapor flows. A porous medium formulation is used for the wick region. Evaporation and condensation at the liquid–vapor interface are modeled using kinetic theory. The influence of the wick microstructure on evaporation and condensation mass fluxes at the liquid–vapor interface is accounted for by integrating a microstructure-level evaporation model (micromodel) with the device-level model (macromodel). Meniscus curvature at every location along the wick is calculated as a result of this coupling. The model accounts for the change in interfacial area in the wick pore, thin-film evaporation, and Marangoni convection effects during phase change at the liquid–vapor interface. The coupled model is used to predict the performance of a heat pipe with a screen-mesh wick, and the implications of the coupling employed are discussed.     

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.     

Leidenfrost boiling of methanol droplets on hot porous/ceramic surfaces

An experimental and analytical study of film boiling methanol droplets on a porous/ceramic surface is reported. Droplet evaporation times in the wetting and film boiling regimes were measured on a polished stainless-steel surface and three ceramic/alumina surfaces of 10%, 25% and 40% porosity. It was found that the Leidenfrost temperatures increased as surface porosity increased. The Leidenfrost point of the 10% and 25% porous surfaces were nearly 100 K higher and 200 K higher, respectively, than that of the polished stainless-steel surface; methanol droplets could not be levitated on the 40% porous surface at surface temperatures as high as 620 K, which was the maximum surface temperature which could be imposed on this particular material with our apparatus. The evaporation time of liquid deposited on this surface was thus almost two orders of magnitude lower than for levitated droplets on the three other surfaces tested at the same temperature. In the Leidenfrost regime droplets evaporated faster on the porous surfaces than on the stainless-steel surface, and the evaporation time decreased with increasing surface porosity at the same surface temperature. The reduced evaporation times were thought to have their origin in a decrease of the vapor film thickness separating the droplet from the ceramic surface due to vapor absorption and flow within the ceramic material. An analysis of flow in a horizontal channel bounded by an impermeable ẇall above and a permeable wall of finite thickness below was used to model the film boiling process. The results provided a basis for correlating our evaporation time measurements.     

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.     

Droplet evaporation in a turbulent high-pressure freestream – A numerical study

This paper presents a 3D numerical model for predicting the evaporation of a droplet exposed to a turbulent, high-pressure and high-temperature gaseous nitrogen freestream. The governing complete set of time-dependent conservation equations of mass, momentum, energy, and species concentration for both gas- and liquid-phase are solved numerically. The turbulence term in the conservation equations of the gas-phase is modeled by using the shear-stress transport (SST) closure model. In addition, variable thermophysical properties, unsteadiness of the gas and liquid phases, radiation, non-ideal gas behavior, and solubility of gas into the droplet are all accounted for in the numerical model. A wide range of freestream conditions is explored. The present numerical predictions revealed that the freestream turbulence intensity still has an effect on the droplet vaporization even at significantly high-pressure and high-temperature conditions, although this effect weakens with an increase in both ambient pressure and temperature. More importantly, new correlations are proposed to account for the effects of freestream ambient conditions on the droplet vaporization process.     

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.     

MRI investigation of the evaporation of embedded liquid droplets from porous surfaces under different drying regimes

A combination of in situ one-dimensional ¹H magnetic resonance profiling and two-dimensional imaging has been applied to study the shape and subsequent dynamic evaporation behaviour of a single liquid droplet after impact onto a porous surface. Diethyl-malonate (DEM) droplets are initially embedded in the porous substrate by impingement, and are then evaporated over a period of several hours; the surface of the substrate being ventilated by a controlled airflow. The configuration is intended to mimic the behaviour of droplets evaporating into atmospheric flows. In order to evaluate the influence of the airflow at the surface of the porous medium, different experimental configurations were tested by varying the speed of the airflow stream above the porous surface. The method produces several types of data, including images of impinged droplets inside the porous substrate and their development with time during the evaporation episode, one-dimensional concentration profiles through the substrates, and corresponding estimates of the mass fraction of liquid remaining, evaporation rate and mass flux per unit area. The results obtained show that although liquid droplets tend to evaporate faster and present larger evaporation rates when exposed to a more efficient removal of vapour from the surface, the limiting effects of the porous medium are even more evident.     

Development of a mathematical model for predicting water vapor mass generated in micro-explosion

This paper describes a mathematical model for predicting the mass of water vapor generated in micro-explosion. First, a single droplet experiment was carried out. A W/O (water/oil) emulsified fuel droplet suspended by a thermocouple was heated by a halogen spot heater, and micro-explosion was observed using a high-speed video camera. The progress of the coalescence of the dispersed water droplet was observed while droplet was heated, and an aggregated water droplet was formed in the oil layer. Based on the measured micro-explosion characteristics, a mathematical model for predicting water vapor mass generated in micro-explosion was proposed. The size of the aggregated water droplet just before micro-explosion was measured to verify the proposed mathematical model. Under certain assumptions, mass and energy conservation equations were applied to micro-explosion process, and an equation to calculate water vapor mass generated in micro-explosion was derived. The derived equation and some measurement results provide enough information to calculate water vapor mass generated in micro-explosion. The calculated diameter of the water droplet, which changed to vapor in micro-explosion, was compared to that of the aggregated water droplet just before micro-explosion. The calculated results roughly agreed with experimental ones, and the validity of the proposed model was verified.     

A microscale model for thin-film evaporation in capillary wick structures

A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.     

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.     

Evaporation of droplets into a background gas: Kinetic modelling

A new kinetic model for droplet evaporation into a high pressure background gas, approximated by air, is described. Two regions above the surface of the evaporating droplet are considered. These are the kinetic region, where the analysis is based on the Boltzmann equation, and the hydrodynamic region. It is assumed that the mass fluxes leaving the kinetic region and the corresponding diffusion fluxes in the hydrodynamic region are matched. A modified version of the previously developed method of direct numerical solution of the Boltzmann equation is used. It is assumed that the mass flux leaving the droplet’s surface is the maximal one (evaporation coefficient is equal to 1). The model and numerical algorithm allowed us to calculate the value of the net evaporation coefficient, defined as the ratio of the actual mass flux leaving the kinetic region and the maximal possible mass flux. The values of this coefficient for diesel fuel (approximated by n-dodecane) were shown to be much less than 1 for droplet surface temperatures less than 650 K. For these droplets, the kinetic effects predicted by the new model turned out to be negligible when the contribution of air in the kinetic region was ignored. These effects, however, appear to be noticeable, and larger than those predicted by the approximate analysis, if the contribution of air in the kinetic region is taken into account. It is recommended that the kinetic effects are taken into account when accurate analysis of diesel fuel droplet evaporation is essential.     

Transient modeling of heat,mass and momentum transfer of an evaporating cerium nitrate solution droplet with a surrounding shell in a rf thermal argon–oxygen plasma under reduced pressure

A model was developed to study the evaporation of a solution droplet surrounded by a porous crust in a stagnant rf Ar–O₂ thermal plasma under reduced pressure. This model considered a three phase system: a liquid core of dissolved Ce(NO₃)₃ · 6H₂O in water, a porous crust of homogeneously precipitated spherical crystals of equal size containing water vapor, and an Ar–O₂ plasma under reduced pressure. The model was solved considering a receding solution/crust interface in an ALE frame using temperature and composition dependant thermophysical properties. Darcy flow with a Knudsen correction to account for the gaseous flow through a porous media composed of nano-sized crystals was employed. The strength of the solid/liquid interface was calculated by computing the strength of liquid bridges formed at this interface. This value was compared to the pressure build-up caused by solvent evaporation and the point of crust breakage was determined at different operating conditions. The effects of plasma gas temperature, pressure and composition, droplet size, size of precipitated crystals and crust porosity on crust bursting were studied. The results showed that crust bursting occurred for all the conditions analyzed and that plasma temperature, droplet size and the size of the precipitated crystals had a significant effect on pressure build-up.     

Numerical analysis of the influence of two-phase flow mass and heat transfer on n-heptane autoignition

This paper investigates the influence of liquid fuel presence on the autoignition of n-heptane/air mixtures over a wide range of conditions encountered in internal combustion engines. To this end, evaporating droplet physics and skeletal chemistry mechanisms are simultaneously solved considering a homogeneous constant-pressure reactor. A skeletal mechanism is introduced to account for specific kinetics behavior in the Negative Temperature Coefficient (NTC) region. The impact of mass and heat source terms during evaporation is emphasized by comparing a two-phase flow scenario with a purely gaseous case. The competition between fuel vapor availability and the evaporation-induced gas temperature decrease is specific to two-phase flow autoignition. On the one hand, droplet evaporation delay restricts the gaseous local fuel/air equivalence ratio and consequently the kinetics runaway. On the other hand, temperature reduction due to evaporation may either reduce or enhance chemical reactivity, depending on the local thermodynamic conditions lying either inside or outside the NTC region. By simultaneously accounting for evaporation source terms and skeletal chemistry, we can reproduce the already experimentally observed transformation of the NTC region into a Zero Temperature Coefficient (ZTC) region depending on thermodynamic conditions and droplet size. The ZTC phenomenon appears when combustion heat-release starts before complete droplet evaporation. Since the ZTC behavior can be captured using the point source approach, in which droplets are considered only as zero-dimensional source terms of mass and energy, the present results pave the way for future exploration of NTC chemistry in sprays with a direct numerical simulation of discrete particles considering detailed chemistry and turbulent flows.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

Investigation of heat and mass transfer between the two phases of an evaporating droplet stream using laser-induced fluorescence techniques: Comparison with modeling

Heat and mass exchanges between the two phases of a spray is a key point for the understanding of physical phenomena occurring during spray evaporation in a combustion chamber. Development and validation of physical models and computational tools dealing with spray evaporation requires experimental databases on both liquid and gas phases. This paper reports an experimental study of evaporating acetone droplets streaming linearly at moderate ambient temperatures up to 75 °C. Two-color laser-induced fluorescence is used to characterize the temporal evolution of droplet mean temperature. Simultaneously, fuel vapor distribution in the gas phase surrounding the droplet stream is investigated using acetone planar laser-induced fluorescence.Temperature measurements are compared to simplified heat and mass transfer model taking into account variable physical properties, droplet-to-droplet interactions and internal fluid circulation within the droplets. The droplet surface temperature, calculated with the model, is used to initiate the numerical simulation of fuel vapor diffusion and transport in the gas phase, assuming thermodynamic equilibrium at the droplet surface. Influence of droplet diameter and droplet spacing on the fuel vapor concentration field is investigated and numerical results are compared with experiments.     

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。     

Large eddy simulation of dilute reacting sprays: Droplet evaporation and scalar mixing

Large eddy simulation (LES) of turbulent reacting sprays is performed to investigate the interactions of droplet evaporation and subfilter scalar mixing processes. A stochastic method is proposed to generate the subfilter fluctuations in gas-phase reactive scalars in the framework of a mixture-fraction-based combustion model. The subfilter fluctuations of the gas-phase temperature and composition, seen by droplets, are used to refine the estimates of the interphase heat/mass transfer rates. Gas-phase combustion is described by the flamelet progress variable approach. The effects of droplet evaporation on subfilter scalar mixing are considered by solving the transport equation for the subfilter mixture fraction variance. The mixture fraction that is valid instantaneously in both the gas and the liquid phases is adopted and its implication on the modeling of the evaporation source term in the subfilter variance equation is discussed. The modeling approach has been applied to the Sydney dilute reacting sprays. To account for uncertainty in the modeling of scalar dissipation rates in spray flames, a parametric study is performed for the constant in the scalar dissipation model for the subfilter variance equation. The effects of subfilter fluctuations on droplet evaporation are found to depend on the inflow condition of the pre-evaporated gas-phase mixture and the liquid injection rate in the present dilute reacting sprays.     

Investigation of the evaporation of embedded liquid droplets from porous surfaces using magnetic resonance imaging

For the first time, results are presented from studies using magnetic resonance imaging techniques to follow the behaviour of single water droplets evaporating from porous surfaces. The droplets are initially embedded in the porous substrate by impingement, and are then evaporated over a period of several hours, the surface of the substrate being ventilated by a controlled airflow. The configuration is intended to mimic the behaviour of droplets evaporating into atmospheric flows from surfaces such as sand, or concrete. The method produces several types of data, including images of impinged droplets inside the porous substrate and their development with time during the evaporation episode, one-dimensional concentration profiles through the substrates, and corresponding estimates of the mass fraction of liquid remaining, evaporation rate and mass flux per unit area. The results obtained show that the impinged droplet resides in the porous medium in a shape similar to a semi-spheroid. The results also indicate that the transport of liquid by capillary diffusion has a very strong influence upon the evaporation process, providing a challenge to the simple receding evaporation-front assumption that is utilised in many modelling procedures.