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.     

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.     

Numerical analysis of the interactions between evaporating droplets in a monodisperse stream

A numerical simulation of evaporation in a monodisperse droplet stream is proposed, taking into account the transient state of the evaporation, and the non-uniform mass and heat transfer coefficients on the droplet surface. These investigations emphasize the strong interaction effects between closely spaced droplets in a dense spray, reducing significantly the transfer coefficients. Moreover, the Marangoni force becomes more significant than the viscous force, driving the internal motion of the droplet and affecting the temperature fields. Otherwise, a better understanding of the evaporation phenomenon around closely spaced droplets will help to refine the existing models used in dense sprays.     

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.     

Heat and mass transfer in evaporating droplets in interaction: Influence of the fuel

The prediction of heat and mass transfer in fuel sprays is a key issue in the design of combustors where the fuel is injected in a liquid form. The development and validation of new physical models requires reliable experimental data. This paper reports on an experimental study to characterize the Nusselt and Sherwood numbers of monodisperse droplets made of fuels having different volatilities and evaporating into flowing hot air. Simultaneous measurements of the droplet size and mean temperature allowed evaluating the heat fluxes that take part in the evaporation. The experimental Nusselt and Sherwood numbers are then compared to the case of an isolated droplet. It appears that these numbers are particularly dependent on the interactions between the droplets in a way that depends on the fuel nature.     

New approaches to numerical modelling of droplet transient heating and evaporation

New approaches to numerical modelling of droplet heating and evaporation by convection and radiation from the surrounding hot gas are suggested. The finite thermal conductivity of droplets and recirculation in them are taken into account. These approaches are based on the incorporation of new analytical solutions of the heat conduction equation inside the droplets (constant or almost constant h) or replacement of the numerical solution of this equation by the numerical solution of the integral equation (arbitrary h). It is shown that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. This solution is applied to the first time step, using the initial distribution of temperature inside the droplet. The results of the analytical solution over this time step are used as the initial condition for the second time step etc. This approach is applied to the numerical modelling of fuel droplet heating and evaporation in conditions relevant to diesel engines, but without taking into account the effects of droplet break-up. It is shown to be more effective than the approach based on the numerical solution of the discretised heat conduction equation inside the droplet, and more accurate than the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating and evaporation allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.     

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.     

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。     

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.     

高温气流中双液滴蒸发过程实验研究

建立了液滴蒸发的实验系统,采用悬挂液滴法对高温气流中单、双液滴的蒸发特性进行研究.实验结果表明：双液滴实验时的液滴蒸发过程与单液滴蒸发过程类似;液滴间相互作用使液滴周围蒸汽的浓度增大,气液传质浓度差减小,液滴与周围环境的传质速度降低,使蒸发速率减小;在纯辐射环境中液滴间相互作用对蒸发过程的影响较强,在辐射对流环境中液滴间相互作用对蒸发过程的影响较弱.     

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...     

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 model for droplet evaporation near Leidenfrost point

The droplet evaporation process after impinging on a solid wall near Leidenfrost point is theoretically analyzed. Considering the change of heat transfer effective in the evaporation process, it is divided into recoil stage and spherical stage, and the heat transfer models in these two stages are built, respectively. The effect of initial Weber number, initial droplet diameter, solid surface superheat and wettbility are included in the models. A correlation for predicting evaporation lifetime is obtained based on the theoretical analysis and experimental results. By comparing analysis results with experimental data, it is concluded that the evaporation process can be predicted by present model. The results imply that Leidenfrost point may be not the turning point of heat transfer mechanism. The effect of drop size and Weber number are also analyzed.     

Interaction of transfer processes during unsteady evaporation of water droplets

The change of water droplets state is modelled numerically under various heat and mass transfer conditions during their unsteady evaporation. The modelling is performed using the method of combined analytic–numeric research of heat and mass transfer in a two-phase “droplets–gas” flow. The algorithm of an iterative research is constructed for the analytically obtained system of integral equations. Regularities of heat transfer process interaction are examined. The dependence of the droplet state change on its heating manner is determined. Unsteadiness and interaction of transfer processes, as well as selectivity of radiant absorption in water droplets are evaluated. It is indicated that cognition of the droplet state change regularities in the case of conductive heating is very important in determination of two-phase flow and in construction of an engineering research method.     

Laminar droplet flow in combined hydrodynamically and thermally developing region of circular tubes

Forced convective heat transfer to laminar droplet flow in the combined hydrodynamically and thermally developing region of a circular tube is studied numerically for constant heat flux conditions. The saturated liquid droplets in the vapor flow are considered as equivalent heat sinks distributed in the superheated vapor stream. Numerical calculations are performed for the variations of droplet size, mean vapor velocity, and the local Nusselt number in the streamwise direction until the single-phase fully developed condition is reached. The important roles of the liquid droplets and the developing vapor velocity on the forced convective heat transfer to droplet flow in the combined entrance region of a circular tube are clearly demonstrated.     

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.     

Monodisperse droplet heating and evaporation: Experimental study and modelling

Results of experimental studies and the modelling of heating and evaporation of monodisperse ethanol and acetone droplets in two regimes are presented. Firstly, pure heating and evaporation of droplets in a flow of air of prescribed temperature are considered. Secondly, droplet heating and evaporation in a flame produced by previously injected combusting droplets are studied. The phase Doppler anemometry technique is used for droplet velocity and size measurements. Two-colour laser induced fluorescence thermometry is used to estimate droplet temperatures. The experiments have been performed for various distances between droplets and various initial droplet radii and velocities. The experimental data have been compared with the results of modelling, based on given gas temperatures, measured by coherent anti-stokes Raman spectroscopy, and Nusselt and Sherwood numbers calculated using measured values of droplet relative velocities. When estimating the latter numbers the finite distance between droplets was taken into account. The model is based on the assumption that droplets are spherically symmetrical, but takes into account the radial distribution of temperature inside droplets. It is pointed out that for relatively small droplets (initial radii about 65 μm) the experimentally measured droplet temperatures are close to the predicted average droplet temperatures, while for larger droplets (initial radii about 120 μm) the experimentally measured droplet temperatures are close to the temperatures predicted at the centre of the droplets.     

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.     

高频感应等离子场中液滴运动蒸发过程模拟

建立在高频感应热等离子体环境下单个溶液液滴的运动蒸发模型,采用数值计算的方法模拟了液滴在等离子体射流中的运动和传热过程,分析了不同操作参数对液滴运动蒸发过程的影响.结果表明:液滴初始入射尺寸越小,表面溶质质量分数达到饱和状态所用时间越短;初始入射速度越快,表面溶剂蒸发速度越快,溶质结晶析出时间越短;入射角较大时,液滴会被反向涡流卷吸,表面浓度达到饱和状态的时间较长.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.