Numerical simulation and experimental study of heat and mass transfer in fuel droplet evaporation

ORIGINALNumerical simulation and experimental study of heat and mass transfer in fuel droplet evaporationPeng Zhao •Guoxiu Li •Yusong YuReceived:21January 2013/Accepted:27February 2014ÓSpringer-Verlag Berlin Heidelberg 2014Abstract Heat and mass transfer in fuel droplet evapo-ration are investigated through numerical simulation and experimental study.The effect of liquid-phase heat transfer is studied using the temperature difference between the gas-and liquid-phase droplets,different turbulent intensity and oscillatory flow frequency.For the two-droplet array,some differences in heat and mass transfer mechanisms are found.For different spacing of the two-droplet array,the down-stream droplet evaporation is affected by the lead droplet.List ofsymbolsA Surface area normal (m 2)D Binary diffusivity (m 2/s)E Energy (kg m 2/s 2)h Heat transfer coefficient [W/(m 2K)]D H V Latent heat (kJ/kg)k Thermal conductivity (W/m k)_m 00V The mass flux of vapour [kg/(m 2s)]_m 00g The mass flux of air [kg/(m 2s)]l Characteristic length (m)p Pressure (Pa)S Source term T Temperature (K)t Time (s)U The mean velocity (Reynolds averaged)(m/s)Greek symbols a Volume fraction q Density (kg/m 3)Subscripts eff Effective q qth fluid l Liquid phase g Gas phase v Vapour x X direction y Y direction z Z direction C Critical V Flow velocity (m/s)Y Mass fraction Supersciptsi,j i or jth species m Mixture1IntroductionDroplet heat and mass transfer has received great attention in recent decades [1]and are of great importance in many combustion systems,such as internal combustion engines and turbine machines.Hiroshi Nomura [2]conducted an experimental study of stagnant single droplet evaporation in a microgravity high-temperature and high-pressure environment.When the pressure is 0.1–2.0Mpa,the slope of the curve of the square of the droplet diameter increases with time initially and then remains constant.At 5.0MPa,the temperature remains below the critical temperature and the latter part of the slope is reduced.Within theP.Zhao ÁG.Li (&)ÁY.YuDeparment of Power and Control Engineering,Beijing Jiaotong University,Beijing,China e-mail:gxli@ P.Zhaoe-mail:emailzp@Heat Mass TransferDOI 10.1007/s00231-014-1317-1experimental pressure range,droplet lifetime decreases as the temperature increases.Chauveau et al.[3]studied the n-decane droplet evaporation process under thermal envi-ronments of normal gravity and microgravity.Results show that when the ambient temperature is below950K,droplet evaporation deviates from the d2law under conditions of microgravity.In addition,in the same test environment, droplet life under microgravity conditions is longer than droplet life under normal gravity conditions.When the ambient temperature exceeds950K,the experimental results of droplet evaporation agree well with d2laws and the mass-transfer rate of droplets is the same as that under normal gravity and microgravity conditions.Hojat Ghas-semi et al.[4]experimentally studied the droplet evapo-ration characteristics of single-component and multi-component suspensions in quartz glass under normal gravity and different environmental conditions.The com-ponents include heptane and hexadecane,both of which have different evaporation rates and boiling points.The details of droplet heating and evaporation can be obtained from the multi-dimensional model.There are two methods that have been developed for multi-dimensional model of droplet evaporation,one-fluid method and two-fluid method[5].For one-fluid method,a set of governing equations are solved,while for two-fluid method,the governing equations for each phases are solved.In the last decades,two-fluid method has been widely used to investigate the problem of droplet evaporation.The two-fluid method usually assumes that the droplet main-tains the rigid spherical shape during the process of droplet evaporation.Masoudi and Sirignano[6,7]investigated the three-dimensional interaction between the advecting vortex and an evaporating droplet.The droplet convective heat transfer number is sensitive to the initial position and structure of the advecting vortex.Furthermore,the vertical structures affect the mass and heat transfer mechanisms in spray combustion systems.The study by Zhang[8]used two-fluid model to simulate a evaporating fuel droplet in a forced convective environment.Good agreement was observed between numerical predictions and experimental data.A two-way coupling method was proposed taking into account the interactions between evaporating droplets in a monodisperse stream by Frackwiak et al.[9].Castanet et al.[10]compared temperaturefields obtained by two-colour laser-inducedfluorescence and the two-way cou-pling method.They found that the frictional stresses were strongly reduced due to the small spacing between the droplets.There have been a few studies using one-fluid method for analysis of droplet evaporation.The main advantage of one-fluid method is it can consider the deformation of evaporating droplet due to interface tracking and interface capturing methods.The volume-of-fluid(VOF)method[11]has been intro-duced in the studies of droplet evaporation in recent years.The VOF method is one of the interface capturing methods.Jan Schlottke[12]studied the droplet evaporation process under incompressibleflow using three-dimensional direct numerical simulation,applied the VOF method to capture the deforma-tion of the surface of the droplets and calculated the evapo-ration rate based on Fick’s law of diffusion.Banerjee[13] studied stratified two-phaseflow using the VOF multiphase model.The object of the study was the evaporation rate of binary mixtures of ethanol and iso-octane for a two-dimen-sional tilt pipeline surface.Haelssig et al.[14]conducted a direct numerical simulation of heat and mass transfer using the VOF method,with heat and mass transfer phenomena in pipe flow as the object of study.Bergeles et al.[15]presented the VOF approach for the computation of the evaporation process of a liquid droplet impinging onto a hot substrate using an adaptive local grid refinement technique at the liquid–gas interface.They focus on mainly on the droplet shape evolution during droplet impingement on a heated surface.The calcu-lations have been done in both two-dimensional axisymmetric and fully three-dimensional domains.The algorithm of evaporated massflux considers the kinetic model.Strotos et al.[16]made a numerical comparison against Fick’s law,kinetic model and conventional hydrodynamic model for evaporation of droplets impinging and depositing on heated solid walls using the VOF method.A coupled model based on kinetic model and conventional hydrodynamic model was formulated for the computation of droplet evaporation in contact with the hot wall.Banerjee[17]performed a numerical study to ana-lyse evaporation of a single droplet composed of a binary mixture of ethanol and iso-octane using VOF multiphase model.Effect of free stream temperature and composition, liquid phase temperature and composition on droplet evapo-ration was studied.Briones et al.[18]conducted a numerical investigation of neutrally hydrophobic water microdroplet evaporation on aflat,isothermal surface using the explicit VOF model with dynamic meshing and variable-time step-ping.There is good agreement between experimental data and simulation results for the droplet volume,dynamic contact angle,contact radius and apex height.The current paper is focused on the numerical simula-tion and experimental study of heat and mass transfer in fuel droplet evaporation.First,temperature closed-loop control of the high-temperature experimental system of droplet evaporation is established.A systematic analysis of the evaporation characteristics of the fuel droplets is con-ducted under environmental temperature changes.Fuel droplet evaporation experimental results are obtained to verify the numerical model.Second,the effect of the liquid-phase heat transfer process is studied based on temperature differences between gas-and liquid-phase droplets.Finally,for the two-droplet array,differences inHeat Mass Transferheat and mass transfer mechanism are found between the upstream and downstream droplets in the droplet evapo-ration process.Upstream droplets are not influenced by downstream droplets.The heat and mass transfer mecha-nism of the upstream droplet is basically identical to that of the single droplet.Thus,we focus on the heat and mass transfer mechanism of the downstream droplet.2Experimental set-upFor diesel engines,the evaporation process of fuel droplets has a greater impact on its performance.Diesel is composed of hydrocarbons,including alkanes,cycloalkanes,alkenes, alkynes,dienes and aromatic hydrocarbons,while a large proportion is alkanes.Cetane number of n-heptane is56and Cetane number of diesel is50,so n-heptane is used as a single component Diesel surrogate fuel in this study[19,20].The experimental apparatus used for the single droplet evaporation is shown in Fig.1.Photographs of droplet shape were recorded using a high-speed camera.The ambient temperature of the experiment varied from300to 600K.The experimental system of droplet evaporation was composed of the following parts:constant volume quartz glass jars,single droplet formation device,high-speed camera,temperature controller and resistance wire.The most critical issue for designing an experimental rig of droplet evaporation in high ambient temperature is to establish a more stable temperature environment.Constant volume device having inside diameter,100mm and length, 200mm was made of quartz glass to visualize the evapo-ration process of single droplet.Single droplet is suspended at the tip of a micro injector and diameter of the injector tip is from0.1to0.5mm.The inherent errors in the experi-mental data are from heat transfer between droplet and the injector tip,the high speed camera and experimental uncertainties.Heat transfer between droplet and the injec-tor tip can be negligible because the diameter of the injector tip is very small.The ambient temperature of droplet is sustained to a nearly constant value using a closed-loop control heating system.Images of droplets are captured by REDLAKE Pro X-4plus high speed camera. The highest speed of the camera is10,000frame/s.3Calculation modelIn this numerical study,the liquid and gas phases are simulated by the VOF multiphase model.The gas phase includes the vapour and the air.aðx;tÞ¼0\a\118<:If the value is0,it indicated that the cell is full of gas phase.If the value is1,it indicated that the cell is full of liquid phase.Furthermore,if the value is0\a\1,it indicated that the cell isfilled with gas phase and liquid phase.The slope and curvature in the phase interface is calculated by the value of volume fraction of the adjacent cells,thereby the discrete equations can be solved.An advantage of the VOF method is its ability to capture the deformation of the droplet.The variable a q represents the volume fraction of the q thfluid.Thefluid may be described by the incompressible Navier–Stokes equations because of its low Mach number.The continuity equation,momentum equation and energy equation are shared between the two phases.The governing equations and source terms are as follows.Volume offluid equationo a qþv~r a q¼S aqqð1ÞS a l¼Àm000ið2ÞS a g¼m000ið3Þ0\a q\1ð4ÞContinuity equationo qo tþrÁðq uÞ¼0ð5ÞMomentum equationoðq v~ÞþrÁðq v~v~Þ¼Àr pþrÁ½lðr v~þr v~TÞþF stþq g~þS mð6ÞS m¼ð1À2aÞm000i v~ð7ÞEnergy equationoo tðq EÞþrÁ½v~ðq EþpÞ ¼rÁðk eff r TÀhJÞþS eð8ÞS e¼Àm000i h i fgð9ÞSpecies equationHigh speed camera Computer Light sourceElectrical resistance wireexperimental systemHeat Mass Transferoo tðq q a q Y qÞþrÁðq q a q v~q Y qÞ¼ÀrÁa q"J qþS sð10ÞS s¼m000ið11ÞIn this study,the purely diffusion-controlled model is used to study droplet evaporation.This model assumes phase equilibrium at the interface and calculates the droplet evaporation rate using Fick’s law.Fick’s law describes the rate at which one species diffuses through the other[21]. The massflow of vapour associated with bulkflow per unit area is equal to the massflow of vapour per unit area plus the massflow of vapour associated with molecular diffu-sion per unit area.The massflow of vapour is expressed as follows:_m000¼D vg q g1ÀY F;sr Y VÁAV cellð12ÞLarge eddy simulation(LES)wasfirst proposed by Sma-gorinsky in1963[22].In LES model,large eddies are resolved by the N–S equations directly.However,small eddies cannot be resolved directly,Subgrid-Scale Models are introduced to model the small eddies.In this study, Smagorinsky-Lilly Subgrid-Scale Model[23]is used for the calculations of droplet evaporation in forced convection.The study of droplet evaporation is investigated using ANSYS FLUENT12.0.The computational domain is two-dimensional structured mesh.Boundary conditions are indicated in Fig.2,including a velocity inlet condition at the left side,free-slip wall conditions on the lateral boundaries, an outflow condition at the right side and an axis symmetrycondition on the axis line.After calculations of grid inde-pendence,size of grid is determined of0.0526mm.4Results and discussion4.1Experimental resultsFigure3shows variations in the squared nondimensional droplet diameter at an ambient temperature of300K.Ini-tial diameter of the droplet is1.45mm.The n-heptane droplets are completely evaporated when the corrected time t/d02is34.37s/mm2.Figure4shows the photographs of the evaporating n-heptane droplet at an ambient temperature of300K.As shown in Fig.4,at the ambient temperature of300K,the n-heptane droplet evaporates slowly.At0s,the shape of the droplet is spherical.At48s,the volume of the droplet is reduced by half and the droplet becomes ellipsoidal.At 108s,the droplet completely evaporates.As shown in Fig.5,the evaporation time of the fuel droplets varies at different ambient temperatures.The corrected time for the complete evaporation of the droplet is34.67s/mm2at an ambient temperature of300K whilst the corrected time for the complete evaporation of the droplet is7.79s/mm2at an ambient temperature of350K. As well,the corrected time for the complete evaporation of the droplet is0.97s/mm2at an ambient temperature of 550K.The above analysis shows that the evaporation time of n-heptane droplets continuously decreases as the ambi-ent temperature increases.4.2ValidationThis section focuses on the validation of the numerical simulation model of droplet evaporation.Considering the limitations of the experimental apparatus,the temperature distribution inside the droplets is difficult to obtain. Numerical simulation is performed to investigate theflow field of the droplets.The parameters of the numerical simulation of droplet evaporation are shown in Table1.Figure6shows the droplet evaporation experimental results versus the numerical results at an ambient temper-ature of550K.Figure6shows that the numericalresultsFig.3Ratio of the square of n-heptane droplet diameter at300KHeat Mass Transferare close to the experimental results.The maximum error between the numerical simulation and experimental results is 2%.Thus,the multi-dimensional numerical model is accurate,reliable and can be used in further studies.Another validation is given together with the experi-mental data by Nomura et al.[2]which were obtained under micro-gravity conditions.The parameters of the numerical simulation of droplet evaporation are shown in Table 2.Figure 7shows that the numerical results are close to the experimental results.The maximum error between the numerical simulation and experimental results is 3%.4.3Simulation resultsThe difference in temperature between the gas and liquid phases can influence the liquid-phase heat transfer process.However,no relevant study on changes in the droplet internal temperature field as a result of different conditions during the process of fuel droplet evaporation has yet been published.The effect of radiation is ignored.Figure 8shows the differences in temperature fields of various temperature differences between the gas phase and the liquid phase.The temperature field is in the range 300–310K.The parameters of the numerical simulation of droplet evaporation are shown in Table 3.As shown in Fig.8,when D T is 56K,a high-tempera-ture region appears inside the droplet,the high-temperature is relatively low and the maximum temperature is 302K.When D T is 200K,the high-temperature region areat = 0s t = 4st = 8st = 12s t = 16st = 24s t = 32s t = 40s t = 48s t = 56 st = 60s t = 68s t = 76s t = 80s t = 84s(Unit:10-1mm)t = 92s t = 96s t = 100s t = 104s t = 108 sFig.4High-speedphotographs of n-heptane droplet evaporation process at 300KFig.5High-speed photography of the n-heptane droplet evaporationprocess at 300KTable 1Parameters for the fuel droplet evaporation simulation ParametersUnits Values Initial droplet diameter m 0.000548Ambient pressure bar 1Ambient temperature K 550Initial droplet temperature K 300Density of n-heptane liquid kg/m3683.72Density of n-heptane vapour kg/m3 4.25Density of airkg/m31.225Heat Mass Transferincreases gradually,and the temperature is approximately 303K.With the increase in temperature difference the area of the high-temperature region is gradually increased as well.When D T is 700K,the maximum temperature of the high-temperature region reaches 308K.The emergence of the high-temperature region is mainly due to the inhomo-geneity of the droplet internal flow field.Figure 9shows the differences in temperature fields of various turbulent intensities.The simulation condition isfor a free-stream mean velocity of 3.2m/s and a range of turbulence intensity from 10to 40%.For different turbu-lence intensity,there is a big difference on the internal temperature of droplets.With increase of the turbulence intensity,regions area of high temperature inside droplets gradually increase.When turbulence intensity is 0–20%,positions of the high-temperature region are same.When turbulence intensity is 30–40%,the high-temperature region tends to be uniformly distributed.In order to consider the effect of oscillation air flows,the velocity inlet boundary is described according to Eq.(13)[24].U 1¼U 0sin ð2p ft Þð13ÞAs can be seen from Fig.10,for different oscillating flow frequency,there is a little difference on temperature distribution of droplets.The positions of high-temperature region of each droplet are similar.However,temperature of the high temperature region gradually increases with increase of the oscillation frequency.During the process of droplet evaporation,droplets are not uniformly heated.Temperature rises in the process of droplet evaporation,the distribution ofhigh-temperatureFig.6Comparison of experimental and simulation values of n-hep-tane droplet evaporation at 550KTable 2Parameters for the fuel droplet evaporation simulation ParametersUnits Values Initial droplet diameter m 0.00035Ambient pressure bar 1Ambient temperature K 466Initial droplet temperatureK300Fig.7Comparison of experimental and simulation values of n-hep-tane droplet evaporation at 466KT= 56KT= 100K T= 200KT= 300K T= 400KT= 700K310 308 306304 302 300Fig.8Effect of different temperature differences on the liquidustemperature at 5msTable 3Parameters for the fuel droplet evaporation simulation ParametersUnits Values Initial droplet diameter m 0.000526Inlet velocity m/s 3.2Ambient temperature K 356Initial droplet temperature K 300Ambient pressurebar1Heat Mass Transferregions is near of vertical and horizontal positions of the flow through circumferential temperature distributions of droplets at the phase interface.Heating rate of droplets becomes faster with increase of the turbulence intensity.This is mainly due to fluctuating velocity of gas flow field becomes larger,thus accelerating the process of heat transfer.The diesel spray field is simplified into a two-droplet array.Figure 11shows the computational domain of the two-droplet array.The interaction between the two droplets will be discussed further in this study.Figure 12shows the temperature distribution of the two-droplet array when the space between the two droplets is equal to 2.5times the droplet diameter.The left image shows the temperature distribution of the upstream droplet whilst the right image shows the temperature distribution of the downstream droplet.At t =5ms,the temperatures of the upstream and downstream droplets have substan-tially the same distribution.Furthermore,the distribution of the high-temperature region occurs at the same positions.At t =10ms,the temperature distribution of the upstream droplet is different from that of the downstream droplet.The high-temperature region of the upstream droplet is widely distributed inside the droplet and the temperature distribution is even whereas a smaller area of high-tem-perature distribution of the downstream droplet is observed and the high-temperature region is concentrated at the front and center location.Most of the temperature region is approximately 300K.At t =15ms,the temperature inside the droplet of the upstream droplet is higher than that of the downstream droplet.Therefore,for the two-dropletarray,the temperature of the downstream droplet is rela-tively lower because of the effect of the upstream droplet.Figure 13shows the comparison of average tempera-tures between the upstream droplet and the downstream droplet when the space between the two droplets is equal to 2.5times the droplet diameter.The average temperature of the upstream droplet is quite different from that of the downstream droplet,the former being higher than the lat-ter.At t =5ms,the average temperature of the upstream droplet is 302.2K whereas the average temperature of the downstream droplet is 301.5K.The difference between the two droplets is 0.2%.At t =20ms,the average temper-ature of the upstream droplet is 302.8K whereas the average temperature of the downstream droplet is 301.64K.The temperature difference between the two droplets is about 0.4%and caused by the effect of the vapour of the upstream droplet.Given that thetemperatureFig.9Effect of different turbulence intensity on the liquid-phase temperature at 5msFig.10Effect of different oscillatory flow frequency on droplet’s liquidus temperature at 5msFig.11The computational domain of the double droplet arrayHeat Mass Transferof the fuel vapour is lower than the temperature of the surrounding air,the average temperature of the down-stream droplet is lower as well.Figure 14shows a comparison of the ratios of the squares of the droplet diameter ratio between the upstream droplet and the downstream droplet when the space between the two droplets is equal to 2.5times the droplet diameter.Several differences may be observed between the upstream droplet and the downstream droplet.The evapo-ration rate of the upstream droplet is greater than that of the downstream droplet.At t =1ms to 15ms,the droplet diameter squared ratio is greater than 1,which is mainly due to the vapour wake of the upstream droplet in contact with the downstream droplet,and the vapour changes into liquid.With increasing temperature,the droplets gradually evaporate and the droplet evaporation rate is accelerated after t =15ms.At different droplet spacings,the downstream droplet is located at different vapour wake positions.Thus,different droplet spacings greatly affect the droplet evaporation.We will discuss the effect of different droplet spacings on the process of droplet evaporation.The expressions 2.5d,5d,7.5d and 10d respectively represent droplet spacings equal to 2.5times,5times,7.5times and 10times the droplet diameter.Figure 15shows the mass fraction distribution of fuel vapour in the two-droplet array with different droplet spacings.The downstream droplet is located at different vapour wake positions of the upstream droplet for different droplet spacings.When the droplet spacing is equal to 2.5d,the downstream droplet is located at the denser fuel vapourwake,thus greatly affecting the evaporation of the down-stream droplet.Moreover,the temperature of the vapour wake is lower than that of the surrounding air and the effect of vapour wake on the downstream droplet is relatively large.The effects between the two droplets become smaller with increasing droplet spacing.When the droplet spacing is equal to 10d,the downstream droplet is at the tail of the vapour wake of the upstream droplet.Thus,the effect of the upstream droplet on the downstream droplet is rela-tively small.Figure 16shows average temperature of fuel vapor at different droplets spacing.The average temperature is average temperature of fuel vapour phase within the size of droplet diameter at different droplets spacing.As can be seen from the figure,the average temperature of the fuel vapour varies at different spacings.When droplet spacing is 2.5d,the average temperature of fuel vapour is 342.74K.Fig.12Comparison of temperatures between the upstream and downstream droplets in a double dropletarrayFig.13Comparison of temperature between the upstream and downstream droplets with spacing of2.5dFig.14Comparison of the ratios of the square of the diameter between the upstream and downstream droplets with spacing of 2.5dHeat Mass TransferWhen droplet spacing is 10d,the average temperature of fuel vapour is 350.69K.The maximum of difference of average temperatures is 8K.As the droplet spacing increases,the average temperature of the fuel vapour also increases.At different droplet spacing,the droplets at dif-ferent temperatures,and therefore it affect the heat and mass transfer of downstream droplets.5ConclusionA large eddy simulation of the VOF model is developed to study droplet evaporation in a forced convective environ-ment under different turbulent fluctuations,which includes turbulence intensity and oscillatory flow.The major find-ings of the present study are as follows.a.Experimental studies of diesel droplet evaporation process are performed under different temperature environments.Results show that when the ambient temperature is relatively low,the diesel fuel droplets first pass through the initial heating stage and then quickly evaporate.At different ambient temperatures,when the temperature is higher,the diesel droplet evaporates sooner.The evaporation time of the n-hep-tane droplets continue to decrease as the ambient temperature rises.b.The distribution of the high-temperature region of the droplet is substantially at the same position.As the temperature difference increases,the temperature of the high-temperature region also increases.Tempera-ture rises in the process of droplet evaporation,the distribution of high-temperature regions is near of vertical and horizontal positions of the flow through circumferential temperature distributions of droplets at the phase interface.Heating rate of droplets becomes faster with increase of the turbulence intensity.This ismainly due to fluctuating velocity of gas flow field becomes larger,thus accelerating the process of heat transfer.c.Several differences in average temperature may be observed between the two droplets and the average temperature of the upstream droplet is always greater than that of the downstream droplet.The differences in average temperature between the two droplets are due to the vapour wake distribution in the upstream droplet.Acknowledgments This work is supported by National Natural Science Foundation of China under Grant 51076008,the Ph.D.Pro-grams Foundation of Ministry of Education of China (No.20110009110023)and the Fundamental Research 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