Finite-rate evaporation and droplet drag effects in spherical flame front propagation through a liquid fuel mist

An evolution equation for a laminar flame front propagating into an air and liquid fuel mist cloud is derived for the first time, accounting for both the finite-rate evaporation of the fuel droplets and the slip velocity between them and their host environment. The asymptotic analysis employed in developing the equation exploits the usual inverse large activation energy parameter associated with chemical reaction in the flame and a small drag parameter. It is demonstrated that, in the no-slip velocity case, increasing the vaporization Damköhler number can produce flame extinction, presumably due to the more intense heat loss incurred due to droplet heat absorption necessary for vaporization. Droplet drag can also induce extinction due to the longer residence time of the droplets in any locale (than if there was no slip), leading to more vaporization with greater attendant heat loss. The predicted results for droplet velocity are compared to independent experimental data from the literature with good qualitative agreement.     

An assessment on convective and radiative heat transfer modelling in tubular solid oxide fuel cells

Four models of convective and radiative heat transfer inside tubular solid oxide fuel cells are presented in this paper, all of them applicable to multidimensional simulations. The work is aimed at assessing if it is necessary to use a very detailed and complicated model to simulate heat transfer inside this kind of device and, for those cases when simple models can be used, the errors are estimated and compared to those of the more complex models.     

Modelling of biofuel droplets dispersion and evaporation

Alternative renewable fuels are more and more important due to increasing oil prices, environmental concerns and their potential to preserve the agricultural activity. For the case of biofuels derived from agricultural crops, several possibilities can be considered, such as raw oil, oil-derived methyl esters, bioethanol or mixtures with conventional fuels (diesel fuel or gasoline). The straight use of vegetable oils and their derivates poses some problems on the mixture formation process and droplet evaporation, that are essentially derived from their much higher viscosity (up to five times the viscosity of the diesel fuel) and higher boiling temperature. The present paper presents a numerical study on evaporating biofuel droplets injected through a turbulent cross-stream. This study uses an Eulerian/Lagragian approach to account for turbulent transport, dispersion, evaporation and coupling between both processes in practical spray injection systems, which usually include air flows in the combustion chamber-like swirl, tumble and squish in I.C. engines or cross-flow in boilers and gas turbines. An array of evaporating biofuel droplets through a cross-flow is studied, and a comparison of the droplet fuel dispersion and evaporation with conventional fuels is performed. The results obtained with DF-2 and RME showed that an homogeneous mixture can only be obtained with very high levels of pre-heating, and the use of ethanol (obtained from sugar or starch crops) may be a better alternative in ignition-assisted combustion systems, while RME can be successfully used as an alternative fuel in applications that utilize diffusion flames.     

Transport processes and associated irreversibilities in droplet combustion in a convective medium

A mathematical model of the combustion of a droplet surrounded by hot gas with a uniform free stream motion is made from the numerical solution of conservation equations of heat, mass and momentum in both the carrier and the droplet phases. The gas-phase chemical reaction between the fuel vapour and the oxidizer is assumed to be single-step and irreversible. The phenomenon of ignition is recognised by the sudden rise of temperature in the temperature/time histories at different locations in the carrier phase. To ascertain the process irreversibilities, the instantaneous rate of entropy production and its variation with time have been determined from the simultaneous numerical solution of the entropy conservation equations for both the gas and liquid phases. The relative influences of pertinent input parameters, namely the initial Reynolds number Re_i, the ratio of the free stream to initial temperature T_∞ and the ambient pressure on (i) the local and average Nusselt numbers, (ii) the life histories of burning fuel drops, and (iii) the entropy generation rate in the process of droplet combustion have been established.     

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.     

Transient burning of a convective fuel droplet

The transient burning of an n-octane fuel droplet in a hot gas stream at 20 atmosphere pressure is numerically studied, with considerations of droplet regression, deceleration due to the drag of the droplet, internal circulation inside the droplet, variable properties, non-uniform surface temperature, and the effect of surface tension. An initial envelope flame is found to remain envelope in time, and an initial wake flame is always transitioned into an envelope flame at a later time, with the normalized transition delay controlled by the initial Reynolds number and the initial Damkohler number. The initial flame shape is primarily determined by the initial Damkohler number, which has a critical value of Da₀=1.02. The burning rates are modified by the transition, and are influenced by the intensity of forced convection which is determined by initial Reynolds number. The influence of surface tension is also studied as the surface temperature is non-uniform. Surface tension affects the liquid motion at the droplet surface significantly and affects the change of surface temperature and burning rate modestly. The influence of surface tension generally increases with increasing initial Reynolds number within the range without droplet breakup. We also studied cases with constant relative velocity between the air stream and the droplet. The results show that in these cases the initial envelope flame still remains envelope, but the evolution from an initial wake flame to an envelope flame is inhibited. Validation of our analysis is made by comparing with a published porous-sphere experiment Raghavan et al. (2005) [6] which used methanol fuel.     

Modelling and evaluation of heating strategies for high temperature polymer electrolyte membrane fuel cell stacks

Experiments were conducted on two different cathode air cooled high temperature PEM (HTPEM) fuel cell stacks; a 30 cell 400 W prototype stack using two bipolar plates per cell, and a 65 cell 1 kW commercial stack using one bipolar plate per cell. The work seeks to examine the use of different heating strategies and find a strategy suited for fast start-up of the HTPEM fuel cell stacks. Fast start-up of these high temperature systems enables use in a wide range of applications, such as automotive and auxiliary power units, where immediate system response is needed. The development of a dynamic model to simulate the temperature development of a fuel cell stack during heating can be used for assistance in system and control design. The heating strategies analyzed and tested reduced the start-up time of one of the fuel cell stacks from 1 h to about 6 min.     

A simplified model for bi-component droplet heating and evaporation

A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribution of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat conduction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the simplified model with the activity coefficient equal to 1 for the interpretation of the time evolution of temperatures measured with errors more than several degrees.     

Mono-component fuel droplet evaporation in the presence of background fuel vapor

A simplified set of equations is examined for the problem of droplet evaporation. The equations employ the Clausius–Clapeyron (CC) boundary condition for the surface fuel-vapor, which is responsible for mathematical behaviors that include an initial condensation stage of droplet swelling followed by an evaporation stage. Numerical methods of analysis are used in conjunction with an asymptotic analysis of each of the three stages: (I) condensation; (II) transition; and (III) evaporation. Droplet evaporation in partial condensation environments is discussed.     

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.     

Experimental study on evaporation characteristics of single and multiple fuel droplets

In this work, evaporation experiments of multiple droplets are carried out in a stagnant hot atmospheric environment (573, 673 and 773 K) using high-speed backlit image technique. Three fuel droplets with nearly same initial diameter are suspended at intersections of two 0.1 mm quartz fibers. The normalized droplet spacing (s/d₀) of three droplets is 2.25. The results show that the evaporation process of single, edge and central fuel droplet containing three stage: initial heating, unsteady evaporation and quasi-steady evaporation stage. Classical d² law is still suitable for edge and central droplet at quasi-steady evaporation stage. The third stage of edge and central droplet accounts for more than 60% of droplet lifetime at low temperatures and about 50% at high temperatures. The evaporation rate constant of edge and central droplet increases and droplet lifetime decreases with increasing ambient temperature. The evaporation time of edge and central droplet at first and third stage is higher than single droplet, but lower than single droplet in the second stage. More importantly, the evaporation interactions between droplets is significant at low temperature. Compared with single droplet, the lifetime of central droplet is increased by 31.8%, 18.6% and 25.9%, respectively.     

The effect of ambient pressure on the evaporation of a single droplet and a spray

The effect of ambient pressure on the evaporation of a droplet and a spray of n-heptane was investigated using a model for evaporation at high pressure. This model considered phase equilibrium using the fugacities of the liquid and gas phases for the behavior of a gas being real, and its importance in the calculation of the evaporation of a droplet or spray at high pressures was demonstrated. For the evaporation of a single droplet, the fact that the droplet's lifetime increased with pressure at a low ambient temperature, but decreased at high temperatures, was explained with pressure and the droplet's temperature determining phase equilibrium. In this study, it was also found that the evaporation of a spray can be explained in terms of multiplex dependencies of the atomization and evaporation of a single droplet. The evaporation of a spray was enhanced by increasing the ambient pressure and this effect was more dominant at higher ambient temperatures.     

加热板液滴蒸发的理论分析及实验研究

液滴蒸发是由气-液浓度差驱动的一种常见而复杂的扩散现象.通过实验与理论相结合对去离子水在玻璃表面和有机硅油表面的蒸发特性进行研究,测量了液滴接触角和接触直径随时间的动态演变过程.结果 发现:玻璃表面的液滴蒸发为典型的定底半径模式和混合模式;而液滴在有机硅油表面较为特殊,除了定底半径模式和混合模式还有周期性的黏滑模式.出...     

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.     

Effects of gravity and ambient pressure on liquid fuel droplet evaporation

An axisymmetric numerical model has been developed to conduct a study of single droplet evaporation over a wide range of ambient pressures both under normal and microgravity conditions. Results for droplet lifetime as a function of ambient pressure and initial droplet diameter are presented. The enhancement in the droplet evaporation rate due to natural convection is predicted. This enhancement becomes more dominant with increasing ambient pressure due to the increase in the Grashof number. The higher the ambient pressure, the closer the Grashof number remains to its initial value throughout most of the droplet lifetime because of the droplet swelling and the heat-up of the droplet interior. Results should be particularly of interest to researchers conducting experiments on droplet evaporation at elevated pressures within a normal gravity environment. The model developed is in good agreement with experimental data at low pressures. Explanations have been provided for its deviation at high pressures.     

A molecular dynamics simulation investigation of fuel droplet in evolving ambient conditions

Molecular dynamics simulations are applied to model fuel droplet surrounded by air in a spatially and temporally evolving environment. A numerical procedure is developed to include chemical reactions into molecular dynamics. The model reaction is chosen to allow investigation of the position of chemical reactions (gas phase, surface, liquid phase) and the behavior of typical products (alcohols and aldehydes). A liquid droplet at molecular scale is seen as a network of fuel molecules interacting with oxygen, nitrogen, and products of chemical fuel breakdown. A molecule is evaporating when it loosens from the network and diffuses into the air. Naturally, fuel molecules from the gas phase, oxygen and nitrogen molecules can also be adsorbed in the reverse process into the liquid phase. Thus, in the presented simulations the time and length scales of transport processes – oxygen adsorption, diffusion, and fuel evaporation are directly determined by molecular level processes and not by model constants. In addition, using ab initio calculations it is proven that the reaction barriers in liquid and gas phases are similar.     

Air-cooled micro-porous heat exchangers for thermal management of fuel cells

This paper presents 3D numerical simulation of an air-cooled metal foam heat exchanger with potential application in thermal management of fuel cell systems in general and Proton Exchange Membrane Fuel Cells, PEMFCs, in particular. It has been shown that the new design can lead to a uniform temperature distribution for the heated plate especially at higher air flow speeds. The heat transfer enhancement because of the foams leads to an increase in the pressure drop which is, interestingly, comparable to that of water-cooled PEMFCs. Other potential benefits of the application of metal foams for fuel cell thermal management are briefly discussed and estimated.     

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets is suggested and tested in Diesel engine-like conditions. The model is based on the assumption that properties of components are weak functions of the number of carbon atoms in the components (n). The components with relatively close n are replaced by the quasi-components with properties calculated as average properties of the a priori defined groups of actual components. Thus the analysis of heating and evaporation of droplets consisting of many components is replaced by the analysis of heating and evaporation of droplets consisting of relatively few quasi-components. In contrast to previously suggested approaches to modelling the heating and evaporation of droplets consisting of many components, the effects of temperature gradient and quasi-component diffusion inside droplets are taken into account. The model is applied to Diesel fuel droplets, approximated as a mixture of 21 components C_nH_2n+2 for 5 ? n ? 25, which correspond to a maximum of 20 quasi-components with average properties for n = n_j and n = n_j+1, where j varies from 5 to 24. It is pointed out that droplet surface temperatures and radii, predicted by a rigorous model taking into account the effect of all 20 quasi-components, are very close to those predicted by the model, using just five quasi-components. Errors due to the assumptions that the droplet thermal conductivity and species diffusivities are infinitely large cannot be ignored in the general case.     

A numerical investigation of evaporation characteristics of a fuel droplet suspended from a thermocouple

Numerical simulations of combined natural convection–conduction in a droplet of n-dodecane suspended from a thermocouple were carried out, taking into consideration evaporation, and the effect of thermocouple diameter on the evaporation characteristics was investigated. The calculated temperature history of the droplet is in good agreement with experimental results; both show that the rate of heating decreases with increasing thermocouple diameter. The maximum error in temperature due to the thermocouple increases linearly with increasing thermocouple diameter. Thus, in investigations involving a droplet suspended from a thermocouple, it is preferable to use a thermocouple with the smallest possible diameter.