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.     

Transient convective burning of interactive fuel droplets in double-layer arrays

The transient convective burning of n-octane droplets interacting within double-layer arrays in a hot gas flow perpendicular to the layers is studied numerically, with considerations of droplet surface regression, deceleration and relative movement due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Each layer in the double-layer array is a periodic droplet array aligned orthogonal to the free stream direction. The droplets in different layers are arranged either in tandem or staggered. Several different flame structures are found for the double-layer arrays. The transient behaviors of the droplets in both upstream and downstream layers are studied and compared, for various initial relative stream velocity and initial transverse droplet spacing. The average surface temperature and vaporization rate for the front (or upstream) droplets and back (or downstream) droplets are influenced by the flame structure. The front droplets in a double-layer array behave similarly to the droplets in a single-layer array for the streamwise droplet spacing considered in this study. The back droplets approach the front droplets because they generally have lower drag.     

Recent advances in droplet vaporization and combustion

Recent progress on understanding the fundamental mechanisms governing droplet vaporization and combustion are reviewed. Topics include the classical d²-Law and its limitations; the major transient processes of droplet heating and fuel vapor accumulation; effects due to variable transport property assumptions; combustion of multicomponent fuels including the miscible fuel blends, immiscible emulsions, and coal-oil mixtures, finite-rate kinetics leading to ignition and extinction; and droplet interaction. Potentially promising research topics are also suggested.     

Alcohol droplet vaporization in humid air

Experimental and theoretical investigations were conducted for the vaporization of a single alcohol droplet in air with various degrees of humidity. Experimental results show that the vaporization of a volatile alcohol, such as methanol and ethanol, is accompanied by the simultaneous condensation of water vapor on the droplet surface and its subsequent diffusion into the droplet interior such that the associated condensation heat release greatly facilitates the initial gasification rate of alcohol. However, for alcohols which are less volatile, or for liquids which are not miscible with water, atmospheric moisture has practically no effect on the droplet gasification rate. Theoretical results substantiate the above observation.     

Fuel droplet vaporization and spray combustion theory

A critical review is presented of modern theoretical developments on problems of droplet vaporization in a high-temperature environment and of spray combustion. Emphasis is placed upon analytical and computational contributions to the theory with some mention of empirical evidence. Four areas of basic phenomena are discussed in some detail: (i) droplet slip and internal circulation, (ii) transient heating of the droplets, (iii) multicomponent fuel vaporization, and (iv) combustion and vaporization of droplet arrays, groups, and sprays. Various relationships amongst these phenomena are analyzed as well. Several other problem areas are given brief mention. Future directions are suggested.     

A generalized analysis for liquid-fuel vaporization and burning

A generalized method is presented for vaporization and combustion of multiple-droplet arrays, liquid films, pools, and streams. Conditions are explained for the existence of a mass flux potential function that is independent of fuel type and scalar boundary conditions and satisfies the three-dimensional Laplace’s equation. Gas-phase properties, composition, and flame location are functions only of the potential function, specified scalar boundary conditions, and fuel type. Variable properties are considered. Flame stand-off distances for liquid interfaces near wet-bulb temperatures are predicted more accurately with variable properties. Flame location and transport properties are found for decane, heptane, and methanol fuels, with different ambient conditions. The analysis also applies to vaporization without combustion and to combustion with transient liquid-phase heating.     

Oscillatory vaporization and acoustic response of droplet at high pressure

Open-loop dynamic responses of vaporizing droplet to high-frequency pressure waves are theoretically-numerically investigated. Conservation equations for liquid and gas phases are solved separately for spherically symmetric vaporization and transports, and flow parameters are matched at liquid–vapor interfacial boundary. The pressure-coupled response of the droplet vaporization is commanded by the coupling between the acoustic and thermal processes occurring in an immediate vicinity of the interfacial boundary. The vaporization response strongly depends on the ambient pressure, and the acoustic instabilities are expected at higher pressures and lower frequencies.     

High pressure droplet vaporization; effects of liquid-phase gas solubility

Numerical results are presented for an n-hexane droplet initially at 300 K evaporating into nitrogen, for ambient pressures, P_x, 1–100 atm and ambient temperatures, T_x, 500–1500 K. At low P_x (<30 atm), droplet lifetimes predicted with or without liquid-phase gas solubility are very close. At high P_x, the model neglecting solubility either underestimates the droplet lifetime (low T_x) or breaks down by failing to predict vapor-liquid equilibria (high T_x). At high enough P_x, heat-up is extremely important throughout the entire droplet lifetime. In a fuel rich environment, relatively low T_x, and high T_x, substantial condensation occurs before the onset of vaporization.     

Forced convection droplet evaporation with finite vaporization kinetics and liquid heat transfer

Stagnation point calculations, including the effects of liquid phase heat transfer and finite rate evaporation kinetics, are presented for the case of a high Reynolds number flow over a vaporizing droplet. A correlation is developed to compute the entire droplet vaporization rate from the stagnation point results. Numerical emphasis is placed on high temperature, rapid vaporization processes such as occur in flight vehicle engines, and sufficient calculations are presented to allow estimates for any given case to be made.     

Influence of physical mechanisms on soot formation and destruction in droplet burning

The dynamic parameters influencing soot formation and destruction in droplet burning are studied through time-resolved photography and sampling. Results show that, except for excessively sooty situations, the instantaneous amount of soot present follows the same trend as the instantaneous flame size, that near-complete oxidation of soot can be achieved by confining it within the regressing, closed flame, and that weak convection promotes soot oxidation while early extinction can lead to substantial soot emission. The effects of blending a sooty component with a nonsooty component of different relative volatility have also been investigated.     

Sooting characteristics of isolated droplet burning in heated ambients under microgravity

This paper presents an investigation into the sooting characteristics of isolated droplets (for fuel n-decane) burning in heated ambients in microgravity. A backlit video view of the droplet was taken to determine the soot shell size and to judge the transient soot generation according to qualitative amount of soot. The independent experiment variables were the ambient temperature and initial droplet diameter. Soot generation was higher for initially larger droplets when compared at the same burning time normalized with the initial droplet diameter squared (called normalized burning time). At the same absolute burning time there existed an obvious initial transient period after ignition in which the stated relationship was not satisfied. This transient time increased with increasing the ambient temperature. There was a peak in the soot generation at about 1000 K throughout the lifetime of the droplet. The soot shell size was generally larger for an initially bigger droplet at the same instantaneous droplet diameter or normalized burning time. At the same absolute burning time, however, an initially smaller droplet exhibited larger relative soot shell sizes (the soot shell size normalized with the initial droplet diameter). The soot shell size increased monotonically with increasing ambient temperature. This is due to the increase in the Stefan flow drag with the larger burning rate at the higher temperature. The consequent result is that the soot shell sizes are much larger for droplets burning in heated ambients than for droplets burning in room-temperature ambients.     

Flame propagation through an air-fuel spray mixture with transient droplet vaporization

Flame initiation and propagation through an air/fuel vapor/fuel drop system is numerically modeled in a cylindrical one-dimensional closed combustor. An unsteady formulation of the flow problem eliminates the cold-boundary difficulty and gas-phase ignition problem. A velocity lag between the gas and the liquid phase is allowed and unsteady heat transfer to the droplets is taken into account. The surface temperature of the droplet is evaluated by using an unsteady spherically symmetric formulation of the droplet heat conduction problem with no internal motion and with a time-varying heat flux specified at the surface as a boundary condition. Results have been obtained for two commercially important fuels, namely, n-octane and n-decane. The activation energy and the preexponential factor in the Arrhenius-type expression for chemical rate, along with initial temperature, initial droplet size, stoichiometric ratio, and diffusivity are parametrically varied and flame speed and flame temperatures are observed. Flame speed is seen to increase with increasing preexponential factor, decreasing activation energy, increasing ambient temperature, decreasing initial droplet radii, and increasing diffusivities. It is also observed that unlike premixed combustion, heterogeneous combustion gives rise to local variations of equivalence in the axial direction. This phenomenon could give rise to a secondary diffusion flame in the wake of a propagating flame and produce local variations in the flame temperature.     

Multicomponent fuel droplet vaporization and combustion using spectral theory for a continuous mixture

The Quasi-Steady vaporization and combustion of a multicomponent, spherically symmetrical droplet composed of a thermodynamically ideal mixture of mutually soluble fuels is analyzed theoretically by approximating the discrete mixture by a Continuous Mixture (CM). The CM is described locally by a general Probability Density Function (PDF), which is approximated by a truncated spectral expansion with a number of ‘components’ much smaller than the number of chemical components in the original mixture. Two methods (Galerkin and Orthogonal Collocation OC) are proposed, discussed, and OC is used, to solve the evolution of the spectral governing equations. The present paper generalizes the methods employed in most earlier Continuous Mixture Theory (CMT) studies, in which the PDF describing the mixture is assumed to have a predetermined mathematical form. These methods are illustrated for the practical cases of vaporization and combustion of individual droplets of gasoline, diesel or aviation fuel JP4. The results show that in most cases our spectral OC provides useful results with as few as six spectral pseudocomponents.     

A Burke-Schumann analysis of dual-flame structure supported by a burning droplet

Droplet combustion experiments carried out onboard the International Space Station, using pure fuels and fuel mixtures, have shown that quasi-steady burning can be sustained by a non-traditional flame configuration, namely a “cool flame” burning in the “partial-burning” regime where both fuel and oxygen leak through the low-temperature-controlled flame-sheet. Recent experiments involving large, bi-component fuel (n-decane and hexanol, 50/50 by volume) droplets at elevated pressures show that the visible, hot flame becomes extremely weak while the burning rate remains relatively high, suggesting the possible simultaneous presence of “cool” and “hot” flames of roughly equal importance. The radiant output from these bi-component droplets is relatively high and cannot be accounted for only by the presence of a visible hot flame. In this analysis we explore the theoretical possibility of a dual-flame structure, where one flame lies close to the droplet surface, called the “cool flame”, and the other farther away from the droplet surface, termed the “hot flame”. A Burke-Schumann analysis of this dual structure seems to indicate that such flame structures are possible over a limited range of initial conditions. These theoretical results can be compared against available experimental data for pure and bi-component fuel droplet combustion to test how realistic the model may be.     

Solar energy harvesting and a water droplet cleaning of micropost arrays surfaces

Solar energy harvesting in dusty environments initiates many challenges for sustainable operation of photovoltaic panels. Environmental dust reduces photovoltaic device performance and requires regular cleaning of active surfaces. Self-cleaning of surfaces by water droplets offers advantages in terms of reduced cost and sustainable operation. The present study investigates dust removal from hydrophobic and optically transparent micropost arrays surfaces in relation to solar energy applications. The micropost arrays are replicated using polydimethylsiloxane (PDMS) casting on textured silicon wafers. The replicated micropost arrays result in hydrophobic surface with contact angle of about 147.6° ± 5° and the hysteresis of 16° ± 2°. In relation to self-cleaning, water droplet behavior on the inclined replicated micropost arrays is simulated and droplet movement is examined experimentally. The optical transmittance of micropost arrays is tested in outdoor dusty environments. It is found that droplet slides on the inclined micropost surface and expanding droplet size enhances the sliding velocity. Alkaline dust compounds dissolve in droplet while increasing pH from 4.35 to 7.94 and surface tension from 0.072 to 0.120 N/m. This alters droplet pinning and lowers the sliding velocity from 0.2 to 0.15 m/s. Optical transmittance of the samples was tested in outdoor dusty environments improve considerably by sliding water droplet cleaning on daily bases (transmittance reduces only 3% or less as reference to surface being kept indoor environments). Hence, introducing micropost arrays on photovoltaic panel protective cover surface can provide self-cleaning effect, via droplet rolling, while slightly reducing optical transmittance of cover glass (approximately 2.5%-3%) in outdoor environments.     

Clustering effects on liquid oxygen (LOX) droplet vaporization in hydrogen environments at subcritical and supercritical pressures

A droplet-in-bubble approach has been incorporated into a previously developed high-pressure droplet vaporization model to study the clustering effects on a liquid oxygen (LOX) droplet evaporating in hydrogen environments under both sub- and supercritical conditions. A broad range of ambient pressures and temperatures are considered. Results indicate that pressure exerts strong influence on droplet vaporization behaviors in a dense cluster environment. Increasing ambient pressure reduces droplet interactions and significantly decreases the droplet vaporization time. The effect of ambient temperature on droplet interactions is found to be very weak. The present study is intended to illuminate the underlying physics of droplet clustering phenomena in combustion devices.     

Vaporization of a liquid by direct contact in another immiscible liquid Part I: vaporization of a single droplet Part II: vaporization of rising multidroplets

The present work is an experimental and theoretical study of the vaporization by direct contact of refrigerant R113 and n-pentane dispersed into a column of water flowing countercurrently. The vaporization of a single droplet in a stagnant liquid medium, and the evaporation of a multidroplet flowing system are studied. A formalism has been developed to determine the effective exchange surface for the bubble-droplet during its rise in an immiscible liquid. The numerical results are in good agreement with the experiments. The mechanical equilibrium of a bubble-droplet was studied when considering only the surface tension forces. The results obtained in the precedent analysis about the liquid-liquid area estimation were explained. Experiments were performed to investigate the influence of the different parameters on the behaviour of the direct contact vapour generator. A dimensional analysis based on characteristic transfer times was done. From this point of view correlations were established for determining the volumetric heat transfer coefficient and the exchange efficiency. For a multidroplet flowing system an analytical model was proposed giving the evolution of the void fraction and the temperature of each fluid along the exchange column. Experimental and numerical results were compared.     

Simulation of transient convective burning of an n-octane droplet using a four-step reduced mechanism

The transient burning of an n-octane fuel droplet in a hot gas stream is numerically studied using a four-step reduced mechanism, with considerations of droplet surface 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. Two different types of the four-step mechanism are examined and found almost identical. The four-step mechanism has earlier instant of the wake-to-envelope transition than the one-step mechanism at low ambient temperature, but this difference between the two mechanisms diminishes when the ambient temperature is increased. The four-step mechanism has smaller mass burning rate for a wake flame but greater mass burning rate for an envelope flame than the one-step mechanism. The two mechanisms have small differences in the critical initial Damkohler number. Lower ambient temperature yields later wake-to-envelope transition and smaller mass burning rate. Higher ambient pressure has greater overall mass burning rate because of greater gas density and thus greater concentrations of reactants for a major part of the lifetime. Greater ambient mass fraction of oxygen yields faster oxidation kinetics and greater Damkohler number. As the ambient mass fraction of oxygen increases, the instant of wake-to-envelope transition advances for an initial wake flame, and finally the initial flame becomes an envelope flame when the ambient mass fraction of oxygen exceeds some critical value. A correlation is developed for the critical initial Damkohler number in terms of the ambient temperature, ambient pressure, and ambient mass fraction of oxygen.     

Importance of dissociation equilibrium and variable transport properties on estimation of flame temperature and droplet burning rate

By using droplet combustion in oxidizer-rich environments as a model problem, the present investigation demonstrates both experimentally and theoretically that variable transport properties and flame dissociation are important factors which influence the bulk combustion charateristics, such as the fuel consumption rate and the flame temperature and location. A simplified, internally consistent methodology is proposed for the evaluation of these properties by analyzing the transport aspects of the problem and separately determining the characteristics of the flame in dissociation equilibrium through adiabatic flame temperature calculation, with allowance for the falsification of the oxidizer concentration due to diffusional stratification.