On the validity of quasi-steady assumption in transient droplet combustion

A study on droplet combustion in unsteady force convection at high pressure under microgravity conditions was performed. The hysteresis loop of the instantaneous burning rate of a single suspended 1-butanol droplet was observed for the first time. Results showed that the classical quasi-steady film model cannot describe droplet combustion in an unsteady flow. Based on precise experimental observation and by utilizing dimensional analysis of the energy conservation equation, a new criterion is herein proposed for the condition in which the quasi-steady assumption is valid and for that in which it is not. The dimensional analysis led to formulation of a new time scale. Based on the time scale which we call the response-time-scale, a new Damköhler number, termed the response-Damköhler-number was formulated. Using the definition of the new time scale and that of the Damköhler number, unsteady behaviors of droplet combustion under conditions of various pressures and varying force convection were examined. Finally, using the response-Damköhler-number and the deviation factor between the actual instantaneous burning rate and the burning rate predicted by the quasi-steady theory, droplet combustion was categorized into four specific regimes. This study is also of fundamental interest in terms of the effects of turbulence on droplet evaporation and combustion in spray flames.     

Simplified model for droplet combustion in a slow convective flow

An idealized model for droplet vaporization or combustion in the Burke-Schumann reaction-sheet approximation is analyzed in terms of a Peclet number based on the Stefan velocity, taken to be of order unity, for Lewis numbers of unity and for small values of a parameter ?, defined as the ratio of the convective velocity far from the droplet to the Stefan velocity at its surface. Asymptotic solutions for the velocity, pressure, and mixture-fraction fields are obtained through second order in ?. The results are employed to calculate the effects of convection on the burning rate and on the flame shape. The prediction that the burning-rate constant increases linearly with ? for small values of ? is shown to be consistent with available experimental data. It is demonstrated that reasonable values of diffusivities provide approximate agreement of predicted burning rates and flame shapes with results of measurements.     

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.     

Analysis of quasi-steady combustion of Jatropha bio-diesel

Quasi-steady gas-phase combustion of Jatropha bio-diesel in a mixed convective air environment is studied both experimentally and numerically. Porous sphere experiments have been conducted to measure the mass burning rates and observe the flame shapes of spherical particles fed with bio-diesel. A numerical model has been developed to simulate the experiments. The Jatropha bio-diesel has been considered as a single component fuel (C₁₈H₃₄O₂). Transient governing equations in the gas-phase alone are solved through the finite volume approach employing non-orthogonal control volumes in a semi-collocated mesh. Thermo-physical properties are evaluated based on the local temperature and the species concentrations. A single step global reaction with five species (C₁₈H₃₄O₂, O₂, N₂, CO₂ and H₂O) is employed to model the finite rate kinetics. Results have been obtained for a range of mixed convective flow conditions. Comparisons of the results with those of diesel combustion have been made in few cases. It is observed that the burning rate of bio-diesel is less by about 11% than those for diesel for the same air velocity and sphere size.     

Tethered methanol droplet combustion in carbon-dioxide enriched environment under microgravity conditions

Tethered methanol droplet combustion in carbon dioxide enriched environment is simulated using a transient one-dimensional spherosymmetric droplet combustion model that includes the effects of tethering. A priori numerical predictions are compared against recent experimental data. The numerical predictions compare favorably with the experimental results and show significant effects of tethering on the experimental observations. The presence of a relatively large quartz fiber tether increases the burning rate significantly and hence decreases the extinction diameter. The simulations further show that the extinction diameter depends on both the initial droplet diameter and the ambient concentration of carbon dioxide. Increasing the droplet diameter and ambient carbon dioxide concentration both of them lead to a decrease in the burning rate and increase in the extinction diameter. The influence of ambient carbon dioxide concentration on extinction shows a sharp transition in extinction for larger size droplets (d_o > 1.5 mm) due to a change in the mode of extinction from diffusive to radiative control. In addition predictions from the numerical model is compared against a recently developed simplified theoretical model for predicting extinction diameter for methanol droplets, where the presence and heat transfer contribution of the tether is not taken into account implicitly. The numerical results suggest some limitation in the theoretical modeling assumptions for favorable comparisons with the experimental data.     

Numerical study of Marangoni convection during transient evaporation of two-component droplet under forced convective environment

Numerical simulations of the evaporation of stationary, spherical, two-component liquid droplets in a laminar, atmospheric pressure, forced convective hot-air environment are presented. The transient two-phase numerical model includes multi-component diffusion, a comprehensive method to deal with the interface including the surface tension effects and variation of thermo-physical properties as a function of temperature and species concentration in both liquid- and vapor-phases. The model has been validated using the experimental data available in literature for suspended heptane–decane blended droplets evaporating under a forced convective air environment. The validated model is used to study the vaporization characteristics of heptane–decane droplets under different convective conditions. For an initial composition having 75% by volume of more volatile fuel component, the evaporation transients are presented in terms of variations in interface quantities. Flow, species and temperature fields are presented at several time instants to show the relative strengths of forced convection and Marangoni convection. Results show that at low initial Reynolds numbers, the solutal Marangoni effects induce a flow-field within the liquid droplet, which opposes the flow of the external convective field. The strength of this liquid-phase flow field increases with the consumption of the more volatile fuel component.     

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.     

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.     

Current status of droplet and liquid combustion

The present understanding of spray combustion in rocket engine, gas turbine, Diesel engine and industrial furnace applications is reviewed. In some cases, spray combustion can be modeled by ignoring the details of spray evaporation and treating the system as a gaseous diffusion flame; however, in many circumstances, this simplification is not adequate and turbulent two-phase flow must be considered. The behavior of individual droplets is a necessary component of two-phase models and recent work on transient droplet evaporation, ignition and combustion is considered, along with a discussion of important simplifying assumptions involved with modeling these processes. Methods of modeling spray evaporation and combustion processes are also discussed including: one-dimensional models for rocket engine and prevaporized combustion systems, lumped zone models (utilizing well-stirred reactor and plug flow regions) for gas turbine and furnace systems, locally homogeneous turbulent models, and two-phase models. The review highlights the need for improved injector characterization methods, more information of droplet transport characteristics in turbulent flow and continued development of more complete two-phase turbulent models.     

Advances in droplet array combustion theory and modeling

A review of research on the subject of the vaporization and burning of fuel droplets configured in a prescribed array is presented, including both classical works and research over the past decade or two. Droplet arrays and groups and the relation to sprays are discussed. The classical works are reviewed. Recent research on transient burning and vaporization of finite arrays with Stefan convection but without forced convection is presented, including extensions to non-unitary Lewis number and multi-component, liquid fuels. Recent results on transient, convective burning of droplets in arrays are also examined. In particular, transient convective burning of infinite (single-layer periodic and double-layer periodic) and finite droplet arrays are discussed; attention is given to the effects of droplet deceleration due to aerodynamic drag, diameter decrease due to vaporization, internal liquid circulation, and arrays with moving droplets in tandem and staggered configurations. Flame structure is examined as a function of spacing between neighboring droplets and Damköhler number: individual droplet flames versus group flames and wake flames versus envelope flames. Based on existing knowledge of laminar droplet array and spray combustion theory, experimental evidence, and turbulent studies for non-vaporizing and non-reacting two-phase flows, comments are made on the needs and implications for the study of turbulent spray and array combustion.     

Phenomenology of electrostatically charged droplet combustion in normal gravity

Experimental findings are provided on the effect of electrostatically charging a fuel on single-burning droplet combustion in normal gravity. It was established that significant modification of the flame morphology and the droplet burning time could be achieved, solely by the droplet charge, without the application of external electric fields. Negative charging of the droplets of mixtures of isooctane with either ethanol or a commercially available anti-static additive generated intense motion of the flame and abbreviated the droplet burning time by as much as 40% for certain blend compositions. Positive charging of the droplets generated almost spherical flames, because electrostatic attraction toward the droplets countered the effect of buoyancy. By comparing combustion of droplets of the same conductivity but different compositions, coupling of electrostatics with combustion chemistry was established.     

Development of a zero-dimensional Diesel combustion model. Part 1: Analysis of the quasi-steady diffusion combustion phase

The aim of this work is to identify and quantify the influence of injection parameters and running conditions on Diesel combustion. This theoretical–experimental analysis is the basis for the development of a zero-dimensional Diesel combustion model. The objective of this first part is to analyze the physical variables and processes that control the central phase of the quasi-steady Diesel diffusion combustion. For that purpose, a parameter as the apparent combustion time (ACT) characteristic of a diffusion combustion process has been used. This parameter allows to obtain explicit relations between, on the one hand, the injection rate law and in-cylinder conditions (air density, oxygen concentration…), and on the other hand, the rate of heat release. Results show a good correlation between the ACT and the instantaneous values of in-cylinder gas density, injection velocity, oxygen concentration and the nozzle diameter.     

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.     

Acoustic excitation of droplet combustion in microgravity and normal gravity

This experimental study focused on methanol droplet combustion characteristics during exposure to external acoustical perturbations in both normal gravity and microgravity. Emphasis was placed on examination of excitation conditions in which the droplet was situated (1) at or near a velocity antinode (pressure node), where the droplet experienced the greatest effects of velocity perturbations, or (2) at a velocity node (pressure antinode), where the droplet was exposed to minimal velocity fluctuations. Acoustic excitation had a significantly greater influence on droplet-burning rates and flame structures in microgravity than in normal gravity. In normal gravity, acoustic excitation of droplets situated near a pressure node produced only very moderate increases in burning rate (about 11–15% higher than for nonacoustically excited, burning droplets) and produced no significant change in burning rate near a pressure antinode. In microgravity, for the same range in sound pressure level, droplet burning rates increased by over 75 and 200% for droplets situated at or near pressure antinode and pressure node locations, respectively. Observed flame deformation for droplets situated near pressure nodes or antinodes were generally consistent with the notion of acoustic radiation forces arising in connection with acoustic streaming, yet both velocity and pressure perturbations were seen to affect flame behavior, even when the droplet was situated precisely at or extremely close to node or antinode locations. Displacements of the droplet with respect to node or antinode locations were observed to have a measureable effect on droplet burning rates, yet acoustic accelerations associated with such displacements, as an analogy to gravitational acceleration, did not completely explain the significant increases in burning rate resulting from the excitation.     

Isolated n-heptane droplet combustion in microgravity: “Cool Flames” – Two-stage combustion

Recent experimentally observed two stage combustion of n-heptane droplets in microgravity is numerically studied. The simulations are conducted with detailed chemistry and transport in order to obtain insight into the features controlling the low temperature second stage burn. Predictions show that the second stage combustion occurs as a result of chemical kinetics associated with classical premixed “Cool Flame” phenomena. In contrast to the kinetic interactions responsible for premixed cool flame properties, those important to cool flame droplet burning are characteristically associated with the temperature range between the turnover temperature and the hot ignition. Initiation of and continuing second stage combustion involves a dynamic balance of heat generation from diffusively controlled chemical reaction and heat loss from radiation and diffusion. Within the noted temperature range, increasing reaction temperature leads to decreased chemical reaction rate and vice versa. As a result, changes of heat loss rate are dynamically balanced by heat release from chemical reaction rate as the droplet continues to burn and regress in size. At reaction temperatures below the turnover, heat loss over takes the heat release rate and extinction occurs. Should heat release exceed heat loss as the temperature increases to that for hot ignition, initiation of a high temperature burning phase may be possible. Parametric study on factors leading to initiation of the second stage burning phenomena are studied. Results show that both carbon dioxide and helium diluents can promote initiation of low temperature burning at smaller initial drop diameters than found with nitrogen as diluent. Small amounts of carbon dioxide and helium in the ambient is sufficient to activate the phenomena. The chemical kinetics dictating the second stage combustion and extinction process is also discussed.     

An experimental investigation of sootshell formation in microgravity droplet combustion

Spherically symmetric droplet combustion experiments were performed at the NASA Glenn Research Center (GRC) 2.2 second drop tower in Cleveland, OH in an effort to better understand the mechanism leading to sootshell formation. Rapid insertion of a blunt plunger was used to remove the symmetric sootshell that formed during the period of quasi-steady burning. This allowed for the observation of sootshell re-formation. Soot particles were formed near the flame front and migrated towards the droplet to ultimately reside at the sootshell location. These experiments helped to bring about a better understanding of soot transport in microgravity droplet combustion.     

Gas-phase entropy generation during transient methanol droplet combustion

A numerical model was used to investigate gas-phase entropy generation during transient methanol droplet combustion in a low-pressure, zero-gravity, air environment.A comprehensive formulation for the entropy generation in a multi-component reacting flow is derived. Stationary methanol droplet combustion in a low ambient temperature (300 K) and a nearly quiescent atmosphere was studied and the effect of surface tension on entropy generation is discussed. Results show that the average entropy generation rate over the droplet lifetime is higher for the case that neglects surface tension. Entropy generation during the combustion of methanol droplets moving in a high-temperature environment (1200 K), as seen in a typical spray combustion system, is also presented. Entropy generation due to chemical reaction increases and entropy generation due to heat and mass transfer decreases with an increase in initial Reynolds number over the range of initial Reynolds numbers (1–100) considered. Contributions due to heat transfer and chemical reaction to the total entropy generation are greater than the contribution due to mass transfer. Entropy generation due to coupling between heat and mass transfer is negligible. For moving droplets, the lifetime averaged entropy generation rate presents a minimum value at an initial Reynolds number of approximately 55.     

Surface tension effects during low-Reynolds-number methanol droplet combustion

A numerical investigation of methanol droplet combustion in a zero-gravity, low-pressure, and low-temperature environment is presented. Simulations have been carried out using a predictive, transient, and axisymmetric model, which includes droplet heating, liquid-phase circulation, and water absorption. A low initial Reynolds number (Re₀=0.01) is used to impose a weak gas-phase convective flow, introducing a deviation from spherical symmetry. The resulting weak liquid-phase circulation is greatly enhanced due to surface tension effects, which create a complex, time-varying, multicellular flow pattern within the liquid droplet. The complex flow pattern, which results in nearly perfect mixing, causes increased water absorption within the droplet, leading to larger extinction diameters. It is shown that, for combustion of a 0.43-mm droplet in a nearly quiescent environment (Re₀=0.01) composed of dry air, the extinction diameter is 0.11 mm when surface tension effects are included, and 0.054 mm when surface tension effects are neglected. Experimental work available in the literature for a 0.43-mm droplet reported extinction diameters in the range of 0.16 to 0.19 mm. Results for combustion in a nearly quiescent environment (Re₀=0.01) with varying initial droplet diameters (0.16 to 1.72 mm) show that including the effect of surface tension results in approximately linear variation of the extinction diameter with the initial droplet diameter, which is in agreement with theoretical predictions and experimental measurements. In addition, surface tension effects are shown to be important even at initial Reynolds numbers as high as 5.