Microgravity droplet combustion: effect of tethering fiber on burning rate and flame structure

Droplets tethering on fibers has become a well established technique for conducting droplet combustion experiments in microgravity conditions. The effects of these supporting fibers are frequently assumed to be negligible and are not considered in the experimental analysis or in numerical simulations. In this work, the effect of supporting fibers on the characteristics of microgravity droplet combustion has been investigated numerically; a priori predictions have then been compared with published experimental data. The simulations were conducted using a transient one-dimensional spherosymmetric droplet combustion model, where the effect of the supporting fiber was implicitly taken into account. The model applied staggered convective flux finite volume method combined with high-order implicit time integration. Thermal radiation was evaluated using a statistical narrow band radiation model. Chemical kinetics and thermophysical properties were represented in rigorous detail. Tether fiber diameter, droplet diameter, ambient pressure and oxygen concentration were varied over a range for n-decane droplets in the simulations. The results of the simulations were compared to previously published experiments conducted in the Japan Microgravity Center (JAMIC) 10 second drop tower and the NASA Glenn Research Center (GRC) 5.2 second drop tower. The model reproduces closely nearly all aspects of tethered n-decane droplet burning phenomena, which included droplet burning history, transient and average burning rate, and flame standoff ratio. The predictions show that the presence of the tethering fiber significantly influences the observed burning rate, standoff ratio, and extinction.     

Observation of droplet motion during flame spread on three-fuel-droplet array with a pendulum suspender

Flame spread on a fuel droplet array has been studied as a simple model of spray combustion. A three-fuel-droplet array with a pendulum suspender was employed to investigate interactions between flame spread and droplet motion in the axial direction. Initial droplet diameter was 0.8 mm, and fuel was n-heptane. A silicon carbide pendulum suspender of 15 μm in diameter and 30 mm in length was used for the third droplet. The first fixed droplet was ignited by electric spark. Behavior of the flame and the third droplet was observed using a high-speed video camera with an image intensifier. Particle tracking velocimetry (PTV) measurements were performed to explain the behavior of the third movable droplet. The dimensionless droplet span, which is the average of droplet-to-droplet distances divided by the average initial diameter of the three droplets, was varied from 2.5 to 8 for observing flame spread, and fixed at 5.5 for PTV measurements. It was observed that the third droplet moved away from the second droplet before the flame spread to the third droplet. The displacement of the third droplet is remarkable when the dimensionless droplet span is close to the limit of flame spread. This implies that the movement of the droplet decreases the dimensionless span of the flame spread limit and the flame spread speed near the flame spread limit. Results of PTV measurements suggest that the heat expansion wave, caused by ignition of the premixture which was accumulated around the second droplet, and the burned gas flow from the second droplet pushed away the third droplet; then natural convection, induced by the flames of the first and second droplets, drew the third droplet to the second droplet. The heat expansion wave and the burned gas flow of the second droplet reached nearly 12 in dimensionless span.     

A semi-analytical,multizone model of droplet combustion with varying properties

A multizone droplet burn model is developed to account for changes in the thermal and transport properties as a function of droplet radius. The formulation is semi-analytical – allowing for accurate and computationally efficient estimates of flame structure and burn rates. Zonal thermal and transport properties are computed using the Cantera software, pre-tabulated for rapid evaluation during run-time. Model predictions are compared to experimental measurements of burning n-heptane, ethanol and methanol droplets. An adaptive zone refinement algorithm is developed that minimizes the number of zones required to provide accurate estimates of burn time without excess zones. A sensitivity study of burn rate and flame stand-off with far-field oxygen concentration is conducted with comparisons to experimental data. Overall agreement to data is encouraging with errors typically less than 20% for predictions of burn rates, stand-off ratio and flame temperature for the fuels considered.     

Binary collision of a burning droplet and a non-burning droplet of xylene: Outcome regimes and flame dynamics

The binary collisions of a burning droplet and a non-burning droplet of xylene are experimentally investigated. The experimental parameters span an extensive range of Weber number and impact parameter, covering the collision outcome regimes of coalescence, reflexive separation, and stretching separation. A high-speed camera captures the temporal details of the collision process, involving flame spread, visible radiation, and flame distributions around droplets. For reflexive separation and stretching separation, the flame from the droplet spreads to the ligament, surrounding it during the interaction process, and then spreads around separated droplets and satellite droplets. Highly-interactive flames are formed in-between the droplets, with very sooty flames generated for most collisions. For the coalescence case, a swirling flame forms around the rotating coalesced droplet. For similar Weber numbers, visible flame radiation is compared for different collision regimes. The visible flame radiation changes more significantly for the reflexive and stretching separation cases than it does for the coalescence case. The change of the averaged visible flame radiation for reflexive separation and stretching separation is more than two times higher than that for coalescence. The map of three different collision regimes is plotted in the Weber number versus impact parameter domain and compared with available theoretical model predictions. Although the different outcomes of collision with the presence of flame can be well predicted by the model, using fluid properties determined by the averaged properties of the two droplets, the dynamics of the detailed processes involved in the collisions are very interesting and have strong implications on overall combustion behavior that go well beyond the mapped regimes.     

Ignition and combustion of a falling, single sodium droplet

Ignition and combustion of a single sodium droplet has been studied experimentally, by use of a falling droplet. It is found that the ignition delay time increases first gradually and then rapidly, with decreasing initial temperature and/or oxygen concentration, and reaches the limit of ignitability, because of the suppression of surface reaction in the ignition stage. It is also found that with decreasing droplet diameter, the ignition delay time first decreases gradually, because of the decrease in the droplet mass to be heated, and then increases steeply, because of the enhancement of heat loss from the droplet surface. As for the effect of the relative speed, it is found that the ignition delay time increases with increasing relative speed, because of the enhanced heat loss. Experimental comparisons with the analytical results have also been conducted to elucidate dominant parameters, and it is confirmed that a set of comprehensive parameters in the literature can be useful in correlating dominant parameters that influence the ignition delay and/or the limit of ignitability. Furthermore, the analysis has been extended to determine the critical size for the ignition and that for the minimum ignition delay time. Combustion behavior after the ignition has also been examined, and it is found that d²-law can hold for the sodium droplet combustion. In addition, it is found that the burning rate-constant without forced convection has nearly the same value as those for usual hydrocarbon droplets, while the sodium combustion in air is quite similar to that of the usual hydrocarbon fuel in an oxidizer-rich environment.     

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

The transient convective burning of n-octane droplets interacting within single-layer arrays in a hot gas flow perpendicular to the layer is studied numerically, with considerations of droplet surface regression, deceleration due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Infinite periodic arrays, semi-infinite periodic arrays with one row of droplets (linear array) or two rows of droplets, and finite arrays with nine droplets with centers in a plane are investigated. All arrays are aligned orthogonal to the free stream direction. This paper compares the behavior of semi-infinite periodic arrays and finite arrays with the behavior of previously studied infinite periodic arrays. Furthermore, it identifies the critical values of the initial Damköhler number for bifurcations in flame behavior at various initial droplet spacing for all these arrays. The initial flame shape is either an envelope flame or a wake flame as determined by the initial Damköhler number, the array configuration and the initial droplet spacing. The critical initial Damköhler number separating initial wake flames from initial envelope flames decreases with increasing interaction amongst droplets at intermediate droplet spacing (when the number of rows in the array increases or the initial droplet spacing decreases for a specific number of rows in the array). In the transient process, an initial wake flame has a tendency to develop from a wake flame to an envelope flame, with the moment of wake-to-envelope transition advanced for the increasing interaction amongst droplets at intermediate droplet spacing. For the array with nine droplets with centers in a plane, the droplets at different types of positions have different critical initial Damköhler number and different wake-to-envelope transition time for initial wake flame.     

General solvation motifs of a charged linear macroion in an aqueous droplet

ABSTRACT

We explore the solvation patterns of a charged rigid and semi-rigid linear macroion in an aqueous droplet. The solvation patterns are summarised in an empirical ‘phase diagram’ on the parameter space defined by the length of the macroion and its charge density. In the study, we employ molecular dynamics and atomistic modelling. The macroion is represented by a positively charged carbon nanotube. Linear macroion-solvent interactions in droplets are distinct from those of spherical ions because of the interplay among several factors such as the tendency of the solvent to form spherical droplets in order to minimise the surface energy, the constraint on the charge of a spherical droplet imposed by the Rayleigh limit, the solvation energy of the macroion and its length. The combination of all these factors may lead to a variety of solvent distributions along the rigid rod such as asymmetric solvation of the linear macroion, formation of spiky ‘star’-like distribution of solvent, partial wetting of the rod by a droplet. The study provides insight into the solvation of macroions in droplets with applications in electrosprayed macroions and atmospheric aerosols. We also propose a possible path of generating a sequence of nanoparticles of different shapes (spheres, multi-point stars) along a linear macromolecule by exploiting the various solvation patterns.     

Nonane droplet combustion with and without buoyant convection: Flame structure, burning rate and extinction in air and helium

The burning and extinction characteristics of isolated small nonane droplets are examined in a buoyant convective environment and in an environment with no external axial convection (as created by doing experiments at low gravity) to promote spherical droplet flames. The ambience is air and a mixture of 30%O₂/70%He to assess the influence of soot formation. The initial droplet diameter (D_o) ranges from 0.4 to 0.95 mm. Measurements are reported of the extinction diameter and time to extinction, and of the evolution of droplet diameter, flame diameter, soot shell diameter, burning rate, and broadband radiative emissions.In a buoyancy-free environment for air larger droplets burn slower than smaller droplets for the range of D_o examined, which is attributed to the influence of soot. In the presence of a buoyant flow in air, no influence of D_o is observed on the burning rate while the buoyant flames are still heavily sooting. The effect of D_o is believed to be due to a combination of dominance of the nonluminous, nonsooting, portion of the buoyant flame around the forward half of the droplet on heat transport and the secondary role of the luminous wake portion of the flame. In a non-sooting helium inert at low gravity, no effect of D_o is found on the evolution of droplet diameter.Flame extinction is observed only in the 30%O₂/70%He ambience. For all of the observations, extinction appears to occur before the disappearance of the droplet which is then followed by a period of evaporation. The extinction diameter and time to extinction increases with D_o and an empirical correlation is presented for these two variables.     

The role of cool-flame chemistry in quasi-steady combustion and extinction of n-heptane droplets

Experiments on the combustion of large n-heptane droplets, performed by the National Aeronautics and Space Administration in the International Space Station, revealed a second stage of continued quasi-steady burning, supported by low-temperature chemistry, that follows radiative extinction of the first stage of burning, which is supported by normal hot-flame chemistry. The second stage of combustion experienced diffusive extinction, after which a large vapour cloud was observed to form around the droplet. In the present work, a 770-step reduced chemical-kinetic mechanism and a new 62-step skeletal chemical-kinetic mechanism, developed as an extension of an earlier 56-step mechanism, are employed to calculate the droplet burning rates, flame structures, and extinction diameters for this cool-flame regime. The calculations are performed for quasi-steady burning with the mixture fraction as the independent variable, which is then related to the physical variables of droplet combustion. The predictions with the new mechanism, which agree well with measured autoignition times, reveal that, in decreasing order of abundance, H₂O, CO, H₂O₂, CH₂O, and C₂H₄ are the principal reaction products during the low-temperature stage and that, during this stage, there is substantial leakage of n-heptane and O₂ through the flame, and very little production of CO₂ with no soot in the mechanism. The fuel leakage has been suggested to be the source of the observed vapour cloud that forms after flame extinction. While the new skeletal chemical-kinetic mechanism facilitates understanding of the chemical kinetics and predicts ignition times well, its predicted droplet diameters at extinction are appreciably larger than observed experimentally, but predictions with the 770-step reduced chemical-kinetic mechanism are in reasonably good agreement with experiment. The computations show how the key ketohydroperoxide compounds control the diffusion-flame structure and its extinction.     

Microgravity experiments on droplet motion during flame spreading along three-fuel-droplet array

Flame spreading along a fuel droplet array at microgravity has been studied as a simple model of spray combustion. A three droplet array with a pendulum suspender was employed to investigate interactions between flame spreading and droplet motion in the array direction. Initial droplet diameter was 0.8 mm and fuel was n-heptane. A silicon carbide pendulum suspender of 15 μm in diameter and 30 mm in length was used for the third droplet. The first fixed droplet was ignited by electric spark. Behavior of the flame and the third droplet was observed using a high-speed video camera. Dimensionless span, which is the averaged droplet span divided by the averaged initial diameter of the three droplets, was varied from 2.7 to 10. Large displacement of the movable droplet was observed after group flame grew around the movable droplet. As the initial dimensionless span increased, the averaged droplet speed after the occurrence of flame spreading to the movable droplet increased steeply, taking the maximum value around 5 in initial dimensionless span, and then decreased gradually. The movable droplet advanced toward the second droplet in small spans and moved away from the second droplet in large spans. The direction of the motion changed around 4.6 in initial dimensionless span. Flame spread induction time from the second to the third droplet increased exponentially as the initial dimensionless span was increased. The induction time of flame spreading to a movable droplet was longer than that of flame spreading to a fixed droplet. From calculations of flame spreading along a 20-droplet array, it was predicted that the droplet speed nearly converged after flame spread to the sixteenth droplet. The maximum speed of the nineteenth droplet appeared around 7.5 in the initial dimensionless span.     

Microgravity experiments of single droplet combustion in oscillatory flow at elevated pressure

An experimental study for 1-butanol single droplet flames in constant and oscillatory flow fields was conducted under microgravity conditions at elevated pressure. In the constant flow experiments, flow velocities from 0 to 40 cm/s were tested. Using obtained data of d², the burning rate constants were evaluated. The burning rate constant in the quiescent condition was also calculated successfully at high pressure by the extrapolation method based on the Frössling relation. In the oscillatory flow experiments, the flow velocities were varied from 0 to 40 cm/s at the frequencies of 2–40 Hz. Results showed that the burning rate constant during the droplet lifetime varied following the quasi-steady relation at 0.1 MPa; however, in the conditions with higher frequencies at 0.4 MPa, the average burning velocity became larger than that for the constant flow case with the velocity equivalent to the maximum velocity in the oscillatory flow. Under the condition where the burning rate constant increased, it was observed that the flame did not sufficiently move back upstream, leading to enhancement of the heat transfer from the flame to the droplet surface. Therefore, the instantaneous burning rate constant increased. To investigate the mechanism of such flame behavior, the ratio of two characteristic times, τ_f/τ_D (τ_f: flow oscillation characteristic time, τ_D: diffusion characteristic time), were compared. As the flow oscillatory frequency increased, τ_f/τ_D becomes smaller. τ_f/τ_D also became smaller at high pressure. If τ_f/τ_D is small due to the small mass diffusion rate, the droplet flame could not move back to the appropriate position for the minimum velocity in steady flow, leading to an increase of the burning rate constant, especially in the case of higher frequency at high pressure.     

An analytical study of droplet combustion under microgravity: Quasi-steady transient approach

An analytical model based on an assumption of combined quasi-steady and transient behavior of the process is presented to exemplify the unsteady, sphero-symmetric single droplet combustion under microgravity. The model used in the present study includes an alternative approach of describing the droplet combustion as a process where the diffusion of fuel vapor residing inside the region between the droplet surface and the flame interface experiences quasi-steadiness while the diffusion of oxidizer inside the region between the flame interface and the ambient surrounding experiences unsteadiness. The modeling approach especially focuses on predicting; the variations of droplet and flame diameters with burning time, the effect of vaporization enthalpy on burning behavior, the average burning rates and the effect of change in ambient oxygen concentration on flame structure. The modeling results are compared with a wide range of experimental data available in the literature. It is shown that this simplified quasi-steady transient approach towards droplet combustion yields behavior similar to the classical droplet theory.     

Experimental study of the effect of helium/nitrogen concentration and initial droplet diameter on nonane droplet combustion with minimal convection

In this paper, we study the influence of inert concentration and initial droplet diameter on nonane (C₉H₂₀) droplet combustion in an environment that promotes spherical droplet flames. The oxygen concentration is fixed while the inert is varied between nitrogen and helium. A range of initial droplet diameters (D_o) are examined in each ambient gas: 0.4 mm < D_o < 0.8 mm; and an oxidizing ambiance consisting of 30% oxygen (fixed) and 70% inert (fixed), with the inert in turn composed of mixtures of nitrogen and helium in concentrations of 0, 25, 50, 75, and 100% N₂. The experiments are carried out at normal atmospheric pressure in a cold ambiance (room temperature) under low gravity to minimize the influence of convection and promote spherical droplet flames. For burning within a helium inert (0% N₂), the droplet flames are entirely blue and there is no influence of initial droplet diameter on the local burning rate (K). With increasing dilution by nitrogen, droplet flames show significant yellow luminosity indicating the presence of soot and the individual burning histories show K reducing with increasing D_o. The evolution of droplet diameter D(t) is nonlinear for a given D_o in the presence of either helium or nitrogen inerts indicating that soot formation has little to do with nonlinear burning. A correlation is presented of the data in the form where the effective burning rate, K′, and ε are concentration-dependent. Correlations for these parameters are presented in the paper.     

Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.     

The three-dimensional numerical simulation of aluminized composite solid propellant combustion

A three-dimensional numerical framework is presented that examines the burning of aluminized solid propellants. The numerical solver accounts for heat conduction in the solid, combustion in the gas phase, and coupling of these by means of a level set method. The aluminium particles are treated as heat conducting solid spheres. The aluminium particle detachment process is modelled using level sets, but once the particle becomes free from the surface, its subsequent motion in the gas phase is governed by particle dynamics. Some preliminary calculations of the three-dimensional combustion field supported by a pack with embedded aluminium particles are presented.     

The extended IEM mixing model in the framework of the composition PDF approach: applications to diesel spray combustion

A steady, two-dimensional corner flame is established when fuel and oxidizer enter the reaction zone in mutually perpendicular directions. A model problem in which the velocity fields are linear functions of spatial position is utilized to study the resulting flame. The flame structure is comprised of a diffusion flame surrounded on either side by fuel-rich and fuel-lean partially premixed laminar flames, similar to, but distinct from, triple flames. Using suitable coordinate transformations and change of variables, the governing equations in the thermodiffusive approximation are recast into a form akin to classical triple flames, with the strain rate appearing as the eigenvalue. A new exact integral representation of the solution to the mixture fraction equation is then utilized and high activation energy asymptotics are applied to solve approximately for the resulting flame shape, the imposed strain rate and, most significantly, the position of flame stabilization. This theoretically predicted flame is computed numerically, and comparisons are made between theory and computation.     

Analysis of combustion regimes and conditional statistics of autoigniting turbulent n-heptane sprays

DNS is performed for a statistically one dimensional layer of a spray region resembling diesel engine conditions. The group and collective combustion regimes are identified according to the ratio of the chemical and transport time scales for a single droplet. The statistics in group combustion are similar with those in gas phase combustion. The collective combustion regime involves interspersed rich regions with different dissipation characteristics. Reasonable agreements are shown with the scaled AMC model and the linear evaporation model in the ranges of meaningful probability. Initially the evaporation terms are dominant in the budgets of the conditional enthalpy equation. After ignition the chemical reaction term becomes dominant to be balanced by the time rate of change term. For modeling turbulent spray combustion it may not be essential to consider detailed micro structures around each droplet, unless in the droplet combustion regime.     

Experimental and numerical characterization of a turbulent spray flame

A turbulent ethanol spray flame is characterized through quantitative experiments using laser-based imaging techniques. The data set is used to validate a numerical code for the simulation of spray combustion. The spray burner has been designed to generate a stable flame without the use of a bluff body or a pilot flame facilitating numerical simulations. The experiments include spatially-resolved measurements of droplet sizes (Mie/LIF-dropsizing and PDA), droplet velocity (PDA), liquid-phase temperature (2-color LIF temperature imaging with Rhodamine B) and gas-phase temperature (multi-line NO-LIF temperature imaging). The measurements close to the nozzle exit are used to determine the initial conditions for numerical simulations. An Eulerian–Lagrangian model including spray flamelet modeling is applied to calculate the development of the spray. Good agreement with the experimental data is found. The experimental data set and the numerical results will be published on a website to allow other groups to evaluate their experimental and/or numerical data.