Conditional statistics of nonreacting and reacting sprays in turbulent flows by direct numerical simulation

Conditional statistics concerning evaporation and combustion of a spray are investigated in homogeneous, isotropic, and decaying two-dimensional (2D) turbulence. Randomly distributed, polydisperse droplets of n-heptane go through single-step combustion chemistry. Attention is focused on parametric effects of initial Sauter mean radius (SMR), turbulence level and droplet velocity in both reacting and nonreacting cases. A simple linear model for the conditional evaporation rate is proposed and validated against DNS data. A conventional β-probability density function (pdf) is shown to be valid with no peak occurring on the fuel side. The amplitude mapping closure (AMC) model works well for the conditional scalar dissipation rate with evaporating and reacting sprays. Parametric study shows that initial SMR and droplet velocity are major factors affecting conditional flame structures, whereas the effect of reaction is not significant except during autoignition.     

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.     

Direct numerical simulation of diluted combustion by evaporating droplets

Diluted combustion has been studied using DNS in a three-dimensional temporally developing reacting shear-layer with the oxidizer stream laden with evaporating droplets. The gaseous phase is described in the Eulerian frame while the discrete droplet phase is treated in the Lagrangian frame, with strong two-way coupling between the two phases through mass, momentum and energy exchange. Grid-resolution-independent results have been obtained in cases without and with droplets. A comprehensive parametric study has been conducted by varying the initial Stokes number (St₀) and mass loading ratio (MLR₀). Detailed field analysis has been conducted to examine the complex nonlinear interactions among droplet dynamics, evaporation, turbulence and combustion, and so on. Effects of evaporating droplets on averaged flow and combustion quantities have also been presented. In particular, the conditional scalar dissipation rate is found to be enhanced by evaporating droplets, which suggests that they can promote micromixing and combustion under certain conditions, in addition to their roles in combustion suppression. The transport equation for the mixture fraction variance has been analyzed, with a focus on the vaporization-related source terms. Such source terms exhibit more complex local variations in the present shear-flow non-premixed flame configuration, compared with the case in the homogeneous decaying turbulence configuration of Réveillon and Vervisch (2000).     

Effects of temperature and equivalence ratio on the ignition of n-heptane fuel spray in turbulent flow

Direct numerical simulations were performed to study the autoignition process of n-heptane fuel spray in a turbulent field. For the solution of the carrier gas fluid, the Eulerian method is employed, while for the fuel droplets, the Lagrangian method is used. Droplets are initialized at random locations in a two-dimensional isotropic turbulent field. A chemistry mechanism for n-heptane with 44 species and 112 reactions was adopted to describe the chemical reactions. Three cases with the same initial global equivalence ratio (0.5) and different initial gas phase temperatures (1100, 1200, and 1300 K) were simulated. In addition, two cases with initial global equivalence ratios of 1.0 and 1.5 and initial temperature 1300 K were simulated to examine the effect of equivalence ratio. Evolution of temperature, species mass fraction, reaction rate, and the joint PDF of temperature and equivalence ratio are presented. Effects of the initial gas temperature and equivalence ratio on vaporization and ignition are discussed. A correlation was derived relating ignition delay times to temperature and equivalence ratio. It was confirmed that with the increase of initial temperature, the autoignition occurs earlier. With the increase of the initial equivalence ratio, however, autoignition occurs later due to a larger decrease in gas phase temperature caused by fuel droplet evaporation. The results obtained in this study are expected to be constructive in understanding fuel spray combustion, such as that in homogeneous charge compression ignition systems.     

Transported scalar PDF calculations of autoignition of a hydrogen jet in a heated turbulent co-flow

The joint scalar PDF method, as implemented in FLUENT, was used to simulate the autoignition of a jet of hydrogen in a turbulent co-flow of heated air. While the autoignition phenomenon is intermittent in the experiment, ensemble-averaged data on the effect of the flow on ignition length are available, which enables us to compare them with the steady state calculations.Results of sensitivity tests showed that the choice of chemical mechanism affects the calculation more than the mixing model and model constants. Further calculations for different initial conditions (i.e. temperature and velocity of the jet T _jet and U _jet and the co-flow T _air and U _air) have been done using a set of parameters selected after the sensitivity study. Scatter plots and conditional scalar profiles confirmed that the ignition is always initiated in lean mixture fractions. The ignition length was predicted with good accuracy for the case of U _jet>U _air but not so well for the case of U _jet≈U _air. For the equal velocity case, increasing the velocity resulted in delayed autoignition time (defined as the ignition length divided by the mean velocity), in agreement with the experimental trend. The results give credence to the use of the joint scalar PDF method for autoignition in non-premixed flows.     

Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Autoignition of condensed hydrocarbon fuels in non-premixed flows at elevated pressures

Experimental and computational investigation is carried out to elucidate the fundamental mechanism of autoignition of n-heptane, n-decane, and n-dodecane in non-premixed flows at elevated pressures up to 6 bar. The counterflow configuration is employed. In this configuration, an axisymmetric flow of a gaseous oxidizer stream is directed over the surface of an evaporating pool of liquid fuel. The oxidizer stream is a mixture of oxygen and nitrogen. The experiments are conducted at a fixed value of mass fraction of oxygen and at a fixed low value of strain rate. The temperature of the oxidizer stream at autoignition, T_ig, is measured as a function of pressure, p. Computations are carried out using skeletal mechanisms constructed from a detailed mechanism and critical conditions of autoignition are predicted. The experimental data and predictions show that, for all fuels tested, T_ig decreases with increasing p. At a fixed value of p, T_ig for n-dodecane is the lowest, followed by n-decane and n-heptane. This indicates that n-dodecane is the most easily ignited, followed by n-decane and n-heptane. This is in agreement with previous experimental and computational studies at 1 atm, where a similar order of reactivities for these fuels was observed at low strain rates. Flame structures at conditions before and at conditions immediately after autoignition are calculated. A noteworthy finding is that low temperature chemistry is found to play a dominant role in promoting autoignition. The influence of low temperature chemistry is found to increase with increasing pressure.     

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.     

Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor

Three-dimensional n-heptane spray flames in a swirl combustor are investigated by means of direct numerical simulation (DNS) to provide insight into realistic spray evaporation and combustion as well as relevant modeling issues. The variable-density, low-Mach number Navier–Stokes equations are solved using a fully conservative and kinetic energy conserving finite difference scheme in cylindrical coordinates. Dispersed droplets are tracked in a Lagrangian framework. Droplet evaporation is described by an equilibrium model. Gas combustion is represented using an adaptive one-step irreversible reaction. Two different cases are studied: a lean case that resembles a lean direct injection combustion, and a rich case that represents the primary combustion region of a rich-burn/quick-quench/lean-burn combustor. The results suggest that premixed combustion contribute more than 70% to the total heat release rate, although diffusion flame have volumetrically a higher contribution. The conditional mean scalar dissipation rate is shown to be strongly influenced, especially in the rich case. The conditional mean evaporation rate increases almost linearly with mixture fraction in the lean case, but shows a more complex behavior in the rich case. The probability density functions (PDF) of mixture fraction in spray combustion are shown to be quite complex. To model this behavior, the formulation of the PDF in a transformed mixture fraction space is proposed and demonstrated to predict the DNS data reasonably well.     

Laser-induced fluorescence of tracers dissolved in evaporating droplets

Laser-induced fluorescence (LIF)-based spray volume and droplet-size measurements rely on assumptions about the evaporation or accumulation of fluorescent tracers during the evaporation of the droplets. We investigate the time-dependent variation of droplet-size and LIF signal intensity of CO₂-laser-heated evaporating water droplets doped with rhodamine 6G. After an initial decrease of fluorescence intensity by 30% due to temperature-dependent diffusion of oxygen into the droplets, the LIF signal remains constant, indicating that the tracers have fully accumulated in the droplet. This evaporation-independent signal can be used as a reference for Mie-scattering-based droplet surface-area measurements that will allow the sensitive observation of spray evaporation and droplet breakup. PACS 42.62.Fi; 32.50.+d; 42.62.Cf     

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.     

Multiple mapping conditioning of turbulent jet diffusion flames

The multiple mapping conditioning (MMC) approach is applied to two non-piloted CH₄/H₂/N₂ turbulent jet diffusion flames with Reynolds numbers of Re = 15,200 and 22,800. The work presented here examines primarily the suitability of MMC to simulate CH₄/H₂ flames with varying Re numbers. The equations are solved in a prescribed Gaussian reference space with only one stochastic reference variable emulating the fluctuations of mixture fraction. The mixture fraction is considered as the only major species on which the remaining minor species are conditioned. Fluctuations around the conditional means are ignored. It is shown that the statistics of the mapped reference field are an accurate model for the statistics of the physical field for both flames. A transformation of the Gaussian reference space introduced in previous work on MMC is used to express the MMC model in the same form as CMC. The most important advantage of this transformation is that the conditionally averaged scalar dissipation term is in a closed form. The corresponding temperature and reactive species predictions are generally in good agreement with experimental data. The application to real laboratory flames and the assessment of the new conditional scalar dissipation model for the closure of the singly conditioned CMC equation is the major novelty of this paper. The results are therefore primarily examined with respect to changes of the conditionally averaged quantities in mixture fraction space.     

Simulation of the autoignition and combustion of <Emphasis Type="Italic">n</Emphasis>-heptane droplets using a detailed kinetic mechanism

The autoignition and combustion of n-heptane droplets are simulated using a detailed kinetic mechanism. A mathematical model, based on first principles, contains no adjustable parameters. The burning rate constants for the combustion of droplets are calculated over a wide range of pressures, temperature, fuel-to-oxidizer equivalence ratios of the gas-droplet suspension, and droplet diameters. The calculated and measured delay times of autoignition of droplets are compared. The calculation results agree well with the available experimental data. The detonability of gas-droplet suspensions with partial pre-evaporation of fuel is estimated.     

Influence of nitrogen in aluminum droplet combustion

The influence of nitrogen on the aluminum droplet combustion under forced convection conditions has been studied. An aerodynamic levitation technique of millimetric size liquid droplets heated with a CO₂ laser has been adopted to characterize the combustion of aluminum droplets and, in particular, to observe the surface phenomena. The determination of the burning rate and of the droplet temperature in several atmospheres (H₂O/O₂, H₂O/Ar, H₂O/N₂, and air) has shown that they depend only on the nature and concentration of the oxidizers (O₂ and H₂O); a comparison of experiments in nitrogen and in argon containing mixtures demonstrated that N₂ did not influence the gas phase combustion. However, for nitrogen containing atmospheres we observed the formation of solid aluminum nitride (AlN) at the droplet surface after a latency time depending on the nitrogen pressure. AlN first interacts with the oxide cap producing an aluminum oxynitride, then completely covers the droplet, and finally prevents combustion. The existence of a latency time varying with the nitrogen pressure suggests that the AlN formation is controlled by heterogeneous kinetics. The phenomenon of oxide cap regression during combustion was also observed in all gases, and it is attributed to a chemical decomposition process of alumina by aluminum forming gaseous Al_xO_y species. Therefore, nitrogen effects are significant at the droplet surface rather than in the gas phase, and it is suggested that N₂ is probably one of the main species causing the manifestation of unsteady processes during aluminum droplet burning.     

Influence of the initial parameters of spray water on its motion through a counter flow of high-temperature gases

The motion of spray water through a counter flow of high-temperature gases is experimentally studied on a macroscopic level using optical techniques for diagnostics of two-phase liquid-gas and vapor-liquid flows. It is found that the initial temperature, concentration of typical impurities, and dispersity of water influence the component composition of the forming gas-vapor-droplet mixture. The integral characteristics of evaporation of solitary droplets with initial sizes (conditional characteristic radii) of 3–5 mm and a spray water flow with droplets less than 0.5 mm across through a high-temperature gaseous medium are compared.     

A molecular dynamics study of fuel droplet evaporation in sub- and supercritical conditions

Evaporation processes of a fuel droplet under sub- and supercritical ambient conditions have been studied using molecular dynamics (MD) simulations. Suspended n-dodecane droplets of various initial diameters evaporating into a nitrogen environment are considered. Both ambient pressure and temperature are varied from sub- to supercritical values, crossing the critical condition of the chosen fuel. Temporal variation in the droplet diameter is obtained and the droplet lifetime is recorded. The time at which supercritical transition happens is determined by calculating the temperature and concentration distributions of the system and comparing with the critical mixing point of the n-dodecane/nitrogen binary system. The dependence of evaporation characteristics on ambient conditions and droplet size is quantified. It is found that the droplet lifetime decreases with increasing ambient pressure and/or temperature. Supercritical transition time decreases with increasing ambient pressure and temperature as well. The droplet heat-up time as well as subcritical to supercritical transition time increases linearly with the initial droplet size d₀, while the droplet lifetime increases linearly with ${\mathrm{d}}_0^2$. A regime diagram is obtained, which indicates the subcritical and supercritical regions as a function of ambient temperature and pressure as well as the initial droplet size.     

About diagnosis of submicron droplets in a gas-droplet flow

Possibilities and limitations of the optical diagnostic methods for small-size (about 1 m) droplets in the gasdroplet flows are discussed. Here we show the possibility for restoration of the functions of droplet distribution and droplet average size on the basis of measurements of ultradispersed particle parameters formed from microdroplet flows after droplet evaporation.     

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

LES based investigation of autoignition in turbulent co-flow configurations

The impact of turbulence on the autoignition of a diluted hydrogen jet in a hot co-flow of air is studied numerically. The LES combustion model used is successfully validated against experimental measurements and 3D DNS. Parametric studies are then carried out by separately varying turbulent intensity and integral length scale in the co-flow, while keeping all other boundary conditions unchanged. It is found that the impact of turbulence on the location of autoignition is non-trivial. For weak to mild turbulence, with a turbulent time scale larger than the minimum ignition delay time, autoignition is facilitated by increased turbulence. This is due to enhanced mixing between fuel and air, creating larger most reactive mixture fraction regions. On the other hand, for turbulent time scales smaller than the ignition delay time, the increased scalar dissipation rate dominates over the effect of increased most reactive mixture fraction regions, which leads to a rise in the autoignition length. Turbulence–chemistry interaction mechanisms are analysed in order to explain these observations.     

A study of ignition and combustion of liquid hydrocarbon droplets in premixed fuel/air mixtures in a rapid compression machine

The combustion of two fuels with disparate reactivity such as natural gas and diesel in internal combustion engines has been demonstrated as a means to increase efficiency, reduce fuel costs and reduce pollutant formation in comparison to traditional diesel or spark-ignited engines. However, dual fuel engines are constrained by the onset of uncontrolled fast combustion (i.e., engine knock) as well as incomplete combustion, which can result in high unburned hydrocarbon emissions. To study the fundamental combustion processes of ignition and flame propagation in dual fuel engines, a new method has been developed to inject single isolated liquid hydrocarbon droplets into premixed methane/air mixtures at elevated temperatures and pressures. An opposed-piston rapid compression machine was used in combination with a newly developed piezoelectric droplet injection system that is capable of injecting single liquid hydrocarbon droplets along the stagnation plane of the combustion chamber. A high-speed Schlieren optical system was used for imaging the combustion process in the chamber. Experiments were conducted by injecting diesel droplet of various diameters (50 µm < d_o < 400 µm), into methane/air mixtures with varying equivalence ratios (0 < ϕ < 1.2) over a range of compressed temperatures (700 K < T_c < 940 K). Multiple autoignition modes was observed in the vicinity of the liquid droplets, which were followed by transition to propagating premixed flames. A computational model was developed with CONVERGE™, which uses a 141 species dual-fuel chemical kinetic mechanism for the gas phase along with a transient, analytical droplet evaporation model to define the boundary conditions at the droplet surface. The simulations capture each of the different ignition modes in the vicinity of the injected spherical diesel droplet, along with bifurcation of the ignition event into a propagating, premixed methane/air flame and a stationary diesel/air diffusion flame.