Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.     

Investigation of interaction between methanol fed tandem porous spheres burning in a mixed convective environment

Flame interaction during the burning of two porous spheres in tandem arrangement fed with methanol and subjected to a mixed convective environment, has been studied experimentally and numerically. Porous sphere technique is employed for experimentally simulating the burning characteristics of methanol transpired spheres of different sizes, separated by fixed distances. The mass burning rates from both the spheres and visible flame stand-off distances from the sphere surfaces have been measured in the experiments. In the numerical simulations, transient, axisymmetric, mass, momentum, species and energy conservation equations are solved using a finite volume technique based on non-orthogonal semi-collocated grids. Features of the numerical model include finite rate chemistry and temperature and mixture composition dependent thermo-physical properties. Burning of tandem porous spheres in an air stream flowing vertically upwards, at atmospheric pressure has been simulated for different sphere sizes, separation distances and free stream velocities. The numerical predictions have been compared with experimental results. Results reveal that when two spheres burn one over the other, the transition from envelope to wake flame is delayed when compared with that of an isolated sphere. For two spheres of same diameter burning one over the other, depending on the separation distance, flame blows-off after the occurrence of transition from envelope to wake flame in the bottom sphere. For the case of larger sphere at the top, either the flame stabilises in the recirculation zone formed in between the spheres or the flame from the smaller sphere lifts off and stabilises near the front portion of the larger sphere, depending on the separation distance. At higher separation distances, around four times the diameter of the sphere, both the spheres burn independently. The burning rate undergoes complex variations with air stream velocity depending on the sphere sizes and separation distances.     

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.     

Numerical modelling of ion transport in flames

This paper presents a modelling framework to compute the diffusivity and mobility of ions in flames. The (n, 6, 4) interaction potential is adopted to model collisions between neutral and charged species. All required parameters in the potential are related to the polarizability of the species pair via semi-empirical formulas, which are derived using the most recently published data or best estimates. The resulting framework permits computation of the transport coefficients of any ion found in a hydrocarbon flame. The accuracy of the proposed method is evaluated by comparing its predictions with experimental data on the mobility of selected ions in single-component neutral gases. Based on this analysis, the value of a model constant available in the literature is modified in order to improve the model's predictions. The newly determined ion transport coefficients are used as part of a previously developed numerical approach to compute the distribution of charged species in a freely propagating premixed lean CH₄/O₂ flame. Since a significant scatter of polarizability data exists in the literature, the effects of changes in polarizability on ion transport properties and the spatial distribution of ions in flames are explored. Our analysis shows that changes in polarizability propagate with decreasing effect from binary transport coefficients to species number densities. We conclude that the chosen polarizability value has a limited effect on the ion distribution in freely propagating flames. We expect that the modelling framework proposed here will benefit future efforts in modelling the effect of external voltages on flames. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/13647830.2015.1090018.     

Spray flame dynamics with oscillating flow and droplet grouping

The co-flow laminar spray diffusion flame in an oscillating flow field is investigated. Mild slip is permitted between the droplets and their host surroundings and droplet grouping resulting from the host flow oscillations is accounted for. The spray is modelled using the sectional approach and a perturbation analysis using a small sectional Stokes number is utilised for solving the liquid phase governing equations. The effect of droplet grouping is described through a specially constructed model for the vaporisation Damkohler number. The large chemical Damkohler number assumption is adopted and a formal analytical solution is developed for Schwab-Zeldovitch parameters through which the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results based on the solutions demonstrate how the phenomenon of droplet grouping can lead to the existence of multiple flame sheets as a result of the dynamic change in the type of the main homogeneous flame from under- to over-ventilated as the flow field oscillates. Concomitant fluctuating thermal fields are also shown to be present indicating a potential impact on undesirable pollutants production.     

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.     

Combustion characteristics and detailed simulations of surrogates for a Tier II gasoline certification fuel

An experimental and numerical study of combustion of a gasoline certification fuel (‘indolene’), and four (S4) and five (S5) component surrogates for it, is reported for the configurations of an isolated droplet burning with near spherical symmetry in the standard atmosphere, and a single cylinder engine designed for advanced compression ignition of pre-vaporized fuel. The intent was to compare performance of the surrogate for these different combustion configurations and to assess the broader applicability of the kinetic mechanism and property database for the simulations. A kinetic mechanism comprised of 297 species and 16,797 reactions was used in the simulations that included soot formation and evolution, and accounted for unsteady transport, liquid diffusion inside the droplet, radiative heat transfer, and variable properties. The droplet data showed a clear preference for the S5 surrogate in terms of burning rate. The simulations showed generally very good agreement with measured droplet, flame, and soot shell diameters. Measurements of combustion timing, in-cylinder pressure, and mass-averaged gas temperature were also well predicted with a slight preference for the S5 surrogate. Preferential vaporization was not evidenced from the evolution of droplet diameter but was clearly revealed in simulations of the evolution of mixture fractions inside the droplets. The influence of initial droplet diameter (D_o) on droplet burning was strong, with S5 burning rates decreasing with increasing D_o due to increasing radiation losses from the flame. Flame extinction was predicted for D_o =3.0 mm as a radiative loss mechanism but not predicted for smaller D_o for the conditions of the simulations.     

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.     

Turbulent scalar fluxes in H2-air premixed flames at low and high Karlovitz numbers

The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion have been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen-air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multispecies system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two-dimensional anisotropy due to strong heat release whereas a three-dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multispecies systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sub-grid scalar flux closures, a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray–Moss–Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of large eddy simulations.     

The diminishment of specific heat and surface tension of coolant droplet in a dropwise evaporation process: A novel methodology to enhance the heat transfer rate

The rate of dropwise evaporation is significantly altered by additives, such as benzene, n-hexane and acetone in water. These additives change some of the thermal and physical properties of the coolants, which have significant impact on various parameters that controls the droplet evaporative cooling, such as sensible, heat extraction period, droplet momentum and contact area. The open literature does not reveal the effects of the aforesaid additives on the dropwise evaporation. Therefore, in the current work, an attempt has been made to investigate the effects of above-mentioned additives on dropwise evaporation rate and reveal the mechanism involved. The droplet evaporative cooling experiments are conducted on a 2 mm thick AISI 304 steel plate (10 × 10 mm). The result shows that with increment in benzene and n-hexane concentration in water, the evaporation time significantly reduces. This is attributed to the decreasing surface tension, specific heat and contact angle. However, in case of acetone, the reduction in evaporation time is achieved only up to a concentration of 300 ppm, beyond which the evaporation time increases. This is because of the significant consumption of time in recoiling of the droplet. In addition to the above, the mechanism for the aforesaid enhancement process is tried to reveal by developing the models. For the validation of the developed equations, experimental results are compared with the numerically computed data. The comparison discloses that the developed model is quite accurate and shows insignificant variation from the experimental results. R² and RMSE are also calculated for both the developed models and based on minimum recommended RMSE; the best model is also suggested.     

Experimental and numerical investigation of ester droplet combustion: Application to butyl acetate

This paper presents an experimental and numerical study of the combustion of isolated n‑butyl acetate droplets in the standard atmosphere. Numerical simulations are reported using a model that incorporates unsteady gas and liquid transport, variable properties, and radiation. Three skeletal mechanisms of n‑butyl acetate, derived from a large detailed mechanism comprised of 819 species and 52,698 reactions, were used in the numerical simulations to evaluate the influence of the kinetic mechanism on burning. The reduced mechanisms comprised 212 species and 5413 reactions, 157 species and 3089 reactions, and 105 species and 1035 reactions. The numerical model did not include soot formation, though qualitatively mild sooting was noted only for droplets larger than 0.7 mm. The numerical predictions were in good agreement with experimental measurements of droplet and flame diameters. Flame extinction was numerically predicted which was attributed to a decrease of the characteristic diffusion time relative to the chemical time as droplet burned. Effects of initial droplet diameter on the evolution of maximum gas temperature (T_max) and peak mole fractions of CO₂ and CO are also examined numerically.     

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.     

Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures

Laminar burning velocities of dimethyl ether (DME) and air premixed flames at elevated pressures up to 10 atm were measured by using a newly developed pressure-release type spherical bomb. The measurement system was validated using laminar burning velocities of methane–air flames. A comparison with the previous experimental data shows an excellent agreement and demonstrates the accuracy and reliability of the present experimental system. The measured flame speeds of DME–air flames were compared with the previous experimental data and the predictions using the full and reduced mechanisms. At atmospheric pressure, the measured laminar burning velocities of DME–air flames are in reasonable agreement with the previous data from spherical bomb method, but are much lower than both predictions and the experimental data of the PIV based counterflow flame measurements. The laminar burning velocities of DME–air flames at 2, 6, and 10 atm were also measured. It was found that flame speed decreases considerably with the increase of pressure. Moreover, the measured flame speeds are also lower than the predictions at high pressures. In addition, experiments showed that at high pressures the rich DME–air flames are strongly affected by the hydrodynamic and thermal-diffusive instabilities. Markstein lengths and the overall reaction order at different equivalence ratios were extracted from the flame speed data at elevated pressures. Sensitivity analysis showed that reactions involving methyl and formyl radicals play an important role in DME–air flame propagation and suggested that systematic modification of the reactions rates associated with methyl and formyl formations are necessary to reduce the discrepancies between predictions and measurements.     

A computational framework for predicting laminar reactive flows with soot formation

Numerical modeling is an attractive option for cost-effective development of new high-efficiency, soot-free combustion devices. However, the inherent complexities of hydrocarbon combustion require that combustion models rely heavily on engineering approximations to remain computationally tractable. More efficient numerical algorithms for reacting flows are needed so that more realistic physics models can be used to provide quantitative soot predictions. A new, highly-scalable combustion modeling tool has been developed specifically for use on large multiprocessor computer architectures. The tool is capable of capturing complex processes such as detailed chemistry, molecular transport, radiation, and soot formation/destruction in laminar diffusion flames. The proposed algorithm represents the current state of the art in combustion modeling, making use of a second-order accurate finite-volume scheme and a parallel adaptive mesh refinement (AMR) algorithm on body-fitted, multiblock meshes. Radiation is modeled using the discrete ordinates method (DOM) to solve the radiative transfer equation and the statistical narrow-band correlated-k (SNBCK) method to quantify gas band absorption. At present, a semi-empirical model is used to predict the nucleation, growth, and oxidation of soot particles. The framework is applied to two laminar coflow diffusion flames which were previously studied numerically and experimentally. Both a weakly-sooting methane–air flame and a heavily-sooting ethylene–air flame are considered for validation purposes. Numerical predictions for these flames are verified with published experimental results and the parallel performance of the algorithm analyzed. The effects of grid resolution and gas-phase reaction mechanism on the overall flame solutions were also assessed. Reasonable agreement with experimental measurements was obtained for both flames for predictions of flame height, temperature and soot volume fraction. Overall, the algorithm displayed excellent strong scaling performance by achieving a parallel efficiency of 70% on 384 processors. The proposed algorithm proved to be a robust, highly-scalable solution method for sooting laminar flames.     

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.     

Influence of water mist on propagation and suppression of laminar premixed flame

The combustion of premixed gas mixtures containing micro droplets of water was studied using one-dimensional approximation. The dependencies of the burning velocity and flammability limits on the initial conditions and on the properties of liquid droplets were analyzed. Effects of droplet size and concentration of added liquid were studied. It was demonstrated that the droplets with smaller diameters are more effective in reducing the flame velocity. For droplets vaporizing in the reaction zone, the burning velocity is independent of droplet size, and it depends only on the concentration of added liquid. With further increase of the droplet diameter the droplets are passing through the reaction zone with completion of vaporization in the combustion products. It was demonstrated that for droplets above a certain size there are two stable stationary modes of flame propagation with transition of hysteresis type. The critical conditions of the transition are due to the appearance of the temperature maximum at the flame front and the temperature gradient with heat losses from the reaction zone to the products, as a result of droplet vaporization passing through the reaction zone. The critical conditions are similar to the critical conditions of the classical flammability limits of flame with the thermal mechanism of flame propagation. The maximum decrease in the burning velocity and decrease in the combustion temperature at the critical turning point corresponds to predictions of the classical theories of flammability limits of Zel'dovich and Spalding. The stability analysis of stationary modes of flame propagation in the presence of water mist showed the lack of oscillatory processes in the frames of the assumed model.     

Combustion characteristics and liquid-phase visualisation of single isolated diesel droplet with surface contaminated by soot particles

The combustion generated soot contamination effect on a single diesel droplet ignition and burning was investigated experimentally for the first time. Diesel droplet flame was used to contaminate the droplet to be investigated prior to ignition. Distinct differences in lifetime and stability of the burning of the neat and contaminated droplet samples were observed in their heating, boiling and disruptive phases. For a soot-contaminated droplet surface, the evaporation rate became weaker as a result of slower mass transfer thus contracted the flame formation. Contrary to the burning rate enhancement of droplet with stable and uniform suspension of particles observed by other researchers, the slightest contamination of soot particles in a fuel droplet surface can significantly reduce the burning rate. Denser agglomeration of soot can form a shell on the droplet surface which blocks the flow of gas escaping through the surface thus distort the droplet even further. At late combustion stage, bubbles are observed to rapture on the surface of the soot-contaminated droplet. Strong ejections of volatile liquid and vapour that would explode shortly after parting from the droplet are observed. It seems that the explosion and burning of ejected mixture have little interactions with the enveloped flame surrounding the primary droplet. Enhanced visualisation of droplet liquid-phase has clearly indicated the cause of declining trend in the burning rate and flame stand-off ratio of soot-contaminated diesel droplet. These insights are of significance for understanding the effect of fuel droplet contamination by combustion generated soot particles.     

Numerical study on flame spread of an n-decane droplet array in different temperature environment under microgravity

A series of numerical calculations of flame spread of an n-decane droplet array was conducted at different ambient temperatures (T_a = 300 and 573 K) for S/d₀ from 1.5 to 10, where S is the droplet interval and d₀ is the initial droplet diameter. The authors compared these numerical results with experimental results under similar conditions at different ambient temperatures for the first time in this study. Good qualitative agreement in flame spread behavior between numerical results and microgravity experiments is obtained. Flame spread mode changed with an increase in S/d₀. Also, appearance of the flame spread mode in a stepping-stone manner (Mode III in [Jpn. Soc. Mech. Eng. 68 (672) (2002) 2423]) in a normal temperature environment was verified by numerical calculations and microgravity experiments, although it was not predicted in the theoretical analysis. In addition, good qualitative agreement of flame spread rate V_f versus S/d₀ was obtained between numerical and experimental results, although numerical results were at least twice as large as experimental results. V_f had a maximum peak at a specific S/d₀ for a different ambient temperature. Employment of improved reaction model and consideration for thermal radiation heat transfer are expected to produce quantitatively better results. An increase in surface temperature of unburned droplets and the development of a flammable gas layer around the droplets were promoted in a high-temperature environment, due to an increase in heat transfer from ambient air to the droplet. As a result, V_f was increased by the higher ambient temperature, suggesting that ambient temperature plays a significant role both in the flame spread mode and the flame spread rate through promotion of a flammable gas layer around unburned droplets.     

Thermal quenching and re-ignition of mixed pockets of reactants and products in gas explosions

An approximate solution of the problem of quenching and re-ignition of products/reactants pockets mixed by turbulence is presented. The approach is based on the analysis of thermal regimes of the pocket, but not on the concept of flame stretch. Critical conditions for quenching and re-ignition of the mixed pockets are obtained in a simplified analytical model, and applied to the problem of the sharp difference between the cases of weak and strong flame acceleration in gas explosions. The critical conditions of the mixed eddies in the turbulent flow are shown to depend on the size of the mixed eddies, mixture properties and turbulence intensity. The critical Karlovitz number, Ka, for thermal quenching is shown to increase with the ratio of densities between reactants and products, σ, and with the overall reaction order, n, and to decrease with the Zeldovich number β (dimensionless activation energy) and Lewis number, Le. For the smallest mixed pockets, which are about the size of the laminar flame thickness, the critical Ka-number defines the boundary of the domain of broken flamelets and distributed reaction zones. This number is shown to be of the same order of magnitude as that found from experiments and from direct numerical simulations. The critical conditions for thermal quenching of the largest pockets that can be mixed by turbulence are shown to be independent of the turbulent intensity and could be expressed as a function of σ on β, n, and Le. The mixture properties, thus, may prescribe certain types of flame behavior in turbulent flows. The corresponding critical conditions are linked to the sharp boundary between the cases of weak and strong flame acceleration, which was not satisfactorily explained in previous studies. These critical conditions are shown to have similar critical σ-values and general trends as the experimental data.     

Large eddy simulations of partially premixed ethanol dilute spray flames using the flamelet generated manifold model

The paper presents Large Eddy Simulations (LESs) for the Sydney ethanol piloted turbulent dilute spray flames ETF2, ETF6, and ETF7. The Flamelet Generated Manifold (FGM) approach is employed to predict mixing and burning of the evaporating fuel droplets. A methodology to match the experimental inflow spray profiles is presented. The spray statistical time-averaged results show reasonable agreement with mean and RMS data. The Particle Size Distribution (PSD) shows a good match downstream of the nozzle exit and up to x/D = 10. At x/D = 20 and 30 the PSD is under-predicted for droplets with mean diameter D10 > 20μm and over-predicted for the smaller size droplets. The simulations reasonably predict the reported mean flame structure and length. The effect of increasing the carrier velocity (ETF2–ETF7) or decreasing the liquid fuel injection mass flow rate (ETF2–ETF6) is found to result in a leaner, shorter flame and stronger spray–flow interactions. Higher tendency to local extinction is observed for ETF7 which is closer to blow-off compared to ETF2 and has higher scalar dissipation rates, higher range of Stokes number, and faster droplet response. The possible sources of LES-FGM deviations from the measurements are discussed and highlighted. In particular, the spray time-averaged statistical error contribution is quantified and the impact of the inflow uncertainty is studied. Sensitivity analysis to the pre-vaporized nozzle fuel mass fraction show that such small inflow perturbations (by ±?2% for the ETF2 flame) have a strong impact on the flame structure, and the droplets’ dynamics. Conditional scatter plots show that the flame exhibits wide range of mixing conditions and bimodal mixing lines particularly at upstream locations (x/D?相似文献