Understanding soot particle size evolution in laminar ethylene/air diffusion flames using novel soot coalescence models

Two coalescence models based on different merging mechanisms are introduced. The effects of the soot coalescence process on soot particle diameter predictions are studied using a detailed sectional aerosol dynamic model. The models are applied to a laminar ethylene/air diffusion flame, and comparisons are made with experimental data to validate the models. The implementation of coalescence models significantly improves the agreement of prediction of particle diameters with the experimental data. Sensitivity of the soot prediction to the coalescence parameters is analysed. Finally, an update to the coalescence model based on experimental observations of soot particles in the flame oxidation regions has been introduced to improve its predicting capabilities.     

Numerical study of the effects of gravity on soot formation in laminar coflow methane/air diffusion flames under different air stream velocities

Numerical simulations of laminar coflow methane/air diffusion flames at atmospheric pressure and different gravity levels were conducted to gain a better understanding of the effects of gravity on soot formation by using relatively detailed gas-phase chemistry and complex thermal and transport properties coupled with a semi-empirical two-equation soot model. Thermal radiation was calculated using the discrete-ordinates method coupled with a non-grey model for the radiative properties of CO, CO₂, H₂O, and soot. Calculations were conducted for three coflow air velocities of 77.6, 30, and 5 cm/s to investigate how the coflowing air velocity affects the flame structure and soot formation at different levels of gravity. The coflow air velocity has a rather significant effect on the streamwise velocity and the fluid parcel residence time, especially at reduced gravity levels. The flame height and the visible flame height in general increase with decreasing the gravity level. The peak flame temperature decreases with decreasing either the coflow air stream velocity or the gravity level. The peak soot volume fraction of the flame at microgravity can either be greater or less than that of its normal gravity counterpart, depending on the coflow air velocity. At sufficiently high coflow air velocity, the peak soot volume fraction increases with decreasing the gravity level. When the coflow air velocity is low enough, soot formation is greatly suppressed at microgravity and extinguishment occurs in the upper portion of the flame with soot emission from the tip of the flame owing to incomplete oxidation. The numerical results provide further insights into the intimate coupling between flame size, residence time, thermal radiation, and soot formation at reduced gravity level. The importance of thermal radiation heat transfer and coflow air velocity to the flame structure and soot formation at microgravity is demonstrated for the first time.     

Investigation of mass and energy coupling between soot particles and gas species in modelling ethylene counterflow diffusion flames

A numerical model is developed aiming at investigating soot formation in ethylene counterflow diffusion flames. The mass and energy coupling between soot solid particles and gas-phase species is investigated in detail. A semi-empirical two-equation model is chosen for predicting soot mass fraction and number density. The model describes particle nucleation, surface growth, and oxidation. A detailed kinetic mechanism is considered for the gas phase and the effect of considering radiation heat losses is also evaluated. Simulations were done for a range of conditions that produce low-to-significant amounts of soot using three strategies: first by changing the strain rate imposed on the flow field, second, by changing the oxygen content in the oxidant stream, and third, by changing the pressure. Additionally, the effect of the transport model chosen was analysed. The results showed that, for the flames studied and within the limits of the present work, the soot and gas radiation terms are of primary importance for numerical simulations. Additionally, it was shown that the soot mass and thermodynamic properties coupling terms are, in general, a second-order effect, with an importance that increases as soot amount increases. As a general recommendation, the radiation terms have always to be considered, whereas full coupling has to be employed only when the soot mass fraction, Y_S, is equal to or larger than 0.008. If a higher precision is required, with errors less than 1%, full coupling should be taken into account for Y_S ≥ 0.002. For lower soot amounts, the coupling through soot mass and thermodynamic properties may be neglected as a first approximation, but an error on the total mass conservation will be present. Additionally, discrepancies from considering different transport models (detailed or simplified) are larger than those found from not fully coupling the phases.     

The effect of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame

The influence of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame was investigated by numerical simulation using three different transport property calculation methods. One simulation included preferential diffusion and the other two neglected preferential diffusion. The results show that the neglect of preferential diffusion or the use of unity Lewis number for all species results in a significant underprediction of soot volume fraction. The peak soot volume fraction is reduced from 8.0 to 2.0 ppm for the studied flame when preferential diffusion is neglected in the simulation. Detailed examination of numerical results reveals that the underprediction of soot volume fraction in the simulation neglecting preferential diffusion is due to the slower diffusion of some species from main reaction zone to PAH and soot formation layer. The slower diffusion of these species causes lower PAH formation rate and thus results in lower soot inception rate and smaller particle surface area. The smaller surface area further leads to smaller surface growth rate. In addition, the neglect of preferential diffusion also leads to higher OH concentration in the flame, which causes the higher specific soot oxidation rate. The lower inception rate, smaller surface growth rate and higher specific oxidation rate results in the lower soot volume fraction when preferential diffusion is neglected. The finding of the paper implies the importance of preferential diffusion for the modeling of not only laminar but maybe also some turbulent flames.     

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.     

Soot formation and temperature field structure in co-flow laminar methane-air diffusion flames at pressures from 10 to 60 atm

The effects of pressure on soot formation and the structure of the temperature field were studied in co-flow methane-air laminar diffusion flames over a wide pressure range, from 10 to 60 atm in a high-pressure combustion chamber. The selected fuel mass flow rate provided diffusion flames in which the soot was completely oxidized within the visible flame envelope and the flame was stable at all pressures considered. The spatially resolved soot volume fraction and soot temperature were measured by spectral soot emission as a function of pressure. The visible (luminous) flame height remained almost unchanged from 10 to 100 atm. Peak soot concentrations showed a strong dependence on pressure at relatively lower pressures; but this dependence got weaker as the pressure is increased. The maximum conversion of the fuel’s carbon to soot, 12.6%, was observed at 60 atm at approximately the mid-height of the flame. Radial temperature gradients within the flame increased with pressure and decreased with flame height above the burner rim. Higher radial temperature gradients near the burner exit at higher pressures mean that the thermal diffusion from the hot regions of the flame towards the flame centerline is enhanced. This leads to higher fuel pyrolysis rates causing accelerated soot nucleation and growth as the pressure increases.     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4 Sunderland, P. B., Krishnan, S. S and Gore, J. P. 2004. Effects of oxygen enhancement and gravity on normal and inverse laminar jet diffusion flames. Combust. Flame, 136: 254–256. [Crossref], [Web of Science ®] , [Google Scholar]] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O₂ mole fraction in N₂) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ～0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.     

Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

The interplay between chemistry and transport is addressed by exploring the coupling between the spatial and temporal scales of one-dimensional laminar premixed combustion in reactive mixtures described by detailed chemical kinetics and multicomponent transport. System dynamics are investigated in the neighbourhood of the equilibrium state; in so doing, the time scales associated with modes of varying wavelength for the complete unsteady, spatially inhomogeneous system are obtained. The results reveal that short wavelength modes are dominated by diffusion-based time scales, and long wavelength modes are dominated by reaction-based time scales. The analysis further identifies critical wavelengths where the effects of reaction and diffusion are balanced, and it is seen that the critical wavelengths are well estimated by classical diffusion theory.     

Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames

A model is presented for a one-dimensional laminar premixed flame, propagating into a rich, off-stoichiometric, fresh homogenous mixture of water-in-fuel emulsion spray, air and inert gas. Due to its relatively large latent heat of vaporisation, the water vapour acts to cool the flame that is sustained by the prior release of fuel vapour. To simplify the inherent complexity that characterises the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. The main purpose is to investigate the steady-state burning velocity and burnt temperature as functions of parameters such as initial water content in the emulsified droplet and total liquid droplet loading. In particular, the influence of micro-explosion of the spray’s droplets on the flame’s characteristics is highlighted for the first time. Steady-state analytical solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the micro-exploding emulsion droplets is established. A linear stability analysis is also performed and reveals the manner in which the micro-explosions influence the neutral stability boundaries of both cellular and pulsating instabilities.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames

The effects of flow compression and flame stretch on the accurate determination of laminar flame speeds at normal and elevated pressures using propagating spherical flames at constant pressure or constant volume are studied theoretically and numerically. The results show that both the compression-induced flow motion and flame stretch have significant impacts on the accuracy of flame speed determination. For the constant pressure method, a new method to obtain a compression-corrected flame speed (CCFS) for nearly constant pressure spherical bomb experiments is presented. Likewise, for the constant volume method, a technique to obtain a stretch-corrected flame speed (SCFS) at elevated pressures and temperatures is developed. The validity of theoretical results for both constant pressure and constant volume methods is demonstrated by numerical simulations using detailed chemistry for hydrogen/air, methane/air, and propane/air mixtures. It is shown that the present CCFS and SCFS methods not only improve the accuracy of the flame speed measurements significantly but also extend the parameter range of experimental conditions. The results can be used directly in experimental measurements of laminar flame speeds.     

An investigation of flame zones and burning velocities of laminar unconfined methane-oxygen premixed flames

Numerical and experimental investigations of unconfined methane-oxygen laminar premixed flames are presented. In a lab-scale burner, premixed flame experiments have been conducted using pure methane and pure oxygen mixtures having different equivalence ratios. Digital photographs of the flames have been captured and the radial temperature profiles at different axial locations have been measured using a thermocouple. Numerical simulations have been carried out with a C2 chemical mechanism having 25 species and 121 reactions and with an optically thin radiation sub-model. The numerical results are validated against the experimental and numerical results for methane-air premixed flames reported in literature. Further, the numerical results are validated against the results from the present methane-oxygen flame experiments. Visible regions in digital flame photographs have been compared with OH isopleths predicted by the numerical model. Parametric studies have been carried out for a range of equivalence ratios, varying from 0.24 to 1.55. The contours of OH, temperature and mass fractions of product species such as CO, CO₂ and H₂O, are presented and discussed for various cases. By using the net methane consumption rate, an estimate of the laminar flame speed has been obtained as a function of equivalence ratio.     

3-D simulation of soot formation in a direct-injection diesel engine based on a comprehensive chemical mechanism and method of moments

Here, we propose both a comprehensive chemical mechanism and a reduced mechanism for a three-dimensional combustion simulation, describing the formation of polycyclic aromatic hydrocarbons (PAHs), in a direct-injection diesel engine. A soot model based on the reduced mechanism and a method of moments is also presented. The turbulent diffusion flame and PAH formation in the diesel engine were modelled using the reduced mechanism based on the detailed mechanism using a fixed wall temperature as a boundary condition. The spatial distribution of PAH concentrations and the characteristic parameters for soot formation in the engine cylinder were obtained by coupling a detailed chemical kinetic model with the three-dimensional computational fluid dynamic (CFD) model. Comparison of the simulated results with limited experimental data shows that the chemical mechanisms and soot model are realistic and correctly describe the basic physics of diesel combustion but require further development to improve their accuracy.     

Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames

Absorption and scattering of laser-induced incandescence (LII) intensities by soot particles present between the measurement volume and the detector were numerically investigated at detection wavelengths of 400 and 780 nm in a laminar coflow ethylene/air flame. The radiative properties of aggregated soot particles were calculated using the Rayleigh-Debye-Gans polydisperse fractal aggregate theory. The radiative transfer equation in emitting, absorbing, and scattering media was solved using the discrete-ordinates method. The radiation intensity along an arbitrary direction was obtained using the infinitely small weight technique. The effects of absorption and scattering on LII intensities are found to be significant under the conditions of this study, especially at the shorter detection wavelength and when the soot volume fraction is higher. Such a wavelength-dependent signal-trapping effect leads to a lower soot particle temperature estimated from the ratio of uncorrected LII intensities at the two detection wavelengths. The corresponding soot volume fraction derived from the absolute LII intensity technique is overestimated. The Beer-Lambert relationship can be used to describe radiation attenuation in absorbing and scattering media with good accuracy provided the effective extinction coefficient is adequately.     

Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model

Soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame is modeled with a PAH-based soot model and an advanced sectional aerosol dynamics model. The mass range of solid soot phase is divided into 35 discrete sections and two variables are solved for in each section. The coagulation kernel of soot aggregates is calculated for the entire Knudsen number regime. Radiation from gaseous species and soot are calculated by a discrete-ordinate method with a statistical narrow-band correlated-k based band model. The discretized sectional soot equations are solved simultaneously to ensure convergence. Parallel computation with the domain decomposition method is used to save computational time. The flame temperature, soot volume fraction, primary particle size and number density are well reproduced. The number of primary particles per aggregate is overpredicted. This discrepancy is presumably associated with the unitary coagulation efficiency assumption in the current sectional model. Along the maximum soot volume fraction pathline, the number-based and mass-based aggregate size distribution functions are found to evolve from unimodal to bimodal and finally to unimodal again. The different shapes of these two aggregate size distribution functions indicate that the total number and mass of aggregates are dominated by aggregates of different sizes. The PAH-soot condensation efficiency γ is found to have a small effect on soot formation when γ is larger than 0.5. However, the soot level and primary particle number density are significantly overpredicted if the PAH-soot condensation process is neglected. Generally, larger γ predicts lower soot level and primary particle number density. Further study on soot aggregate coagulation efficiency should be pursued and more experimental data on soot aggregate structure and size distribution are needed for improving the current sectional soot model and for better understanding the complex soot aggregation phenomenon.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

Computational and experimental investigation of the interaction of soot and NO in coflow diffusion flames

A combined computational and experimental investigation that examines the relationship of soot formation and NO in coflow ethylene air diffusion flames is presented. While both NO and soot formation are often studied independently, there is a need to understand their coupled relationship as a function of system parameters such as fuel type, temperature and pressure. The temperature decrease due to radiative losses in systems in which significant soot is produced can affect flame length and other temperature-dependent processes such as the formation of NO. The results of a computational model that includes a sectional representation for soot formation with a radiation model are compared against laser-induced fluorescence measurements of NO. The sooting characteristics of these flames have been studied previously. Experimentally, a laser near 225.8 nm is used to excite the γ(0, 0) band in NO. Spectrally resolved fluorescence emission is imaged radially, for the (0, 0), (0, 1), (0, 2), (0, 3), and (0, 4) vibrational bands, at varying axial heights to create a two-dimensional image of NO fluorescence. A reverse quenching correction is applied to the computational results to determine an expected fluorescence signal for comparison with experimental results. Modeling results confirm that Fenimore NO is the dominant mechanism for NO production and suggest that for lightly sooting flames (peak soot volume fraction < 0.5 ppm), soot reduces only the Zeldovich NO formation (by a factor of two). For flames with increased soot levels (peak soot volume fraction ∼ 4 ppm), the model indicates not only that Zeldovich NO decreases by a factor of 2.5 through radiation loss, but that non-Zeldovich NO is reduced in the top center of the flame by about 30% through the oxidation of soot.     

Effects of pressure rise rate on laminar flame speed under normal and engine-relevant conditions

Laminar flame speed (LFS) is one of the most important physicochemical properties of a combustible mixture. At normal and elevated temperatures and pressures, LFS can be measured using propagating spherical flames in a closed chamber. LFS is also used in certain turbulent premixed flame modelling for combustion in spark ignition engines. Inside the closed chamber or engine, transient pressure rise occurs during the premixed flame propagation. The effects of pressure rise rate (PRR) on LFS are examined numerically in this study. One-dimensional simulations are conducted for spherical flame propagation in a closed chamber. Detailed chemistry and transport are considered. Different values of PRR at the same temperature and pressure are achieved through changing the spherical chamber size. It is found that the effect of PRR on LFS is negligible under the normal and engine-relevant conditions considered in this study. This observation is then explained through the comparison between the unsteady and convection terms in the energy equation for a premixed flame.     

Characterization of heat recirculation effects on the stabilization of edge flames in the near-wake of a mixing layer

A fundamental study aimed at investigating the stabilization characteristics of edge flames established in the near-wake of two merging streams, one containing fuel and the other oxidizer, is presented, with the main focus placed on the effects of the thermal interaction between the flame and the splitter plate. To this end, a diffusive-thermal model characterized by constant gas density and transport coefficients is used for conditions at which flame liftoff is likely to occur. It is assumed that the incoming streams are of equal strain rates, that the fuel and oxidizer are supplied in stoichiometric proportion, and that the mass diffusivities of the reactants are equal, such that the resulting combustion field is symmetric with respect to the centerline extending from the splitter plate. The results indicate that the plate has a negligible effect on the edge flame unless the tip of the plate intrudes into the preheat zone of the curved premixed flame segment forming the edge flame. In an overall adiabatic system, the heat conducted from the flame to the plate is completely recirculated back to the reactants via the lateral surfaces of the plate, thus supporting an excess enthalpy flame in the near-wake. The average output heat flux, defined as the total heat output through the lateral surfaces of the plate divided by the characteristic length associated with the temperature variation along the plate, is identified as an appropriate measure to characterize the heat recirculation efficiency.