Axisymmetric Laminar Diffusion Flames Research Articles

Water vapor and soot spatial characteristics retrieve of axisymmetric optically-thin laminar diffusion flame based on visible and near-infrared multi-spectral light field imaging

The comprehension of the distribution of gaseous species and soot particles plays a pivotal role in investigating the combustion process of a flame. A highly effective method to accomplish this is by extracting visible and near-infrared emission information from flames. In this study, we present a novel near-infrared multi-spectral light field imaging model that enables the concurrent extraction of gas and soot property distributions within a flame. A synthetic test of ethylene diffusion flame is assessed using the proposed reconstruction method. The mole fraction of gaseous water, together with the flame temperature and soot volume fraction, are decoupled spectrally using near-infrared and visible wavelengths. The results demonstrate a reliably retrieved temperature range of 1400 K to 2050 K, accurately reconstructing the actual distributions of soot volume fraction and gaseous water mole fraction. Minor influences on the imaging results and property reconstruction are observed due to uncertainties arising from the reconstruction method, absorption function, reconstruction wavelength for H2O mole fraction, and signal-to-noise ratio. This study serves as a theoretical guide for the future development of practical near-infrared multi-spectral light field imaging techniques for rapid and robust flame diagnostic purposes related to soot and gas properties.

A Combustion Kinetic Model Based on the Fast Chemistry Assumption: Application to Non-Sooty and Sooty Laminar Diffusion Flames

ABSTRACT In this article, a combustion kinetic model based on the fast chemistry (FC) assumption is proposed to compute the finite reaction rate of gaseous species in laminar diffusion flames. The algorithm developed for this purpose is numerically robust and relies on the adiabatic flame temperature to limit the fuel consumption rate. While there is no FC model specifically developed for laminar flames, the Eddy Dissipation Model (EDM) correction scheme for laminar regimes is taken as the reference model. The proposed model addresses the shortcomings of the reference model, i.e. the sensitivity to the transport time scale and the cell size and the need to calibrate a numerical constant repeatedly. The new model formulation does not rely on any numerical constant and completely removes the dependency on the cell size and the species transport time scale, as shown for multiple counterflow and axisymmetric laminar diffusion flames. Furthermore, the proposed model provides consistent temperature and species mass fraction predictions across the mentioned flames. Finally, a sooty axisymmetric flame is simulated using the mentioned models to investigate the numerical interaction between combustion and soot chemistry. The results show that the reference model requires recalibration to capture the temperature and soot volume fraction distributions while the proposed model yields reasonably accurate temperature and soot predictions.

Structure and nitric oxide formation in laminar diffusion flames of ammonia–hydrogen and air

In this work, we present an investigation of the structure and formation of nitrogen oxides (NOx) in an axisymmetric laminar diffusion flame in which an ammonia–hydrogen fuel stream is surrounded by co-flowing air. Green ammonia, produced using renewable energy, is a promising carbon-free fuel for replacing hydrocarbon fuels over a diverse range of combustion applications. A key challenge for ammonia combustion is to understand the kinetics of nitrogen oxide formation for designing low-NOx combustion systems. In this experimental study, ammonia fuel is blended with hydrogen to increase fuel reactivity, with a fuel composition range of 15%–100% hydrogen. NOx emissions and fuel slip are measured by downstream sampling of NO, NO2, N2O and NH3 with a Fourier Transform Infrared (FTIR) gas analyzer. Flame structure is visualized by planar laser-induced fluorescence (LIF) for NO, NH, and OH radicals, as well as OH* by filtered chemiluminescence. Species concentration profiles are compared to predictions from 2-dimensional axisymmetric numerical models of the laminar flame using recent kinetic mechanisms developed for ammonia combustion. No measurable ammonia slip was recorded for any fuel composition, in agreement with model predictions. Good agreement between predictions and measurements was obtained for exhaust nitrogen oxide concentrations and for in-flame radical profiles, although larger variation and deviations are observed for predictions of NO2 and N2O than for NO. Numerical predictions for spatial distribution of flame radicals and flame liftoff height also showed good agreement with LIF and chemiluminescence measurements. For high fuel hydrogen content, the measured NH and NO profiles are shifted inward toward the fuel outlet, away from the peak temperature contour. Reaction path analysis is used to illustrate the important contributions to NO creation and destruction, including the differing role of key reaction pathways with varying fuel hydrogen content.

A layer-peeling method for signal trapping correction in planar LII measurements of statistically steady flames

This work presents a layer-peeling (LP) algorithm to correct the signal trapping effect in planar laser-induced incandescence (LII) measurements of soot volume fraction. The method is based on measurements of LII signals captured by an intensified CCD camera at a series of parallel planes across a diffusion flame. A method based on presumed function (PF) of soot volume fraction is also proposed for comparison. The presented methods are numerically tested based on synthetic LII signals emitted from a simulated axisymmetric laminar diffusion flame using the CoFlame code. Numerical results showed that the LP method is able to correct the signal trapping effect, even for fairly large optical thicknesses and in a wide range of detection wavelengths. The correction decreases the relative errors induced by neglecting the trapping effect considerably. The signal trapping effect correction is less important for the determination of integrated soot quantities such as radially integrated soot volume fraction or total soot loading. Planar LII measurements were carried out and calibrated in order to test the method experimentally in a coflow flame. The LP, PF and a simplified analytical (SA) model were compared. The results indicate that the differences in soot volume fraction of 1 ppm or about 15% are obtained in zones of maximum soot loading of 6.5 ppm when the trapping effect is accounted for. Also, the LP and SA methods were found computationally efficient and accurate compared to the PF method. Although the study was performed in a canonical laminar axisymmetric flame, the proposed method can be applied to any statistically steady 3D flame.

On the effects of varying coflow oxygen on soot and precursor nanoparticles in ethylene laminar diffusion flames

This paper reports an experimental investigation of the effects of varying the oxygen concentration in the oxidizer stream on the formation and evolution of soot and precursor nanoparticles in an axisymmetric ethylene laminar coflow diffusion flame. The optical diagnostics employ temporally and spectrally resolved point-measurements of 266 nm excited scattering and laser-induced fluorescence, combined with 1064 nm excited laser-induced incandescence. Previous studies have indicated that oxygen enhancement changes soot volume fraction in sooting flames. However, the effects of coflow oxygen concentration on soot precursors are not well understood, and this aspect is addressed explicitly here. A set of eight flames is studied where the oxygen concentration in the coflow stream is varied from 19 to 40%, by volume, while the chemical composition of the jet stream is kept constant at 60% C2H4 / 40% N2. Oxygen enhancement in the coflow leads to a change in flame temperatures, luminosity, and flame length. It is found that the concentration of precursor nanoparticles increases with coflow oxygen. A combination of higher temperatures, red-shifting, and increased decay-times suggest structural growth in precursor nanoparticles with increasing coflow oxygen. In all flames, a similarity of particle evolution is noted with axial location, and this includes the presence of an intermediate stage during the transformation of precursors to soot. Moreover, the structural transformation from aliphatic to aromatic features is shifted towards the beginning of the precursor region when coflow oxygen is increased. It is found that structural growth starts at a similar temperature, regardless of coflow oxygen concentration. Soot volume fraction and primary soot particle diameter increase with coflow oxygen enrichment up to a threshold oxygen volume fraction, after which both the soot volume fraction and diameter decrease with further oxygen enrichment.

Combustion of Iron Particles Suspension in Laminar Premixed and Diffusion Flames

ABSTRACT In the work, the combustion regimes of iron particles (d10 = 4.7 µm) in a laminar pre-mixed flame (LPF) and in an axisymmetric laminar diffusion flame (LDF) are studied. For (LPF), we studied the effect of variations in gas suspension of the concentrations of fuel Cf = 0.4 ÷ 0.6 kg/m3 and oxygen CO2 = 21 ÷ 40%, and for (LDF), pure oxygen blowing and variation in the iron concentration Cf = 0.4 ÷ 1.5 kg/m3. The results of particle temperature measurements in the combustion zone of LPF and LDF, the dispersed and phase composition of the combustion products (depending on the concentration of fuel and oxidizer) are presented. It is shown that, under certain conditions, iron particles in LPF switch to a “high-temperature” diffusion mode of combustion. This mode is accompanied by intensification of gas-phase reactions and leads to a two-mode particle size distribution of combustion products. In this mode of combustion of a gas suspension (at temperatures much lower than the boiling point of iron), the mass yield of a nanoscale fraction of combustion products reaches tens of percent and increases with increasing oxygen concentration in LPF. This mode of iron particles combustion was not observed in LDF. The features of the thermal structure of the diffusion dust flame are analyzed. It is shown that in LDF the burning time of metal particles in the diffusion mode is proportional to the particle radius (in the kinetic mode), and should depend on the concentration of fuel and the size of the burner.

A decomposition method for the simultaneous reconstruction of temperature and soot volume fraction distributions in axisymmetric flames

This paper presents a method for the simultaneous reconstruction of temperature and soot volume fraction distributions in axisymmetric flames. In the proposed method, the radiation temperature and emissivity are determined using a multi-wavelength method. Then, based on the decomposition of the emissivity, the soot volume fraction distribution is reconstructed. Accordingly, the temperature distribution is calculated using the reconstructed local radiation source terms under a single wavelength. Based on a correction formula proposed in this paper, a further correction process is conducted, and the soot volume fraction and temperature distributions are successively obtained. Simulations are conducted with the temperature and soot volume fraction distributions at two different heights from the flame burner of an axisymmetric ethylene laminar diffusion flame. In the simulations, normal random errors are superimposed, and the radiation temperature and emissivity are calculated based on the intensities at three wavelengths corresponding to the R, G, and B channels of color cameras. Good agreement with the assumed data is obtained, which verifies the performance of the proposed method. Additionally, comparison with the results obtained using the widely-used two-color reconstruction method indicates that the proposed method exhibits a more stable performance with smaller errors. Moreover, the proposed method can take advantage of measurement at multiple wavelengths. Based on the multi-wavelength data captured using a hyperspectral imaging device, the measurement results of an axisymmetric ethylene laminar diffusion flame using the proposed method are also presented.

On the Effects of Carbon Dioxide as a Diluent on Precursor Nanoparticles and Soot in Axi-symmetric Laminar Coflow Diffusion Flames

ABSTRACT The impact on the use of carbon dioxide (CO2) as a diluent in the fuel and oxidizer streams on the formation and evolution of precursor nanoparticles and soot in axisymmetric ethylene laminar coflow diffusion flames is experimentally explored using optical diagnostics in this paper. The optical diagnostics employed are based on temporally and spectrally resolved point measurements of laser-induced fluorescence, elastic scattering, and laser-induced incandescence. The measurements provide insight to indicative structure and concentration of precursor nanoparticles, and enable the determination of volume fraction and mean diameter of soot. Previous studies have indicated that the use of CO2 as a diluent compared to nitrogen can reduce soot formation through both chemical and thermal effects. However, the effect of CO2 addition on precursor nanoparticles’ concentrations and structure is not well understood, hence exploring the impact of CO2 on precursor nanoparticles is one of the primary aims of this study. Flames with CO2 as a diluent in the jet only, coflow only, and both streams are identified and investigated. For the flames studied with respect to the replacement of N2 with CO2: i), the soot volume fraction and mean soot diameter is reduced, and ii) precursor nanoparticles concentration is reduced, and the structural transformation is delayed.

Measurement of temperature and wavelength-dependent emissivity distributions using multi-wavelength radiation thermometry

A multi-wavelength radiation thermometry method used to determine the temperature and wavelength-dependent emissivity according to spectroscopic radiation intensities is presented. Over a predetermined temperature range, with a set step size, the method traverses the temperature range, and for each temperature, inversely fits a spectral line according to the intensity in the middle of the wavelength region, based on the Rayleigh approximation. The temperature with the spectral line closest to the measured spectral line is considered to be the optimum temperature at that accuracy level. Then, near that optimum temperature, the temperature range and step size are narrowed, to determine the optimum temperature at higher levels of accuracy. Iterating on this method until reaching the required accuracy level, the temperature can be achieved, and the wavelength-dependent emissivity can also be determined. Simulation verification was conducted showing good anti-noise performance and rapid processing capacity. Temperature and emissivity distributions for six heights of an axisymmetric laminar diffusion flame with 194 mL/min ethylene and 240 L/min air were given. Results show that along the line of sight, the radiation temperatures exhibit an average effect of the local temperatures, while the emissivity exhibits a cumulative effect of the absorption coefficients.

A method for measurement of spatially resolved radiation intensity and radiative fraction of laminar flames of gaseous and solid fuels

This work introduces a new method for determination of spatially resolved radiation intensity and radiative fraction for axisymmetric laminar diffusion flames by using a modified DSL-R camera employed to collect monochromatic, 900 nm, images and a Schmidt-Boelter heat flux gauge. A novel instrument, Milligram-scale Flame Calorimeter, is employed to supply the flame with either gaseous fuel or solid fuel pyrolyzate and measure the total heat release rate associated with the combustion process. The high spatial resolution provided by the images of the camera allows for a multi-emitter treatment of the 20–60 mm tall flames. The flames’ shapes and monochromatic radiation intensity profiles are extracted from the images. Using the radiation transport equations formulated for the system’s specific geometry, the monochromatic radiation intensities are related to the total heat flux gauge readings collected at several distances from the base of the flame. Subsequently, spatially resolved total radiation intensity data are obtained. Integration of this intensity over the flame surface yields the radiation heat release rate, of which the ratio to the total heat release rate yields the radiative fraction. In this work, methane, propane and acetylene flames have been studied to validate this methodology (covering a wide range of sooting conditions), while polyethylene-fueled flames above and below the smoke point have been analyzed to demonstrate the method’s applicability to solid fuels. The results show that the method produces values that are consistent with previous studies, particularly when the assumptions of the previous studies are replicated. Additionally, the data indicate that for flame heights that are all below (or all above) the smoke point, the value of the maximum total radiation intensity does not depend on the total heat release rate. This behavior of the maximum radiation intensity suggests that said parameter is a good candidate to correlate with the radiative properties of turbulent flames.

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB0601900), the National Natural Science Foundation of China (Grant Nos. 51827808, 51821004, and 51406095), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2018ZD03 and 2017ZZD005), and Science and

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation, demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.

Integrated research of a multi-wavelength method in anisotropic scattering flame on soot temperature and radiative coefficient reconstruction.

At present, the studies of scattering flame problems combined with multi-wavelength reconstruction technology are rather limited. In this paper, a multi-wavelength method combined with a collocation spectral method (CSM)-discrete ordinates method (DOM) forward method is developed for the simultaneous reconstruction of temperature and inhomogeneous radiative coefficient of an axisymmetric laminar ethylene diffusion flame. The scattering source term in the radiative transfer equation is solved by the forward solution method based on DOM, which couples a spatial scheme of CSM and the spherical rings arithmetic progression quadrature. The Tikhonov regularized method is employed to overcome the ill-posed matrix to obtain the global radiative source term. The boundary radiation intensity is input into the algorithm as a known value for inversion of temperature, absorption coefficient, and scattering coefficient. The retrieval results demonstrate that the temperature and the radiation parameters of the scattering flame can be well reconstructed for the flame with axisymmetric distribution, even for the flame with noisy data. In addition, the scattering coefficient is more difficult to rebuild than temperature. The inversion accuracy does not deteriorate with a slight increase in noise. Also, the addition of scattering terms to the proposed algorithm can improve the accuracy in reconstructing the radiation parameters. The developed method in this paper would be useful for multispectral algorithms, which could be used in later experiments based on hyperspectral techniques.

Artificial compressibility method on half-staggered grid for laminar radiative diffusion flames in axisymmetric coordinates

ABSTRACTArtificial compressibility method is extended to solve the low Mach variable density Navier–Stokes equations for the simulation of axisymmetric laminar radiative diffusion flames. A combustion model based on the generalized state relationships for species mass fractions and temperature is adopted and the radiation heat loss is estimated as a fraction of heat of combustion. Conventional finite difference method along with a total variation diminishing scheme is used for the spatial discretization on nonuniform half-staggered grid layouts. To reach the steady-state condition, a three-step low-storage explicit Runge–Kutta method is used. The accuracy of the proposed method is reported for confined and unconfined diffusion flames.

Unified behavior of soot production and radiative heat transfer in ethylene, propane and butane axisymmetric laminar diffusion flames at different oxygen indices

An experimental study was conducted to investigate the effects of oxygen index on the flame geometry, soot production and radiative loss in laminar over-ventilated co-flow buoyant axisymmetric diffusion flames at atmospheric pressure. Three gaseous hydrocarbon fuels, namely ethylene, propane, and butane, were considered. The oxygen index was varied from 21% to 37% and several mass flow rates were used. These conditions were chosen to keep the flames under the smoke point. Soot volume fraction and temperature were deduced from line-of-sight attenuation and two-color emission measurements, respectively. A scaling analysis based on the smoke point height was developed in order to unify the sooting behavior of the flames investigated. This analysis produced correlations for the flame height, the maximum soot volume fraction, the maximum integrated soot volume fraction and the radiant fraction at the smoke point.

Diffusion-flame flickering as a hydrodynamic global mode

The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

MC-Smooth: A mass-conserving, smooth vorticity–velocity formulation for multi-dimensional flows

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and Nspec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity–velocity formulation.

Skeletal mechanism modelling of n-heptane/oxygen laminar coflow flame structure at pressures

A skeletal reaction mechanism of n-heptane combustion is developed and validated. The axisymmetric laminar co-flow diffusion flames of n-heptane/oxygen are simulated using the skeletal mechanism at elevated pressure, and the chemical reaction paths in three reaction zones of flame are presented. The n-heptane/oxygen flame height decreases from 8.8 to 5.6mm with the increase of pressure from 0.1 to 2MPa, and the Roper’s formulation is not expected for the prediction of n-heptane/oxygen flame height. The maximum volume fraction of soot increases with pressure as fv,max∝P2. The ratio of flame height to soot oxidation length of the n-heptane/oxygen flames is close to unity (1.037–1.121).

Assessment of semi-empirical soot production models in C1–C3 axisymmetric laminar diffusion flames

The objective of this work is to assess the accuracy and limitations of three different semi-empirical soot models: an acetylene/benzene flamelet based two-equation soot model developed by Lindstedt (1994) [4] (in: H. Bockhorn, pp. 417–441) and two laminar smoke point (LSP) based soot models developed by Lautenberger et al. (2005) [15] (Fire Saf. J., 40, pp. 141–176) and by Yao et al. (2011) [14] (Fire Saf. J., 46, pp. 371–387). This task is performed by simulating twenty-seven C1–C3 hydrocarbon-air flames, consisting of normal (NDF) and inverse (IDF) diffusion flames and covering a wide range of residence times and fuel sooting propensities. The acetylene/benzene based soot model predicts the maximum soot volume fractions and the peaks of the integrated soot volume fraction within a factor of 2 of measurements. However, two pre-exponential factors for the surface growth process, one for the C1–C2 hydrocarbons and the other for the C3 hydrocarbons, were necessary in order to obtain this agreement. LSP soot model results are also within a factor of 2 of the measurements for most of the propane, ethylene, propylene and acetylene NDFs. For weakly sooting fuels, such as methane and ethane, the LSP concept overestimates soot production rates. In addition, the model of Lautenberger et al. was found to provide a better description of the soot production in the ethylene IDFs than that of Yao et al. Eventually, computed radiant fractions were compared with experimental data for propane, ethylene and propylene NDFs, showing that predictions using the models of Lindstedt and Lautenberger are on the whole within 10% of the experimental data.

Modeling curvature effects in diffusion flames using a laminar flamelet model

The goal of this paper is to investigate the effects of curvature of mixture fraction iso-surfaces on the transport of species in diffusion flames. A general flamelet formulation is derived mathematically considering both curvature effects and differential diffusion effects. These theoretical results suggest that curvature does not play a role in the transport process irrespective of the flame curvature if species transport is described with a unity Lewis number. On the other hand, a curvature-induced term becomes explicit when differential diffusion effects are considered, and it acts as a convective term in mixture fraction space. It is found that this term needs to be taken into account when the radius of curvature is comparable or smaller than the local flame thickness. For the proper integration of the flamelet equations, the scalar dissipation rate and curvature dependences on mixture fraction are modeled by considering two basic curved one-dimensional flame configurations. The flamelet equations accounting for curvature effects are solved with various prescribed curvature values. Results indicate that the mass fraction profiles of species with very small or large Lewis numbers are shifted significantly in mixture fraction space by the inclusion of curvature. Differential diffusion effects are enhanced by negative curvature values and suppressed by positive curvature values. In cases where flame curvature is not uniform, the curvature-induced convective term generates gradients along mixture fraction iso-surfaces, which enhance tangential diffusion effects. Budget analysis is performed on an axisymmetric laminar coflow diffusion flame to highlight the importance of the curvature-induced convective term compared to other terms in the full flamelet equation. A comparison is made between full chemistry simulation results and those obtained using planar and curved flamelet-based chemistry tabulation methods.

Measurement of the spatially distributed temperature and soot loadings in a laminar diffusion flame using a Cone-Beam Tomography technique

A new low-cost optical diagnostic technique, called Cone Beam Tomographic Three Colour Spectrometry (CBT-TCS), has been developed to measure the planar distributions of temperature, soot particle size, and soot volume fraction in a co-flow axi-symmetric laminar diffusion flame. The image of a flame is recorded by a colour camera, and then by using colour interpolation and applying a cone beam tomography algorithm, a colour map can be reconstructed that corresponds to a diametral plane. Look-up tables calculated using Planck's law and different scattering models are then employed to deduce the temperature, approximate average soot particle size and soot volume fraction in each voxel (volumetric pixel). A sensitivity analysis of the look-up tables shows that the results have a high temperature resolution but a relatively low soot particle size resolution. The assumptions underlying the technique are discussed in detail. Sample data from an ethylene laminar diffusion flame are compared with data in the literature for similar flames. The comparison shows very consistent temperature and soot volume fraction profiles. Further analysis indicates that the difference seen in comparison with published results are within the measurement uncertainties. This methodology is ready to be applied to measure 3D data by capturing multiple flame images from different angles for non-axisymmetric flame.