Axisymmetric Flame Research Articles

Spline-based Abel Transform (SAT) radial property reconstruction for noise and trapping correction: Application to axisymmetric sooting flames

In combustion research, optical diagnostics often necessitate Abel inversion to deconvolve the measurements of axisymmetric flames, especially to determine local soot temperature fields from integrated flame radiative emission measurements. However, traditional Abel inversion methods can considerably amplify experimental noise, especially towards the flame centerline. Although various strategies exist to mitigate this issue, they typically do not address the correction of signal trapping within the flame. The present paper introduces an adapted Abel inversion tool that combines resistance to experimental noise with a mechanism to correct signal trapping effects. The tool employs noise-free Abel inversion using piecewise spline functions. Its effectiveness is validated through numerical comparisons with conventional methods. The practical application is demonstrated in the measurement of soot temperature in a canonical laminar diffusion ethylene flame. This is achieved by using multi-wavelength line-of-sight attenuation (LOSA) and emission measurements. The tool corrects for the signal trapping effect in emission data by integrating extinction profiles, thus enabling a more precise soot temperature analysis. The current study also compares two techniques of temperature measurement based on thermal emission: traditional two-color pyrometry and a calibrated emission and absorption ratio method. The study further explores the effects of signal trapping, scattering contribution, and the absorption function ratio on soot temperature determination based on experimental profiles. The findings suggest that signal trapping and scattering contributions have a negligible impact on measurements at the wavelengths examined. However, the choice of absorption function ratio significantly influences the outcomes of two-color pyrometry, highlighting the advantage of the one color emission/absorption technique for the determination of sooting flames temperature measurements.

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.

SootImage: An image recreation, post-processing validation procedure for sooting axisymmetric flames

Validation is a vital part of any computational fluid dynamics study. Validation is done by comparing the computed results to the experimental measurements performed in a known configuration. In sooting flames, such a comparison is non-trivial since the measurements have a wide range of uncertainty due to difficulties in directly measuring soot volume fractions. This work introduces a different way to verify the computations using a software package called SootImage. In this proposed methodology, comparisons are not made directly to the computed properties of interest (soot volume fraction and temperature). Instead, a post-processing procedure is performed to obtain an image of the flame based on the computed properties. This reconstructed image is compared to an actual image of the flame being studied. The algorithm of the image reconstruction utilized within SootImage is presented in detail. Finally, the usage of SootImage is demonstrated on a co-flowing, laminar ethylene/air diffusion flame. Program summaryProgram Title: SootImageCPC Library link to program files:https://doi.org/10.17632/nc5myw64km.1Developer's repository link:https://github.com/VictorChernov/SootImageLicensing provisions: CC BY NC 3.0Programming language: MATLABNature of problem: The software allows comparing images of a real flame with the recreated image of a simulated flame. This requires two major steps. One is the recreation of the image of an axisymmetrical flame from the computed soot volume fraction and temperature fields for a known camera and optical configuration. The second is cropping and position images to obtain a meaningful comparison.Solution method: The solution recreates the image by integrating the soot thermal radiation over a line-of-sight. Soot is assumed to emit as gray body. The integrated radiation is passed through the color filters of the camera and is translated to pixel values. After the process is done for the whole flame, the width, height and origin of both flames are found, and images that can be easily compared are created.

Quantitative 2D reconstruction of temperature and OH concentration in axisymmetric flames based on ultraviolet broadband absorption tomography

Absorption tomography plays a crucial role in quantitatively imaging temperature and absolute concentration in combustion. However, there is scarce research on the tomography of OH radicals, which are significant for combustion diagnostics. This study presented a new tomography method to image OH radicals, termed ultraviolet broadband absorption tomography (UV-BAT). Three strategies were proposed to solve the nonlinear problem in UV-BAT tomography, namely all-spectra fitting, weak-absorption approximation, and multi-temperature approximation. The proposed UV-BAT method was applied for OH imaging in methane/air axisymmetric laminar Bunsen flames with different equivalence ratios (ϕ = 0.9, 1.0, and 1.1). The reconstructed OH distributions showed distinctive structures of Bunsen flames including premixed and diffusion flame areas. The accuracy of the UV-BAT method was validated by comparing tomography results with computational fluid dynamics (CFD) simulations using the USC-Mech II mechanism, demonstrating good agreement in two-dimensional (2D) temperature and OH concentration distributions. This novel method offers new opportunities for tomographic reconstruction of free radicals such as OH and temperature in small-scale flames.Novelty and significanceThis study demonstrated a novel tomography imaging method using ultraviolet broadband absorption spectroscopy to reconstruct temperature and radical concentration in combustion. This method possesses high sensitivity to free radicals and employs compact and inexpensive equipment, making it one of the most viable methods for realizing free radical absorption tomography. The 2D imaging of OH radicals using this method based on axisymmetric absorption tomography was accomplished for the first time. In conclusion, this study enriched the diagnostic methods of flame radicals based on absorption spectroscopy and provided new ideas for small-scale temperature tomography.

Line-of-Sight Temperature Profile Reconstruction of Axisymmetric Laminar Flame by Multispectral Dispersion Spectroscopy

Line-of-Sight Temperature Profile Reconstruction of Axisymmetric Laminar Flame by Multispectral Dispersion Spectroscopy

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.

Modeling Flame Transfer Functions of an Industrial Premixed Burner

Abstract This paper presents an analysis of the unsteady heat release rate response of industrially relevant axisymmetric premixed flames to harmonic velocity perturbations. The heat release rate response, quantified using the flame transfer function (FTF) definition, is measured from an acoustically forced swirl burner under perfectly premixed conditions. To understand the features of the measured FTF, a physics-based analytical model is developed in this study. To describe the heat release rate dynamics, a model for the flame spatiotemporal response is derived in the linear limit using the G-equation formulation. Inputs to the flame response model are selected to be consistent with values observed in the corresponding industrial burner, based on experimental and numerical studies. The relative contributions of acoustic and convecting vortical disturbances on specific features of the FTF are explored in this study. The results highlight the importance of capturing the appropriate disturbance velocity field as an input to the flame response model for accurate FTF predictions.

BPNN model based AI for the estimation of soot data from flame luminosity emissions in H2/N2 diluted ethylene laminar diffusion flames

Advanced combustion devices and alternative fuels like hydrogen require an estimation of the impact of such changes on engine exhaust emissions of regulated pollutants like soot. Huge experimental data are then required to be collected and post-processed, both in academic and industrial setups. Machine learning and artificial intelligence can be employed to reduce cost and time. This study presents a Back Propagation Neural Network (BPNN) model that has been validated and optimized for the simultaneous prediction of soot volume fraction, temperature and particle sizes from flame luminosity measurements. The compatibility, robustness and reliability of neural network models in terms of fuel composition and flow rate variations was analyzed , by varying both fuel flow rate and fuel stream dilution in axisymmetric diffusion flame burning in a coflow of air. BPNN model predicted results were contrasted against those obtained through laser diagnostics. A detailed analysis of the performance of BPNN model, based on an extensive experimental study revealed indifference to N2/H2 dilution and fuel flow rate variations. Furthermore, an original BPNN model is optimized to improve learning rate and to reduce computation cost, by applying a Bayesian algorithm which continuously monitors and minimizes an error function. It was concluded that a training set size of three was sufficient to predict soot field parameters with a fair prediction accuracy. These results have direct implication for the application of proposed technique in practical combustion equipment where operating parameter, e.g. Air–fuel ratio and EGR, show both gradual and instantaneous variations and affect both performance and emissions. These results clearly demonstrate the robustness of this technique which offers opportunities for real-time, in situ, monitoring of practical combustion devices. Hence, Real-time data of sooting characteristics of flames can be used to both monitor and control pollutant emissions by integrating a response strategy in the system.

Flash-back, blow-off, and symmetry breaking of premixed conical flames

Hydrodynamic and thermal-diffusive effects subject premixed flames to intrinsic instabilities that strongly influence their shape and propagation/stabilization characteristics. However, the interaction and coupling of intrinsic flame dynamics with background flow gradients and boundary conditions remain poorly understood. This paper presents a global nonlinear bifurcation analysis of burner-stabilized laminar premixed conical flames with varying reaction rates and reactant diffusivities, respectively parameterized by the Damköhler number Da and the Lewis number Le. Using a dimensionless formulation of the reacting, weakly-compressible Navier–Stokes equations, the dynamics of flash-back, blow-off, and cellular instability are explored in a fully-coupled framework. Our analysis identifies steady conical flame states over a finite range of Da and Le, limited by saddle–node bifurcations corresponding to spontaneous blow-off of the axisymmetric flame below a Le-dependent lower critical Da value and spontaneous boundary-layer flash-back beyond a higher critical Da value. Furthermore, the analysis reveals that the conical flame loses its axisymmetry via circle–pitchfork bifurcations as Le or Da decrease or increase beyond respective critical values. These bifurcations are shown to correspond to stationary three-dimensional global modes describing steady polyhedral or tilted flame structures, each associated with distinct azimuthal periodicities. Statement of SignificanceThis work presents a bifurcation analysis of laminar premixed conical flames within a fully-coupled flame/flow model. By considering variations in reaction rate and reactant diffusivity, the analysis identifies saddle–node bifurcations corresponding to spontaneous flash-back and blow-off of the axisymmetric flame. It also identifies axisymmetry breaking bifurcations associated with transitions to steady three-dimensional polyhedral and tilted flame states. These global instabilities indicate that hydrodynamic and thermal-diffusive effects strongly influence a flame’s steady structure in the azimuthal dimension even when no instabilities appear in the plane of symmetry. As such, future analyses of flame dynamics should rule out symmetry-breaking behaviors before adopting a two-dimensional computational framework.

Single Spectral Line Method for TDLAS Imaging of Temperature and Water Vapor Concentration

A single spectral line method for gas temperature as well as concentration extraction was proposed by using iterations with a fuzzy proportional–integral-derivative (PID) controller in tunable diode laser absorption spectroscopy (TDLAS). Usually, two or more spectral lines are essential to extract temperatures from coupled gas concentration and pressure. The proposed method utilized the line shape of a single absorption spectrum to decouple gas parameters along the laser path simultaneously and simplified the optical implementations. Differential equations of the Voigt profile were introduced at multiple wavenumbers to extract gas parameters from a single spectral line. A fuzzy PID controller was utilized to iteratively achieve the single spectral line from widely existed overlapping spectra. A relative temperature error within 2.5% at reference temperatures ranged from 300 to 2300 K was achieved by using the spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7444.35\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> from noise free data. At low temperatures below 350 K, the proposed method using the single spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7181.14\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> yielded smaller errors in noisy cases, and the temperature errors were verified within 5 °C on the water-based thermostat below 100 °C using the single spectral line. Experiments of axisymmetric counterflow flames at different heights were also implemented. The proposed method effectively reconstructed distributions of flame temperature and water vapor concentration inside, by only using a single spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7444.35\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> .

Parameter Fitting-Based Fast Imaging of Axisymmetric Flame Temperature Field Using Wavelength-Modulated Lateral Shearing Interferometry

Parameter Fitting-Based Fast Imaging of Axisymmetric Flame Temperature Field Using Wavelength-Modulated Lateral Shearing Interferometry

High-precision gaseous flame temperature field measurement based on quadriwave-lateral shearing interferometry

Quadriwave-lateral shearing interferometry (QLSI) has a broad utilization in quantitative phase imaging (QPI) for refraction-type objects due to its compact structure and stable performance against external disturbance. Here we propose to use the QLSI technique to image and measure the gaseous flame temperature field distribution in high precision. The quantitative phase image of an axisymmetric candle flame is firstly reconstructed from the wire-mesh-like QLSI interferogram, and then the three-dimensional temperature field distribution is calculated with the axisymmetric projection transform algorithm. Compared to the conventional digital holographic interferometry (DHI) based on Mach-Zehnder architecture, the proposed method possesses a high-precision measurement and better stability in disturbed environment, benefiting from the compact common-path structure of QLSI. The temperature measurement errors of the proposed QLSI method are ±5.0 K and ±5.3 K in the presence of airflow disturbance and mechanical vibration, respectively, while those of the DHI method are ±7.6 K and ±12.9 K, respectively.

Estimation of laminar flame speeds using axisymmetric bunsen flames: Molecular transport effects

Intricacies associated with the estimation of laminar flame speed using the axisymmetric Bunsen flame technique were assessed, through parametric direct numerical simulations. The study involved methane-air mixtures at atmospheric pressure and temperature, and both the flame cone angle and flame surface area methods were utilized to estimate the laminar flame speeds based on conditions used in recent relevant experimental studies. The results provided insight into the details of the flame structure and allowed for the assessment of various non-idealities and the attendant uncertainties associated with the estimation of laminar flame speeds. Additionally, molecular transport effects were investigated by altering the fuel diffusivity, in order to evaluate its impact on the flame structure and propagation under the presence of negative stretch. The modification of fuel diffusivity was found to affect the burning rate as stretch varies. Under fuel rich conditions, decreasing the fuel diffusivity was found to have an opposite effect on the heat release and thus the burning rate, when compared to positively stretched flames that have been investigated recently in a similar manner. The reported results are expected to provide guidance in flame propagation experiments using the convenient Bunsen flame method at near-atmospheric or elevated pressures, as well as insight into the effects of negative stretch that has, compared to positive, attracted less attention in past studies.

Tri-zone flame spatial structure imaging combined with endogenic polarized scattering.

We propose a multi-mode optical imaging method to retrieve the 2D and 3D spatial structures of the preheating, reaction, and recombination zones of an axisymmetric steady flame. In the proposed method, an infrared camera, a visible light monochromatic camera, and a polarization camera are triggered synchronously to capture 2D flame images, and their corresponding 3D images are reconstructed by combining different projection position images. The results of the experiments conducted indicate that the infrared and visible light images represent the flame preheating and flame reaction zones, respectively. The polarized image can be obtained by computing the degree of linear polarization (DOLP) of raw images captured by the polarization camera. We discover that the highlighted regions in the DOLP images lie outside the infrared and visible light zones; they are insensitive to the flame reaction and have different spatial structures for different fuels. We deduce that the combustion product particles cause endogenic polarized scattering, and that the DOLP images represent the flame recombination zone. This study focuses on the combustion mechanisms, such as the formation of combustion products and quantitative flame composition and structure.

Three-dimensional reconstruction of flame temperature and H2O concentration using water vapor integrated spectral band emission

Efficient and accurate reconstruction of flame temperature and species concentration is very useful for combustion monitoring. In this work, the integrated spectral band ratio (ISBR) method, which uses the ratio of two integrated spectral radiative intensities to infer temperature, is applied to reconstruct three-dimensional flame temperature and H2O concentration distributions. First, the ratio of two integrated spectral radiative intensities is justified by gas radiation theory to only depend on gas temperature, and the influence of gas concentration and pressure on the ratio is negligible. Then, a spectral band pair is carefully selected for the measurement with an atmospheric path between the detector and the flame. In the selected spectral bands, CO2 and CO emissions are negligible compared to H2O emission, and atmospheric absorption can be ignored. Meanwhile, gas temperature is monotonically related to the ratio of integrated spectral radiative intensities. When the uncertainty of the ratio is 2%, the error of reconstructed temperature is less than 38K with gas temperature close to 3000K, and the error decreases as the gas temperature goes down. Finally, numerical experiments on reconstruction of axisymmetric and non-axisymmetric flames are carried out. Results show that three-dimensional distributions of flame temperature and H2O concentration can be reconstructed with high accuracy.

Edge Effects on Simultaneous Reconstructions of Flame Temperature and Soot Volume Fraction Profiles by a CCD Camera.

In this paper, the influence of the edge effect on the simultaneous reconstruction of axisymmetric flame temperature and soot volume fraction profiles by a single CCD camera was investigated in detail. The reconstruction accuracy of the flame temperature profile and soot volume fraction was insensitive to the measurement error of the coefficient matrix. When the signal to ratio (SNR) of the measurement system for both the radiation intensity and coefficient matrix was as low as 46 dB, the reconstruction accuracy for both temperature and soot volume fraction was acceptable and was more influenced by the radiation intensity measurement error. The reconstruction of the flame temperature and soot volume fraction was greatly influenced by the edge effect. When the flame edge with weak radiation signals was ignored during the reconstruction, the relative reconstruction error for the temperature and soot volume fraction increased from the flame center to the edge, and reached an unacceptable value at the reconstruction boundary, especially for the soot volume fraction. The flame image boundary could be chosen as the unified reconstruction boundary to reconstruct the two-dimensional distribution of the temperature and soot volume fraction with satisfactory accuracy. The low soot volume fraction could influence the reconstruction accuracy for both the temperature and soot concentration in non-sooting regions. Moreover, there was no obvious regularity between the reconstruction accuracy of the temperature and soot volume fraction and the extension of the reconstruction boundary.

Relations Between Statistics of Three-Dimensional Flame Curvature and its Two-Dimensional Counterpart in Turbulent Premixed Flames

The relations between the actual flame curvature probability density function (PDF) evaluated in three-dimensions and its two-dimensional counterpart based on planar measurements have been analytically derived subject to the assumptions of isotropy and statistical independence of various angles and two-dimensional curvature. These relations have been assessed based on Direct Numerical Simulation (DNS) databases of turbulent premixed (a) statistically planar and (b) statistically axisymmetric Bunsen flames. It has been found that the analytically derived relation interlinking the PDFs of actual three-dimensional curvature and its two-dimensional counterpart holds reasonably well for a range of curvatures around the mean value defined by the inverse of the thermal flame thickness for different turbulence intensities across different combustion regimes. The flame surface is shown to exhibit predominantly two-dimensional cylindrical curvature but there is a significant probability of finding saddle type flame topologies and this probability increases with increasing turbulence intensity. The presence of saddle type flame topologies affects the ratios of second and third moments of two-dimensional and three-dimensional curvatures. It has been demonstrated that the ratios of second and third moments of two-dimensional and three-dimensional curvatures cannot be accurately predicted based on two-dimensional measurements. The ratio of the third moments of two-dimensional and three-dimensional curvatures remains positive and thus the qualitative nature of curvature skewness can still be obtained based on two-dimensional curvature measurements. As the curvature skewness is often taken to be a marker of the Darrius-Landau instability, the conclusion regarding the presence of this instability can potentially be taken from the two-dimensional curvature measurements.

Meshed axisymmetric flame simulation and temperature reconstruction using light field camera

Axisymmetric flames are widely used in research on flame combustion mechanisms and mass and heat transfer because of their simple structure and applicability to complex reactions and transfer calculations. A new optical diagnostic method named light field camera has been validated as applicable for online detection of the temperature field of an axisymmetric flame. Reconstruction algorithms can be used to estimate the distribution of the flame temperature from the light field images and validated by setting a known distribution of temperature and radiative properties. In the present study, a model of meshed axisymmetric flame light field imaging was put forward. The complicated distribution of temperature and radiative properties were considered in the model after validation using two absorption coefficients arranged at different region. An axisymmetric laminar coflow diffusion ethylene flame was modeled to generate input data. Then, the Lucy–Richardson and nearest neighbor filtering deconvolution algorithms were applied to the refocused light field images for sectional reconstruction of the temperature field. Under the condition of high temperature and soot generated from ethylene flame, the obtained reconstructed temperature was comparable to the input temperature from 1400 K to 2000 K, within the detectable radiative intensity range of the light field camera.

U-Net applied to retrieve two-dimensional temperature and CO[formula omitted] concentration fields of laminar diffusion flames

Direct absorption spectroscopy measurement of the 4.3μm CO2 using interband cascade laser with a high spectral resolution, provides theoretical feasibility to retrieve the spatial distribution of CO2 temperature and concentration in flames. However, retrieving temperature and concentrations from the line-of-sight spectral measurements involves solving non-linear and ill-posed problems. Traditional reconstruction algorithms for axisymmetric flames require multiple line-of-sight measurements in both axial and radial directions. The complicated experimental system limits the reconstruction efficiency. Here, a novel reconstruction model is proposed and demonstrated based on the U-Net model, a fully convolutional network model composed by a encoder–decoder path forming a symmetric U-shaped architecture, which only requires measurements of the central axis of the flame to simultaneously and efficiently reconstruct the two-dimensional temperature and CO2 concentration fields for axisymmetric flames. The U-Net model is trained using datasets from simulated temperature, CO2 concentration and their corresponding spectral optical thickness. The proposed U-Net model has been applied to reconstruct the two-dimensional temperature and CO2 concentration fields of two previously measured laminar diffusion flames. Comparing with results from the traditional Abel inversion and two-line atomic fluorescence thermometry methods, the U-Net reconstruction model can better preserve the spatial continuity and correlation of flame temperature and CO2 concentration from information hidden in the flame spectral images, which considerably simplifies the measurement system and improves the reconstruction performance.

Geometry characterization and thermal radiation prediction of buoyant square and line diffusion flames based on 3D flame reconstruction

This paper presents an experimental study on the instantaneous and mean geometrical features and radiation properties of buoyant square and line diffusion flames with heat release rates (Q˙) of 5.0–30.0 kW using the visual hull reconstruction method. Equal fuel exit areas were selected for the square and linear burners to reveal the effect of fire source shape on the combustion process. Results show that the reconstructed three-dimensional (3D) instantaneous flames could well reflect the temporal evolutions of the square and line flames. The instantaneous flame surface area and volume exhibit excellent synchronization with time. Consistent with the predictions based on the turbulent mixing concepts, the mean flame surface area and volume of the square flame are lower than the line flame under equal Q˙. The heat release rates per unit surface area remain unchanged, and the heat release rates per unit volume decrease slightly with Q˙ for the square and line flames. The mean beam lengths, calculated from the mean flame surface area and volume of the 3D flame shape, increase with Q˙ steadily for the two types of flames. A 3D flame radiation model is developed based on the reconstructed 3D instantaneous flame shape. It could accurately predict the instantaneous and time-averaged radiative heat fluxes in the near-field and far-field for axisymmetric and non-axisymmetric flames.