Flame Surface Density Research Articles

Modeling the initial flame acceleration in an obstructed channel using large eddy simulation

The propagation and acceleration of a flame surface past obstructions in a closed square channel was investigated using large eddy simulation. The dynamic Smagorinsky–Lilly subgrid model and the Boger flame surface density combustion model were used. The geometry is essentially two-dimensional with fence-type obstacles distributed on the top and bottom surfaces, equally spaced along the channel length at the channel height. Flame propagation, however, is three dimensional as ignition occurs at a point at the center of the channel cross-section. The effect of obstacle blockage ratio on the development of the flame structure was investigated by varying the obstacle height. Three-dimensional cases were simulated from the initiation of a combustion kernel through spark ignition to the acceleration of the flame front at speeds up to 80 m/s. The transition from laminar flame propagation to turbulent flame propagation within the “thin reaction zone” regime was observed in the simulations. By analyzing the development of the three dimensional flame surface and unburned gas flow field, the formation of several flame structures observed experimentally are explained. Global quantities such as the total flame area and centerline flame velocity were ascertained and compared to the experimental data. High amplitude oscillations in the centerline flame velocity were found to occur from a combination of the unburned gas flow field and fluctuations in the volumetric burning rate.

G061056 球状伝播予混合乱流火炎の火炎面密度に及ぼす当量比の影響([G061-05] 熱工学部門,一般セッション(5) : ふく射,燃焼(1))

G061056 球状伝播予混合乱流火炎の火炎面密度に及ぼす当量比の影響([G061-05] 熱工学部門,一般セッション(5) : ふく射,燃焼(1))

Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames

The tomographic reconstruction of OH* chemiluminescence was performed on two interacting turbulent premixed bluff-body stabilized flames under steady flow conditions and acoustic excitation. These measurements elucidate the complex three-dimensional (3D) vortex–flame interactions which have previously not been accessible. The experiment was performed using a single camera and intensifier, with multiple views acquired by repositioning the camera, permitting calculation of the mean and phase-averaged volumetric OH* distributions. The reconstructed flame structure and phase-averaged dynamics are compared with OH planar laser-induced fluorescence and flame surface density measurements for the first time. The volumetric data revealed that the large-scale vortex–flame structures formed along the shear layers of each flame collide when the two flames meet, resulting in complex 3D flame structures in between the two flames. With a fairly simple experimental setup, it is shown that the tomographic reconstruction of OH* chemiluminescence in forced flames is a powerful tool that can yield important physical insights into large-scale 3D flame dynamics that are important in combustion instability.

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for “ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to “ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observed.

Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling

In this paper it is investigated whether the Flame Surface Density (FSD) model, developed for turbulent premixed combustion, is also applicable to stratified flames. Direct Numerical Simulations (DNS) of turbulent stratified Bunsen flames have been carried out, using the Flamelet Generated Manifold (FGM) reduction method for reaction kinetics. Before examining the suitability of the FSD model, flame surfaces are characterized in terms of thickness, curvature and stratification. All flames are in the Thin Reaction Zones regime, and the maximum equivalence ratio range covers 0.1⩽φ⩽1.3. For all flames, local flame thicknesses correspond very well to those observed in stretchless, steady premixed flamelets. Extracted curvature radii and mixing length scales are significantly larger than the flame thickness, implying that the stratified flames all burn in a premixed mode. The remaining challenge is accounting for the large variation in (subfilter) mass burning rate. In this contribution, the FSD model is proven to be applicable for Large Eddy Simulations (LES) of stratified flames for the equivalence ratio range 0.1⩽φ⩽1.3. Subfilter mass burning rate variations are taken into account by a subfilter Probability Density Function (PDF) for the mixture fraction, on which the mass burning rate directly depends. A priori analysis point out that for small stratifications (0.4⩽φ⩽1.0), the replacement of the subfilter PDF (obtained from DNS data) by the corresponding Dirac function is appropriate. Integration of the Dirac function with the mass burning rate m=m(φ), can then adequately model the filtered mass burning rate obtained from filtered DNS data. For a larger stratification (0.1⩽φ⩽1.3), and filter widths up to ten flame thicknesses, a β-function for the subfilter PDF yields substantially better predictions than a Dirac function. Finally, inclusion of a simple algebraic model for the FSD resulted only in small additional deviations from DNS data, thereby rendering this approach promising for application in LES.

Multiply conditioned analyses of stratification in highly swirling methane/air flames

The effects of stratification on a series of highly swirling turbulent flames under globally lean conditions (ϕg=0.75) are investigated using a new high-spatial resolution multi-scalar dataset. This dataset features two key properties: high spatial resolution which approaches the 60 micron optical limit of the measurement system, and a wavelet oversampling methodology which significantly reduces the influence of noise. Furthermore, the very large number of realizations (30,000) acquired in the stratified cases permits statistically significant results to be obtained even after aggressive conditioning is applied. Data are doubly conditioned on equivalence ratio and the degree of stratification across the flame in each instantaneous realization. The influence of stoichiometry is limited by conditioning on the equivalence ratio at the location of peak CO mass fraction, which is shown to be a good surrogate for the location of peak heat release rate, while the stratification is quantified using a linear gradient in equivalence ratio across the instantaneous flame front. This advanced conditioning enables robust comparisons with the baseline lean premixed flame. Species mass fractions of both carbon monoxide and hydrogen are increased in temperature space under stratified conditions. Stratification is also shown to significantly increase thermal gradients, yet the derived three-dimensional flame surface density is shown to be relatively insensitive to stratification. Whilst the presence of instantaneous stratification broadens the curvature distribution relative to the premixed case, the degree of broadening is not significantly influenced by the range of global stratification ratios examined in this study.

Two-dimensional direct numerical simulation evaluation of the flame-surface density model for flames developing from an ignition kernel in lean methane/air mixtures under engine conditions

Flame surface density (FSD) models are often used in premixed turbulent combustion modeling to provide closure in large eddy simulations (LES) and Reynolds-averaged simulations. In the present study, data obtained from direct numerical simulation, with reduced chemistry, of flames developing from ignition kernels in lean methane-air mixtures is used to study the accuracy of the FSD modeling terms for LES applications. This study is conducted at elevated temperature and pressure conditions relevant to lean-burn natural gas engines. The closure models for four terms in the FSD transport equation are studied. It is observed that the propagation term as resolved by the LES grid adequately models the actual propagation term without additional sub-grid scale modeling. On the other hand, the closure of the curvature term requires a sub-grid scale model. Two sub-grid scale curvature models are studied and it is seen that there are differences between the actual and the modeled curvature terms during the early evolution of the ignition kernel. The agreement improves as the developing flame approaches a statistically steady-state. The modeling of the sub-grid convection term is analyzed and differences between the actual and the modeled terms are observed to grow during the transient evolution of the ignition kernel. A sub-grid scale model for the closure of the strain rate term shows disagreement at both early and late stages of kernel growth. In general, the sensitivity of the strain rate and curvature models to the filter width is found to be greater than for convection and propagation.

Measurements of the Three-Dimensional Structure of Flames at Low Turbulence

The development of spark-ignited flame kernels in a turbulent field is strongly dependent upon the nature of the three-dimensional (3-D) turbulence adjacent to the ignition source. The turbulence scales vary in 3-D from shot to shot, resulting in successive flame kernels developing differently and thereby causing cyclic variations in, for example, spark ignition engines. It is necessary to quantify the scales affecting the flame at any instant for the accurate measurement of burn rate of such flame kernels, which requires visualization of the flame surface in 3-D. The experiments reported here employ a multiple sheet mie-scattered light technique to successfully characterize a nonstabilized expanding turbulent flame kernel in 3-D. A novel algorithm was developed to construct the flame surface in 3-D, which enabled accurate calculation of parameters such as flame surface density, reaction progress variables, and turbulent flame thickness.

Large eddy simulations of the Darmstadt turbulent stratified flame series

Large-eddy simulations of the Darmstadt turbulent stratified flame (TSF) burner are presented. The TSF burner is operated under a wide variety of conditions. A case without stratification or shear, and one with stratification but no shear, are considered for validation purposes. A combined mixture fraction and reaction progress variable approach is used, with the reaction rate modelled by a fractal flame wrinkling flame surface density model, where the laminar flame speed is obtained as a function of the mixture fraction. The simulation results and the suitability of the modelling approach are verified and validated through comparison of mean and variance of axial and radial velocity, temperature and mixture fraction with experimental data. The effects of stratification on the flame flow field are then studied by comparing the two reactive simulations, and studying the impact of the cross-scalar dissipation rate term. Finally, the occurrence of potential back- or front-supported stratification is examined through statistical analysis of the flame normal directions. The modelling approach employed was found to produce very good predictions of the TSF burner, with both back- and front-supported stratification modes occurring, the former being considerably more likely.

Influence of turbulence–kernel interactions on flame development in lean methane/air mixtures under natural gas-fueled engine conditions

Direct numerical simulations (DNS) with reduced chemistry are carried out to study the influence of flow velocity and length scales on flames developing from flame kernels in lean methane/air mixtures. This study is conducted at elevated temperature and pressure conditions relevant to lean-burn natural gas engines. There are two effects which come into consideration: the interaction of turbulence with the kernel and the interaction with the local flame. A range of scales is selected so that interactions in different regimes can be studied. A flame surface density (FSD) approach is used to determine the evolution of flame area and study how the length and velocity scales enhance or diminish flame development. From the perspective of engine performance, it is observed that shorter length scales lead to faster growth of flame kernels. The ratio of kernel diameter to length scale ratio is identified as an independent controlling variable and its effect is studied by varying the initial size of the flame kernel. Smaller ratios result in a faster increase in the flame area. It is also observed that larger velocity scales lead to higher rates of heat release.

Turbulent Reynolds number dependence of flame surface density transport in the context of Reynolds averaged Navier–Stokes simulations

The influence of turbulent Reynolds number Ret on the statistical behaviour and modelling of flame surface density (FSD) transport has been analysed using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with values of Ret ranging from 20 to 100. The variation of Ret is brought about by modifying the Damköhler and Karlovitz numbers independently of each other. The findings indicate that the qualitative behaviour of the various terms of the FSD transport equation remains unaffected by the changes in turbulent Reynolds number, but their relative contributions to the transport of FSD are affected to some extent. The effects of turbulent Reynolds number on the modelling of the turbulent transport term, the tangential strain rate term and the combined propagation and curvature terms are addressed in detail. It is demonstrated that model parameters for the turbulent transport and tangential strain rate term exhibit turbulent Reynolds number dependence for small values of Ret and assume asymptotic values for Ret⩾50. By contrast, the model parameters for the combined propagation and curvature term are found to be insensitive to the variation of turbulent Reynolds number. Existing models for the turbulent transport term and the tangential strain rate term are modified to account for the observed turbulent Reynolds number dependence.

Turbulent premixed flame front dynamics and implications for limits of flamelet hypothesis

Turbulent premixed flames of methane–air and propane–air stabilized on a Bunsen-type burner were studied to investigate the dynamics and structure of the flame front at a wide range of turbulence intensities. The non-dimensional turbulence rms velocity, rms velocity divided by the laminar flame velocity, covered the range from about 3 to 24. The equivalence ratio was varied from 0.6 (0.7 for propane) to stoichiometric. The flame front data were obtained using planar Rayleigh imaging, and particle image velocimetry was used to measure instantaneous velocity field for the experimental conditions studied. The gradients of temperature profiles decreased noticeably with increasing non-dimensional turbulence rms velocity. Flame front curvature statistics indicated that the curvature probability density functions are highly symmetric. Frequency of crossing from negative to positive (and vice versa) curvatures did not show any clear sensitivity to non-dimensional turbulence rms velocity, but decreased by increasing fuel–air equivalence ratio. The product of curvature and diffusivity, a crucial term in the level-set equation proposed for the thin reaction zones regime, was found to be very small as compared to laminar burning velocity, but the product of rms curvature and diffusivity was higher than the laminar burning velocity. Flame surface densities integrated over the flame brush volume did not show any sensitivity to the non-dimensional turbulence rms velocity. Some of the single shot Rayleigh temperature profiles at higher turbulence intensities were radically different than those at lower intensities which are similar to laminar flame profiles. These findings question the validity of the flamelet hypothesis in the thin reaction zones regime where Karlovitz number exceeds unity.

Turbulent premixed flame characteristics of a CO/H2/O2 mixture highly diluted with CO2 in a high-pressure environment

Characteristics of turbulent premixed flames of a CO/H2/O2 mixture highly diluted with CO2 (CO/H2/CO2/O2 flame) at high pressures up to 1.0MPa were experimentally investigated. The CO/H2 ratio, equivalence ratio and CO2 mole fraction were determined considering the typical composition of coal gasification syngas, laminar burning velocity, adiabatic flame temperature and stoichiometry for IGCC gas-turbine combustors connected to CCS systems. OH–PLIF and flame radiation measurement were performed for Bunsen-type flames stabilized in a high-pressure chamber. Using OH–PLIF images, flame surface density, mean volume of turbulent flame regions and turbulent burning velocity were calculated and compared with those for CH4/air flames and model coal gasification syngas flames burnt with air (CO/H2/CO2/air flame). The flame surface density for the CO/H2/CO2/O2 flames was much greater than that for the CH4/air flames, even greater than that of the CO/H2/CO2/air flames, presumably due to less flame passivity against turbulent vortex motion caused by smaller Markstein length and smaller scales of flame wrinkles at high pressure. The mean volume of the turbulent flame region for the CO/H2/CO2/O2 flames was close to that of CO/H2/CO2/air flames, while much smaller than that of the CH4/air flames, which was also explicable based on the Markstein length effects on turbulent flames at high pressure. ST/SL of the model syngas flames was larger than that of the CH4/air flames and it was noted that the difference in turbulence Reynolds number caused by smaller kinematic viscosity of the CO/H2/CO2/O2 mixture should be considered to understand the ST/SL characteristics. Total radiation intensity of the CO/H2/CO2/O2 flame was about 1.6 times stronger than that of CH4/air flames due to the very high CO2 concentration, CO2 being a highly radiative species, indicating very high heat-load for gas-turbine combustors that should be considered for combustor design.

Scalar dissipation rate modelling for Large Eddy Simulation of turbulent premixed flames

The statistical behaviours of scalar dissipation rate (SDR) in the context Large Eddy Simulations (LES) of turbulent premixed combustion have been analysed using a simplified chemistry based Direct Numerical Simulations (DNS) data of a turbulent V-flame. The filter size dependence of the SDR is analysed in detail and it has been demonstrated that the filtered reaction rate can be satisfactorily closed using the Favre filtered SDR provided the filter width, Δ, remains greater than the thermal flame thickness, δth. Due to the close relation between the SDR and generalised Flame Surface Density (FSD), the dependence of the FSD on filter size has also been addressed. It has been found that a fractal dimension based power-law model satisfactorily captures the global and local behaviours of the generalised FSD in the context of LES. The fractal dimension and the inner cut-off scale for flame surface based on the volume-averaged value of the FSD are found to be in good agreement with previous analytical, experimental and DNS studies. The ratio of the volume-integrated filtered value of density-weighted SDR to its resolved component exhibits a power-law in terms of Δ with an inner cut-off scale scaling with δth. A power-law based model with a global exponent and inner cut-off scale is found to be insufficient to capture the local variations of SDR possibly due to its multi-fractal nature. An algebraic model for SDR, which was originally proposed for Reynolds Averaged Navier Stokes simulations, has been extended here for LES, which is found to satisfactorily capture both the global and local behaviours of SDR.

The structure of turbulent stratified and premixed methane/air flames II: Swirling flows

Experimental results are presented from a series of turbulent methane/air stratified flames stabilized on a swirl burner. Nine operating conditions are considered, systematically varying the level of stratification and swirl while maintaining a lean global mean equivalence ratio of ϕ¯=0.75. Scalar data are obtained from Rayleigh/Raman/CO laser induced fluorescence (CO-LIF) line measurements at 103μm resolution, allowing the behavior of the major combustion species—CH4, CO2, CO, H2, H2O and O2—to be probed within the instantaneous flame front. The corresponding three-dimensional surface density function and thermal scalar dissipation rate are investigated, along with geometric characteristics of the flame such as curvature and flame thickness. Hydrogen and carbon monoxide levels within the flame brush are raised by stratification, indicating models with laminar premixed flame chemistry may not be suitable for stratified flames. However, flame surface density, scalar dissipation and curvature all appear insensitive to the degree of stratification in the flames surveyed.

Dynamic flame surface density modelling of flame deflagration in vented explosion

The propagation of transient, turbulent premixed flames in a vented explosion chamber in the presence of a series of obstacles is numerically investigated by a dynamic formulation for the Flame Surface Density (FSD) with the Large Eddy Simulations (LES) technique. The chemistry is modelled by a one-step overall reaction, which simulates the reaction of a stoichiometric propane-air mixture. The FSD modelling in the reaction rate model is numerically employed with two different sub-grid scale (SGS) models. The first one is based on an empirical correlation of the SGS velocity fluctuations and the second one is based on similarity ideas involved in solving the wrinkled flame front considered as a fractal surface. The numerical predictions are analyzed and compared against an algebraic, simple FSD model together with experimental data. The calculations show that the dynamic FSD models provide superior results as compared with the algebraic FSD model. The comparisons demonstrate the importance of the contributions from the unresolved FSD and provide good agreement with experimental data for the flame structure, overpressure, and burning velocities.

Large Eddy Simulation of Turbulent Combustion in a Spark-Assisted Homogenous Charge Compression Ignition Engine

A large eddy simuation (LES) model is presented for simulation of spark-assisted homogeneous charge compression ignition combustion. The model is based on tabulated chemical kinetic rate for ignition and flame surface density for flame propagation, taking into account interaction between flame propagation introduced by the spark and auto-ignition due to charge compression. The model is used to simulate the combustion process in an experimental HCCI engine, with operation conditions ranging from spark-ignition controlled flame propagation to auto-ignition controlled HCCI combustion. The model is shown to be able to predict the combustion behavior observed in previous engine experiments. With low initial temperature, the SI flame mode prevails; with high initial temperature, the HCCI mode prevails. With moderate initial temperature, the SI flame and HCCI ignition interact more closely, which results in higher sensitivity to the initial temperature and turbulence conditions. This may be the reason of the observed high cyclic variation in the experiments.

A PDF combustion model for turbulent premixed flames

In this paper we propose a novel model for turbulent premixed flames in the corrugated flamelet regime. The model combines the premixed flamelet approach with a BML ansatz in a PDF framework. For this purpose we introduce a progress variable, which is zero for unburnt and equal to one for reacting and burnt state. The probability that the progress variable switches from zero to one depends on the flame surface density (FSD). The FSD itself is modeled based on a modified flame residence time starting when the progress variable switches to one. To account for flame curvature, collapse and cusp formation, a stretch factor consistent with existing FSD transport equation source terms is employed to modify the flame residence time. To evolve the sensible enthalpy, conditional mixing is applied, which prevents mixing across the flame front. If the progress variable is one, a premixed flamelet is employed. With this approach, some model difficulties related to solving transport equations for the mean FSD and progress variable are overcome. For example, counter-gradient diffusion and FSD transport due to flame propagation appear in closed form. The combination of the BML approach with a flamelet model leads to more accurate temperature predictions, which is demonstrated for the Aachen flames F1–F3.

Flame structure changes resulting from hydrogen-enrichment and pressurization for low-swirl premixed methane–air flames

With the current focus on alternate and renewable fuels, fuel flexibility has become a driving factor in the design of new turbines. Flame stability is heavily impacted by the presence of hydrogen in the fuel stream (as is common in many alternative fuels). This study examines how the flame dynamics change in response to the systematic addition of hydrogen in a low-swirl lean premixed methane–air burner. Stability maps for these test cases show that adding hydrogen broadens the blow-off limits, with 20% hydrogen resulting in a 7% change while 40% hydrogen results in a 35% larger stable region. The most dramatic manifestation of hydrogen addition is the greatly decreased radius of curvature of the local flame surface, which is visible from the increased wrinkling of the flame front. Increases in both pressure and hydrogen enrichment result in higher means and variances of flame front curvatures. The flame surface density is in agreement with the aforementioned flame front curvature PDFs in that increasing the pressure and hydrogen concentration leads to an increase in the maximum flame surface density.

Large eddy simulation of a growing turbulent premixed flame kernel using a dynamic flame surface density model

The relevant description of a flame kernel growth in homogeneous isotropic turbulence environment is a key ingredient for the simulation of combustion in spark-ignited internal combustion engine. A small flame kernel burns at an increasing rate as it grows and becomes progressively more and more wrinkled by the prevailing turbulence. Large eddy simulation (LES) models based on algebraic expressions for the turbulent flame speed, the flame surface density or the flame wrinkling factor cannot reproduce such a situation because they assume an equilibrium between turbulence and flame wrinkling which is generally not reached during the simulation as the flame is laminar at early stages. A possible solution is to solve an additional balance equation for the flame surface density or for the wrinkling factor but a promising alternative is to implement a dynamic model where the wrinkling factor, measuring the subgrid scale flame surface, is automatically determined along the computation from the known instantaneous resolved flame front. A Germano-like identity expresses the conservation of the total flame surface at filter and test filter scales to automatically adjust the parameter of a fractal-like wrinkling factor model from the instantaneous resolved flame front characteristics. This model is tested against the experimental data of Renou et al. (2000) [33] to reproduce the temporal evolution of the flame kernel growth. For a range of ignition parameters, preliminary results are in good agreements with experimental data and show that the model parameter evolves with time and depends on operating conditions, validating the dynamic procedure.