Planar Flame Research Articles

The effects of steam addition on the unstable behavior of hydrogen-air lean premixed flames under the adiabatic and non-adiabatic conditions

The effects of steam addition on the unstable behavior of hydrogen-air lean premixed flames under the adiabatic and non-adiabatic conditions were investigated using numerical calculations. We adopted the detailed chemical reaction mechanism for hydrogen-oxygen combustion, modeled with seventeen reversible reactions of eight reactive species and a diluent. Two-dimensional unsteady reactive flow was treated, based on the compressible Navier-Stokes equations. The burning velocity of a planar flame decreased as the steam addition and heat loss increased. A sufficiently small disturbance was superimposed on a planar flame to study the characteristics of intrinsic instability. We obtained the relation between the growth rate and wave number, i.e. the dispersion relation, and the linearly most unstable wavelength, i.e. the critical wavelength. As the steam addition increased, the unstable range became narrower, and the critical wavelength became longer. Taking account of heat loss, we obtained smaller growth rates and narrower unstable range. The superimposed disturbance developed owing to intrinsic instability, and then the cellular shape of flame fronts appeared. In cellular flames, compared with planar flames, high (low) concentration of active chemical species was found in downstream of convex (concave) fronts. This was caused by high (low) temperature at convex (concave) fronts due to the diffusive-thermal effects. The concentration of active chemical species became lower with increasing the steam addition and heat loss, which was because of the reduction of flame temperature. Moreover, the burning velocity of a cellular flame increased monotonically with an increase in the scale of premixed flames. The burning velocity of a cellular flame normalized by that of a planar flame increased as the steam addition and heat loss increased. The numerical results denoted that the steam addition and heat loss had a great influence on the unstable behavior of hydrogen-air lean premixed flames.

Principal strain rate evolution within turbulent premixed flames for different combustion regimes

The statistical behaviors of the principal strain rates and its evolution in turbulent premixed flames have been analyzed using a three-dimensional direct numerical simulations dataset of statistically planar turbulent premixed flames with different turbulence intensities spanning from the corrugated flamelet regime to the thin reaction zone regime. It has been found that the scalar gradient predominantly aligns collinearly with the most extensive principal strain rate eigendirection within the flame for large values of Damköhler numbers and small values of turbulence intensities and Karlovitz numbers. However, this tendency weakens with the increasing turbulence intensity, which, for a given integral length scale, amounts to a decrease (an increase) in the Damköhler (Karlovitz) number. Moreover, it has been observed that the terms due to molecular diffusion, pressure Hessian, and the correlation between pressure and density gradients play key roles in the evolution of principal strain rates for flames with large values of Damköhler numbers and small values of Karlovitz numbers. However, the relative importance of the terms arising from the correlation between pressure and density gradients and the pressure Hessian relative to the strain rate and vorticity contributions of the principal strain rate transport diminishes with the increasing Karlovitz number and decreasing Damköhler number. The statistical behaviors of the mean values of the terms of the transport equation of the principal strain rate have been explained based on the relative alignments of principal strain rate eigenvectors with vorticity, pressure gradient, and the eigenvectors of the pressure Hessian tensor. The findings of the current analysis suggest that the pressure gradient and pressure Hessian tensor play key roles in the evolution of principal strain rates within premixed turbulent flames, and their influence needs to be accounted for high fidelity modeling of the tangential strain rate and scalar–turbulence interaction terms of the flame surface density and scalar dissipation rate transport equations, respectively. This provides possible explanations for the modification in the alignment of the reactive scalar gradient with local principal strain rates in premixed flames in comparison to that in non-reacting turbulent flows.

The relation between flame surface area and turbulent burning velocity in statistically planar turbulent stratified flames

The relation between turbulent burning velocity and flame surface area for turbulent stratified flames has been analyzed using a direct numerical simulation database. The simulations have been carried out for different initial turbulence intensities and initial integral length scales of equivalence ratio fluctuation for a given root-mean-square value in a globally stoichiometric mixture. Additionally, statistically similar turbulent premixed flames have been considered for comparison. The turbulent burning velocity and flame surface area for stratified flames are found to be significantly smaller than in premixed flames for slow mixing cases (large scalar integral length scale and low turbulence intensity), although this trend weakens in fast mixing cases (low scalar integral length scale and high turbulence intensity). In slow mixing cases, the increase in the burning rate occurs at a smaller proportion than the increase in the flame surface area. The contributions of the components arising from tangential diffusion of displacement speed and cross-scalar dissipation rate to the turbulent burning velocity are found to be negligible in comparison to that arising from the combined reaction and normal diffusion component for all cases. The increased probability of finding fuel-lean and fuel-rich mixture affects the contribution of turbulent burning velocity arising from the combined reaction and normal diffusion component of displacement speed for slow mixing cases. Front-supported flame elements dominate over back-supported flame elements for large scalar length scale cases, but this behavior reverses for small scalar length scale cases. These findings suggest that increases in the burning rate and flame surface area do not take place in the same proportions for turbulent stratified combustion.

Recent Progress in Hydrogen Flammability Prediction for the Safe Energy Systems

Many countries consider hydrogen as a promising energy source to resolve the energy challenges over the global climate change. However, the potential of hydrogen explosions remains a technical issue to embrace hydrogen as an alternate solution since the Hindenburg disaster occurred in 1937. To ascertain safe hydrogen energy systems including production, storage, and transportation, securing the knowledge concerning hydrogen flammability is essential. In this paper, we addressed a comprehensive review of the studies related to predicting hydrogen flammability by dividing them into three types: experimental, numerical, and analytical. While the earlier experimental studies had focused only on measuring limit concentration, recent studies clarified the extinction mechanism of a hydrogen flame. In numerical studies, the continued advances in computer performance enabled even multi-dimensional stretched flame analysis following one-dimensional planar flame analysis. The different extinction mechanisms depending on the Lewis number of each fuel type could be observed by these advanced simulations. Finally, historical attempts to predict the limit concentration by analytical modeling of flammability characteristics were discussed. Developing an accurate model to predict the flammability limit of various hydrogen mixtures is our remaining issue.

A 2-D DNS study of the effects of nozzle geometry, ignition kernel placement and initial turbulence on prechamber ignition

A parametric direct numerical simulation study was conducted to investigate the effects of the initial flow field (quiescent or turbulent), nozzle inlet sharpness and width, main chamber composition (lean and stoichiometric), and ignition kernel placement in a two-dimensional prechamber (PC) ignition system. The strongly coupled operating and geometric parameters determine the time at which the flame exits the prechamber, the transient structure and penetration of the initially cold and subsequently hot reactive jet and their impingement on the lower main chamber (MC) wall, affecting the combustion mode and the fuel consumption rate. The temperature of the flame reaching and crossing the nozzle is affected by the flame exit time and is significantly lower than the adiabatic flame temperature of the planar flame, although no quenching is observed. Interaction with the flow field (strong small scale vortices for narrow and sharp entry nozzles, large vortices for wide nozzles) generated close to the exit increases the surface area of the flame and its interaction with the MC mixture. Jet penetration and impingement on the lower MC wall is determined by combustion in the PC and the flow field it generates in the main chamber. Impingement results in large scale vortical structures, which further contribute to the flame area increase and accelerate the consumption of the MC charge at later times. For the conditions studied, budget analysis shows that the main combustion mode is premixed deflagration with locally enhanced or reduced reactivity. Local flame–flame interactions which are more pronounced close to the nozzle exit and the lower MC wall can increase the propagation speed up to six times compared to the planar flame. The evolution of the probability density functions of different quantities is used to characterize the strongly transient process.

Numerical study of the premixed ammonia-hydrogen combustion under engine-relevant conditions

Recently, ammonia is considered to be an energy medium for hydrogen or energy storage and ammonia/hydrogen can be a potential fuel blend for the spark-ignition engine. Nevertheless, the combustion properties of ammonia/hydrogen mixtures could be distinctive under different initial conditions. In this study, several essential combustion properties, including laminar burning velocity, minimum ignition energy, NOx and ammonia emissions, combustion efficiency, and mixture heating values of ammonia/hydrogen/air premixed combustion were extensively studied under a wide range of equivalence ratios (ϕ), hydrogen fractions (α) and different compression ratio using one-dimensional laminar planar flame and compared with stoichiometric methane, methanol, and ethanol combustion. The behavior of NOx generation changing with ϕ and α was analyzed in detail. Results showed that most properties of ammonia/hydrogen combustion could be comparable to that of hydrocarbon fuels under engine-relevant conditions, except for the mixture heating value is slightly lower in all conditions. Besides, the NO mole fraction non-monotonically changes with ϕ and α due to the competition between the effects caused by the reduction of nitrogen-atom species and the enrichment of H/O radicals. The NO mole fraction of stoichiometric ammonia/hydrogen could be even lower than that of hydrocarbons. Considering the properties of hydrocarbon fuels as a reference, promising working conditions for ammonia/hydrogen mixtures are ϕ from 1.0 to 1.05 and α from 40% to 60%. Besides, a high compression ratio is more suitable for ammonia/hydrogen mixtures due to the excellent knock resistance ability of NH3/H2 and better improvement than hydrocarbon fuels under high compression ratio.

Identification of the anti-diffusion coefficient for the linear Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky equation is a fourth-order partial differential equation used as a model for physical phenomena such as plane flame propagation and phase of turbulence. The inverse problem of recovering the second-order coefficient from the knowledge of the solution in final time, for the linear version of the equation, is studied in this article. The inverse problem is formulated as a regularized nonlinear optimization problem, from which the local uniqueness and the stability are proved. Finally, an algorithm for the reconstruction of the coefficient is proposed and several numerical simulations are presented.

Data driven analysis and prediction of MILD combustion mode

Abstract Direct numerical simulation (DNS) data of moderate or intense low-oxygen dilution (MILD) combustion and a planar flame are analysed to identify quantities influencing the unique features of co-existing combustion modes and develop a model to identify them in MILD combustion. The results show the existence of direct relationship between the scalar dissipation and reaction rates in MILD combustion, whereas the correlation is weaker than the planar flame. Also, rotational turbulent motions identified by the enstrophy-strain balance also show a substantial influence on the MILD combustion field, via the principal component analysis, suggesting the mechanism by which the non-flamelet part of reaction zones is controlled. A neural network (NN)-based model was proposed to identify the filtered local combustion mode for MILD combustion fields in LES context. The NN is trained based on DNS data of MILD combustion at two different conditions for different filter sizes. The model assessment was performed using the third MILD condition having a higher Ka and dilution level than those of the two training data sets. Several filter sizes ranging from 0.5 to 2.0 times of a corresponding laminar flame thickness were considered, and also prediction performance of a “zeroth-order model” is compared with that of the NN-based prediction. The assessment shows very high correlation between the NN-based prediction and the mode directly obtained from DNS. The predicted local combustion mode could be used to exploit advantages of both flamelet and non-flamelet-type combustion models to predict co-existing MILD reaction zones.

On the validity of Damköhler's second hypothesis in statistically planar turbulent premixed flames in the thin reaction zones regime

The validity of Damköhler's second hypothesis, which was originally proposed for premixed combustion for conditions where the large scale turbulent timescale remains smaller than the chemical timescale and the integral length scale remains smaller than the flame thickness, has been assessed for a range of Damköhler and Karlovitz numbers (i.e. 0.2≤Da≤3.0 and 0.58≤Ka≤33.34) using a three-dimensional DNS database of statistically planar turbulent premixed flames subjected to forced unburned gas turbulence. It has been found that Damköhler's first hypothesis remains valid for all cases considered in this work irrespective of the combustion regime. By contrast, Damköhler's second hypothesis does not hold in the strict sense for the thin reaction zones regime flames with small values of Damköhler number. However, the ratio of the turbulent flame speed normalised by laminar burning velocity and the square root of the ratio of turbulent diffusivity to mass diffusivity converges to a value of the order of unity for the flames with high turbulence intensity and low Damköhler number in the thin reaction zones regime. Under this condition, Damköhler's second hypothesis, in an order of magnitude sense, can be considered to be valid alongside Damköhler's first hypothesis. A scaling analysis has been carried out using the equilibrium of the tangential strain rate and curvature terms in the Flame Surface Density transport equation to demonstrate that Damköhler's second hypothesis can be expected to be valid only in an order of magnitude sense for the thin reaction zones regime flames with small values of Damköhler number.

An analysis of the stabilization of fire whirls

Stabilization of the flame base at the bottom Ekman boundary layer of the fire whirl under strong circulation is analytically and numerically studied. The problem is relevant for fire safety and the associated understanding of the generation mechanism of the newly discovered whirling flame, the so-called blue whirl. Based on the dynamic balance of the triple flame propagation speed and the local flow velocity at the bottom boundary layer, theoretical solutions of the liftoff position, rf, and the critical blowout limit represented by its Ekman number, EkBt, are derived. The theoretical results agree well with the numerical results both qualitatively and quantitatively. It is shown that the response of rf to the system Damköhler number, Da, forms a typical C-shaped curve and there are two solutions of rf for relatively large Da, with the one closer to the edge of the fuel pool being stable while the other being unstable. Explicit solution of the blowout limit shows that EkBt∝(SLS)4/3, where SLS is the stoichiometric planar flame speed. This is because not only the triple flame propagation speed linearly increases as SLS increases, but the flame front can also reach a position closer to the edge of the fuel pool where the flow velocity is lower. The effect of the transversal radial velocity gradient (TVG) at the Ekman boundary layer on the stabilization of the fire whirl is also investigated. The TVG makes the flame harder to liftoff and blowout and the effect of which can be described by a non-dimensional parameter, λ, which represents the ratio of the flame curvature and the TVG. The TVG normally plays a secondary role in the triple flame propagation due to the relatively large flame curvature of the triple flame.

Optimized chemistry for Large Eddy Simulations of wrinkled flames

State-of-the-art LES models have made significant progress in the prediction of heat release and flame propagation for a wide range of combustion regimes. Predicting pollutants remains however a difficult issue, especially in situations where sub-grid scale wrinkling is high. A novel strategy, named COPLES (Chemistry OPtimized for LES), is presented in this paper to account for the effect of sub-grid scale wrinkling on pollutants formation in a transported chemistry context and under flamelet regime assumption. New chemical mechanisms are built through an optimization process to recover the properties of filtered flames. Two alternative formulations are proposed. The first one consists in optimizing the COPLES parameters to retrieve the structure of Filtered Planar Flame (FPF) and to include separately the impact of sub-grid scale wrinkling. The second formulation targets directly a collection of Filtered Wrinkled Flamelets (FWF), so that the influence of turbulence on the chemical flame structure is intrinsically accounted for. The two approaches are successfully validated on 1-D freely propagating premixed flames and then challenged against the standard Thickened Flame for LES model on a turbulent premixed swirled combustor, experimented at Cambridge University. Whereas all formulations retrieve the temperature field, the COPLES-FWF model improves significantly the prediction of CO formation.

Structure and stability characteristics of turbulent planar flames with inhomogeneous jet in a concentric flow slot burner

Turbulent flames with compositionally inhomogeneous mixtures are common in many combustion systems. Turbulent jet flames with a circular nozzle burner were used earlier to study the impact of inhomogeneous mixtures, and these studies showed that the nozzle radius affects the flame stability. Accordingly, planar turbulent flames with inhomogeneous turbulent jet are created in a concentric flow slot burner (CFSB) to avoid this effect in the present study. The stability characteristics, the mixing field structure, and the flame front structure were measured, and the correlations between stability and the mixing field structure were investigated. The mixture fraction field was measured in non-reacting jets at the nozzle exit using highly resolved Rayleigh scattering technique, and the flame front was measured in some selected turbulent flames using high-speed Planar Laser-Induced Fluorescence (PLIF) of OH technique. The data show strong correlations between flame stability and the range of mixture fraction fluctuations. The flames are highly stabilized within a mixing field environment with the range of fluctuation in mixture fraction close to the range of the flammability limits. The mixing field structure is also illustrated and discussed using a mixing regime diagram and showed that the scatter of the data of the different cases is consistent with the classified mixing regimes. Lean flames are stabilized in the current slot burner. The flame front structure topology varies consistently from thin, small curvature at the low level of turbulence and higher equivalence ratio to more wrinkled, larger curvature, but a thicker structure at a higher level of turbulence and lower equivalence ratio.

Gradient Trajectory Analysis of the Burning Rate in Turbulent Premixed Jet Flames

ABSTRACT An analysis of the combustion process along gradient trajectories is presented for a set of Direct Numerical Simulations of turbulent premixed jet flames at different Reynolds numbers and approximately constant Karlovitz numbers. The variation of the jet Reynolds number, ranging from 5600 to 22400, is achieved by increasing the width of the jet and keeping the bulk velocity constant, which also implies approximately constant values of the turbulence intensities across the flames. The flames considered are nominally in the thin-reaction zone regime of the Borghi-Peters diagram of turbulent combustion. The thickening of the inner reaction layer and its enhancement with increasing Reynolds number, observed in previous works on the same database, is linked here to the presence of extremal points in the temperature field (local maxima in the low temperature side and minima in the high temperature side) in the vicinity or inside the inner reaction layer. Therefore, an enhancement of the turbulent flame speed is linked to the interruption of the flamelet structure by turbulence and not by the thickening of the entire flamelet itself. In addition to the expected large thickening of the formaldehyde layer, the layers of species which are characteristic of the inner reaction zone, such as OH and O, show a significant thickening and these species are observed several flame thicknesses ahead of the turbulent flame surface. Finally, it is shown that, in the regions where the inner reactive layer is thickened, the local fuel consumption rate is reduced in comparison to a laminar planar flame, but the total burning rate integrated over the entire flame structure is larger due to the increased volume of the reactive layer. These observations highlight the importance of assessing the balance between two competing phenomena related to high Karlovitz numbers. The first is the effect of turbulence strain and stirring on the chemistry, which usually decreases the local burning rate. The second is the effect on the species fields, which might experience modifications in their topology, such as the introduction of local extremal points, and significant thickening of the volumes between their isosurfaces.

Deep learning-based model for progress variable dissipation rate in turbulent premixed flames

A deep neural network (DNN) based large eddy simulation (LES) model for progress variable dissipation rate in turbulent premixed flames is presented. The DNN model is trained using filtered data from direct numerical simulations (DNS) of statistically planar turbulent premixed flames with n-heptane as fuel. Training data was comprised of flames with varying turbulence levels leading to a range of Karlovitz numbers. Through a-priori tests the DNN model is shown to predict the subfilter contribution to progress variable dissipation rate accurately over a range of filter widths and for all Karlovitz numbers examined in this study. Superior performance of the DNN model relative to an established physics-based model is also demonstrated. Additionally, transferability of the DNN model is highlighted by a-priori evaluation of the model using filtered DNS data from multiple cases with different Karlovitz numbers and fuel species than those that were used for training the model.

On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation

The Kuramoto-Sinelshchikov equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking in account the combined influence of diffusion and thermal conduction of the gas on the stability of a plane flame front. In this paper, we prove the well-posedness of the classical solutions for the initial-boundary value problem for this equation, under appropriate boundary conditions.

Propagation of heterogeneous and homogeneous planar flames in fuel droplet mists

Propagation of one-dimensional planar flames laden with fuel droplets is theoretically investigated in this work. Localized homogeneous and heterogeneous flames are considered, characterized by different relative locations of dispersed droplets and propagating flame front. With the assumption of large activation energy for the chemical reaction, correlations describing flame propagation speed, flame temperature, evaporation onset front and completion front are derived. The influences of droplet and fuel properties on propagation of fuel-droplet-laden planar flames are studied. The results indicate that the flames are enhanced under fuel-lean conditions but weakened under fuel-rich conditions. Both effects are intensified with increased droplet mass loading. Fuel vapor and temperature gradient are observed in the post-flame evaporation zone of heterogeneous flames. Evaporation completion front location is considerably affected by the droplet diameter, but the evaporation onset front varies little with droplet properties. Flame bifurcation occurs with high droplet mass loading under fuel-rich mixture, leading to multiplicity of flame propagation speed as well as droplet evaporation onset and completion fronts. Sprayed fuels with larger latent heat of vaporization would weaken the flame enhancement effect under fuel-lean conditions, due to larger evaporation heat loss. Moreover, for homogeneous flames, evaporative heat loss only occurs in the pre-flame zone. However, for heterogeneous flames, heat loss from the post-flame evaporation zone becomes dominant for relatively large droplets. Besides, for fuel-lean mixtures laden with medium-sized fuel droplets, the propagation speed of heterogeneous flames increases with Lewis number, due to the enhanced fuel vapor diffusion in the post-flame zone.

Reduced chemistry for sound generation by planar annihilation in premixed methane/hydrogen flames

Sound generation by planar flame annihilation for methane/hydrogen/air premixed flames is investigated using one-dimensional (1D) fully-resolved simulations. The Foundational Fuel Chemistry Model (FFCM) is used to undertake the simulations for different initial pressures and temperatures, for volumetric mixtures of 0 to 100% hydrogen in the fuel mixture. For cases with 25% to 80% of hydrogen in the fuel mixture three stages of annihilation are observed. The first stage exhibits a gradual flame extinction coupled with the generation of a pressure wave with a long wavelength. The second stage features a more rapid extinction as the flame accelerates towards the symmetry axis, producing a sharp pressure drop. The final stage exhibits a gradual decrease in pressure due to slow reactions such as CO oxidation. The contribution of the first stage increases as more hydrogen is added to the fuel. These stages are not distinctive when the fuel is pure hydrogen. The time derivative of the heat release rate is verified to be the dominant source of sound for annihilation events. A correlation linking the sound amplitude from planar annihilation events to key flame parameters is demonstrated to work for the studied fuel blends. The FFCM is then reduced using a modified Directed Relation Graph with Error Propagation and Sensitivity Analysis (DRGEPSA) method with error bounds based on the laminar flame speed, sL. A good agreement between the sL predictions for the reduced and the detailed mechanisms are found. Furthermore, the developed reduced mechanisms in this work are shown to predict the generated sound by flame annihilation accurately.

A comparison of entrainment velocity and displacement speed statistics in different regimes of turbulent premixed combustion

The statistics of entrainment velocity, defined as the displacement speed of an enstrophy isosurface, which can be taken to be the interface between turbulent/non-turbulent regions, have been analysed using a Direct Numerical Simulation database of statistically planar H2-air flames with a range of different Karlovitz numbers. It has been found that the component of the entrainment velocity arising from molecular dissipation plays a leading order role for all values of Karlovitz number, whereas the relative importance of the baroclinic torque and dilatation rate weakens with increasing Karlovitz number. By contrast, the relative contribution of the entrainment velocity component arising from vortex-stretching strengthens with increasing Karlovitz number Ka. The mean entrainment velocity remains positive for the case representing the corrugated flamelets regime (i.e. Ka<1), whereas it assumes negative values in the cases with large values of Karlovitz number (i.e. Ka≫1). The magnitude of the ratio of the mean values of entrainment velocity to the mean values of flame displacement speed conditional upon non-dimensional temperature within the flame front remains of the order of unity irrespective of Karlovitz number. However, the probability density functions of entrainment velocity exhibit considerably higher probabilities of finding large magnitudes than in the case of flame displacement speed. The alignments between the normal vector on the enstrophy isosurface and local principal strain rates have been found to be qualitatively similar to the corresponding alignments between flame normal and local principal strain rates, and the same holds true for the distributions of curvature shape factor of reaction progress variable and enstrophy isosurfaces. These findings indicate that the isosurface topologies and the alignments of normal vectors with local principal strain rates for enstrophy and reaction progress variable exhibit qualitatively similar behaviours. Consequently, turbulence and combustion modelling strategies cannot be considered in isolation in premixed turbulent flames.

Nonlinear Flame Dynamics for Laminar Flame in a Co-flow Mixing Layer with Widely Varying Premixedness: Preferential Diffusion and Stoichiometry Effects

ABSTRACT Intrinsic oscillations arising due to thermo-diffusive mechanism have been studied numerically in the literature for laminar flames having Lewis number greater than unity. In the previous work, the Lewis numbers of fuel and oxidizer are assumed to be equal and the unburnt mixture to be in stoichiometric in proportion. Here, the study is extended to relax these assumptions. In the first part of the present work, the Lewis numbers of fuel and oxidizer are varied individually keeping the overall mixture stoichiometric. The simulations are run for laminar flames stabilized near to a cold burner in a co-flow mixing layer generated by a fuel rich stream and oxidizer rich stream. The premixedness of the unburnt mixture is varied using a premixedness parameter defined in the previous work. This parameter characterizes upstream mixture-fraction gradients such that it approaches unity for zero mixture-fraction gradient and zero when the mixture-fraction gradient is infinite. Thus, upon ignition, different flame structures like, planar premixed flame, triple flames and an edge flame can be observed, as this parameter is varied from zero to unity. Simulations are run to study large time behavior for various values in this range of premixedness. Intrinsic oscillations in the total reaction rate (integrated over the domain) are observed for a combination of values of Lewis numbers of fuel and oxidizer. These are presented as series of contour plots of amplitude of total reaction rate onto a 2D plane with Lewis number of fuel on x-axis and Lewis number of oxidizer on y-axis for various values of premixedness. It is found that the contours of constant amplitude are nearly linear for diffusion flame and partially premixed flames, thus validating the effective Lewis number definition hitherto defined for diffusion flames. Hence, this effective Lewis number can determine the onset of oscillations and also their magnitude. But for weakly curved triple flames, there is significant variation, where the constant amplitude lines are curved. Also, the amplitude of oscillations observed for weakly curved triple flames is much higher than that for other flames. Apart from intrinsic oscillations the shape and structure of triple flame is also studied. It is found that premixed flame branches of a triple flame are highly asymmetric about the trailing edge diffusion flame. The change in the location of triple point is also observed. In the second part of the work, the assumption of the overall stoichiometric ratio being unity is relaxed to understand the effect of the off-stoichiometric mixture on the shape and stability of flame. However, the Lewis numbers of the fuel and oxidizer are maintained to be equal. The maximum intensity of oscillations is observed at an equivalence ratio of 0.3 for partially premixed flames and at around unity for premixed flames.

Subgrid modeling of intrinsic instabilities in premixed flame propagation

This work is devoted to the investigation and subgrid-scale modeling of intrinsic flame instabilities occurring in the propagation of a deflagration wave. Such instabilities, of hydrodynamic and thermodiffusive origin, are expected to be of particular relevance in recent technological trends such as in the use of hydrogen as a clean energy carrier or as a secondary fuel in hydrogen enriched combustion. A dedicated set of direct numerical simulations is presented and used, in conjunction with coherent literature results, in order to develop scaling arguments for the propagation speed of self-wrinkled flames which are also supported by the outcomes of a weakly non-linear model, namely the Sivashinsky equation. The observed scaling is based on the definition of the number of unstable wavelengths in a reference hydrodynamic lengthscale, in other words the ratio between the neutral or cutoff lengthscale of intrinsic instabilities and the lateral domain of a planar flame. The scalings are then employed to develop an algebraic model for the wrinkling factor in the context of a flame surface density closure approach. An a-priori analysis shows that the model correctly captures the flame wrinkling caused by intrinsic instability at sub grid level. A strategy to include the developed self-wrinkling model in the context of a turbulent combustion model is finally discussed on the basis of the turbulence induced cut-off concept.