Flame Curvature Research Articles

Flame dynamic insights into pollutant production characteristics of NH[formula omitted]/H[formula omitted]/air combustion during turbulent flame–wall interaction

A turbulent premixed NH3/H2/air flame with Damköhler number Da = 0.004 has been simulated using direct numerical simulations (DNS) with detailed chemistry. The flame is propagating in a fully-developed turbulent channel flow with friction Reynolds number Reτ = 313. The global and local production speeds of NO, N2O and NH3 have been analyzed. Special attention is paid on the flame dynamic insights into the pollutant production characteristics during the flame–wall, flame–turbulence and flame–flame interaction process. Finally, important findings have been concluded: (1) The unburned NH3 is reduced in the turbulent case due to the smaller quenching distance; (2) The N2O consumption speed would decrease just before flame quenching on the wall in the turbulent case, due to the thickened flame thickness, which is contradictory to the laminar case; (3) Effect of flame curvature on pollutant production speeds should be combined with the effect of flame surface density; (4) Low Damköhler number flame tends to produce more N2O and less NO, due to the more frequent flame–flame interaction events. These findings would help to better understand the pollutant production characteristics of turbulent premixed NH3/H2/air flames in lab-scale burners with strong flame–wall interactions.Novelty and Significance StatementThe novelty of this research is summarized into 3 points: (1) It is, to our knowledge the first time, pollutant production characteristics are investigated in detail for the premixed NH3/H2/air flame propagating in a fully developed turbulent boundary layer; (2) The effects of flame–wall, flame–turbulence and flame–flame interactions, the underlying reasons and controlling mechanisms are investigated in detail, which has not yet been (comprehensively) done in previous studies; (3) Novel and important findings have been concluded for the wall effects, turbulence effects (including flame curvature and surface density function effects) and flame–flame interaction effects. Some of these findings have never been reported before, but important for the comprehensive understanding of the pollutant production characteristics. It is significant because understanding the turbulence and wall effects on NO, N2O and NH3 production characteristics in the premixed NH3/H2/air flames is crucial for the future clean combustion energy system design.

Assessing turbulence–flame interaction of thermo-diffusive lean premixed H2/air flames towards distributed burning regime

Simultaneous laser-induced fluorescence of OH radicals and particle image velocimetry, and quasi-simultaneous 1D Raman/Rayleigh and 2D Rayleigh scattering measurements are used to investigate the effects of Karlovitz number (by varying the equivalence ratio) and residence time (by varying the axial measurement location) on the internal flame structures of lean premixed hydrogen/air turbulent jet flames. The turbulent flow fields, instantaneous macroscopic flame structures, and thermochemical states of a set of lean premixed hydrogen/air turbulent flames with varying initial equivalence ratio of 0.3, 0.4, and 0.45 at a constant bulk velocity of 100m/s are discussed. With an increasing equivalence ratio, the Karlovitz number derived from the turbulent flow fields decreases rapidly from 7690 to 260 and 100, determined at a downstream location of x/D=7. At the highest Karlovitz number (i.e., the lowest equivalence ratio), a distributed burning is observed in the jet flame as turbulent transport dominates over molecular mixing, and the effects of differential diffusion and flame curvature are suppressed. With decreasing Karlovitz number, intense burning regions characterized by elevated local equivalence ratio, high water mole fraction, and super-adiabatic flame temperatures are observed in association with positive flame curvature. The same combustion diagnostics are applied to another lean premixed hydrogen/air turbulent flame with an initial equivalence ratio of 0.4 and a bulk velocity of 200m/s at selected downstream locations of x/D=3.5, 7, 10.5, and 14 to assess the effects of developing turbulence and residence time. Corresponding Karlovitz numbers are 680, 730, 775, and 690, as the local turbulent intensity changes along downstream locations. While flame structures reveal characteristics towards distributed burning at lower x/D, a locally intense burning region appears at higher x/D together with positive curvature. This is mainly because the turbulence develops with increasing x/D and the flame surface is more disturbed and curved by turbulent eddies with increasing turbulence length scales. The highly diffusive hydrogen is locally concentrated by positively curved flame surfaces, resulting in fuel-rich burning regions at a higher temperature. This indicates that, as velocity fluctuations increase in axial direction, turbulence can also promote thermo-diffusive instabilities to a certain extent, increasing the mixture inhomogeneity in temperature space by interacting with the differential diffusion effect of hydrogen at atmospheric pressure.Novelty and significanceThe novelty of the current work is the focus on turbulence–chemistry interactions of premixed hydrogen/air jet flames at high turbulence and ultra lean conditions. Comprehensive experimental results including the turbulent flow fields (particle image velocimetry), instantaneous flame structures (laser-induced fluorescence of OH radicals) and internal thermochemical states (quasi-simultaneous 1D Raman/Rayleigh and 2D Rayleigh scattering imaging) of hydrogen/air jet flames are analyzed and discussed. The data sets with well-characterized boundary conditions and high measurement accuracy, are crucial for validation and development of numerical simulation models.

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Choice of reaction progress variable under preferential diffusion effects in turbulent syngas combustion based on detailed chemistry direct numerical simulations

The combustion of hydrogen and carbon-monoxide mixtures, so-called syngas, plays an increasingly important role in the safety context of non-fossil energy generation, more specifically in the risk management of incidents in process engineering plants for ammonia synthesis and in nuclear power plants. In order to characterize and simulate syngas/air combustion on industrially relevant scales, subgrid modelling is required, which is often based on a reaction progress variable. To understand the influence of different fuel compositions, turbulence intensities and flame topologies on different possible definitions of reaction progress variable, detailed chemistry direct numerical simulations data of premixed, lean hydrogen/air and syngas/air flames has been considered. A reaction progress variable based on normalized molecular oxygen mass fraction has been found not to capture the augmentation of the normalized burning rate per unit flame surface area in comparison to the corresponding 1D unstretched premixed flame due to preferential diffusion effects. By contrast, reaction progress variables based on other individual species, such as hydrogen, can capture the augmentation of the rate of burning well, but exhibit a pronounced sensitivity to preferential diffusion effects, especially in response to flame curvatures. However, a reaction progress variable based on the linear combination of the main products can accurately represent the temperature evolution of the flame for different mixtures, turbulence intensities and varying local flame topology, while effectively capturing the augmentation of burning rate due to preferential diffusion effects. However, its tendency to assume values larger than 1.0 in the regions of super-adiabatic temperatures poses challenges for future modeling approaches, whereas the reaction progress variable based on hydrogen mass fraction remains bound between 0.0 and 1.0 despite showing deviations in comparison to corresponding variations obtained from the unstretched laminar flame depending on flame curvature variations.

Effects of Pressure and Characteristic Scales on the Structural and Statistical Features of Methane/Air Turbulent Premixed Flames

In this study, the highly nonlinear and multi-scale flame-turbulence interactions prevalent in turbulent premixed flames are examined by using direct numerical simulation (DNS) datasets to understand the effects of increase in pressure and changes in the characteristic scale ratios at high pressure. Such flames are characterized by length-scale ratio (ratio of integral length scale and laminar thermal flame thickness) and velocity-scale ratio (ratio of turbulence intensity and laminar flame speed). A canonical test configuration corresponding to an initially laminar methane/air lean premixed flame interacting with decaying isotropic turbulence is considered. We consider five cases with the initial Karlovitz number of 18, 37, 126, and 260 to examine the effects of an increase in pressure from 1 to 10 atm with fixed turbulence characteristics and at a fixed Karlovitz number, and the changes to characteristic scale ratios at the pressure of 10 atm. The increase in pressure for fixed turbulence characteristics leads to enhanced flame broadening and wrinkling due to an increase in the range of energetic scales of motion. This further manifests into affecting the spatial and state-space variation of thermo-chemical quantities, single point statistics, and the relationship of heat-release rate to the flame curvature and tangential strain rate. Although these results can be inferred in terms of an increase in Karlovitz number, the effect of an increase in pressure at a fixed Karlovitz number shows differences in the spatial and state-space variations of thermo-chemical quantities and the relationship of the heat release rate with the curvature and tangential strain rate. This is due to a higher turbulent kinetic energy associated with the wide range of scales of motion at atmospheric pressure. In particular, the magnitude of the correlation of the heat release rate with the curvature and the tangential strain rate tend to decrease and increase, respectively, with an increase in pressure. Furthermore, the statistics of the flame-turbulence interactions at high pressure also show sensitivity to the changes in the characteristic length- and velocity-scale ratios. The results from this study highlight the need to accurately account for the effects of pressure and characteristic scales for improved modeling of such flames.

Effect of water content in ethanol on flame front wrinkling and curvature in a spark-ignition engine using OH PLIF imaging

The production of ethanol fuel involves separating water and ethanol by distillation and dehydration in an energy intensive process. To reduce the carbon footprint, hydrous ethanol is seen as a promising alternative. This study focused on the effect of water content in ethanol on flame development in a single-cylinder optical spark-ignition engine. Ethanol with 0%, 4% and 10% water content per volume was used with Port Fuel Injection (PFI) and Direct Injection (DI) for homogeneous and heterogeneous mixture preparation. Tests were also conducted with iso-octane for comparison. Flames captured by Planar Laser Induced Fluorescence (PLIF) of OH were spatially filtered to remove scales larger than the flame size, then the flame brush was quantified in terms of thickness, crossing frequency between instantaneous and filtered contours, and curvature. Increasing water content resulted in slower flame growth, with 10% hydrous exhibiting marginally higher flame speed than iso-octane. PFI led to faster flame growth and thicker flame brushes than DI at the same timing after ignition. When the brush thickness was normalised by flame radius, all hydrous fuels and iso-octane exhibited similar values with PFI, whilst anhydrous ethanol exhibited the thickest normalised brush. The alcohols maintained similar normalised thicknesses with DI and iso-octane exhibited the thickest normalised brush. When flames of the same radii were considered with PFI at the same timing, the fuels with sequentially lower laminar burning velocity were associated with larger crossing frequency. For PFI, increasing water content resulted in decreased flame roundness irrespective of size, with the 4% hydrous and iso-octane exhibiting similar values. With DI, anhydrous ethanol flames were rounder than the 4% hydrous when averaged over all cycles, but marginally rounder than the 10% hydrous and iso-octane. Increasing water content widened the curvature distribution and increased the mean with PFI. Flame roundness decreased with increase in mean curvature and Lewis number for both PFI and DI.

Plasma assisted combustion of different biogas mixtures in low swirl burner

This study explores the impact of plasma driving frequency on diverse biogas compositions, emphasizing flame behaviour by analysing spatial emissions of OH*, C2*, and CH* from plasma-assisted flames. Experimental investigation performed combusting mixtures with 25 % and 60 % CH4 in CO2 under lean combustion conditions with the varying fuel equivalence ratios from 0.71 to 0.83 and plasma discharge frequencies from 60 to 120 kHz resulting in higher energy density.Obtained results indicate that the plasma assistance notably enhances flame stability under lean fuel conditions with increasing frequency from 80 to 120 kHz. The discharge frequency of 60 kHz indicates insufficient energy to enhance combustion of low calorific value mixtures as the flame lift-off height increases approximately by 0.43–1.5 % for the mixture of 25 vol% CH4 in CO2 and by 0.26–7.7 % for the mixture of 60 vol% CH4 in CO2. Changing the plasma frequency from 80 to 120 kHz, the flame position is shifted closer to the burner nozzle for both mixtures and the highest effect is determined at 120 kHz. The flame lift-off height is reduced by 2.43–16.34 % for the mixture with 25 vol% of CH4 and by 3.57–51.28 % for the mixture with 60 % of CH4. The plasma-assisted combustion leads to improved combustion efficiency as CO emissions are reduced from 1550 ppm to 45 ppm for biogas mixture, but in the case of low calorific value gas, the CO emissions increase linearly with the frequency increase even the flame curvature and stability is improved.

Internal flame structures of thermo-diffusive lean premixed H2/air flames with increasing turbulence

Turbulent flow fields, instantaneous flame structures, and internal thermo-chemical states of lean premixed hydrogen/air jet flames at an initial equivalence ratio of 0.4 are experimentally investigated by simultaneous laser-induced fluorescence of hydroxyl radicals (OH-LIF) and particle image velocimetry (PIV), and quasi-simultaneous 1D Raman/Rayleigh and 2D Rayleigh scattering measurements over a range of Karlovitz numbers (Ka) from 50 to 730. At low Ka, intense burning characterized by elevated local equivalence ratio, high water mole fraction (XH2O), and super-adiabatic flame temperature is mainly observed in post-flame regions surrounded by positively curved flame surfaces, where the fast diffusive hydrogen is locally focused. The flame features stronger differential diffusion and curvature effects than that in the planar laminar flame, which indicates that both molecular and turbulent mixing play significant roles, and thermo-diffusive instabilities have synergistic interactions with turbulence at low turbulence level. With increasing Ka, the burning intensity in corresponding regions is weakened, even though the flame surface is more disturbed by the turbulence. At the highest Ka, no intense burning region is observed in the jet flame as the turbulent transport dominates over the molecular diffusion. In the temperature domain, the conditional means of hydrogen mole fraction (XH2) and local equivalence ratio feature effects of diffusive instabilities with broad distributions at low-Ka conditions. Elevated XH2O and local equivalence ratios with super-adiabatic flame temperatures are observed, which is attributed to differential diffusion in hydrogen-containing mixtures and the fuel focusing effect near positively curved flame surfaces. At high Ka, the XH2 shows a more linear decreasing trend and the local equivalence ratio profile becomes flatter over temperature with a narrower distribution, indicating the dominance of turbulent mixing.

Local statistics of turbulent spherical expanding flames for NH3/CH4/H2/air measured by 10 kHz PIV

In this paper, we present high-speed particle image velocimetry measurements to quantify combustion-induced turbulence and turbulent stretch rate effects on flame propagation in a fan-stirred constant-volume combustion vessel. Three stoichiometric fuel/air mixtures including methane/air, methane/hydrogen/air and ammonia/methane/air were tested. The expansion rate of flame radius is found to scale with a half-power law of the mean-radius based Reynolds number. Measurements of velocity in the reactant zone show that the gas mean and rms velocity increase within the flame brush then gradually decrease when approaching the detection edge. Combustion enhances the measured non-reacting flow turbulence by ∼64 % within the reactant side of the flame brush of this expanding spherical flame. The evolution of rms velocity is found to be insensitive to pressure but sensitive to initial turbulent intensity and laminar flame speed, scaling with Reynolds number in a similar manner as the rate of expansion of the flame radius. Hydrogen blending shows the largest absolute value of rms velocity increase, but ammonia blending leads to the largest increase in rms velocity relative to laminar flame speed. The pdfs of 2D curvature are broadened as u′ and p increase but gradually saturate at high u′ for all mixtures, those of stretch rate are widened by flame speed. The temporal evolution of statistical flame stretch rates suggests the tangential stretch rate is larger than and anti-correlated with the normal stretch, and that there is a strong positive correlation between instantaneous flame propagation rate and the rms strain rate. Finally, the mean flame curvature and mean stretch rate are found to be near zero as flame propagates outwardly.

Effects of cryogenic temperature on turbulent premixed hydrogen/air flames

As a carbon-free fuel, hydrogen (H2) is of increasing importance in the development of low-emission engines. Due to a low volumetric energy density, H2 is preferably stored at cryogenic temperatures (Tu≤100 K). In this context, it is indispensable to investigate the combustion behavior of hydrogen at such low temperatures. Although some studies focused on the ignition and detonation of hydrogen, investigations about premixed H2/air flame propagation interacting with turbulence at cryogenic temperatures are rather scarce. In this work, stoichiometric turbulent premixed H2/air flames are studied at cryogenic temperature (Tu=100K) and normal temperature (Tu=300K), using three-dimensional direct numerical simulations with detailed chemistry and transport. It is found that at cryogenic temperature, dimensionless turbulent flame speed and flame surface area increase significantly due to Darrieus–Landau instability (DLI) induced by a large expansion ratio. Since the effective Lewis numbers of the two cases are close to unity, the diffusive-thermal instability (DTI) is negligible in the cases. Furthermore, it is found that there are substantial differences in the peaks of HO2 and H2O2 mass fractions between the two cases, probably due to smaller local flame curvatures at cryogenic temperature. Moreover, the results indicate that the flame response to stretch is not sensitive to the change of the initial temperature. A larger fractal inner cutoff scale is found at Tu=100K, suggesting that the flame exhibits more large-scale flame wrinkling than that at Tu=300K due to the impact of DLI. All these facts lead to the conclusion that cryogenic temperature can significantly promote large-scale flame wrinkling, increase turbulent flame speed and flame surface area, and affect intermediate species distribution. This suggests that combustion of cryogenic H2 may have a high risk of flashback.

Numerical analysis and flamelet modeling of NO[formula omitted] formation in a thermodiffusively unstable premixed hydrogen flame at elevated-pressure conditions

Fuel-lean premixed hydrogen flames are thermodiffusively unstable and cellular structures over a wide range of length-scales are formed due to strong differential diffusion of hydrogen. Pressure promotes the thermodiffusive instabilities due to the increase in Zeldovich number and the relevant reaction pathways. As the local stoichiometry and temperature correlate with the thermodiffusive instabilities, the NOx formation mechanism is expected to be complicated in fuel-lean hydrogen flames at elevated-pressure conditions. In this work, the characteristics and the NOx formation mechanism of thermodiffusively unstable premixed hydrogen flames at elevated-pressure conditions are investigated through direct numerical simulation (DNS). The designed operating conditions were motivated by findings in experiments investigating NOx emissions in pure hydrogen combustion at elevated-pressure conditions. The flame characteristics are assessed by means of the global burning velocity, flame surface area, stretch factor, and PDFs of curvature and length-scale of cellular structures. The conditioned thermo-chemical quantities are analyzed with respect to the progress variable and curvature to illustrate the key correlations. The contributions of elementary reactions to the NOx formation are quantified and the important reaction pathways are identified in a reaction pathway analysis. The global burning velocity is significantly increased with increasing pressure, which mainly results from the increased reactivity. The positive curvature is more prominent in the elevated-pressure case, which results in a higher probability of smaller cells. Different from the atmospheric case, where the NNH reaction pathway is dominant, the N2O reaction pathway is the most important under elevated-pressure conditions, which suggests the strong correlations of NOx formation with curvature values. To incorporate the wide range of curvatures in a flamelet model, an extended flamelet tabulation method based on the composition space model is proposed. The performance of the composition space model in predicting the important radicals and NOx species is evaluated through an a priori analysis. The composition space model gives better predictions of the radicals and the production and consumption rates of the NOx species compared to conventional flamelet models that do not consider the effects of local flame curvature.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain – Part I: Characteristic patterns

Thermodiffusive instabilities can have a leading order effect on flame propagation for lean premixed hydrogen flames. Many simulation studies have been performed to study this effect, but almost exclusively in two-dimensional (2D) or domain sizes too small to support the characteristic large-scale features of the instability. The main purpose of this study is to quantify the differences of 3D and 2D flames using simulations on sufficiently large domains. To this end, direct numerical simulations (DNS) of thermodiffusively unstable laminar premixed hydrogen flames stabilized in 3D domains were performed. The effects of confinement on the flame dynamics are rigorously investigated by varying the domain size. The flame burning velocity shows a strong dependence on the domain size when the lateral domain width is less than 50 laminar flame thicknesses. The characteristic patterns of the thermodiffusively unstable flame are analyzed in detail, including the instantaneous flame structure, global burning velocity, flame surface area, stretch factor, curvature distribution, and the cell size. The effects of the computational setup (2D vs. 3D) on the local flame front curvature and the distributions of the thermo-chemical quantities are quantified through a conditional analysis. The formation and destruction mechanisms of the distinct cellular structures observed in the 3D domain are analyzed focusing on the interactions between the flame dynamics and the flow field, and the contributions of the production of flame surface density, kinematic restoration, and curvature dissipation are quantified. Compared with the corresponding 2D simulation, the flame surface area in the cut plane of the 3D configuration is similar, yet the burning velocity and the stretch factor are increased. The reason for this is the difference in curvature statistics in 2D and 3D. In 3D, larger extreme curvature values are obtained, leading to quantitatively different distributions of the thermo-chemical variables. For example, the peak H radical concentration in the 3D simulation is about twice higher than in the 2D simulation.Novelty and significance statementThe novelty of the present work includes the following aspects:(i) First large-scale 3D DNS of laminar lean premixed hydrogen flame on domain large enough to obtain domain-independent results.(ii) First quantitative assessment of characteristic patterns of 3D thermodiffusively unstable premixed hydrogen flames.(iii) First quantitative assessment of differences between 2D and 3D thermodiffusively unstable premixed hydrogen flames for domain-independent results.

The effect of mixture inhomogeneity and turbulence on the flame front curvature and flame surface density of turbulent planar flames of natural gas

The present study is an extension of our earlier mixing field investigation in partially premixed flames. In the current work, the link between the mixing field and flame structure, and hence flame curvature and surface density are experimentally studied. The flame structure is captured using a high-speed OH-PLIF technique, whereas the crosswise mixing fields were previously presented in our earlier study. A concentric flow slot burner is employed for producing turbulent planar partially premixed natural gas flames at different levels of mixture inhomogeneity. The effects of the level mixture inhomogeneity, the equivalence ratio, the air to fuel stream velocity ratio, and Reynolds number “Re” on the flame characteristics are investigated. The link between the previously reported data on the mixing field and the flame structure are examined. The correlations between the mixing field and the flame structure were clearly observed in the current study. That is, as the mixture becomes highly inhomogeneous, in rich input jet conditions cases, altering Reynolds number and the mixing length led to a pronounced change in both flame structure and flame curvature while altering L/D influences the flame structure. On the other hand, the effects of the mixing length and Reynolds number on the flame structure and curvature in a more homogeneous mixture were not significant. The data showed that the flame surface density was inversely proportional to the level of the mixture inhomogeneity and directly proportional to the Reynolds number. The significant effect of the jet equivalence ratio on the level of mixture inhomogeneity leads to a significant change in the flame structure and flame curvature. In addition, if the mixture inhomogeneity is less pronounced the variation s of the mixing length and Reynolds number lead to minimal effects on the flame structure and flame curvature.

The effect of flame curvature and flame base movement on the frequency response of a conical Bunsen flame

We create a general model for the tracking of a premixed flame sheet. This model is based on a Lagrangian formulation of the interface motion, which is more computationally efficient than the level-set formulation solved on a grid. We apply this model to a conical Bunsen flame in which flame-base oscillations and flame stretch effects are also considered. We demonstrate that the flame-front dynamics, the heat release rate perturbations, and the flame transfer function (FTF) are affected by three features: (i) the velocity field locally perturbing the flame-front, (ii) the flame-base oscillations normal to the steady flame-front propagating along the flame and (iii) the flame-base oscillations tangential to the flame-front reducing and increasing the flame-length. We provide a physical explanation for the saturation of the FTF phase shift with increasing forcing frequency, which is found experimentally. We show why a n−τ model with fixed τ cannot model this simple flame and that, when building a quantitatively-accurate model of a thermoacoustic system containing this flame, the flame dynamics need to be simulated directly or modelled more accurately than with the n−τ model. The flame model used in this paper has been designed to be differentiable so that it can be used for rapid data assimilation using Laplace’s method. Code is provided so that the user can generate the FTF of a conical premixed flame with any set of parameters and any flame-base trajectory.

Evolution of Flame Displacement Speed Within Flame Front in Different Regimes of Premixed Turbulent Combustion

A transport equation for the flame displacement speed evolution in premixed flames is derived from first principles, and the mean behaviours of the terms of this equation are analysed based on a Direct Numerical Simulation database of statistically planar turbulent premixed flames with a range of different Karlovitz numbers. It is found that the regime of combustion (or Karlovitz number) affects the statistical behaviour of the mean contributions of the terms of the displacement speed transport equation which are associated with the normal strain rate and curvature dependence of displacement speed. The contributions arising from molecular diffusion and flame curvature play leading order roles in all combustion regimes, whereas the terms arising from the flame normal straining and reactive scalar gradient become leading order contributors only for the flames with high Karlovitz number values representing the thin reaction zones regime. The mean behaviours of the terms of the displacement speed transport equation indicate that the effects arising from fluid-dynamic normal straining, reactive scalar gradient and flame curvature play key roles in the evolution of displacement speed. The mean characteristics of the various terms of the displacement speed transport equation are explained in detail and their qualitative behaviours can be expounded based on the behaviours of the corresponding terms in the case of 1D steady laminar premixed flames. This implies that the flamelet assumption has the potential to be utilised for the purpose of any future modelling of the unclosed terms of the displacement speed transport equation even in the thin reaction zones regime for moderate values of Karlovitz number.

On the flame transfer function models for laminar premixed conical and V- flames considering the stretch effect

This paper investigates a predictive model that considers the impact of stretch on the dynamic response of laminar premixed conical and V- flames; the flame stretch consists of two components: the flame curvature and flow strain. The steady and perturbed flame fronts are determined via the linearized G-equation associated with the flame stretch model. Parameter analyses of the effects of Markstein length L, flame radius R and unstretched flame aspect ratio β are also conducted. Results show that the flame stretch reduces the steady flame height, with this effect being more significant for larger Markstein lengths and smaller flame sizes. The effects of flame stretch on perturbed flames are evaluated by comparing the flame transfer function (FTF) considering the flame stretch and not. For flames of different sizes, the impact of flame stretch on FTF gain can be divided into three regions. When both β and R are relatively small, due to the decrease in steady flame height and the impact of flow strain, the FTF gain increases. As β and R gradually increase, the FTF gain of the conical flame oscillates periodically while the FTF gain of the V-flame decreases, primarily due to the flame curvature enhancing the flame front disturbance and the wrinkle counteracting effect. When β and R are large, a disruption in wrinkle counteracting effect ensues, leading to a significant increase in FTF gain. Furthermore, as the actual flame height is reduced, the flame stretch also reduces the FTF phase lag which is related to the disturbance propagation time from the flame root to the tip.

Interaction of a turbulent flame with the very-large-scale structures in a channel flow

Combustion processes taking place in large-scale burners may need to consider the impact of the recently identified very-large-scale motions (VLSM) appearing in wall-bounded turbulent flows. While VLSM in non-reacting, cold flows have been found to be important and noticeably impact turbulence statistics, the possible influence of VLSM on turbulent premixed flames has not been considered up to now to the best of our knowledge. The present study investigates the interaction of a turbulent flame with VLSM in a channel flow using direct numerical simulations (DNS). Detailed chemical kinetics have been used to compute a H2 flame. The turbulent channel flow corresponds to Reτ= 280, while the premixed flame is associated to a Damköhler number Da = 0.167. First, VLSM have been identified for the non-reacting flow by proper orthogonal decomposition (POD). Interestingly, the propagation of the turbulent flame is found to have a negligible effect on the VLSM, highlighting their resilience. At the same time, the VLSM do not modulate strongly the flame structure, while it is noticeably affected by small-scale vortices. This decoupling might be explained by the very different length scales of both processes, the VLSM covering the full channel length, while the turbulent flame is characterized by small-scale structures. In the same manner, the characteristic time scales also differ widely, the flame time scale being much faster than the characteristic time of the VLSM. The flame curvature is positively correlated with the fluctuating streamwise velocity when the flame is still far from the wall. When approaching the wall, flame quenching takes place in a complex process. Overall, it appears for the present conditions that VLSM do not impact directly the turbulent flame propagation, but there is still an indirect impact through the modifications of the turbulence statistics.

Stretch Effects in Large Eddy Simulation of Turbulent Premixed Bunsen Flames

ABSTRACT The stretch effects in large eddy simulation (LES) of a turbulent lean propane-air premixed Bunsen flame in the wrinkled flamelet regime are investigated. A simple approach to model the subgrid-scale flame stretch is proposed. It is based on the analysis which shows that, when the surface-filtered strain rate in a subgrid-scale stretch model is approximated using the volume-filtered velocity field solved for in LES, heat release and associated gas expansion in the filtered flame brush tend to artificially alter the wrinkling of resolved flame fronts. To minimize such artifacts, it is suggested that the volume-filtered strain rate on the unburned side of the filtered flame brush be used to approximate the surface-filtered strain rate and projected through the filtered flame brush. The results show the importance of mitigating the artificial heat release effects when considering the strain effects in LES. The relative importance of the curvature stretch is also investigated in terms of the mean and local effects. For a Bunsen flame with a positive Markstein number, the mean flame curvature effect tends to increase the total burning rate by enhancing the laminar flame speed near the flame tip, while the local flame curvature effect tends to decrease the total burning rate by suppressing the wrinkling of the resolved flames. It is found that the competition between the two makes the overall curvature effects not influence the total burning rate much for the flame investigated here, as compared with the strain effects.

Effects of Mixture Distribution on the Structure and Propagation of Turbulent Stratified Slot-Jet Flames

The influence of mixture stratification on the development of turbulent flames in a slot-jet configuration has been analysed using Direct Numerical Simulation data. Mixture stratification was imposed at the inlet by varying the equivalence ratio between 0.6 and 1.0 with different alignments to the reaction progress variable gradient: aligned gradients (back-supported), opposed gradients (front-supported) and misaligned gradients. An additional premixed case with a global equivalence ratio of 0.8 was simulated for comparison. The flame is shortest for the front-supported case, followed by the premixed flame, with the back-supported and misaligned gradient flames being the tallest and of comparable size. This behaviour has been explained in terms of the variations of the mean equivalence ratio within the flame and the volume-integrated reaction rate in the streamwise direction. The difference in mixture composition for these cases results in significant variations in the burning rate, flame area, flame wrinkling and flame brush thickness in the streamwise direction. The globally front-supported case has the highest volume-integrated burning rate and flame area, while the back-supported case has the lowest. The misaligned scalar gradient case exhibits qualitatively similar behaviour to that of the globally back-supported case. The burning intensity is unity for a major part of the flame length but assumes values greater than unity towards the flame tip where the effects of flame curvature become strong. All cases predominantly exhibit the premixed mode of combustion within the flamelet regime, so flamelet assumption-based reaction rate closures, originally proposed for premixed combustion, were evaluated using a priori analysis. The terms which require improved closures have been identified and existing closures have been improved where necessary. It was found that the global nature of mixture stratification does not influence the performance of the mean reaction rate closures or the parameterisation of marginal probability density functions of scalars in turbulent stratified mixture combustion.

Ensemble-averaged kinematics of harmonically oscillating turbulent premixed flames

Direct numerical simulation (DNS) was used to characterize the kinematics of ensemble-averaged flame position in harmonically oscillating turbulent premixed flames. The flames are stabilized on a harmonically oscillating flame holder, and the fuel consists of methane and hydrogen at a volume ratio of 10:3 and is mixed with air at the stoichiometric ratio. Turbulence intensities of 3.7, 8.6, and 13.3% are simulated, and each turbulent flame is simulated for 20 forcing periods for ensemble averaging. A laminar flame speed calculation method is derived based on the G-equation framework; the new method reproduces the reference laminar flame speed and the laminar Markstein length. The turbulent flame speed shows strong linear correlation with the ensemble-averaged flame curvature. The turbulent flame speed at zero flame curvature increases proportional to the turbulence intensity, while the turbulent Markstein length is independent of turbulence intensity. When the flame is far from the oscillating flame holder, the correlations between the turbulent flame speed and the flame curvature exhibit either piecewise linear or power-law dependencies. At these locations, the turbulent Markstein length at high curvature is similar to the laminar Markstein length. When a power law model is applied, the turbulent flame speed dependency asymptotes to 0.7 powers of the ensemble-average flame curvature at the turbulence conditions considered here.