Turbulent Premixed Flames Research Articles

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.

DNS study on reactivity stratification with prechamber H[formula omitted]/air turbulent jet flame to enhance NH[formula omitted]/air combustion in gas engines

The present study investigates turbulent flame dynamics and pollutant emission characteristics in a prechamber/main chamber system. A H2/air turbulent jet flame issued from the prechamber penetrates into the NH3/air mixture found in the main chamber. Recent experimental studies have demonstrated that this configuration is very promising for future NH3 combustion in gas engines. In the present work, 3D direct numerical simulations (DNS) with detailed chemistry have been carried out in the above configuration. The dynamics of the turbulent premixed flame in the prechamber (flame thickness, flame propagation speed) and the structure of the turbulent stratified flame in the main chamber are investigated. It is found that the stratified flame thickness is becoming thicker as the flame propagates within the NH3/air mixture. The flame displacement speed is slowing down in a first phase, before becoming faster again after jet-induced turbulence starts to decay. A chemical explosive mode analysis (CEMA) has been done to distinguish between ignition, flame propagation, and local extinction events both for the premixed flame in the prechamber and the stratified flame in the main chamber. The temporal evolution of the identified modes are consistent with the flame dynamics and help to explain the later increase in flame displacement speed. NO emission characteristics in the main chamber have also been investigated. The NO production speed first increases, reaches a plateau, before being reduced during later flame propagation; stratification is important to explain the NO emission characteristics. Compared to the laminar NH3/air flame, the NO production speed is obviously larger in the present configuration, mainly due to the reduced contribution of the NO destruction reactions in the fuel pathway. Compared to premixed NH3/H2/air flames with H2 volume ratios found in practical systems (typically ≥ 0.4), the NO production speed is lower in the present configuration, demonstrating its superiority for practical applications. Finally, conventional heat release rate (HRR) markers are evaluated for the stratified flame. They approximate quite well the general structure of the flame front, but lead to noticeable quantitative errors.

Turbulent flame speed based on the mass flow rate: Theory and DNS

Starting with an integral formulation of average mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking Damköhler’s hypotheses. Major approximations and interim results are validated using a large Karlovitz number, unity Lewis number, Direct Numerical Simulation (DNS) dataset of n-heptane/air mixture, computed with reduced chemistry. A length scale quantifying the fluctuation distance of the isotherms within the premixed flame structure is analysed.

Backscatter of scalar variance in turbulent premixed flames

To explore the direction of inter-scale transfer of scalar variance between subgrid scale (SGS) and resolved scalar fields, direct numerical simulation data obtained earlier from two complex-chemistry lean hydrogen–air flames are analysed by applying Helmholtz–Hodge decomposition (HHD) to the simulated velocity fields. Computed results show backscatter of scalar (combustion progress variable$c$) variance, i.e. its transfer from SGS to resolved scales, even in a highly turbulent flame characterized by a unity-order Damköhler number and a ratio of Kolmogorov length scale to thermal laminar flame thickness as low as 0.05. Analysis of scalar fluxes associated with the solenoidal and potential velocity fields yielded by HHD shows that the documented backscatter stems primarily from the potential velocity perturbations generated due to dilatation in instantaneous local flames, with the backscatter being substantially promoted by a close alignment of the spatial gradient of mean scalar progress variable and the potential-velocity contribution to the local SGS scalar flux. The alignment is associated with the fact that combustion-induced thermal expansion increases local velocity in the direction of$\boldsymbol {\nabla } c$. These results call for development of SGS models capable of predicting backscatter of scalar variance in turbulent flames in large eddy simulations.

Model assessment of synthetic jets for turbulent combustion experiments

Understanding turbulent premixed flames is essential to predict and optimize advanced combustion strategies, but critical capability gaps exist for collecting and validating measurements such as turbulent flame speed. Here, we evaluate synthetic jets as a new, promising turbulence generation device for constant-volume combustion chambers, quantitatively assessing turbulence intensity and spatial uniformity in a hypothetical 4,189-cm3 vessel for various premixture conditions.Graphic

Analysis of Water Droplet Interaction with Turbulent Premixed and Spray Flames Using Carrier Phase Direct Numerical Simulations

ABSTRACT Carrier-phase direct numerical simulations (DNS) of n-heptane/air combustion with water droplet injection are reported in this paper. The influence of water droplet injection has been analyzed for statistically planar gaseous premixed flames and spray flames where the fuel is supplied in the form of monodisperse fuel droplets. The effects of water injection in both types of flames are compared, including their sensitivities on the initial diameter of water droplets. The simulations are based on an Eulerian-Lagrangian-Lagrangian approach to consider the multi-phase interaction and the simultaneous effects of n-heptane and water droplets. It is shown that the two types of flames are different in terms of several aspects. In particular, the spray flames are characterized by lower temperatures, and their propagation speed is lower than for premixed flames. The main reason for these differences lies in the gaseous equivalence ratio experienced by the reaction zone. For the cases investigated here, where the overall equivalence ratio is unity, the spray combustion occurs under predominantly fuel-lean conditions. Furthermore, the flame temperature is influenced by the initial diameter of water droplets, which affects the strength of thermal expansion within the flame. This in turn influences the evaporation characteristics of both fuel and water droplets due to different residence times within the flame. Although the effects of water droplets on the combustion mode are dependent on the relative position within the spray flame, the net effect is a partial shift from non-premixed to premixed mode. At the same time, the spray combustion occurs under relatively fuel-richer conditions with water injection and these trends appear consistently in laminar and turbulent flows.

E-POD investigations of turbulent premixed flame dynamics approaching lean blow-out conditions

Thanks to the continuous computational power increase, the use of high-fidelity computational fluid dynamics (CFD) simulations is nowadays customary, especially in the gas turbines design process. The extraordinary temporal and spatial detail of such analyses generate large datasets, which must be carefully studied to correlate different quantities and gain information to characterize the behavior of combustor designs. Several advanced post-processing tools have been proposed; however, the Extended-POD (E-POD) holds the greatest potential for turbulent combustion applications when the mutual influence of different quantities is the main goal of the investigation. The present work investigates the application of the E-POD to an LES model of a perfectly-premixed, swirl-stabilized, methane-air flame approaching Lean-Blow-Out. Leveraging the validation against the experimental data at two different operating conditions on a laboratory test case, the numerical model has been used to collect several quantities of interest for shedding light on the flow-flame interaction near the blow-out. The post-processing algorithm has been used to highlight the differences between two conditions approaching the extinction at distinct air-flow velocities. It has been found that, when the burner is operated with a higher velocity, the flame is subjected to a cyclic low-frequency breakdown around the internal recirculation zone, leading to an ingestion of cold products from the external parts of the combustor toward the center. Although other local effects acting on the flame brush have been found in both conditions, they are related mainly to higher order coherent structures with a lower energy content. As a result, their impact onto flame stability is found to be of secondary importance since their limited interaction with flame stabilization. The work shows that E-POD represents a powerful tool for investigating the key features of flame dynamics even at near-blow-out conditions, constituting a valid algorithm for interpreting the results of CFD analyses on gas turbines combustors.

Investigation of reaction-induced subgrid scalar mixing in LES/FDF simulations of turbulent premixed flames

Modeling molecular mixing remains a key issue for the filtered density function (FDF) method. We propose a new closure for the mixing timescale of each individual chemical species. A posteriori tests demonstrate the advantages of the proposed model, highlighting its potential to be employed in FDF simulations of turbulent reacting flows.

Application of machine learning in low-order manifold representation of chemistry in turbulent flames

The Uniform Conditional State (UCS) and the Multidimensional Flamelet Manifold (MFM) models are methods for the tabulation of chemistry in simulations of turbulent flames. The high-dimensionality of the tables these models generate and many possible combinations of the values for the input variables necessitate the allocation of a considerable size of memory during CFD calculations. This issue becomes even more problematic when adding more conditioning variables to the model. In this study, two Artificial Intelligence (AI)-based approaches referred to as Decision Tree (DT) and Artificial Neural Network (ANN) are developed and tested to provide in situ chemistry representation. The goal is to predict four parameters (outputs) accurately with low memory demand and computational cost. The trained AI models are then employed for simulation of a turbulent premixed flame. Comparison of the results from the AI-based approaches to those from the conventional UCS model shows acceptable agreement. The memory and CPU requirements from the different approaches are compared. It is found that the ANN model reduces the size of the chemistry table by around 92%. Conversely, the DT-based model reduces the size of the chemistry model by only 40%. The CPU time for using the DT model during the CFD calculations was around 10% shorter than the conventional approach while it was 8% higher for the ANN model. It was concluded that, based on the particular applications, different AI-based methods can facilitate an efficient representation of the chemistry manifold.

A Comparison between Statistical Behaviours of Scalar Dissipation Rate between Homogeneous MILD Combustion and Premixed Turbulent Flames

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures.

Modeling of flame transfer function of a conical turbulent premixed flame with variable flame speed

Modeling of flame transfer function of a conical turbulent premixed flame with variable flame speed

Effects of body force on the statistical behaviour and modelling of scalar variance in turbulent premixed flames

The effects of body force/external pressure gradient on the statistical behaviours of the reaction progress variable variance and the terms of its transport equation have been investigated for different turbulence intensities using DNS data of statistically planar flames. Since the extent of flame wrinkling increases with the strengthening of body force promoting unstable stratification, the scalar variance has been found to decrease under strong body force promoting stability. This trend is particularly strong for low turbulence intensities where the probability density function of the reaction progress variable cannot be approximated by a bimodal distribution. Therefore, an algebraic relation for the reaction progress variable variance, derived based on a presumed bimodal probability density function of reaction progress variable, cannot be used for general flow conditions. The contributions of chemical reaction and scalar dissipation rates in the scalar variance transport equation remain leading order source and sink, respectively for all cases irrespective of the strength and direction of the body force. The counter-gradient type transport is found to weaken with increasing body force magnitude when the body force is directed from the heavier unburned gas to the lighter burned gas side of the flame brush, and vice versa. Although a scalar dissipation rate-based reaction rate closure can be utilised to model the reaction rate contribution to the scalar variance transport accurately, the dissipation rate contribution due to the gradient of the Favre-averaged reaction progress variable cannot be ignored and it plays a key role for large magnitudes of body force promoting stable stratification. An algebraic closure of the scalar dissipation rate, originally proposed for high Damköhler number combustion, has been modified for the thin reaction zones regime combustion by incorporating the effects of Froude number. This model has been shown to predict the scalar dissipation rate accurately for all cases considered here.

Suppression of the turbulent kinetic energy and enhancement of the flame-normal Reynolds stress in premixed jet flames at small Lewis numbers

We report the effects of the Lewis number on the turbulent kinetic energy, Reynolds stresses, and scalar fluxes in premixed jet flames with strong mean shear. The direct numerical simulation (DNS) of piloted turbulent premixed jet flames is performed under the same condition except for different Lewis numbers to isolate the Lewis number effects. The turbulence intensity within the mean flame brush is found to decay more rapidly along the axial distance with a smaller Lewis number. This Lewis number dependence results from the coupling of the mean shear and the combustion heat release, where the mean shear is the primary source of turbulence production. We show that, under the strain imposed by the mean shear and turbulence fluctuation, the heat release of premixed jet flames is significantly enhanced at the Lewis number smaller than unity, which is represented by the rising flamelet consumption speed and flame surface area. As a consequence, the mean shear within the flame brush is suppressed at small Lewis numbers via the dilatation effect, and the weakened mean shear production causes the fast turbulence suppression along the axial direction. The enhanced heat release at small Lewis numbers also increases the flame-normal Reynolds stress, and leads to the counter-Boussinesq behavior of the shear Reynolds stress and the counter-gradient transport of scalar fluxes. We model the Lewis number effects on local turbulence and scalar transport using the stretched laminar flame speed and thickness, and achieve overall good estimations of the flame-normal Reynolds stress and scalar transport at small Lewis numbers.

[formula omitted]-[formula omitted] and [formula omitted]-[formula omitted] studies of filtered probability density function models and NO formation prediction in turbulent stratified premixed combustion using machine learning

Accurate prediction of NO formation in turbulent stratified premixed combustion using large eddy simulation (LES) is challenging. In the present work, a reaction rate method for NO source modeling in the context of LES was proposed with the focus being placed on accurate modeling of the filtered probability density functions (FPDFs) and joint FPDFs. The NO source and various NO pathways from a direct numerical simulation (DNS) database of turbulent stratified premixed flames were conditionally averaged the progress variable and mixture fraction to provide the lookup table. A random forest (RF) model was developed for the FPDFs/joint FPDFs of the mixture fraction and progress variable. The β-PDF model was also analyzed for comparison. First, the FPDFs and joint FPDFs predicted by the β-PDF and RF models for the progress variable and mixture fraction were compared with those from the DNS data. It was found that the FPDFs and joint FPDFs by the RF model agree well with those from the DNS. In contrast, the β-PDF model failed to accurately capture the joint FPDFs as the correlations of the mixture fraction and progress variable are neglected. Then, the filtered NO source and various NO pathways were modeled a-priori using the lookup table and the joint FPDFs for turbulent stratified premixed flames. The results showed that the RF model reproduces the filtered NO source and NO pathways very well, and performs much better than the β-PDF model. Finally, a-posterior validation of the model performance was carried out in the context of LES. Various quantities from the LES were compared with the DNS filtered quantities. The results showed that the LES/RF model outperforms the LES/β-PDF model in the a-posterior simulation. Overall, the LES/RF model is promising for NO formation modeling using the reaction rate method a-priori and a-posterior in LES of turbulent stratified premixed combustion.

Flame/turbulence interaction in ammonia/air premixed flames at high karlovitz numbers

Turbulent premixed flames subjected to extreme levels of turbulence exhibit reaction zone broadening and thinning. Instantaneous flame structures visualized using advanced laser diagnostic methods have shown significantly different behaviours of flame/turbulence interaction in jet flames stabilized on burners of different sizes. This paper aims to reconcile the controversy about flame broadening on burners of different sizes. Premixed ammonia/air flames are investigated owing to the importance of ammonia in the future carbon-free energy system. Due to the low laminar flame speed of ammonia/air mixture, the intensity of turbulence (u′/SL) can be 5 times higher than that of methane/air flames at the same jet velocities. Planar laser-induced fluorescence (PLIF) imaging and large eddy simulation based on detailed chemical kinetics are carried out to systematically study the structures of ammonia/air premixed jet flames under extreme levels of turbulence conditions, with u′/SL up to 240 and Karlovitz number up to 3019. Consistent with the observation in methane/air jet flames reported in the literature, the reaction zones of premixed ammonia/air jet flames show significantly different behaviour on burners of different sizes under similar Karlovitz number conditions. It is found that reaction zone broadening in jet flames is a spatially evolving process, not only depending on the local eddy/flame interaction but also on the upstream history. The onset of distributed reaction zones is found to take place at positions located several jet orifice diameters above the burner and thereafter eddies are self-produced in the reaction layer due to the continuous vortex stretch interacting in the layer and broadening the reaction zone. The flames on a large burner have turbulence eddies of larger integral length scales that do not fit directly inside the reaction zones, and as such the eddies could not broaden the reaction zones.

Diffusive effects of hydrogen on pressurized lean turbulent hydrogen-air premixed flames

To understand the turbulence-chemistry interaction of lean hydrogen-air premixed flames at elevated pressures, we conduct a series of high-fidelity direct numerical simulations with detailed chemistry and transport by increasing pressure from 1 up to 7 atm. For a fixed ratio of the root-mean-square turbulent velocity fluctuation to the laminar flame speed, two sets of simulations were conducted: one for a fixed ratio of integral length scale to the laminar flame thickness and the other one for a fixed integral length scale. We observe that the turbulent flame speed and volume-integrated heat release rate (HRR) increase with pressure due to the promoted chemical effects. To elucidate the enhanced chemical effects, we conduct a budget analysis of diffusive transport and reaction rate of hydrogen and examine the conditionally-averaged flame structure. As opposed to the laminar flames, the diffusive effects of hydrogen for turbulent flames are found to increase with pressure in a more non-linear way, which significantly enhances the radical pool generation, leading to abundant H radical that is required for the rate of the pressure-sensitive reaction H + O2(+M) = HO2(+M) to be accelerated at higher pressures. Due to the strong diffusive transport of hydrogen for pressurized turbulence, not only does another small HRR peak emerge upstream, but also the location of the main HRR peak is moved towards the upstream region. Furthermore, the probability density function (PDF) of the flame curvature, computed for the isosurface associated with maximal diffusive transport of hydrogen, shows a clear trend of the PDF peak shifting to larger positive values as pressure increases. Simulations with the inclusion of thermal diffusion are also carried out at atmospheric and elevated pressure conditions to quantify the Soret effect. It is found that the magnitude of the hydrogen diffusion rate is augmented by thermal diffusion, affecting its mass fraction distribution. The mean turbulent flame speed is enhanced by approximately 8% and 7% for the 1 and 7 atm conditions, respectively.

Single- and dual-channel nanosecond repetitively pulsed discharges at small and large spark gaps for turbulent premixed spherical flame initiation

This paper reports laminar/turbulent ignition probability (Pig,L/Pig,T) of single- and dual-channel nanosecond-discharge (SN and DN) at small and large inter-electrode gaps (dgap = 0.8 mm and 2.0 mm) using a lean n-butane/air mixture in a double-chamber fan-stirred explosion facility capable of generating near-isotropic turbulence over wide ranges of pulsed repetitive frequency (PRF = 1–100 kHz) and r.m.s. turbulence fluctuation velocity (urms = 0–4.9 m/s). The new DN configuration consists of two parallel anode electrodes with 2.6 mm apart and one central cathode electrode on the same vertical plane, which can generate two spatially separated and temporally synchronized discharges having an almost twice larger initial kernel size than the SN configuration. We apply the same total ignition energy Etot≈18 mJ via a train of 9 pulses/6 pulses for SN/DN experiments, each pulse having Eig≈2.2 mJ (SN) and/or 3.3 mJ (DN) except for the first pulse with the same 0.8 mJ regardless of PRF and dgap. Unlike the common notion that the larger ignition kernel leads to higher Pig,L, it is found that the DN configuration at small dgap = 0.8 mm is totally detrimental for spark ignition (SI) with Pig,L = 0% for all PRFs = 1–100 kHz, while the SN configuration at small dgap = 0.8 mm has its maximum Pig,L = 58% at PRF = 40 kHz showing the synergy effect. But the reverse is found at large dgap = 2.0 mm with Pig,L(DN) > Pig,L(SN). Moreover, when 1 m/s < urms < 4 m/s at PRF = 40 kHz and dgap = 2.0 mm, although both Pig,T(DN) and Pig,T(SN) decrease with increasing urms, Pig,T(DN) is noticeably higher than Pig,T(SN) showing ignition enhancement of dual-channel sparks at large dgap, Pig,T(DN) = Pig,T(SN) = 100% when urms < 1 m/s, and Pig,T(DN) = Pig,T(SN) = 0 % when urms ≥ 4.2 m/s. Finally, high-speed schlieren images of SN/DN kernel evolutions are used to comprehend these results that may be useful for the ignition strategy in lean-burn SI engines.

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. In this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e.ϕ = 0.9 and ϕ = 1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity DT was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including DT in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H2 and other radicals and the enhanced NO pathways in negatively curved regions.

Effects of water droplet injection on turbulent premixed flame propagation: a direct numerical simulation investigation

The influence of water droplet injection on the propagation rate of statistically planar stoichiometric n-heptane-air flames has been analysed based on three-dimensional carrier phase Direct Numerical Simulations for different turbulence intensities and different initially mono-sized droplets. It has been found that most water droplets do not completely evaporate within the flame due to their large latent heat of evaporation for the conditions considered here. Thus, the cooling effect due to the extraction of latent heat during the evaporation of water droplets dominates over the dilution of the concentration of reactants and gives rise to smaller reaction rate of reaction progress variable and thicker flame front than in the corresponding premixed turbulent flame without droplets. These effects (a) strengthen with decreasing droplet size due to higher rate of evaporation for smaller droplets, but (b) weaken with an increase in turbulence intensity. The interaction of water droplets with the flame affects the density-weighted displacement speed through its reaction and molecular diffusion components and the magnitudes of these components remain much greater than the components due to cross-scalar dissipation rate and two-phase coupling. The flame-water droplet interaction for the parameter range considered here acts to reduce the mean density-weighted displacement speed, consumption speed and turbulent flame speed, and this reduction becomes increasingly prominent with decreasing droplet diameter. However, it has been found that the presence of water droplets does not alter the qualitative nature of the strain rate and curvature dependences of both density-weighted displacement speed and consumption speed for the range of parameters considered here, but the correlation strength is altered by the presence of water droplets.

Memory effects of local flame dynamics in turbulent premixed flames

A premixed and thermo-diffusively unstable turbulent hydrogen-air flame-in-a-box case is simulated in conjunction with the flame particle tracking (FPT) method. The flame is located in the flamelet regime. The focus lies on the assessment of memory effects in local flame dynamics. By tracking flame particles on an iso-surface of the flame during flame-turbulence interaction, the time history of flame speed and flame stretch can be recorded for each point on the flame iso-surface in a Lagrangian reference frame. The results reveal a time delay between the local flame speed and flame stretch signal, showing that previous values of flame stretch affect currently observed values of flame speed. Furthermore, by choosing flame particles whose trajectories are dominated by single frequencies, the time delay can be quantified. While plotting instantaneous values of flame speed and flame stretch results in a large scattering for turbulent flames, a quasi-linear correlation can be achieved by shifting the time signal of flame stretch according to the time delay. The time delay itself depends on the local flow time scale, which is expressed as a local Damköhler number. There is, however, an important difference between consumption and displacement speed. While most analyses in the literature are limited to the flame displacement speed, the flame consumption speed is evaluated for each flame particle in this work as well, which shows a strong correlation with the local equivalence ratio even at unsteady conditions. As the flame particles move toward regions with more negative flame stretch, the consumption speed decreases as the flame locally extinguishes. At the same time, the diffusive component of the displacement speed increases, as the tangential component of the diffusive flux increases in regions with strong negative flame curvature.