Direct numerical simulations (DNS) of statistically planar flames at moderate and high Karlovitz number (Ka) have been used to perform an a priori evaluation of a presumed-PDF model approach for filtered reaction rate in the framework of large eddy simulation (LES) for different LES filter sizes. The model is statistical and uses a presumed shape, based here on a beta-distribution, for the sub-grid probability density function (PDF) of a reaction progress variable. Flamelet tabulation is used for the unfiltered reaction rate. It is known that presumed PDF with flamelet tabulation may lead to over-prediction of the modelled reaction rate. This is assessed in a methodical way using DNS of varying complexity, including single-step chemistry and complex methane/air chemistry at equivalence ratio 0.6. It is shown that the error is strongly related to the filter size. A correction function is proposed in this work which can reduce the error on the reaction rate modelling at low turbulence intensities by up to 50%, and which is obtained by imposing that the consumption speed based on the modelled reaction rate matches the exact one in the flamelet limit. A second analysis is also conducted to assess the accuracy of the flamelet assumption itself. This analysis is conducted for a wide range of Ka, from 6 to 4100. It is found that at high Ka this assumption is weaker as expected, however results improve with larger filter sizes due to the reduction of the scatter produced by the fluctuations of the exact reaction rate.@en

Multi-scale analysis of turbulence-flame interaction is performed using experimental data sets from three methane- and propane-fired premixed, turbulent V-flames, at an approach flow turbulent Reynolds number of 450 and a ratio of r.m.s. fluctuating velocity from the mean to laminar flame speed of between 2.1 and 3.0, straddling the border between corrugated flamelets and thin reaction zone in the Borghi-Peters diagram. The measurements were made in the plane of a single laser sheet using stereo particle image velocimetry SPIV and planar laser-induced fluorescence to measure three orthogonal components of velocity and flame OH. Methods to approximate the remaining, unmeasured, out of plane derivatives are described. The instantaneous SPIV images were bandpass filtered at user-specified characteristic length scales Lω and Ls (for vorticity and strain rate, respectively) resulting in instantaneous bandpass-filtered velocity fields, u̲bLω and u̲bLs, which were further analysed to give the bandpass filtered vorticity field, ω̲Lω=∇×u̲bLω, the strain-rate field, eijLs, and the tangential strain rate field aTLs. This work quantifies two aspects of turbulence-flame interaction. The first aspect is that of the flame interaction of eddies of size Ls on the turbulence, as found by the statistics of the alignment of vorticity with strain rate. We find that vortical eddies with scale about Lω=2δth (where δth is the flame thickness) are stretched by Ls structures which are larger than about 2 Lω, with this factor broadly true also for vortical eddies of scales Lω=4δth and Lω=6δth. Within the limitations of the data set, these findings are consistent with those in the literature on reacting and non-reacting flows, suggesting that the premixed flame has had little influence on the vortex stretching mechanism. The second aspect of turbulence-flame interaction examined is that of flame surface-averaged tangential strain rate imparted by eddies. Eddies with length scales Ls smaller than 3 or 4δth are likely to have the strongest individual contribution but eddies of this length scale and smaller may contribute only about 1/5th of the total tangential strain rate. This is to be compared with the value of 10% that has been reported in the literature based on analysis of DNS predictions of premixed flames at turbulent Reynolds numbers up to 110. Eddies with length scale Ls larger than about 20δth contribute a negligible amount to the total tangential strain rate. We have found no evidence that the Lewis number up to about 1.8 has an observable effect, but this may reflect the limitations of the current experiment. In the context of large eddy simulations (LES) of premixed combustion, these results are preliminary experimental evidence supporting the suggestion that resolving turbulence scales down to a few multiples of δth might be adequate to capture much of the flame straining caused by turbulence.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Direct Numerical Simulations (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed to identify the contributions of the autoignition and flame modes. This is performed using an extended Chemical Explosive Mode Analysis (CEMA) which accounts for diffusion effects allowing it to discriminate between deflagration and autoignition. This analysis indicates that in premixed MILD combustion conditions, the main combustion mode is ignition for all dilution and turbulence levels and for the two reactant temperature conditions considered. In non-premixed conditions, the preponderance of the ignition mode was observed to depend on the axial location and mixture fraction stratification. With a large mixture fraction lengthscale, ignition is more preponderant in the early part of the domain while the deflagrative mode increases further downstream. On the other hand, when the mixture fraction lengthscale is small, sequential autoignition is observed. Finally, the various combustion modes are observed to correlate strongly with mixture fraction where lean mixtures are more likely to autoignite while stoichiometric and rich mixtures are more likely to react as deflagrative structures.@en

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.@en

A simple model based on a Perfectly Stirred Reactor (PSR) was proposed for moderate or intense low-oxygen dilution (MILD) combustion. The PSR calculation covers the entire flammability range and the tabulated chemistry approach was applied with a presumed joint probability density function (PDF). The jet in hot and diluted coflow experimental set-up under MILD conditions was simulated using PSR model for two oxygen dilution levels. The unheated fuel jet consists of 50% CH4 and 50% H2. The computed results for mean temperature major and minor species mass fractions were compared with the experimental data and simulation results through a multi-environment transported PDF approach. A good agreement was observed at three different axial locations for these comparisons despite peak value overprediction of CO formation suggesting that MILD combustion can be effectively modeled by the proposed PSR model with lower computational cost.@en

Direct numerical simulation (DNS) data of freely propagating turbulent premixed flame of stoichiometric hydrogen air mixture inside a closed vessel is analysed to study a sub-grid combustion closure based on unstrained flamelet approach. This modeling framework needs closures for the sub-grid scale (SGS) reaction rate and scalar dissipation rate. The results show that the closure models for these two SGS quantities work quite well. The dissipation rate closure involves a scale dependent parameter, βc, which is related to the flame curvature induced effects. The reactivity of reactant mixture increases with time in isochoric combustion because the mixture temperature and pressure increase with time. This also influences the parameter βc and thus the dynamic evaluation of this parameter is investigated using the DNS data.@en

Multiscale analysis of turbulence-flame interaction is performed using direct numerical simulation (DNS) data of premixed flames. Bandpass filtering method is used to educe turbulent eddies of various sizes and their vorticity and strain rate fields. The vortical structures at a scale of Lω are stretched strongly by the most extensional principal strain rate of eddies of scale 4Lω, which is similar to the behaviour in non-reacting turbulence. Hence, combustion does not influence the physics of vortex stretching mechanism. The fractional contribution from eddies of size Ls to the total tangential strain rate is investigated. The results highlight that eddies larger than two times the laminar flame thermal thickness contributes predominantly to flame straining and eddies smaller than 2δth contributes less than 10% to the total tangential strain rate for turbulence intensities, from u′/sL = 1.41 to u′/sL = 11.25, investigated here. The cutoff scale identified through this analysis is larger than the previous propositions and the implication of this finding to subgrid scale premixed combustion modelling is discussed.@en

Various commonly used markers for heat release are assessed using direct numerical simulation (DNS) data for Moderate or Intense Low-oxygen Dilution (MILD) combustion to find their suitability for non-premixed MILD combustion. The laser-induced fluorescence (LIF) signals of various markers are synthesized from the DNS data to construct their planar (PLIF) images which are compared to the heat release rate images obtained directly from the DNS data. The local OH values in heat releasing regions are observed to be very small compared to the background level coming from unreacted mixture diluted with exhaust gases. Furthermore, these values are very much smaller compared to those in burnt regions. This observation rises questions on the use of OH-PLIF for MILD combustion. However, the chemiluminescent image obtained using OH* is shown to correlate well with the heat release. Two scalar-based PLIF markers, (OH × CH2O) and (H × CH2O), correlate well with the heat release. Flame index (FI) and chemical explosive mode analyses (CEMA) are used to identify premixed and non-premixed regions in MILD combustion. Although there is some agreement between the CEMA and FI results, large discrepancies are still observed. The schlieren images deduced from the DNS data showed that this technique can be used for a quick and qualitative identification of MILD combustion before applying expensive laser diagnostics.@en

The criterion used to define MILD combustion in non-premixed condition is analysed using Direct Numerical Simulation (DNS) of MILD combustion of methane-diluted air established with internal exhaust gas recirculation. The simulations reveal multiple interacting reaction zones in MILD combustion which are extremely different from conventional combustion. Furthermore, DNS deduced S-curves highlight the role of chemically active species. Specifically, the temperature rise is accompanied with an increase in the scalar dissipation rate of mixture fraction, which is quite contrasting to the classical S-curve from the classical flame theories. This observation is explained on a physical basis.@en

Direct numerical simulations of Moderate or Intense Low-oxygen Dilution combustion inside a cubical domain are performed. The computational domain is specified with inflow and outflow boundary conditions in one direction and periodic conditions in the other two directions. The inflowing mixture is constructed carefully in a preprocessing step and has spatially varying mixture fraction and reaction progress variable fields. Thus, this mixture includes a range of thermo-chemical states for a given mixture fraction value. The combustion kinetics is modelled using a 58-step skeletal mechanism including a chemiluminescent species, OH*, for methane–air combustion. The study of reaction zone structures in the physical and mixture fraction spaces shows the presence of ignition fronts, lean and rich premixed flames and non-premixed combustion. These three modes of combustion are observed without the typical triple-flame structure and this results from the spatio-temporally varying mixture fraction field undergoing turbulent mixing and reaction. The flame index and its pdf are analysed to estimate the fractional contributions from these combustion modes to the total heat release rate. The lean premixed mode is observed to be quite dominant and contribution of non-premixed mode increased from about 11% to 20% when the mean oxygen mole fraction in the inflowing mixture is reduced from about 2.7% to 1.6%. Also, the non-premixed contribution increases if one decreases the integral length scale of the mixture fraction field. All of these results and observations are explained on physical basis.@en

Direct Numerical Simulation (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed to gather insights on autoignition and flame propagation in MILD combustion. Unlike in conventional combustion, the chemical reactions occur over a large portion of the computational domain. The presence of ignition and flame propagation and their coexistence are studied through spatial and statistical analyses of the convective, diffusive and chemical effects in the species transport equations. Autoignition is observed in regions with lean mixtures because of their low ignition delay times and these events propagate into richer mixtures either as a flame or ignition. This is found to be highly dependent on the mixture fraction length scale, ℓZ, and autoignition is favoured when ℓZ is small.@en

Direct numerical simulations (DNS) of low and high Karlovitz number (Ka) flames are analysed to investigate the behaviour of the reactive scalar sub-grid scale (SGS) variance in premixed combustion under a wide range of combustion conditions (regimes). An order of magnitude analysis is performed to assess the importance of various terms in the variance evolution equation and the analysis is validated using the DNS results. This analysis sheds light on the relative behaviour among turbulent transport and production, scalar dissipation and chemical processes involved in the evolution of the SGS variance at different Ka. The common expectation is that the variance equation shifts from a reaction-dissipation balance at low Ka to a production–dissipation balance at high Ka with diminishing reaction contribution. However, in large eddy simulation (LES), a high Ka alone does not make the reaction term negligible, as the relative importance of the reaction term has a concurrent increase with filter size. The filter size can be relatively large compared with the Kolmogorov length scale in practical LES of high Ka flames, and as a consequence a reaction–production–dissipation balance may prevail in the variance equation even in a high Ka configuration, and this possibility is quantified using the DNS analysis in this work. This has implications from modelling perspectives, and therefore two commonly used closures in LES for the SGS scalar dissipation rate are investigated a priori to estimate the importance of the above balance in LES modelling. The results are explained to highlight the interplay among turbulence, chemistry and dissipation processes as a function of Ka.@en

Polycyclic aromatic hydrocarbons (PAHs) are the carcinogenic components of soot. Detailed understanding of PAH formation characteristics is required for development of effective strategies to curtail PAH formation and reduce soot in combustion devices. This study presents an experimental methodology to analyse PAH formation characteristics of a non-premixed methane-air flame with and without hydrogen (H2) addition, using simultaneous planar laser induced fluorescence (PLIF) imaging of PAH and hydroxyl radical (OH). OH PLIF was used to represent peak temperature regions in the flame front. One-dimensional, opposed-jet laminar non-premixed flame simulations were also carried out for the same fuel mixture conditions. This work describes comparison of trends from both sets of studies. PAH fluorescence intensity values were observed to increase with increasing height above burner, however this rate of increase reduced with H2 addition. This observed rate of change in PAH fluorescence (that is, PAH growth characteristics) is indicative of the sooting potential of the fuel mixture. PAH fluorescence from experiments and PAH concentration from simulation show strong reduction with increase in H2 addition. The percentage reduction in PAH fluorescence signal with H2 addition closer to the burner tip was of a similar magnitude to that observed with flame simulations. The reduction in PAH with H2 addition could be attributed to the reduction in acetylene and propargyl concentrations, and reduced H-abstraction rates, which reduced the availability of active sites for PAH growth. The proposed experimental methodology for PAH measurements can be readily applied to any fuel mixtures.@en

A cyclonic burner operating under moderate or intense low-oxygen dilution (MILD) conditions is simulated using a perfectly stirred reactor (PSR) incorporated within a tabulated chemistry approach. A presumed joint probability density function method is used with appropriate submodels for the turbulence-chemistry interaction. Non-adiabatic effects are included in the PSR calculation to take into account the effects of non-negligible wall heat loss in the burner. Five different operating conditions are investigated, and the computed mean temperatures agree well with measurements. A substantial improvement is observed when the non-adiabatic PSR is used, highlighting the importance of heat transfer effects for burner configurations involving internal exhaust gas recirculation. Furthermore, enhanced reaction homogeneity is observed in this cyclonic configuration for the globally lean case, leading to a more spatially uniform temperature variation with MILD combustion.@en

A study is conducted to identify advantages and limitations of existing large-eddy simulation (LES) closures for the subgrid-scale (SGS) kinetic energy using a database of direct numerical simulations (DNS). The analysis is conducted for both reacting and nonreacting flows, different turbulence conditions, and various filter sizes. A model, based on dissipation and diffusion of momentum (LD-D model), is proposed in this paper based on the observed behavior of four existing models. Our model shows the best overall agreements with DNS statistics. Two main investigations are conducted for both reacting and nonreacting flows: (i) an investigation on the robustness of the model constants, showing that commonly used constants lead to a severe underestimation of the SGS kinetic energy and enlightening their dependence on Reynolds number and filter size; and (ii) an investigation on the statistical behavior of the SGS closures, which suggests that the dissipation of momentum is the key parameter to be considered in such closures and that dilatation effect is important and must be captured correctly in reacting flows. Additional properties of SGS kinetic energy modeling are identified and discussed.@en

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighboring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Reλ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales, allowing one to determine the fluxes between these scales and to interrogate the role of nonlocal (in physical space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale Lω are stretched mostly by straining structures of size 3Lω to 5Lω, and the stretching by eddies of sizes larger than 10Lω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Reλ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.@en

Multiscale analysis of wall-bounded turbulent premixed flames is performed using three-dimensional direct numerical simulation data of flame-wall interaction (FWI). The chosen configuration represents head-on quenching of a turbulent statistically planar stoichiometric methane-air flame by an isothermal inert wall. Different turbulence intensities and chemical mechanisms have been analyzed. A bandpass filtering technique is utilised to analyze the influence of turbulent eddies of varying size and the statistics of vorticity and strain rate fields associated with them. It is found that the presence of the flame does not alter the mechanism of vortex stretching in turbulent flows when the flame is away from the wall, but in the case of FWI, the mechanism of vortex stretching is altered due to a reduction in the contribution from non-local strain, and the small scales of turbulence start to contribute to the flame straining process. The results indicate that small scale eddies do not contribute to the tangential strain rate when the flames are away from the walls, whereas the contribution from the small scales to the tangential strain rate increases when the flame is in the vicinity of the wall. It is also found that the choice of chemical mechanism does not influence the underlying fluid mechanical processes involved in FWI.@en