High Karlovitz Number Research Articles

Large eddy simulation/dynamic thickened flame modeling of a high Karlovitz number turbulent premixed jet flame

Due to the complex multiscale interaction between intense turbulence and relatively weak flames, turbulent premixed flames in the thin and broken reaction zones regimes exhibit strong finite-rate chemistry and strain effects and are hence challenging to model. In this work, a laboratory premixed jet flame in the broken reaction zone, which has recently been studied using direct numerical simulation (DNS), is modeled using a large eddy simulation (LES)/dynamic thickened flame (DTF) approach with detailed chemistry. The presence of substantial flame thickening due to strong turbulence-chemistry interactions, which can be characterized by a high Karlovitz number (Ka), requires the DTF model to thicken the flame in an adaptive way based on the local resolution of flame scales. Here, an appropriate flame sensor and strain-sensitive flame thickness are used to automatically determine the thickening location and thickening factor, respectively. To account for finite-rate chemistry and strain effects, the chemistry is described in two different ways: (1) detailed chemistry denoted as full transport and chemistry (FTC), and (2) tabulated chemistry based on a strained premixed flamelet (SPF) model. The performance of the augmented LES/DTF approach for modeling the high Ka premixed flame is assessed through detailed a posteriori comparisons with DNS of the same flame. It is found that the LES/DTF/FTC model is capable of reproducing most features of the high Ka turbulent premixed flame including accurate CO and NO prediction. The LES/DTF/SPF model has the potential to capture the impact of strong turbulence on the flame structure and provides reasonable prediction of pollutant emissions at a reasonable computational cost. In order to identify the impact of aerodynamic strain, the turbulent flame structure is analyzed and compared with unstrained and strained premixed flamelet solutions. The results indicate that detailed strain effects should be considered when using tabulated methods to model high Ka premixed flames.

Turbulent scalar fluxes in H2-air premixed flames at low and high Karlovitz numbers

The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion have been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen-air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multispecies system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two-dimensional anisotropy due to strong heat release whereas a three-dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multispecies systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sub-grid scalar flux closures, a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray–Moss–Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of large eddy simulations.

Direct numerical simulation of a high Ka CH4/air stratified premixed jet flame

Direct numerical simulation (DNS) of a high Karlovitz number (Ka) CH4/air stratified premixed jet flame was performed and used to provide insights into fundamentals of turbulent stratified premixed flames and their modelling implications. The flame exhibits significant stratification where the central jet has an equivalence ratio of 0.4, which is surrounded by a pilot flame with an equivalence ratio of 0.9. A reduced chemical mechanism for CH4/air combustion based on GRI-Mech3.0 was used, including 268 elementary reactions and 28 transported species. Over five billion grid points were employed to adequately resolve the turbulence and flame scales. The maximum Ka of the flame in the domain approaches 1400, while the jet Damköhler number (Dajet) is as low as 0.0027. The flame shows early stages of CH4/air combustion in the near field and later stages in the far field; the separation of combustion stages can be largely attributed to the small jet flow timescale and the low Dajet. The gradient of equivalence ratio in the flame normal direction, dϕ/dn, is predominantly negative, and small-scale stratification was found to play an important role in determining the local flame structure. Notably, the flame is thinner, the burning is more intense, and the levels of the radical pools, including OH, O and H, are higher in regions with stronger mixture stratification. The local flame structure is more strained and less curved in these regions. The mean flame structure is considerably influenced by the strong shear, which can be reasonably predicted by unity Lewis number stratified premixed flamelets when the thermochemical conditions of the reactant and product are taken locally from the DNS and the strain rates close to those induced by the mean flow are used in the flamelet calculation. An enhanced secondary reaction zone behind the primary reaction zone was observed in the downstream region, where the temperature is high and the fuel concentration is negligible, consistent with the observed separation of combustion stages. The main reactions involved in the secondary reaction zone, including CO + OH⇔CO2 + H (R94), H + O2 + M⇔HO2 + M (R31), HO2 + OH⇔H2O + O2 (R82) and H2 + OH⇔H2O + H (R79), are related to accumulated intermediate species including CO, H2, H, and OH. The detailed mechanism of intermediate species accumulation was explored and its effect on chemical pathways and heat release rate was highlighted.

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Leeff = 0.99 and a lean hydrogen–air flame with Leeff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.

Effects of combustion heat release on velocity and scalar statistics in turbulent premixed jet flames at low and high Karlovitz numbers

Theoretical scaling arguments for turbulent premixed combustion indicate that the pressure-dilatation source of turbulent kinetic energy becomes significant at low Karlovitz numbers, leading to potential invalidation of commonly-used turbulence models developed for non-reacting flow. Based on these arguments, a critical Karlovitz number is defined, below which dilatation effects are expected to become significant. Velocity and scalar statistics are obtained from Direct Numerical Simulation (DNS) calculations of low Mach number spatially-evolving turbulent premixed planar jet flames. At fixed bulk Reynolds number and stoichiometric equivalence ratio, two simulations are performed at Karlovitz numbers above and below the critical Karlovitz number. Hydrogen combustion with detailed transport is modeled using a detailed nine-species chemical kinetic mechanism, and coflows of combustion products are used to ensure flame stability at uniform equivalence ratio. The analysis of these statistics focuses on three key areas. First, the influence of the velocity-pressure gradient source of turbulent kinetic energy is confirmed at a low Karlovitz number, and the unimportance of these effects is confirmed at a high Karlovitz number. Similar effects are observed for the chemical source term in the scalar variance budgets. Second, the degree of alignment between the Reynolds stress tensor (scalar flux) and the strain-rate tensor (scalar gradient), the foundation of a majority of the turbulence models used in reacting flows, is assessed with the DNS databases. Additionally, consistency of anisotropic Reynolds stress and strain-rate tensor invariants is assessed using invariant maps. While good alignment and consistency are obtained for statistics and invariants at a high Karlovitz number, both alignment and consistency degrade at a low Karlovitz number. Third, turbulence models formulated for non-reacting flow are modified algebraically in the Bray–Moss–Libby (BML) formalism for turbulent premixed combustion. A variable efficiency function is defined to capture the regime dependence of heat release effects in these models. Model performance is evaluated at Karlovitz numbers above and below the critical Karlovitz number using the DNS databases, and satisfactory prediction of counter-gradient transport in the flame-normal direction is obtained. However, heat release effects are also observed in the flame-parallel directions in the low-Karlovitz number simulation, and the models developed in the formalism for statistically planar flames fail to capture these effects. Furthermore, in the low-Karlovitz number case, redistributive effects are active on the shear components of the Reynolds stress, which are not considered in the BML formalism. More advanced turbulence models are therefore necessary for turbulent premixed jet flames below the critical Karlovitz number.

Structures of turbulent premixed flames in the high Karlovitz number regime – DNS analysis

Lean premixed turbulent methane-air flames have been investigated using direct numerical simulations (DNS) for different Karlovitz numbers (Ka), ranging from 65 to 3350. The flames are imposed to a high intensity small-scale turbulent environment, corresponding to high Ka conditions, and the effect on the flame structure is investigated during the transition from initial laminar flame to highly distorted turbulent flame. The focus is on the internal structure of different sub-layers of these flames. The preheat layer, fuel consumption layer and oxidation layer are characterized by the distribution of formaldehyde, the fuel consumption rate and the CO consumption rate, respectively. Different measures that quantify sub-layer thickness for turbulent flames have been defined and analyzed. The flame brush is broadened with time while the local thickness (excluding large scale wrinkling) of all three layers initially show thinning due to the interaction of the flame with the turbulent flow field. As time passes, the local thickness of the preheat layer and fuel consumption layer are restored while the oxidation layer remains thinned due to suppression of CO consuming reactions. As Ka increases there is an increasing probability of finding thinned, large gradient regions in each of these sub-layers. The contribution to the evolution of flame thickness from normal strain rate, chemical reaction and normal and tangential diffusion is analyzed in terms of a gradient transport equation. The relative size of the terms changes as Ka increase and, in particular, the term due to chemical reactions loses its relative significance. The observed thinning of the local flame structure is attributed to the preferential alignment of the flame normal with the compressive strain rate eigenvectors. Such alignment provides a mechanism for the flame thinning, consistent with the behavior of non-reacting scalars. A preferred angle of about 20 degrees is observed between the flame normal and the compressive strain rate eigenvector.

Effects of turbulence and strain rate on hydrogen-enriched high Karlovitz number lean premixed methane flames

Effects of hydrogen addition at constant heat release, with the influence of turbulence and strain for lean methane-air turbulent counterflow premixed flames in the distributed regime (high Karlovitz number), are investigated using large eddy simulation (LES). Fuel mixtures of up to 60% of hydrogen in volume are considered, and sub-filter turbulence/chemistry interaction is modelled using the finite rate chemistry partially stirred reactor (PaSR) approach combined with detailed kinetics of a skeletal mechanism based on GRI-MECH3.0. Local flame structure and species formation are examined at different turbulence conditions. With constant heat release, hydrogen addition shows its benefits as species emission decreases with a more stable flame. By increasing integral length scale of turbulent structures, global strain rate of the flame is more significant, leading to an increase in flame thickness and reduction in the formation of intermediate species, pollutant NO and heat release. At higher strain rate, ratio of turbulent to laminar flame speed increases faster with increased hydrogen content of fuel, and the flame structure displays more wrinkling and is shorter as a consequence of faster mixing. It is also found that flame and heat release are less influenced by stretch when hydrogen is present within the fuel mixture, indicating the potential of hydrogen substitution for reaching a defined power output while reducing pollutant emissions.

A direct numerical simulation study of flame structure and stabilization of an experimental high Ka CH4/air premixed jet flame

In the present work, a direct numerical simulation (DNS) of an experimental high Karlovitz number (Ka) CH4/air piloted premixed flame was analyzed to study the inner structure and the stabilization mechanism of the turbulent flame. A reduced chemical mechanism for premixed CH4/air combustion with NOx based on GRI-Mech3.0 was used, including 268 elementary reactions and 28 transported species. The evolution of the stretch factor, I0, indicates that the burning rate per unit flame surface area is considerably reduced in the near field and exhibits a minimum at x/D = 8. Downstream, the burning rate gradually increases. The stretch factor is different between different species, suggesting the quenching of some reactions but not others. Comparison between the turbulent flame and strained laminar flames indicates that certain aspects of the mean flame structure can be represented surprisingly well by flamelets if changes in boundary conditions are accounted for and the strain rate of the mean flow is employed; however, the thickening of the flame due to turbulence is not captured. The spatial development of displacement speeds is studied at higher Ka than previous DNS. In contrast to almost all previous studies, the mean displacement speed conditioned on the flame front is negative in the near field, and the dominant contribution to the displacement speed is normal diffusion with the reaction contribution being secondary. Further downstream, reaction overtakes normal diffusion, contributing to a positive displacement speed. The negative displacement speed in the near field implies that the flame front situates itself in the pilot region where the inner structure of the turbulent flame is affected significantly, and the flame stabilizes in balance with the inward flow. Notably, in the upstream region of the turbulent flame, the main reaction contributing to the production of OH, H+O2⇔O+OH (R35), is weak. Moreover, oxidation reactions, H2+OH⇔H+H2O (R79) and CO+OH⇔CO2+H (R94), are influenced by H2O and CO2 from the pilot and are completely quenched. Hence, the entire radical pool of OH, H and O is affected. However, the fuel consumption layer remains comparably active and generates heat, mainly via the reaction CH4+OH⇔CH3+H2O (R93).

Direct numerical simulations of a high Karlovitz number laboratory premixed jet flame – an analysis of flame stretch and flame thickening

This article reports an analysis of the first detailed chemistry direct numerical simulation (DNS) of a high Karlovitz number laboratory premixed flame. The DNS results are first compared with those from laser-based diagnostics with good agreement. The subsequent analysis focuses on a detailed investigation of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected. The net flame stretch is demonstrated to be a small residual of large competing terms: the positive tangential strain term and the negative curvature stretch term. The latter is found to be driven by flame speed–curvature correlations and dominated in net by low probability highly curved regions. Flame thickening is demonstrated to be substantial on average, while local regions of flame thinning are also observed. The rate of change of the flame thickness (as measured by the scalar gradient magnitude) is demonstrated, analogously to flame stretch, to be a competition between straining tending to increase gradients and flame speed variations in the normal direction tending to decrease them. The flame stretch and flame thickness analyses are connected by the observation that high positive tangential strain rate regions generally correspond with low curvature regions; these regions tend to be positively stretched in net and are relatively thinner compared with other regions. High curvature magnitude regions (both positive and negative) generally correspond with lower tangential strain; these regions are in net negatively stretched and thickened substantially.

A priori filtered chemical source term modeling for LES of high Karlovitz number premixed flames

Assumptions behind closure models for the filtered source term are studied a priori using results from DNS of turbulent n-heptane/air premixed flames at varying Karlovitz numbers. Simulations with both detailed chemistry and tabulated chemistry, as well as unity and non-unity Lewis numbers, are used to determine if finite-rate chemistry and differential diffusion effects affect the filtered chemical source terms. While the unfiltered source term shows large fluctuations, the filtered source terms from detailed chemistry and tabulated chemistry are in good agreement at sufficiently large filter widths (Δ ≳ lF). Using the concept of optimal estimators, it is shown that a tabulation approach using the filtered progress variable and its variance can predict accurately the filtered chemical source terms. Finally, the filtered source terms from the DNS are compared to predictions from two commonly assumed sub-filter probability density function models. Both models show deviations from the filtered DNS source terms but predict accurately the mean turbulent flame speed. The results illustrate the potential of using simple tabulated chemistry approaches based on presumed PDFs for LES of premixed flames in the thin and distributed reaction zones regimes.

Effect of turbulence–chemistry interactions on chemical pathways for turbulent hydrogen–air premixed flames

This paper considers the kinetic pathways of hydrogen oxidation in turbulent, premixed H2–air flames. It assesses the relative roles of different reaction steps in H2 oxidation relative to laminar flames, and the degree to which turbulence–chemistry interactions alters the well understood oxidation pathway that exist in laminar flames. This is done by analyzing the turbulent, lean (ϕ= 0.4), H2–air flame DNS database from Aspden et al. [17]. The relative roles of dominant reaction steps in heat release and radical formation/consumption are analyzed at different Karlovitz numbers and compared with laminar stretched flame calculations from counterflow flames and perfectly stirred reactors. It is found that both the progress variable conditioned and spatially integrated contributions of the dominant reactions remain qualitatively similar between a highly turbulent and a laminar unstretched flame. Larger changes, up to a factor of about two, occur in the relative roles of reactions with secondary influences on heat release and radical production/consumption. These results suggest that the kinetic routes through which H2 is oxidized remain essentially constant between laminar, unstretched flames and high Karlovitz number flames.

A numerical study of diffusive effects in turbulent lean premixed hydrogen flames

Three-dimensional direct numerical simulation of lean premixed hydrogen flames is used to explore the influence of species and thermal diffusion and viscosity on the flame structure and turbulent flame response. The leading-order flame response is shown to be due to the global Lewis number with little influence from the other species. The previously-reported observation of decorrelation of fuel consumption and heat release at high Karlovitz numbers is shown to be solely due to atomic hydrogen diffusion. Finally, it is shown that the suppression of turbulence through the flame cannot be attributed to an increase in viscosity due to the increase in temperature, but that the effect is not negligible. It is further argued that turbulence–flame interactions are better described considering Kolmogorov’s second similarity hypothesis (rather than the first); specifically, by a Karlovitz number that is defined based on the inertial subrange (i.e. the energy dissipation rate) rather than the dissipation subrange (i.e. viscosity or equivalently Kolmogorov scale quantities).

A comparison between direct numerical simulation and experiment of the turbulent burning velocity-related statistics in a turbulent methane-air premixed jet flame at high Karlovitz number

A three-dimensional (3D) direct numerical simulation (DNS) of an experimental turbulent premixed jet flame at high Karlovitz number was studied. The DNS resolution adequately resolves both the flame and turbulence structures. A reduced chemical mechanism for premixed CH4/air flames with NOx based on GRI-Mech3.0 was used, including 268 elementary reactions, and 28 transported species. Consistent post-processing methods were applied to both the DNS and experimental data to evaluate turbulent burning velocity-related statistics, namely the flame surface density (FSD), and the flame curvature. Good agreement was achieved for the 2D comparisons. The DNS data were further analysed and provide 3D statistics unattainable from the experiment. The ratio of the 3D and 2D flame surface densities was estimated. The results are comparable with other values reported for various experimental flames. The 3D and 2D flame curvatures were also compared and their distributions are shown to be quite different owing to the round on-average geometry. Instantaneous images of the heat release surrogate, [CH2O][OH], between the DNS and experiment agreed qualitatively. Various other experimentally obtainable surrogates for heat release rate including [CH2O][H], [CH2O][O], [HCO], and [CH] are also evaluated and compared using the DNS. The inner structure of the flame was compared between the DNS and experiment in terms of the joint PDFs of OH concentration and temperature. Generally good agreement was obtained; discrepancies may be due to the inconsistency of assumed equilibrium levels of OH concentration in the co-flow.

Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence.

Large eddy simulation of lean turbulent hydrogen-enriched methane-air premixed flames at high Karlovitz numbers

Large eddy simulation (LES) is employed to investigate the effects of hydrogen within the fuel mixture for lean CH4–H2 turbulent premixed flames in the distributed reaction zone (high Karlovitz number). The subfilter combustion term representing the interaction between turbulence and chemistry is modelled using the partially stirred reactor (PaSR) model, along with complex chemistry using a skeletal mechanism based on the GRI-MECH3.0, to handle mixtures up to 60% of hydrogen in volume. The influence of hydrogen enrichment at high turbulence levels is studied by means of the local flame structure, and the assessment of species formation inside the flame. Results show that with higher hydrogen content, the flame displays a higher degree of wrinkling and is shorter because of a higher turbulent flame speed. The local structure of the flame is mainly affected by the turbulence but differential diffusion effects still play a role in the flame front aspect, especially when hydrogen addition becomes important. Concerning the formation of intermediate species and pollutants, by increasing the amount of hydrogen in the fuel mixture at fixed equivalence ratio, more emissions are reported. This is expected as the mixture reactivity (heat release) increases when substituting methane by hydrogen in the unburned mixture.

Turbulence-flame interactions in DNS of a laboratory high Karlovitz premixed turbulent jet flame

In the present work, direct numerical simulation (DNS) of a laboratory premixed turbulent jet flame was performed to study turbulence-flame interactions. The turbulent flame features moderate Reynolds number and high Karlovitz number (Ka). The orientations of the flame normal vector n, the vorticity vector ω and the principal strain rate eigenvectors ei are examined. The in-plane and out-of-plane angles are introduced to quantify the vector orientations, which also measure the flame geometry and the vortical structures. A general observation is that the distributions of these angles are more isotropic downstream as the flame and the flow become more developed. The out-of-plane angle of the flame normal vector, β, is a key parameter in developing the correction of 2D measurements to estimate the corresponding 3D quantities. The DNS results show that the correction factor is unity at the inlet and approaches its theoretical value of an isotropic distribution downstream. The alignment characteristics of n, ω and ei, which reflect the interactions of turbulence and flame, are also studied. Similar to a passive scalar gradient in non-reacting flows, the flame normal has a tendency to align with the most compressive strain rate, e3, in the flame, indicating that turbulence contributes to the production of scalar gradient. The vorticity dynamics are examined via the vortex stretching term, which was found to be the predominant source of vorticity generation balanced by dissipation, in the enstrophy transport equation. It is found that although the vorticity preferentially aligns with the intermediate strain rate, e2, the contribution of the most extensive strain rate, e1, to vortex stretching is comparable with that of the intermediate strain rate, e2. This is because the eigenvalue of the most extensive strain rate, λ1, is always large and positive. It is confirmed that the vorticity vector is preferentially positioned along the flame tangential plane, contributing to the dominance of cylindrical curvature of the flame front. Finally, the effect of heat release on the turbulence-flame interactions is examined. It is found that heat release has only limited impact on the statistics due to the minor role played by the strain rate induced by heat release rate in the current high Ka flame.

Fuel and chemistry effects in high Karlovitz premixed turbulent flames

Direct numerical simulations of turbulent premixed flames at high Karlovitz numbers are performed using detailed chemistry. Different fuels, chemical mechanisms, and equivalence ratios are considered and their effects on turbulent flame speed, geometry of the reaction zone, and fuel burning rate are analyzed. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Heavy fuels with above unity Lewis numbers are considered. In the unity Lewis number limit, the n-heptane, iso-octane, toluene, and methane flames at a given reaction zone Karlovitz number present similar normalized turbulent flame speeds and fuel burning rates close to their respective laminar values. When differential diffusion effects are included, the turbulent flame speeds are lower than their unity Lewis number counterparts due to a reduction in the fuel burning rate. The turbulent reaction zone surface areas increase with the turbulence intensity but are not strongly affected by fuel, equivalence ratio, chemical mechanism, or differential diffusion. The geometry of the reaction zone is studied through the probability density functions of strain rate and curvature which are very similar when normalized by Kolmogorov scales at the reaction zone. The dependence of the chemical source terms on the scalar dissipation rate in the unity Lewis number case is shown and the distributions of scalar dissipation rate on the reaction surface are similar to those of passive scalars in homogeneous isotropic turbulence. The reduced burning rates in the presence of differential diffusion are discussed. The present results indicate that mean turbulent flame properties such as burning velocity and fuel consumption can be predicted with the knowledge of only a few global laminar flame properties. Once normalized by the corresponding laminar flame quantities, fuel and chemistry effects in high Karlovitz number premixed turbulent flames are mostly limited to differential diffusion.

Vorticity transformation in high Karlovitz number premixed flames

To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τη. As τη is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulent flames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

ABSTRACTA method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.

Micro-scale Mixing in Turbulent Constant Density Reacting Flows and Premixed Combustion

DNS datasets for inert and reactive scalars in statistically homogeneous and stationary turbulence of constant density fluid, and for turbulent premixed flames in an inflow-outflow configuration and in a jet are examined. The objective is to gain a better physical understanding of mixing to use in modeling molecular diffusion terms. Classical descriptions in term of either scalar fluctuation moments or pdf conservation equations can be related to transport of iso-scalar surfaces by turbulent convection and molecular diffusion. The kinematics and propagation speeds of iso-surfaces are theoretically analyzed. The effective normal strain rate, which combines flow and diffusion-reaction induced processes, emerges as an essential variable; scalar gradients and dissipation rates increase for negative effective normal strains and decrease for positive ones. It is argued that the characteristic mixing time should be proportional to the inverse of the effective normal strain rate. The latter displays drastically different behaviors for constant density turbulence, with predominantly positive values, and for flows with significant heat release, with mostly negative ones. The former turbulent flows cause scalars to become less dissipative as time progresses, whereas the latter increase scalar dissipation. Functional dependences of the molecular diffusion rate conditioned on composition are sought. It is suggested that the characteristic mixing time is determined by the different interrelated processes, mainly in the limits of very low and very high Karlovitz numbers.