Thin Reaction Zones Research Articles

Scalar dissipation rate transport conditional on flow topologies in different regimes of premixed turbulent combustion

The Favre-averaged scalar dissipation rate transport conditional on local flow topologies in premixed turbulent flames has been analysed based on a detailed chemistry Direct Numerical Simulation database of statistically planar turbulent hydrogen-air premixed flames with an equivalence ratio of 0.7 representing the corrugated flamelets, thin reaction zones and broken reaction zones regimes of premixed turbulent combustion. The local flow topologies have been categorised by the values of the three invariants of the velocity gradient tensor and the statistical behaviour of the Favre-averaged scalar dissipation rate conditional on these flow topologies has been analysed in detail for different choices of reaction progress variable. The qualitative behaviour of the scalar-turbulence interaction term in the Favre-averaged scalar dissipation rate transport equation has been found to be affected by the regime of combustion, whereas the chemical reaction rate gradient contribution to the scalar dissipation rate transport has been found to be affected by the choice of the reaction progress variable. The topologies, which exist for all values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in premixed turbulent flames for all regimes of combustion. In addition, the flow topologies, which are obtained only for positive values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in the case representing the corrugated flamelets regime combustion. An unstable nodal flow topology, which is representative of a counter-flow configuration, has been found to be a dominant contributor to the Favre-averaged scalar dissipation rate transport for all regimes of combustion irrespective of the choice of reaction progress variable.

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.

Low-temperature chemistry in n-heptane/air premixed turbulent flames

The effects of low-temperature chemistry (LTC) on n-heptane/air premixed turbulent flames in the thin reaction zones regime are investigated using direct numerical simulations (DNS) with reduced multi-step chemistry (129-species, 1234-reaction mechanism reduced from CaltechMech). An initial mixture of n-heptane/air at an equivalence ratio of 0.7, unburnt temperature of 650 K, and atmospheric pressure, which is in the negative temperature coefficient (NTC) region, is considered. The focus is put on three separate aspects: 1) LTC in turbulent hot flames propagating in this unburnt (fresh) mixture, 2) turbulent hot flames (with LTC) propagating in a mixture that has undergone first-stage ignition, and 3) turbulent cool flames. These types of flames can all be encountered in modern gasoline compression ignition and diesel engines for example. For the first aspect, it is found that LTC has negligible effect for the conditions considered. For the second aspect, at constant Karlovitz number, the increase in turbulent flame speed (relative to that of turbulent hot flames propagating in the unburnt mixture) due to partial ignition of the reactants is attributed to the increase in laminar flame speed, as opposed to turbulence–LTC interaction. Furthermore, the reaction zone is affected by turbulence in the same way as hot flames propagating in an unburnt mixture. For the third aspect, the first DNS of turbulent cool premixed n-heptane/air flames are presented. Under the current conditions, the initial laminar cool flames are strongly affected by auto-ignition, which is expected to occur under engine conditions, and has an ignition front structure. As the turbulent flames develop, turbulent diffusion becomes sufficiently large to initiate self-propagation of the cool flames. The flames are observed to propagate upstream steadily until they reach the inlet. The steady-state turbulent flames are found to have a highly distributed reaction zone. Nevertheless, their reaction zone structure is found to approach that of the reference (self-propagating) laminar flame (which is significantly different than that of the initial ignition fronts). In addition, this strong turbulence does not affect the global chemical pathways compared to those in the reference laminar flame. Finally, their normalized turbulent flame speed is comparable to that of hot flames at similar Karlovitz numbers.

Surface Density Function statistics in hydrogen-air flames for different turbulent premixed combustion regimes

ABSTRACTThe choice of reaction progress variable (RPV) on the statistical behavior of the surface density function (SDF) and the strain rates, which govern the evolution of SDF, have been analyzed using a detailed chemistry Direct Numerical Simulation (DNS) database of freely propagating statistically planar -air flames with an equivalence ratio of 0.7. The DNS database consists of three cases spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. For this analysis, the RPV is defined based on the mass fractions of H2, O2 and H2O. The mean variations of the SDF and the flame displacement speed, , have also been found to be dependent on the choice of the RPV. The progressive weakening (strengthening) of the preferential alignment of the RPV gradient with the most extensive (compressive) principal strain rate with increasing Karlovitz number leads to changes in the behaviors of normal and tangential strain rates from one combustion regime to another. The differences in displacement speed statistics for different choices of RPV affect the behaviors of the normal strain rate due to flame propagation and curvature stretch. The relative thickening/thinning of the reaction layers of the major species has been explained in terms of the statistics of effective normal strain rate experienced by the -isosurfaces for different choices of RPVs.

A simplified model of local flame structure in thin reaction zones regime

In thin reaction zones regime, frequently localized flame quenching occurs, due to which a portion of reactant would mix with productions before burning. A simplified flame model, which takes account of this reactant–product mixing effect, was put forward. On the basis of this model, local flamelet characteristics were analyzed by both theoretical and numerical methods. The results show that flame structure and propagation could be notably influenced by reactant–product mixing. A thickened postflame high OH concentration zone and a double-peak profile of active radicals were predicted, which are in accordance with existing direct numerical simulation results but can’t be reflected by traditional models.

Simulation of propane-air premixed combustion process in randomly packed beds

Real geometric structures of randomly packed beds are modeled using the discrete element software LIGGGHTS. The wall-adapting local eddy-viscosity (WALE) model and the EBU-Arrhenius combustion model are used to simulate the propane-air premixed combustion process in the randomly packed beds, and the calculated results are compared with experimental data. The results reveal that the turbulence model and combustion model used in this paper are reasonable. Next, propagation velocity, area, mean vorticity and fractal dimension of a flame surface are calculated at various time points with different inlet velocities to investigate the changes in flame characteristics during the combustion process and the effect of increasing the inlet velocity. According to our results, the flame propagation velocity changes do not exhibit a clear trend over time. However, the variation trends of the two curves under the different inlet velocities are similar. In addition, the fractal dimension exhibits no obvious rule of increasing or decreasing during the combustion process. The area and mean vorticity of the flame surface increase with time. However, the rules of increase are not exactly the same. In addition, the flame regimes at various time points are identified. The results reveal that the turbulent premixed flames in a packed bed under two inlet velocities are concentrated in the thin reaction zone.

THE KINETICS OF CaO ASSISTED PATTUKKU CHARCOAL STEAM GASIFICATION

Abstract Coal is a solid fuel that can be converted into syngas through gasification process. To obtain optimum gasification process design and operation, in-depth understanding of the influential parameters is required. This study aims to investigate the effect of temperature on the gasification process and to obtain its kinetics parameters. The study was carried out in a tubular reactor equipped with a heater and a condenser. Steam was used as gasifying agent, while CaO was employed as a CO2 adsorbent. The charcoal from coal was subjected to gasification at temperatures of 600°C, 700°C, and 800°C. The ratio of charcoal and CaO was 1:1. The gasification process lasted for 60 minutes with gas sample was taken every 15 minutes for composition analysis. The results showed that a temperature increase of 100°C caused a proportional increase of conversion of about 75% higher. The value of activation energy (Ea) and exponential factor (ko) were 46.645kJ/mole and 328.3894/min, respectively. For mass transfer parameters, values of activation energy for surface diffusion (Es) and surface diffusivity factor (as) were 81.126 kJ/mole and 0.138/min, respectively. Keywords: gasification; mathematical model; Pattukku coal char; steam; Thin Reaction Zone Model

Hybridization Melting Between Continent‐Derived Sediment and Depleted Peridotite in Subduction Zones

AbstractTo better constrain the processes by which subducted continent‐derived sediment and the overlying mantle wedge react to produce hybrid magmas, we have performed a series of high‐pressure interaction experiments involving a phyllitic metasediment and a depleted peridotite (dunite) from the Mediterranean section of the Alpine‐Himalayan orogenic belt at 2–3 GPa. Two different experimental methods were compared, namely, the reaction of separate, juxtaposed peridotite and metasediment blocks (reaction experiments) and capsules in which the two rocks were included as an intimately mixed powder before the experiments (mixed experiments). In reaction experiments, only the metasediment partially melted, and a marked, thin reaction zone dominated by orthopyroxene formed between the dunite and phyllite blocks. In contrast, a hybrid melt phase was found in all mixed experiments. Trace element analyses indicated that Cs, Rb, Ba, Th, U, Nb, Ta, Zr, and Hf were strongly incompatible, together with marked light rare earth element/heavy rare earth element fractionation. The reaction with peridotite can significantly affect the mobility of medium rare earth element, heavy rare earth element, and transition elements during sediment‐mantle interaction, enriching them in hybrid melts. In addition, the nature of the sedimentary starting materials can considerably affect trace element behavior in resulting hybrid melts. There is a significant resemblance between the trace element distribution patterns of hybrid melts produced in our experiments and those of natural postcollisional potassium‐rich volcanic rocks from the eastern Mediterranean region. The experiments show that phlogopite is not necessarily required in the source to produce the SiO2‐richer end of the range of K‐rich magmas.

Morphology and structure of hydrogen–air turbulent premixed flames

Direct numerical simulations of turbulent premixed planar flames in the corrugated flamelets and thin reaction zones regimes are analysed to investigate the effect of turbulence on the flame structure and morphology. A tool based on topological invariants called shapefinders, consisting of the planarity and filamentarity, is applied to assess the flame morphology. Several statistics show that the filamentarity, which represents lumped effects of the turbulence on the flame morphology, is closely correlated with the Damköhler number, but not with the Karlovitz number. To investigate which scale of turbulent fluctuations is responsible for the flame morphology evolution, the conditional averages of the Kolmogorov length scale and the Taylor microscale are studied. The conditional averages show strong correlation between the Taylor microscale and the filamentarity, while similar strong correlation is not observed for the Kolmogorov length scale. These results suggest that the turbulence–flame interaction relevant to the flame morphology occurs at the length scale greater than the Taylor microscale for relatively large Damköhler number conditions. The fractal dimension is computed for the DNS and filtered reaction progress variable fields with different filter sizes. The computed fractal dimensions between the resolved and the Taylor-microscale filtered fields are almost identical. Also, it was shown that 93–97% of flame surface area is recovered when the filter size of the Taylor microscale is used. However, this fraction rapidly decreases when the integral length scale is used for the filter size. A similar trend was observed for the flame wrinkling factor.

Modelling of the transition of a turbulent shock-flame complex to detonation using the linear eddy model

In the current study, the influence of turbulent mixing and local reaction rates on the transition to detonation of a turbulent shock-flame complex was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane–oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final stages of deflagration to detonation transition (DDT). The modelling procedure adopted was a grid-within-a-grid approach: The compressible linear eddy model for large eddy simulation (CLEM-LES). It was found that average turbulent velocity fluctuations greater than the laminar flame speed by an order of magnitude were required in order to maintain wave velocities above the Chapman–Jouguet (CJ)-deflagration velocity threshold, a precursor requirement for detonation re-initiation to occur. It was also found that sufficient turbulent burning on the flame surface was required in order to drive pressure waves to sufficiently strengthen the leading shock wave, locally, in order to trigger auto-ignition hot spots in the wave front. These local explosion events, which were found to burn out through turbulent surface reactions, drive transverse pressure waves outward. Upon subsequent shock reflections or interactions of the transverse waves, new local explosion events occurred, which further strengthened the adjacent leading shock wave above the CJ-detonation speed. Eventually, through this process, the wave sustained the CJ-detonation speed, on average, through the cyclic mechanism of local explosion events followed by turbulent surface reactions. Finally, combustion of the flame acceleration process was found to lie within the thin-reaction zones regime.

Effects of Karlovitz Number on Flame Surface Wrinkling in Turbulent Lean Premixed Methane-Air Flames

ABSTRACTDirect numerical simulations are carried out to study the effects of the Karlovitz number (Ka) on the surface wrinkling of lean methane-air flames of equivalence ratio 0.5 and non-dimensional turbulence intensities (urms/SL) of 2–25. The mixture pressure is 20 bar and temperature is 810 K to simulate approximate conditions in lean-burn natural gas engines. The Karlovitz number varies from 1.1–49.4, and the Damköhler (Da) number from 0.26–3.2, corresponding to turbulent premixed combustion in the thin reaction zone regime. With increasing Ka, there is increased probability of forming highly curved surfaces locally. The distribution of the shape factor of the local surface does not vary with Ka. The surface-averaged tangential strain rate is proportional to the Ka for flames in the thin reaction zone regime. By examining the flame displacement speed on the flame surface, it is found that on a highly curved surface, irrespective of whether it is convex or concave, flame stretch becomes negative due to the negative propagation term. The functional dependence of the conditional mean flame displacement speed on curvature is only weakly dependent on Ka and the shape factor. The physical insights derived from the analysis are applied to the modeling of the flame surface density equation.

Enstrophy transport conditional on local flow topologies in different regimes of premixed turbulent combustion

Enstrophy is an intrinsic feature of turbulent flows, and its transport properties are essential for the understanding of premixed flame-turbulence interaction. The interrelation between the enstrophy transport and flow topologies, which can be assigned to eight categories based on the three invariants of the velocity-gradient tensor, has been analysed here. The enstrophy transport conditional on flow topologies in turbulent premixed flames has been analysed using a Direct Numerical Simulation database representing the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) combustion regimes. The flame in the CF regime exhibits considerable flame-generated enstrophy, and the dilatation rate and baroclinic torque contributions to the enstrophy transport act as leading order sink and source terms, respectively. Consequently, flow topologies associated with positive dilatation rate values, contribute significantly to the enstrophy transport in the CF regime. By contrast, enstrophy decreases from the unburned to the burned gas side for the cases representing the TRZ and BRZ regimes, with diminishing influences of dilatation rate and baroclinic torque. The enstrophy transport in the TRZ and BRZ regimes is governed by the vortex-stretching and viscous dissipation contributions, similar to non-reacting flows, and topologies existing for all values of dilatation rate remain significant contributors.

Effects of Karlovitz number on turbulent kinetic energy transport in turbulent lean premixed methane/air flames

Direct numerical simulations of lean methane/air flames are carried out to study the effects of premixed combustion on turbulence. The equivalence ratio of the flame is 0.5 and non-dimensional turbulence intensities (urms/SL) are between 2 and 25. The mixture pressure is 20 bars and temperature is 810 K to simulate approximate conditions in lean-burn natural gas engines. The Karlovitz number (Ka) varies from 1.1 to 49.4, and the Damköhler number (Da) varies from 0.26 to 3.2 corresponding to turbulent premixed combustion in the thin reaction zone (TRZ) regime. It is found that turbulence kinetic energy (TKE) and its dissipation rate decrease monotonically across the flame brush while the integral length scale increases monotonically for flames in the TRZ regime. The transport equation of TKE is then examined, and the scaling of the terms in the equation is discussed. It is found that the sink term which represents molecular diffusion and viscous dissipation is the dominant term in the TKE balance and it scales with the square of Ka. The relative importance of the other terms with respect to the dissipation term is studied. With increasing Ka, the other terms in the TKE balance become less important compared to the dissipation term.

A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

The present work aims at modeling the entire convection flux overline {rho mathbf {u}W} in the transport equation for a mean reaction rate overline {rho W} in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for overline {rho mathbf {u}W} are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, overline {rho {u}W}, and mean, tilde {u}overline {rho W}, convection fluxes is well pronounced, with the turbulent flux, overline {rho u^{prime prime }W^{prime prime }}, showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux overline {rho mathbf {u}W} reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.

Thin Reaction Zone Model for Evaluating the Mechanisms that Control the Char Gasification Process: 1. Quasi-steady State

Reaction mechanism takes place in char gasification was tested by kinetic studies. A modified kinetic model (thin reaction zone model) was developed to evaluate the mechanisms controlling the process of gasification. The model was compared to the experimental data of char gasification using steam as gasification agent. The gasification was carried out at 600– $$800\,{^{\circ }}\hbox {C}$$ for 60 min. The model assuming the mass transfer of steam through the ash layer controls the reaction rate work well. The average error at operating temperatures of 600, 700, and $$800\,{^{\circ }}\hbox {C}$$ was 2.89, 1.75, and 3.26% respectively.

Flame thickness and conditional scalar dissipation rate in a premixed temporal turbulent reacting jet

The flame structure corresponding to lean hydrogen–air premixed flames in intense sheared turbulence in the thin reaction zone regime is quantified from flame thickness and conditional scalar dissipation rate statistics, obtained from recent direct numerical simulation data of premixed temporally-evolving turbulent slot jet flames [1]. It is found that, on average, these sheared turbulent flames are thinner than their corresponding planar laminar flames. Extensive analysis is performed to identify the reason for this counter-intuitive thinning effect. The factors controlling the flame thickness are analyzed through two different routes i.e., the kinematic route, and the transport and chemical kinetics route. The kinematic route is examined by comparing the statistics of the normal strain rate due to fluid motion with the statistics of the normal strain rate due to varying flame displacement speed or self-propagation. It is found that while the fluid normal straining is positive and tends to separate iso-scalar surfaces, the dominating normal strain rate due to self-propagation is negative and tends to bring the iso-scalar surfaces closer resulting in overall thinning of the flame. The transport and chemical kinetics route is examined by studying the non-unity Lewis number effect on the premixed flames. The effects from the kinematic route are found to couple with the transport and chemical kinetics route. In addition, the intermittency of the conditional scalar dissipation rate is also examined. It is found to exhibit a unique non-monotonicity of the exponent of the stretched exponential function, conventionally used to describe probability density function tails of such variables. The non-monotonicity is attributed to the detailed chemical structure of hydrogen-air flames in which heat release occurs close to the unburnt reactants at near free-stream temperatures.

Assessment of Finite Rate Chemistry Large Eddy Simulation Combustion Models

Large Eddy Simulations (LES) of a swirl-stabilized natural gas-air flame in a laboratory gas turbine combustor is performed using six different LES combustion models to provide a head-to-head comparative study. More specifically, six finite rate chemistry models, including the thickened flame model, the partially stirred reactor model, the approximate deconvolution model and the stochastic fields model have been studied. The LES predictions are compared against experimental data including velocity, temperature and major species concentrations measured using Particle Image Velocimetry (PIV), OH Planar Laser-Induced Fluorescence (OH-PLIF), OH chemiluminescence imaging and one-dimensional laser Raman scattering. Based on previous results a skeletal methane-air reaction mechanism based on the well-known Smooke and Giovangigli mechanism was used in this work. Two computational grids of about 7 and 56 million cells, respectively, are used to quantify the influence of grid resolution. The overall flow and flame structures appear similar for all LES combustion models studied and agree well with experimental still and video images. Takeno flame index and chemical explosives mode analysis suggest that the flame is premixed and resides within the thin reaction zone. The LES results show good agreement with the experimental data for the axial velocity, temperature and major species, but differences due to the choice of LES combustion model are observed and discussed. Furthermore, the intrinsic flame structure and the flame dynamics are similarly predicted by all LES combustion models examined. Within this range of models, there is no strong case for deciding which model performs the best.

Multi-species PLIF study of the structures of turbulent premixed methane/air jet flames in the flamelet and thin-reaction zones regimes

Simultaneously planar laser-induced fluorescence (PLIF) measurements of OH, CH, CH2O and toluene are carried out to investigate the structures of turbulent premixed methane/air jet flames in the flamelet regime and the thin-reaction zones regime. A premixed flame jet burner of an inner diameter of 1.5mm is employed. Stoichiometric methane/air mixtures introduced as a jet are ignited and stabilized in a hot co-flow generated by a coaxial porous plug pilot flame surrounding the jet. The Reynolds number for the studied jet ranges from 960 to 11,500 with the characteristic Karlovitz number ranging from 1 to 60. The focus of this study is on the characterization of the structures and turbulent burning velocity of premixed flames in the flamelet and the thin-reaction zones regimes. The preheat zone is analyzed using the CH2O and toluene PLIF fields, whereas the reaction zone is analyzed using the CH and OH PLIF fields. Laser Doppler Anemometer (LDA) measurements are performed to characterize the turbulence field and it is noted that when the Reynolds/Karlovitz number increases a successive thickening of the preheat zone is observed, whereas the reaction zone, characterized by the CH layer maintains nearly the same thickness. The heat release zone, characterized by the combination of the OH and CH2O PLIF fields, is shown to nearly maintain the same thickness under the present experimental conditions. The flame surface wrinkle ratio is shown to be Reynolds number and Karlovitz number independent when the Reynolds number is high enough such that the smallest wrinkle scales reach to the length scales of the thin reaction layers. The global fuel consumption speed of the jet flame is analyzed using the toluene PLIF field and the OH PLIF field. A discrepancy in the two consumption velocities is found as the Karlovitz number increases. This is found to be a result of the broadening of the oxidation zone. These findings provide experimental support to the flamelet and thin-reaction zone regime hypotheses of turbulent premixed combustion.

Effects of dissipation rate and diffusion rate of the progress variable on local fuel burning rate in premixed turbulent flames

The validity of the premixed flamelet equations and the dependence of the fuel burning rate on the parameters involved in these equations have been investigated using a large series of direct numerical simulations of turbulent premixed flames in the thin reaction zones (TRZ) and the distributed reaction zones (DRZ) regimes. Methane, toluene, n-heptane, and iso-octane fuels were considered over a wide range of unburnt conditions and turbulence characteristics. Flames with unity and non-unity Lewis numbers were investigated separately to isolate turbulence-chemistry interaction from differential diffusion effects. In both cases, the flamelet equations, which rely on the assumption of a thin reaction zone, are locally valid throughout the TRZ regime, more precisely up to a Karlovitz number at the reaction zone of 10 (based on the definition used in this paper). Consistent with this result, in the unity Lewis number limit, the fuel burning rate is strongly correlated with the dissipation rate of the progress variable, the only parameter in the flamelet equations. In the non-unity Lewis number case, the burning rate is a strong function of both the dissipation rate and the diffusion rate, both of which are parameters in the flamelet equations. In particular, the correlation with these parameters is significantly better than with curvature or tangential strain rate.

A mixing timescale model for TPDF simulations of turbulent premixed flames

Transported probability density function (TPDF) methods are an attractive modeling approach for turbulent flames as chemical reactions appear in closed form. However, molecular micro-mixing needs to be modeled and this modeling is considered a primary challenge for TPDF methods. In the present study, a new algebraic mixing rate model for TPDF simulations of turbulent premixed flames is proposed, which is a key ingredient in commonly used molecular mixing models. The new model aims to properly account for the transition in reactive scalar mixing rate behavior from the limit of turbulence-dominated mixing to molecular mixing behavior in flamelets. An a priori assessment of the new model is performed using direct numerical simulation (DNS) data of a lean premixed hydrogen–air jet flame. The new model accurately captures the mixing timescale behavior in the DNS and is found to be a significant improvement over the commonly used constant mechanical-to-scalar mixing timescale ratio model. An a posteriori TPDF study is then performed using the same DNS data as a numerical test bed. The DNS provides the initial conditions and time-varying input quantities, including the mean velocity, turbulent diffusion coefficient, and modeled scalar mixing rate for the TPDF simulations, thus allowing an exclusive focus on the mixing model. The new mixing timescale model is compared with the constant mechanical-to-scalar mixing timescale ratio coupled with the Euclidean Minimum Spanning Tree (EMST) mixing model, as well as a laminar flamelet closure by Pope and Anand (1984). It is found that the laminar flamelet closure is unable to properly capture the mixing behavior in the thin reaction zones regime while the constant mechanical-to-scalar mixing timescale model under-predicts the flame speed. The EMST model coupled with the new mixing timescale model provides the best prediction of the flame structure and flame propagation among the models tested, as the dynamics of reactive scalar mixing across different flame regimes are appropriately accounted for.