Turbulent burning velocity of hydrogen–air premixed propagating flames at elevated pressures

Lewis number represents the thermo-diffusive effects on laminar flames. That of hydrogen–air mixture varies extensively with the equivalence ratio due to the high molecular diffusivity of hydrogen. In this study, the influences of pressure and thermo-diffusive effects on spherically propagating premixed hydrogen–air turbulent flames were studied using a constant volume fan-stirred combustion vessel. It was noted that the ratio of the turbulent to unstretched laminar burning velocity increased with decreasing equivalence ratio and increasing mixture pressure. Turbulent burning velocity was dominated by three factors: (1) purely hydrodynamic factor, turbulence Reynolds number, (2) relative turbulence intensity to reaction speed, the ratio of turbulence intensity to unstretched laminar burning velocity, and (3) sensitivity of the flame to the stretch due to the thermo-diffusive effects, Lewis and Markstein numbers. A turbulent burning velocity correlation in terms of Reynolds and Lewis numbers is presented.     

Transported PDF modeling of high-Reynolds-number premixed turbulent flames

The transported PDF approach, closed at the joint composition-enthalpy level, is applied to model premixed turbulent flames at a wide range of Reynolds numbers. The initial aim of the study is to establish the impact of closure approximations for the scalar dissipation rate upon the relationship between turbulence fluctuations and predicted turbulent burning velocities. The cases considered feature stoichiometric methane-air flames with the chemical source term extracted from a detailed chemistry simulation of the corresponding unstrained laminar flame. The transported PDF approach is subsequently combined with a systematically reduced C/H/O mechanism featuring 142 reactions and 14 solved and 15 steady-state species and applied to piloted premixed stoichiometric methane-air flames investigated experimentally by Chen et al. [Combust. Flame 107 (1996) 223-226]. The cases considered here feature Re=24,200 (flame F3) and 52,500 (flame F1) and Damköhler numbers approaching unity. The effects of variations in the time-scale ratio (2?C??8) and heat losses to the burner were investigated, along with the impact of an extended algebraic relationship for the scalar dissipation rate that accounts for small-scale properties. Comparisons with experimental data show that the modified Curl's model and the extended scalar dissipation-rate closure produce turbulent burning velocities in close agreement with measurements. The study further indicates that a closure at the joint scalar level combined with comprehensive chemistry has the potential to reproduce the detailed chemical structure of premixed turbulent flames. The importance of boundary conditions and comprehensive scalar statistics, including the scalar dissipation rate, is also emphasized by the study.     

Effects of strain rate,turbulence, reactant stoichiometry and heat losses on the interaction of turbulent premixed flames with stoichiometric counterflowing combustion products

Intense strain, turbulence, heat transfer, and mixing with combustion products can affect premixed flames in practical combustion devices. These effects are systematically studied in turbulent premixed CH₄/N₂/O₂ flames using a reactant versus product counterflow system and independently varying bulk strain rate, turbulent Reynolds number, equivalence ratio of the reactant mixture, and temperature of the stoichiometric counterflowing combustion products. The flow field and the turbulent flames are investigated using particle image velocimetry (PIV) measurements and laser-induced fluorescence (LIF) imaging of OH. The OH-LIF images are used to identify the interface between the counterflowing streams, referred to here as the gas mixing layer interface (GMLI). The flame response for different flow conditions is compared in terms of the probability of localized extinction along the GMLI, the turbulent flame brush thickness, and flame position relative to the GMLI, by using an OH-LIF-based progress variable. The probability of localized extinction at the GMLI increases as the separation between the turbulent flame brush and the GMLI decreases. Flame fronts in the vicinity of the GMLI are more likely to extinguish as a result of heat losses, dilution of the reaction zone by the product stream, and large local strain rates. A higher probability of localized extinction at the GMLI is induced by either a larger bulk strain rate or a slower flame speed. As the turbulent Reynolds number increases, the corresponding increase in turbulent flame brush thickness enhances the interactions of the flame fronts with the GMLI. Heat losses are substantially less significant for cases in which the turbulent flame brush is sufficiently separated from the GMLI. For flames in close proximity to the GMLI, the effects of the product stream on the flame front differ for lean and rich reactant mixtures. These disparities are attributed in part to differences in the ignitibility of the reactant mixtures by the hot product stream.     

On the structure of the near field of oxy-fuel jet flames using Raman/Rayleigh laser diagnostics

An experimental study on turbulent non-premixed jet flames is presented with focus on CO₂-diluted oxy-fuel combustion using a coflow burner. Measurements of local temperatures and concentrations of the main species CO₂, O₂, CO, N₂, CH₄, H₂O and H₂ were achieved using the simultaneous line-imaged Raman/Rayleigh laser diagnostics setup at Sandia National Laboratories. Two series of flames burning mixtures of methane and hydrogen were investigated. In the first series, the hydrogen molar fraction in the fuel was varied from 37% to 55%, with a constant jet exit Reynolds number Re_Fuel of 15,000. In the second series the jet exit Reynolds number was varied from 12,000 to 18,000, while keeping 55% H₂ molar fraction in the fuel. Besides local temperatures and concentrations, the results revealed insights on the behaviour of localized extinction in the near-field. It was observed that the degree of extinction increased as the hydrogen content in fuel was decreased and as the jet Reynolds number was increased. Based on the distribution of the temperature, a fully burning probability index able to quantify the degree of extinction along the streamwise coordinate was defined and applied to the present flame measurements. A comparison of measured conditional mean of mass fractions and laminar flame calculations underlined the significant level of differential diffusion in the near-field that tended to decrease farther downstream. The results also showed high local CO levels induced by the high content of CO₂ in the oxidizer and flame products. A shift of maximum flame temperature was observed toward the rich side of the mixture fraction space, most likely as a consequence of reduced heat release in the presence of product dissociation. Main characteristics of laser Raman scattering measurements in CO₂-diluted oxy-fuel conditions compared to air-diluted conditions are also highlighted. Most data, including scalar fluctuations and conditional statistics are available upon request.     

The structure of partially premixed methane flames in high-intensity turbulent flows

Direct numerical simulations (DNS) are conducted to study the structure of partially premixed and non-premixed methane flames in high-intensity two-dimensional isotropic turbulent flows. The results obtained via “flame normal analysis” show local extinction and reignition for both non-premixed and partially premixed flames. Dynamical analysis of the flame with a Lagrangian method indicates that the time integrated strain rate characterizes the finite-rate chemistry effects and the flame extinction better than the strain rate. It is observed that the flame behavior is affected by the “pressure-dilatation” and “viscous-dissipation” in addition to strain rate. Consistent with previous studies, high vorticity values are detected close to the reaction zone, where the vorticity generation by the “baroclinic torque” was found to be significant. The influences of (initial) Reynolds and Damköhler numbers, and various air-fuel premixing levels on flame and turbulence variables are also studied. It is observed that the flame extinction occurs similarly in flames with different fuel-air premixing. Our simulations also indicate that the CO emission increases as the partial premixing of the fuel with air increases. Higher values of the temperature, the OH mass fraction and the CO mass fraction are observed within the flame zone at higher Reynolds numbers.     

Experimental annular stratified flames characterisation stabilised by weak swirl

A burner for the investigation of lean stratified premixed flames propagating in intense isotropic turbulence has been developed. Lean pre-mixtures of methane at different equivalence ratios were divided between two concentric co-flows to obtain annular stratification. Turbulence generators were used to control the level of turbulence intensity in the oncoming flow. A third annular weakly swirling airflow provided the flame stabilisation mechanism. A fundamental characteristic was that flame stabilisation did not rely on flow recirculation. The flames were maintained at a position where the local mass flux balanced the burning rate, resulting in a freely propagating turbulent flame front. The absence of physical surfaces in the vicinity of the flame provided free access for laser diagnostics. Stereoscopic Planar Image Velocimetry (SPIV) was applied to obtain the three components of the instantaneous velocity vectors on a vertical plane above the burner at the point of flame stabilisation. The instantaneous temperature fields were determined through Laser Induced Rayleigh (LIRay) scattering. Planar Laser Induced Fluorescence (PLIF) of acetone was used to calculate the average equivalence ratio distributions. Instantaneous turbulent burning velocities were extracted from SPIV results, while flame curvature and flame thermal thickness were calculated using the instantaneous temperature fields. The PDFs of these quantities were analysed to consider the separate influence of equivalence ratio stratification and turbulence. Increased levels of turbulence resulted in the expected higher turbulent burning velocities and flame front wrinkling. Flames characterised by higher fuel gradients showed higher turbulent burning velocities. Increased fuel concentration gradients gave rise to increased flame wrinkling, particularly when associated with positive small radius of curvature.     

Burning rates and surface characteristics of hydrogen-enriched turbulent lean premixed methane–air flames

The burning rates and surface characteristics of hydrogen-enriched turbulent lean premixed methane–air flames were experimentally studied by laser tomography visualization method using a V-shaped flame configuration. Turbulent burning velocity was measured and the variation of flame surface characteristics due to hydrogen addition was analyzed. The results show that hydrogen addition causes an increase in turbulent burning velocity for lean premixed CH₄–air mixtures when turbulent level in unburned mixture is not changed. Moreover, the increase of turbulent burning velocity is faster than that of the corresponding laminar burning velocity at constant equivalence ratio, suggesting that the kinetics effect is not the sole factor that results in the increase in turbulent burning velocity when hydrogen is added. The further analysis of flame surface characteristics and brush thickness indicates that hydrogen addition slightly decreases local flame surface density, but increases total flame surface area because of the increased flame brush thickness. The increase in flame brush thickness that results in the increase in total surface area may contribute to the faster increase in turbulent burning velocity, when hydrogen is added. Besides, the stretched local laminar burning velocity may be enhanced with the addition of hydrogen, which may also contribute to the faster increase rate of turbulent burning velocity. Both the variation in flame brush thickness and the enhancement in stretched local laminar burning velocity are due to the decreased fuel Lewis number when hydrogen is added. Therefore, the effects of fuel Lewis number and stretch should be taken into account in correlating burning velocity of turbulent premixed flames.     

Measurements in turbulent premixed bluff body flames close to blow-off

The structure of unconfined lean premixed methane–air flames stabilized on an axisymmetric bluff body has been examined for conditions increasingly closer to blow-off and during the blow-off event. Fast imaging (5 kHz) of OH¹ chemiluminescence and OH-PLIF and PIV (at 1 kHz) were used to obtain instantaneous and time-averaged images, temporal sequences, spectra of OH, 2-D estimates of flame surface density, curvature, turbulence statistics, and measurements of the duration of the blow-off transient. Blow-off was approached by slowly reducing the fuel flow rate, and the flame shape was seen to change from a cylindrical shape at stable burning conditions, with the flame brush closing across the flow at conditions close to the blow-off condition. This was followed by entrainment of fresh reactants from the downstream end of the recirculation zone (RZ), and fragmentation of the downstream flame parts. Just before the blow-off event, reaction fronts were observed inside the RZ, with progressive fragmentation occurring, leading to a shorter flame brush. Complete extinction occurred once the flame at the attachment point had been destroyed, and stabilization at the shear layers was no longer possible. Measurements showed a gradual reduction in FSD during the approach to blow-off and during the extinction event itself, and higher values of flame front curvature at conditions approaching extinction. The local Karlovitz number was estimated based on the local turbulence velocity and lengthscale characteristics and it reached a maximum value of about 10 at the location where the flame bends towards the axis. Quantification of the duration of the blow-off event showed that it was an order of magnitude longer than the characteristic timescale of the burner d/U_b. The measurements reported here are useful for model validation and for exploring the changes in turbulent premixed flame structure as extinction is approached.     

Flame brush characteristics and burning velocities of premixed turbulent methane/air Bunsen flames

The flame brush characteristics and turbulent burning velocities of premixed turbulent methane/air flames stabilized on a Bunsen-type burner were studied. Particle image velocimetry and Rayleigh scattering techniques were used to measure the instantaneous velocity and temperature fields, respectively. Experiments were performed at various equivalence ratios and bulk flow velocities from 0.7 to 1.0, and 7.7 to 17.0 m/s, respectively. The total turbulence intensity and turbulent integral length scale were controlled by the perforated plate mounted at different positions upstream of the burner exit. The normalized characteristic flame height and centerline flame brush thickness decreased with increasing equivalence ratio, total turbulence intensity, and longitudinal integral length scale, whereas they increased with increasing bulk flow velocity. The normalized horizontal flame brush thickness increased with increasing axial distance from the burner exit and increasing equivalence ratio. The non-dimensional leading edge and half-burning surface turbulent burning velocities increased with increasing non-dimensional turbulence intensity, and they decreased with increasing non-dimensional bulk flow velocity when other turbulence statistics were kept constant. Results show that the non-dimensional leading edge and half-burning surface turbulent burning velocities increased with increasing non-dimensional longitudinal integral length scale. Two correlations to represent the leading edge and half-burning surface turbulent burning velocities were presented as a function of the equivalence ratio, non-dimensional turbulence intensity, non-dimensional bulk flow velocity, and non-dimensional longitudinal integral length scale. Results show that the half-burning surface turbulent burning velocity normalized by the bulk flow velocity decreased as the normalized characteristic flame height increased.     

Piloted methane/air jet flames: Transport effects and aspects of scalar structure

Previously unpublished results from multiscalar point measurements in the series of piloted CH₄/air jet flames [R.S. Barlow, J.H. Frank, Proc. Combust. Inst. 27 (1998) 1087-1095] are presented and analyzed. The emphasis is on features of the data that reveal the relative importance of molecular diffusion and turbulent transport in these flames. The complete series A-F is considered. This includes laminar, transitional, and turbulent flames spanning a range in Reynolds number from 1100 to 44,800. Results on conditional means of species mass fractions, the differential diffusion parameter, and the state of the water-gas shift reaction all show that there is an evolution in these flames from a scalar structure dominated by molecular diffusion to one dominated by turbulent transport. Long records of 6000 single-point samples at each of several selected locations in flame D are used to quantify the cross-stream (radial) dependence of conditional statistics of measured scalars. The cross-stream dependence of the conditional scalar dissipation is determined from 6000-shot, line-imaging measurements at selected locations. The cross-stream dependence of reactive scalars, which is most significant in the near field of the jet flame, is attributed to radial differences in both convective and local time scales of the flow. Results illustrate some potential limitations of common modeling assumptions when applied to laboratory-scale flames and, thus, provide a more complete context for interpretation of comparisons between experiments and model calculations.     

Turbulent burning velocity of stoichiometric syngas flames with different hydrogen volumetric fractions upon constant-volume method with multi-zone model

Syngas has been widely concerned and tested in various thermo-power devices as one promising alternative fuel. However, little is known about the turbulent combustion characteristics, especially on outwardly propagating turbulent syngas/air premixed flames. In this paper, the outwardly propagating turbulent syngas/air premixed flames were experimentally investigated in a constant-volume fan-stirred vessel. Tests were conducted on stoichiometric syngas with different hydrogen volumetric fractions (X_H2, 10%–90%) in the ambience with different initial turbulence intensity (u'_rms, 0.100 m/s~1.309 m/s). Turbulent burning velocity was taken as the major topic to be studied upon the multi-zone model in constant-volume propagating flame method. The influences of initial turbulent intensity and hydrogen volumetric fraction on the turbulent flame speed were analysed and discussed. An explicit correlation of turbulent flame speed was obtained from the experimental results.     

Piloted jet flames of CH4/H2/air: Experiments on localized extinction in the near field at high Reynolds numbers

Measurements of temperature and major species concentrations, based on the simultaneous line-imaged Raman/Rayleigh/CO-LIF technique, are reported for piloted jet flames of CH₄/H₂ fuel with varying amounts of partial premixing with air (jet equivalence ratios of ?_j = 3.2, 2.5, 2.1 corresponding to stoichiometric mixture fraction values of ξ_st = 0.35, 0.43, 0.50, respectively) and varying degrees of localized extinction. Each jet flame is operated at a fixed and relatively high exit Reynolds number (60,000 or 67,000), and the probability of localized extinction is increased in several steps by progressively decreasing the flow rate of the pilot flame. Dimensions of the piloted burner, originally developed at Sydney University, are the same as for previous studies. The present measurements complement previous results from piloted CH₄/air jet flames as targets for combustion model calculations by extending to higher Reynolds number, including more steps in the progression of each flame from a fully burning state to a flame with high probability of local extinction, and adding the degree of partial premixing as an experimental parameter. Local extinction in these flames occurs close to the nozzle near a downstream location of four times the jet exit diameter. Consequently, these data provide the additional modeling challenge of accurately representing the initial development of the reacting jet and the near-field mixing processes.     

Effects of the external turbulence on centrally-ignited spherical unstable Ch4/H2/air flames in the constant-volume combustion bomb

In the present study, we conducted experiments to investigate the effects of external turbulence on the development of spherical H₂/CH₄/air unstable flames developments at two different equivalence ratios associated with different turbulent intensities using a spherical constant-volume turbulent combustion bomb and high speed schlieren photography technology. Flame front morphology and acceleration process were recorded and different effects of weak external turbulent flow field and intrinsic flame instability on the unstable flame propagation were compared. Results showed the external turbulence has a great influence on the unstable flame propagation under rich fuel conditions. For fuel-lean premixed flames, however, the effects of external turbulence on the morphology of the cellular structure on the flame front was not that obvious. Critical radius decreased firstly and then kept almost unchanged with the augment of the turbulence intensity. This indicated the dominating inhibiting effect of flame stretch on the turbulent premixed flame at the initial stage of the flame front development. Beyond the critical radius, the acceleration exponent was found increasing with the enhancement of initial turbulence intensity for fuel-lean premixed flames. For fuel-rich conditions, however, the initial turbulence intensity had little effect on acceleration exponent. In order to evaluate the important impact of the intrinsic flame instability and external turbulent flow field for spherical propagating premixed flames, intrinsic flame instability scale and average diameter of vortex tube were calculated. Intrinsic flame instability scale decreased greatly and then stayed unchanged with the propagation of the flame front. The comparison between intrinsic flame instability scale and average diameter of vortex tube demonstrated that the external turbulent flow filed will be more important for the evolution of wrinkle structure in the final stage of the flame propagation, when the turbulence intensity was more than 0.404 m/s.     

Onset of cellular instability in adiabatic H2/O2/N2 premixed flames anchored to a flat-flame heat-flux burner

The onset of cellular instability in adiabatic H₂/O₂/N₂ premixed flames anchored to a heat-flux burner is investigated numerically. Both hydrodynamic instability and diffusional-thermal instability are shown to play an important role in the onset of cellular flames. The burner can effectively suppress cellular instability when the flames are close to the burner, otherwise the burner can suppress the instabilities only at large wavenumbers. Because of differential diffusion, local extinction can occur in lean H₂/O₂/N₂ flames. When the flames develop to take on cellular shapes, the surface length, the overall heat release rate and the mean burning velocity are all increased. For near stoichiometric fuel-rich flames the mean burning velocity can increase by as much as 20%–30%. For lean flames with an equivalence ratio of 0.56, the mean burning velocity can be 2–3 times of the burning velocity of the corresponding planar flame.     

Effect of differential diffusion on turbulent lean premixed hydrogen enriched flames through structure analysis

This study presents the flame structure influenced by the differential diffusion effects and evaluates the structural modifications induced by the turbulence, thus to understand the coupling effects of the diffusively unstable flame fronts and the turbulence distortion. Lean premixed CH₄/H₂/air flames were conducted using a piloted Bunsen burner. Three hydrogen fractions of 0, 30% and 60% were adopted and the laminar flame speed was kept constant. The turbulence was generated with a single-layer perforated plate, which was combined with different bulk velocities to obtain varied turbulence intensities. Quasi-laminar flames without the plate were also performed. Explicit flame morphology was obtained using the OH-PLIF. The curvature, flame surface density and turbulent burning velocity were measured. Results show that the preferential transport of hydrogen produces negatively curved cusps flanked with positively curved bulges, which are featured by skewed curvature pdfs and consistent with the typical structure caused by the Darrieus-Landau instability. Prevalent bulge-cusp like wrinkles remain with relatively weak turbulence. However, stronger turbulence can break the bulges to be finer, and induce random positively curved cusps, therefore to destroy the bulge-cusp structures. Evident positive curvatures are generated in this process modifying the skewed curvature pdfs to be more symmetric, while the negative curvatures are not affected seriously. From low to high turbulence intensities, the hydrogen addition always strengthens the flame wrinkling. The augmentation of flame surface density and turbulent burning velocity with hydrogen is even more obvious at higher turbulence intensity. It is suggested that the differential diffusion can persist and even be strengthened with strong turbulence.     

Can we characterize turbulence in premixed flames?

Modeling of premixed turbulent combustion involves averaging reaction rates in turbulent flows. The focus of most approaches to resolving this problem has been placed on determining the dependence of the mean rate of product creation on the laminar flame speed SL, the rms turbulence velocity u^′, etc. The goal of the present work is to draw attention to another issue: May the input quantity u^′ for a model of be considered to be known? The point is that heat release substantially affects turbulence and, hence, turbulence characteristics in premixed flames should be modeled. However, standard moment methods for numerically simulating turbulent flows do not allow us to evaluate the true turbulence characteristics in a flame. For instance, the Reynolds stresses in premixed flames are affected not only by turbulence itself, but also by velocity jump across flamelets. A common way to resolving this problem consists of considering the Reynolds stresses conditioned on unburned (or burned) mixture to be the true turbulence characteristics. In the present paper, this widely accepted but never proved hypothesis is put into question, first, by considering simple model constant-density problems (flame motion in an oscillating one-dimensional laminar flow; flame stabilized in a periodic shear, one-dimensional, laminar flow; turbulent mixing). In all the cases, the magnitude of velocity fluctuations, calculated using the conditioned Reynolds stresses, is affected by the intermittency of reactants and products and, hence, is not the true rms velocity. Second, the above claim is further supported by comparing balance equations for the mean and conditioned Reynolds stresses. The conditioned Reynolds stresses do not characterize the true turbulence in flames, because conditional averaging cuts off flow regions characterized by either high or low velocities.     

A comparison of the emission and impingement heat transfer of LPG–H2 and CH4–H2 premixed flames

Experiments were performed to add hydrogen to liquefied petroleum gas (LPG) and methane (CH₄) to compare the emission and impingement heat transfer behaviors of the resultant LPG–H₂–air and CH₄–H₂–air flames. Results show that as the mole fraction of hydrogen in the fuel mixture was increased from 0% to 50% at equivalence ratio of 1 and Reynolds number of 1500 for both flames, there is an increase in the laminar burning speed, flame temperature and NO_x emission as well as a decrease in the CO emission. Also, as a result of the hydrogen addition and increased flame temperature, impingement heat transfer is enhanced. Comparison shows a more significant change in the laminar burning speed, temperature and CO/NO_x emissions in the CH₄ flames, indicating a stronger effect of hydrogen addition on a lighter hydrocarbon fuel. Comparison also shows that the CH₄ flame at α = 0% has even better heat transfer than the LPG flame at α = 50%, because the longer CH₄ flame configures a wider wall jet layer, which significantly increases the integrated heat transfer rate.     

High-speed OH-PLIF imaging of extinction and re-ignition in non-premixed flames with various levels of oxygenation

This paper presents high-speed (HS) images of OH-PLIF collected at a repetition rate of 5 kHz along the entire length of turbulent, pilot-stabilised flames approaching global blow-off. Measurements are made in flames of compressed natural gas, CNG (similar to Sydney flames L, B, M [1]), CNG–air (similar to Sandia flames D and E [4]) as well as CNG–O₂ flames with varying O₂ concentrations. Although the HS-OH-PLIF images are only qualitative, they are found to be of sufficient spatial and temporal resolution to relay the evolution of extinction and re-ignition events. Three types of structures, common to all the flames studied here, are identified: ‘breaks’, ‘closures’ and ‘growing kernels’. Events of ‘breaks’ are counterbalanced by the occurrence of ‘closures’ which reconnect the flame sheet and maintain stable combustion particularly in the upstream regions of flames. Applying simple but effective data processing tools, it is found that the rate at which ‘breaks’ grow in the flames is faster that the rate at which they close. The measured speeds as well as the differential between the rates of growth and closures are consistent with the behaviour of edge-flames implying that these structures may play a significant role in the dynamics of extinction/re-ignition. Other contributors to re-ignition are found to be ‘growing kernels’ advected from upstream regions in the flames. As the flames approach global blow-off, these kernels become the main mechanism for re-ignition further downstream and their rate of growth is shown to vary significantly although the factors affecting such growth need to be explored further.     

Basic considerations in the turbulent flame propagation in premixed gases

A general discussion is given of some fundamental problems of turbulent flame propagation in premixed gases. The following subjects are considered in greater detail: Stability of laminar flames in turbulent flow, shear wave-flame interaction, flame generated turbulence, influence of small scale turbulence on flame propagation and structure of turbulent flames at high Reynolds numbers. The principal object of this study is to describe the basic physical facts which have to be taken into consideration in the modeling of turbulent flames in gases without giving a detailed survey of all the research that has been carried out in the field.     

An a priori model for the effective species Lewis numbers in premixed turbulent flames

An a priori model for the effective species Lewis numbers in premixed turbulent flames is presented. This a priori   analysis is performed using data from a series of direct numerical simulations (DNS) of lean (?=0.4$?=0.4$) premixed turbulent hydrogen flames, with Karlovitz number ranging from 10 to 1562 (Aspden et al., 2011). The conditional mean profiles of various species mass fraction versus temperature are evaluated from the DNS and compared to unstretched laminar premixed flame profiles. The turbulent flame structure is found to be different from the laminar flame structure. However, the turbulent flame can still be mapped onto a laminar flame with an appropriate change in the Lewis numbers of the different species. A transition from “laminar” Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured. A model for those effective Lewis numbers with respect to the turbulent Reynolds number is developed. This model is derived from a Reynolds-averaged Navier–Stokes (RANS) formulation of the reactive scalar and temperature balance equations. The dependency of the effective Lewis numbers on the Karlovitz number instead of the Reynolds number is discussed in this paper. Unfortunately, given that the ratio of the integral length to the laminar flame thickness is fixed throughout this series of DNS, a change in the Karlovitz number is equivalent to a change in the Reynolds number. Incorporating these effective Lewis numbers in simulations of turbulent flames would have several impacts. First, the associated laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the turbulent premixed combustion regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used, and a dependency on the effective Lewis numbers has to be introduced. Finally, a turbulent flame speed model that takes into account these effective Lewis numbers is proposed.