Substantiating a fractal-based algebraic reaction closure of premixed turbulent combustion for high pressure and the Lewis number effects

A comprehensive set of nearly 100 atmospheric and high-pressure flame data of Kobayashi et al. are a good source for numerical analysis to address two main aspects in premixed turbulent combustion—high-pressure influence and effects of fuel type on the reaction rate. The present work deals with the lucid and realizable fractal-based reaction rate closure from Lindstedt and Váos (LV model) for premixed flames in the thin-flame limit. In this study, the reaction source term is customized on the eddy viscosity closure of turbulent transport, for practical reasons. Computed results from the LV model show the right qualitative trends with the experimental findings, as a function of turbulence. However, quantitative predictions of the original model are partly too low, and preclude the effects of pressure and fuel type on the reaction rate. With an extensive parametric study, based on numerical findings as well as on theoretical argumentation, the LV model is substantiated for these two effects. Results from the proposed tuned LV model are found to be in very good agreement with most of the measured data.     

Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames

The behaviour of the turbulent scalar flux in premixed flames has been studied using Direct Numerical Simulation (DNS) with emphasis on the effects of Lewis number in the context of Reynolds-averaged closure modelling. A database was obtained from DNS of three-dimensional freely propagating statistically planar turbulent premixed flames with simplified chemistry and a range of global Lewis numbers from 0.34 to 1.2. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport, whereas flames with higher Lewis numbers tend to exhibit gradient transport. The Reynolds-averaged transport equation for the turbulent scalar flux is analysed in detail and the performance of existing models for the unclosed terms is assessed with respect to corresponding quantities extracted from DNS data. Based on this assessment, existing models which are able to address the effects of non-unity Lewis number on turbulent scalar flux transport are identified, and new or modified models are suggested wherever necessary. In this way, a complete set of closure models for the scalar flux transport equation is prescribed for use in Reynolds-Averaged Navier-Stokes simulations.     

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.     

Conditionally averaged balance equations for modeling premixed turbulent combustion in flamelet regime

Balance equations for mass, velocity, and Reynolds stresses conditioned either to an unburned or to a burned mixture are derived from standard mass conservation, Navier-Stokes, and combustion progress variable balance equations by assuming that the probability of finding intermediate states of a reacting mixture is much less than unity. The derived equations contain three unclosed terms controlled by flamelet structure and flamelet statistics, whereas other unclosed terms are not straightforwardly affected by heat release and have counterparts in models of nonreacting flows. Equations of this type offer an opportunity to facilitate modeling the effects of heat release on turbulence. The modeling of these effects is further simplified if flamelet structure perturbations by turbulent eddies are neglected.     

Modelling and simulation of lean premixed turbulent methane/hydrogen/air flames with an effective Lewis number approach

Recent work on reaction modelling of turbulent lean premixed combustion has shown a significant influence of the Lewis number even at high turbulence intensities, if different fuels and varied pressure is regarded. This was unexpected, as the Lewis number is based on molecular transport quantities (ratio of molecular thermal diffusivity to mass diffusivity), while highly turbulent flames are thought to be dominated from turbulent mixing and not from molecular transport. A simple physical picture allows an explanation, assuming that essentially the leading part of the wrinkled flame front determines the flame propagation and the average reaction rate, while the rear part of the flame is of reduced importance here (determining possibly the burnout process and the flame brush thickness but not the flame propagation). Following this argumentation, mostly positively curved flame elements determine the flame propagation and the average reaction rate, where the influence of the preferential molecular diffusion and the Lewis number can easily seen to be important. Additionally, an extension of this picture allows a simple derivation of an effective Lewis number relation for lean hydrogen/methane mixtures. The applicability and the limit of this concept is investigated for two sets of flames: turbulent pressurized Bunsen flames, where hydrogen content and pressure is varied (from CNRS Orléans), and highly turbulent pressurized dump combustor flames where the hydrogen content is varied (from PSI Baden). For RANS simulations, comparison of flame length data between experiment and an effective Lewis number model shows a very good agreement for all these flames with hydrogen content of the fuel up to 20 vol.%, and even rather good agreement for 30% and 40% hydrogen.     

Experimental study of Markstein number effects on laminar flamelet velocity in turbulent premixed flames

Effects of turbulent flame stretch on mean local laminar burning velocity of flamelets, , were investigated experimentally in an explosion vessel at normal temperature and pressure. In this context, the wrinkling, At/Al, and the burning velocity, ut, of turbulent flames were measured simultaneously. With the flamelet assumption the mean local laminar burning velocity of flamelets, , was calculated for different turbulence intensities. The results were compared to the influence of stretch on spherically expanding laminar flames. For spherically expanding laminar flames the stretched laminar burning velocity, un, varied linearly with the Karlovitz stretch factor, yielding Markstein numbers that depend on the mixture composition. Six different mixtures with positive and negative Markstein numbers were investigated. The measurements of the mean local laminar burning velocity of turbulent flamelets were used to derive an efficiency parameter, I, which reflects the impact of the Markstein number and turbulent flame stretch—expressed by the turbulent Karlovitz stretch factor—on the local laminar burning velocity of flamelets. The results showed that the efficiency is reduced with increasing turbulence intensity and the reduction can be correlated to unsteady effects.     

Emission characteristics and heat release rate surrogates for ammonia premixed laminar flames

Ammonia is a carbon-free fuel that has the potential to meet increasing energy demand and to reduce CO₂ emissions. In the present work, the characteristics of pollutant emissions in ammonia premixed laminar flames are investigated using one-dimensional simulations, and heat release rate (HRR) surrogates for ammonia combustion are proposed. Both atmospheric and high-pressure conditions were considered, and four representative mechanisms for ammonia combustion were employed. It is shown that the total emission of NO and NH₃ achieves a minimum around an equivalence ratio (?) of 1.1 under atmospheric conditions, and there is no noticeable emission of NO and NH₃ for ? = 1.1 ~ 1.5 under high-pressure conditions. Three HRR surrogates, [NH₃][OH], [NH₂][O], and [NH₂][H], were proposed based on the analysis of HRR and elementary reaction profiles. The performance of HRR surrogates was found to vary with equivalence ratios. For example, with the Miller mechanism, [NH₃][OH], [NH₂][O], and [NH₂][H] have the best performance under atmospheric conditions at ? = 1.15, 0.95 and 1.05, respectively, and under high-pressure conditions at ? = 1.11, 0.87 and 0.96, respectively. Similar conclusions can also be drawn with other mechanisms. These findings provide valuable insights into emission control and flame identification of ammonia combustion.     

Direct numerical simulation of hydrogen addition in turbulent premixed Bunsen flames using flamelet-generated manifold reduction

Direct numerical simulations of a lean premixed turbulent Bunsen flame with hydrogen addition have been performed. We show the results for a case with equivalence ratio of 0.7 and a molar fractional distribution of 40% H₂ and 60% CH₄. The flamelet-generated manifold technique is used to reduce the chemistry; flamelets with different equivalence ratios and inflow temperature are used to account for stretch effects that are enhanced by preferential diffusion. The three-dimensional simulation clearly shows enhanced burning velocity in regions convex toward the reactants and reduced burning velocity with possible extinction in regions concave toward the reactants. To obtain these effects it was found to be necessary to include two three-dimensional transport equations with essentially different diffusivities. This point is illustrated by comparison of the results with cases in which either a single transport equation was used or two transport equations with minor differences in diffusivities were used. These latter cases incorporated preferential diffusion in the 1D flamelets (and thus in the manifold), but not in the three-dimensional transport. Thus the three-dimensional preferential diffusion effects are shown to enhance curvature and thereby to increase the turbulent burning velocity and reduce the mean flame height. In addition the turbulent burning velocity increases because hydrogen addition leads to a larger laminar flamelet consumption speed. To demonstrate this second effect, results of the cases mentioned above are compared to the results of simulations of the Bunsen flame with 0% hydrogen added to the fuel.     

Effects of Lewis number on flame surface density transport in turbulent premixed combustion

The transport of flame surface density (FSD) in turbulent premixed flames has been studied using a database obtained from Direct Numerical Simulation (DNS). Three-dimensional freely propagating developing statistically planar turbulent premixed flames have been examined over a range of global Lewis numbers from 0.6 to 1.2. Simplified chemistry has been used and the emphasis is on the effects of Lewis number on FSD transport in the context of Reynolds-averaged closure modelling. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport of FSD, whereas flames with higher Lewis numbers tend to exhibit gradient transport of FSD. Stronger heat release effects for lower Lewis number flames are found to lead to an increase in the positive (negative) value of the dilatation rate (normal strain rate) term in the FSD transport equation with decreasing Lewis number. The contribution of flame curvature to FSD transport is found to be influenced significantly by the effects of Lewis number on the curvature dependence of the magnitude of the reaction progress variable gradient, and on the combined reaction and normal diffusion components of displacement speed. The modelling of the various terms of the FSD transport equation has been analysed in detail and the performance of existing models is assessed with respect to the terms assembled from corresponding quantities extracted from DNS data. Based on this assessment, suitable models are identified which are able to address the effects of non-unity Lewis number on FSD transport, and new or modified models are suggested wherever necessary.     

Measurements of the heat release rate integral in turbulent premixed stagnation flames with particle image velocimetry

A new definition of turbulent consumption speed is proposed in this work that is based on the heat release rate integral, rather than the mass burning rate integral. Its detailed derivation and the assumptions involved are discussed in a general context that applies to all properly defined reaction progress variables. The major advantage of the proposed definition is that it does not require the thin-flame assumption, in contrast to previous definitions. Experimental determination of the local turbulent displacement speed, SD, and the local turbulent consumption speed, SC, is also demonstrated with the particle image velocimetry technique in three turbulent premixed stagnation flames. The turbulence intensity of these flames is of the same order of the laminar burning velocity. Based on the current data, a model equation for the local mean heat release rate is proposed. The relationship between SD and SC is discussed along with a possible modeling approach for the turbulent displacement speed.     

Asymptotic analysis of transport properties and burning velocities for premixed hydrocarbon flames

IntroductionThe fundamental meChedsm Of a p~xed flamewith the flow near the front stagnation point of a platewall has receiVed considerable attention in the field ofcombushon, which helps us to realize the behavior offlame Propagation. The CO~thew teChnique,inboduced by Law and coworkers["n, has produced theIndnar flame speed data that are ~ntiy usedextensively fof validation Of chemical ldnetics and themodeling of turbulent combustion. The laminar flamespeed is an important Property of a …     

Lewis number effect on the propagation of premixed flames in narrow adiabatic channels: Symmetric and non-symmetric flames and their linear stability analysis

The propagation of premixed flames with different Lewis numbers in a planar channel subject to a Poiseuille flow is considered within the diffusive-thermal model for steady and time-dependent cases. It was found that, depending on the Lewis number and the flow rate, symmetric and non-symmetric flames are possible. The existence of multiple steady solutions in cases of the low Lewis number is demonstrated. The time-dependent simulations carried out for high Lewis number flames also showed the symmetric and non-symmetric oscillatory solutions.Linear stability analysis of two-dimensional steady-states was performed using a practical method developed in the paper and applied to calculate the main eigenvalue. It was shown that for symmetric flames with a low Lewis number the increase in the flow rate leads to a loss of stability with subsequent formation of non-symmetric solutions. For flames with a high Lewis number the Poiseuille flow produces a stabilization effect. The results of the stability analysis were successfully compared with the results of direct numerical simulations.     

Strained flamelets for turbulent premixed flames, I: Formulation and planar flame results

A strained flamelet model is proposed for turbulent premixed flames using scalar dissipation rate as a parameter. The scalar dissipation rate of reaction progress variable is a suitable quantity to describe the flamelet structure since it is governed by convection-diffusion-reaction balance and it is defined at every location in the flamelets, which are represented by laminar flames in reactant-to-product opposed flow configuration. The mean reaction rate is obtained by using the flamelets reaction rate and the joint pdf of the progress variable and its dissipation rate. The marginal pdf of the progress variable is presumed to be β-pdf and the pdf of the conditional dissipation rate is taken to be log-normal. The conditional mean dissipation rate is obtained from modelled mean dissipation rate. This reaction rate closure is assessed using RANS calculations of statistically planar flames in the corrugated flamelets and thin reaction zones regimes. The flame speeds calculated using this closure are close to the experimental data of Abdel-Gayed et al. (1987) [27] for flames in both the regimes. Comparisons with other reaction rate closures showed the benefits of the strained flamelets approach.     

Generation of PDFS for flame curvature and for flame stretch rate in premixed turbulent combustion

Experimentally derived pdfs of turbulent, premixed, flame curvatures from a variety of sources, for a wide range of conditions are surveyed and a suitable expression sought to generalize these. This proves to be one based on the Damköhler number, Da. This is tantamount to normalizing the curvature by multiplying it by the Taylor scale of turbulence. It enables the distribution of flame curvature when normalized by the laminar flame thickness, to be expressed in terms of the Karlovitz stretch factor, K, and the turbulent Reynolds number, R_l. The value of the pdf at zero curvature is linearly related to Da^1/2.The pdf expressions of Yeung et al. [3] obtained from numerical simulations are used for the strain rate distribution and, on the assumption that these and that for flame curvature are statistically independent, values of flame stretch rate pdfs are generated numerically. It is necessary to define an appropriate surface to define the burning velocity, flame stretch rate, and appropriate Markstein numbers. Two surfaces are considered and employed in the computations, one located at the start of the preheat zone, the other at the start of the reaction zone. The latter seems more rational and gives the better generalisation of the pdfs of flame stretch rate.An assumed linearity of laminar burning velocity with flame stretch rate, extending over both positive and negative stretch rates, enables flame stretch rate pdfs to be generated. It is concluded that negative values of burning velocity are unlikely and that burning velocities should tend to zero rather than attain negative values. This modifies the derivation of flame stretch rate pdfs. These depend on the Markstein number, Karlovitz stretch factor and turbulent Reynolds number. Computations suggest that, for values of K above 0.1 and of R_l above 100, the pdf of stretch rate is similar to that of strain rate. At very low values of K and negative values of Markstein number, pronounced flamelet instability might be anticipated.     

Hybrid presumed pdf and flame surface density approaches for Large-Eddy Simulation of premixed turbulent combustion: Part 1: Formalism and simulation of a quasi-steady burner

Extended Coherent Flame Model for Large-Eddy Simulation (ECFM-LES) and Presumed Conditional Moments-Flame Prolongation of Intrisic Low Dimensional Manifolds (PCM-FPI) are some of the combustion models exploited for Large-Eddy Simulations (LES) of turbulent premixed flames. Combustion is then either modeled by tracking the flame surface density or by combining computations of flamelets with presumed probability density functions (pdf). The first approach enables to control the turbulent flame speed but models chemical kinetics in a simplified manner. The second directly accounts for detailed chemistry via the flamelet structure but the turbulent propagation speed cannot be easily estimated a priori. Simple one-dimensional tests are then performed in this study to evaluate flame velocities of PCM-FPI. A restricted operating range of this model, that enables to retrieve an evolution of the propagating speed similar to ECFM-LES predictions, is highlighted. This zone is limited in terms of filter width and sub-grid scale turbulent viscosity. An attractive alternative to both ECFM-LES and PCM-FPI approaches thus appears to be a model integrating their respective main strengths. For this purpose, two hybrid models are proposed in this paper and tested through LES of a lean-premixed turbulent swirling flame. Results in terms of statistics for temperature and mass fractions of chemical species are compared to experimental data and to previous results already obtained with PCM-FPI. The coupled models enable to properly locate the reaction zone via the flame surface density closures along with a correct prediction of the chemistry evolution in the flame front.