Algebraic Flame Surface Density Research Articles

Flame Surface Density based mean reaction rate closure for Reynolds averaged Navier Stokes methodology in turbulent premixed Bunsen flames with non-unity Lewis number

The Flame Surface Density (FSD) based mean reaction rate closure proposed by Prof. K.N.C. Bray and co-workers in the context of Reynolds Averaged Navier-Stokes simulations has been a-priori analysed using a Direct Numerical Simulation (DNS) database of turbulent premixed Bunsen flames with different characteristic Lewis numbers representing the strict flamelet regime (i.e. high Damköhler number and low Karlovitz number combustion). The statistical behaviours of stretch factor, orientation factor and wrinkling length scale have been assessed for non-unity Lewis number conditions to identify their Lewis number dependencies. The assumption of presumed bimodal distribution has been found to be rendered invalid close to the nozzle exit where the unresolved wrinkling remains relatively small even when the flow parameters at the nozzle exit represent high Damköhler number and low Karlovitz number conditions. Although the PDF of reaction progress variable shows some resemblance to a bimodal distribution away from the nozzle exit, the Bray-Moss-Libby expressions which can be derived for infinitely large values of Damköhler number have been found to show considerable deviations from the Reynolds averaged reaction progress variable and reaction progress variable variance extracted from DNS data even though these cases represent the wrinkled/corrugated flamelets regime combustion based on nozzle exit conditions. This suggests that it might be necessary to solve a modelled scalar variance transport equation even in the strict flamelet regime instead of using the algebraic relation for the scalar variance. It has been found that the characteristic Lewis number has a major influence on the orientation factor, wrinkling length scale, and the stretch factor. Furthermore, these parameters are found to be (sometimes strong) functions of the axial distance from the nozzle exit. Known parameterisations for the wrinkling length scale and the stretch factor have been shown to be unable to capture the correct variation across the flame brush based on a-priori analysis of DNS data. The variability of the orientation factor and the inadequacy of existing relations to approximate other quantities such as the stretch factor, wrinkling factor and the Reynolds averaged reaction progress variable have the potential to severely limit the performance of algebraic FSD based mean reaction rate closures in turbulent premixed flames within the flamelet regime.

A priori assessment of convolutional neural network and algebraic models for flame surface density of high Karlovitz premixed flames

Accurate modeling of the unresolved flame surface area is critical for the closure of reaction source terms in the flame surface density (FSD) method. Some algebraic models have been proposed for the unresolved flame surface area for premixed flames in the flamelet or thin reaction zones (TRZ) regimes where the Karlovitz number (Ka) is less than 100. However, in many lean combustion applications, Ka is large (Ka > 100) due to the strong interactions of small-scale turbulence and flames. In the present work, a direct numerical simulation (DNS) database was used to evaluate the performance of algebraic FSD models in high Ka premixed flames in the context of large eddy simulations. Three DNS cases, i.e., case L, case M and case H, were performed, where case L is located in the TRZ regime with Ka < 100 and case M and case H are located in the broken reaction zones regime with Ka > 100. A convolutional neural network (CNN) model was also developed to predict the generalized FSD, which was trained with samples of case H and a small filter size, and was tested in various cases with different Ka and filter sizes. It was found that the fraction of resolved FSD increases with increasing filtered progress variable c̃ and decreasing subgrid turbulent velocity fluctuation u′Δ. The performance of CNN and algebraic models was assessed using the DNS database. Overall, the results of algebraic models are promising in case L and case M for a small filter size; the CNN model performs generally better than the algebraic models in high Ka flames and the correlation coefficient between the modeled and actual generalized FSD is greater than 0.91 in all cases. The effects of c̃ and u′Δ on the performance of different models for various cases were explored. The algebraic models perform well with large values of c̃ and small values of u′Δ in high Ka cases, which indicates that they can be applied to high Ka flames in certain conditions. The performance of the CNN model is better than the algebraic models for a large filter size in high Ka cases.

Investigation of pressure and the Lewis number effects in the context of algebraic flame surface density closure for LES of premixed turbulent combustion

Large scale industrial combustion devices, for example, internal combustion engines, gas turbine combustors, etc., operate under high-pressure conditions and utilize a variety of fuels. Unfortunately, the majority of the current numerical combustion modelling approaches are not fully validated for high-pressure and the non-unity Lewis number ( $$\hbox {Le} =$$ thermal diffusivity/mass diffusivity) effects in premixed turbulent combustion. In any case, a numerical model needs to be checked for the effects of these parameters to guarantee generality of the model. In the present study, these two critical features of the models are numerically explored utilizing fundamental elements of several algebraic flame surface density reaction rate closure models accessible in the open literature. The Lewis number impact is likewise examined utilizing LES of recently published subgrid scale fractal flame surface density model, which indicated acceptable results for high and low-pressure methane fuelled applications. The computed numerical results are compared with an extensive experimental dataset for lean methane and propane fuels featuring various flow and turbulence conditions at operating pressures in the range of 1–10 bar. The quantitative results from most of the selected models do not show the experimentally observed trends at high-pressures and for non-unity Le number fuels. Modifications to the models are incorporated to reflect effects of these two important parameters utilizing a broad parametric investigation resulting in a satisfactory agreement with the experimental data.

Algebraic Flame Surface Density Modelling of High Pressure Turbulent Premixed Bunsen Flames

Performance of representative algebraic flame surface density (FSD) models have been a-priori assessed based on a direct numerical simulation database consisting of four turbulent premixed Bunsen flames at four different pressure levels. Results indicate that for a given resolution of the flame front, the considered algebraic FSD closures perform in a qualitatively similar manner irrespective of pressure variation. However, for a given computational mesh, the performance deteriorates as flame thickness decreases with increasing pressure. Additionally, the contribution of the subgrid scale surface-filtered density-weighted tangential diffusion component of the displacement speed tends to increase with pressure increment, further complicating the modelling of FSD. Further analysis also indicate that the inner cut-off scale normalized by the thermal flame thickness increases with increasing pressure, possibly due to the presence of Darrieus–Landau instability which is more likely to occur at higher pressure due to a larger ratio of hydrodynamic length scale to thermal flame thickness.

Development of a RANS Premixed Turbulent Combustion Model Based on the Algebraic Flame Surface Density Concept

Recently, a fractal-based algebraic flame surface density (FSD) premixed combustion model has been derived and validated in the context of large eddy simulation (LES). The fractal parameters in the model, namely the cut-off scales and the fractal dimension were derived using theoretical models, experimental and direct numerical simulation (DNS) databases. The model showed good performance in predicting the premixed turbulent flame propagation for low to high Reynold numbers (Re) in ambient as well as elevated pressure conditions. Several LES combustion models have a direct counterpart in the Reynolds-averaged Navier–Stokes (RANS) context. In this work, a RANS version of the aforementioned LES subgrid scale FSD combustion model is developed. The performance of the RANS model is compared with that of the original LES model and validated with the experimental data. It is found that the RANS version of the model shows similarly good agreement with the experimental data.

Assessment of Algebraic Flame Surface Density Closures in the Context of Large Eddy Simulations of Head-On Quenching of Turbulent Premixed Flames

ABSTRACTThe applicability of algebraic large eddy simulation (LES) closures of flame surface density (FSD) for head-on quenching of premixed turbulent flames by an isothermal inert wall has been assessed using 3D direct numerical simulations (DNS) data for different values of root-mean-square turbulent velocity fluctuation, Damköhler and Karlovitz numbers. An algebraic FSD closure, which has been reported to perform relatively satisfactorily among several available models, has been considered for this analysis alongside a model, which has recently been used for LES of flame-wall interaction. The applicability of previously proposed near-wall damping factors for flame surface wrinkling and consumption rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations has also been assessed for LES based on the current a-priori DNS analysis. It has been found that existing models considered for this analysis do not predict the near-wall behavior of the FSD accurately for all cases considered here. Furthermore, the widely used expression (where and are the unburned gas density and the laminar burning velocity, respectively) has been found to overpredict the combined reaction rate and molecular diffusion term in the near-wall region but the agreement between these terms gets better away from the wall. However, does not sufficiently capture the local behavior of the density-weighted surface filtered displacement speed so the correlation coefficient between and the combined reaction rate and molecular diffusion term remains much smaller than unity. It has been found that the damping factors proposed for RANS are not suitable for LES, and they severely damp the near-wall magnitudes of FSD and the combined reaction rate and molecular diffusion term and lead to significant under-predictions. Based on this a-priori analyses new near-wall modifications to the generalized FSD and the combined reaction and molecular diffusion term have been proposed in the context of LES, which have been found to capture both qualitative and quantitative trends obtained from DNS data.

A priori and a posteriori analyses of algebraic flame surface density modeling in the context of Large Eddy Simulation of turbulent premixed combustion

ABSTRACTThe flame surface density (FSD) based reaction rate closure is one of the most important methodologies of turbulent premixed flame modeling in the context of Large Eddy Simulations (LES). The transport equation for the Favre-filtered reaction progress variable needs closure of the filtered reaction rate and the subgrid scalar flux (SGSF). The SGSF in premixed turbulent flames has both gradient and countergradient components, where the former is typically modeled using eddy diffusivity and the latter can be modeled either on its own or in combination with the filtered reaction rate term using an appropriate wrinkling factor. The scope of the present work is to identify an explicit SGSF closure for the optimum performance in combination with an already established LES FSD model. The performance of different SGSF models for premixed turbulent combustion has been assessed recently by the authors using a Direct Numerical Simulation (DNS) database of freely propagating turbulent premixed flames with a range of different values of turbulent Reynolds number. The two most promising models have been implemented in the LES code. The modeling methodology identified based on a priori DNS analysis is assessed further a posteriori by comparing the LES simulation results of turbulent methane Bunsen flames with the well-documented experimental data. A significant change of the overall flame speed is not observed for different SGSF models. However, the flame shape and thickness respond to the modeling of SGSF. Considering the fact that the SGSF models have very different characteristics, the overall effect on the LES results in this work is smaller than expected. An extension of a previous a priori DNS analysis provides detailed explanations for the observed behavior.

Adaptation of a dynamic wrinkling model to an engine configuration

The dynamic model proposed by Charlette et al. represents an interesting alternative to the FSD balance equation to predict the transient growth of a flame kernel. The dynamic wrinkling model coupled to the algebraic Flame Surface Density (FSD) model of Boger et al. is here evaluated for the first time in an internal combustion engine configuration. Preliminary tests enable to evidence practical difficulties when applying the model to this type of complex configuration. Improvements are proposed to adapt the model to the engine configuration. Final simulations are performed on a spark ignition engine configuration, using both the adapted dynamic model and an equilibrium wrinkling formulation. The results are compared to the ones obtained by Robert et al. on the same configuration using the ECFM-LES model solving a FSD balance equation. The dynamic model proves to very well predict out-of-equilibrium values and to account for cycle-to-cycle variabilities, as the model parameter is calculated on the fly. On the contrary, the results obtained using the equilibrium formulation clearly demonstrate that the flame-turbulence equilibrium assumption is not adapted to such configurations.

Large Eddy Simulations of a turbulent premixed swirl flame using an algebraic scalar dissipation rate closure

Large Eddy Simulations (LES) of a swirl-stabilised turbulent premixed flame in the well-known TECFLAM burner configuration have been carried out by solving transport equations of Favre-filtered reaction progress variable and mixture fraction. A recently proposed closure for the Scalar Dissipation Rate (SDR) is used for the modelling of the filtered reaction rate of reaction progress variable, whereas the Favre filtered mixture fraction is used to account for mixture stratification due to entrainment. The computational results are utilised to analyse the nature of stratification at representative locations in the swirl flame to gain physical insight into the flame structure. Additionally, two algebraic Flame Surface Density (FSD) closures, which were found to perform well in a previous analysis (Ma et al., 2013), are used for the modelling of the filtered reaction rate of reaction progress variable. The predictions of SDR closure are compared to the corresponding results obtained from algebraic FSD closures. The predictions of SDR based simulations show reasonably good agreement with experimental findings; the level of accuracy is at least comparable to that achieved with algebraic FSD models and to the results reported in the literature.

Validation and implementation of algebraic LES modelling of scalar dissipation rate for reaction rate closure in turbulent premixed combustion

The closure of the filtered reaction rate of the reaction progress variable using an algebraic model for Favre-filtered Scalar Dissipation Rate (SDR) N∼c in turbulent premixed combustion has been assessed in the context of Large Eddy Simulations (LES). This assessment consists of a priori Direct Numerical Simulation (DNS) analysis based on freely propagating statistically planar turbulent premixed flames and a posteriori analysis, involving the LES simulations of a well-documented rectangular dump combustor configuration with sudden expansion (i.e. ORACLES burner) and a premixed flame stabilised on a triangular bluff body flame holder (i.e. Volvo Rig). It has been found that the newly developed SDR model satisfactorily captures N∼c obtained from explicitly filtered DNS data. The predictions of this SDR based LES closure in the ORACLES burner and Volvo Rig configurations exhibit good agreement with experimental results without requiring any major modification to the model parameters. The predictions of the SDR model for the LES of the ORACLES burner and Volvo Rig have been compared to those of two algebraic Flame Surface Density (FSD) models, which yielded satisfactory agreement with experimental data in a previous analysis. The performance of the SDR based closure remains either comparable to or better than the FSD based closures for the two test configurations considered in this analysis.

A posteriori testing of the flame surface density transport equation for LES

Flame Surface Density (FSD) models for Large Eddy Simulation (LES) are implemented and tested for a canonical configuration and a practical bluff body stabilised burner, comparing common algebraic closures with a transport equation closure in the context of turbulent premixed combustion. The transported method is expected to yield advantages over algebraic closures, as the equilibrium of subgrid production and destruction of FSD is no longer enforced and resolved processes of strain, propagation and curvature are explicitly accounted for. These advantages might have the potential to improve the ability to capture large-scale unsteady flame propagation in situations with combustion instabilities or situations where the flame encounters progressive wrinkling with time. The initial study of a propagating turbulent flame in wind-tunnel turbulence shows that the Algebraic Flame Surface Density (FSDA) method can predict an excessively wrinkled flame under fine grid conditions, potentially increasing the consumption rate of reactants to artificially higher levels. In contrast, the Flame Surface Density Transport (FSDT) closure predicts a smooth flame front and avoids the formation of artificial flame cusps when the grid is refined. Five FSDA models and the FSDT approach are then applied to the LES of the Volvo Rig. The predicted mean velocities are found to be relatively insensitive to the use of the FSDT and FSDA approaches, whereas temperature predictions exhibit appreciable differences for different formulations. The FSDT approach yields very similar temperature predictions to two of the tested FSDA models, quantitatively capturing the mean temperature. Grid refinement is found to improve the FSDT predictions of the mean flame spread. Overall, the paper demonstrates that the apparently complicated FSD transport equation approach can be implemented and applied to realistic, strongly wrinkled flames with good success, and opens up the field for further work to improve the models and the overall FSDT approach.

A posteriori testing of algebraic flame surface density models for LES

In the application of Large Eddy Simulation (LES) to premixed combustion, the unknown filtered chemical source term can be modelled by the generalised flame surface density (FSD) using algebraic models for the wrinkling factor Ξ. The present study compares the behaviour of the various models by first examining the effect of sub-grid turbulent velocity fluctuation on Ξ through a one-dimensional analysis and by the LES of the ORACLES burner (Nguyen, Bruel, and Reichstadt, Flow, Turbulence and Combustion Vol. 82 [2009], pp. 155–183) and the Volvo Rig (Sjunnesson, Nelsson, and Max, Laser Anemometry, Vol. 3 [1991], pp. 83–90; Sjunnesson, Henrikson, and Löfström, AIAA Journal, Vol. 28 [1992], pp. AIAA–92–3650). Several sensitivity studies on parameters such as the turbulent viscosity and the grid resolution are also carried out. A statistically 1-D analysis of turbulent flame propagation reveals that counter gradient transport of the progress variable needs to be accounted for to obtain a realistic flame thickness from the simulations using algebraic FSD based closure. The two burner setups are found to operate mainly within the wrinkling/corrugated flamelet regime based on the premixed combustion diagram for LES (Pitsch and Duchamp de Lageneste, Proceedings of the Combustion Institute, Vol. 29 [2002], pp. 2001–2008) and this suggests that the models are operating within their ideal range. The performance of the algebraic models are then assessed by comparing velocity statistics, followed by a detailed error analysis for the ORACLES burner. Four of the tested models were found to perform reasonably well against experiments, and one of these four further excels in being the most grid-independent. For the Volvo Rig, more focus is placed upon the comparison of temperature data and identifying changes in flame structure amongst the different models. It is found that the few models which largely over-predict velocities in the ORACLES case and volume averaged in a previous a priori DNS analysis (Chakraborty and Klein, Physics of Fluids, Vol. 20 [2008], p. 085108), deliver satisfactory agreement with experimental observations in the Volvo Rig, whereas a few of the other models are only able to capture the experimental data of the Volvo Rig either quantitatively or qualitatively.

Dynamic flame surface density modelling of flame deflagration in vented explosion

The propagation of transient, turbulent premixed flames in a vented explosion chamber in the presence of a series of obstacles is numerically investigated by a dynamic formulation for the Flame Surface Density (FSD) with the Large Eddy Simulations (LES) technique. The chemistry is modelled by a one-step overall reaction, which simulates the reaction of a stoichiometric propane-air mixture. The FSD modelling in the reaction rate model is numerically employed with two different sub-grid scale (SGS) models. The first one is based on an empirical correlation of the SGS velocity fluctuations and the second one is based on similarity ideas involved in solving the wrinkled flame front considered as a fractal surface. The numerical predictions are analyzed and compared against an algebraic, simple FSD model together with experimental data. The calculations show that the dynamic FSD models provide superior results as compared with the algebraic FSD model. The comparisons demonstrate the importance of the contributions from the unresolved FSD and provide good agreement with experimental data for the flame structure, overpressure, and burning velocities.

A PrioriAssessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation ofDis proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD.

Effects of Turbulent Reynolds Number on the Performance of Algebraic Flame Surface Density Models for Large Eddy Simulation in the Thin Reaction Zones Regime: A Direct Numerical Simulation Analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Rethas been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Retand Ka before reaching an asymptotic value for large values of Retand Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel’dovich flame thicknessηi/δzdoes not exhibit any significant dependence on Retfor the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width.

An assessment of large eddy simulations of premixed flames propagating past repeated obstacles

This paper presents an assessment of Large Eddy Simulations (LES) in calculating the structure of turbulent premixed flames propagating past solid obstacles. One objective of the present study is to evaluate the LES simulations and identify the drawbacks in accounting the chemical reaction rate. Another objective is to analyse the flame structure and to calculate flame speed, generated overpressure at different time intervals following ignition of a stoichiometric propane/air mixture. The combustion chamber has built-in repeated solid obstructions to enhance the turbulence level and hence increase the flame propagating speed. Various numerical tests have also been carried out to determine the regimes of combustion at different stages of the flame propagation. These have been identified from the calculated results for the flow and flame characteristic parameters. It is found that the flame lies within the ‘thin reaction zone’ regime which supports the use of the laminar flamelet approach for modelling turbulent premixed flames. A submodel to calculate the model coefficient in the algebraic flame surface density model is implemented and examined. It is found that the LES predictions are slightly improved owing to the calculation of model coefficient by using submodel. Results are presented and discussed in this paper are for the flame structure, position, speed, generated pressure and the regimes of combustion during all stages of flame propagation from ignition to venting. The calculated results are validated against available experimental data.

A priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation

Flame surface density (FSD) based reaction rate closure is one of the most important approaches in turbulent premixed flame modeling. The algebraic models for FSD based on power laws often require information about the fractal dimension D and the inner cut-off scale ηi. In the present study, two three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames are analyzed among which the flame in one case belongs to the corrugated flamelet (CF) regime, whereas the other falls well within the thin reaction zone (TRZ) regime. It is found that D for the flame in the TRZ regime is greater than the value obtained for the flame in the CF regime. For the flame within the TRZ regime, the fractal dimension is found to be 7/3, which is the same as D for a material surface in a turbulent environment. For the flame in the CF regime, ηi is found to scale with the Gibson scale, whereas ηi is found to scale with the Kolmogorov length scale for the flame in the TRZ regime. Based on these observations a new algebraic model for FSD is proposed, where D and ηi are expressed as functions of Karlovitz number. The performances of the new and existing algebraic models for FSD are compared with the corresponding values obtained from DNS databases.