Simulations Of Turbulent Flames Research Articles

Soot modeling of oxygen-depleted and highly sooty turbulent buoyant flames using the In Situ Adaptive Tabulation (ISAT) method

In this paper, a newly developed LSP-based soot (LSPTwoEq) modeling is systematically assessed in the Large Eddy Simulation (LES) of various turbulent buoyant flames against a previously developed LSP-based soot (LSPOneEq) model. Two turbulence-soot interaction (TSI) closure schemes are formulated based on the Eddy Dissipation Concept (EDC). Accordingly, two soot modeling frameworks consisting of the mentioned soot and their corresponding TSI models are applied in the simulations. An in situ Adaptive Tabulation (ISAT) implementation is also proposed to speed up the simulation of the TSI model formulated for the LSPTwoEq model. The results indicate that the proposed soot modeling framework is significantly more accurate for ethylene flames in reduced oxygen concentrations and a highly sooty toluene flame. The accuracy of both frameworks is comparable for the ethylene flame with an air co-flow. The speed-up gained by using the ISAT scheme is found to be a factor of four for the ethylene flame with an air co-flow and the toluene flame. It is larger than nine for the ethylene flames with reduced oxygen co-flow.

Large eddy simulation of turbulent non-premixed oxy-fuel jet flames with different Reynolds numbers

Due to differences in the physical and chemical properties of CO2 and N2, along with a reduction in the momentum ratio between oxidant and fuel streams, the local extinction of oxy-fuel flames is significantly more pronounced compared to conventional air–fuel flames, which poses challenges in the design and operation of oxy-fuel burners. This study further validates the species-weighted flamelet/progress variable (FPV) model proposed in previous work [Jiang et al., 2023], particularly in oxy-fuel flames characterized by highly local extinction. Large eddy simulations were conducted on the Sandia oxy-fuel jet diffusion flame at various Reynolds numbers. The predictions are systematically compared with experimental data, and the influence of Reynolds number on local extinction is thoroughly analyzed. The results demonstrate that the numerical simulation effectively predicts mean temperature, species mass fractions, differential diffusion parameters (ZHC), and local extinction in oxy-fuel jet flames across a wide range of Reynolds numbers. The errors in predicted mean temperature and mass fractions exhibit a slight increase with rising Reynolds numbers, yet remain below 15 %. As the Reynolds number increases from 12,000 to 18,000, the predicted peak ZHC decreases by 30 %, and the beneficial effect of preferential diffusion of H2 weakens, while the adverse effect of CO2 on combustion becomes stronger.

LES of turbulent partially-premixed flames using reaction–diffusion manifold-reduced chemistry with a consistent gradient estimate determined “on the fly”

This paper devises and applies a method for determining consistent, system-adapted reaction–diffusion manifolds (REDIM) for turbulent partially-premixed combustion. The method is an extension of a previous technique which was limited to laminar flames. It adapts a REDIM to the scalar gradients present in a given reacting flow by an iterative procedure, in which gradients from REDIM-reduced simulations are used to create a new and improved REDIM. An application of the method is demonstrated using large eddy simulations (LES) of a turbulent partially-premixed methane/air flame as the “gradient estimate generating” flame simulation. Compared to the previous laminar flame studies, the turbulent flame features less sharp gradient-scalar correlations because of the strong scattering of data. Methods for capturing the scatter in scalar-gradient correlations are applied, allowing us to assess the influence of the scatter on the resulting REDIM. Also, the fact that turbulent flame simulations often involve spatial filtering operations which tend to reduce the magnitude of the gradients is taken into account by comparing the REDIM output to quasi-direct numerical simulation (qDNS) data. It is found that the gradients devised from the filtered simulations are by a factor of 2–3 below those of the more fully resolved qDNS. Nevertheless, the REDIM devised from the LES predicts the states of the qDNS with good accuracy. Overall, observations show that the method can produce realistic reduced models also for systems with complex interactions of chemical reaction, molecular transport and flow, like partially-premixed turbulent flames.

Two-zone subgrid combustion model for large eddy simulations of buoyant diffusion flames

This work presents the development of a novel two-zone subgrid combustion model (SCM) recently designed to incorporate the finite-rate kinetics in the large eddy simulations of buoyant turbulent diffusion flames in which turbulence might not be fully developed. The reaction rate is evaluated as the mass-weighted average of contributions by the higher-temperature flamelet zone and the lower-temperature surrounding. The volume fraction of the flamelet zone and the time scale responsible for the inter-zone transfer are determined by the expected thickness of the laminar diffusion flamelet existing in the grid cell, and by wrinkling its surface by the unresolved turbulent eddies. This approach is applicable to an arbitrary level of turbulence (quantified by the subgrid Reynolds number) thereby overcoming the limitation of the conventional eddy dissipation concept formulated for the high-Re flames. Advancing the previous study [1], the flamelet status at every time step is evaluated by solving transient equations of heat and mass transfer between the subgrid zones. Effective kinetic parameters for the simplified global reaction of fuel oxidation are derived from experimental data for autoignition delay in methane-air and n-heptane-air mixtures and are shown to capture transition from the low- to high-temperature measurement datasets including the NTC (negative temperature coefficient) interval. With these kinetic parameters, the SCM is validated against the measurements in the unconfined methane-air flame produced by the UMD line burner and then applied to predict the development and extinction of the heptane-air flame in an under-ventilated enclosure. In the first case, flame extinction is predicted at the oxygen concentrations consistent with the experimental values. In the second scenario, global low-frequency oscillations of the heat release rate are predicted prior to flame extinction.

A detailed of analysis of joint soot volume fraction/temperature statistics in non-premixed jet flame: Implication for soot emission turbulence/radiation interaction

The main objective of this study is to provide insights on the modelling of soot emission Turbulence Radiation Interaction (TRI) through a detailed analysis of the joint SVF/temperature statistics in turbulent non-premixed flames. The analysis relies on RANS/Transported Probability Density Function (TPDF) simulation of the Sandia ethylene jet turbulent non-premixed flame. RANS/TPDF predictions reproduce with fidelity the exhaustive set of experimental data, namely the flame structure, the soot and temperature statistics including the soot intermittency, and the radiative outputs. The marginal PDF of SVF exhibits the typical shape of an intermittent process and can be decomposed into a non-sooting mode and a sooting mode, with this latter being reasonably represented by a truncated Gaussian PDF. As expected, the marginal PDF of temperature can be reasonably represented by a clipped Gaussian PDF whereas that of the soot temperature follows a significantly narrower PDF as soot is fully oxidized in the fuel rich side of the flame. Analysis of the joint SVF/temperature PDF shows that both SVF/temperature and SVF/soot temperature first-order cross correlations are positive in the soot formation region and becomes strongly negative in the region of strong soot emission. The TPDF predictions are analysed a priori to design a new joint presumed PDF (PPDF) of SVF and temperature through the Gaussian copula. The Gaussian copula-based PPDF depends on six parameters, namely the five related to the marginal PDFs of SVF and temperature added to the first-order cross-correlation coefficient of SVF and temperature. Mean soot emission term computed with the copula-based PPDF agrees very well with the reference TPDF solution over the entire flame and improves significantly the solutions obtained by neglecting either TRI or the correlation between SVF and temperature. These results indicate that the Gaussian copula-based joint PPDF model is a good candidate to interpret soot emission-related experimental data in turbulent non-premixed flames.

Soot Modeling in Large Eddy Simulation of Turbulent Buoyant Flames Using the Laminar Smoke Point and the Eddy Dissipation Concept

ABSTRACT The paper presents a comprehensive set of Large Eddy Simulations (LES) of turbulent diffusion buoyant flames with a focus on soot modeling. Combustion modeling is based on the Eddy Dissipation Model (EDM) with an infinitely fast chemistry approach. Soot formation and oxidation are modeled with finite-rate chemistry based on the Laminar Smoke Point (LSP) concept. A turbulence-soot interaction model is proposed based on the Eddy Dissipation Concept (EDC) to close the chemical sink/source term for soot. A novel aspect of the modeling is the hybrid EDC formulation, where the mean chemical source term is a weighted average of a laminar term and a turbulent term, based on the local turbulent Reynolds number. The correct limiting behavior in the laminar regime is demonstrated for a laminar ethylene flame. Improvements in soot predictions near the fuel injection are obtained for a 13.7 cm-diameter turbulent ethylene flame and a 30 cm-diameter heptane flame. Additionally, the influence of the combustion model on soot predictions is carefully examined, especially with respect to the mixing time scale formulation and the related influence of the cell size (used as filter width in LES). A proposed dynamic model allows obtaining improved results even in under-resolved simulations and mitigating mesh sensitivity for soot predictions.

A-posteriori analysis of a data-driven filtered wrinkled flamelet model for thermodiffusively unstable premixed flames

State-of-the-art turbulent combustion models do not account for the effects of intrinsic flame instabilities, which are known to have a non-negligible effect, under technically relevant conditions, in thermodiffusively unstable flames such as those of hydrogen-based fuels. In this work, a data-driven modeling framework for filtered, laminar, self-wrinkling flames subject to intrinsic instabilities is presented and proposed as a stepping stone for the development of turbulent combustion models for large eddy simulation. In this context, data-driven refers to the use of small- and medium-sized resolved simulations, explicitly filtered in physical space, as data sources for the development of filtered tables. For consistency, all the unclosed terms of the filtered governing equations are then written according to the filtered tabulated chemistry formalism. The a-posteriori analysis of the modeling framework indicates that medium-scale simulations, which conversely to the small-scale ones feature at least one characteristic flame-finger, are needed for the generation of the data-driven tables. Furthermore, a laminar wrinkling factor, accounting for the sub-filter cellular wrinkling, should also be used. The presented results show promise for the extension of this modeling framework to the simulation of turbulent flames, as well as to multi-step chemistry and detailed thermo-transport modeling. Statement of SignificanceIt is nowadays well-known that intrinsic flame instabilities have a leading order impact on the propagation of premixed flames in thermodiffusively unstable mixtures, such as lean hydrogen-air premixed flames. This work presents the first a-posteriori analysis of a combustion model for filtered, albeit laminar, large-scale, intrinsically unstable premixed flames. The novelty of the presented data-driven model lies in the use of data obtained from filtering direct numerical simulations performed for paradigmatic small and medium-scale cases, instead of standard one-dimensional flamelets.

Numerical simulation of turbulent premixed flames with the conditional source-term estimation model using Bernstein polynomial expansion

Conditional Source-term Estimation (CSE) is a turbulence-chemistry interaction model similar to CMC, except that the conditional scalars are calculated from unconditional ones using an integral equation. This problem is inherently ill-posed and should be regularised. Recently, an efficient regularisation approach based on Bernstein polynomial expansion was proposed by Mahdipour and Salehi (Combust. Flame, 2022) in an a priori analysis using DNS data. This work implements this approach in a reacting flow solver, and two laboratory-scale turbulent premixed flames are simulated in the Reynolds-Averaged Navier-Stokes (RANS) context. The turbulent intensity in the first flame is low, and the results show that, unlike the conventional CSE approach, the new approach can accurately predict the flamelet conditional averages. Furthermore, the predicted averaged velocity field and major and minor species mass fractions compare favourably with the experimental measurements. The turbulent intensity in the second flame is relatively higher, and the predicted conditional averages should deviate from an unstrained laminar flame solution. The new approach can correctly predict this trend as well as the flame height in this flame. The computational cost of the new CSE approach is also substantially reduced compared to the regular CSE approach.

Simulation of turbulent premixed flames with machine learning - tabulated thermochemistry

The numerical integration of the differential equations describing chemical kinetics consumes the majority of computational time in combustion simulations that involve direct coupling of chemistry and flow, such as transported probability density function (PDF) methods, direct numerical simulation (DNS), conditional moment closure (CMC), unsteady flamelet, multiple mapping closure (MMC), thickened flame model, linear eddy model (LEM), partially stirred reactor (PaSR) as in OpenFOAM and laminar flame computation. This step can be accelerated by tabulation, and artificial neural networks (ANNs) have recently emerged as a powerful technique in this domain. To be applicable to a wide family of problems, an ANN tabulation approach must be based on data generated by an abstract process, rather than from the turbulent flame to be simulated. In the present work, the hybrid flamelet/random data and multiple multilayer perceptrons (HFRD-MMLP) method (Ding et al., Combust. Flame 231, 111493, 2021) for non-premixed flames is taken as a basis to develop a thermochemistry tabulation method for premixed flames. In the spirit of maintaining an essentially random data set that still originates in meaningful composition states, a set of one-dimensional premixed flame simulations is employed to generate data that are used as starting points for a random data generation process and subsequently discarded. The approach is applied to large eddy simulations (LES) of the Cambridge/Sandia swirl burner in configurations five and six, with the transported PDF method employed to provide closure for the filtered reaction source terms and the stochastic fields method used for numerical solution. Very good agreement in both major and minor species is observed between the LES-PDF simulations using direct integration of the reaction source term and the ones with the ANNs. Furthermore, the average time taken for reaction source term computations is reduced by fourteen times, while memory requirements constitute only 1.4 MB.

Development of a novel subgrid combustion model for buoyant turbulent diffusion flames

A novel approach is presented to incorporate finite rate reactions in modeling of turbulent diffusion flame, with the existence of unresolved flamelets inside the CFD grid cells taken into account. This approach, called SCM (subgrid combustion model), is applied in large eddy simulations of the UMD line burner flames. With the global kinetic parameters fitted for the measurement data and detailed simulations of autoignition in stoichiometric methane-air mixture, as well as for the extinction strain rate in the opposed non-premixed jets, the SCM model is shown to replicate the mean temperature profiles in unsuppressed flame with mean total heat release of 50 kW. For flame suppression via dilution of the oxidizer flow by nitrogen, the lift-off and extinction of non-anchored flame are predicted in agreement with the experimental data. The SCM is designed as a tool to allow for the finite rate kinetics effects in large eddy simulations of buoyant turbulent diffusion flames, with the focus on weakly turbulent regions, in which applicability of conventional combustion models is limited.

Turbulent burning velocity and thermodiffusive instability of premixed flames.

Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermodiffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λ_{n} that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained, and (ii) simulations of turbulent flames are performed by varying the width from Λ<Λ_{n} (in this case, the instability is suppressed) to Λ>Λ_{n} (in this case, the instability may grow). Moreover, simulations are performed either using mixture-averaged transport properties (low Lewis number flames) or setting diffusivities of all species equal to heat diffusivity of the mixture (equidiffusive flames), with all other things being equal. Obtained results show a significant increase in turbulent burning velocity U_{T} when the boundary Λ=Λ_{n} is crossed in weak turbulence, but almost equal values of U_{T} are computed at Λ<Λ_{n} and Λ>Λ_{n} in moderately turbulent flames characterized by a Karlovitz number equal to 3.4 or larger. These results imply that thermodiffusive instability of laminar premixed flames substantially affects burning velocity in weak turbulence only, in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev. E 107, 015102, (2023)10.1103/PhysRevE.107.015102).

LES of premixed jet flames subjected to extreme turbulence using flamelet-generated manifolds: a comparison of unstrained and strained flamelets

Two piloted premixed CH 4 /air jet flames with extreme turbulence are modelled using the Flamelet-Generated Manifold (FGM) method in the context of Large Eddy Simulation (LES). Free-propagating and reactant-to-product laminar flames are adopted to build unstrained and strained chemical databases, respectively. Detailed comparison of the LES-FGM results using the unstrained/strained databases is conducted which is validated against the direct numerical simulation results. The results show that whether including straining effects in the database will not influence the modelling of temperature and major species (e.g. CH 4 , O 2 and CO 2 ), but using a strained database is essential for predictions of intermediate minor species (e.g. H 2 , CH 2 O, OH and CO). The main reason is that the major species and temperature are almost insensitive to the straining due to the supportive effects from the pilot flame, which also tentatively explains why the unstrained database can be employed to model these strong turbulent flames. In contrast, the intermediate minor species are more prone to the straining, so that using a strained database is crucial. The preferential diffusion effects on the species and temperature predictions are examined to be negligible. It is proposed that adding extra transport equations for these minor species also leads to satisfactory predictions if using an unstrained database, which helps to include the straining effects on the minor species. This study is expected to be significant in high-fidelity simulations of strong turbulent flames using flamelet-tabulated combustion models.

Large-eddy simulation of the Darmstadt multi-regime turbulent flame using flamelet-generated manifolds

The Darmstadt multi-regime turbulent flame MRB26b is modelled using the Flamelet-Generated Manifold (FGM) in the context of Large Eddy Simulation (LES). Laminar free-propagating premixed flames are used to build a premixed chemical database, and laminar counter-flow flames are adopted to build a non-premixed and a partially premixed database. A detailed comparison of the LES-FGM results with the experimental data using the three databases is conducted, combining two sub-filter closure models, i.e., the PPDF (Presumed Probability Density Function) and DTF (Dynamically Thickened Flame). It is found that different databases lead to similar modelling of velocity, temperature, mixture fraction and major species (e.g., CH4, O2, CO2 and H2O). However, the intermediate minor species CO and H2 are better predicted using the two databases based on counter-flow flames due to a better inclusion of the fuel/air mixing and straining effects. Similar to previous studies, using the DTF model is observed to over-predict CO and H2. This is revealed to be a combined effect of the artificial flame front thickening and flame wrinkling loss, which is characterized by a lower variance of the progress variable. Comparatively, better minor species predictions are obtained using the PPDF without flame thickening. A correction method is proposed and validated to improve the minor species prediction for the DTF model. The combustion regimes and flame propagation directions are also examined. The results are significant for high-fidelity simulation of multi-regime turbulent flames using the flamelet-tabulated combustion model.

A Numerical Study of Flow Structures and Flame Shape Transition in Swirl-Stabilized Turbulent Premixed Flames Subject to Local Extinction

ABSTRACT Large Eddy Simulations (LES) of turbulent lean-premixed flames of V- and M-shape are presented. A simple algebraic closure with the ability to capture finite-rate chemistry effects is used for subgrid reaction rate modeling. The V-shaped flame is stabilized in the inner shear layer between a swirling annular jet and a central recirculating bubble in a sudden expansion duct. The M-shaped flame is stabilized in the inner and outer shear layer, adjoining the corner recirculation zone induced by the vertical step. The focus of the study is on the flow fields and shapes of the flames, which distinguish themselves through different heat load and sensitivity to local extinction. Good agreement with measurements is observed for the cold and the reacting flow cases. The numerical results suggest that the entrainment of hot gases into the outer recirculation zone occurs close to the impingement point of the swirling annular jet on the wall and this process is strongly dependent on intense vortical structures in the outer shear layer. The results further suggest that local extinction influences the position of the flame in the inner shear layer and, thereby, also the intensity of the local entrainment process.

Combustion studies of MMA/[formula omitted] for a hybrid rocket motor

Poly(methyl methacrylate) (PMMA) is the synthetic polymer of methyl methacrylate (MMA), which is used in a multitude of everyday applications, can also be used as a solid fuel in hybrid rockets. When used as a fuel in a combustion chamber, PMMA undergoes thermal decomposition and phase-change (solid-to-gas), where gaseous MMA (C5H8O2) is the primary product. The gaseous MMA then undergoes combustion with an oxidizer. Experimental studies of this combustion chamber have been performed in literature, and this study helps produce high-fidelity simulations, which can match experimental observations while giving access to more data in the combustion chamber. Simulations of turbulent diffusion flames are performed with gaseous MMA introduced through the combustion chamber walls. Two different diffusion models are used alongside a finite-rate chemistry model to observe the effects of differential diffusion. The rate of inflow of MMA is controlled by the temperature field in the combustion chamber, and the results from the 3D simulation are comparable to 1D counterflow diffusion flame simulations. Simulations are also performed with a tabulated chemistry model developed to improve the computational efficiency and with two different internal diameters to analyze the geometric effects. If one wishes to capture the flow field profiles and fuel regression rate, chemistry effects need to be included. If one wishes to capture the internal chemistry profiles of the combustion products, differential diffusion effects are important. The fuel regression rate and the radial chemistry profiles from the simulations are compared with the experimental results and show good agreement.

Self-adaptive turbulence eddy simulation of a premixed jet combustor

The self-adaptive turbulence eddy simulation (SATES) is employed to investigate the lean premixed methane/air turbulent flame in a single-nozzle model gas turbine combustor, in which the high axial momentum jet issuing from an off-center nozzle facilitates the development of a large-scale, dominant lateral recirculation zone that stabilizes the flame. For turbulence modeling, the SATES method can dynamically adjust the proportion of resolving and modeling of turbulent scales according to the local grid scale and turbulence length scales, thus depressing the gird-sensitivity in large eddy simulation (LES) calculation. For combustion modeling, the thickened flame model with a reduced chemistry mechanism is integrated into the SATES turbulence modeling framework to capture the unsteady flame dynamics. The accuracy of SATES results is assessed against experimental data, as well as the ones from LES and the detached eddy simulation (DES) of this burner with the same combustion model and grids. The predicted length of large-scale recirculation of the flow field by SATES is significantly better than that by LES and DES with low mesh resolution. Detailed comparisons show that the SATES adaptively improves the modeling degree of near-wall turbulence to improve the prediction accuracy with the low grid resolution. Similar to LES, the SATES method does not cause serious delay of shear layer instability and weakening of flame wrinkle observed in DES. The study demonstrates the suitability and accuracy of the hybrid turbulence modeling methods of SATES for complex turbulent flame simulations coupled with suitable combustion model.

Numerical Simulation of Hydrogen-air Turbulent Diffusion Flame

The hydrogen-air turbulent diffusion flame - DLR H3 (benchmark test case at the International workshop on Measurement and computation of turbulent non-premixed flames, Naples, July 1996) [http://www.sandia.gov/TNF/1stWorkshop/TNF1.html], is numerically modeled using commercial CFD software CFD++. For simplicity, a 5 degree sector of the domain is considered. Good comparison is obtained for the non-dimensional quantities reported in the literature [Cheng T.-C., Fruechtel G., Neuber A., Lipp F., Hassel E. P. and Janicka J., 1995, "Experimental data base for numerical simulations of turbulent diffusion flames," Forschung im Ingenieurwesen, 61 (6), pp. 165-171].

Direct numerical simulations of methane, ammonia-hydrogen and hydrogen turbulent premixed flames

Three turbulent premixed flames with the same unstretched laminar flame speeds and thicknesses are analyzed and compared using 3D Direct Numerical Simulation (DNS) in a slot burner configuration at atmospheric conditions: a CH4/air flame at ϕ=1, an NH3−H2/air (46% vol. H2) at ϕ=1 and an H2/air flame at ϕ=0.45.While both stoichiometric methane and ammonia-hydrogen flames behave similarly, the lean hydrogen flame brush is twice as short with less flame surface, and exhibits significant alteration of its local flame structure: for the H2 flame, the thickness of flamelets decreases significantly while burning rates increase drastically. This is observed for flame elements convexly curved with respect to fresh reactants (positive curvature) because of preferential diffusion, where thermo-diffusive instabilities generate long-tail structures that continuously head toward the fresh gases, and also for near-flat flame elements because of local strain effects. Opposite behaviors are observed for flame elements concavely curved (negative curvature) where fuel depletion caused by unfocusing of hydrogen and strain effects are unable to increase the consumption, even leading to near-extinction of the flame. The turbulent methane and ammonia-hydrogen flames studied in this work do not exhibit the instabilities seen in the pure hydrogen flame. However, local flame-flame interactions are observed in the cusp regions of all three flames, which significantly increase the displacement speed as well as flame surface destruction.A 1D-3D comparison indicates that strain effects in regions of low curvature and preferential diffusion effects in regions of positive curvature can be modeled using counterflow flamelets to account for stretch effects on the turbulent hydrogen flame propagation in addition to turbulent wrinkling.

A self-consistent extension of flamelet theory for partially premixed combustion

Orthogonal coordinate systems represent an attractive alternative for the formulation of two-dimensional composition space equations for partially premixed combustion: They avoid the need of closure models for a cross scalar dissipation rate and allow for a direct recovery of the corresponding flamelet equations in the asymptotic limits of non-premixed and premixed combustion. Despite these remarkable features, this kind of coordinate system still presents some important unsolved issues, which have limited their application so far. These difficulties are mainly associated with i) the lack of an appropriate formalism for the definition of two variables having orthogonal gradients in the entire flame domain and ii) the absence of corresponding closure models for the gradients of these variables in two-dimensional composition space. In the present work, it is shown how a Lagrangian interpretation of the flamelet derivative allows solving both problems. More specifically, after the mixture fraction, Z, is adopted as first coordinate, the proposed approach allows to derive i) two-dimensional composition space equations for all reactive scalars, ii) a transport equation for a modified reaction progress variable, φ, satisfying the desired orthogonality condition, ∇Z·∇φ=0, and iii) two-dimensional composition space equations for gZ=|∇Z| and gφ=|∇φ|. The obtained set of two-dimensional equations in orthogonal composition space is general and it can describe different flames of interest. In order to illustrate the capabilities of the formulation, the equations are then specialized for planar flames with unity Lewis number, obtaining in this way a solvable set of composition space equations in orthogonal coordinates. After an appropriate numerical approach is introduced, the resulting 2D equations are solved to analyze the interaction between premixed flamelets with a strain rate prescribed along the Z-dimension controlling the interaction. Both flame structures and budgets of the scalar gradient equations are studied and the results provide new insights into the physics of scalar gradients in two-dimensional composition space. Finally, conceivable coupling strategies of the present formulation with CFD codes for the simulation of turbulent flames are discussed.

A computationally efficient approach for soot modeling with discrete sectional method and FGM chemistry

A novel approach for the prediction of soot formation in combustion simulations within the framework of discrete sectional method (DSM) based univariate soot model and Flamelet Generated Manifold (FGM) chemistry, referred to as FGM-CDSM, is proposed in this study. The FGM-CDSM considers the clustering of soot sections derived from the original soot particle size distribution function (PSDF) to minimize the computational cost. Unlike conventional DSM, in FGM-CDSM, governing equations for soot mass fractions are solved for the clusters, by using a pre-computed lookup table with tabulated soot source terms from the flamelet manifold, while the original soot PSDF is re-constructed in a post-processing stage. The flamelets employed for the manifold are computed with detailed chemistry and the complete sectional soot model. A comparative assessment of FGM-CDSM is conducted in laminar diffusion flames for its accuracy and computational performance against the detailed kinetics-based classical sectional model. Numerical results reveal that the FGM-CDSM can favorably reproduce the global soot quantities and capture their dynamic response predicted by detailed kinetics with a good qualitative agreement. Furthermore, compared to detailed kinetics, FGM-CDSM is shown to substantially reduce the computational cost of the complete reacting flow simulation with soot particle transport. Primarily, the use of FGM reduces the overall calculation by about two orders of magnitude compared to detailed kinetics, which is advanced further with the clustering of sections at a low memory footprint. Therefore, the present work demonstrates the promising capabilities of FGM-CDSM in the context of computationally efficient soot calculations and provides an excellent framework for extending its application to the simulations of turbulent sooting flames.