Reaction-diffusion Manifold Research Articles

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.

An iterative methodology for REDIM reduced chemistry generation and its validation for partially-premixed combustion

Partially-premixed flames (PPFs) incorporate effects of both premixed and non-premixed types of reaction zones. The modelling of PPFs using manifold-based model reduction methods faces some inherent difficulties due to the underlying assumptions of a-priori identification of the type of combustion system. In this work, the reaction–diffusion manifold (REDIM) model reduction method is applied to study PPFs. The REDIM method requires minimal prior knowledge about the type of combustion system, which makes it a suitable method for studying PPFs. It allows incorporating system-specific diffusion (gradients) terms in a generic way so that the manifold can evolve according to the diffusion related information provided by the combustion system. In this way, a prior identification of the type of combustion system is no longer needed. This work utilises an iterative methodology to generate REDIM chemistry tables so that the reduced manifold can be iteratively converged very close to the detailed manifold according to the gradients of the reduced coordinates provided by the physical combustion system in each iteration step. In addition, a new method is proposed to provide the gradient estimates of the reduced coordinates during the generation of REDIM from the scattered gradient data in REDIM reduced CFD calculations. Laminar triple flames, a special case of PPFs, with two types of mixture fraction gradients are selected as the target cases to assess the presented iterative methodology. REDIM reduced calculations are compared with simulations based on detailed finite-rate kinetics. It is found that in the final iteration steps, temperature and all considered major and minor species mass fraction profiles are very well predicted by the REDIM reduced calculations.

Influence of the chemical kinetics on the prediction of turbulent non-premixed jet CH_4 flames

The present work focuses on the five different chemical mechanisms coupled with probability density function (PDF) model to represent the local extinction and re-ignition flame characteristics of the well-known Sandia Flames D–F. These five mechanisms span from the Foundational Fuel Chemistry Model (FFCM) mechanism involving 38 species to the Glarborg mechanism involving 150 species. The coupled computational fluid dynamics (CFD) and transported-PDF method are used for the turbulence modeling, and the reaction–diffusion manifolds (REDIMs) are used as an advanced technique for the simplification of chemical kinetics and to speed up the numerical computation. It is demonstrated that these chemical mechanisms have an ability to represent the degree of local extinction and re-ignition accurately. Furthermore, the sensitivity analysis shows that the degree of local extinction is very sensitive to only several key elementary reactions, and an analysis on the turbulence–chemistry interaction investigates the influence of these elementary reactions.

The hierarchy of low-dimensional manifolds in the context of multiple mapping conditioning mixing model

A new model to couple the multiple mapping conditioning (MMC) mixing model with manifold based simplified chemistry is proposed. The concept is based on the fact that the system state can be locally confined to a manifold with lower dimension, which is embedded in the manifold with higher dimension. Therefore, in the framework of the MMC mixing model, particles to be mixed must be selected such that they are localized in the reference variable space with the dimension which corresponds to the minimum number of the progress variables describing the thermo-kinetic states locally. This can be achieved by comparing the physical mixing time-scale with the chemical time-scales describing the movement on the slow manifold, and the dimension of the necessary reference variables can be determined automatically. The present work uses an IEM-based MMC mixing model and Reaction-Diffusion Manifolds (REDIMs) as the simplified chemistry, but it can be extended easily to other mixing models. The proposed methodology is validated by testing the well-known non-premixed Sandia Flame D and F, and the results show good agreement with experimental results and those obtained using the detailed chemistry.

Reaction diffusion manifolds (REDIMs) applied to soot formation in ethylene counterflow non-premixed flames: an uncoupled methodology

Reaction diffusion manifolds (REDIMs) applied to soot formation in ethylene counterflow non-premixed flames: an uncoupled methodology

Reduced modeling of the NOx formation based on the reaction-diffusion manifolds method for counterflow diffusion flames

The accurate prediction of the NOx formation has gained great attention in view of clean combustion. In this direction, a reliable reduction technique for the chemical kinetics is important to capture the NOx formation accurately with reduced computational costs for the practical turbulent combustion processes. This work focuses on the hierarchical construction of Reaction-Diffusion Manifolds (REDIM) to include the NOx chemistry, which is well-known to be governed by very slow chemical reactions. Based on the hierarchical structure of the REDIM method, a two-dimensional (2D) and a three-dimensional (3D) REDIM model are generated, without any principle extension of the REDIM method. Sample calculations of NOx formation in methane/air non-premixed counterflow flames verify the REDIM method for both steady and transient processes.

Model reduction on the fly: Simultaneous identification and application of reduced kinetics for the example of flame-wall interactions

In manifold-based reduced models, a manifold is often generated based on an a-priori identification. Subsequently, a successful reduced kinetic computation is largely dependent on the proper choice of the model assumptions. To relax this restriction, a model reduction on the fly technique is proposed for the Reaction-Diffusion Manifold (REDIM) method in the present study. The method is applied to a stoichiometric CH4-air side-wall quenching (SWQ) configuration, where gradients of species and enthalpy both exist.Several reduced kinetic simulations with evolving REDIMs are performed. The first computation starts with a REDIM generated based on a very rough gradient estimation (constant values). Afterwards, each calculation uses the REDIM generated based on a gradient estimation from its previous reduced kinetics. The results from the first reduced kinetic simulation show considerable deviations from the detailed kinetics. As soon as after one iteration, the results get much more accurate, and already match quite well with the reference results. Afterwards, the results show minor changes with more iterations. Through these reduced kinetic simulations, the capability of the model reduction on the fly technique to accurately describe the SWQ process at a reduced computational cost has been demonstrated, and it shows to be a promising method which can be applied to other configurations, too.

A manifold-based reduction method for side-wall quenching considering differential diffusion effects and its application to a laminar lean dimethyl ether flame

In the present study, reduced kinetics considering both differential diffusion effects and strong heat losses, based on the Reaction–Diffusion Manifold (REDIM) method, formulated and constructed in generalized coordi-nates, is proposed. The approach fully coupled to a CFD solver is applied to the side-wall quenching (SWQ) of a laminar premixed dimethyl ether–air flame at an equivalence ratio of 0.83 where differential diffusion effects are non-negligible and a detailed transport model is required. To the best of the authors’ knowledge, this is the first study to take into account differential diffusion effects in manifold-based reduced kinetic models for complex scenarios such as the SWQ process, while previous studies with reduced models simply adopted a unity Lewis number assumption. Additionally, this is the first combined experimental-numerical study, including simulations with manifold-based reduced models, for SWQ with differential diffusion.To consider differential diffusion effects, strong heat losses, and their interactions, two different reduced kinetic models based on a three-dimensional and a two-dimensional REDIM, respectively, are formulated and assessed. The performance of the reduced kinetics is evaluated by comparison with detailed kinetics and experimental data for global quenching characteristics, local thermo-chemical states and stretch distribution in the near-wall region. It is found that major features observed in the detailed kinetic computation and experiment are well reproduced by both reduced kinetic simulations. The capability of the reduced kinetics to describe the multiple physical phenomena present in the SWQ configuration, such as differential diffusion, heat losses, flame quenching and stretch effects is demonstrated. The two different reduced kinetic models are compared to each other and the advantages and disadvantages of each method are discussed, which can be useful when choosing the modeling approach for more complex configurations.

Extension of the Reaction-Diffusion Manifold method to systems with ionization

The Reaction-Diffusion Manifold (REDIM) method is a generic manifold based reduced kinetic model that has been applied to various combustion systems. In this work, it is extended and applied to combustion processes including charged species. In order to incorporate ions in the REDIM method, electrons and ions are accounted for in the coupling of kinetics and molecular transport. The REDIM method is extended to account for a very detailed transport model. This transport model can handle full detailed transport and accounts for ambipolar diffusion of the charged species. The suggested method is validated and demonstrated for laminar flat methane/air flames at different temperatures. A two-dimensional REDIM is generated, which can be used for premixed flames with different temperatures of the unburnt gas. The two-dimensional reduced kinetic model is validated by comparing the computational results of detailed and REDIM reduced kinetics. It is shown that the reduced scheme reproduces the results of detailed simulations very accurately, and that the REDIM concept can be extended to reaction systems with ionized species.

Reaction-Diffusion Manifolds including differential diffusion applied to methane/air combustion in strong extinction regimes

Detailed chemistry simulations of turbulent reacting flows involving combustion of hydrocarbons can easily exceed the available computational resources, depending on the dimensions of the chemical system. Previous work of the authors showed how the combination of the Eulerian Stochastic Fields (ESF) model with tabulated chemistry based on 2-dimensional Reaction-Diffusion Manifolds (REDIM) provided a significant computational speed-up, compared to the finite rate ESF solver. In this work, the behaviour for flame F, featuring a strong degree of extinction, is further investigated. A comparison is performed for 2D and 3D databases, both using simplified and detailed transport, where the scalar dissipation rate is included as the third table parameter. The results show that the upstream sections are well captured by the REDIM built for detailed transport, while the downstream sections are better captured by the simplified transport database. While a 3D-REDIM based on simplified transport seems to be necessary to capture the extinction events, a 2D-REDIM with differential diffusion already provides satisfactory results. Overall, the use of a 3D-REDIM with differential diffusion better describes the global behaviour of flame F.

Sensitivity of reaction–diffusion manifolds (REDIM) method with respect to the gradient estimate

In this work, a mathematical formulation for the calculation of the sensitivity of manifold-based simplified chemistry with respect to the scalar gradient is derived. This methodology allows to answer how important the scalar gradient is for the Reaction–Diffusion Manifolds (REDIM) reduced chemistry and how sensitive the reduced scheme is with respect to the gradient estimate. Based on the governing REDIM evolution equation, the sensitivity equation is derived in form of a linear in-homogeneous partial differential equation system of second order with non-constant coefficients. Some examples including simple reaction systems and real combustion systems are shown to validate the approach. Moreover, the developed sensitivity analysis can also be used in other manifold-based methods.

Reaction-Diffusion Manifolds (REDIM) Method for Ignition by Hot Gas and Spark Ignition Processes in Counterflow Flame Configurations

ABSTRACT Ignition processes in laminar counterflow configuration using both detailed and reduced chemistry based on the Reaction-Diffusion Manifolds (REDIM) method are investigated. We choose in this work: (i) ignition by hot gas and (ii) spark ignition. The temporal development of thermo-kinetic quantities (e.g. temperatures and species concentrations) are compared. It is demonstrated that the two-dimensional REDIM reduced chemistry is accurate enough to predict the time evolution of different thermo-kinetic quantities compared with the detailed solutions for flows perturbed by different strain rates. Furthermore, the two-dimensional REDIM model for the spark ignition process can reproduce values of the minimal ignition energy very well. This confirms the concept and quality of the REDIM reduced model, which can be then further applied for turbulent flame simulations.

Coupling the Multiple Mapping Conditioning Mixing Model with Reaction-diffusion Databases in LES of Methane/air Flames

ABSTRACT The Multiple Mapping Conditioning (MMC) model for sparse Lagrangian Large-Eddy Simulations (LES) is coupled with tabulated chemistry based on reaction-diffusion manifolds (REDIM). In addition to assessing the reduction in computational cost compared to direct integration on the fly, a comparison with the previously implemented REDIM solver based on the Eulerian Stochastic Fields (ESF) is performed. The methane/air Sandia flames D and E are selected as a benchmark, which are amenable to a 2D REDIM database having a passive scalar and one progress variable as dimensions. A comparison between direct integration ESF and MMC shows that the latter gives better predictions of the conditional means and fluctuations, offering at the same time a significantly reduced computational cost. When coupled with REDIM, MMC and ESF models provide similar results, indicating the significant sensitivity of the predictions to the thermochemical states which are restricted to the same REDIM manifold. When the states are projected back onto the REDIM surface in the direction where the progress variables remain almost constant, accuracy is lost in the cold fuel-lean region with MMC. Furthermore, the computational performance gain in MMC compared to ESF is reduced when the REDIM tabulation is used, pointing to non-chemistry related computational bottlenecks in the MMC algorithms.

Simulation of side-wall quenching of laminar premixed flames with manifold-based reduced kinetic models implemented in generalised coordinates

Side-wall quenching (SWQ) is one of the generic configurations for flame-wall interaction and has been widely investigated through simulations using detailed and reduced chemical kinetics. In all previous related studies using manifold-based reduced kinetic models, the reduced model equations are solved in thermokinetic coordinates. This study, by contrast, will for the first time conduct SWQ simulations based on reduced model equations in generalised coordinates. The implementation has been validated by comparison to both simulation results using detailed kinetics and experimental data. Comparing the results of computations solving reduced model equations in generalised coordinates to those in thermokinetic coordinates, it is found that there are only slight differences when the manifold is perfectly invariant, while large discrepancies appear if the manifold is not exactly invariant. Under the latter condition, only reduced model equations in generalised coordinates yield correct results. Within the combined framework of reduced model equations in generalised coordinates and the so-called reaction–diffusion manifold for tabulation, the sensitivity with respect to the gradient estimation is investigated to find out what degree of simplification is reasonable for SWQ simulations.

A novel model for incorporation of differential diffusion effects in PDF simulations of non-premixed turbulent flames based on reaction-diffusion manifolds (REDIM)

In this work, reaction-diffusion manifold (REDIM) reduced chemistry is used in the simulation of turbulent non-premixed flames based on a transported-probability density function model. Differential molecular diffusion is applied in the generation of the manifolds. This is the first work to consider the gradients of the reduced variables as additional parameters in the REDIM model, and one-directional gradients are utilized to generate the REDIM reduced chemistry. Hereby, the influence of turbulence on differential molecular diffusion is automatically considered in terms of reduced variable gradients, and the physical transport properties (e.g., diffusion coefficients) are used in a detailed way, without any additional modeling (e.g., unity-Lewis number assumption). Although the scalar gradients appear as multi-directional in a general turbulent reacting flow, previous direct numerical simulation analysis reveals that REDIMs generated from one-directional gradients can accurately describe the system featuring multi-directional gradients, if this one-directional gradient has a major effect on the chemistry. Here, it is proposed to obtain such gradients under the hypothesis that the flame structure is locally one-dimensional at each spatial position. In order to retrieve the gradients of the reduced variables for the interpolation of the thermo-kinetic states from the REDIM table, the sub-grid gradient is evaluated here from the particle fields. The well-known Sandia series of flames is selected to validate the proposed algorithm. The results show that the new algorithm can reproduce the thermo-kinetic quantities with high accuracy for all investigated flames.

Validation of an Eulerian Stochastic Fields Solver Coupled with Reaction\u2013Diffusion Manifolds on LES of Methane/Air Non-premixed Flames

The Eulerian stochastic fields (ESF) combustion model can be used in LES in order to evaluate the filtered density function to describe the process of turbulence–chemistry interaction. The method is typically computationally expensive, especially if detailed chemistry mechanisms involving hydrocarbons are used. In this work, expensive computations are avoided by coupling the ESF solver with a reduced chemistry model. The reaction–diffusion manifold (REDIM) is chosen for this purpose, consisting of a passive scalar and a suitable reaction progress variable. The latter allows the use of a constant parametrization matrix when projecting the ESF equations onto the manifold. The piloted flames Sandia D–E were selected for validation using a 2D-REDIM. The results show that the combined solver is able to correctly capture the flame behavior in the investigated sections, although local extinction is underestimated by the ESF close to the injection plate. Hydrogen concentrations are strongly influenced by the transport model selected within the REDIM tabulation. A total solver performance increase by a factor of 81% is observed, compared to a full chemistry ESF simulation with 19 species. An accurate prediction of flame F instead required the extension of the REDIM table to a third variable, the scalar dissipation rate.

Large Eddy Simulation of Lean Premixed Swirling Flames via Dynamically Thickened Flame Model Coupling with the REDIM Chemistry Table

In this paper, the so-called REDIM–DTF sub-grid scale combustion model is proposed to improve the well-known dynamically thickened flame (DTF) combustion model by combining the DTF modeling strategy with the reaction-diffusion manifold (REDIM) chemistry table, which is generated from a detailed reaction mechanism. The new model is then used to calculate two lean premixed swirling flames in the PRECCINSTA combustor via large eddy simulation. The radial profiles of velocity, temperature, and species concentration, as well as the flame surface area and vortex structure are analyzed. The results are in good overall agreement with the corresponding experiment, and the performance of the REDIM–DTF model is very similar to that of the DTF model. The predicted CO mass fraction profiles, however, show a relatively larger discrepancy between the original DTF model and the proposed REDIM–DTF model, which is thought to be due to different reaction mechanisms used. As a smaller number of species transport equations are solved in the REDIM–DTF model, its computational efficiency is about 15% higher than that of the original DTF model.

REDIM-PFDF modelling of turbulent partially-premixed flame with inhomogeneous inlets using top-hat function for multi-stream mixing problem

Present study focuses on numerical investigation of two important partially-premixed inhomogeneous types of flames using REDIM-PFDF sub-grid scale combustion model. REDIM-PFDF model is based on the reaction-diffusion manifold (REDIM) technique and presumed filtered density function (PFDF) method. The detailed chemical kinetics is reduced into a two-dimensional chemistry table which is using the mass fractions of CO2 (YCO2) and N2 (YN2) as the reduced coordinates. The shapes of the Filtered Density Function (FDF) for YCO2 and YN2 are presumed to be clipped Gaussian and top-hat, respectively. We find that the top-hat function, in context of LES, is a suitable option to deal with multi-stream mixing problem. The comparison between LES and experimental data shows that the mixture fraction and mass fractions of several species are in a good agreement with the experimental data. The characteristics of two flames are also analyzed by comparing their OH mass fractions and CO2 production rates.

Reduced modeling of Flame-Wall-Interactions of premixed isooctane-air systems including detailed transport and surface reactions

In this work, the Reaction-Diffusion Manifold (REDIM) method, a method for model reduction, is applied to a premixed isooctane-air system with Flame-Wall-Interactions (FWI). In order to provide a highly accurate reduced kinetic model, a detailed model for the diffusive processes is applied and complex boundary conditions that account for heterogeneous wall reactions are implemented.The REDIM is constructed and validated by comparing results of detailed and reduced kinetics in the system state space. The results of the reduced computations are compared with those of the detailed computations. It is shown that the reduced kinetics reproduce the results of the FWI very accurately. In particular, the difference between detailed kinetics with and without wall reactions is larger than the difference between detailed and reduced kinetics with heterogeneous wall reactions, which demonstrates the quality of the model reduction.

Comparative analysis of Reaction-Diffusion Manifold based reduced models for Head-On- and Side-Wall-Quenching flames

In this study, multi-dimensional molecular transport phenomena during Flame-Wall-Interactions (FWI) and their effects on model reduction strategies are investigated. In order to access the problem, the standard configurations of a two-dimensional Side-Wall Quenching (SWQ) flame and a one-dimensional Head-On Quenching (HOQ) flame are used and compared. In the case of the SWQ configuration it is shown that the gradients of the species scatter significantly both in the physical space and in the state space. Moreover, the gradient vector of the specific enthalpy describing energy losses towards the wall is not aligned with the gradient vectors of the species, which can be considered as a typical case while a flame in application might approach to the wall at any arbitrary transversal direction. This observation motivates to take the gradients’ scattering and multi-dimensional transport phenomena into account during model reduction to describe reliably the quenching process.The Reaction-Diffusion Manifold (REDIM) method is applied in this work. The method allows to take into account multi-dimensional transport in a very generic way. In order to generate the REDIM, gradient estimates are approximated by using a Singular-Value Decomposition (SVD) of SWQ detailed gradients fields. Two-dimensional REDIMs for both cases are constructed and compared to each other. Different transport (diffusion) models are implemented to compare quantitatively the manifolds with HOQ and SOQ gradients estimates. The comparison shows that the differences between reduced models with varying transport models is significantly larger than the differences for varying configurations (multidimensional gradient estimates). This justifies the use of a relatively simple REDIM for more complicated geometries and configurations. This simplifies the treatment and model reduction procedure significantly for such complicated transient phenomena.