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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Numerical simulations of reactive flows are still a challenge when using full detailed kinetic mechanisms, which are becoming larger and larger to incorporate most of the combustion phenomena. One strategy to overcome this issue and simplify the treatment of the chemical kinetics is to use manifold-based methods, and one representative of this class is the Reaction–Diffusion Manifolds (REDIM). In the present work, the REDIM is applied for the first time to study soot formation in ethylene/air counterflow non-premixed flames. A simplified semi-empirical model for soot formation based on acetylene that describes nucleation, surface growth, and oxidation is used, and an uncoupled framework between gas phase and the formation of particulate matter is presented. Validation is carried out for laminar flames, and the results show that REDIM can predict with good accuracy the slow process of soot formation. [ABSTRACT FROM AUTHOR]

In recent decades, energy consumption has increased considerably and fossil fuel reserves have been decreasing. Biofuels are a renewable energy source, which reduces dependence on fossil fuels and brings environmental benefits. Thus, a better understanding of the processes of energy transformation through the combustion of biofuels is necessary. Combustion is described by the equations of continuity, momentum, conservation of chemical species and energy. As there is a strong coupling between these equations, the computational cost to solve them is high. Thus, it is necessary to reduce the number of species and reactions of kinetic mechanisms. This work presents the modeling and simulation of laminar jet diffusion flames of hydrogen and methyl formate with coflow. The one-dimensional REDIM and the Rosenbrock methods were used to solve the chemical problem. The results obtained for the main combustion products were compared with experimental data, showing reasonable agreement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The local heat-release rate and the thermo-chemical state of laminar methane and dimethyl ether flames in a side-wall quenching configuration are analyzed. Both, detailed chemistry simulations and reduced chemistry manifolds, namely Flamelet-Generated Manifolds (FGM), Quenching Flamelet-generated Manifolds (QFM) and Reaction-Diffusion Manifolds (REDIM), are compared to experimental data of local heat-release rate imaging of the lab-scale side-wall quenching burner at Technical University of Darmstadt. To enable a direct comparison between the measurements and the numerical simulations, the measurement signals are computed in all numerical approaches. Considering experimental uncertainties, the detailed chemistry simulations show a reasonable agreement with the experimental heat-release rate. The comparison of the FGM, QFM and REDIM with the detailed simulations shows the high prediction quality of the chemistry manifolds. For the first time, the thermo-chemical state during quenching of a dimethyl ether-air flame is examined numerically. Therefore, the carbon monoxide and temperature predictions are analyzed in the vicinity of the wall. The obtained results are consistent with previous studies for methane-air flames and extend these findings to more complex oxygenated fuels. Furthermore, this work presents the first comparison of the QFM and the REDIM in a side-wall quenching burner. [ABSTRACT FROM AUTHOR]

Reduced models for the evaporation and decomposition of urea-water solution in exhaust gas systems are developed to improve computational efficiency for detailed simulations. The models describe a droplet or wall film of urea water solution in hot exhaust gas, which is simulated in detail including gas phase chemistry and an evaporation model for the urea decomposition. The time scales of all involved processes are analyzed and it is found that only during the phase of urea decomposition transport and chemistry are coupled, while there is no significant chemistry during the preceding phase of water evaporation and no significant transport after complete evaporation and decomposition. Based on these results reduced models for all phases are suggested and a two-dimensional tabulated model for the processes in the gas phase and the urea decomposition phase is developed, which accurately reproduces the results of detailed simulations. [ABSTRACT FROM AUTHOR]

The dynamic behaviour and structures of laminar counterflow diffusion methane flames under oscillatory strain rates are investigated based on both detailed and reduced chemistry. It is known both from experiment and numerical studies that flame can deviate from its quasi-steady manner for high frequencies, which makes the well-known steady laminar flamelet model questionable. In this work, the Reaction-diffusion manifolds (REDIM) concept for simplified chemistry is applied to study the laminar counterflow diffusion flames with oscillating strain rates. In the construction of REDIM, one needs little knowledge of the studied system, and the REDIM reduced chemistry can cover both stable and unstable (extinction) regimes of the studied system. It is shown that the REDIM can capture both the steady and unsteady behaviours of the flame structures even for high frequencies, where the standard laminar steady flamelet approach is not appropriate. [ABSTRACT FROM AUTHOR]

During the last decades, tabulated chemistry approaches, like manifold-based concepts to implement model reduction, have become a widespread, promising and accurate method to take chemical reactions into account in computing reacting flows. However, there is a number of crucial issues concerning the generation and implementation of the tabulated chemistry approaches. These concern the way manifolds of the arbitrary dimension are generated, parametrised (i.e. tabulated) preserving fast/slow decomposition and implemented rigorously by the formulation of a reduced model in a coordinate independent manner. This study discusses these problems in detail and suggests generic solutions based on the Reaction–Diffusion Manifolds (REDIM) method. A REDIM tabulated chemistry concept obtained by using the hierarchical nature of the invariant slow system manifolds is presented. Numerical aspects of the implementation are in the focus of the paper. It is shown how the concept is implemented to overcome most problems without a-priori knowledge of the considered system behaviour. As a basic example for discussion and illustration synthesis, gas/air combustion in premixed, freely propagating flames is used. [ABSTRACT FROM AUTHOR]

For general reacting flows the numerical simulation faces two main challenges. One is the high dimensionality and stiffness of the governing conservation equations due to detailed chemistry, which can be solved by using simplified chemical kinetics. The other one is the difficulty of modeling the coupling of turbulence with thermo-chemical source term. The probability density function (PDF) method allows to calculate turbulent reacting flows by solving the thermal-chemical source term in closed form. Usually, the PDF method for turbulent processes such as mixing processes and the reduction method for chemical kinetics are developed separately. However, coupling of both processes plays an important role for the numerical accuracy. To investigate the importance of coupling between turbulence and simplified chemistry, two different coupling strategies for mixing and reduced chemistry are discussed and tested for the well-known Sandia Flames E and F, in which there is a strong interaction between turbulence and chemical kinetics. The EMST mixing model is chosen for turbulent mixing, while the Reaction-Diffusion Manifolds (REDIMs) is used as simplified chemistry. However, the proposed strategies are also valid for other mixing models and manifold based simplified chemistry. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Combustion simulations involve the modeling of chemical kinetics, and due to the complexity of detailed mechanisms, chemistry reduction techniques are necessary. One model reduction strategy is the reaction-diffusion manifold (REDIM) method, and to obtain the REDIM, an evolution equation must be solved till its stationary solution and a gradient estimation is needed, provided e.g. from flamelet solutions with detailed chemistry. In this work, the REDIM technique is applied to simulate methane/air turbulent flames based on a simplified gradient estimation. This strategy uses less information in constructing the REDIM, increasing computational efficiency while reducing computational costs. Validation is performed for non-premixed laminar flames. A RANS/transported-PDF framework for the simulation of turbulent reacting flows is presented and used to validate the proposed model. Results show that the simplified gradient estimation is enough to simulate turbulent flames at moderate Reynolds number, which demonstrates the suitability of REDIM as reduced kinetic model in reactive flows. [ABSTRACT FROM AUTHOR]

Aims: The aim of this study was analyze drought characteristics for 9 districts of Muğla that have long-term precipitation data. To identify drought characteristics such as the number of drought periods and drought durations, and generating maps for visually demonstrating districts where drought is more effective. Methods and Results: Monthly precipitation data from 1968 to 2011 have been transferred to ReDIM software. SPI values for each station were calculated for 12-month SPI. Some of the results obtained were mapped using Geographical Information Systems (GIS). According to the results obtained for the 12-month SPI analysis under the "SPI <-1" drought period, the maximum number of dry periods with a 1-month period was observed in Fethiye 10 times, Koycegiz 9 times and Dalaman 7 times. The number of dry periods in other stations was between 2 and 5 times. The longest drought period (26 months) was observed in Milas, 24 months in Yatagan and 22 months in Bodrum and Mugla stations. Milas, Yatagan and Bodrum have to be care more for future hydrological drought conditions. Conclusions: According to the results of analysis 30 years monthly precipitation data. It has been determined that the frequency of drought has increased and the number of drought months has increased gradually. Therefore; more attention should be paid to the effective use of water resources in this area. Significance and Impact of the Study: Determination of the current situation related to drought periods and durations in Muğla according to the monthly precipitation data of the last 30 years. The areas affected by drought were identified. It was suggested to take necessary protection measures against drought in these areas. [ABSTRACT FROM AUTHOR]

Abstract Numerical simulation of turbulent reacting flow is still a challenging task. For the efficient computational simulation and applicability for technical systems, simplifications for both chemistry and turbulence are needed. However, both simplifications are typically treated separately, without considering the coupling between them. In manifold based simplified chemical models, it is assumed that the full thermokinetic state is restricted to slow manifolds, while the turbulent mixing processes pull the states off the manifold. We derive a strategy based on the Global Quasi-linearization (GQL) that allows an efficient coupling of manifold based reduction methods with mixing models in transported Probability Density Function (PDF) models for turbulent reacting flows. The GQL approach identifies a suitable choice of the reaction progress variables which allows a direct application of the mixing models on the reduced variables without having to perform mixing in the full state space and back relaxation to the manifold. To test the validity of the reduced variable, it has been applied for PDF-modeling of a turbulent flame. For the turbulent flame with strong turbulence-reaction interaction, the local-extinction and re-ignition can be captured very well. [ABSTRACT FROM AUTHOR]

In this paper, the quenching of a laminar premixed flame at a cold inert wall is investigated. Transient system behavior of the quenching flame is studied both by using well known and widely used reaction mechanisms. Reduced models are developed for each particular mechanism. The different detailed mechanisms are applied and reduced by implementing a manifold-based approach - the REDIM method. The flame quenching is studied by using numerical simulations and by comparing different reaction mechanisms as well as different transport models and their corresponding reduced models. It is demonstrated that the results obtained by the detailed and reduced mechanisms differs much less than the results for different detailed mechanisms. This confirms the quality of the reduced model and verifies the reduced method developed by the REDIM approach. [ABSTRACT FROM AUTHOR]

Abstract The problem of a reduced model formulation for combustion processes is discussed in the present study. For this purpose, different reduced model equations are proposed and applied for the transient regime of a head-on quenching flame. The so-called Reaction-Diffusion manifolds (REDIM) with different reduced model equations are used as an example. The strategies can, however, be applied to other manifold models, too. The results of the computations with detailed kinetics are compared to the results of computations with reduced kinetics. It is shown, that the very common reduced model equation in physical variables with a constant parametrization matrix leads to an error. The reduced model equation in generalized coordinates and an alternative reduced model equation in physical variables presented in this work reproduce the system behavior as expected. Moreover, the differences between the two different reduced model equations in physical variables are discussed. [ABSTRACT FROM AUTHOR]

Turbulent stratified combustion is often found in practical combustion devices, however, for large eddy simulations (LES) of it is still a challenge. In the present work, LES of the Darmstadt turbulent stratified flame (TSF) cases are conducted. In total, one isothermal flow case A-i2 and four reacting cases with different combinations of stratification and shear, i.e., A-r, C-r, E-r, G-r cases, are simulated. The employed sub-grid scale (SGS) combustion model is the REDIM-PFDF model, in which the chemical kinetics is reduced into a two-dimensional chemistry look-up table by the reaction-diffusion manifolds (REDIM) method, which performs a model reduction based on the coupling of the chemical kinetics with molecular transport. The fluctuation of scalars within the LES filter volume is modeled by the presumed filtered density function (PFDF). The overall good agreement of the statistics of velocity, temperature and species with the experimental data demonstrates the capability of the REDIM-PFDF model for TSF. Additionally, the probability distributions of the alignment angle, α, between the reaction layer and mixing layer, are analyzed in detail. It is shown that the probability distributions of the alignment angel vary with the axial distance from the jet nozzle. It also reveals that, with a stronger turbulence, the stratification effect can be weakened and the probability difference for finding ‘back-supported’ and ‘front-supported’ flame modes tends to decrease. [ABSTRACT FROM AUTHOR]

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In the current paper the so-called REaction–DIffusion Manifold (REDIM) method of model reduction is discussed within the framework of standard singular perturbation theory. According to the REDIM a reduced model for the system describing a reacting flow (accounting for chemical reaction, advection and molecular diffusion) is represented by a low-dimensional manifold, which is embedded in the system state space and approximates the evolution of the system solution profiles in space and in time. This pure geometric construction is reviewed by using Singular Perturbed System (SPS) theory as the only possibility to formalize, to justify and to verify the suggested methodology. The REDIM is studied as a correction by the diffusion of the slow invariant manifold defined for a pure homogeneous system. A main result of the study is an estimation of this correction to the slow invariant manifold. A benchmark model of Michaelis-Menten is extended to the system with the standard diffusion described by the Laplacian and used as an illustration and for validation of analytic results. Let us remark that the Michaelis-Mentens model is not explicit SPS. We use so-called Global Quasi-Linearization (GQL) method to find a linear change of variable that rearranges the Michaelis–Mentens model as an explicit SPS. [ABSTRACT FROM AUTHOR]

Chemistry pre-tabulation is well suited to include information of detailed reaction kinetics at reasonable computational costs to allow for simulations of realistic devices. In order to evaluate its accuracy in the near wall region, a study with numerical simulations of flame–wall-interaction is performed in this work. A laminar side-wall-quenching scenario is considered to judge on the prediction of the global flame behavior as well as on local species formation of practical relevance. The configuration considered represents a subsection of a side-wall-quenching burner introduced recently with the purpose of numerical validation in mind. The measured temperature and carbon-monoxide concentration are used to identify deficiencies of the tabulated chemistry approach. Furthermore, detailed chemistry simulations are carried out to identify the root cause for those deficiencies. The corresponding analysis is based on the transformation of the species transport equation into the composition space where the physical significance of the scalar dissipation rates provides clear indications regarding the pre-tabulation assumptions. The evaluation of individual terms allows to quantify the interaction of flamelets in the near-wall region where diffusive fluxes cause a departure from the presumed manifold. Based on this analysis, improvements are then suggested. First, as a proof of concept, the direct tabulation of the thermo-chemical states obtained by the detailed chemistry simulation is applied to evaluate whether the reduction to controlling variables is in general possible in such a physical scenario. Second, as an alternative way of pre-tabulating, the reaction-diffusion-manifold (REDIM) approach is then adopted. By building the REDIM based on a gradient estimate from a computationally inexpensive transient one-dimensional flame–wall-interaction simulation it is possible to obtain realistic dissipation rates without a-priory knowledge. By this approximation a significant gain in prediction is achieved when compared to the original tabulation. [ABSTRACT FROM AUTHOR]

In this work, the Reaction-Diffusion-Manifold (REDIM) is applied for Flame-Wall-Interactions with heterogeneous wall reactions. There are two major issues that have to be considered: A reduced description that text captures transient regimes like flame quenching has to be generated, and the boundary condition for the reduced system that accounts for heterogeneous wall reactions has to be specified. Since the extinction at the wall is governed by at least two processes (chemical reactions and heat loss to the wall), a two-dimensional manifold is chosen for the reduced description to construct a REDIM which can handle heat loss and extinction. For solving the issue of the boundary conditions, two different types of boundaries have to be defined. The boundary condition for the wall is specified via a gradient estimate which is given via the surface reaction rate. For those boundaries, which are not defined as boundaries in physical space, the gradient guess is projected onto the tangential space of the manifold’s boundary. Before solving the REDIM evolution equation, a spatial gradient estimate and an initial guess for the manifold have to be defined. Both are obtained from detailed sample solutions of the transient system, which were performed with the in-house program INSFLA. Afterwards, the REDIM evolution equation is integrated to the stationary state and the necessary data for subsequent simulations are stored in REDIM-tables. The problem of a head-on flame quenching at a cold wall is studied for premixed methane-air-flames at different pressures. In order to validate the reduced model, the generated REDIM-tables are used for computations with the same model configuration than the detailed computation, and species like CO are investigated as a function of the temperature T for different positions near the wall (such an investigation for experimental results was also carried out in Mann et al. for the pressure of 1 bar and the mass fraction of CO Mann et al., 2014). The reduced model reproduces the behavior of the extinction very well and both the detailed as well as the reduced simulations show a good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

A numerical investigation is carried out to study ignition events of different premixed stoichiometric fuel/air mixtures by hot exhaust gas jets. The simulations are performed for premixed, stoichiometric hydrogen/air, ethylene/ air and propane/air mixtures in configurations relevant to safety applications. The ignition events of the different fuel/air mixtures by their corresponding exhaust gas jet are examined qualitatively analyzing processes and conditions leading to ignition. A stand-alone probability density function (PDF) method in connection with a projection method (PM) to calculate the mean pressure is used to model the turbulent flow. The transport equation for the joint velocity - turbulent frequency - scalar PDF is solved by a Monto Carlo/particle method. In order to reduce the computational costs concerning the chemical kinetics the reaction diffusion manifolds (REDIM) technique is used to get an appropriate reduced kinetic scheme. [ABSTRACT FROM AUTHOR]

In this work, we present a reduced model for treating chemical reactions in combustion simulations, with special attention on combustion in IC engines. The model which is based on low-dimensional manifolds in state space, is able to describe auto-ignition, burning in quasi homogeneous media as well as chemical reactions which are strongly coupled with molecular transport, like, e.g., in flame propagation. A coupling scheme is developed for existing concepts for reduced treatment of combustion, namely a progress variable model (PVM) and the reaction-diffusion manifold approach (REDIM). We discuss a simple, robust method for this coupling, based on an additional variable, namely the normalized strength of molecular transport. The implementation and behavior of the resulting coupled model are shown. To demonstrate the performance of the model, numerical simulations of representative combustion scenarios are performed, both with fully detailed calculations and with the reduced model. The comparison of results obtained with detailed and reduced computation shows that the strongly reduced model, which requires only five independent variables in total, still can accurately predict a wide range of combustion-relevant scenarios. [ABSTRACT FROM AUTHOR]

The focus of this study is the development of a robust and accurate algorithm for model reduction of chemical kinetics for near wall reacting flows. The so-called Reaction-Diffusion Manifold (REDIM) method is employed for this purpose. The problem statement represents a fundamental difficulty for manifolds based model reduction concepts, since it is necessary to account for flame-wall interactions that perturb the system states by heat loss and catalytic reactions. Omitting the latter still leaves the task to find a reduced description, that is valid not only for flames experiencing heat loss in a stationary burning regime, but also in a transient regime, where flame quenching occurs. It is shown that the REDIM method is capable to account for these processes. The application of the approach is illustrated by the methane/air combustion system in a simple geometry with a cold inert wall, but with a detailed chemical reaction mechanism. [ABSTRACT FROM AUTHOR]

The manifolds based model reduction strategy has become a key approach in detailed modelling and simulations of reacting flows. The methodology has very important advantages over other reduction strategies, namely, a very low dimensionality of the resulting reduced model and a high accuracy of the results. In the present study the problem of model reduction of premixed combustion systems is discussed. The method of Reaction–Diffusion Manifolds (REDIM) is further developed to handle generically high dimensional reduced models. Three main problems of manifold based model reduction strategies were in the focus of the study: the generation of manifolds of arbitrary dimension, the definition of the manifold domain for the specific problem and the independence of a priori information from detailed calculations. Hierarchical structure of the manifold with respect to dimensionality together with a natural geometrical observation that the manifold should degenerate on its boundary allow us to overcome the first two problems for this type of model reduction. A simple but meaningful example of a syngas/air system is used to illustrate the insensitivity of the reduced model with respect to detailed system information, i.e., detailed system gradients. To validate the reduced model the relaxation process of perturbed flame profiles is investigated. The results of comparison of the reduced and detailed transient solutions show a great potential for the suggested methodology to handle the premixed combustion systems. [ABSTRACT FROM AUTHOR]

The Reaction Diffusion Manifold (REDIM) method requires specifying an estimate of the system’s gradients as an input to characterize the molecular transport effects. So far, applications used a gradient estimate taken from simple combustion scenarios, like one-dimensional flame simulations. However, because the reduced model is typically used in turbulent combustion simulations, gradient estimates from a representative turbulent combustion scenario appear more appropriate. In this work, we study how gradients from Direct Numerical Simulations (DNS) of a turbulent flame can be incorporated into the REDIM method. A method for analyzing scalar gradients from a DNS simulation, and for representing them in a form that is usable in the REDIM method, is presented and applied. The analysis reveals a hierarchical structure in the local gradient directions of different scalars, which enables construction of gradient estimates on different levels of complexity (and fidelity). It is shown how these different levels appear in the dissipation terms of the REDIM equation. The influence of varying the detail of the DNS-based gradient estimate is studied, and it is found that the addition of the more complex levels has minor influence only on the REDIM. It can have an influence, however, onto the dynamics of the combustion system on the REDIM, i.e., onto the trajectory that the system takes on the REDIM. [ABSTRACT FROM AUTHOR]

Nowadays the mathematical description of chemically reacting flows uses very often reaction mechanisms with far above hundred or even thousand chemical species (and, therefore, a large number of partial differential equations must be solved), which possibly react within more than a thousand of elementary reactions. These chemical kinetic processes cover time scales from nanoseconds to seconds. An analogous scaling problem arises for the length scales. Due to these scaling problems the detailed simulation of three-dimensional turbulent flows in practical systems is beyond the capacity of even today's super-computers. Using simplified sub-models is a way out of this problem. The question arising in mathematical modeling of reacting flows is then: How detailed, or down to which scale has each process to be resolved (chemical reaction, chemistry-turbulence-interaction, molecular transport processes) in order to allow a reliable description of the entire process. Both the chemical source term and the transport term have one important property, namely, they cause the existence of low-dimensional attractors in composition space. When these manifolds can be constructed (described) and parametrized by a small number of variables, it can be used to reformulate and reduce the mathematical description for modeling reacting flows. In this work the hierarchical nature of these low-dimensional manifolds of slow motions is discussed. It is demonstrated how this important feature of reacting flows is accounted for by the standard model reduction methods (like e.g. PEA and QSSA methods) as well as by recently developed concepts of model reduction. The use of the hierarchical nature for identification of the low-dimensional manifolds to devise hierarchical modeling concepts (e.g. for turbulent reacting flows) is additionally discussed. [ABSTRACT FROM AUTHOR]

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. • Reduced kinetics including differential diffusion and strong heat loss is proposed. • A combined experimental-numerical study for a laminar dimethyl ether–air SWQ flame. • Two different reduced kinetic models are formulated and assessed. [ABSTRACT FROM AUTHOR]

Understanding the ignition of combustible mixtures by hot jets of burnt gases plays an important role in explosion protection. In this work a PDF method in conjunction with a reaction–diffusion manifold (REDIM) is used to investigate the ignition of a hydrogen/air mixture by a hot turbulent jet. In accordance with experimental results it is observed in numerical investigations that after an ignition delay time, the ignition is typically initiated at the jet head vortex. The scope of the current work is to investigate the mechanisms leading to ignition and explain the processes governing the ignition delay time as well as the ignition location. It is shown that macro- as well as micromixing and the chemical kinetics have a profound influence on the ignition process and that a realistic model for the ignition process has to account for all these processes in combination with a transient description of the jet penetration. [ABSTRACT FROM AUTHOR]

A numerical investigation is carried out to study the ignition of a hydrogen/air mixture by a hot turbulent jet. A stand-alone probability density function method is used to model the turbulent reacting flow. In order to reduce the computational cost of chemical reactions, a reaction diffusion manifold technique is applied for an automatic mechanism reduction. The ignition delay time and the ignition length are investigated with respect to various inlet temperatures as well as the nozzle diameter and the jet inlet velocity. The simulation results reveal that immediately after a discharge of the hot exhaust gas from the nozzle, the hot gas cools down due to the strong turbulent mixing with the cold ambient mixture. However, further downstream where the turbulent mixing intensity is reduced, the heat release due to chemical reactions overcomes the heat dissipation, which eventually leads to ignition. [ABSTRACT FROM PUBLISHER]

In the present study the reaction-diffusion manifolds (REDIM) method for model reduction is applied to detect extinction strain rates of highly diluted hydrogen/nitrogen and air counter-flow diffusion non-premixed flames at different ambient pressures. The considered problem inhibits miscellaneous challenges for modeling of reactive flows and is therefore well suited for testing the REDIM reduction method. First of all, by assigning critical strain rates the model’s ability to capture transient system behavior is investigated. Moreover, critical system regimes of extinction are strongly influenced by the pressure dependence of chain branching and termination mechanisms. This leads to a nonmonotonic dependence between system pressure and extinction limits. The aim of the present work is to find out to what extent the REDIM method is capable to reproduce these complex chemical chain branching and termination channels. Furthermore, in highly diluted hydrogen counter-flow diffusion flames the fast molecular transport of radicals into the reaction zone is strongly affecting the flame stability. Consequently, detailed transport models must be considered in this critical case, which represents an additional task for the reduced model. In the present work, results of reduced simulations based on the REDIM method are compared with detailed calculations and experimental data to show the ability of the REDIM model reduction method to account for such critical regimes of nonstationary combustion processes and to reproduce the nonmonotonic function of critical strain rate dependent on the system pressure in the case of a detailed transport model. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, lean premixed flames featuring local extinction are simulated numerically by Large Eddy Simulations (LES) and investigated experimentally by one-dimensional, spatially resolved Raman scattering. Two unconfined piloted lean premixed natural gas/air flames with equivalence ratios ϕ =0.71 and 0.65 are studied. The Reaction–Diffusion Manifold (REDIM) technique is employed together with the presumed joint Filtered Density Function (FDF) to carry out the LES. In the present work, two reduced coordinates, the CO2 and N2 mass fractions, are considered in the REDIM look-up table, and the joint FDF of them is modelled in terms of two statistically independent FDFs. Good overall agreement between the experimental data and the LES results is obtained. Scatter plots from measurements and instantaneous data from LES show states with local extinction, mainly in the leaner flame. The results demonstrate the capability of the proposed REDIM-presumed joint FDF method to deal with the phenomenon of local extinction in lean premixed flames. [Copyright &y& Elsevier]

Abstract: The efficient simulation of technical combustion processes requires a reduced description of the thermochemical state. Especially in the case of turbulent combustion, appropriate reduction methods are required to save computational costs, while preserving a desired accuracy. The current work deals with the application of the so-called reaction-diffusion manifold (REDIM) method. It is used to identify a two-dimensional manifold in the composition space, describing the thermochemical states of an unconfined, lean premixed, piloted, turbulent methane/air flame. This stratified flame is an interesting case, because it coveres different flamelet regimes, namly premixed flamelets and premixed flamelets mixing with air, which complicates the application of flamelet methods. Although the REDIM method is not restricted to a specific flamelet regime, previous works dealt either with premixed or diffusion flames. Thus in the current work, the application of the REDIM method is extended to an intermediate flamelet regime. The application of the method is demonstrated step by step, which includes the detailed description of determining an initial manifold and of estimating gradients. Eventually a two-dimensional manifold for a physically motivated gradient estimation is presented and analyzed by a comparison to detailed flamelet trajectories. The discussion shows, that the manifold accounts for important premixed and diffusion scenarios of the turbulent flame. Therefore the REDIM can be used in subsequent CFD simulations, which is not part of the current work. [Copyright &y& Elsevier]

Abstract: In the present work non-stationary behavior of the counter-flow diffusion flame is examined in the context of the recently developed approach of model reduction called REaction–DIffusion Manifolds (REDIM) method. It is a natural extension of the ILDM approach which takes into account both the chemical reaction and the diffusion processes. It has been developed to treat both premixed and non-premixed regimes of combustion. In this work we investigate the ability of the concept to describe transient processes of extinction and re-ignition. A very simple flame configuration and transport model are considered in this current study for the sake of transparency because the main focus is on the transient and non-stationary behavior of flames. H2/O2/N2 combustion system is considered in a non-premixed counter-flow diffusion 1D flame configuration. This study shows how the REDIM concept performs in the transient regimes; it interprets the effect of local extinction and reigniting phenomena using detailed and reduced models. It shows how the unstable/transient behavior of a detailed system can be successfully accounted with the help of the REDIM based reduced model. [Copyright &y& Elsevier]

Abstract: The modeling of a reacting swirling flow behind a bluff-body burner (SM1) in the framework of RANS and transported scalar PDF is presented. The EMST mixing model is applied and the composition space is reduced to mixture fraction (Z) and a progress variable (CO2 mass fraction, ) by means of a Reaction Diffusion Manifold (REDIM). With an ad hoc adjustment of the turbulent Schmidt number, the mean flow and mixing fields obtained are comparable to LES results from the literature. The REDIM reduction of the composition space to is discussed and its validity for the present swirling flame is first considered by an a priori comparison with experimental data. The – scatter plots from the transported PDF calculation show the capacity to reproduce the mixing between fresh air and hot products in the recirculation zone above the bluff-body. However, too little scatter is observed. The study of tracer trajectories helps to better understand the capacities and limitations of the modeling approach. Zones where mixing competes with reaction can be identified, and coincide with the highly rotating collar region where local extinction is expected to take place. However, in our modeling, the competition between mixing and reaction is not enough to lead to local extinction. An important modeling deficiency is claimed to be the use of a mean time scale in the EMST mixing model, which limits the possibilities to model high scalar dissipation rate events. [Copyright &y& Elsevier]

Abstract: Chemically reacting flows are governed by a strong interaction of chemical kinetics with molecular transport properties. Therefore, reduced models for such systems have to take into account both the chemical reaction and the diffusion processes, in particular if detailed transport models are used which account for effects of differential as well as for thermal diffusion. In order to deal with this problem the recently developed reduction method, the so-called reaction–diffusion manifolds (REDIM) method that accounts for the transport properties and their influence onto a reduced system’s state space is extended to handle effects of detailed transport models. The syngas/air combustion system, as a transparent example where non-equal diffusivities play an important role, is considered for both premixed and non-premixed 1D flame configurations. 1D and 2D reduced models are compared to detailed system solutions and validate the approach. [ABSTRACT FROM AUTHOR]