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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]

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]

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]

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]

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]

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]

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]

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: 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]