Reaction-diffusion Manifold Research Articles

Study of Extinction Limits of Diluted Hydrogen-Air Counter-Flow Diffusion Flames with the Redim Method

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.

Numerical Investigation of Ignition in a Transient Turbulent Jet by Means of a PDF Method

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.

Ignition by transient hot turbulent jets: An investigation of ignition mechanisms by means of a PDF/REDIM method

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.

A Unified Reduced Model for Auto-Ignition and Combustion in Premixed Systems

In this paper, two complementary chemistry model reduction methods for combustion simulations are further developed and combined. A progress variable model (PVM), which follows the idea of trajectory generated manifolds (TGLDM), is tailored for describing auto-ignition in situations where the influence of<br />molecular transport on chemical reaction is weak, like auto-ignition in media with weak scalar gradients. The other model using the reaction diffusion manifold approach (REDIM) is designed for situations where the interaction of chemistry with molecular transport is essential. The formulation of both models is discussed and implementational issues of each single model are given. Also, each model is tested in its respective range of applicability (quasi-homogeneous combustion under steady/unsteady physical boundary conditions for the PVM, combustion in fields with essential scalar gradients for REDIM). The coupling of the two models into a unified model, which covers combustion in both regimes and during the transitions between regimes, is discussed, based on the global quasi-linearization concept (GQL).

Large Eddy Simulation of the PRECCINSTA burner

For the first time the Reaction–Diffusion Manifold (REDIM) technique is implemented together with a presumed Filtered Density Function (FDF) to carry out Large Eddy Simulation (LES) of lean premixed swirling flames in the well-known PRECCINSTA burner. The REDIM approach reduces detailed chemical kinetics based on low-dimensional reaction–diffusion manifolds in composition space, so that many species can be accurately estimated at a relatively low computational cost via a look-up table. In the present work, only one reduced coordinate, the CO2 mass fraction, is considered in the REDIM look-up table. Implementation of the REDIM/FDF model is performed with two presumed FDF shapes, top-hat and clipped Gaussian. Two premixed flames are simulated, with equivalence ratios 0.75 and 0.83, respectively. Velocity, temperature and species concentration profiles are discussed and compared to the experimental data. The results are in good overall agreement with the corresponding experiment. It is also shown that the LES results obtained with the two presumed FDFs are very similar and the reason for this is analysed.

Reaction-diffusion manifolds for unconfined, lean premixed, piloted, turbulent methane/air systems

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.

Large Eddy Simulations and experimental studies of turbulent premixed combustion near extinction

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.

On transient behavior of non-premixed counter-flow diffusion flames within the REDIM based model reduction concept

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.

Transported scalar PDF calculations of a swirling bluff body flame (‘SM1’) with a reaction diffusion manifold

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, YCO2) 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 (Z,YCO2) is discussed and its validity for the present swirling flame is first considered by an a priori comparison with experimental data. The (Z,YCO2) – 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.

Reaction-Diffusion Manifolds and Global Quasi-linearization: Two Complementary Methods for Mechanism Reduction

The paper outlines the current state in the model reduction of systems governing reacting flows by manifold methods. The main idea of such approaches is based on the fact that any reduced model defines a manifold of low dimen- sion imbedded in the system composition/state space. In this respect the decomposition into relatively fast and slow mo- tions due to multiple time scales present in the system is a crucial property of the reacting system. It allows the application of the geometrical framework of slow and fast invariant manifolds to model reduction. Recently developed approaches, namely, the so-called Reaction-Diffusion Manifolds (REDIMs) and Global-Quasi Linearization (GQL) are in the focus of this work. The methods extend and follow the well known ILDM method. The paper discusses both the theoretical basis of the approaches and detailed implementation schemes for studying, reducing and simulating the reacting flows systems. Simple yet containing all features of the reacting flows models of n-heptane/air and syngas/air systems are used to illus- trate and verify the methods.

Implementation of REDIM reduced chemistry to model an axisymmetric laminar diffusion methane–air flame

The goal of this work is to analyze the use of automatically reduced chemistry by the Reaction–Diffusion Manifold (REDIM) method in simulating axisymmetric laminar coflow diffusion flames. Detailed chemical kinetic models are usually computationally prohibitive for simulating complex reacting flows, and therefore reduced models are required. Automatic reduction model approaches usually exploit the natural multi-scale structure of combustion systems. The novel REDIM approach applies the concept of invariant manifolds to treat also the influence of the transport processes on the reduced model, which overcomes a fundamental problem of model reduction in neglecting the coupling of molecular transport with thermochemical processes. We have considered a previously well studied atmospheric pressure nitrogen-diluted methane–air flame as a test case to validate the methodology presented here. First, one-dimensional and two-dimensional REDIMs were computed and tabulated in lookup tables. Then, the full set of governing equations are projected on the REDIM and implemented in the object-oriented C++ Gascoigne code with a new add-on library to deal with the REDIM tables. The projected set of governing equations have been discretized by the Finite Element Method (FEM) and solved by a GMRES iteration preconditioned by a geometric multigrid method. Local grid refinement, adaptive mesh and parallelization are applied to ensure efficiency and precision. The numerical results obtained using the REDIM approach have shown very good agreement with detailed numerical simulations and experimental data.

The extension of the reaction/diffusion manifold concept to systems with detailed transport models

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.

Reaction-Diffusion Manifolds and Global Quasi-linearization: Two Complementary Methods for Mechanism Reduction~!2009-09-09~!2009-11-17~!2010-06-15~!

Reaction-Diffusion Manifolds and Global Quasi-linearization: Two Complementary Methods for Mechanism Reduction~!2009-09-09~!2009-11-17~!2010-06-15~!

Elimination of Fast Modes in the Coupled Process of Chemistry and Diffusion in Turbulent Nonpremixed Flames: An Application of the REDIM Approach

A computational study has been made of bluff-body stabilized turbulent jet flames with strong turbulence-chemistry interaction (Sydney Flames HM1 and HM3). The wide range of scales in the problem is described using a combination of a standard second moment turbulence closure, a joint scalar transported probability density function (PDF) method and the Reaction-Diffusion Manifold (REDIM) technique. The latter provides a reduction of a detailed chemistry mechanism, taking into account effects of laminar diffusion. In an a priori test it is evaluated to what extent the single shot experimental data are located on the reaction-diffusion manifold. Next, computed spatial profiles of mean and variance of independent and dependent scalar variables and profiles of conditional averages and variances (conditional on mixture fraction) are compared to the experimental results. The quality of these predictions is interpreted in relation to the a priori analysis. In general, simulations using the REDIM approach for reduction of detailed C2-chemistry confirm earlier findings for micro-mixing model behavior, obtained with a skeletal Cl-mechanism. Nevertheless it is concluded that the experiments show important features that are not described by the currently used REDIM.

Problem adapted reduced models based on Reaction–Diffusion Manifolds (REDIMs)

In this work a novel modification of the REDIM method is presented. The method follows the main concept of decomposition of time scales. It is based on the assumption of existence of invariant slow manifolds in the thermo-chemical composition space (state space) of a reacting flow. A central point of the current modification is its capability to include both transport and thermo-chemical processes and their coupling into the definition of the reduced model. This feature makes the method more problem oriented, and more accurate in predicting the detailed system dynamics. The manifold of the reduced model is approximated by applying the so-called invariance condition together with repeated integrations of the reduced model in an iterative way. The latter is needed to improve the estimate of gradients of the reduced model parameters (coordinates which define the reduced manifold locally). To verify the approach one-dimensional stationary laminar methane/air and syngas/air flames are investigated. In particular, it is shown that the adaptive REDIM method recovers the full stationary system dynamics governed by detailed chemical kinetics and the molecular transport in the case of a one dimensional reduced model and, therefore, includes the so-called flamelet method as a limiting case.

Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence–chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N 2 and CO 2 mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl’s micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.

The extension of the ILDM concept to reaction–diffusion manifolds

In the present work, the method of simplifying chemical kinetics based on Intrinsic Low-Dimensional Manifolds (ILDMs) is modified to deal with the coupling of reaction and diffusion processes. Several problems of the ILDM method are overcome by a relaxation to an invariant system manifold (Reaction–Diffusion Manifold – REDIM). This relaxation process is governed by a multidimensional parabolic partial differential equation system, where, as an initial solution, an extended ILDM is used. Furthermore, a method for the solution and tabulation of the manifold is proposed in terms of generalized coordinates, with a subsequent procedure for the integration of the reduced system on the found manifold. This modification of the ILDM significantly improves the performance of the concept and allows us to extend its area of applicability. Illustrative comparative calculations of detailed and reduced models of flat laminar flames verify the approach.