Ulrich Maas

Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space

A general procedure for simplifying chemical kinetics is developed, based on the dynamical systems approach. In contrast to conventional reduced mechanisms no information is required concerning which reactions are to be assumed to be in partial equilibrium nor which species are assumed to be in steady state. The only “inputs” to the procedure are the detailed kinetics mechanism and the number of degrees of freedom required in the simplified scheme. (Four degrees of freedom corresponds to a four-step mechanism, etc.) The state properties given by the simplified scheme are automatically determined as functions of the coordinates associated with the degrees of freedom. Results are presented for the CO/H2/air system. These show that the method provides accurate results even in regimes (e.g., at low temperatures) where conventional mechanisms fail.

Ignition processes in hydrogenoxygen mixtures

Abstract Ignition processes in the hydrogenoxygen system were simulated by solving the corresponding conservation equations (i.e., conservation of mass, energy, momentum, and species mass) for one-dimensional geometries using a detailed reaction mechanism and a multispecies transport model. An additional source term in the energy conservation allowed the treatment of induced ignition, and a realistic model for the destruction of reactive species at the vessel surface was used to treat auto-ignitions in static reactors. Spatial discretization using finite differences and an adaptive grid point system led to a differential-algebraic equation system, which was solved numerically by extrapolation or by backward differencing codes. Comparisons with experimental works show that one common reaction mechanism is able to simulate shock-tube-induced ignitions (modeled by treating the reaction system as a homogeneous mixture heated up by the shock wave) as well as the three explosion limits of the hydrogenoxygen system. Minimum ignition energies are calculated for various mixture compositions, pressures, radii of the external energy source, and ignition times, and it is shown that for long ignition times the “uniform pressure assumption” is a quite good approximation for computing minimum ignition energies.

Implementation of simplified chemical kinetics based on intrinsic low-dimensional manifolds

A general procedure for simplifying chemical kinetics and its use in reacting flow models is developed, which is based on the dynamical systems approach. In contrast to conventional reduced mechanisms no information is required concerning which reactions are to be assumed to be in partial equilibrium nor which species are assumed to be in steady state. Based on a local eigenvector analysis, the method identifies the fast time scales of the chemical reaction systems, which differ typically by orders of magnitude. Assuming that the fastest relaxation processes in chemical reactions proceed infinitely fast (i.e., are in local equilibrium), it is then possible to reduce the state space globally, such that it can be described by means of only a small number of reaction progress variables. The only “inputs” to the procedure are the detailed kinetics mechanism and the number of degrees of freedom required in the simplified scheme. Then the state properties given by the simplified scheme are automatically determined as functions of the coordinates associated with the degrees of freedom. A tabulation procedure allows an efficient use of the results in CFD codes. Furthermore a general procedure for coupling the reduced mechanism with other than chemical processes like flow and molecular transport is discussed. Results are presented for the CO/H2/air system both for a simple homogeneous closed system and a flow reactor.

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.

Laminar flame calculations using simplified chemical kinetics based on intrinsic low-dimensional manifolds

During the last 10 years, a great success has been achieved in the field of detailed mathematical modeling of combustion processes. However, most detailed models are restricted to the simulation of simple one-dimensional laminar flames and the extension of detailed kinetic models to general reacting flows of practical importance (e.g., turbulent flow in internal combustion engines) is computationally prohibitive. Thus, simplified kinetic models have to be used. Recently, we presented a mathematical model, the method of intrinsic low-dimensional manifolds (ILDM), which reduces the chemical kinetics automatically. The only inputs to the procedure are the detailed reaction mechanism and the desired number of degrees of freedom. The reduction of the kinetics is performed using the assumption that the fastest timescales are in local equilibrium and can be decoupled. This paper discusses the implementation of the method in reacting flow calculations. The procedure is developed for general three-dimensional reacting flows, which are governed by the system of conservation equations, and the coupling of the reduced chemical kinetics with molecular transport processes and convection is discussed. Then, the mathematical model is verified by sample calculations of structures of laminar premixed flat flames, which provide a simple, but realistic test case. Examples, which verify the approach, are shown for H 2 −O 2 and syngas-air flames. Even for these simple examples, a considerable speedup of the computations is observed. However, the method can also be used for other fuels and, thus, will allow an efficient treatment of combustion systems of practical importance.

Development of a parallel direct simulation code to investigate reactive flows

Abstract Solving the Navier-Stokes equations with detailed modeling of the transport and reaction terms remains at the present time a very difficult challenge. Direct simulations of two-dimensional reactive flows using accurate models for the chemical reactions generally require days of computing time on todays most powerful serial vector supercomputers. Up to now, realistic three-dimensional simulations remain practically impossible. Working with parallel computers seems to be at the present time the only possible solution to investigate more complicated problems at acceptable costs, however, lack of standards on parallel architectures constitutes a real obstacle. In this paper, we describe the structure of a parallel two-dimensional direct simulation code using detailed transport, thermodynamic and reaction models. Separating the modules controlling the parallel work from the flow solver, it is possible to get a high compatibility degree between parallel computers using distributed memory and message-passing communication. A dynamic load-balancing procedure is implemented in order to optimize the distribution of the load among the different nodes. Efficiencies obtained with this code on many different architectures are given. First examples of application conceding the interaction between vortices and a diffusion flame are shown in order to illustrate the possibilities of the solver.

Monte Carlo PDF modelling of a turbulent natural-gas diffusion flame

A piloted turbulent natural-gas diffusion flame is investigated numerically using a 2D elliptic Monte Carlo algorithm to solve for the joint probability density function (PDF) of velocity and composition. Results from simulations are compared to detailed experimental data: measurements of temperature statistics, data on mean velocity and turbulence characteristics and data on OH. Conserved-scalar/constrained-equilibrium chemistry calculations were performed using three different models for scalar micro-mixing: the interaction by exchange with the mean (IEM) model, a coalescence/dispersion (C/D) model and a mapping closure model. All three models yield good agreement with the experimental data for the mean temperature. Temperature standard deviation and PDF shapes are generally predicted well by the C/D and mapping closure models, whereas the IEM model gives qualitatively incorrect results in parts of the domain. It is concluded that the choice of micro-mixing model can have a strong influence on the quali...

SPARK IGNITION OF TURBULENT METHANE/AIR MIXTURES REVEALED BY TIME-RESOLVED PLANAR LASER-INDUCED FLUORESCENCE AND DIRECT NUMERICAL SIMULATIONS

By use of high-speed planar laser-induced fluorescence (PLIF) imaging, the evolution of turbulent reactive flows was recorded and studied in real time in a filmlike manner. The technique was used to track the concentration field of the OH radical, which was produced during spark ignition of a turbulent methane/air mixture. The results were compared qualitatively to a two-dimensional direct numerical simulation of the same system using a detailed chemical mechanism and a detailed transport model.

Numerical simulation of spark ignition including ionization

A detailed understanding of the processes associated with spark ignition, as a first step during combustion, is of great importance for clean operation of spark ignition engines. In the past 10 years, a growing concern for environmental protection, including low emission of pollutants, has increased the interest in the numerical simulation of igniton phenomena to guarantee sucessful flame kernel development event for lean mixtures. However, the porcess of spark ignition in a combustible mixture is not yet fully undrstood. The use of detailed reaction mechanisms, combined with electrodynamical modeling of the spark, is necessary to optimize spark ignition for lean mixtures. This work presents the simulation of the coupling of flow, chemical reactions, and transport with discharge processes including ionization in order to investigate the development of a stable flame kernel initiated by an electrical park in methane/air mixtures. A transport model taking into account the interactions of charged particles has been incorporated in the flow model. This model is based on the Chapman-Enskog theory with an extension for polyatomic gases and considers resonant charge transfer and ambipolar diffusion for the computation of the transport coefficients. A two-dimensional code to simulate the early stages of flame development, shortly after the breakdown discharge, has been developed. The modeling includes an equation for the electrical field. The spark plasma channel left behind by the breakdown is incorporated into the initial conditions. Due to the fast expansion of the plasma channel, a complicated flowfield develops after the emission of a shock wave by the expanding channed. The second phase, that is, the development of a propagating flame and the flame kernel expansion, can last up to several milliseconds and is dominated by diffusive processes and chemical reactions.

Ignition processes in carbon-monoxide-hydrogen-oxygen mixtures

Ignition processes in the carbon monoxide-hydrogen-oxygen system are simulated by solving the corresponding conservation equations (i.e. conservation of mass, energy, momentum and species mass) for one-dimensional geometries using a detailed reaction mechanism and a multi-species transport model. An additional source term in the energy conservation equation allows the treatment of induced ignition, and a realistic model for the destruction of reactive species at the vessel surface is used to treat auto-ignitions in static reactors. Spatial discretization using finite differences and an adaptive grid point system leads to a differential/algebraic equation system which is solved numerically by extrapolation or backward differencing codes. Minimum ignition energies are calculated for various mixture compositions and radii of the external energy source. Ignition limits are computed, and a sensitivity analysis shows the rate-limiting reactions.