A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

计算奇异摄动法在燃烧反应系统简化中的应用

采用计算奇异摄动法构造典型燃烧反应系统的简化化学动力模型,基于燃烧反应控制方程寻找理想基向量,借助所得理想基向量实现快慢反应模态间的解耦,并给出参与性指数、原子团指针和重要性指数等关键参数,进而构造快模态状态方程和简化化学动力模型.典型CO-CH₄-Air混合燃烧反应系统的计算结果表明,由计算奇异摄动法得到的简化燃烧反应系统是原燃烧反应系统很好的近似.     

Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of “minimal relaxation” of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.     

Simple global reduction technique based on decomposition approach

Large and complex (nonlinear) models of chemical kinetics are one of the major obstacles in simulations of reacting flows. In the present work a new approach for an automatic reduction of chemical kinetics models, the so-called Global Quasi-Linearization (GQL) method is presented. The method is similar to the ILDM and CSP approaches in the sense that it is based on a decomposition into fast/slow motions and on slow invariant manifolds, but has a global character which allows us to overcome difficulties with the application of slow invariant manifolds and significantly simplifies the construction procedure for approximation of the slow invariant system manifold. The method is implemented within the standard ILDM method and applied to a number of model examples and to a meaningful combustion chemistry model.     

Tabulated chemistry approaches for laminar flames: Evaluation of flame-prolongation of ILDM and flamelet methods

The present study considers the performance of tabulation methods for numerical simulation of complex chemical kinetics in laminar combusting flows and compares their predictions to results obtained by direct calculation. Two tabulation methods are considered: the Flame Prolongation of Intrinsic low-dimensional manifold (FPI) method and Steady Laminar Flamelet Model (SLFM). The FPI method is of current interest as it is a potentially unifying approach capable of dealing with both premixed and non-premixed flames for gaseous fuels. SLFM tabulation methods are popular for non-premixed flames and form a good basis for comparing the performance of the FPI approach. The performance of each method is also evaluated by comparing the results to the direct simulation of the laminar flames using two chemical kinetic schemes: simplified chemistry involving five species and one reaction and detailed chemistry involving 53 species and 325 reaction steps. As part of the evaluation process, the computational cost of each method is also assessed. The laminar flames considered in this study include: freely propagating laminar premixed flames, a two-dimensional axisymmetric methane–air opposed-jet diffusion flame, and a two-dimensional axisymmetric methane–air co-flow diffusion flame. Both tabulation methods are implemented in a parallel adaptive mesh refinement (AMR) framework for solving the complete set of governing partial differential equations. These equations are solved using a fully-coupled finite-volume formulation on body-fitted multi-block quadrilateral mesh. Significant improvements in terms of reduced computational requirements, as measured by both storage and processing time, are demonstrated for the tabulated methods.     

Acceleration of chemistry computations in two-dimensional detonation induced by shock focusing using reduced ISAT

A reduced in situ adaptive tabulation (RISAT) method, which was originally proposed by Pope (Combustion Theory and Modelling, 1997, 1, 41–36), is developed for the applications of multidimensional transient reactive flow computations. The RISAT method, which based on the storage/retrieval operation processes of data, employs the constant approximation of chemical reactions and the dynamic deletion of a data table to limit the table size during the computations. It is incorporated in the computations of two-dimensional detonation of CH₄/O₂ premixed gas induced by shock waves focusing to enhance the computational performance of combustion chemistry. The effects of query tolerance and table size on the computational efficiency are examined. A maximum chemical speedup factor of 17.88 can be obtained by using the RISAT, without losing the computational accuracy. It is concluded from the computational results that the RISAT method is strongly dependent on the table size, tolerance and physics of transient reactive flow problems.     

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.     

A multi-zone chemistry mapping approach for direct numerical simulation of auto-ignition and flame propagation in a constant volume enclosure

A direct numerical simulation (DNS) coupling with multi-zone chemistry mapping (MZCM) is presented to simulate flame propagation and auto-ignition in premixed fuel/air mixtures. In the MZCM approach, the physical domain is mapped into a low-dimensional phase domain with a few thermodynamic variables as the independent variables. The approach is based on the fractional step method, in which the flow and transport are solved in the flow time steps whereas the integration of the chemical reaction rates and heat release rate is performed in much finer time steps to accommodate the small time scales in the chemical reactions. It is shown that for premixed mixtures, two independent variables can be sufficient to construct the phase space to achieve a satisfactory mapping. The two variables can be the temperature of the mixture and the specific element mass ratio of H atom for fuels containing hydrogen atoms. An aliasing error in the MZCM is investigated. It is shown that if the element mass ratio is based on the element involved in the most diffusive molecules, the aliasing error of the model can approach zero when the grid in the phase space is refined. The results of DNS coupled with MZCM (DNS-MZCM) are compared with full DNS that integrates the chemical reaction rates and heat release rate directly in physical space. Application of the MZCM to different mixtures of fuel and air is presented to demonstrate the performance of the method for combustion processes with different complexity in the chemical kinetics, transport and flame–turbulence interaction. Good agreement between the results from DNS and DNS-MZCM is obtained for different fuel/air mixtures, including H₂/air, CO/H₂/air and methane/air, while the computational time is reduced by nearly 70%. It is shown that the MZCM model can properly address important phenomena such as differential diffusion, local extinction and re-ignition in premixed combustion.     

Analysis of methane–air edge flame structure

We study the structure of a methane–air edge flame stabilized against an incoming mixing layer. The flame is computed using detailed chemical kinetics, and the analysis is based on computational singular perturbation theory. We focus on examination of the dynamical fast/slow structure of the flame, exploring the distribution of time-scales, the composition of the related specific modes and the effective low-dimensional structure. We also study the importance of chemical/transport processes for both major species and radicals in the flame, analyzing the information available from slow/fast importance indices as compared to reaction flux analysis. Results provide enhanced understanding of the flame, outlining the role of different chemical and transport processes in its observed structure.     

Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane–air and iso-octane–air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.     

Multidimensional chemistry coordinate mapping approach for combustion modelling with finite-rate chemistry

A multidimensional chemistry coordinate mapping (CCM) approach is presented for efficient integration of chemical kinetics in numerical simulations of turbulent reactive flows. In CCM the flow transport is integrated in the computational cells in physical space, whereas the integration chemical reactions are carried out in a phase space made up of a few principal variables. Each cell in the phase space corresponds to several computational cells in the physical space, resulting in a speedup of the numerical integration. In reactive flows with small hydrocarbon fuels two principal variables have been shown to be satisfactory to construct the phase space. The two principal variables are the temperature (T) and the specific element mass ratio of the H atom (J _H). A third principal variable, σ=?J _H·?J _H, which is related to the dissipation rate of J _H, is required to construct the phase space for combustion processes with an initially non-premixed mixture. For complex higher hydrocarbon fuels, e.g. n-heptane, care has to be taken in selecting the phase space in order to model the low-temperature chemistry and ignition process. In this article, a multidimensional CCM algorithm is described for a systematic selection of the principal variables. The method is evaluated by simulating a laminar partially remixed pre-vaporised n-heptane jet ignition process. The CCM approach is then extended to simulate n-heptane spray combustion by coupling the CCM and Reynolds averaged Navier–Stokes (RANS) code. It is shown that the computational time for the integration of chemical reactions can be reduced to only 3–7%, while the result from the CCM method is identical to that of direct integration of the chemistry in the computational cells.     

Quantitative Radar REMPI measurements of methyl radicals in flames at atmospheric pressure

Spatially resolved quantitative measurements of methyl radicals (CH₃) in CH₄/air flames at atmospheric pressure have been achieved using coherent microwave Rayleigh scattering from Resonance enhanced multi-photon ionization, Radar REMPI. Relative direct measurements of the methyl radicals were conducted by Radar REMPI via the two-photon resonance of the $ 3p^{2} A_{2}^{\prime \prime } 0_{0}^{0} $ state and subsequent one-photon ionization. Due to the proximity of the argon resonance state of 2s ²2p ⁵4f [7/2, J = 4](4+1 REMPI by 332.5 nm) with the CH₃ state of $ 3p^{2} A_{2}^{\prime \prime } 0_{0}^{0} $ (2+1 REMPI by 333.6 nm), in situ calibration with argon was performed to quantify the absolute concentration of CH₃. The REMPI cross sections of CH₃ and argon were calculated based on time-dependent quantum perturbation theory. The measured CH₃ concentration in CH₄/air flames was in good agreement with numerical simulations performed using detailed chemical kinetics. The Radar REMPI method has shown great flexibility for spatial scanning, large signal-to-noise ratio for measurements at atmospheric pressures, and significant potential to be straightforwardly generalized for the quantitative measurements of other radicals and intermediate species in practical and relevant combustion environments.     

Strain rate and fuel composition dependence of chemiluminescent species profiles in non-premixed counterflow flames: comparison with model results

A detailed comparison has been conducted between chemiluminescence (CL) species profiles of OH^?, CH^?, and C₂ ^?, obtained experimentally and from detailed flame kinetics modeling, respectively, of atmospheric pressure non-premixed flames formed in the forward stagnation region of a fuel flow ejected from a porous cylinder and an air counterflow. Both pure methane and mixtures of methane with hydrogen (between 10 and 30 % by volume) were used as fuels. By varying the air-flow velocities methane flames were operated at strain rates between 100 and 350 s^?1, while for methane/hydrogen flames the strain rate was fixed at 200 s^?1. Spatial profiles perpendicular to the flame front were extracted from spectrograms recorded with a spectrometer/CCD camera system and evaluating each spectral band individually. Flame kinetics modeling was accomplished with an in-house chemical mechanism including C₁–C₄ chemistry, as well as elementary steps for the formation, removal, and electronic quenching of all measured active species. In the CH₄/air flames, experiments and model results agree with respect to trends in profile peak intensity and position. For the CH₄/H₂/air flames, with increasing H₂ content in the fuel the experimental CL peak intensities decrease slightly and their peak positions shift towards the fuel side, while for the model the drop in mole fraction is much stronger and the peak positions move closer to the fuel side. For both fuel compositions the modeled profiles peak closer to the fuel side than in the experiments. The discrepancies can only partly be attributed to the limited attainable spatial resolution but may also necessitate revised reaction mechanisms for predicting CL species in this type of flame.     

H2/air autoignition: The nature and interaction of the developing explosive modes

Appropriate algorithmic tools are employed for the analysis of the explosive modes developing during the autoignition of homogeneous mixtures. The ability of these tools to provide significant physical understanding is demonstrated in the case of the homogeneous ignition of a stoichiometric H₂/air mixture, modelled by two different chemical kinetics mechanisms. It is shown that the ignition process evolves in two stages. The first stage is characterised by the development of two explosive timescales (one fast and one slow), that lead the system away from equilibrium. As the end of the first stage is approached, the two explosive timescales converge, they merge and then they disappear. In the second stage only dissipative timescales develop, which drive the system all the way to equilibrium. It is shown that throughout the first stage the fast explosive timescale is generated by chain reactions. The slow explosive timescale is initially generated by an initiation reaction that produces the radicals required for the start-up of the fast mode, while later on it is generated by reactions that are responsible for the heat released. These findings are validated with sensitivity analysis results for the ignition delay time and are employed in order to clarify the discrepancies in the solution provided by the two different chemical kinetics mechanisms considered.     

The kinetics of the gas-phase reaction between methanol and boron trichloride

Using a spectroscopic complex designed for studying the kinetics of chemical reactions, the rate constant for the gas-phase reaction between a Lewis base and a Lewis acid—CH₃OH + BCl₃ → CH₃OBCl₂ + HCl—at at room temperature and pressures of 1.5–27.9 Torr has been derived for the first time. The complex comprises a reactor embedded in the optical system of a commercial AF-3 Fourier transform IR spectrometer capable of recording the spectra of reactants during the process. The reaction mechanism has been analyzed.     

Theoretical study of the Ru + CH3F reaction

CASSCF-MRMP2 calculations have been performed to analyse the reaction of fluoromethane with a bare ruthenium atom. Potential energy curves emerging from the ground state and the first excited state of the reactants, Ru(⁵F, ³F;d⁷s¹) + CH₃F, were calculated for representative electronic states associated with different approaching modes of the fragments. Whereas no favourable channels correlating with the ground state asymptote were detected for the insertion of the ruthenium atom into the C–H bond of the methyl fluoride molecule, the oxidative addition of the C–F bond of this molecule to the metal atom along the reaction path evolving from the ground state of the fragments leads to the stable inserted product CH₃–Ru–F. Although forming less stable products, insertion of ruthenium into the C–H and C–F bonds of the fluorocarbon molecule can occur through electronic states which emerge from the excited triplet state asymptote.     

Low‐temperature Raman spectra of racemate DL‐Alanine crystals

Raman spectra of DL ‐Alanine crystals were investigated in the 50–3200 cm⁻¹ spectral region for temperatures ranging from 15 to 295 K. The crystalline structure of DL ‐Alanine represents a rare example of an amino acid racemate crystallizing in a non‐centrosymmetric space group. From this study, we have observed changes in the wavenumber of modes associated with both rocking of CO₂⁻ and skeletal vibrations. On the other hand, neither changes in the modes associated to CH or CH₃ vibrations nor substantial modifications of the lattice modes of the crystal were observed. Such result indicates slight changes of the CO₂ group orientation without observation of a solid–solid phase transition in the DL ‐Alanine crystal. Copyright © 2009 John Wiley & Sons, Ltd.