Model Reduction In Chemical Kinetics Research Articles

Chemical kinetic model reduction based on species‐targeted local sensitivity analysis

AbstractReduction of large combustion mechanisms is usually conducted based on the detection and elimination of redundant species and reactions. Reaction elimination methods are mostly based on sensitivity analysis, which can provide insight into the kinetic system, while species elimination methods are more efficient. In this work, the species‐targeted local sensitivity analysis (STLSA) method is proposed to evaluate the importance of species and eliminate non‐crucial species and their related reactions to simplify kinetic models. This paper comprehensively evaluates the effectiveness of STLSA across various combustion scenarios, including high and low‐temperature ignition and laminar flame speed, using diverse mechanisms like USC Mech II, JetSurf 1.0, POLIMI_TOT_1412, NUIGMech1.1 and so on. Comparisons with graph‐based methods, such as DRG and DRGEP, highlight STLSA's superior efficiency and accuracy. Moreover, STLSA is compared to species‐targeted global sensitivity analysis (STGSA), demonstrating significant computation cost savings and comparable model reduction capabilities. The study concludes that STLSA is a robust and versatile tool for mechanism reduction, offering substantial improvements in computational efficiency while maintaining high accuracy in predicting key combustion properties.

Chemical kinetic model reduction through species-targeted global sensitivity analysis (STGSA)

The uncertainty of the rate coefficients of elementary reactions in detailed chemical kinetic mechanisms can affect the predicted species concentrations and global properties. The size of reduced mechanisms generated by reduction methods, such as directed relation graph (DRG), can also be greatly affected by the uncertainties in the rate coefficients, because these methods eliminate species by comparing contributions of the production rates of important species from other species. In order to obtain the optimum reduced mechanism in the uncertainty domain of reaction rate parameters, the species-targeted global sensitivity analysis (STGSA) method is proposed to measure the importance of species in kinetic mechanisms and to simplify them by considering the input uncertainties. The demonstrations are performed for the ethylene oxidation mechanism using the USC-Mech II with 111 species and the n-heptane oxidation mechanism using the JetSurf (version 1.0) with 194 species. It is found that STGSA can accurately identify the redundant global species and generate more compact reduced mechanisms compared with the DRG-based methods, resulting in a 33-species reduced mechanism for ethylene oxidation and a 37-species reduced mechanism for n-heptane oxidation. These reduced mechanisms show accurate predictions for the ignition delay times and laminar flame speeds over a wide range of operating conditions.

H Radical Sensitivity-Assisted Automatic Chemical Kinetic Model Reduction for Laminar Flame Chemistry Retaining: A Case Study of Gasoline–DME Mixture under Engine Conditions

Flame propagation commonly exists in a wide range of engine operating modes. In chemical kinetic model reduction, the prediction of flame speeds must be targeted when engines involve flame propagation. However, the time-consuming nature of 1-D flame code running largely limits the feasibility of trial-and-error type reduction approaches. In this study, an improved automatic reduction scheme is proposed by adding a normalized H radical sensitivity with rate constants. By comparison with flame speed sensitivity, the combination of H radical and flame speed sensitivity can be more accurate to construct the species group relevant to laminar flame chemistry. Then, the newly proposed reduction methodology is applied for the spark ignition-controlled autoignition hybrid combustion (SCHC) with dimethyl ether (DME) as the pilot injection into gasoline, which proves promising in the engine performance by flexible controlling and stabilizing the combustion process. By constructing a new detailed chemical kinetic mod...

Creation of Small Skeletal Models in Kinetic Model Reductions

This paper outlines updates made to a method for chemical kinetic model reduction for use in computational fluid dynamics simulations. Specifically, this method uses a time-integrated flux-based algorithm to find a small skeletal model based on a detailed kinetic model, before optimization of the rate constants, using steepest descent and solution mapping methods. The new method is then applied to the reduction of a methane–air model and a dodecane–air model for two different sets of initial conditions. The results show that the optimized models are able to predict the performance of their respective detailed models over the ranges of conditions for which the optimizations are based. Results for the optimized models are also able to predict the perfectly stirred reactor response better than the optimized models generated using the older method.

Towards improved automatic chemical kinetic model reduction regarding ignition delays and flame speeds

In chemical kinetic model reduction under internal combustion engine conditions, most implementations only consider ignition related chemistry without consideration of flame speed prediction. In practice, flame propagation commonly exists in spark ignition engines, dual-fuel with pilot injection compression ignition engines, reactivity controlled compression ignition engines, and etc. Due to the inherent time-consuming nature, it is impractical to run a 1-D flame code with trial-and-error methods for model reduction, especially when starting with a large chemical kinetic model. In this paper, an improved reduction methodology is proposed for construction of a small set of species that give accurate predictions of both flame speeds and ignition delays. First, a strong correlation is found between the errors of maximum H radical and the errors in prediction of laminar flame speeds. Addition of H to the search targets in graph-based methods is conducted showing improvement in accuracy of flame speed prediction. Second, the normalized flame speed sensitivity with rate constants is analyzed for identifying a set of species that strongly influences the prediction of flame speeds. Finally, a trial-and-error based method is used for further reduction with a 0-D testbed for prediction of ignition only, while keeping the species important to flame chemistry. The newly proposed reduction methodology is used for development of accurate skeletal models predicting both ignition and flame speeds for several hydrocarbon fuels. These skeletal models include methane (27 species), propane (32 species), n-heptane (126 species), and primary reference fuel gasoline surrogates (207 species) with high fidelity to be used in engine simulations.

On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models

ABSTRACT(Chemical) kinetic models in terms of ordinary differential equations correspond to finite-dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow mode description of the full system compute approximations of low-dimensional attracting slow invariant manifolds and parameterize these manifolds in terms of a subset of chosen chemical species, the so called reaction progress variables. The invariance property suggests a slow invariant manifold to be constructed as (a bundle of) solution trajectories of suitable ordinary differential equation initial or boundary value problems. The focus of this work is on a discussion and exploitation for deeper insight of unifying geometric and analytical issues of various approaches to trajectory-based numerical approximation techniques of slow invariant manifolds that are in practical use for model reduction in chemical kinetics. Two basic concepts are pointed out reducing various model reduction approaches to a common denominator. In particular, we discuss our recent trajectory optimization approach in the light of these two concepts. We newly relate both of them within our variational boundary value viewpoint, propose a Hamiltonian formulation and conjecture its relation to conservation laws, (partial) integrability and symmetry issues as novel viewpoints on dimension reduction approaches that might open up new deep perspectives and approaches to the problem from dynamical systems theory.

The application of the QSSA via reaction lumping for the reduction of complex hydrocarbon oxidation mechanisms

The quasi-steady-state approximation (QSSA) has been widely applied for the purposes of chemical kinetic model reduction. Although it is essentially a low-order approximation, it can be shown to lead to significant reductions in the number of fast variables within a mechanism without significant loss of accuracy for model predictions. Due to the couplings between QSSA expressions, the species are commonly solved for using numerical inner iteration techniques. Therefore, although the stiffness of the model system can be reduced, there is a computational overhead in solving the often nonlinear QSSA equations. Greater computational savings can be made where QSS species can be removed from the chemical model via explicit analytical expressions. In many cases these expressions are equivalent to reaction lumping. Where such reaction lumping can be achieved, a reduced mechanism in standard kinetic form can be developed, which contains new lumped reaction rate coefficients, but leads to the removal of QSS species. This paper describes such an approach for mechanisms describing the oxidation of the hydrocarbon fuels n-heptane and cyclohexane, and shows that significant reductions in both species and reactions can be achieved, leading to substantial computational speed-ups. The resulting schemes clearly demonstrate the main atomic flux patterns within the oxidation process. Patterns related to the time-scales of hydrocarbon radical species within alkane oxidation mechanisms are discussed, as well as the potential significance of non-QSS radicals in determining ignition behaviour.

Quasi-equilibrium grid algorithm: Geometric construction for model reduction

The method of invariant grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992; A.N. Gorban, I.V. Karlin, A.Y. Zinovyev, Invariant grids for reaction kinetics, Physica A 333 (2004) 106–154; A.N. Gorban, I.V. Karlin, Invariant Manifolds for Physical and Chemical Kinetics, Lecture Notes Physics 660, Springer, Berlin Heidelberg, 2005, doi: 10.1007/b98103]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold: the invariant grid. A convenient way to get a first approximation of the SIM is given by the spectral quasi-equilibrium manifold (SQEM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992]. In the present paper, a flexible numerical method to construct the discrete analog of a quasi-equilibrium manifold, in any dimension, is presented. That object is named quasi-equilibrium grid (QEG), while the procedure quasi-equilibrium grid algorithm (QEGA). Extensions of the QEM notion are also suggested. The QEGA is a numerical tool which can be used to find a grid-based approximation for the locus of minima of a convex function under some linear constraints. The method is validated by construction of one and two-dimensional grids for a model of hydrogen oxidation reaction.

Approximation of Slow Attracting Manifolds in Chemical Kinetics by Trajectory-Based Optimization Approaches

Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear "reduction equations" particularly difficult in many cases where the gap in intrinsic time scales is not large enough. We demonstrate that trajectory optimization approaches can avoid such severe restrictions by computing numerical solutions that correspond to "maximally relaxed" dynamical modes in a suitable sense. We present a framework of trajectory-based optimization for model reduction in chemical kinetics and a general class of reduction criteria characterizing the relaxation of chemical forces along reaction trajectories. These criteria can be motivated geometrically exploiting ideas from differential geometry and fundamental physics and turn out to be highly successful in example applications. Within this framework, we provide results for the computational approximation of slow attracting low-dimensional manifolds in terms of families of optimal trajectories for a six-component hydrogen combustion mechanism.

Constructive methods of invariant manifolds for kinetic problems

The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space ( the invariance equation ). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics ). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability . A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn ∼1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.

Computing minimal entropy production trajectories: an approach to model reduction in chemical kinetics.

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.