Dynamical system analysis of ignition phenomena using the tangential stretching rate concept

We analyze ignition phenomena by resorting to the stretching rate concept formerly introduced in the study of dynamical systems. We construct a Tangential Stretching Rate (TSR) parameter by combining the concepts of stretching rate with the decomposition of the local tangent space in eigen-modes. The main feature of the TSR is its ability to identify unambiguously the most energetic scale at a given space location and time instant. The TSR depends only on the local composition of the mixture, its temperature and pressure. As such, it can be readily computed during the post processing of computed reactive flow fields, both for spatially homogeneous and in-homogenous systems. Because of the additive nature of the TSR, we defined a normalized participation index measuring the relative contribution of each mode to the TSR. This participation index to the TSR can be combined with the mode amplitude participation Index of a reaction to a mode – as defined in the Computational Singular Perturbation (CSP) method – to obtain a direct link between a reaction and TSR. The reactions having both a large participation index to the TSR and a large CSP mode amplitude participation index are those contributing the most to both the explosive and relaxation regimes of a reactive system. This information can be used for both diagnostics and for the simplification of kinetic mechanisms. We verified the properties of the TSR with reference to three nonlinear planar models (one for isothermal branched-chain reactions, one for a non-isothermal, one-step system, and for non-isothermal branched-chain reactions), to one planar linear model (to discuss issues associated with non-normality), and to test problems involving hydro-carbon oxidation kinetics. We demonstrated that the reciprocal of the TSR parameter is the proper characteristic chemical time scale in problems involving multi-step chemical kinetic mechanisms, because (i) it is the most relevant time scale during both the explosive and relaxation regimes and (ii) it is intrinsic to the kinetics, that is, it can be identified without the need of any ad hoc assumption

Gradient Information and Regularization for Gene Expression Programming to Develop Data-Driven Physics Closure Models

Learning accurate numerical constants when developing algebraic models is a known challenge for evolutionary algorithms, such as Gene Expression Programming (GEP). This paper introduces the concept of adaptive symbols to the GEP framework by Weatheritt and Sandberg (2016) to develop advanced physics closure models. Adaptive symbols utilize gradient information to learn locally optimal numerical constants during model training, for which we investigate two types of nonlinear optimization algorithms. The second contribution of this work is implementing two regularization techniques to incentivize the development of implementable and interpretable closure models. We apply $L_2$ regularization to ensure small magnitude numerical constants and devise a novel complexity metric that supports the development of low complexity models via custom symbol complexities and multi-objective optimization. This extended framework is employed to four use cases, namely rediscovering Sutherland's viscosity law, developing laminar flame speed combustion models and training two types of fluid dynamics turbulence models. The model prediction accuracy and the convergence speed of training are improved significantly across all of the more and less complex use cases, respectively. The two regularization methods are essential for developing implementable closure models and we demonstrate that the developed turbulence models substantially improve simulations over state-of-the-art models

Influence of adversarial training on super-resolution turbulence reconstruction

Supervised super-resolution deep convolutional neural networks (CNNs) have gained significant attention for their potential in reconstructing velocity and scalar fields in turbulent flows. Despite their popularity, CNNs currently lack the ability to accurately produce high-frequency and small-scale features, and tests of their generalizability to out-of-sample flows are not widespread. Generative adversarial networks (GANs), which consist of two distinct neural networks (NNs), a generator and discriminator, are a promising alternative, allowing for both semi-supervised and unsupervised training. The difference in the flow fields produced by these two NN architectures has not been thoroughly investigated, and a comprehensive understanding of the discriminator's role has yet to be developed. This study assesses the effectiveness of the unsupervised adversarial training in GANs for turbulence reconstruction in forced homogeneous isotropic turbulence. GAN-based architectures are found to outperform supervised CNNs for turbulent flow reconstruction for in-sample cases. The reconstruction accuracy of both architectures diminishes for out-of-sample cases, though the GAN's discriminator network significantly improves the generator's out-of-sample robustness using either an additional unsupervised training step with large eddy simulation input fields and a dynamic selection of the most suitable upsampling factor. These enhance the generator's ability to reconstruct small-scale gradients, turbulence intermittency, and velocity-gradient probability density functions. The extrapolation capability of the GAN-based model is demonstrated for out-of-sample flows at higher Reynolds numbers. Based on these findings, incorporating discriminator-based training is recommended to enhance the reconstruction capability of super-resolution CNNs

Multi-modal counterflow flame structure under autoignitive conditions

In practical systems, combustion does not occur in asymptotic limits of nonpremixed flames, premixed flames, or autoignition but rather multiple modes that interact. In canonical configurations, multi-modal combustion is critical in the stabilization of lifted jet flames. At low temperature conditions, such flames are stabilized by a 'triple' flame consisting of regions of premixed and nonpremixed combustion. At high temperature conditions, autoignition is activated, and the role of autoignition versus premixed flame propagation in flame stabilization depends on the local residence time and the local flow speed. While detailed simulations of laminar lifted jet flames are computationally tractable, extension to DNS of turbulent lifted jet flames at reasonable Reynolds numbers is computationally intractable due to the large domain size required. Therefore, the counterflow configuration is investigated as a more compact alternative. In this work, a series of detailed simulations of DME/air laminar counterflow flames at elevated pressure are performed with variations in the stream compositions, temperatures, and velocities to provide flames spanning different combinations of combustion modes, specifically a nonpremixed flame, a 'triple' flame, and a series of flames with all three modes interacting. Similarities and differences between the counterflow flames and the lifted jet flames are explored.</p

G-scheme-based simplification and analysis methodology for hydrocarbon ignition

For the simulation of reactive flows, the use of a simplified model is a common simplification to reduce the computational cost, although the reduced model may introduce significant errors in the simulation. Using the G-Scheme, the local structure of the local tangent space is characterized through the subspaces associated with the slow, active, and fast reactive scales. This specific feature can be of great significance in the analysis of the dynamics with the aim of achieving a low-dimensional description and allowing a time-scale-aware sensitivity analysis of the problem. Such analysis can be exploited to simplify/reduce/understand the reaction dynamics of interest. We have developed specific procedures to generate simplified mechanisms with an a priori known error for chemical kinetics processes, to analyze them in order to understand the role of the most important reactions, and to identify the most important reactions paths of the processes. The procedure is based on a G-Scheme Participation Index that makes use of a G-Scheme generated database. The effectiveness of the procedures to produce simplified mechanisms is demonstrated by applying them to the auto-ignition problems for homogeneous hydrogen/air and hydrocarbon/air mixtures.</p

Comparative study of hybrid multi-timescale and G-scheme methods for computational efficiency with detailed chemical kinetics

To develop a multiscale adaptive reduced chemistry solver (MARCS) for computationally efficient modeling of a reactive flow, the Hybrid Multi-Timescale (HMTS) method and G-Scheme have been evaluated and compared for both homogeneous auto-ignition and 1-D premixed spherical propagating flame calculations with detailed chemical kinetics of hydrogen, methane, dimethyl ether, and n-heptane. It is demonstrated that the CPU time of HMTS and G-Scheme methods depends on the number of species of the kinetic mechanisms, respectively, linearly and to the third power. For ignition, the results show that the G-Scheme method is faster than HMTS method when the species number of the chemical mechanism is below 40. The CPU Time of G-Scheme increases dramatically when the number of species of the detailed mechanisms is increased due to the huge computation cost of matrix inversion and reaction mode decomposition. Specifically, the G-Scheme method is faster at the induction stage of ignition and the near-equilibrium condition after ignition due to the large integration time step determined by the method adaptively. The HMTS method is faster at near the ignition point and for a large kinetic mechanism due to the fast convergence at a small base time step. Therefore, the present results suggest that it is possible an MARCS for computationally efficient modeling of combustion by adaptively taking the advantages of the computation efficiency of the HMTS method and the G-Scheme in different local combustion regimes and reduced mechanism sizes and integrating with the co-related dynamic adaptive chemistry and transport method (CO-DACT).</p

Sensitivity analysis and mechanism simplification using the G-Scheme framework

We have developed specific procedures that utilize the G-Scheme modal decomposition to carry out the sensitivity analysis along-with the numerical integration of chemical kinetics systems, so as to under- stand the roles of the most important reactions, and to identify the most important reaction paths of the processes. The sensitivity information allow to generate skeletal kinetic mechanisms for chemical kinetics mechanism. The procedures are based on participation indices constructed from the G-Scheme dynamics decomposition, but can be applied to databases generated by any numerical solver. The effectiveness of these procedures is demonstrated with reference to the auto-ignition problem of a homogeneous hydro- gen/air mixture

Effects of combustion heat release on velocity and scalar statistics in turbulent premixed jet flames at low and high Karlovitz numbers

Theoretical scaling arguments for turbulent premixed combustion indicate that the pressure-dilatation source of turbulent kinetic energy becomes significant at low Karlovitz numbers, leading to potential invalidation of commonly-used turbulence models developed for non-reacting flow. Based on these arguments, a critical Karlovitz number is defined, below which dilatation effects are expected to become significant. Velocity and scalar statistics are obtained from Direct Numerical Simulation (DNS) calculations of low Mach number spatially-evolving turbulent premixed planar jet flames. At fixed bulk Reynolds number and stoichiometric equivalence ratio, two simulations are performed at Karlovitz numbers above and below the critical Karlovitz number. Hydrogen combustion with detailed transport is modeled using a detailed nine-species chemical kinetic mechanism, and coflows of combustion products are used to ensure flame stability at uniform equivalence ratio. The analysis of these statistics focuses on three key areas. First, the influence of the velocity-pressure gradient source of turbulent kinetic energy is confirmed at a low Karlovitz number, and the unimportance of these effects is confirmed at a high Karlovitz number. Similar effects are observed for the chemical source term in the scalar variance budgets. Second, the degree of alignment between the Reynolds stress tensor (scalar flux) and the strain-rate tensor (scalar gradient), the foundation of a majority of the turbulence models used in reacting flows, is assessed with the DNS databases. Additionally, consistency of anisotropic Reynolds stress and strain-rate tensor invariants is assessed using invariant maps. While good alignment and consistency are obtained for statistics and invariants at a high Karlovitz number, both alignment and consistency degrade at a low Karlovitz number. Third, turbulence models formulated for non-reacting flow are modified algebraically in the Bray–Moss–Libby (BML) formalism for turbulent premixed combustion. A variable efficiency function is defined to capture the regime dependence of heat release effects in these models. Model performance is evaluated at Karlovitz numbers above and below the critical Karlovitz number using the DNS databases, and satisfactory prediction of counter-gradient transport in the flame-normal direction is obtained. However, heat release effects are also observed in the flame-parallel directions in the low-Karlovitz number simulation, and the models developed in the formalism for statistically planar flames fail to capture these effects. Furthermore, in the low-Karlovitz number case, redistributive effects are active on the shear components of the Reynolds stress, which are not considered in the BML formalism. More advanced turbulence models are therefore necessary for turbulent premixed jet flames below the critical Karlovitz number.</p

WAMR - an adaptive wavelet method for the simulation of compressible reacting flow.: Part II. The parallel algorithm

The Wavelet Adaptive Multiresolution Representation (WAMR) algorithm is parallelized using a domain decomposition approach suitable to a wide range of distributed-memory parallel architectures. The method is applied to the solution of two unsteady, compressible, reactive flow problems and includes detailed diffusive transport and chemical kinetics models. The first problem is a cellular detonation in a hydrogen-oxygen-argon mixture. The second problem corresponds to the ignition and combustion of a hydrogen bubble by a shock wave in air. In both cases, results agree favorably with previous computational results.</p

Budgets of flame-conditioned second-order turbulence statistics in low and high Karlovitz number turbulent premixed jet flames

Small-scale heat release in low Karlovitz number turbulent premixed combustion significantly affects large-scale turbulence dynamics through nonlinear interactions occurring within the flame structure. These interactions result in flame-local changes to the alignment of the Reynolds stress and scalar fluxes with the mean gradients that lead to failure of commonly-used Boussinesq and gradient diffusion-type turbulence models. In this work, flame-conditioned second-order turbulence statistics, that is, velocity correlations and cross-correlations conditioned on a reaction progress variable, are computed following the concept of Conditional Moment Closure (CMC). By conditioning on a local flame coordinate, this statistical basis removes effects of flame motion that are responsible for the observed statistical misalignment at low Karlovitz number. The turbulent kinetic energy (TKE) is evaluated using data from Direct Numerical Simulation (DNS) of spatially-evolving turbulent premixed jet flames at low and high Karlovitz numbers. The evolution equations are derived, and budgets of these equations are computed in the two Karlovitz number cases. In analysis of these budgets, more precise mechanisms of interaction between combustion heat release and turbulence are suggested, and implications for modeling efforts are discussed.</p