Computational Singular Perturbation Research Articles

OME[formula omitted]/air mixtures: The structure and propagation mechanism of their laminar premixed flames

Oxymethylene dimethyl ethers (CH3O(CH2O)xCH3 or OMEx) are synthetic substitutes of diesel and jet fuel. They can achieve soot-less combustion and have been shown to exhibit favourable ignition characteristics. With the aim to explore their combustion physics, the structure of their flames is analysed using the algorithmic tools of the Computational Singular Perturbation (CSP) method. It is demonstrated that the flame structure and the mechanism for its propagation is encapsulated in the fastest explosive mode, introduced by chemical dynamics in a narrow region of the flame front. This narrow region extends around the point where the maximum heat release rate (MHRR) is recorded. CSP diagnostics identify (i) reactions H + O2→ O + OH and CO + OH → CO2 + H beyond MHRR as initiating an upstream diffusion of heat and H radicals, both of which are generated by the exothermic reaction H2 + OH → H2O + H, (ii) a downstream convective motion that ensues and (iii) chemical activity that is initiated ahead of MHRR and sustained by the convective transport of fuel and oxygen. CSP also identifies differences in the action of the upstream diffusion of heat and H radicals and of the downstream transport of fuel and oxidiser. It is also shown that the fastest explosive mode far from the neighbourhood of MHRR has no influence on the structure and propagation of the flame front. Although OME2−4/air mixtures exhibit drastically different dynamics in the context of homogeneous autoignition, very small differences are recorded in terms of flame structure and propagation. The findings suggests that, since practically all major processes driving the flame front propagation are similar to those of hydrocarbons, OMEx fuels can be used as “drop-in” fuels in currently employed burners.

Family of Skeletal Reaction Mechanisms for Methane–Oxygen Combustion in Rocket Propulsion

Analyzing methane–oxygen rocket propellant combinations requires suitable modeling of the major chemical reaction processes. Although several detailed kinetic mechanisms for methane oxidation in air exist, most do not reproduce the reaction pathways of high-pressure methane–oxygen combustion, typical of liquid rocket engines. Moreover, when large-scale computational fluid dynamics simulations are pursued, detailed reaction schemes are not computationally viable. In the present study, we identify a reliable detailed kinetic scheme for liquid rocket applications, and then we perform a wide reduction campaign leveraging computational singular perturbation theory. Enforcing various reduction targets, we obtain a family of seven skeletal schemes, including 11–39 species. Each mechanism targets different combustion modes, namely, homogeneous ignition, complex flows and flame extinction, premixed burning, reaction processes under intense turbulent mixing, and largely off-stoichiometric mixtures, typical of rocket engine preburners. We test the skeletal mechanisms against meaningful validation targets, attaining appreciable predictive accuracy compared with the detailed parent scheme. We expect the proposed family of skeletal schemes to offer a wide and flexible range of solutions—in terms of size, accuracy, and dominant combustion mode—for performing large-scale yet cost-affordable computational fluid dynamics of methane–oxygen flames under rocket-engine-relevant conditions.

Application of static integrated skeletal reduction and tabulation of dynamic adaptive chemistry in the combustion simulation of ethylene-fueled scramjet combustor.

The high-fidelity reduced mechanism is one of the key elements in the combustion simulation of scramjet combustors to reveal their combustion and flow phenomena. In the present work, the hierarchically constructed NUIGMech1.2 (2857 species and 11 814 reactions) is applied to the combustion simulation of an ethylene-fueled scramjet combustor using the method of static integrated skeletal reduction and tabulation of dynamic adaptive chemistry (TDAC). The integrated skeletal reduction strategy successively consists of species elimination using the revised directed relation graph with error propagation method of fixed species scheme and improved sensitivity analysis method, and reactions elimination based on computational singular perturbation importance index. A preferred ethylene skeletal mechanism (26 species and 117 reactions) is obtained through the integrated skeletal reduction strategy under target working conditions of temperature range of 900-1800 K, pressure range of 1-4 atm, and equivalence ratio range of 0.25-5.0. The compact skeletal mechanism is comprehensively validated against the experimental results of ignition delay times, laminar flame speeds, and key species concentration profiles. Meanwhile, it shows consistent results with the detailed mechanism on the adiabatic flame temperature profiles and "S"-curves. When applying this skeletal mechanism to combustion simulations of ethylene-fueled scramjet combustor with double parallel cavities, the path flux analysis method and in situ adaptive tabulation algorithm of TDAC is further utilized to speed up the chemical reaction solution process at run-time. Under the scramjet and ramjet modes, the corresponding simulation results in terms of flame luminosity images, schlieren images, and static pressure distributions, coincide well with those of experimental measurements. The combustion and flow characteristics of the two modes are investigated and analyzed comparatively based on above results and combustion performance parameters. Present work contributes to the application of fuel kinetic mechanisms in scramjet combustor combustion simulation.

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. We have implemented CSP in a C++ open-source library CSPlib1 using the Kokkos2 parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS. Program summaryProgram Title: CSPlibCPC Library link to program files:https://doi.org/10.17632/p9gb7z54sp.1Developer's repository link:https://github.com/sandialabs/csplibLicensing provisions: BSD 2-clauseProgramming language: C++Nature of problem: Dynamical systems can involve coupled processes with a wide range of time scales. The computational singular perturbation (CSP) method offers a reformulation of these systems which enables the use of dynamically-based diagnostic tools to better comprehend the dynamics by decoupling fast and slow processes. CSPlib is an open-source software library for analyzing general ordinary differential equation (ODE) and differential algebraic equation (DAE) systems, with specialized implementations for detailed chemical kinetic ODE/DAE systems. It relies on CSP for the analysis of these systems. CSPlib has been used in gas kinetic and heterogeneous catalytic kinetic models.Solution method: CSP analysis seeks a set of basis vectors to linearly decompose the right-hand side (RHS) of a dynamical system in a manner that decouples fast and slow processes. The CSP basis vectors are often well approximated with the right eigenvectors of the RHS Jacobian. And the left basis vectors are found by the inversion of the matrix, whose columns are the CSP basis vectors. Accordingly, the right and left CSP basis vectors are orthonormal. CSP defines mode amplitudes as the projections of the left basis vectors on the RHS; the time scales as the reciprocals of the RHS Jacobian eigenvalue magnitudes; and the CSP pointers, which are the element-wise multiplication of the transpose of the right CSP basis vectors with the left CSP basis vectors. For kinetic models that can be cast as the product of a generalized stoichiometric matrix and a rate of progress vector, CSP defines the participation index, which represents the contribution of a chemical reaction to each mode. Further, it defines the slow and fast importance indices, which describe the contribution of a chemical reaction to the slow and fast dynamics of a state variable, respectively. These indices are useful in diagnostic studies of dynamical systems and the construction of simplified models.Additional comments including restrictions and unusual features: CSPlib is a portable library that carries out many CSP analyses in parallel and can be used in modern high-performance platforms.

An enhanced Sample-Partitioning Adaptive Reduced Chemistry method with a-priori error estimation

Reactor-based approaches for handling the Turbulence–Chemistry-Interactions closure have the advantage of embedding finite-rate chemistry in the combustion model of RANS and LES simulations, which might be crucial for the solution accuracy when complex combustion regimes are investigated. However, the numerical solution of the chemical ODEs is burdened with stiffness and increased dimensionality, especially when large detailed mechanisms are required. To this end, the Sample-Partitioning Adaptive Reduced Chemistry (SPARC) methodology couples adaptive chemistry and machine learning to speed-up the chemistry integration in reactive flows simulations. It consists in building a library of skeletal mechanisms, associated to clusters of similar thermo-chemical states identified in a training dataset, and then, at run-time, each computational cell is assigned to a specific cluster, whose skeletal mechanism is retrieved and employed for the time integration. Such workflow builds on four interacting blocks, i.e., training dataset generation, clustering, mechanism simplification, and classification, and its success tightly depends on the quality of each block, which generally results from a combination of theoretical, methodological, and computational choices. In this paper, we explore the effects of the mechanism simplification strategy on the SPARC performance and we develop an ad-hoc procedure that automatically identifies the cluster-wise optimal reduction parameters, delivering a higher global reduction and therefore a larger computational speed-up compared to a standard approach, along with an explicit a-priori control on accuracy. We implement and test this novel procedure on a RANS simulation of the Adelaide Jet-in-hot-coflow (AJHC) burner, and we attain a ∼2x CPU time improvement with respect to the simulation obtained with a 36-species detailed mechanism.Novelty and significance This work makes a contribution towards the acceleration of chemistry integration in reactive flows simulations. More specifically, the Sample-Partitioning Adaptive Reduced Chemistry method, which couples adaptive chemistry and machine learning, is enhanced with automatic target species definition and a-priori error estimation. The novelties lie in the utilization of the computational singular perturbation (CSP) reduction algorithm, which provides means for automatically identifying an adaptive set of target species, and in the definition of a novel strategy for assessing the performance of the reduced mechanisms in the pre-processing phase, with the goal of estimating a measure of accuracy of the upcoming CFD simulation.

A data-driven reduced-order model for stiff chemical kinetics using dynamics-informed training

A data-based reduced-order model (ROM) is developed to accelerate the time integration of stiff chemically reacting systems by effectively removing the stiffness arising from a wide spectrum of chemical time scales. Specifically, the objective of this work is to develop a ROM that acts as a non-stiff surrogate model for the time evolution of the thermochemical state vector (temperature and species mass fractions) during an otherwise highly stiff and nonlinear ignition process. The model follows an encode-forecast-decode strategy that combines a nonlinear autoencoder (AE) for dimensionality reduction (encode and decode steps) with a neural ordinary differential equation (NODE) for modeling the dynamical system in the AE-provided latent space (forecasting step). By means of detailed timescale analysis by leveraging the dynamical system Jacobians, this work shows how data-based projection operators provided by autoencoders can inherently construct the latent spaces by removing unnecessary fast timescales, even more effectively than physics-based counterparts based on an eigenvalue analysis. A key finding is that the most significant degree of stiffness reduction is achieved through an end-to-end training strategy, where both AE and neural ODE parameters are optimized simultaneously, allowing the discovered latent space to be dynamics-informed. In addition to end-to-end training, this work highlights the vital contribution of AE nonlinearity in the stiffness reduction task. For the prediction of homogeneous ignition phenomena for H2-air and C2H4-air mixtures, the proposed ROM achieves several orders-of-magnitude increase in the integration time step size when compared to (a) a baseline CVODE solver for the full-chemical system, (b) statistical technique – principal component analysis (PCA), and (c) computational singular perturbation (CSP), a vetted physics-based stiffness-reducing modeling framework.

Driving mechanisms of high-cetane number, synthetic fuel autoignition: The case of OME[formula omitted

Oxymethylene dimethyl ethers (CH3O(CH2O)xCH3 or OMEx) are potential synthetic substitutes of diesel and jet fuel that can be acquired through CO2 recycling and have the unique “clean” feature that they do not contain C-C bonds in their atom chain, but only C-O, and therefore can combust without soot. Also, they present favourable ignition characteristics and high cetane numbers. In order to determine ignition control strategies, the dominant oxidation pathways must be identified. To this end, autoignition of OME2−4/air mixtures is studied using the tools of Computational Singular Perturbation algorithm. It is shown that as the length of the atom chain x increases, ignition delays become shorter. This is because, at the very early stages of the process, H-abstraction and fuel break-up reactions realize in a larger number of ways for larger x. The process develops first through a chemical runaway that tends to slow-down autoignition and then through a thermal runaway that tends to speed-up autoignition at a progressively stronger rate. It is shown that the total heat release is independent of x, although the ignition delay becomes shorter with increasing x. The two stable intermediates H2O2 and CH2O are shown to shorten ignition delays, when used as additives in the initial mixtures. It is demonstrated that OMEx synthetic fuels offer the capability of soot-less combustion, combined with ignition control.

Asymptotic analysis of detonation development at SI engine conditions using computational singular perturbation

The occurrence and intensity of the detonation phenomenon at spark-ignition (SI) engine conditions is investigated, with the objective to successfully predict super-knock and to elucidate the effect of kinetics and transport at the ignition front. The computational singular perturbation (CSP) framework is employed in order to investigate the chemical and transport mechanisms of deflagration and detonation cases in the context of 2D high-fidelity numerical simulations. The analysis revealed that the detonation development is characterised by: (i) stronger explosive dynamics and (ii) enhanced role of convection. The role of chemistry was also found to be pivotal to the detonation development which explained the stronger explosive character of the system, the latter being an indication of the system's reactivity. The role of convection was found to be enhanced at the edge of the detonating front. Moreover, the increased contribution of convection was found to be related mainly to heat convection. Remarkably, the detonation front was mainly characterised by dissipative and not explosive dynamics. Finally, diffusion was found to have negligible role to both examined cases.

Automated adaptive chemistry for Large Eddy Simulations of turbulent reacting flows

Large Eddy Simulations (LES) of turbulent reacting flows carried out with detailed kinetic mechanisms have a key role for the discovery of the physical and chemical processes occurring in combustion systems, and are essential for the development of efficient, stable, and non-pollutant technologies. Nevertheless, these simulations require a large amount of computational resources, making their utilization for large-scale systems, such as industrial burners and gas turbines, impractical. In this work, we combine state-of-the-art machine learning algorithms and model reduction methods to deliver a fully automated strategy for performing LES with adaptive chemistry. This strategy is based on the Sample-Partitioning Adaptive Chemistry (SPARC) algorithmic procedure, which consists of four steps: the generation of a training dataset, its partitioning in clusters, the generation of a set of reduced chemical mechanisms specifically tailored to each cluster and, lastly, the numerical simulation of the case of interest with adaptive chemistry enabled by an on-the-fly classification of every grid point.The SPARC approach has already been demonstrated to substantially reduce the computational effort of reactive flows simulations. However a non-negligible level of user interventions is needed, upon which the method’s success critically depend. Therefore, with the goal of boosting the performance of this workflow and minimise the user-specified degrees of freedom, we plug in and exploit the Local Principal Component Analysis augmented with an automated Bayesian-optimised search for optimal clustering solutions, and the Computational Singular Perturbation method with an additional layer of automation based on the Tangential Stretching Rate for minimally-sized reduced mechanisms. We employ a cheap and easy-to-generate 1-dimensional-flames training database and we demonstrate the efficiency, accuracy and robustness of this strategy with an application to LES of the Adelaide Jet in Hot Coflow (AJHC) burner, a turbulent reacting flow exhibiting intense turbulence-chemistry interactions.

Comparative review of the chemical dynamics underlying five models of ammonia fuel oxidation

Five frequently employed chemical kinetics mechanisms for ammonia oxidation are analyzed and compared, in the context of homogeneous adiabatic autoignition. The analysis focuses on the ignition delay and is based on the explosive mode that is shown to drive the process. Using algorithmic tools based on the Computational Singular Perturbation algorithm, the reactions responsible for the generation of the explosive mode are identified, along with the variables (species mass fractions and temperature) that associate the most to this mode. Comparison of these sets of reactions and variables, obtained for each mechanism, allows to correlate the differences in the predictions from the mechanisms with specific reactions. The major differences identified, which lead to different ignition delay times, relate to (i) the relative duration of chemical and thermal runaways (a sizeable chemical runaway develops only in some mechanisms) and (ii) the dominant chemistry during the chemical runaway (chemistry involving species with two nitrogen atoms is active only in some mechanisms). The major similarities identified refer to the thermal runaway and in particular to (i) the chemical activity, which is supported mainly by OH-producing reactions and by reactions producing their reactants and (ii) the thermal activity, which is dominated by strongly exothermic OH-consuming reactions.

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis-Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed.

A reduced chemical kinetic mechanism of diesel fuel for HCCI engines

A reduced mechanism of diesel fuel was developed on the basis of Wang’s mechanism. First, for removing the unimportant reactions, an importance index was defined on the basis of computational singular perturbation (CSP). Choosing the importance index of 0.0065, the 140 unimportant reactions were removed, and obtained a smaller mechanism of 403 elementary reactions. Second, 32 global quasi-steady-state (QSS) species were found with the threshold value of 0.005. Finally, the smallest mechanism containing 77-species was obtained. By contrast with the ignition delay time of the original Wang’s mechanism, the maximum error of the final 77-species mechanism was 7.2 %. The final mechanism was also performed with the original Wang’s mechanism and the experiments date from the selected homogeneous charge compression ignition (HCCI) engine, the good overlap of curves was obtained and the maximum error of the simulation results was less than 10 %.

Dimensionality reduction and unsupervised classification for high-fidelity reacting flow simulations

The development of reduced-order combustion models able to accurately reproduce the physics of reactive systems has been a highly challenging aspect of numerical combustion research in the recent past. The complexity of the problem can be reduced by identifying and using low-dimensional manifolds able to account for turbulence-chemistry interactions. Recently, Principal Components Analysis (PCA) has shown its potential in reducing the dimensionality of a chemically reactive system while minimizing the reconstruction error. The present work demonstrates the application of the Manifold Generated by Local PCA (MG-L-PCA) approach in direct numerical simulation (DNS) of turbulent flames. The approach is enhanced with an unsupervised clustering based on Vector Quantization PCA (VQPCA) and an on-the-flyPCA-based classification technique. The reduced model is then applied on a three-dimensional (3D) turbulent premixed NH3/air flame by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. Results are compared with both a detailed reaction mechanism and a Computational Singular Perturbation (CSP) reduced skeletal mechanism. A comparison between training the reduced model using one-dimensional (1D) and 3D data sets is also included. Overall, the MG-L-PCA allows not only for a reduction in the number of transport equations, but also a significant reduction in the stiffness of the system, while providing highly accurate results.

Computational singular perturbation method for the non-standard FitzHugh-Nagumo system

An effective computational singular perturbation (CSP) method for solving the non-standard FitzHugh-Nagumo system is constructed and evaluated by detailed algebra factorization. Furthermore, our studies illustrate a geometric CSP framework with the layer and reduced problems for the non-standard FitzHugh-Nagumo system. Finally, the first two CSP manifolds and two CSP fast fibers are also presented for the FitzHugh-Nagumo system by one-step and two-step CSP updates in this context. The CSP method can further describe Fenichel manifolds and facilitate a better understanding of the dynamic properties of complex neuron models or circuit neural models.

Dominant dynamics of n-butanol/air autoignition and the influence of additives

The algorithm of Computational Singular Perturbation is used in order to study autoignition dynamics and formaldehyde emission during isochoric, adiabatic n-butanol oxidation. It is shown that n-butanol autoignition has a significant chemical runaway for low initial temperatures and a limited one for high initial temperatures. Autoignition is supported mainly by the dissociation of H2O2 to OH and, to a lesser extent, by the attack of HO2 on the parent fuel that produces H2O2. The algorithmic analysis points to the pivotal role of mainly H2O2 and secondarily CH2O in the process and it is shown that addition of these two species to the initial mixture can shorten the ignition delay time substantially. The strong effect of H2O2 is based on the near elimination of the chemical runaway, because of the generation of a substantial OH pool very early in the process. The formation of formaldehyde in the products is shown to be practically insensitive to a very wide variety of additives for a given overall equivalence ratio, even when these additives had a substantial effect on ignition delay. This is attributed to the fact that, for combustion with air at a given equivalence ratio, the relative proportion of C/H/O atoms in the initial mixture does not change much, independently of the precise configuration of the molecules that constitute the fuel mixture and the additive. As a result, methodologies for the control and reduction of aldehyde and ketone emissions should be based on equivalence ratio, pressure, and temperature control, rather than the use of additives.

PyCSP: A Python package for the analysis and simplification of chemically reacting systems based on Computational Singular Perturbation

PyCSP is a Python package for the analysis and simplification of chemically reacting systems, using algorithms based on the Computational Singular Perturbation (CSP) theory. It provides tools for the local characterization of the chemical dynamics, enabled by the recognition of a convenient projection basis which carries out a timescale-based uncoupling. The tools supplied within the package allow one to identify the rate-controlling chemical reactions, the intrinsic chemical timescales, the driving chemical timescale and indicators of the system's explosive or dissipative propensity. Possible applications are the analysis of numerical simulations of reacting flows, and the reduction of chemical kinetics models, based on the CSP information. This manuscript provides a brief overview of the foundations of CSP, a description of the libraries, and demonstrations of the features implemented in PyCSP with code examples, along with practical advices and guidelines for users. Program summaryProgram Title:PyCSPCPC Library link to program files:https://doi.org/10.17632/59pw7pvkkb.1Developer's repository link:https://github.com/rmalpica/PyCSPLicensing provisions: MITProgramming language: PythonSupplementary material: Code documentation and Python scripts employed to generate the figures.Nature of problem: The evermore increasing availability of high-performance computing resources, and the compelling need for more advanced and sustainable energy conversion devices, based on unconventional combustion regimes and alternative fuels, are driving towards an unprecedented massive production of data in numerical simulations of reacting flows. The research questions behind the production of such huge datasets are typically related to (i) the fundamental understanding of combustion phenomena, and (ii) the development of reduced order models and/or turbulence-chemistry interaction sub-grid scale (closure) models, both with the aim of accelerating large scale simulations of real combustion devices.Solution method: Both categories of research questions can widely benefit from the numerical tools available in PyCSP. The computational singular perturbation (CSP) framework allows one to extract concise information from chemically reacting systems, automatically and at reasonable cost. This is especially useful when the dataset is so massive and the number of degrees of freedom so large, i.e., hundreds of species/reactions per cell, that even a visual inspection becomes unmanageable. PyCSP offers a fast, user-friendly implementation of numerous analysis tools, enabling a more systematic data processing and, ultimately, providing the user with a deeper physical understanding of the problem under investigation. Moreover, the CSP theoretical framework can be exploited to generate reduced order models (ROMs), tailored to and to be employed in specific applications, in order to drastically reduce the computational cost of a numerical simulation, while retaining accuracy in global observables. The ROM is in the form of a skeletal kinetic mechanism of adjustable fidelity, or an adaptive chemistry integrator.Additional comments including restrictions and unusual features:PyCSP relies on Cantera, an open-source suite of tools for problems involving chemical kinetics, thermodynamics, and transport processes, to efficiently incorporate detailed chemical thermo-kinetics models into the CSP calculations.

Application of reduced mechanism by DRGEP-CSP approach to the numerical simulation of biogas diluted with the H2-CO2 couple

A numerical simulation was used to investigate an approach of reduction of the chemical kinetics coupled with two methods: Computational Singular Perturbation (CSP) and Directed Relation Graph with Propagation Error (DRGEP), in order to simulate the laminar premixed Biogas diluted by the H2-CO2. In this reduction approach, DRGEP allowed the identification of important species, elementary reactions involving unimportant species were eliminated from the detailed mechanism. To have a skeletal mechanism containing a minimum number of elementary reactions, the CSP method was used. The skeletal mechanism reduced by the DRGEP-CSP approach was opted for the simulation of biogas diluted by the H2-CO2 couple, given its high fidelity with the detailed mechanism. This reduction approach was applied to the laminar premixed flame biogas with the effect of varying the proportion of H2 and CO2. It emerges from the results that this reduction approach has a wide field of application in the study of the numerical combustion of biogas. It also appears that, the dilution of the biogas by H2-CO2 couple has a significant influence on the laminar flame speed and temperature over a wide range of aeration factors.

Chemical dynamics of the autoignition of near-stoichiometric and rich methanol/air mixtures

The homogeneous, isochoric and adiabatic autoignition of rich methanol mixtures is analysed using algorithmic tools of Computational Singular Perturbation. It is shown that ignition delay decreases as the equivalence ratio ϕ increases, due to the faster production of OH radicals via the reactions CHOH + HO CHOH + HO and HO (+M) OH + OH (+M). After ignition and for sufficiently rich mixtures the phenomenon of super-adiabatic temperature (SAT) is observed; i.e. the temperature after ignition decreases with time. This feature is accompanied by the appearance of an explosive mode. With increasing values of ϕ, SAT becomes more pronounced and the explosive mode becomes faster; i.e. its time scale is shortened. SAT is due to the fact that as ϕ increases the role of hydrogen chemistry diminishes and the explosive character of the process is basically generated by endothermic dissociation reactions of carbon-containing species that cause an increase in number of molecules and a temperature decrease.

Algorithmic asymptotic analysis: Extending the arsenal of cancer immunology modeling

The recent advances in cancer immunotherapy boosted the development of tumor-immune system models, with the aim to indicate more efficient treatments. Physical understanding is however difficult to be acquired, due to the complexity and the multi-scale dynamics of these models. In this work, the dynamics of a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8+ T cells and circulating lymphocytes is examined. It is first shown that the long-term evolution of the system towards high-tumor or tumor-free equilibria is determined by the dynamics of an initial explosive stage of tumor progression. Focusing on this stage, the algorithmic Computational Singular Perturbation methodology is employed to identify the underlying mechanisms confining the system’s evolution and the governing slow dynamics along them. These insights are preserved along different tumor-immune system and patient-dependent realizations. On top of these identifications, a novel reduced model is algorithmically constructed, which accurately predicts the dynamics of the system during the explosive stage and includes half of the parameters of the detailed model. The present analysis demonstrates the potential of algorithmic asymptotic analysis for acquiring physical understanding and for simplifying the complexity of cancer immunology models. Along with the current techniques on the field, this analysis can provide guidelines for more effective treatment development.

An adaptive time-integration scheme for stiff chemistry based on computational singular perturbation and artificial neural networks

We leverage the computational singular perturbation (CSP) theory to develop an adaptive time-integration scheme for stiff chemistry based on a local, projection-based, reduced order model (ROM) freed of the fast time-scales. Its construction is such that artificial neural networks (ANN) can be plugged-in as cheap surrogates of the local projection basis, which is a state function, to alleviate the computational cost, without sacrificing the geometrical and physical foundation of the method. In fact, the solver relies on the synthetic basis in place of the more expensive on-the-fly calculated basis, i.e. the eigenvectors of the Jacobian matrix of the chemical source term, to define the local slow invariant manifold (SIM) and the projection matrix, then integrates explicitly the projected, i.e., non-stiff, chemical source term.We explore the feasibility of the ANN-accelerated CSP solver by training a set of ANNs to predict the projection basis vectors given the local chemical composition in a hydrogen/air homogeneous reactor problem. To enhance the smoothness of the basis vectors and reduce the reconstruction error, we introduce a constrained Jacobian formulation which removes the state heterogeneity due to the presence of temperature along with chemical species, and takes the derivatives enforcing the absolute enthalpy conservation. The test problem highlights the robustness of this ANN approach, arising from the relatively low requirements on the basis accuracy with respect to the requested integration accuracy.