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Biogeochemical reactive transport models (RTMs) are key for understanding the evolution of the quality of groundwater systems and their interaction with anthropogenic activities. The inherent stiffness of these models, within which bio‐geochemical reactions and transport processes take place simultaneously across diverse time scales, poses significant computational challenges. The development of current RTMs is characterized by a tradeoff between accuracy and computational efficiency. Our study introduces a novel approach grounded on Computational Singular Perturbation (CSP) with the aim of efficiently solving stiff biogeochemical RTMs in groundwater systems. We integrate the CSP concept and algorithm with a reactive transport model associated with a groundwater system. Our results document that this yields a significant improvement in terms of efficiency while maintaining accuracy. For demonstration and evaluation purposes, we apply the approach to a collection of typical groundwater biogeochemical RTMs including H2O2 production/consumption, Cr(VI) adsorption‐desorption equilibrium, and denitrification processes within riparian aquifers. The new approach is then evaluated against traditional apparent rate (AR) and Equilibrium‐kinetic (EK) methods. Our results reveal that the new approach effectively identifies fast species and simplifies reaction networks, thus significantly reducing stiffness and computational costs while maintaining remarkable accuracy. Overall, our approach offers a robust and efficient solution for modeling stiff biogeochemical processes in groundwater systems. Its successful application to diverse reaction networks highlights its potential for broad implementation in environmental and engineering contexts, paving the way for accurate and computationally feasible groundwater quality assessments. Key Points: We develop a new approach to solve stiff biogeochemical reactive transport models efficiently and accurately in groundwaterOur new approach rests on a time scale analysis of modeled species through computational singular perturbationThe approach enables one to simplify the model by reducing the number of species associated with its formulation [ABSTRACT FROM AUTHOR]

We present “on the fly” algorithmic criteria for the accuracy and stability (non-stiffness) of reduced models constructed with the quasi-steady state and partial equilibrium approximations. The criteria comprise those introduced in Goussis (Combust Theor Model 16:869–926, 2012) that addressed the case where each fast time scale is due to one reaction and a new one that addresses the case where a fast time scale is due to more than one reactions. The development of these criteria is based on the ability to approximate accurately the fast and slow subspaces of the tangent space. Their validity is assessed on the basis of the Michaelis–Menten reaction mechanism, for which extensive literature is available regarding the validity of the existing various reduced models. The criteria predict correctly the regions in both the parameter and phase spaces where each of these models is valid. The findings are supported by numerical computations at indicative points in the parameter space. Due to their algorithmic character, these criteria can be readily employed for the reduction of large and complex mathematical models. [ABSTRACT FROM AUTHOR]

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 %. [ABSTRACT FROM AUTHOR]

In order to obtain physical insights on ammonia combustion, which is characterised by exceptionally long ignition delays and increased NOx emissions, the autoignition dynamics of an ammonia/air mixture is analysed using the diagnostics tools derived from the Computational Singular Perturbation (CSP) methodology. The results are compared to the autoignition dynamics of a methane/air mixture of same initial conditions. Methane was chosen for comparison because, even though the two molecules have a formal similarity, the ignition delay of methane is more than 10 times shorter than the one of ammonia. By using the CSP diagnostics tools, we identified the dominant chemical pathways that relate to the explosive components that drive the system towards ignition for both cases. Furthermore, the reactions that hinder the ammonia ignition were identified. This led to the determination of an interesting difference in the electronic configuration of the molecules of the two fuels, which is the root of their drastically different oxidation dynamics. In particular, it was shown that the autoignition process starts with the formation of methyl (CH 3 ) and amine (NH 2 ) radicals, through dehydrogenation of methane and ammonia, respectively. In the methane case, the methyl-peroxy radical (CH 3 –O–O–) then forms, which initiates a chemical runaway that lasts for approximately 2/3 of the ignition delay and leads to the gradual oxidation of carbon to CO 2 . In the ammonia case, though, the structure of NH 2 is such that it is not possible to form NH 2 –O–O–. As a result, the chemical runaway is suspended. [ABSTRACT FROM AUTHOR]

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.

Detailed gas‐phase chemical kinetic models are widely used in combustion research, and many new mechanisms for different fuels and reacting conditions are developed each year. Recent works have highlighted the need for error checking when preparing such models, but a useful community tool to perform such analysis is missing. In this work, we present a simple online tool to screen chemical kinetic mechanisms for bimolecular reactions exceeding collision limits. The tool is implemented on a user‐friendly website, cloudflame.kaust.edu.sa, and checks three different classes of bimolecular reactions; (ie, pressure independent, pressure‐dependent falloff, and pressure‐dependent PLOG). In addition, two other online modules are provided to check thermodynamic properties and transport parameters to help kinetic model developers determine the sources of errors for reactions that are not collision limit compliant. Furthermore, issues related to unphysically fast timescales can remain an issue even if all bimolecular reactions are within collision limits. Therefore, we also present a procedure to screen ultrafast reaction timescales using computational singular perturbation. For demonstration purposes only, three versions of the rigorously developed AramcoMech are screened for collision limit compliance and ultrafast timescales, and recommendations are made for improving the models. Larger models for biodiesel surrogates, tetrahydropyran, and gasoline surrogates are also analyzed for exemplary purposes. Numerical simulations with updated kinetic parameters are presented to show improvements in wall‐clock time when resolving ultrafast timescales. [ABSTRACT FROM AUTHOR]

The computational singular perturbation (CSP) method is an algorithm which iteratively approx- imates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis [Twenty-Second Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, 1989, pp. 931{941], the convergence of the CSP method has been explored in depth; however, rigorous applications have been confined to the standard framework, where the separation between \slow" and \fast" variables is made explicit in the dynamical system. This paper adapts the CSP method to nonstandard slow-fast systems having a normally hyperbolic attracting critical manifold. We give new formulas for the CSP method in this more general context, and provide the first concrete demonstrations of the method on genuinely nonstandard examples. [ABSTRACT FROM AUTHOR]

Two-dimensional direct numerical simulation (DNS) databases of bluff-body-stabilized lean hydrogen flames representative of complicated reactive–diffusive system are analysed using the combined approach of computational singular perturbation (CSP) and tangential stretching rate (TSR) to investigate chemical characteristics in blow-off dynamics. To assess the diagnostic approaches in flame and blow-off dynamics, Damköhler number and TSR variables are applied and compared. Four cases are considered in this study showing different flame dynamics such as the steadily stable mode, local extinction by asymmetric vortex shedding, convective blow-off and lean blow-out. DNS data points in positive explosive eigenvalue conditions were subdivided into four different combinations in TSR and extended TSR space and categorized in four distinct characteristic regions, such as kinetically explosive or dissipative and transport-enhanced or dissipative dynamics. The TSR analysis clearly captures the local extinction point in the complicated vortex shedding and allows an improved understanding of the distinct chemistry-transport interactions occurring in convective blow-off and lean blow-out events. [ABSTRACT FROM AUTHOR]

This article presents a numerical study of a jet-in-hot-coflow (JHC) burner which emulates Moderate or Intense Low-oxygen Dilution (MILD) conditions. Such combustion regime offers reduction in pollutant emissions and improvements in efficiency. However, some phenomena like the relations between auto-ignition and flame propagation, local extinction and re-ignition are not easily detected by experimental analysis or through the inspection of CFD calculations. The advanced post-processing tools based on the theories of computational singular perturbation (CSP) and tangential stretching rate (TSR) are adopted to investigate the Large Eddy Simulation (LES) results of the JHC burner with different coflow oxygen levels. A topological characterization of the flowfield is achieved employing the local number of chemically exhausted modes, highlighting regions that share similar dynamical features. Strong chemical activity, denoted by a small number of exhausted modes, is found in the fuel/coflow mixing layer and, to a minor extent, in the coflow/air mixing layer, exhibiting correlation with the higher heat release rate zones. The analysis of the reactive layers with TSR suggests that the flame under MILD condition is initiated by auto-ignition. Moreover, the investigation of the TSR participation indices (PIs) mark the local extinction and re-ignition zone for the low oxygen level case, indicating that the lack of oxygen in the coflow suppresses the path to produce final combustion products and heat—thus reducing the reactivity of the whole system. [ABSTRACT FROM AUTHOR]

Abstract Multi-stage heat release is an important feature of hydrocarbon auto-ignition that influences engine operation. This work presents findings of previously unreported three-stage heat release in the auto-ignition of n-heptane/air mixtures at lean equivalence ratios and high pressures. Detailed homogenous gas-phase chemical kinetic simulations were utilized to identify conditions where two-stage and three-stage heat release exist. Temperature and heat release profiles of lean n-heptane/air auto-ignition display three distinct stages of heat release, which is notably different than two-stage heat release typically reported for stoichiometric fuel/air mixtures. Concentration profiles of key radicals (HO 2 and OH) and intermediate/product species (CO and CO 2) also display unique behavior in the lean auto-ignition case. Rapid compression machine measurements were performed at a lean equivalence ratio to confirm the existence of three-stage heat release in experiments. Laser diagnostic measurements of CO concentrations in the RCM indicate similar concentration-time profiles as those predicted by kinetic modeling. Computational singular perturbation was then used to identify key reactions and species contributing to explosive time scales at various points of the three-stage ignition process. Comparisons with two-stage ignition at stoichiometric conditions indicate that thermal runaway at the second stage of heat release is inhibited under lean conditions. H + O 2 chain branching and CO oxidation reactions drive high-temperature heat release under stoichiometric conditions, but these reactions are suppressed by H, OH, and HO 2 radical termination reactions at lean conditions, leading to a distinct third stage of heat release. [ABSTRACT FROM AUTHOR]

NO formation, which is one of the main disadvantages of ammonia combustion, was studied during the isochoric, adiabatic autoignition of ammonia/air mixtures using the algorithm of Computational Singular Perturbation (CSP). The chemical reactions supporting the action of the mode relating the most to NO were shown to be essentially the ones of the extended Zeldovich mechanism, thus indicating that NO formation is mainly thermal and not due to fuel-bound nitrogen. Because of this, addition of water vapor reduced NO formation, because of its action as a thermal buffer, but increased ignition delay, thus exacerbating the second important caveat of ammonia combustion, which is unrealistically long ignition delay. However, it was also shown that further addition of just 2% molar of H2O2 does not only reduce the ignition delay by a factor of 30, but also reverses the way water vapor affects ignition delay. Specifically, in the ternary mixture NH3/H2O/H2O2, addition of water vapor does not prolong but rather shortens ignition delay because it increases OH radicals. At the same time, the presence of H2O2 does not affect the influence of H2O in suppressing NO generation. In this manner, we were able to show that NH3/H2O/H2O2 mixtures offer a way to use ammonia as carbon-less fuel with acceptable NOx emissions and realistic ignition delay.

Pre-ignition engine cycles leading to super-knock were simulated with a 48 species skeletal iso -octane mechanism to identify the dominant reaction pathways that are present in super-knock. To mimic pre-ignition, a deflagration front was generated via a hot spot that is placed over the piston at close proximity to the end-wall. Computational singular perturbation (CSP) was used to analyze the chemical dynamics at various in-cylinder locations: a point at the center of the cylinder where the deflagration front consumes the air/fuel mixture and two points located at 3 mm from the end-wall where super-knock and mild knock occur. The CSP analysis of the point at the center of the cylinder reveals weak two-stage ignition-like dynamics with a short second stage. At the other points, a pronounced two-stage ignition is displayed with a long second stage. A distinct contribution of formaldehyde (CH 2 O) at the second stage of ignition that adds to fast explosive modes in the super-knock points is not observed in the point at the center. A comparison between knock and super-knock analysis indicates that a similar set of reactions is responsible for the abnormal behavior but the fast explosive time scales are comparatively slower for knock, indicating lower reactivity, which results in the reduced intensity of knock. The analyzed results decoded important reactions responsible for the occurrence of super-knock. [ABSTRACT FROM AUTHOR]

The dynamics of a homogeneous adiabatic autoignition of an ammonia/air mixture at constant volume was studied, using the algorithmic tools of Computational Singular Perturbation. Since ammonia combustion is characterized by both unrealistically long ignition delays and elevated NO x emissions, the time frame of action of the modes that are responsible for ignition was analyzed by calculating the developing time scales throughout the process and by studying their possible relation to NO x emissions. The reactions that support or oppose the explosive time scale were identified, along with the variables that are related the most to the dynamics that drive the system to an explosion. It is shown that reaction H 2 O 2 (+M) → OH + OH (+M) is the one contributing the most to the time scale that characterizes ignition and that its reactant H 2 O 2 is the species related the most to this time scale. These findings suggested that addition of H 2 O 2 in the initial mixture will influence strongly the evolution of the process. It was shown that ignition of pure ammonia advanced as a slow thermal explosion with very limited chemical runaway. The ignition delay could be reduced by more than two orders of magnitude through H 2 O 2 addition, which causes only a minor increase in NO x emissions.

Modeling MILD (Moderate or Intense Low-oxygen Dilution) combustion is well known to be computationally demanding due to the need of an accurate description of the chemistry, because the low Damköhler number. The present work investigates the potentials of Rate-Controlled Constrained Equilibrium for the dimension reduction of kinetic schemes for a burner fed with a mixture of ethylene and air emulating MILD combustion conditions. A method based on the Computational Singular Perturbation theory is proposed for the identification of the species to be retained in the reduced representation of the chemistry. A significant reduction was achieved by using only 10 species (out of 34 species in the full kinetic scheme) and 3 elements; the results from the reduced model were in very good agreement with those of the full kinetic scheme. The sensitivity of predictions to the turbulence and combustion models was also preliminary assessed, indicating the need of modifying the residence time constant of the Eddy Dissipation Concept for MILD combustion conditions. [ABSTRACT FROM AUTHOR]

Auto-ignition characteristics of compositionally homogeneous reactant mixtures in the presence of thermal non-uniformities and turbulent velocity fluctuations were computationally investigated. The main objectives were to quantify the observed ignition characteristics and numerically validate the theory of the turbulent ignition regime diagram recently proposed by Im et al. 2015 [29] that provides a framework to predict ignition behavior a priori based on the thermo-chemical properties of the reactant mixture and initial flow and scalar field conditions. Ignition regimes were classified into three categories: weak (where deflagration is the dominant mode of fuel consumption), reaction-dominant strong, and mixing-dominant strong (where volumetric ignition is the dominant mode of fuel consumption). Two-dimensional (2D) direct numerical simulations (DNS) of auto-ignition in a lean syngas/air mixture with uniform mixture composition at high-pressure, low-temperature conditions were performed in a fixed volume. The initial conditions considered two-dimensional isotropic velocity spectrums, temperature fluctuations and localized thermal hot spots. A number of parametric test cases, by varying the characteristic turbulent Damköhler and Reynolds numbers, were investigated. The evolution of the auto-ignition phenomena, pressure rise, and heat release rate were analyzed. In addition, combustion mode analysis based on front propagation speed and computational singular perturbation (CSP) was applied to characterize the auto-ignition phenomena. All results supported that the observed ignition behaviors were consistent with the expected ignition regimes predicted by the theory of the regime diagram. This work provides new high-fidelity data on syngas ignition characteristics over a broad range of conditions and demonstrates that the regime diagram serves as a predictive guidance in the understanding of various physical and chemical mechanisms controlling auto-ignition in thermally inhomogeneous and compositionally homogeneous turbulent reacting flows. [ABSTRACT FROM AUTHOR]

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction. [ABSTRACT FROM AUTHOR]

We discuss how the Tangential stretching rate (TSR) analysis, originally developed and tested for spatially homogeneous systems (batch reactors), is extended to spatially non homogeneous systems. To illustrate the effectiveness of the TSR diagnostics, we study the ignition transient in a non premixed, reaction–diffusion model in the mixture fraction space, whose dependent variables are temperature and mixture composition. The reactive mixture considered is syngas/air. A detailed H2/CO mechanism with 12 species and 33 chemical reactions is employed. We will discuss two cases, one involving only kinetics as a model of front propagation purely driven by spontaneous ignition, the other as a model of deflagration wave involving kinetics/diffusion coupling. We explore different aspects of the system dynamics such as the relative role of diffusion and kinetics, the evolution of kinetic eigenvalues, and of the tangential stretching rates computed by accounting for the combined action of diffusion and kinetics as well for kinetics only. We propose criteria based on the TSR concept which allow to identify the most ignitable conditions and to discriminate between spontaneous ignition and deflagration front. [ABSTRACT FROM AUTHOR]

The effect of selected additives on the ignition delay of ethanol (EtOH)/air and dimethylether (DME)/air mixture is investigated. Computational Singular Perturbation (CSP) tools are utilized in an effort to determine algorithmically which species to select as additives and it is established that CSP can identify species whose addition to the mixture can affect ignition delay. However, this is not a necessary condition for additives to be effective. Additives that are not identified by CSP can have a substantial effect on ignition delay, provided that they drastically alter the prevailing chemistry, by altering the instant in time when the thermal runaway regime develops. Some of the additives that were studied computationally are unstable radicals whose injection in practical mixtures is unrealistic. However, chemically stable, relatively light species were also determined that can drastically affect ignition delay, such as hydrogen peroxide, formaldehyde and acetaldehyde. [ABSTRACT FROM AUTHOR]

The dynamics of n -heptane/air mixtures in perfectly stirred reactors (PSR) is investigated systematically using bifurcation and stability analysis and time integration. A skeletal mechanism of n -heptane constructed by entropy production analysis is employed, which is extensively validated for different conditions with respect to the ignition delay time, laminar flame speed, and the typical hysteretic behavior observed in PSRs. The significantly reduced size of the skeletal mechanism, enables the extension of the bifurcation analysis to multiple parameters. In addition to residence time, the effect of equivalence ratio, volumetric heat loss and the simultaneous variation of residence time and inlet temperature on the reactor state are investigated using one- and two-parameter continuations. Multiple ignition and extinction turning points leading to steady state multiplicity and oscillatory behavior of both the strongly burning and the cool flames are found, which can lead to oscillatory (dynamic) extinction. The two-parameter continuations revealed isolas and codimension-two bifurcations (cusp, Bogdanov–Takens, and double Hopf). Computational Singular Perturbation (CSP) and entropy production analysis were used to probe the complex kinetics at interesting points of the bifurcation diagrams. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The reactions responsible for the initial development of the time scale that characterizes the autoignition of a homogeneous stoichiometric CH4/air mixture are identified algorithmically using the computational singular perturbation method. The analysis considers a wide range of initial temperatures and pressures, located below and above the explosion limit. The major role of reactions CH3 + O2 → CH3O + O (at high temperatures), CH3 + O2 → CH2O + OH (at low temperatures), and CH2O + O2 → HCO + HO2 (at intermediate temperatures) is identified. The results provide some additional insights regarding the significance to the initiation of the process of some reactions that are generally considered to become active at later times [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

The operator-splitting schemes for integration of stiff diffusion–reaction systems were found to fail in error control, i.e. incurring O (1) relative errors, with splitting time steps larger than that required for fully explicit integration, when significant non-chemical radical sources are present. It was shown that, by excluding the transport term from the chemistry integration, errors by orders of magnitude may occur in radical concentrations solved in the chemistry sub-step, resulting in significant errors in the major species. The failing scenario is demonstrated with a toy problem and an unsteady perfectly-stirred reactor (PSR) for hydrogen/air with significant H radical concentration at inlet. A dynamic adaptive method for hybrid integration (AHI) of stiff chemistry is then proposed as a substitute for the operator-splitting schemes in such cases. The AHI method can obtain accurate solutions by integrating the fast species and reactions implicitly and the non-stiff terms, including slow reactions and non-chemical source terms, explicitly. Specifically, fast species and reactions are identified on-the-fly based on their analytically derived timescales, the rates of slow variables are evaluated explicitly and those of fast species are evaluated partial-implicitly. As such, the number of variables to be implicitly solved at each integration time step is reduced to the number of the fast species, resulting in a smaller Jacobian matrix and consequently lower computational cost compared with the fully implicit solvers. The hybrid method is validated in auto-ignition for hydrogen/air with different equivalence ratios and initial temperatures, and compared with the Strang splitting scheme for the toy problem and the unsteady PSR. Results show significant improvement in accuracy using the AHI method. [ABSTRACT FROM AUTHOR]

Transient two-dimensional simulations of fuel-lean H 2 /air combustion were performed in a 2-mm-height planar channel coated with platinum, using detailed hetero-/homogeneous chemistry and transport as well as heat conduction in the solid wall. The developed model resolved, for the first time, all relevant spatiotemporal scales in a practical channel-flow reactor configuration. A parametric study was carried out to investigate the effects of wall material, inlet velocity, and inlet temperature on the fundamental catalytic and gas-phase combustion processes. Computational singular perturbation (CSP) analysis identified the key catalytic reactions affecting light-off and homogeneous ignition. Homogeneous ignition crucially depended on the OH desorbing fluxes from the catalyst, while flame propagation and stabilization involved time scales of a few milliseconds. During the short duration of the light-off event, the ensuing Stefan velocity appreciably altered the flow field. Predictions of time accurate numerical simulations were further compared against those of a code relying on the quasisteady state assumption, and the specific conditions under which the latter was invalidated were identified. Finally, CSP analysis unraveled the reasons for the high computational cost of the fully transient 2-D simulations. The surface reaction mechanism exhibited a high stiffness with fastest time scales of the order of 10 - 12 s, pertaining to the hydrogen adsorption and to the H(s) + O(s) = OH(s) + Pt(s) reactions. These time scales were in turn six orders of magnitude shorter than the ones associated with gas-phase chemistry or with a simplified single-step catalytic reaction. [ABSTRACT FROM AUTHOR]

Abstract: The dynamics and stabilization of fuel lean premixed /air atmospheric pressure flames in meso-scale channels were investigated numerically, using detailed gas phase chemistry and transport. Experiments in a channel flow reactor by means of chemiluminescence detection of the excited OH radical allowed for model validation at steady conditions and identification of the conditions at which unsteady flame dynamics were present. A detailed parametric study of the influence of wall temperature and ratio on the ensuing flame dynamics was performed. The numerical results revealed different flame modes which included oscillatory ignition, random ignition spots, as well as steady weak and V-shaped flames. The wall temperature stability intervals of these modes changed with the ratio. The richest variety was found for molar ratios between 4 and 10, while at lower ratios the random and the weak modes were absent. At higher ratios all the dynamic modes were suppressed. The Computational Singular Perturbation (CSP) method was used to obtain insights into the physicochemical processes responsible for the weak flames, which were found at relatively high inflow velocities compared to previous studies, and V-shaped flames. A kinetic explanation of the phenomena was supported by the CSP analysis. [Copyright &y& Elsevier]

Detailed chemical kinetic models coupled with transport process models require tremendous computational resources in numerical simulation of reactive flows. In order to reduce the computational cost in numerical simulations, skeletal and reduced chemical kinetics mechanisms are used instead of detailed chemical kinetics mechanism. The Directed Relation Graph (DRG) method is applied to GRI-3 kinetics mechanism for a spatially homogeneous constant-pressure model of methane/air autoignition at 1 atm pressure, 1000 k initial temperature and equivalence ratio of 1. The algorithm is used to identify species which their presence has little effect on the final results. These species are referred to as unimportant. The elementary reactions containing the unimportant species are eliminated from kinetics mechanism. The DRG simulation results are compared and validated by detailed chemical kinetics results. Also the results are compared with Computational Singular Perturbation method (CSP) which identifies unimportant elementary reactions. DRG method proved to be computationally more efficient, since it eliminates unimportant species instead of elementary reactions from the full mechanism as in CSP. [ABSTRACT FROM AUTHOR]

Abstract: The results of a detailed, step-by-step, asymptotic analysis of the signaling system are reported, in the case where the system exhibits limit cycle behavior. The analysis is based on the dimensional form of the model and exploits the various fast/slow time scale gaps that develop as the solution evolves along the limit cycle. It is shown that under the action of fast time scales of dissipative character, the limit cycle is confined on a low-dimensional surface in the phase space. The cycle can be divided in three parts, each one related to a different characteristic time scale. The first part refers to the slow rate of release in the cytoplasm. The second part refers to the even slower rate by which the free enters into the nucleus. The last part refers to the fast rate by which the nuclear is first produced and then depleted. It is demonstrated that these and many other findings (regarding the fast variables, the equilibrated fast processes, the rate limiting and/or driving steps, etc.) can be acquired by simple algorithmic tools. [Copyright &y& Elsevier]

Abstract: In the last decade, the interest towards non-petroleum based fuels is strongly increased due to the current concerns about the impact of the transport system on atmospheric pollutions, mainly due to CO2 emissions. Ethanol, either blended with conventional fuels or in its pure form, is one of such fuels already in use in the automotive industries. As an example, the flex-fuel engines are designed to employ gasoline from 10% up to 85% of ethanol (E10, E85). In this work, the oxidation kinetics of ethanol with air has been considered and analyzed in an ambient at high pressure, ranging from 4 to 6MPa, by means of a Computational Singular Perturbation methodology. This study starts from a detailed kinetic reaction mechanism, which is extensively used in the literature and is made up by 235 reversible reactions among 46 chemical species. This mechanism has been used to get several families of simplified (skeletal) mechanisms by considering equivalence ratios in the range 0.2–2.0 and two sets of initial temperatures (900–1200K and 1200–1700K). The skeletal mechanisms have been validated by comparing the temperature and major chemical species profiles and the ignition delay time with those obtained by employing the detailed mechanism. Advantages and limitations of these mechanisms are highlighted. The accuracy of the skeletal mechanisms is very good in the range of equivalence ratio and temperature considered in the simplification procedure. Moreover, it is shown that a further simplification of the reaction mechanism is obtained by narrowing the range of equivalence ratio instead of the range of temperature. The most simplified skeletal mechanisms show an error in the prediction of temperature and fuel profiles lower than 3%, except for the case of low temperature and lean mixtures, where the maximum error increases up to 14%. Finally, the main reaction pathways are analyzed to show how the most important intermediate chemical species and products characterize the skeletal mechanisms for different values of equivalence ratio and temperature. The skeletal mechanisms are given as Supplementary data. The reader can refer to such data for the entire set of the retained reactions and species for each skeletal mechanism. [Copyright &y& Elsevier]

Abstract: To provide insights into auto-ignition characteristics in low temperature combustion (LTC) engine conditions, computational singular perturbation (CSP) analysis is used to gain fundamental understanding into classification of ignition regimes in n-heptane air mixtures in the presence of temperature and composition inhomogeneities. Parametric studies are conducted using high-fidelity simulations with detailed chemistry and transport. In particular, a key interest is to understand different ignition behavior of the n-heptane mixture at the negative-temperature coefficient (NTC) versus the non-NTC conditions. The CSP analysis for the reference homogeneous system yields the number of exhausted modes (M) at various stages during the ignition event. In addition, the merging of two explosive modes is observed at the onset of auto-ignition. For the one-dimensional system, the M profiles along with the importance index (IT ) measured in the upstream of the ignition front are used to determine whether the front propagation is the spontaneous (IT →0) or deflagrative (IT →1) regime. At the relatively large temperature fluctuation considered herein, the mixture at non-NTC conditions shows initially a deflagration front which is subsequently transitioned into a spontaneous ignition front. For the mixtures at the NTC conditions which exhibit two-stage ignition behavior, the 1st stage ignition front is found to be more likely in the deflagration regime. On the other hand, the 2nd stage ignition front occurs almost always in the spontaneous regime because the upstream mixture contains active radical species produced by the preceding 1st stage ignition front. The effects of differently correlated equivalence ratio stratification are also considered and the results are shown to be consistent with previous findings. [Copyright &y& Elsevier]

Abstract: Currently, most detailed chemical kinetic mechanisms for combustion are still not comprehensive enough and update of key reaction rate is still required to improve the combustion mechanisms. The development of systematic mechanism reduction methods have made significant progress, and have greatly facilitated analysis of the reaction mechanisms and identification of important species and key reactions. In the present work, time-integrated element flux analysis is employed to analyze a skeletal combustion mechanism of a tri-component kerosene surrogate mixture, consisting of n-decane, n-propylcyclohexane, and n-propylbenzene. The results of element flux analysis indicate that major reaction pathways for each component in the surrogate model are captured by the skeletal mechanism compared with the detailed mechanism. After that, sensitivity analysis (SA) and chemical explosive mode analysis (CEMA) are conducted to identify the dominant ignition chemistry. The SA and CEMA results demonstrate that the ignition of n-decane and n-propylcyclohexane is sensitive only to the oxidation chemistry of H2/CO and C1–C4 small hydrocarbons, while the ignition of n-propylbenzene is very sensitive to the initial reactions of n-propylbenzene and related aromatic intermediates. This demonstrates that the hierarchic structure should be maintained in the reduction of detailed mechanism of substituted aromatic fuels. The skeletal mechanism is further reduced by combining the computational singular perturbation (CSP) method and quasi steady state approximation (QSSA). A 34-species global reduced mechanism is obtained and validated over a wide range of parameters for ignition. [Copyright &y& Elsevier]

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H2–air and CH4–air ignition, over a range of initial conditions. For CH4–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy. [ABSTRACT FROM PUBLISHER]

Abstract: The computational singular perturbation (CSP) technique is applied as an automated diagnostic tool to classify ignition regimes encountered in homogeneous charge compression ignition (HCCI) engines. Various model problems representing HCCI combustion are simulated using high-fidelity computation with detailed chemistry for hydrogen–air system. The simulation data are then analyzed by CSP. In a homogeneous system, the occurrence of two branches of explosive eigenvalues characterizes chain-branching and thermal ignition. Their merging point serves as a good indicator of the completion of the explosive stage of ignition. However, the merging point diagnostics is insufficient to differentiate spontaneous ignition from deflagration. As an alternate method, the active reaction zones are first identified by the locus of minimum number of fast exhausted time scales (based on user-specified error thresholds). Subsequently, the relative importance of transport and chemistry is determined in the region ahead of the reaction zone. A new index I T , defined as the sum of the absolute values of the importance indices of diffusion and convection of temperature to the slow dynamics of temperature, serves as a criterion to differentiate spontaneous ignition from deflagration regimes. These diagnostic tools are applied to 1D and 2D ignition problems under laminar and turbulent mixture conditions, respectively, allowing automated detection of different ignition regimes at different times and location during the ignition events. The implication of the results in the context of modeling autoignition of nearly homogeneous turbulent mixtures is discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: An automated procedure has been previously developed to generate simplified skeletal reaction mechanisms for the combustion of n-heptane/air mixtures at equivalence ratios between 0.5 and 2.0 and different pressures. The algorithm is based on a Computational Singular Perturbation (CSP)-generated database of importance indices computed from homogeneous n-heptane/air ignition solutions. In this paper, we examine the accuracy of these simplified mechanisms when they are used for modeling laminar n-heptane/air premixed flames. The objective is to evaluate the accuracy of the simplified models when transport processes lead to local mixture compositions that are not necessarily part of the comprehensive homogeneous ignition databases. The detailed mechanism was developed by Curran et al. and involves 560 species and 2538 reactions. The smallest skeletal mechanism considered consists of 66 species and 326 reactions. We show that these skeletal mechanisms yield good agreement with the detailed model for premixed n-heptane flames, over a wide range of equivalence ratios and pressures, for global flame properties. They also exhibit good accuracy in predicting certain elements of internal flame structure, especially the profiles of temperature and major chemical species. On the other hand, we find larger errors in the concentrations of many minor/radical species, particularly in the region where low-temperature chemistry plays a significant role. We also observe that the low-temperature chemistry of n-heptane can play an important role at very lean or very rich mixtures, reaching these limits first at high pressure. This has implications to numerical simulations of non-premixed flames where these lean and rich regions occur naturally. [Copyright &y& Elsevier]

Abstract: A criterion based on computational singular perturbation (CSP) is proposed to effectively distinguish the quasi steady state (QSS) species from the fast species induced by reactions in partial equilibrium. Together with the method of directed relation graph (DRG), it was applied to the reduction of GRI-Mech 3.0 for methane oxidation, leading to the development of a 19-species reduced mechanism with 15 lumped steps, with the concentrations of the QSS species solved analytically for maximum computational efficiency. Compared to the 12-step and 16-species augmented reduced mechanism (ARM) previously developed by Sung, Law & Chen, three species, namely O, CH3OH, and CH2CO, are now excluded from the QSS species list. The reduced mechanism was validated with a variety of phenomena including perfectly stirred reactors, auto-ignition, and premixed and non-premixed flames, with the worst-case error being less than 10% over a wide range of parameters. This mechanism was then supplemented with the reactions involving NO formation, followed by validations in both homogeneous and diffusive systems. [Copyright &y& Elsevier]

Abstract: A 55-species reduced mechanism for n-heptane oxidation was derived from a 188-species skeletal mechanism, which was previously obtained from a detailed mechanism consisting of 561 species using a directed relation graph (DRG). This reduced mechanism was derived by first obtaining a skeletal mechanism with 78 species using DRG-aided sensitivity analysis. The unimportant reactions were eliminated by using the importance index defined in computational singular perturbation (CSP), with a newly posited restriction to treat each reversible reaction as a single reaction. An isomer lumping approach, also developed in the present study, then groups the isomers with similar thermal and diffusion properties so that the number of species transport equations is reduced. It was found that the intragroup mass fractions of the isomers can be approximated as constants in the present reduced mechanism, leading to a 68-species mechanism with 283 elementary reactions. Finally, 13 global quasi-steady-state species were identified using a CSP-based time-scale analysis, resulting in the 55-species reduced mechanism, with 283 elementary reactions lumped into 51 semiglobal steps. Validation of the reduced mechanism shows good agreement with the detailed mechanism for both ignition and extinction phenomena. The inadequacy of the detailed mechanism in predicting the experimental laminar flame speed is also demonstrated. [Copyright &y& Elsevier]

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption–desorption, surface diffusion, and phase transitions. [ABSTRACT FROM AUTHOR]

Abstract: We use a procedure based on the decomposition into fast and slow dynamical components offered by the Computational Singular Perturbation (CSP) method to generate automatically skeletal kinetic mechanisms for the simplification of the kinetics of n-heptane oxidation. The detailed mechanism of the n-heptane oxidation here considered has been proposed by Curran et al. and involves 561 species and 2538 reactions. After carrying out a critical assessment of important aspects of this procedure, we show that the comprehensive skeletal kinetic mechanisms so generated are able to reproduce the main features of n-heptane ignition at various initial pressures and temperatures and equivalence ratios. A by-product of the algorithm that generates the skeletal mechanisms is the identification of the network of important species and reactions at a given state of the kinetic system. The analysis of this network is carried out by resorting to a visual representation of the pathways at selected time instants of the ignition process. Visual inspection of the pathways enables the identification and comparison of the relevant kinetic processes as obtained at different ignition regimes. The graphs are generated by interfacing the model reduction procedure with the open-source package graphviz. [Copyright &y& Elsevier]

A differential system that models the circadian rhythm in Drosophila is analyzed with the computational singular perturbation (CSP) algorithm. Reduced nonstiff models of prespecified accuracy are constructed, the form and size of which are time-dependent. When compared with conventional asymptotic analysis, CSP exhibits superior performance in constructing reduced models, since it can algorithmically identify and apply all the required order of magnitude estimates and algebraic manipulations. A similar performance is demonstrated by CSP in generating data that allow for the acquisition of physical understanding. It is shown that the processes driving the circadian cycle are (i) mRNA translation into monomer protein, and monomer protein destruction by phosphorylation and degradation (along the largest portion of the cycle); and (ii) mRNA synthesis (along a short portion of the cycle). These are slow processes. Their action in driving the cycle is allowed by the equilibration of the fastest processes; (1) the monomer dimerization with the dimer dissociation (along the largest portion of the cycle); and (2) the net production of monomer+dimmer proteins with that of mRNA (along the short portion of the cycle). Additional results (regarding the time scales of the established equilibria, their origin, the rate limiting steps, the couplings among the variables, etc.) highlight the utility of CSP for automated identification of the important underlying dynamical features, otherwise accessible only for simple systems whose various suitable simplifications can easily be recognized. [ABSTRACT FROM AUTHOR]

NO formation, which is one of the main disadvantages of ammonia combustion, was studied during the isochoric, adiabatic autoignition of ammonia/air mixtures using the algorithm of Computational Singular Perturbation (CSP). The chemical reactions supporting the action of the mode relating the most to NO were shown to be essentially the ones of the extended Zeldovich mechanism, thus indicating that NO formation is mainly thermal and not due to fuel-bound nitrogen. Because of this, addition of water vapor reduced NO formation, because of its action as a thermal buffer, but increased ignition delay, thus exacerbating the second important caveat of ammonia combustion, which is unrealistically long ignition delay. However, it was also shown that further addition of just 2% molar of H2O2 does not only reduce the ignition delay by a factor of 30, but also reverses the way water vapor affects ignition delay. Specifically, in the ternary mixture NH 3 /H 2 O/H 2 O 2 , addition of water vapor does not prolong but rather shortens ignition delay because it increases OH radicals. At the same time, the presence of H 2 O 2 does not affect the influence of H 2 O in suppressing NO generation. In this manner, we were able to show that NH 3 /H 2 O/H 2 O 2 mixtures offer a way to use ammonia as carbon-less fuel with acceptable NO x emissions and realistic ignition delay. [ABSTRACT FROM AUTHOR]

The dynamics of a homogeneous adiabatic autoignition of an ammonia/air mixture at constant volume was studied, using the algorithmic tools of Computational Singular Perturbation. Since ammonia combustion is characterized by both unrealistically long ignition delays and elevated NO x emissions, the time frame of action of the modes that are responsible for ignition was analyzed by calculating the developing time scales throughout the process and by studying their possible relation to NO x emissions. The reactions that support or oppose the explosive time scale were identified, along with the variables that are related the most to the dynamics that drive the system to an explosion. It is shown that reaction H 2 O 2 (+M) → OH + OH (+M) is the one contributing the most to the time scale that characterizes ignition and that its reactant H 2 O 2 is the species related the most to this time scale. These findings suggested that addition of H 2 O 2 in the initial mixture will influence strongly the evolution of the process. It was shown that ignition of pure ammonia advanced as a slow thermal explosion with very limited chemical runaway. The ignition delay could be reduced by more than two orders of magnitude through H 2 O 2 addition, which causes only a minor increase in NO x emissions. [ABSTRACT FROM AUTHOR]