Towards predictive combustion kinetic models: Progress in model analysis and informative experiments

One of the key tasks of combustion chemistry research is to develop accurate and robust combustion kinetic models for practical fuels. An accurate and robust kinetic model yields predictions that are highly consistent with experimental measurements over a wide range of operating conditions, with prediction uncertainties that are acceptable. Reliable experimental data generated by various powerful diagnostic techniques continue to play an essential role in the development of such models. This review focuses on the contributions of synchrotron-based species measurements in combustion systems, on model validation, model structure development, and model parameter optimization. Special emphasis is placed on recently reported strategies for informative and reliable experimental data generation, including combustion kinetic model input parameter evaluation, computational cost reduction for model analysis, model-analysis-based experimental design, experimental data treatment and error reduction. Particularly, the active-subspace-based method (ASSM) can reduce the dimensionality of combustion kinetic models and the aritificial-neural-network-based surrogates (ANN-HDMR and ANN-MCMC) can reduce the computational cost significantly. Global-sensitivity-based experimental design methods including sensitivity entropy and surrogate model similarity (SMS) can guide kinetics-information-enriched experimental data generation. Model-analysis-based calibration for experimental errors and feature extraction of experimental targets can improve the experimental data quality. A computational framework (OptEx) enabling the integration of experimental data with mechanism development, experimental design and model optimization, provides a new means to develop reliable kinetic models more efficiently and effectively.     

Spectral uncertainty quantification, propagation and optimization of a detailed kinetic model for ethylene combustion

The ability of a reaction model to predict the combustion behavior of a fuel relies on the rigorous quantification of the kinetic rate parameter uncertainty. Although the accuracy of a detailed kinetic model may be ensured, in principle, by a multi-parameter optimization, the inherent uncertainties in the fundamental combustion targets used for optimization cause the resulting optimized model to be characterized by a finite kinetic parameter space. In this work, spectral expansion techniques are developed and employed to quantify these uncertainties, using an as-compiled, detailed, H₂/CO/C₁-C₄ kinetic model for ethylene combustion as an example. Uncertainty was quantified for both the as-compiled model and the optimized model, and propagated into a wide variety of combustion experiment and conditions. Application of the spectral uncertainty method in mechanism reduction is also discussed.     

Friction-induced vibration: Quantifying sensitivity and uncertainty

The limited success of predictive models of friction-induced vibration can, in part, be attributed to the inherent sensitivity of friction-coupled systems to variations, often uncontrolled, in parameter values such as the friction coefficient. This paper explores the sensitivity and uncertainty of predictions from a modal point of view, using models of a realistic complexity. A method for efficiently estimating prediction error bounds is presented and validated using representative parametric uncertainties. Measurement uncertainties are quantified providing an input for the error-bound analysis. Taken together, this forms the foundation for a direct comparison of predictions with experimental results from sliding contact tests.     

Evaluation of reduced combustion kinetic mechanisms using global sensitivity-based similarity analysis (GSSA)

Reduced combustion kinetic mechanisms, instead of detailed ones, are often used in computational fluid dynamics (CFD) simulations for reduced and frequently even affordable computational cost. The criterion for the evaluation of a reduced mechanism usually focuses on its prediction error for the global properties such as the ignition delay time, while ignoring the detailed features of reaction kinetics such as reaction pathways. In our opinion, good reduced mechanisms should have similar predicting behaviors as the detailed ones, and these behaviors include model predictions for specific targets, prediction error bars, and uncertainty sources for the errors. In this work, a new approach using global sensitivity-based similarity analysis (GSSA) is proposed to compare reduced mechanisms with detailed ones. The similarity coefficient for the reduced mechanism is calculated by similarity method based on Euclidean distance between sensitivity indices of the reduced mechanism and those of the detailed mechanism. The larger the similarity coefficient, the higher the degree of similarity between the reduced and detailed mechanisms. To demonstrate this similarity method, directed relation graph with error propagation (DRGEP) is employed to simplify both the GRI 3.0 mechanism without the NOx chemistry and the JetSurF mechanism consisting of 1459 reactions, resulting in reduced mechanisms with different sizes which can accurately predict the ignition delay times for corresponding fuel mixtures. Similarity analysis is then employed to evaluate these reduced mechanisms. The result shows that the actual reaction kinetic features cannot be replicated by some of the reduced mechanisms. First, the rankings of the important reactions obtained by reduced mechanisms are not consistent with those obtained by the detailed mechanism. Second, by investigating the sensitive reactions, the actual impact of uncertainties in reaction rates on the ignition delay times cannot be presented by reduced mechanisms. The similarity analysis on reduced mechanisms can be used to select a reduced mechanism which shows much better performance to replicate the actual combustion reaction kinetics. GSSA can provide information on the uncertainty sources induced by the reactions parameters of reduced mechanisms for target predictions, which is important for further reduced model optimization and for the sensitivity analysis of CFD simulations.     

Adjoint sensitivity analysis of kinetic,thermochemical, and transport data of nitrogen and ammonia chemistry

Many studies apply sensitivity analysis to explore the impact of reaction kinetic parameters on model predictions. The importance of thermochemical and transport data is often assumed to be relatively low. While this is true for specific combustion properties of hydrocarbons, the role of thermochemical and transport data in combustion processes of nitrogen-containing molecules remains to be investigated. Thus, this work applies adjoint sensitivity analysis to the complete set of parameters in combustion models, i.e., kinetics, thermodynamics, and transport data. This integral approach increases the number of parameters considered in the sensitivity analysis drastically. Compared to forward sensitivity analysis, the adjoint approach is very efficient for a large number of parameters, and analysis with several thousand parameters can be performed in seconds. Nitrogen oxide formation in methane/air flames and laminar burning velocities of ammonia/air flames are considered as prediction targets. Sensitivity analysis results for kinetic, thermochemical, and transport data are compared by jointly considering all appearing parameter uncertainties. The comparison reveals that, due to their importance for the equilibrium constants of elementary reactions, the optimization potential of thermodynamic properties is often similarly high as that of the kinetics parameters. Transport parameters are found to be of the lowest priority for the model development due to their low uncertainties, even though high sensitivities are determined for several of them. More specifically, the analysis for the laminar burning velocities of ammonia/air flames reveals a high optimization potential for parameters in the N₂-amine chemistry, including the molar heat capacities of N₂H₂, N₂H₃, and NH. Interestingly, analyses with different mechanisms reveal strongly diverging results, especially regarding the importance of reactions with OH, which is uncommon when considering the combustion of hydrocarbons.     

From inherent correlation to constrained measurement: Model-assisted calibration in MBMS experiments

Synchrotron-based molecular-beam mass spectrometry (MBMS) can provide detailed species-resolved information to help develop, validate and optimize combustion kinetic models. While quantification of stable species can be achieved within 30% uncertainty, the measured mole fractions of reactive intermediates often have large systematic errors, mainly due to the large uncertainties associated with estimated photoionization cross sections. These measurements are therefore less effective in improving the model accuracy, and it remains a challenge to make full use of those data for important reactive intermediates with relatively large uncertainties. In the present work, we propose a model-assisted calibration method to reduce the uncertainty of the measurements for those reactive species in the MBMS experiments. The method takes advantage of the inherent correlation of the systematic uncertainty in the MBMS measurements and uses the accurate model predictions to calibrate the correlated experimental data. By global uncertainty analysis, the kinetic model for the methanol/O₂ flame was analyzed to select the optimal experimental conditions for which the model prediction of the hydroxymethyl radical (CH₂OH) has the smallest uncertainty. Then the correlation factor for the systematic uncertainty is determined by analyzing the new measurement and the model prediction under the designed condition. The correlation factor determined has been successfully used to calibrate the peak mole fraction of the CH₂OH radical in a laminar premixed methanol flame, reported earlier.     

A novel linear transformation model for the analysis and optimisation of chemical kinetics

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH₃(+M)?CH₄(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.     

Small scales,many species and the manifold challenges of turbulent combustion

A major goal of combustion research is to develop accurate, tractable, predictive models for the phenomena occurring in combustion devices, which predominantly involve turbulent flows. With the focus on gas-phase, non-premixed flames, recent progress is reviewed, and the significant remaining challenges facing models of turbulent combustion are examined. The principal challenges are posed by the small scales, the many chemical species involved in hydrocarbon combustion, and the coupled processes of reaction and molecular diffusion in a turbulent flow field. These challenges, and how different modeling approaches face them, are examined from the viewpoint of low-dimensional manifolds in the high-dimensional space of chemical species. Most current approaches to modeling turbulent combustion can be categorized as flamelet-like or PDF-like. The former assume or imply that the compositions occurring in turbulent combustion lie on very-low-dimensional manifolds, and that the coupling between turbulent mixing and reaction can be parameterized by at most one or two variables. PDF-like models do not restrict compositions in this way, and they have proved successful in describing more challenging combustion regimes in which there is significant local extinction, or in which the turbulence significantly disrupts flamelet structures. Advances in diagnostics, the design of experiments, computational resources, and direct numerical simulations are all contributing to the continuing development of more accurate and general models of turbulent combustion.     

Iterative model-based experimental design for efficient uncertainty minimization of chemical mechanisms

The uncertainties of chemical kinetic model parameters induce uncertainties in model predictions. Automatic optimization and uncertainty minimization techniques have been developed to constrain these uncertainties based on sets of experimental target data for quantities of interest. While such methods were frequently used to optimize models for relatively well-studied systems with large numbers of available targets, only few of these experimental data points may be of crucial importance. In addition, for novel fuel candidates such as biofuels and synthetic fuels, the number of available measurements is generally limited. Thus, an important aspect to be explored in this context is the number of experimental data points required to achieve a certain degree of uncertainty reduction, and the determination of optimal experimental conditions for these. To target this question, a model-based experimental design framework based on the criterion of D-optimality is used in the present work to automatically identify these optimal conditions. As an example, the auto-ignition of dimethyl ether is investigated. The majority of experiments with high priority cover the intermediate- and low-temperature regimes, where the employed prior model exhibits the largest prediction uncertainties. It is also found that 90 % of the maximum observed reduction of average prediction uncertainty in ignition delay times can be achieved based on only the ten most informative experiments alone. The results thus demonstrate that few well-selected measurements allow for efficient model uncertainty reduction, and the employed approach provides an effective means of identifying the optimal conditions, which is useful for further experimental investigation. On the other hand, the inclusion of more experiments into the calibration process still provides additional benefit in terms of the posterior uncertainties of a number of important model parameters, which points to the importance of taking such data into account in case of their availability.     

Mind the gap: Turbulent combustion model validation and future needs

This overview collects a range of well characterized experiments used in the step-wise validation of turbulent combustion models, from gas phase non-premixed jet flames to spray flames, and from simple symmetric jets to real device geometries, focusing primarily on statistically steady state experiments. We discuss how the experiments and models are constructed, approaches to modelling, and the tradeoffs between the level of detail and computational demands. The review highlights a number of experiments used for benchmarking models, selecting a few examples where models have clearly succeeded, as well as some areas where there are clear needs in the experimental database. In particular, the areas of turbulent spray combustion and soot prediction, as well as combustion under high pressures appear as the least developed and present the clearest gaps for both models and experiments. Based on the successful application of advanced methods of uncertainty quantification to a number of problems in reacting flows, we suggest that these methods might be used to advantage in the design of experiments. This would enable an upfront examination of the extent to which comparisons between measurable scalars and velocities allow clear distinction between model features.     

Health risk assessment for nanoparticles: A case for using expert judgment

Uncertainties in conventional quantitative risk assessment typically relate to values of parameters in risk models. For many environmental contaminants, there is a lack of sufficient information about multiple components of the risk assessment framework. In such cases, the use of default assumptions and extrapolations to fill in the data gaps is a common practice. Nanoparticle risks, however, pose a new form of risk assessment challenge. Besides a lack of data, there is deep scientific uncertainty regarding every aspect of the risk assessment framework: (a) particle characteristics that may affect toxicity; (b) their fate and transport through the environment; (c) the routes of exposure and the metrics by which exposure ought to be measured; (d) the mechanisms of translocation to different parts of the body; and (e) the mechanisms of toxicity and disease. In each of these areas, there are multiple and competing models and hypotheses. These are not merely parametric uncertainties but uncertainties about the choice of the causal mechanisms themselves and the proper model variables to be used, i.e., structural uncertainties. While these uncertainties exist for PM2.5 as well, risk assessment for PM2.5 has avoided dealing with these issues because of a plethora of epidemiological studies. However, such studies don’t exist for the case of nanoparticles. Even if such studies are done in the future, they will be very specific to a particular type of engineered nanoparticle and not generalizable to other nanoparticles. Therefore, risk assessment for nanoparticles will have to deal with the various uncertainties that were avoided in the case of PM2.5. Consequently, uncertainties in estimating risks due to nanoparticle exposures may be characterized as ‘extreme’. This paper proposes a methodology by which risk analysts can cope with such extreme uncertainty. One way to make these problems analytically tractable is to use expert judgment approaches to study the degree of consensus and/or disagreement between experts on different parts of the exposure–response paradigm. This can be done by eliciting judgments from a wide range of experts on different parts of the risk causal chain. We also use examples to illustrate how studying expert consensus/disagreement helps in research prioritization and budget allocation exercises. The expert elicitation can be repeated over the course of several years, over which time, the state of scientific knowledge will also improve and uncertainties may possibly reduce. Results from expert the elicitation exercise can be used by risk managers or managers of funding agencies as a tool for research prioritization.     

High-efficiency design of combustion kinetic experiments based on genetic algorithm

Experimental data is essential for the improvement of combustion kinetic models. Experimental design based on model analysis results can screen optimal experimental conditions with maximum information content. However, the computational cost of designing experiments by enumeration becomes unaffordable when an enormity of conditions with different temperatures/pressures/mixtures are to be investigated. An approach to facilitate the efficient discovery of optimal experimental conditions based on the genetic algorithm (GA) is proposed in this work. This approach regards the task of experimental design as an optimization problem to minimize an objective function that measures the information content provided by an experiment. The sensitivity entropy and surrogate model similarity are combined to form the objective function of optimization. Three designs of dimethyl ether experiments are provided to demonstrate the approach. The first case utilizes a benchmark for optimal experiments to validate the effectiveness of GA. The results show that GA can achieve better design results than the traditional enumeration strategy with less than 10% computational cost. The second case illustrates how GA is applied in the design of multiple experiments. The last one is an application in designing multiple experiments of various types, including ignition, species measurements in a jet-stirred reactor (JSR) and a plug flow reactor (PFR). The model parameters are calibrated with the designed experimental data using a Bayesian-based optimization approach. The uncertainties of model parameters are significantly reduced after the optimization.     

A normalised residence time transport equation for the numerical simulation of combustion with high-temperature air

This study concerns the numerical simulation of turbulent non-premixed combustion in highly preheated air streams. One of the objectives is to settle an efficient computational procedure to proceed with the numerical simulation of large-scale industrial devices. It is also expected that the availability of such a computational framework may facilitate comprehensive sensitivity analyses as well as the development of mathematical models able to represent turbulence-chemistry interactions (TCI) in such conditions. Based on the salient physical ingredients that characterise scalar mixing, propagation, and self-ignition processes, a turbulent combustion modelling framework is thus introduced and applied to the numerical simulation of well-documented laboratory flames. In the corresponding geometries, the bulk flow velocities of the reactants streams can reach rather large values, which lead the flame to lift from the burner rim. Partially premixed flame edges thus stabilise the whole flame structure and the temperature of the oxidising stream can be increased by vitiation with burned gases so as to promote the corresponding flame-stabilisation processes. For sufficiently large values of the vitiated airstream temperature, self-ignition mechanisms may be triggered thus leading to a competition between mixing, propagation, and ignition processes. In this context, the ratio of the residence time to the self-ignition delay is thought to be a relevant variable to delineate the possible influence of ignition phenomena. Therefore, a modelled transport equation for this normalised residence time is considered. The performance of the corresponding modelling proposal is analysed with special emphasis placed on its ability to reproduce ‘memory’ or ‘lagrangian’ effects related to thermal aging processes. In this respect, it is noteworthy that the present set of computations makes use of tabulated quantities associated to (i) steady laminar one-dimensional diffusion flamelets, so as to describe the composition of combustion products, (ii) steady laminar one-dimensional premixed flamelets, to describe the flame brush propagation, and (iii) temporal evolution of zero-dimensional homogeneous mixtures to account for the possible occurrence of self-ignition phenomena. In particular, the tabulated self-ignition time value is used to evaluate the increase in the normalised residence time. Finally, two modelling parameters are put into evidence and studied through a detailed sensitivity analysis.     

煤粉炉内辐射图象处理和燃烧过程数值模拟相结合初探

1引言大型电站锅炉炉膛内的燃烧过程是发生在相对较大空间内的、不断脉动的、具有强烈三维特征的复杂物理和化学过程。因为实际炉膛尺寸太大,以至于还没有建立适用的可视化技术手段[1],只能对其缩小了的模型在实验室进行研究[2.3]。作者在炉膛煤粉燃烧二维温度分布检测研究[4]的基础上,提出了以多幅辐射图像处理为基础的三维温度分布检测方法[5]。本文将建立较为严密的辐射图象信息同炉内燃烧过程的关系式,并借助燃烧过程数值模拟技术来估计炉内燃烧介质辐射特性参数非均匀分布,改进以辐射图象处理为基础的炉内三维燃烧温度分布检测方…     

Info-gap robust design with load and model uncertainties

This paper develops a new structural design concept which incorporates uncertainties in both the load and the structural model parameters. Info-gap models of uncertainty are used to represent uncertainty in the power spectral density of the load and in parameters of the vibration model of the structure. It is demonstrated that any design which optimizes functional performance will also minimize the robustness to uncertainty. Since uncertainties are prevalent in many applications, this paper argues that it is necessary to satisfy critical performance requirements (rather than to optimize performance), and to maximize the robustness to uncertainty. The design implications of this robust-satisficing approach are demonstrated with several heuristic structural design examples. It is shown that design preferences depend upon performance requirements: preferences between designs can be reversed when performance requirements change. Also, we show that the info-gap robustness function provides an attractive tool for adjudicating between conflicting objectives in multi-criteria design.     

多孔焦炭燃烧特性的模型构建及数值模拟

焦炭燃烧在固体含碳燃料燃烧进程中占有主导地位,常规燃烧温度范围内(1273～1700 K)的焦炭燃烧过程研究及其模型化对于燃烧设备的设计和优化具有重要的意义。本文根据实际炉内的炭粒燃烧情况,将焦炭燃烧的模拟过程分解成几个环节分别进行研究,即热解后焦炭的初始化学反应活性、焦炭燃烧中化学活性变化、外部氧的扩散对于内孔燃烧的影响,并给出了相关过程的模型计算式。通过与已有管式炉实验结果的比较,新模型的预测结果能较好地反映焦炭的真实燃烧状况。与目前常用的焦炭燃烧模型相比,本模型具备一定的燃料通用性,计算负荷低且能保持相当的预测精度,可耦合到大型燃烧计算程序之中,更为有效地指导实际燃烧设备的优化设计。     

A quantitative explanation for the apparent anomalous temperature dependence of OH + HO2 = H2O + O2 through multi-scale modeling

Kinetic models for complex chemical mechanisms are comprised of tens to thousands of reactions with rate constants informed by data from a wide variety of sources – rate constant measurements, global combustion experiments, and theoretical kinetics calculations. In order to integrate information from distinct data types in a self-consistent manner, a framework for combustion model development is presented that encapsulates behavior across a wide range of chemically relevant scales from fundamental molecular interactions to global combustion phenomena. The resulting kinetic model consists of a set of theoretical kinetics parameters (with constrained uncertainties), which are related through kinetics calculations to temperature/pressure/bath-gas-dependent rate constants (with propagated uncertainties), which in turn are related through physical models to combustion behavior (with propagated uncertainties). Direct incorporation of theory in combustion model development is expected to yield more reliable extrapolation of limited data to conditions outside the validation set, which is particularly useful for extrapolating to engine-relevant conditions where relatively limited data are available. Several key features of the approach are demonstrated for the H₂O₂ decomposition mechanism, where a number of its constituent reactions continue to have large uncertainties in their temperature and pressure dependence despite their relevance to high-pressure, low-temperature combustion of a variety of fuels. Here, we use the approach to provide a quantitative explanation for the apparent anomalous temperature dependence of OH + HO₂ = H₂O + O₂ – in a manner consistent with experimental data from the entire temperature range and ab initio transition-state theory within their associated uncertainties. Interestingly, we do find a rate minimum near 1200 K, although the temperature dependence is substantially less pronounced than previously suggested.     

An experimental and kinetic modeling study of a four-component surrogate fuel for RP-3 kerosene

Detailed high-fidelity kinetic models of fuels are of great significance by providing guidance for the improvement of the combustion performance in engines and promising the reduction of design cycle of new concept combustors. However, the kinetic modeling works on Chinese RP-3 kerosene, the most widely used civil aviation fuel in China, are meager to date. In this study, a kinetic model, including a surrogate fuel and its combustion kinetic mechanism, were developed to describe the combustion of RP-3. Firstly, a surrogate comprised of components n-dodecane, 2,2,4,6,6-pentamethylheptane (PMH), n-butylcyclohexane and n-butylbenzene (22.82/31.30/19.19/26.69 mol%) was proposed based on the combustion property target matching method. These components are all within the typical molecular size (C10-C14) of jet fuels and thereby can potentially improve the ability of the surrogate in emulating the properties that depend on molecular size. Experiments were then carried out in a heated rapid compression machine and a heated shock tube to evaluate the performance of the surrogate in reproducing the combustion behavior of the target fuel over wide conditions. It is found that the surrogate can reproduce the autoignition characteristics of RP-3 very well. A chemical kinetic mechanism was developed to describe the oxidation of this surrogate. This mechanism was assembled using a published n-butylbenzene sub-mechanism and our previous sub-mechanisms for the other pure components, and was assessed against the present experimental data. The results showed that the simulations agreed well with the experimental data under the investigated conditions, demonstrating that the composition of the surrogate and its mechanism are appropriate to describe the combustion of RP-3. The first-stage ignition negative temperature coefficient behavior and the evolution of key radicals were investigated using the kinetic model.