Experimental Design for Discrimination of Chemical Kinetic Models for

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Experimental design for discrimination of chemical kinetic models for oxy-methane combustion Liming Cai, Stephan Kruse, Daniel Felsmann, Christoph Thies, Kiran K. Yalamanchi, and Heinz Pitsch Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 25, 2017

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Experimental design for discrimination of chemical kinetic models for oxy-methane combustion Liming Cai,∗ Stephan Kruse, Daniel Felsmann, Christoph Thies, Kiran K. Yalamanchi, and Heinz Pitsch Institute for Combustion Technology, RWTH Aachen University, 52056 Aachen, Germany E-mail: [email protected]

Abstract The concept of combustion under oxy-fuel conditions has the potential to reduce greenhouse gas emissions. For the design of combustion devices operating under these conditions, a good understanding of fuel oxidation behavior in terms of chemical kinetic mechanisms is useful. For the oxidation of the main component of natural gas and coal devolatilization products, i. e. methane, various chemical mechanisms are available in the literature validated mostly with experiments using air, and none of them is developed particularly or has been validated extensively for oxy-methane combustion. An important prerequisite for model assessment is high-quality data typically obtained from resource- and time-consuming measurements. The aim of this study is to identify the best methane mechanism for oxy-fuel combustion from a set of models available in the literature with a minimum number of measurements. Five chemical models, which have been validated for the oxidation of methane/air mixtures, are compared in terms of their performance for extinction strain rates, ignition delay times, and laminar burning velocities of oxy-methane mixtures. A model-based experimental design method, i. e. Akaike Weights Design Criterion, is applied to determine the optimal potential measurements. Ideally, ∗ To

whom correspondence should be addressed

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at the conditions of designed experiments, model predictions are nicely separated and thus the best model can be identified by comparison with these measurements. It is shown that the employed experimental design strategy identifies informative experiments for model discrimination efficiently. While measurements of extinction strain rates are proposed to be carried out for flames with small methane mass fractions of the fuel stream and oxygen mass fractions of the oxidizer stream, shock tube experiments are evaluated as equally useful for model discrimination over the investigated range of conditions. Measurements of flame speeds are designed at very small and very large equivalence ratios particularly at relatively high pressures.

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Introduction Natural gas and coal are widely used energy resources for electric power generation. However, combustion of fossil fuels leads to emissions of the greenhouse gas CO2 , which causes global warming. Oxy-fuel combustion, where the fuel is burned with oxygen instead of with air, has been proposed as a technology for carbon capture and storage. 1 The advantage is that nitrogen is avoided and the combustion products therefore consist mostly of carbon monoxide and water, from which CO2 can be easily separated. Since temperatures for combustion with pure oxygen are quite high, the CO2 is typically partly recirculated into the oxidizer. As a consequence, combustion takes place in an O2 /CO2 atmosphere leading to different combustion behavior than in air. CO2 not only has different specific heat and effective Lewis number compared to nitrogen, it is also chemically more active. 2–4 The excess CO2 can participate in reactions either as a reactant or as a third body for collision and thus strongly affects fuel oxidation pathways. For example, the reaction of H radical with CO2 is promoted due to the CO2 enrichment. This reaction competes with the main chain branching reaction H + O2 → O + OH leading inevitably to a strong decrease of flame temperatures and fuel reactivity. As both natural gas and coal devolatilization products consist primarily of methane, the investigation of oxy-methane combustion is therefore of interest. Chemical kinetic mechanisms are often used in computational fluid dynamic (CFD) simulations to represent fuel combustion chemistry. Various kinetic models 5–9 have been proposed in the last twenty years for combustion of methane. While these detailed and reduced models have been extensively and successfully validated for chemical kinetic properties such as ignition delay times and burning velocities of methane/air mixtures over a range of conditions, their performance for oxy-methane combustion has been investigated in only very few studies 2,3 and remains largely unexplored. Due to the thermodynamic and chemical effects of CO2 addition, modifications of chemical mechanisms can be expected for improved model prediction accuracy. 10 Prior to model application in CFD simulations, chemical mechanisms should be validated over wide ranges of operating conditions, which requires large amounts of data from different experimental configurations. However, an alternative, advantageous validation approach is to perform 3


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limited but well-defined measurements to distinguish between different models and subsequently couple the best model with CFD simulations. At the conditions of the ideal experiments, the results for various models are very different from each other, so that the best model can be chosen by comparison with these experimental measurements. A careful choice of the type of measurement and the boundary conditions can reduce the number of time- and resource-consuming experiments. In addition, if the best model is accurate enough for the conditions of interest or is taken as the basis for further model refinement, the efforts of model development are also minimized. Experimental design techniques have been proposed in the past for this and other purposes. 11 While most of the experimental design methodologies fall into the category of model validation and calibration, 11 some techniques focus on model discrimination. The original idea of experimental design for model discrimination was proposed by Hunter and Reiner, 12 who designed experiments by maximizing prediction differences between two rival models. This concept was extended by a series of studies 13,14 to take various competing models and uncertainties of models as well as measurements into account. However, as the methods aim to maximize the overall differences between model predictions, they can preferentially select conditions, at which the results of a group of models are very similar, while they differ strongly from those of other models. Even though a global maximum can be reached at these conditions, this so-called model lumping phenomenon disables the discrimination between models within the group. Recently, Michalik et al. 15 developed a methodology based on the Akaike’s information criterion. The proposed Akaike Weights Design Criterion (AWDC) was shown to prevent model lumping successfully and to identify the best model structure very efficiently, even if numerous rival models were considered. Therefore, this method is employed in this work to distinguish between chemical models for oxy-methane combustion. The goal of this study is to select with a minimum number of experiments, the best chemical model for oxy-methane combustion from a set of models validated for methane/air combustion. Five chemical kinetic mechanisms, which have been successfully tested for methane oxidation under air conditions, are considered as candidates. 5–9 The model performance for extinction strain

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rates, ignition delay times, and burning velocities are of interest and thus will be considered in the experimental design procedure. The AWDC method scans that experimental design space to find the best future experiments and experimental conditions, for which the model predictions have a distribution that allows for a discrimination among them. In the present paper, three different experimental configurations are considered, including a counterflow diffusion flame setup to measure extinction strain rates, a shock tube to measure ignition delay times, and a spherical vessel for measuring laminar burning velocities. For each configuration, a different set of design parameters is specified. The presentation of the present paper is organized as follows: First, the setup of the counterflow burner is described. Then, the experimental design approach is introduced, followed by the details of the considered chemical mechanisms. Subsequently, the results of the experimental design are presented and the measured data sets are compared to the numerical results to identify the best model. The results are discussed in detail.

Counterflow setup The counterflow burner employed in this work is a modified version based on the design of Kortschik et al. 16 A schematic of the counterflow burner is shown in Figure 1. The fuel and oxidizer flows are introduced through two opposed vertical ducts with diameters of D = 27.6 mm adjusted to a nozzle separation distance of L = 13.75 mm. Both flows are shrouded by a nitrogen gas stream injected through a 5 mm wide ring around the nozzles. The nozzles feature an area contraction ratio of 9. Honeycombs are located in the wider section of each nozzle and serve as flow straighteners. Wired meshes are mounted 1 mm and 5 mm upstream of the nozzle exits to achieve homogeneous top-hat velocity profiles. The velocity profiles at the nozzle exits are detected by means of particle image velocimetry (PIV). The gas stream temperatures are detected by K-type thermocouples located close to the nozzle exit. In this study, the oxidizer flow introduced through the top nozzle consists of oxygen and carbon dioxide, which are mixed upstream of the burner

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inlet. To adjust the oxygen mass fraction in the oxidizer stream, mass flow controllers (MFC) of type Alicat MC-10SLPM and of type Alicat MC-20SLPM are used for the O2 and CO2 flows, respectively. The fuel flow is supplied through the bottom part of the burner. For an accurate control of the fuel mixture composition, two mass flow controllers MC-10SLPM and MC-20SLPM are mounted in the CH4 and CO2 lines, respectively. Flow rates are adjusted by mass flow controllers operated by a Lab-View based control-software. All MFCs have an accuracy of 0.8% of adjusted flows and 0.2% of full-scale flow rates.

Figure 1: Schematic illustration of the counterflow setup.

The exit velocity and temperature of the fuel stream are denoted by v1 and T1 , respectively, while the exit velocity of the oxidizer flow is denoted by v2 . According to Seshadri and Williams, 17 the characteristic strain rate of the oxidizer at the stagnation plane is calculated as, √ |v1 | ρ1 2|v2 | (1 + a= √ ), L |v2 | ρ2

(1)

where ρ1 and ρ2 indicate the density of fuel and oxidizer streams, respectively. For this study, flows are kept in momentum balance. Nozzle exit velocities are increased stepwise, until extinction is observed visually. The corresponding strain rate at extinction is then taken as the extinction strain rate. For validation of the present counterflow burner, the extinction strain rates of flames with CH4 /N2 flowing against air were measured at the conditions, where the literature data 2,18 are available. The measured results are compared to the literature data and good agreement is

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observed. Detailed information can be found in the Supplementary material. The uncertainties in the strain rates are mainly attributed to the errors of the mass flow controllers, as the flow rate is a function of the exit velocity. In addition, errors in the flow rates also induce uncertainties in the mixture compositions of the fuel and oxidizer flows. Based on the accuracies of the mass flow controllers, Monte-Carlo simulations are performed to determine the uncertainty distribution of the mixture compositions and the strain rate for each extinction point. Considering a 95% confidence interval of error distributions, the uncertainties in the extinction strain rate are below 3% and the errors in the fuel mass fraction are below 5% for all measurements.

Experimental design methodology AWDC criterion The basis of model-based experimental design methodologies is the choice of objective function used to assess “information content” of future experiments by using models. 11 The AWDC approach relies on the so-called Akaike information criterion (AIC), which is defined as: AIC = −2 log L(η j (e)|η obs , σ obs ) + 2K,

(2)

where K is the number of parameters in the model. The likelihood function L(η j (e)|η obs , σ obs ) is expressed as: n

L(η j (e)|η

obs

,σ

obs

)=∏ i=1

1 2π(σiobs )2

1/2

(ηiobs − ηi, j (ei ))2 exp − , 2(σiobs )2

(3)

where n experimental observations are available, with ηiobs referring to the ith experimental measurement, and σiobs is the uncertainty associated with this measurement. If m different chemistry models are being compared, the model prediction for the ith experiment by the jth model in this set

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of models is given by ηi, j (ei ). The experimental conditions are denoted by ei for the ith experiment. The model with the lowest AIC value is the one with the smallest loss of information and thus can be considered as the best model. 15 However, in the context of experimental design, the fundamental issue is that the experimental measurement, ηiobs , of a future experiment needed to assess the usefulness of that experiment, is not available. Therefore, based on the AIC, Burnham and Anderson 19 reformulated the objective function and proposed Akaike weights to evaluate the probability of models being the correct one. The Akaike weight w of model k is defined as:

wk,c (e, η obs , σ obs ) =

exp(−0.5(AICk − AICc )) , m ∑ j=1 exp(−0.5(AIC j − AICc ))

(4)

where the subscript c refers to the “correct” model used. The correct model is the one that accurately represents the true chemical mechanism. Note that this model is generally not known. If any future experiment should confirm the correctness of a model, or discriminate against the models that are inaccurate, then a new ideal experiment should have Akaike weights close to one for the correct model and close to zero for the inaccurate ones. Or, because such a strong separation between the models might not be possible, the new experiment should be chosen such that the Akaike weight of the best model are as large as possible and for all other models as small as possible. In practice, the correct model is not known. For this reason, a surrogate approach is used by Michalik et al., 15 where each model from the suite of models being tested is sequentially considered as the correct model to evaluate the Akaike weights. With the objective of finding the best experimental condition (e), the optimization criterion (AWDC) is then written as m

max AWDC(e) = e

∑ pqwq,q(e, η obs, σ obs),

(5)

q=1

where AWDC(e) is the objective function that needs to be maximized, and wq,q (e, η obs , σ obs ) is the Akaike weight of model q evaluated under the assumption that model q is correct. The maximization condition is weighted by a prior probability (pq ) of the model q, which indicates 8


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how likely it is that q is the best model. Since that information is typically not available or hard to quantify, it is assumed here that pq = 1/m for all models. This choice also normalizes the AWDC values such that a good choice for e is characterized by a value of unity. The Akaike weights wq,q are obtained as

wq,q (e, η obs , σ obs ) = =

exp(−0.5(AICq − AICq )) m ∑ j=1 exp(−0.5(AIC j − AICq )) 1 −(ηi,q −ηi, j )2 ∑mj=1 ∏ni=1 exp( 2(σ obs )2 i

.

(6)

+ Kq − K j )

This expression removes the experimental observation from the maximization problem, and instead relies on the difference between models and the potential experimental uncertainty to determine the best possible future experiment. Experiments with larger uncertainties have unavoidably lower information content for model discrimination. The experimental condition (ei ) that provides the highest AWDC is then chosen as the next experiment. If all the models are equally good in predicting the data, the Akaike weights wq,q of each models will be close to 1/m and the AWDC value will reach its lowest value 1/m. No model discrimination can thus be performed. For the highest AWDC value, the Akaike weights of each model should be close to one, which requires that each model is far apart from the other models. Therefore, model predictions are nicely separated. 15 The best model can be identified, once the experiment at the proposed condition is performed.

Design Parameters Extinction strain rate measurements were conducted as part of this study in a counterflow burner for flames with CH4 /CO2 fuel and O2 /CO2 oxidizer streams. The methane mass fractions of the fuel stream (YF,1 ), the oxygen mass fractions of the oxidizer stream (YO2 ,2 ), and the temperatures of the oxidizer stream (T2 ) are considered as experiment design parameters. Experiments are then performed at the conditions selected by the AWDC method. Also, experiments are carried out at

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several other conditions, which are suggested as non-informative by the design process, in order to assess the validity of the applied AWDC method. For the ignition delay time measurements in the shock tube, the temperatures, equivalence ratios, pressures, and CO2 mole fractions (XCO2 ) of the initial oxy-methane mixtures are considered as parameters in the design process. Experimental data sets reported by Koroglu et al. 3 are used to emulate the designed experiments. The design process of burning velocity experiments includes the temperatures, equivalence ratios, pressures, and XCO2 of the initial CH4 /O2 /CO2 mixtures as design parameters. Experimental conditions correspond to the measurements performed by Mazas et al., 20 who reported burning velocities for oxy-conditions at atmospheric pressure. However, the experimental design space is extended also to higher pressures and temperatures.

Chemical models Five chemical mechanisms for methane oxidation are compared in this study. The GRI-Mech 3.0 5 (referred to as “GRI” mechanism) has been developed through an automatic optimization for a large number of experimental data sets for methane oxidation and has been widely used in CFD simulations. A kinetic model was developed by Wang et al. 8 for the high temperature oxidation of H2 , CO, and C1 –C4 fuel species. While this mechanism adopted the sub-mechanism of CH4 from the GRI mechanism, 5 it contains different H2 /CO chemistry, which can affect the simulation results of oxy-methane flames strongly. This model is referred to as “USC” mechanism in the following sections. Blanquart et al. 6 proposed a reaction mechanism to describe the oxidation of a set of C0 –C7 hydrocarbon fuels including methane. This mechanism was further updated to include an accurate mechanism for hydrogen oxidation. 21,22 It is referred to as “ITV” mechanism. The San Diego mechanism 9 was derived in 2001 and updated continuously in the past by incorporating improved reaction rates as well as thermodynamic and transport data. The version released on Oct. 4, 2014 was considered in this study and referred to as “SD” model. Recently, AramcoMech 2.0 7 (referred to as “Aramco” mechanism) was developed to characterize the ki-

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netic and thermochemical properties of a number of C1 –C4 based hydrocarbons and oxygenated fuels. 7,23 Note that, while these five mechanisms have been validated by comparing against available data of methane/air mixtures to reveal their accuracies and inaccuracies, their performance for oxy-methane combustion still has to be explored.

Results and discussion The performance of the five methane mechanisms 5–9 for extinction strain rates, ignition delay times, and burning velocities measured under oxy-conditions was explored and compared in the following. The model-based AWDC approach was applied to determine the most informative measurements for model discrimination. The results are presented and discussed in this section.

Extinction strain rates Many of the important application areas of oxy-fuel combustion, such as large-boilers and furnaces, are operated in a nominally non-premixed mode, and counterflow diffusion flames are considered the prototypical one-dimensional configuration to study non-premixed combustion. Extinction limits of diffusion flames are important indicators for flame stability and reaction time scale. The higher specific heat of carbon dioxide results in strongly decreased flame temperatures under oxyconditions and thus affects the extinction characteristics of counterflow flames. Accurate chemical mechanisms for extinction strain rates can be used in CFD calculations to improve designs of combustion devices running under oxy-conditions.

Experimental design YF,1 , YO2 ,2 , and T2 were considered as the experimental design parameters. Table 1 summarizes the values of these parameters used in the design process. The temperature of the fuel stream T1 was excluded from the design process, as its influence on extinction strain rates was found to be minor. 24 In this study, T1 was set to 300 K for all measurements. The five chemical models 5–9 were 11


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employed as the set of models for determining Akaike weights and AWDC values. The uncertainty of measurements of the employed counterflow burner is 3%, as described earlier. While the mechanisms have different model sizes, the important reactions for methane oxidation are identical. 5–9 Therefore, the parameter K of these competing models representing the number of model parameters in 2 was assumed to be same. Numerical simulations were performed using appropriate models in the FlameMaster 25 code, for which the source code is available at www.itv.rwthaachen.de/downloads/flamemaster/. The conservation equations of mass, momentum, and energy and the species balance equations are used in the formulation of the numerical problem with plugflow boundary conditions. Radiative heat loss from CH4 , CO, CO2 , and H2 O and thermal diffusion are taken into account. At both ends of the computational domain, the mass fractions of the reactants and the flow velocities are specified. 24 For certain YF,1 and YO2 ,2 , the velocities of the fuel and oxidizer streams are stepwise increased, while still keeping flows in momentum balance. The conditions, at which the solutions fail to converge in a further increase of velocities, are taken as the critical extinction conditions. This point is approached in an automated adaptive fashion. Table 1: Values of YF,1 , YO2 ,2 , and T2 considered in the experimental design process. Parameters Values YF,1 [-] 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50 0.210, 0.225, 0.233, 0.250, 0.275, 0.300 YO2 ,2 [-] T2 [K] 310, 350, 400, 450, 500 Figure 2 shows the AWDC values computed as a function of YF,1 and YO2 ,2 at T2 = 300 K. Experiments with both low YF,1 ’s and YO2 ,2 ’s show the highest AWDC values. This indicates that the extinction stain rates computed with the five models are nicely separated at those conditions. Hence measurements at those conditions would have a very high information content. Interestingly, small YF,1 combined with large YO2 ,2 give substantially lower AWDC values and only when both mass fractions are large at YF,1 > 0.35 and YO2 ,2 > 0.26, the AWDC values are close to 0.8 for a wide domain of conditions. The Akaike weights of models wq,q at YF,1 = 0.5 and YO2 ,2 = 0.3 are shown in Table 2 as an example. It can be seen that the ITV, 6 USC, 8 and SD 9 mechanisms have Akaike weights of one or close to one, which indicates that these models differ strongly from all 12


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other models. The Akaike weights of the GRI 5 and Aramco 7 models are close to 0.5, which means that lumping of both models occurs. By comparing with data at this condition, both models can be identified as equally inaccurate or accurate. However, a discrimination between these two models is not possible. Thus, an AWDC value of 0.8 results for this condition. Table 2: Akaike weights of models at YF,1 = 0.5, YO2 ,2 = 0.3, and T2 = 310 K. Model GRI 5 ITV 6 Aramco 7 USC 8 SD 9

wq,q 0.498 0.987 0.498 1.000 1.000

At YF,1 = 0,2 and T2 = 310 K, the counterflow flames predicted by the GRI, 5 ITV, 6 and Aramco 7 models extinguish regardless of the applied strain rate for YO2 ,2 smaller than 0.2128, 0.2116, and 0.2121, respectively. Therefore, model discrimination between these three models cannot be performed at YF,1 = 0.2 and YO2 ,2 = 0.21. The Akaike weights of these three models are thus set to 0.333. The extinction strain rates predicted by the USC 8 and SD models 9 at this particular condition differ strongly from each other and are also obviously different from the extinguished solutions obtained using the GRI, 5 ITV, 6 and Aramco 7 models. Therefore, the calculated Akaike weights of these two models are equal to unity. Overall, an AWDC value of 0.6 is determined for this condition, which indicates that the corresponding measurement has a low information content and reflects the observations described above. Note, however, that the neighboring points in either direction, where burning solutions can be obtained for all models, show high AWDC values. The AWDC values computed as a function of YF,1 and T2 at YO2 ,2 = 0.233 are shown in Figure 3. Consistent with previous findings, the highest AWDC values are observed at the conditions with strong CO2 dilution in the fuel stream. It is seen in Figure 3 that the impact of T2 on the AWDC values vanishes with increasing oxidizer temperatures at small YF,1 ’s, even though the extinction strain rates are strongly influenced by T2 . At YF,1 > 0.35, the AWDC values are negligibly influenced by T2 . In terms of model discrimination, the experiments at various oxidizer temperatures

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(a) 3D view

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(b) 2D view

Figure 2: AWDC values for extinction strain rate measurements as a function of YF,1 and YO2 ,2 at T2 = 310 K. are of minor importance.

(a) 3D view

(b) 2D view

Figure 3: AWDC values for extinction strain rate measurements as a function of YF,1 and T2 with YO2 ,2 = 0.233. For YF,1 , YO2 ,2 , and T2 , seven, six, and five different values were considered in generating the AWDC map, as summarized in Table 1. Overall, 210 experiments would have to be performed to cover all these conditions. However, only four experiments are identified as valuable for model discrimination, if a threshold of AWDC > 0.85 is employed. This indicates that, if the experimental design is performed prior to measurements, a maximum reduction of 98% of experimental cost 14


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can be achieved, and while this three-dimensional parameter space would typically not be fully examined, on the order of 40–50 individual experimental points would seem to be a reasonable choice.

Comparison between models and experiments Following the results of experimental design, extinction strain rates were experimentally determined for flames with small YF,1 ’s and YO2 ,2 ’s at an oxidizer temperature of 310 K. In order to evaluate the validity of the applied experimental design method, measurements were also conducted for flames with larger fuel mass fractions, which were not recommended by the experimental design. The results are shown in Figure 4 and Figure 5 in comparison with model predictions. Figure 4 shows the numerical and experimental results for oxy-methane flames with YO2 ,2 = 0.21. The AWDC values reported for these flames are summarized in Table 3. As expected, the predicted extinction strain rates are well separated at YF,1 = 0.25, for which a high AWDC value of 0.98 was reported. The Aramco mechanism 7 gives the most satisfactory result at this condition, while the ITV 6 and GRI 5 models provide reasonable prediction accuracy as well. At YF,1 = 0.3, a model discrimination between the ITV and the Aramco models is infeasible, even though both models provide very high prediction accuracy. Concerning the experimental uncertainties, lumping of three and four models is observed at YF,1 = 0.35 and 0.4, respectively. While these lumped models agree well with the measured data, a discrimination between them is impossible. At this particular YO2 ,2 , the value of experiments in terms of model discrimination decreases with the increased fuel mass fractions, which is well reflected by the AWDC values shown in Table 3. While all the measurements have their contributions to model validation, only the measurement at YF,1 = 0.25 with a reported AWDC value close to one provides additional information about model discrimination. Figure 5 shows the results for oxy-methane flames with a fuel mass fraction of 0.2. While model predictions are separated at the two designed conditions, all the models overpredict the extinction strain rates. With increased oxygen mass fractions of the oxidizer stream, the models 5–9 are of decreasing accuracy.

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180 CH4/CO2 vs O2/CO2 160

1 atm, YO

2,2

= 0.21

140 a [1/s]

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120 Exp. ITV GRI Aramco USC SD

100 80 60 0.25

0.3

0.35 0.4 YF,1 [-]

0.45

0.5

Figure 4: Extinction strain rates as a function of YF,1 for CH4 /CO2 versus O2 /CO2 flames with YO2 ,2 = 0.21. Symbols denote the experimental measurements and solid lines show the numerical results with models. 5–9 Table 3: AWDC values as a function of YF,1 at YO2 ,2 = 0.21 and T2 = 310 K. YF,1 [-] 0.25 0.30 0.35 0.40

AWDC [-] 0.98 0.80 0.73 0.61

It is important to distinguish between the experimental design methods for model validation and discrimination. The experimental design methods for model validation introduce conditions to explore the model performance for a strong variation of factors. Thus, model performance can be assessed comprehensively. This is of particular importance, if only one model is available or of research interest. The methods for model discrimination focus on the cases, where a number of rival models are available, as is the case for oxy-methane combustion. The purpose is to identify the best model as basis for further model refinement or to be applied directly in CFD simulations. Conditions, which are important for model validation, can hence be useless for model discrimination, if the model predictions are similar at these conditions.

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240 220

CH4/CO2 vs O2/CO2 1 atm, YF,1 = 0.2

200 a [1/s]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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180 160

Exp. ITV GRI Aramco USC SD

140 120 100 0.22

0.225

0.23 YO ,2 [-]

0.235

0.24

2

Figure 5: Extinction strain rates as a function of YF,1 for CH4 /CO2 versus O2 /CO2 flames with YF,1 = 0.2. Symbols denote the experimental measurements and solid lines show the numerical results with models. 5–9

Ignition delay times An experimental design process was performed to rank the ignition delay time measurements by considering initial temperatures, equivalence ratios, pressures, and XCO2 as design parameters. The data sets reported by Koroglu et al. 3 were used to emulate future experiments. Recently, Koroglu et al. 3 reported overall 49 ignition delay time measurements of CH4 , O2 , CO2 , and Ar mixtures. The experiments were performed for the temperature range of 1577–2144 K, at pressures of around 0.75 and 3.7 atm, equivalence ratios (φ ) of 0.5, 1, and 2, and CO2 mole fractions of 0, 30, and 60%. Detailed information of data sets is summarized in Table 4. These conditions are considered in the design process. As reported by Koroglu et al., 3 the uncertainties in their ignition delay time measurement were between 12–18%. Thus, an experimental uncertainty of 18% was specified for the design process. Only the GRI, 5 ITV, 6 and Aramco 7 models, which predict extinction rates for the conditions of interest in the present study with reasonable accuracy, were considered as the set of models for experimental design. The results of the design process are shown in Figure 6 and Figure 7. Figure 6 shows the AWDC values as a function of temperature and XCO2 for two pressures of 0.75 and 17


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Table 4: Data sets reported by Koroglu et al. 3 for oxy-methane combustion. Nr. of data sets P [atm] 1 0.75 2 0.75 3 0.75 4 0.75 5 3.7 6 3.7 7 3.7 8 0.75

XCO2 [-] φ [-] 0 1.0 0.3 0.5 0.3 1.0 0.3 2.0 0.3 0.5 0.3 1.0 0.3 2.0 0.6 1.0

3.70 atm. The AWDC values as a function of temperature and equivalence ratio are presented in Figure 7. For all the conditions investigated, the AWDC values are between 0.60–0.85. None of these experiments show significantly large or small AWDC values. The reason is explained in the following section.

(a) p = 0.75 atm, φ = 1.0

(b) p = 3.70 atm, φ = 1.0

Figure 6: AWDC values for ignition delay time measurements as a function of T and XCO2 at φ = 1.0 and p = 0.75 and 3.70 atm.

Comparison between models and experiments Figure 8–Figure 10 present comparisons between models 5–7 and data reported by Koroglu et al. 3 For all the data sets investigated, the GRI mechanism predicts smaller ignition delay times than the ITV and the Aramco mechanisms over a wide temperature range. At around 1818 K 18


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(a) p = 0.75 atm, XCO2 = 0.3

(b) p = 3.70 atm, XCO2 = 0.3

Figure 7: AWDC values for ignition delay time measurements as a function of T and φ at XCO2 = 0.3 and p = 0.75 and 3.70 atm. (1000/T = 0.55), a crossover between predictions of the ITV and Aramco models is observed. At temperatures higher than 2000 K (1000/T < 0.5), the ignition delay times obtained using the Aramco model match those computed with the GRI model. Only at relatively lower temperatures (T < 1667 K and 1000/T > 0.6), a separation between model predictions can be observed, which leads to slightly increased AWDC values, as shown in Figure 6 and Figure 7. Model lumping of the ITV and the Aramco models at the temperature range of 1667–2000 K and of the Aramco and the GRI models at temperatures larger than 2000 K contributes to the moderate AWDC values reported by the design process. For the condition space investigated here, the experimental design process fails to find valuable shock tube experiments for model discrimination. This is confirmed by the comparison between models 5–7 and data 3 shown in Figure 8–Figure 10. Taking the experimental uncertainties into account, none of these three models shows prediction advantages over the other two models. Also, quantitative metrics from the experimental design such as the AWDC value can compare the information content of data from different facilities in absence of experimental data. As demonstrated here, the ignition delay time measurements are not as informative as the extinction measurements for model discrimination. This information is especially important in terms of the

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0.75 atm, φ = 0.5, XCO2 = 0.3

0.75 atm, φ = 1.0, XCO2 = 0.3 1 τig [ms]

1 τig [ms]

Exp. GRI ITV Aramco

0.1

0.45

0.5

0.55

Exp. GRI ITV Aramco

0.1

0.6

0.65

0.45

0.5

1000/T [K-1]

0.55

0.6

0.65

1000/T [K-1]

(a) p = 0.75 atm, φ = 0.5

(b) p = 0.75 atm, φ = 1.0 0.75 atm, φ = 2.0, XCO2 = 0.3

1 τig [ms]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Exp. GRI ITV Aramco

0.1

0.45

0.5

0.55

0.6

0.65

-1

1000/T [K ]

(c) p = 0.75 atm, φ = 2.0

Figure 8: Ignition delay times for oxy-methane mixtures at 0.75 atm. Symbols denote the experimental measurements by Koroglu et al. 3 Solid lines show the numerical results with models. 5–7

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1

3.7 atm, φ = 0.5, XCO2 = 0.3

τig [ms]

τig [ms]

1

0.1

0.01 0.45

Exp. GRI ITV Aramco 0.5

0.55

0.6

3.7 atm, φ = 1.0, XCO2 = 0.3

0.1

Exp. GRI ITV Aramco

0.01 0.45

0.65

0.5

0.55

1000/T [K-1]

(a) p = 3.70 atm, φ = 0.5

τig [ms]

1

0.6

0.65

1000/T [K-1]

(b) p = 3.70 atm, φ = 1.0 3.7 atm, φ = 2.0, XCO2 = 0.3

0.1

Exp. GRI ITV Aramco

0.01 0.45

0.5

0.55

0.6

0.65

-1

1000/T [K ]

(c) p = 3.70 atm, φ = 2.0

Figure 9: Ignition delay times for oxy-methane mixtures at 3.70 atm. Symbols denote the experimental measurements by Koroglu et al. 3 Solid lines show the numerical results with models. 5–7

0.75 atm, φ = 1.0, XCO2 = 0.0

0.75 atm, φ = 1.0, XCO2 = 0.6 1 τig [ms]

1 τig [ms]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Exp. GRI ITV Aramco

0.1

0.45

0.5

0.55

0.6

Exp. GRI ITV Aramco

0.1

0.65

0.45

0.5

-1

0.55

0.6

0.65

-1

1000/T [K ]

1000/T [K ]

(a) p = 0.75 atm, XCO2 = 0.0

(b) p = 0.75 atm, XCO2 = 0.6

Figure 10: Ignition delay times for oxy-methane mixtures at 0.75 atm. Symbols denote the experimental measurements by Koroglu et al. 3 Solid lines show the numerical results with models. 5–7 21


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reduction of experimental efforts. Note that, while none of the measurements reported by Koroglu et al. 3 is identified as important experiment for model discrimination, these experiments are still of major importance for model validation and refinement.

Burning velocities A wide range of initial temperatures (373–673 K), equivalence ratios (0.5–1.5), pressures (1– 30 atm), and mole fractions of CO2 (0.2–0.4) of the CH4 /O2 /CO2 mixtures was scanned by the AWDC method to determine the most informative conditions of laminar burning velocity measurements for model discrimination. Again, the GRI, 5 ITV, 6 and Aramco 7 models were included in the set of models for calculation of AWDC values. An experimental uncertainty of 5% 20 was specified for the screened future measurements.

Figure 11: AWDC values for burning velocity measurements as a function of φ and XCO2 at p = 1.0 atm and T = 373 K. The results of this experimental design process are presented in Figure 11–Figure 13. It can be seen that the calculated AWDC values approach their minimum (= 0.33) over a wide domain 22


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Figure 12: AWDC values for burning velocity measurements as a function of φ and T at XCO2 = 0.2 and p = 1.0 atm.

Figure 13: AWDC values for burning velocity measurements as a function of φ and p at XCO2 = 0.2 and T = 373 K.

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of conditions. In addition, the AWDC values are negligibly influenced by the CO2 content and the temperature of initial mixtures. Large AWDC values (> 0.85) are only observed for very lean and rich mixtures at high pressures of around 25 atm. Mazas et al. 20 reported accurate flame speed data for CH4 /O2 /CO2 mixtures with XCO2 ’s = 0.2 and 0.4 at a temperature of 373 K and atmospheric pressure. Figure 14 shows a comparison of experimental data with burning velocities computed with considered models. As predicted by the experimental design, the models 5–7 cannot be discriminated using low pressure experiments. However, data sets at higher pressures are missing in the literature, but would be very useful for model discrimination and also validation. Due to the possible occurrence of flame instabilities and the development of wrinkles in the experiments, 26 accurate measurements of flame speeds at these designed high-pressure conditions are difficult. Nevertheless, these experiments at very lean conditions and also pressures down to 15 bar as well as at very rich conditions and pressures down to 20 bar have still very high information content. 300

1 atm, 373 K

250 Su0 [cm/s]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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XCO = 0.2 2

200 150 100

XCO = 0.4 2

ITV GRI Aramco

50 0 0.6

0.8

1

1.2

1.4

φ [-]

Figure 14: Burning velocities for CH4 /O2 /CO2 mixtures with XCO2 ’s = 0.2 and 0.4 at 373 K and atmospheric pressure. Symbols denote the experimental measurements. 20 Solid lines show the numerical results with models. 5–7

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Concluding remarks In this study, the experimental design approach is applied to determine the most valuable experiments of extinction strain rates, ignition delays, and laminar burning velocities to distinguish between chemical models for oxy-methane combustion. The applied AWDC method identified the conditions successfully, at which model predictions are well separated and the best model can be chosen by comparison with experimental measurements. It was found that the counterflow measurements at small YF,1 ’s and YO2 ,2 ’s contribute to an efficient model discrimination. By comparing with the data obtained as part of this study, the Aramco mechanism is shown to provide the highest prediction accuracy for extinction strain rates at YO2 ,2 = 0.21. For YO2 ,2 ’s = 0.225 and 0.233, while the predictions of the considered models 5–9 are distributed separately, they all fail to match the data. The best model is thus lacking for these conditions. For the shock tube configuration, ideal experiments for model discrimination are missing over the investigated domain of conditions. For the burning velocity experiments, while optimal conditions are identified successfully, the most beneficial conditions are at high pressure conditions, where experiments are difficult due to the possible occurrence of flame instabilities. The aim of this study is to distinguish between models for oxy-methane combustion with a minimum number of measurements. Among the set of competing models, the one with the highest accuracy for the data of interest is defined as the best model. Nevertheless, it can certainly not be claimed that the model represents the truth in a sense that it incorporates the best chemical kinetic knowledge and can reproduce each target of interest without errors. This definition in conjunction with the applied experimental design method for model discrimination is suitable for cases where numerous competing models are available, as is the case for oxy-methane combustion investigated here. One must carefully note, however, that this kind of experimental design method is of marginal interest for the cases, where models are lacking, as is the case, for instance, for most novel bio-fuels. 27,28 Also, the fact that typically only very few conditions lead to high separation of the models does not imply that only few measurements are required for model development. For model validation, measurements should be performed potentially for different or additional 25


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initial conditions. For this, the conventional factorial experimental design approaches can reduce the experimental efforts, while the designed experiments still probe a wide range of conditions. 29

Acknowledgement This work was performed as part of the collaborative research center SFB/Transregio 129 “Oxyflame”, which is funded by the German Research Foundation (DFG).

References (1) Scheffknecht, G.; Al-Makhadmeh, L.; Schnell, U.; Maier, J. International Journal of Green˘ S–S35. house Gas Control 2011, 5, S16âA ¸ (2) Maruta, K.; Abe, K.; Hasegawa, S.; Maruyama, S.; Sato, J. Proceedings of the Combustion Institute 2007, 31, 1223–1230. (3) Koroglu, B.; Pryor, O.; Lopez, J.; Nash, L.; Vasu, S. Combustion and Flame 2016, 164, 152–163. (4) Li, X.; Jia, L.; Onishi, T.; Grajetzki, P.; Nakamura, H.; Tezuka, T.; Hasegawa, S.; Maruta, K. Combustion and Flame 2014, 161, 1526–1636. (5) Frenklach, M.; Wang, H.; Yu, C.-L.; Goldenberg, M.; Bowman, C.; Hanson, R.; Davidson, D.; Chang, E.; Smith, G.; Golden, D.; Gardiner, W.; Lissianski, V. GRIMech–An Optimized Detailed Chemical Reaction Mechanism for Methane Combustion. http://combustion.berkeley.edu/gri-mech/, 1999; http://www.me.berkeley. edu/gri_mech/. (6) Blanquart, G.; Pepiot-Desjardins, P.; Pitsch, H. Combustion and Flame 2009, 156, 588–607. (7) Metcalfe, W.; Burke, S.; Ahmed, S.; Curran, H. International Journal of Chemical Kinetics 2013, 45, 638–675.

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(8) Wang, H.; You, X.; Joshi, A.; Davis, S.; Laskin, A.; Egolfopoulos, F.; Law, C. USC Mech Version II. High-temperature combustion reaction model of H2 /CO/C1 -C4 compounds. http://ignis.usc.edu/USC_Mech_II.htm, 2007; http://ignis.usc.edu/USC_Mech_ II.htm. (9) San

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(21) Burke, M.; Chaos, M.; Ju, Y.; Dryer, F.; Klippenstein, S. International Journal of Chemical Kinetics 2012, 44, 444–474. (22) Narayanaswamy, K.; Pepiot, P.; Pitsch, H. Combustion and Flame 2014, 161, 866–884. (23) Kéromnès, A.; Metcalfe, W.; Heufer, K.; Donohoe, N.; Das, A.; Sung, C.; Herzler, J.; Naumann, C.; Griebel, P.; Mathieu, O.; Krejci, M.; Petersen, E.; Pitz, W.; Curran, H. Combustion and Flame 2013, 160, 995–1011. (24) Seiser, R.; Pitsch, H.; Seshadri, K.; Pitz, W.; Gurran, H. Proceedings of the Combustion Institute 2000, 28, 2029–2037. (25) Pitsch, H. A C++ computer program for 0D combustion and 1D laminar flame calculations. 1990; http://www.itv.rwth-aachen.de/downloads/flamemaster/. (26) Jerzembeck, S.; Peters, N.; Pepiot-Desjardins, P.; Pitsch, H. Combustion and Flame 2009, 156, 292–301. (27) Cai, L.; Sudholt, A.; Lee, D.; Egolfopoulos, F.; Pitsch, H.; Westbrook, C.; Sarathy, S. Combustion and Flame 2014, 161, 798–809. (28) Cai, L.; Uygun, Y.; Togbé, C.; Pitsch, H.; Olivier, H.; Dagaut, P.; Sarathy, S. Proceedings of the Combustion Institute 2015, 35, 419–427. (29) Aul, C.; Metcalfe, W.; Burke, S.; Curran, H.; Petersen, E. Combustion and Flame 2013, 160, 1153–1167.

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Experimental Design for Discrimination of Chemical Kinetic Models for

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