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On the Importance of a Cycloalkane Functionality in the Oxidation of a Real Fuel Stephen Dooley, Joshua Steven Heyne, Sang Hee Won, Pascal Dievart, Yiguang Ju, and Frederick L. Dryer Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/ef5008962 • Publication Date (Web): 20 Oct 2014 Downloaded from http://pubs.acs.org on November 10, 2014

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On the Importance of a Cycloalkane Functionality in the Combustion Kinetics of a Real Liquid Fuel Stephen Dooley*†, Joshua Heyne†, Sang Hee Won†, Pascal Dievart†, Yiguang Ju†, Frederick L. Dryer† †

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ

*Department of Chemical and Environmental Sciences, University of Limerick, Limerick, Ireland

Abstract Typically real jet fuels are composed primarily of normal, iso, and cyclo-alkanes, along with significant fractions of alkyl aromatics.

This study elucidates fundamentally the influence of the cycloalkane

functionality on the fully prevaporized global combustion kinetic behavior of a fuel mixture composed of n-paraffin, iso-paraffin and alkyl aromatic fractions. Methyl cyclohexane is chosen as representative of this generic functional class. An n-decane/iso-octane/toluene mixture previously applied in surrogate fuel research is used as the reference functional class composition for this study. A second fuel mixture is derived by incorporating ~25 mole % of methyl cyclohexane into this reference component mixture in such a manner that four selected combustion property targets - Derived Cetane Number, Hydrogen-toCarbon ratio, Molecular Weight and Threshold Sooting Index, of both the reference fuel and the new mixture are the same. In so doing, the intention is to regulate the gas phase oxidative reactivity of both fuels while singularly perturbing only the molecular class composition. The specific influence of the cycloalkane functionality on the global gas phase reaction is then tested by experimentally analysing the low, intermediate and hot-ignition reactivity of both fuels and also by analysis of laminar diffusion flame extinction limits measured at 1 atm. These observations indicate that the cycloalkane functionality imparts no distinctive influence on the low temperature alkyl peroxy radical governed global reactivity of complex liquid transportation fuel types, nor do the extinction limit observations indicate any significant effects on global behaviors at high temperatures. However, the cycloalkane functionality does differentially influence the hot-ignition transition, by accelerating the global reactivity equivalent to an 1 ACS Paragon Plus Environment

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increase in reaction temperature of ~20-30 K at 800-900 K (12.5 atm). A kinetic modeling analysis suggests that this modest difference is due to the differential intermediate species population provided by the molecular structures of a branched alkane (of near equal carbon number, iso-octane) versus that provided by methyl cyclohexane. These observations are discussed in the context of the existing literature in terms of; fundamental fuel formulations, surrogate fuels for the replication of global combustion behaviors, and numerical combustion models for real fuels.

Keywords: Surrogate Fuel, Methyl cyclohexane, Kinetic model, Cycloalkane, Hot ignition, Fuel formulation *To whom correspondence should be addressed Dr. Stephen Dooley [email protected]

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1. Introduction Design flexibility for developing advanced combustion systems and revising fuel certification to encompass a wider range of fuel resources are priority endeavors driven by expanding interests in utilizing new alternative fuel resources and improving energy security. More precise/predictive relationships for physical and chemical property effects of jet fuels on global combustion behavior in, and emissions from, multiphase systems such as gas turbines are needed to support these endeavors [1-3]. Petroleum-derived jet fuels consist of the order of hundreds of hydrocarbon components, which may be categorized by molecular size (carbon number) and molecular class, including paraffins, naphthenes, and aromatics [4]. Emerging alternative fuels typically contain different compositional and molecular weight distributions of these classes, frequently without significant quantities of aromatics. The blending of these materials with those derived from petroleum thus leads to additional variability in the molecular composition of finished fuels [1-4]. These complexity and variability issues present severe challenges in understanding how the physical and chemical kinetic properties of liquid fuels relate to the multi-phase combustion and emissions performance of gas turbine engines and limits industry abilities to certify new fuel types. Integral to developing the needed insights and tools for these purposes are concepts for constructing “surrogate fuel” formulations that represent both physical and chemical kinetic properties of a real fuel [5-23]. To replicate detailed physical properties (e.g., distillation curve and vapor dome properties, molecular class distribution over the distillation curve, viscosity, surface tension, density, etc.) may require larger numbers of components of varying molecular weight, as well as chemical class composition [19-23]. There are essentially two approaches to representing both physical and chemical kinetic properties in detailed combustion calculations:


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1) a “physico/chemico” authentic approach [20-22], in which the same set of surrogate components chosen to represent physical properties are also used to represent chemical kinetic properties; 2) a more flexible approach in which the physical properties are represented by a larger number of surrogate components and the chemical kinetic properties are represented by the minimum number of molecular structures utilized in representing physical properties [23]. The physico-chemical authentic approach is significantly less desirable with regards to constructing computational models that describe the combustion process due to the necessary dimensionality of the chemical kinetic model component. The second “model splitting” approach utilizes a single chemical submodel component to represent the specific kinetic properties of each molecular class. Further simplifications may be possible depending on whether the reaction kinetic particulars of each class need be represented to reasonably reproduce the global combustion behavior of the real fuel. In either method, it is important to minimize the numbers of components described with chemical kinetics in order to avoid large numbers of reactions and species. In terms of formulating surrogate fuels to study chemical kinetic behaviors of real fuels, two major questions arise. Firstly, “What global, kinetically related combustion behavior(s) should the surrogate fuel emulate?”, and secondly, “To do so, what component (s) should be selected in formulating the surrogate mixture?” Whilst the former can be answered by consideration of the combustion response under investigation (for example lean blowout, combustion volume requirements and temperature distribution, combustion stability, radiative exchange in the combustion volume, NOX/CO emissions, etc.), the latter issue continues to be addressed mostly upon intuitive insights.

Our research contributions over the past several years [e.g. 14-16, 24-27] have been principally focused on addressing the chemical kinetic related issues, in preparation for adjacent work to develop combined physical property and chemical kinetic property modeling approaches. This work has in part focused on 4 ACS Paragon Plus Environment

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replacing the above need for chemical intuition with quantitative scientific measurements and analysis. We have demonstrated that the chemical class composition of the surrogate can differ significantly from that of the real fuel without degrading the ability of the surrogate mixtures to quantitatively emulate global kinetically influenced fully pre-vaporized combustion properties of real liquid fuels [14-16, 24-27]. These include autoignition delay, laminar burning rates, flame temperatures, laminar diffusive strained extinction, species evolutions and sooting related characteristics. The central important facet of our approach to formulate surrogate mixtures is the use of “combustion property targets” to regulate the combustion behavior of the surrogate to that of the real fuel. Presently, these include the hydrogen-tocarbon ratio (H/C), the derived cetane number (DCN), the average molecular weight (MW) and the threshold sooting index (TSI) of the real fuel under study. The battery of experimental measurements obtained to test this approach strongly support the conclusion that the important aspect in formulating a surrogate composition for kinetic properties is to maintain a reasonable distribution of the distinct chemical functionalities present in the real fuel, not in approximating the original fuel molecular structure or structural class distribution [15].

In work recently published in this journal [27], the combustion property target formulation concepts discussed in our earlier work were applied to produce and test surrogate formulations composed of several hydrocarbon fluids, each having a significant range of molecular weight and chemical class distributions. In our earlier work, surrogates were composed only of mixtures of entirely pure chemical components [14-16, 24-25]. Experimental tests of pre-vaporized chemical reactivities were reported for two different real target jet fuels, a Jet-A (POSF 4658) used in numerous publications as a reference target fuel, and a military JP-8 (POSF 5699), both of which contain about 25-30% cycloalkanes (by mass). Experimental results for the Jet-A surrogate mixture closely parallel the data for the fully pre-vaporized Jet-A real fuel, as well as that of prior surrogate mixtures of n-decane/iso-octane/toluene [14] and ndodecane/iso-octane/n-propylbenzene/1,3,5-trimethyl benzene, [15] all formulated to share the same 5 ACS Paragon Plus Environment

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combustion property targets. The experimental data comparisons for the JP-8 surrogate mixture and real JP-8 were of similar quality to the Jet-A comparisons, but were modestly improved in the temperature range demarking the transition to the hot ignition chemically-branched kinetic mechanism (~850-900 K). The improvement was hypothesized to be partially attributable to the presence of large cycloalkane fraction present in the surrogate fuel formulated for the JP-8, but absent from the surrogate formulated for the Jet-A [27]. Sooting properties of the JP-8 and Jet-A fuels were also compared to those of the respective hydrocarbon fluid surrogates in diffusion flames and in a model gas turbine combustor in an associated work [26]. In each case, similar levels of emulation were observed, demonstrating that the absence of cylcoalkane functionalities in surrogate fuels does not impart significant fidelity losses, even when the target real fuels are comprised of significant fractions of cycloalkanes.

As already noted, the general theme in the literature is to approximate the component molecular class distribution of the real fuel in the surrogate fuel by generic identity and fraction [5-13, 19-23]. However, the quality of emulation to real fuel global combustion behaviors we have reported, including surrogates comprised of hydrocarbon fluids, and pure chemical components, indicates that this may not be the most effective approach. For further example, one might suggest that since most petroleum derived and synthetic paraffinic kerosenes contain weakly branched alkanes as a major fraction, weakly branched alkanes would be important to be included in the surrogate component selection. However, we have shown than the chemical kinetic properties of weakly branched alkanes can be adequately represented by appropriate mixtures of a very highly branched alkane (iso-octane) and normal alkanes (n-decane, ndodecane) as surrogate components [16].

Since cycloalkanes may make up a significant fraction of some real fuels, the question of the inclusion of cycloalkane in surrogate compositions is reasonably raised. The data provided by Dryer et al. [27], infers that the special provision of cycloalkanes impart only very limited extra capability for the surrogate to 6 ACS Paragon Plus Environment

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emulate real fuel pre-vaporized gas phase combustion responses. In this paper, we pursue this query in a scientifically defined manner. Precise experimental evidence and modelling analysis is provided to test the scenario outlined above in the particular case of the generic cycloalkane functionality, thus substantiating if cylcoalkane functionalities ought to be classified as distinct from the normal alkane functionality in terms of impacting global gas phase combustion behaviors.

Note that it is expressly not the objective of the study to formulate an improved surrogate for the particular Jet-A used as example. Moreover, neither is it our intent to replicate in a detailed manner the intermediate species evolution as the oxidation process proceeds, our initial objective has been to closely emulate global combustion behaviors.

The cycloalkane functionality has received a significant amount of attention in the literature through the study of various particular molecules. Experimental and computational studies indicate that these functionalities show complicated combustion behaviors and perhaps unique mechanistic features when oxidised as pure components [28-31]. However, several experimentally-evidence-based contentions in the literature have suggested that the occurrence of chemical kinetically related combustion properties (ignition delay, burning velocity etc.) of transportation fuel-like complex mixtures (real or surrogate fuels) are dominated by the oxidation properties of normal-alkyl functionalities e.g. [14, 15, 17]. Thus, the inference is that the unique processes of cycloalkane functionalities are masked to the extent that they become of limited importance to the accurate replication of the macroscopic combustion behaviors of real fuels and surrogate fuels. The veracity of this hypothesis has important implications for kinetic model construction, as it indicates that cycloalkanes need not be considered in surrogate fuel formulations when present in the real fuel of interest at fractions below some determinable upper limit. Additionally, for potential advanced or alternative fuel formulations that could be significantly different from crude-oil derived fuel formulations (from tar sands, terpenes, bisabolane etc.), this scenario would indicate that 7 ACS Paragon Plus Environment

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there is no discernible effect on the global combustion kinetics of a complex fuel from the presence of a large fraction of cycloalkanes.

A previously demonstrated methodology of surrogate fuel formulation utilising four combustion property targets [14-16] is adapted and leveraged for this objective. Methyl cyclohexane is nominated as a typical cycloalkane fuel component as representative of other cycloalkane functionalities, and added to the previously studied [14] n-decane/iso-octane/toluene 0.42/0.33/0.25 mole fraction mixture at approximately 25 mole %. This is achieved by the formulation procedure described below, such that the combustion property targets of the two fuels are approximately equivalent. Methyl cyclohexane is selected for this work as it is probably the most well studied cycloalkane, and it is less influenced by the normal-alkane character of cycloalkanes with larger alkyl side chains such as n-butyl cyclohexane, thus enabling a more extreme test-case for the objectives stated above.

The gas phase combustion reactivity of the model fuel containing methyl cyclohexane is determined by experimental measurement of homogeneous flow reactor reactivity across the 500–1050 K temperature range at 12.5 atm and a constant residence time of 1.8 seconds and also by measurement of the extinction limits of laminar diffusion flames at 1 atm. These conditions are identical to those exercised in our previous works [14-16, 24-27]. Thus, a direct comparison of the measurements to the previous data sets of cycloalkane-free fuels forms instruction to the objectives outlined above on the extent of any unique influence of the cycloalkane functionality on the mixture reactivity, at least in the specific instances studied here.

2. Experimental 2.1 Experimental Strategy


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The preferred strategy to test the hypotheses described above is to perturb the composition of the simple 1st generation surrogate proposed for the petroleum derived aviation fuel, Jet-A POSF 4658, by the incorporation of significant amounts of methyl cyclohexane. Surrogate mixtures of n-decane/isooctane/toluene (1st generation) and n-dodecane/iso-octane/n-propyl benzene/1,3,5 trimethyl benzene (2nd generation) have both been shown to be valid for respectively emulating premixed, and both premixed and non-premixed kinetically dominated phenomena of complex real fuels [14-16]. The experiment design in this study is to incorporate approximately 25 mole % cycloalkane (as an estimated upper fraction composition of real transportation fuels) into the 1st generation, n-decane/iso-octane/toluene mixture. This is performed by formulating an appropriate composition such that the modified mixture and the original 1st generation surrogate mixture both share the same Derived Cetane Number (DCN), Hydrogen/Carbon (H/C), Molecular Weight (MW) and Threshold Sooting Index (TSI). The intention here is to confirm if this replication of combustion property targets for the two mixtures results in similar or different overall global reactivities for the two fuels. Significant differences in the combustion behaviors would identify a distinctness of the cycloalkane functionality on the global combustion behavior of the multicomponent fuel mixtures.

The use of the Derived Cetane Number (DCN), Hydrogen/Carbon (H/C), Molecular Weight (MW) and Threshold Sooting Index (TSI) as regulators of gas phase combustion behavior has been demonstrated several times [14-16, 25-27] with detailed discussion justifying their selection provided in [14,15] and also very recently in this journal by Dryer et al. [27].

2.2 Fuel Formulation The procedure used to formulate the mixture is as follows. The eighteen-mixture DCN matrix reported for the formulation of the 1st generation surrogate [14] is mapped for the hypothetical addition of methyl cyclohexane at 25 mole % by linearly interpolating between the measured DCN of each mixture and the 9 ACS Paragon Plus Environment

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methyl cyclohexane DCN. Following ASTM D 6890 [32] a methyl cyclohexane DCN of 23.5 ± 1.1 is measured with an Ignition Quality Tester. As an initial operating condition, the DCN is assumed to respond linearly to the mole fraction of these components. The resulting estimated DCNs of the eighteen mixture matrix of n-decane/iso-octane/toluene/methyl cyclohexane is combined with the equivalent H/Cs, MWs and TSIs [33], all of which do properly combine by molar proportionality, and regressed by the Box-Behnken design employed previously [14]. The regression suggests an n-decane/isooctane/toluene/methyl cyclohexane mixture of 0.374/0.169/0.183/0.274 mole fraction to closely match the combustion property targets of the 1st generation surrogate which provides a DCN target of 47.1, Table 1. This mixture is prepared by mass and its DCN is determined by the Ignition Quality Tester following ASTM D 6890 to be 44.7. Therefore, the Box-Behnken regression is inaccurate by ~2.4 DCNs in this parameter space. Utilising this measurement as a centering-factor a sensitivity-factor of -0.061 DCN per mole % methyl cyclohexane added to n-decane/iso-octane/toluene compositions is deduced. This factor is employed to correct the estimated DCNs of the hypothetical formulation matrix. When the regression procedure is repeated on the so-corrected matrix, a 0.422/0.174/0.179/0.225 mole fraction mixture of ndecane/iso-octane/toluene/methyl cyclohexane is suggested to be of DCN 47.4 and also to closely share the remaining combustion property targets with the 1st generation surrogate as per Table 1. This mixture is prepared by mass measurement and determined to be of DCN 47.1 ± 0.6, sharing the desired fidelity of +/- 1 DCNs to the target fuel. Note that it is not possible for any combination of these components to very closely approximate all four combustion property targets of the first generation surrogate simultaneously with the prescribed ~25 mole % of methyl cyclohexane. Here, the TSI parameters are more poorly matched showing a deviation of ~2.5 in the target TSI of 13.7.

The data presented in Table 1 shows the constraining significance of the DCN parameter in fuel formulation to be obvious. The target DCN of 47.1 is higher than the pure component “value” (The cetane number to derived cetane number correlation provided by ASTM D 6890 is strictly valid only within the 10 ACS Paragon Plus Environment

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range of 30-65 DCNs. Thus, many pure components are at or beyond the limits of its applicability.) of all components other than n-decane. Therefore, the addition of the prescribed ~ 25 mole % quantity of the low DCN methyl cyclohexane (23.5) must result in displacing some of the other low DCN components, iso-octane (~17) and toluene (~ 10). Though the target TSI of 13.7 is only approximated by the two fuels, the constraining effect of TSI on the mixture composition is such that the fraction of the only significantly sooting component, toluene, is preferentially preserved, with the major fraction of the incorporated methyl cyclohexane being compensated for by a much lower fraction of iso-octane. The significance of this behavior is expanded upon later.

2.3 Variable Pressure Flow Reactor and Counter Flow Diffusion Flame Burner The gas phase combustion kinetic behavior of this cycloalkane model fuel is measured experimentally at Princeton University in a Variable Pressure Flow Reactor (VPFR) for oxidative reactivity and in a Counter Flow Burner to determine the extinction limits of laminar diffusion flames. The technical and operational details of these apparatus are documented in detail in supporting works [34] and so only essential details of the results are discussed here. The VPFR is employed to determine oxygen, carbon dioxide, carbon monoxide, and water mole fractions, in addition to heat release (∆T) as a function of initial reaction temperature at constant pressure (12.5 atm) and fixed residence time (1.8 s). The uncertainties in the reported flow reactor measurements are O2 ≤4%; H2O ≤5%; CO ≤3%; CO2 ≤3% (no less than 30 ppm) of the reported reading, ±7 K in reported absolute temperatures (relative uncertainties are ±1.5 K), ± 0.2 atm in reported pressures and ±0.02 s in the intended residence time of 1.8 s. Fueldilute conditions are chosen so as to approximate adiabatic reaction conditions making the data more amenable to the zero-dimensional conditions that enable simulation with detailed chemical kinetic models [34]. Carbon concentrations of 0.3 mole % are regulated by mass flow of liquid fuel, corresponding to an oxygen concentration of 0.45 mole % to achieve stoichiometric reaction conditions for each fuel (H/C are very similar, Table 1). 11 ACS Paragon Plus Environment

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The diffusive extinction strain rate of flames of the methyl cycloalkane model fuel is determined as a function of nitrogen dilution at conditions consistent with prior works [14-16]. The temperature of the fuel side is maintained at 500 ± 5 K, and that of the oxidizer side, which is a flow of synthetic air (N2:O2 3.76:1), at 298 K ± 2 K. The estimated ties are ± 5% in the reported extinction limits and less than 3.5% in the reported fuel mass fractions. All chemicals are obtained from The Aldrich Chemical Company at greater than 99% purity and used without further purification.

3. Results and Discussion 3.1 Flow Reactor Reactivity The experimentally determined chemical kinetic reactivity of the methyl cyclohexane model fuel is compared to measurements of Jet-A (POSF 4658) and to its n-decane/iso-octane/toluene surrogate fuel in Figure 2. It can be seen that the addition of large quantities of the three lower reactivity species (comparative to n-decane), is not sufficient to completely retard the low temperature (< 800 K) reactivity of the methyl cyclohexane model fuel. It shares very closely the reactivity exhibited by both the real jetaviation fuel and the 1st generation surrogate. As apparent by comparison of carbon monoxide, water and oxygen concentrations, the degree of emulation of the simple 1st generation n-decane/iso-octane/toluene surrogate fuel to the associated target jet fuel at temperatures lower than ~800 K is very high. However, the transition to the hot-ignition (800-900 K) is mismatched by approximately 20-30 K. A similar discrepancy is observed with the more complex 2nd generation n-dodecane/iso-octane/n-propyl benzene/1,3,5 trimethyl benzene surrogate fuel that matches a wider range of combustion property targets exhibited by the target jet-aviation fuel [15]. Thus, the question is raised as to what extent the discrepancy is due to inadequacies in the combustion property target matching formulation procedure, or in the provision of an accurate chemical composition, as outlined in introduction.


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Further comparison to the reactivity of the methyl cyclohexane model fuel proves informative to this issue. It shows a slightly accelerated rate of reactivity in the hot ignition region, equating to approximately a 20-30 K lower temperature for the same quantity of products formed relative to the ndecane/iso-octane/toluene mixture. From Figure 2, it is apparent that the effect of perturbing the molecular structure composition of the fuel to include a cycloalkane functionality as a significant fraction, whilst simultaneously matching the prescribed combustion property targets, results in a modest but improved modulation of the kinetic reactivity relative to the target real fuel at the condition studied.

3.2 Diffusion Flame Strained Extinction Humer et al. [35] have measured diffusion flame extinction limits of three model fuels composed of 20 vol% methyl cyclohexane with a balance of different normal alkanes and aromatic molecules. While their study was not for the dedicated purpose of understanding the influence of each functionality on the extinction limit, using no measures to regulate the reactivity of the fuels studied, they observe extinction limits of their cycloalkane model fuels that are measurably higher than a reference JP-8 fuel. The result is inconclusive with regard to any distinctive reactivity strengthening power of the cycloalkane (methyl cyclohexane) used as a blend component. The designed fuels of Table 1 allow further analysis of this issue. The extinction limits of diffusion flames of the methyl cyclohexane model fuel in comparison to those of the 1st generation n-decane/iso-octane/toluene surrogate are shown in Figure 3 as a function of fuel mass fraction. In order to emulate diffusion flame extinction limits of a real fuel, it is understood that the diffusive potential of a fuel must be regulated by the matching of some pertinent measure, such as the average molecular weight [15, 24]. The 1st generation surrogate and the methyl cyclohexane model fuel both have molecular weights appreciably lower than that of the targeted Jet-A [15, 27], see Table 1. We have shown in prior work that a molecular weight mismatch of 120 g/mol (1st generation surrogate) relative to 157 g/mol (Jet-A POSF 4658) does not equate to a sufficient approximation of each fuel’s diffusive potential, producing measurably different extinction limits in diffusion flames [15, 24]. Due to 13 ACS Paragon Plus Environment

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the mismatch in diffusive potential, a comparison of the diffusion flame extinction limits of these model fuels to those of Jet-A (POSF 4658) by mass fraction offers little scientific utility, thus it is not reported here. The discussion therefore focuses on the relative reactivities of n-decane/iso-octane/toluene and ndecane/iso-octane/toluene/methyl cylcohexane fuels that do have very similar molecular weights at 120.7 and 118.2 g/mol respectively.

The objective of this study is to scientifically parameterise the effects of introducing a cycloalkyl functionality on the gas phase combustion of a multicomponent fuel mixture. The flow reactor measurements are suitable to probe the low temperature alkylperoxy radical driven chemistry of these fuels, and somewhat separately the hot-ignition high temperature chemistry. The diffusion flame configuration allows for the influence of fuel diffusivity on heat release by the high temperature flame chemical mechanism to be examined. Figure 3 shows the diffusive extinction limits of both model fuels to be very similar on a mass fraction basis. It is noted that the average molecular weights of each fuel are very similar at, 120.7 and 118.2 g/mol, for the n-decane/iso-octane/toluene and the n-decane/isooctane/toluene/methyl cyclohexane compositions respectively, implying equivalence in the rate of mass diffusion. Moreover, the enthalpy of combustion of each fuel per unit mass is also very similar (due to the constraining significance of sharing very similar hydrogen:carbon ratios), at 47.1 and 47.2 kcal/g respectively. Thus, given the equivalence in extinction limits, one may conclude that the chemical kinetic reactivity in high temperature flames of these fuels is very similar, inferring that at atmospheric pressure flame conditions the cycloalkane functionality itself does not significantly influence the radical pool in a manner distinct from the other paraffinic components of the surrogate mixture. This conclusion is consistent with the contention of Ji and Egolfopoulos [36] in their analysis of the premixed flame propagation velocities of binary normal-alkane/cycloalkane mixtures. There, they interpreted that any kinetic coupling between the fuel functionalities has a minor effect on the rate of flame propagation.


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For reference, the extinction limits of the pertinent pure components are also shown in Figure 3 [24]. Here, it is interesting to note the reactivity of n-decane, iso-octane and toluene scales with their expected Derived Cetane Numbers, Table 1. However, the reactivity of methyl cyclohexane is anomalous in this regard as its’ diffusion flame reactivity lies close to that of the high DCN (~65) n-decane, and above that of the DCN ~47 model fuels, despite showing a much lower DCN of ~23.5. This is a further indication that the ASTM D 6890 procedure preferentially tests a fuel’s kinetic potential in the low temperature regime dominated by alkyl peroxy radical initiated chain branching [25, 37-38].

3.3 Kinetic Modeling To the knowledge of the authors, the models of the Milano group [39] are the only proposition in the literature containing any description of the chemistry needed to simulate the oxidation of both model fuels, requiring a concurrent implementation of chemistry for n-decane, iso-octane and toluene in addition to methyl cyclohexane. While it is acknowledged that the model contains simplifying assumptions of chemical lumping at the high molecular weight fuel level, it is deemed prudent to investigate if this approach offers the fidelity required to analyse the nature of the accelerated reactivity of the methyl cyclohexane model fuel relative to the 1st generation surrogate at hot ignition. The model contains 435 species and more than ten thousand reactions. Model calculations of the n-decane/iso-octane/toluene and n-decane/iso-octane/toluene/methyl cyclohexane compositions are compared to the experimental measurements of the methyl cyclohexane model fuel in Figure 4. Model calculations have been performed under constant pressure, adiabatic conditions, with the simulation halted at the experimental residence time and the resulting species fractions compared directly to measurement, the comparison is thus representative, rather than fully quantitative [34]. Simulations are conducted using the AURORA module of Chemkin III [40].


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Firstly, it is observed that the model simulations capture the complicated temperature dependent qualities of the fuel reactivities to quantitative accuracy. Moreover, it is remarkable that such small differences in the trends in reactivity of each fuel are replicated by the model, which also suggests the 1st generation surrogate fuel to be of marginally slower reactivity in the hot-ignition transition relative to the methyl cyclohexane model fuel. Experiment suggests a difference in reactivity equating to an offset of 20-30 K, where the model also suggests an offset, but of < 20 K. Analysis of the model calculations suggests that there are two principle reasons for the shift in reactivity due to the inclusion of methyl cyclohexane to the base fuel of n-decane/iso-octane/toluene; 1) A reduced fraction of the reactivity inhibiting toluene and iso-octane, due to the constraints inherent to the fuel formulation procedure. 2) The production of reactivity enhancing intermediate species due to the alkyl radical betascission mechanism of methyl cyclohexane radicals. Evidence and reasoning supporting this summation is provided by the model analysis below. This is simplified by recognising that the n-decane fraction of both fuels is essentially constant at 42.2-42.7 mole %. Consequently, a concise analysis of the model calculations may be applied by contrasting the reaction flux of methyl cyclohexane relative to that of toluene and iso-octane, the fuel components which methyl cyclohexane displaces in the formulation, as already noted.

Model Analysis – Hot Ignition Transition, n-decane/iso-octane/toluene Considering the hot ignition transition at reference conditions of 850 K and 12.5 atm, methyl cyclohexane, iso-octane and toluene radicals are derived by hydrogen abstraction reactions from each of the respective parent molecules. In the case of methyl cylcohexane, this implies no correlation to the biradical forming carbon-carbon bond decomposition reaction that is peculiar to cycloalkanes as an explanation for the offset reactivity of each fuel. The consumption of these radicals occurs both through addition reactions with molecular oxygen and by beta-bond scission reactions. The partition in reaction 16 ACS Paragon Plus Environment

Page 17 of 38

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Energy & Fuels

paths consuming the alkyl radicals derived from methyl cyclohexane and iso-octane is approximately consistent between both alkanes, at ~69 % and ~65 % respectively, in favour of beta bond scission. Conversely, toluene radicals are consumed characteristically by bi molecular reactions that in turn produce very few active radicals at these conditions [341].

A sensitivity analysis is conducted by the methods described in [40]. The influence exerted by perturbation of the pre-exponent of the rate constant expression of each reaction of the kinetic model on the calculated heat release (∆T) at the hot ignition transition (1.8 s, 12.5 atm and 850 K) is selected to guide analysis. Tables 2 and 3 report the most sensitive reactions and their sensitivity coefficients. The sensitivity coefficients are normalised to the absolute value of the most sensitive reaction, where a minimum value of 5% of the largest sensitivity coefficient is imposed to truncate the reporting. This results in lists of twenty-eight and thirty important reactions for each respective fuel.

The sensitivity analysis of the n-decane/iso-octane/toluene 1st generation surrogate, is dominated by reactions involving the n-decane and toluene submodels, Table 2. It shows that the hydrogen abstraction alkyl radical beta-scission mechanism of n-decane is important to heat release, and that this activity is regulated by the radical consuming capacity of the toluene submodel, where very many different reaction pathways are inter-competitive. The overall reactivity is thus the result of a competition between the radical producing capability of n-decane and the radical consuming nature of toluene and its decomposition products. Importantly, this general analysis was also postulated in prior work, using a different, largely independent, kinetic model construction and considering other data sets of the 1st generation surrogate [14]. The fact that two independent modelling analyses would indicate the same general conclusion is satisfying.

Model Analysis – Hot Ignition Transition, n-decane/iso-octane/toluene/methyl cyclohexane 17 ACS Paragon Plus Environment

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Page 18 of 38

As the methyl cyclohexane model fuel contains 35% less toluene than contained in the first generation surrogate, this competition is lessened, with fewer active radicals being consumed due to the lower proportion of toluene. Thus, the hot ignition may be expected to accelerate. This is indicated in Table 3 where no reactions from the toluene submodel show sensitivity coefficients larger than 5% of the most sensitive reaction. In the case of the methyl cyclohexane model fuel, the body of reactions that are sensitive is shifted toward the small species submodel (H2/O2/C# .5C4H6+.5C5H8+NC5H11+.25C2H4

1684

+0.549

n-decane

NC10H19=>.5CH2CHCH2+.5SC4H7+.5NC7H14+.9C2H4+. 3NC4H8

1683

+0.449

Toluene

C6H5O+C6H5O=>DIBZFUR+H2O

1767

+0.387

Toluene

OH+DIBZFUR=>H2O+.1BIN1B+.75C12H8+CO

9602

+0.348

Toluene

O2+C6H5=C6H5O+O

595

+0.317

Toluene

HO2+C7H7=>C6H5CHO+H+OH

613

+0.235

n-decane

OH+NC10H20

1682

+0.214

Toluene

O+C7H8=RCRESOLO+H

650

+0.165

Toluene

C6H5C2H5=CH3+C7H7

832

+0.145

Toluene

OH+C6H6=H2O+C6H5

485

+0.097

Toluene

H+C7H8=C6H6+CH3

615

+0.095

Toluene

OH+BIPHENYL=>H2O+RBIPHENYL

6462

-0.065

Toluene

H+BIPHENYL=C6H6+C6H5

926

-0.077

Toluene

OH+C6H5OH=>OH+CYC5H6+CO

587

-0.079

Toluene

C6H5+C7H8=C6H5CH2C6H5+H

1149

-0.110

Toluene

O2+C16H9=>C14H9+CO+CO

856

-0.136

Toluene

CH3+C6H5O=>CRESOL

631

-0.137

Toluene

OH+C7H8=>C7H7+H2O

610

-0.171

Toluene

H+C6H5O=CO+CYC5H6

589

-0.178


Energy & Fuels

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n-decane

OH+NC10H20=>H2O+NC10H19

9275

-0.245

Toluene

H+C6H5O(+M)=C6H5OH(+M)

581

-0.281

Toluene

OH+DIBZFUR=>HCO+CO+C10H8

1768

-0.365

Small Species

HO2+HO2=H2O2+O2

13

-0.412

Toluene

C7H7+C7H7=C6H5C2H4C6H5

1040

-0.567

n-decane

NC10H19+O2=>NC10H19O2

1686

-1.000

Table 2. The twenty eight largest sensitivity coefficients for perturbation to rate expression pre-exponent with respect to calculated ∆T at conditions of 850 K, 12.5 atm and 1.8 seconds residence time for the 1st generation Jet-A POSF 4658 surrogate (n-decane/iso-octane/toluene, 0.427/0.33/0.243). † Positive value indicates accelerating influence on reactivity. “Small Species” refers to reactions involving species of carbon numbers less than five.

Reaction Sub Model

Reaction #

Normalised Sensitivity Coefficient †

Small Species

OH+OH(+M)=H2O2(+M)

14

+0.697

Small Species

C2H5OO=>O2+C2H5

488

+0.343

Small Species

HCO+M=CO+H+M

161

+0.163

Small Species

HCO3=>O2+HCO

1798

+0.133

Small Species/MCH

IC3H7OO=>O2+IC3H7

1820

+0.131

iso-octane

IC4H9T-OO=>IC4H9T+O2

1893

+0.052

Small Species/MCH

C3H5OO=>O2+CH2CHCH2

1843

+0.038


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Energy & Fuels

Small Species/MCH

O2+CHCHCH3=>HO2+PC3H4

211

+0.024

Small Species/MCH

NC3H7OO=>O2+NC3H7

1819

+0.023

Small Species

CH3OOH=OH+CH3O

489

+0.020

Small Species

HCO3H=>OH+OH+CO

1801

+0.019

iso-octane

IC8H17-OO=>IC8H17+O2

2029

+0.017

Small Species

O2+CH3CHO=HO2+CH3CO

155

+0.017

Small Species

C2-QOOH=>C2H4+HO2

495

+0.015

MCH

CYC5H8+OH=>C2H4+C2H3CHO+H

1412

+0.015

iso-octane

IC4H9T-OO=>IC4T-QOOH

1896

+0.013

MCH

CYC5H8+H=>C2H4+CH2CHCH2

1411

+0.010

MCH

OH+CYC5H8=>H2O+CYC5H7

7072

-0.078

Small Species/MCH

C3H3+O2=CH2CO+HCO

361

-0.097

iso-octane

HO2+IC4H7=>.8CH3COCH3+.2C3H6O+CH2O

572

-0.103

Small Species

O2+C2H4OH=>CH2O+CH2O+OH

526

-0.107

iso-octane

O2+SC4H7=>SC4H7OO

763

-0.118

Small Species/MCH

O2+IC3H7=>IC3H7OO

1818

-0.146

Small Species

C2H4+H(+M)=C2H5(+M)

83

-0.151

Small Species

O2+HCO=>HCO3

1797

-0.151

Small Species

O2+CH2CHO=>CH2O+OH+CO

223

-0.192

Small Species

O2+C2H3=>CH2CO+OH

219

-0.212

Small Species

O2+C2H5=>C2H5OO

487

-0.364

Small Species

O2+HCO=HO2+CO

17

-0.560

Small Species

H+O2(+M)=HO2(+M)

3

-0.560

Small Species

OH+CH2O=>H2O+HCO

3283

-0.706

Small Species

HO2+HO2=H2O2+O2

13

-1.000


Energy & Fuels

Table 3. The thirty largest sensitivity coefficients for perturbation to rate expression pre-exponent with respect to calculated ∆T at conditions of 850 K, 12.5 atm and 1.8 seconds residence time for the methyl cyclohexane model fuel (n-decane/iso-octane/toluene/methyl cyclohexane, 0.422/0.174/0.179/0.225). “MCH” is methyl cyclohexane, “Small Species/MCH” are reactions where C3 species populations are directly attributable to the consumption of methyl cyclohexane. † Positive value indicates accelerating influence on reactivity. “Small Species” refers to reactions involving species of carbon numbers less than five.

0.00025

0.00020

Species Mole Fraction

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Page 34 of 38

850 K and 12.5 atm Lines: Methyl Cyclohexane Model Fuel Symbols: 1st Generation Surrogate Fuel Ethylene iso-butene

0.00015

0.00010

0.00005

0.00000 0.0

0.5

1.0

1.5

2.0

Time / seconds

Figure 5. Calculated fractions [39] of select species for flow reactor oxidation during the hot ignition transition at 850 K, 12.5 atm, 0.3 % carbon, φ = 1.0 for 1st generation surrogate fuel (symbols), methyl cyclohexane model fuel (lines).


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Energy & Fuels

Reaction Sub Model

Reaction #

Normalised Sensitivity Coefficient †

n-decane


9228

+1.000

n-decane

NC10-QOOH+O2=>NC10-OOQOOH

2091

+0.876

n-decane

NC10-OOQOOH=>NC10-OQOOH+OH

2093

+0.702

iso-octane

IC8-QOOH+O2=>IC8-OOQOOH

2040

+0.170

iso-octane

OH+IC8H18=>H2O+IC8H17

6931

+0.161

Small Species

O2+HCO=>HCO3

1797

+0.149

iso-octane

IC8-OOQOOH=>IC8-OQOOH+OH

2044

+0.104

iso-octane

IC8H17-OO=>IC8-QOOH

2031

+0.101

Small Species

OH+OH(+M)=H2O2(+M)

14

+0.099

n-decane

O2+NC10H21=>NC10H21-OO

2082

+0.094

Toluene

OH+C7H8=>C7H7+H2O

610

+0.093

Small Species


223

+0.078

Small Species

CH3OO+HO2=CH3OOH+O2

505

+0.076

iso-octane

IC8T-QOOH=>IC8H16O+OH

2038

+0.072

n-decane

NC7H13O2=>NC7H13+O2

2025

+0.068

Small Species

O2+CH2CHO=>HO2+CH2CO

293

-0.073

iso-octane

IC8H17-OO=>IC8T-QOOH

2030

-0.076


Energy & Fuels

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Page 36 of 38

n-decane

O2+NC10H21=>NC10H20+HO2

1674

-0.081

iso-octane

IC8T-QOOH=>HO2+IC8H16

2039

-0.082

Small Species

OH+C2H5CHO=>H2O+C2H4CHO

4008

-0.083

Small Species

OH+CH2CO=>HCO+CH2O

183

-0.093

n-decane

NC10-OQOOH=>OH+C2H4CHO+.5CH3CHO+.5CH2O+ .65NC7H14+.19NC5H10

2096

-0.097

iso-octane

IC8-QOOH=>HO2+IC8H16

2035

-0.112

Small Species

HO2+HO2=H2O2+O2

13

-0.119

Small Species

O2+HCO=HO2+CO

17

-0.135

Small Species

OH+CH2O=>H2O+HCO

3283

-0.194

n-decane


9275

-0.263

n-decane

NC10-QOOH=>NC7H14O+OH+.3NC10H20

2086

-0.340

n-decane

NC10-QOOH=>HO2+NC10H20

2087

-0.410

n-decane

NC10-OOQOOH=>NC10-QOOH+O2

2092

-0.702

Table 4. The thirty largest sensitivity coefficients for perturbation to rate expression pre-exponent with respect to calculated ∆T at conditions of 650 K, 12.5 atm and 1.8 seconds residence time for the 1st generation Jet-A POSF 4658 surrogate (n-decane/iso-octane/toluene, 0.427/0.33/0.243). † Positive value indicates accelerating influence on reactivity. “Small Species” refers to reactions involving species of carbon numbers less than five.

Reaction Sub Model

Reaction #

n-decane



9228

Normalised Sensitivity Coefficient † +1.000

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Energy & Fuels

n-decane

NC10-QOOH+O2=>NC10-OOQOOH

2091

+0.920

n-decane

NC10-OOQOOH=>NC10-OQOOH+OH

2093

+0.739

Small Species

HO2+HO2=H2O2+O2

14

+0.372

n-decane

NC10H21-OO=>NC10-QOOH

2084

+0.242

n-decane

NC7H13+O2=>NC7H13O2

2024

+0.203

Small Species

O2+HCO=>HCO3

1797

+0.175

Methyl cyclohexane

MCYC6-QOOH+O2=>MCYC6-OOQOOH

2133

+0.161

Methyl cyclohexane

RMCYC6-OO=>MCYC6-QOOH

2123

+0.123

iso-octane

OH+IC8H18=>H2O+IC8H17

6931

+0.113

Small Species


223

+0.102

iso-octane

IC8-QOOH+O2=>IC8-OOQOOH

2040

+0.101

n-decane

O2+NC10H21=>NC10H21-OO

2082

+0.095

Methyl cyclohexane

RMCYC6+O2=>RMCYC6-OO

2121

+0.080

n-decane

OH+C7H8=>C7H7+H2O

610

+0.077

iso-octane

IC8H17-OO=>IC8T-QOOH

2030

-0.076

n-decane

O2+NC10H21=>NC10H20+HO2

1674

-0.083

Methyl cyclohexane

MCYC6-QOOH=>.5C2H4+CYC6H10+HO2

2127

-0.096

n-decane

O2+CH2CHO=>HO2+CH2CO

293

-0.097

Methyl cyclohexane

RMCYC6-OO=>MCYC6T-QOOH

2128

-0.103

n-decane

NC10-OQOOH=>OH+C2H4CHO+.5CH3CHO+ 2096

-0.105

183

-0.131

.5CH2O+.65NC7H14+.19NC5H10 Small Species

OH+CH2CO=>HCO+CH2O

Small Species

HO2+HO2=H2O2+O2

13

-0.133

Small Species

O2+HCO=HO2+CO

17

-0.159

Small Species

OH+CH2O=>H2O+HCO

3283

-0.177

n-decane


9275

-0.215

n-decane

NC7H13O2=>NC7H13+O2

2025

-0.301


Energy & Fuels

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Page 38 of 38

n-decane

NC10-QOOH=>NC7H14O+OH+.3NC10H20

2086

-0.368

n-decane

NC10-QOOH=>HO2+NC10H20

2087

-0.418

n-decane

NC10-OOQOOH=>NC10-QOOH+O2

2092

-0.737

Table 5. The thirty largest sensitivity coefficients for perturbation to rate expression pre-exponent with respect to calculated ∆T at conditions of 650 K, 12.5 atm and 1.8 seconds residence time for the methyl cyclohexane model fuel (n-decane/iso-octane/toluene/methyl cyclohexane, 0.422/0.174/0.179/0.225). † Positive value indicates accelerating influence on reactivity. “Small Species” refers to reactions involving species of carbon numbers less than five.


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