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Performance

It is emphasized that the calculations presented here are the results of the hierarchical model strategy of the technical construction. At this time, absolutely no adjustments have been made to any parameters of the adopted submodels in order to produce improved performance. As such, the comparison presented below may be viewed as genuine tests of predictability.

Detailed Model Performance in a Homogeneous System: Ignition Delay Time

Firstly, the performance of the fully detailed model (3147 species) against high pressure shock tube ignition delay measurements available for the additional surrogate fuel components, iso-cetane and n-hexadecane, is ascertained.

A. Iso-cetane and n-hexadecane/iso-cetane Shock Tube Ignition Delay

Figure 1 Oehlschlaeger et al. (9) shock tube ignition delay times for fuel in air mixtures of iso-cetane at 33-41 atm (symbols) and model calculations with the detailed model of this study (lines).

Figure 2 Won (Oehlschlaeger) et al. (15) shock tube ignition delay times for stoichiometric fuel in air mixture of n-hexadecane/iso-cetane, 0.459/0.541 at 20 atm (symbols) and model calculations with the detailed model of this study (lines).

Figure 1 presents comparison of the high pressure iso-cetane reflected shock ignition delay data of Oehlschlaeger et al. [9]to the computations of the detailed model between 875-1270 K. The model tracks the equivalence ratio dependence observed by experiment, but the computed ignition delays are approximately twice as long as measured in this Arrhenius-like regime. Comparisons to n-hexadecane ignition delay are not presented here, but we highlight that this general over estimation of alkane ignition delay is a feature of the modeling construct, as noted previously for n-decane and n-dodecane data sets. This behavior is also observed when testing the model against the measurements of the 0.459/0.541 n-hexadecane/iso-cetane mixture reported by Won et al. [15]. While the model is capable of reproducing the data to a reasonable degree, the calculations are marginally longer than experimental measurement, Figure 2.

B. Jet-A POSF 4658 Shock Tube Ignition Delay

Having previously established the performance of the detailed model against surrogate component [3] ignition delay data, Figure 3 presents the ignition delays measured by Wang and Oehlschlaeger [9] for Jet-A POSF 4658 at pressures close to 8, 12, 20 and 40 atm with calculations of the detailed model assuming the 2nd generation surrogate composition (n-dodecane/iso-octane/1,3,5 trimethyl benzene/n-propyl benzene 40.41/29.48/7.28/22.83 mole %). We have previously demonstrated this comparison for phi 1.0 in air at 20 atm conditions [2], but this is the first test of the end-to-end modeling strategy at variable pressures. Wang and Oehlschlaeger [9] have used our earlier modelling construct [1] to simulate this data with the 1st generation n-decane/iso-octane/toluene composition. Figure 3 reports a similar level of agreement, where the modeling methodology traces the pressure dependence to near quantitative accuracy at the highest temperatures, degrading to a more qualitative agreement at the lower temperatures where the complex intermediate temperature chemistry dominates the reacting flux. While the calculated and measured reactivities always trend in the same direction of, highest pressure fastest, lowest pressure slowest, the quantitative mismatch approaches a worse case factor-of-two over-estimation for the 40 atm condition at ~900 K. Overall, while the agreement is encouraging in terms of the applicability of the overall approach, it is to be noted that the model calculations generally show a reactivity somewhat slower than experiment, as exhibited by marginally longer ignition delays than measured.

Figure 4 presents more of the measurements of Wang and Oehlschlaeger, showing the effect of equivalence ratio (in air) on the ignition delay of Jet-A POSF 4658 at 20 atm. As before, the data is simulated assuming the 2nd generation surrogate composition. The simulations generally reproduce the quantitative temperature dependence of the ignition delay, again more accurately at high temperatures than low, with the trends in the equivalence ratio captured in the correct order but quantitatively offset to longer ignition delays at temperatures lower than ~1100 K.

Figure 3 shock tube ignition delay times for stoichiometric fuel in air mixtures of Jet-A POSF 4658 showing effect of pressure (symbols) and model calculations with 2nd generation (n-dodecane/iso-octane/1,3,5 trimethyl benzene/n-propyl benzene 40.41/29.48/7.28/22.83 mole %) Jet-A POSF 4658 surrogate. Lines are simulations with the detailed kinetic model of this study. ']

Figure 4 Wang et al. (9) shock tube ignition delay times for fuel in air mixtures of Jet-A POSF 4658 showing effect of equivalence ratio (symbols) and model calculations with 2nd generation (n-dodecane/iso-octane/1,3,5 trimethyl benzene/n-propyl benzene 40.41/29.48/7.28/22.83 mole %) Jet-A POSF 4658 surrogate. Lines are simulations with the detailed kinetic model of this study.

C. Syntroleum S-8, Shell SPK and Sasol IPK Shock Tube Ignition Delay

Wang and Oehlschlaeger further report ignition delay measurements of stoichiometric fuel-in-air mixtures of the specific synthetic fuels referred to in the formulation section; S-8, iso-paraffinic kerosene, IPK and Synthetic-paraffinic kerosene, SPK, at 20 atm. In the previous dedicated work [16], we have experimentally verified the appropriateness of a 51.9/48.1 mole % mixture of n-dodecane/iso-octane as a valid surrogate fuel for this S-8. Thus, this composition is confidently used to test the ability of the modeling strategy to at least differentiate between the reactivity exhibited by each fuel. The IPK and SPK fuels are simulated under the assumption that the surrogate fuel compositions provided in Table 1 properly emulate the respective target fuels. The comparison is thus quite a genuine test of the end-to-end predictability of the modeling strategy to indicate the reactivity of prototypical alternative liquid fuels. These data are compared to calculations with the detailed model in Figure 5.

Firstly, it is encouraging that both model and experiment indicate that each fuel should converge in reactivity at high temperature (> 1100 K) conditions, where the alkyl radical beta-scission mechanism can be expected to dominate the large radical consumption. Consistent in feature with the previously discussed comparisons of Jet-A at variable pressure and variable equivalence ratio, and also with the iso-cetane, and indeed n-alkane comparisons remarked previously [3], the model suggests ignition delays that are somewhat longer than actually measured. The magnitude of the quantitative offset varies with temperature and from fuel to fuel, but is approximately a factor-of-two at higher temperatures, and somewhat less than this in the negative temperature coefficient regime, with the case of the IPK being an exception. Here, it is impressive that the model would indicate this fuel to be of notably different reactivity in the low temperature regime only, as also observed by experiment. However, the model calculated ignition delays are approximately twice as long as measured.

Figure 5 Wang et al. (9) shock tube ignition delay times for fuel in air mixtures of Jet-A POSF 4658, iso-paraffinic kerosene (IPK) POSF 5642, S-8 POSF 4734 and synthetic paraffinic kerosene (SPK) POSF 5729 at 20 atm, and model calculations with surrogate fuels of Table 1 and the detailed kinetic model of this study. Lines are simulations, symbols are experiment.

Fuel

DCN

H/C

MW /

g mol-1

TSI

Toluene

~17 Ψ ₣

1.14

98.2

40.0*

iso-octane

<10Ψ ₣

2.25

114.2

  6.8*

1,3,5, trimethyl benzene

21.8

1.33

120.2

      62.0*

n-propylbenzene

28.2

1.33

120.2

53.0*

n-decane

~65 Ψ ₣

2.20

142.3

 4.5*

n-dodecane

~78 Ψ ₮

2.16

170.3

 7.0*

iso-cetane

~14.8 Ψ ṁ

2.13

226.4

     22.0*

n-hexadecane

~110.0 Ψ ṁ

2.13

226.4

9.0*

Jet-A POSF 4658 (Conventional)

47.1

1.95

157.5±2#ǂ

24.2#

S-8 POSF 4734 (Natural Gas to Liquid)

58.7

2.14

154.5±1.4ǂ

n/a‡

SPK POSF 5172 (5729) (Coal to Liquid)

58.4

2.24

138.3±2.4ǂ

n/a‡

IPK POSF 7629 (5642) (Natural Gas to Liquid)

31.3

2.195

148.5±1.8ǂ

10

Jet-A POSF 4658 1st Generation Surrogate (mole %)

47.4

2.01

120.7

14.1

n-decane

iso-octane

Toluene

42.7

33.0

24.3

Jet-A POSF 4658 2nd Generation Surrogate (mole %)

48.6

1.96

138.7

20.4

n-dodecane

iso-octane

1,3,5, trimethyl benzene

n-propylbenzene

40.4

29.5

7.3

22.8

S-8 POSF 4734 Surrogate (mole %)

58.7

2.14

143.4

6.8

n-dodecane

iso-octane

51.9

48.1

SPK POSF 5172 Surrogate (mole %)

62.1

2.19

147.9

6.9

n-dodecane

iso-octane

61.0

39.0

IPK POSF 5642 Surrogate (mole %)

31.7†

2.22

155.1

11.1

n-dodecane

iso-octane

n-hexadecane

iso-cetane

5.7

60.7

3.5

30.1

Table 1, Combustion Property Targets of selected alternative aviation fuels, conventional jet-A, and their suggested surrogates. * Measured by Mensch et al [17]. Ψ The cetane number to derived cetane number correlation provided by ASTM D 6890 is strictly valid only within the range of 30-65 DCNs. # Originally reported in [1,2] as 142±20 g/mol and 21.4 (TSI) based upon less accurate molecular weight determination methodology, correction discussed in [18]. ǂ Measured molecular weight by procedure discussed in 18. All parameters are measured in this study, unless ; ‡ Smoke points greater than 50 mm, not measureable within the ASTM D 1322 methodology, thus TSI is not determinable. ₣ Dooley et al. [1]. ₮ Dooley et al. [2]. ṁ Won et al. [15]. Ῑ Dooley et al. [16]. †estimated.

Model #

Fuel

Species #

Short Name

1

iso-cetane

221

ic16_221

2

iso-cetane

213

ic16_213

3

n-hexadecane

145

nc16_145

4

n-hexadecane

110

nc16_110

5

n-hexadecane

100

nc16_100

6

n-hexadecane

85

nc16_85

7

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

1164

S-8_1164

8

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

698

S-8_698

9

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

589

S-8_589

10

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

473

S-8_473

11

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

305

S-8_305

12

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

193

S-8_193

13

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

157

S-8_157

15

IPK surrogate, n-dodecane/iso-octane/ iso-cetane/n-hexadecane, 0.057/0.6-7/0.301/0.035

361

IPK_361

16

IPK surrogate, n-dodecane/iso-octane/ iso-cetane/n-hexadecane, 0.057/0.6-7/0.301/0.035

221

IPK_221

17

S-8 surrogate, n-dodecane/iso-octane, 0.519/0.481

36

S-8_c_36

 

Table 2. List of reduced and compact (“c”) kinetic models generated in this study.

Reduced Model Performance in a Flame Geometry: Laminar Burning Velocity

Several reduced models are produced to test flame performance as detailed by Table 1. The motivation to produce several models for the same purpose but of varying dimension is to provide some confidence that the model computations are fundamental in nature, predictive, and not adversely effected by over reduction.

A. Iso-cetane and n-hexadecane Laminar Burning Velocity

The laminar burning velocities of iso-cetane/air mixtures and n-hexadecane/air mixtures at equivalence ratios of 0.7-1.5 at 1 atm and an unburned gas temperature of 443 K are computed at various levels of detail and compared in Figure 10 to the measurements of Li et al. [19]. Firstly, in two separate counter flow flame studies, Li et al. determine the laminar flame behavior of these isomers to be quite different, with the highly methylated cetane isomer retarded in reactivity by approximately 10% relative to the normal-alkane. As the flame temperatures and Lewis numbers of the isomers are equivalent at comparable conditions, this would indicate an important difference in the chemical kinetic character of each molecule. It can be seen that each of the reduced models reproduce the main body of experimental data reasonably well, accurately deciphering the difference in reactivity of each fuel. More specifically, the model marginally under represents the burning velocity of iso-cetane by ~2-3 cm/s (in ~65 cm/s), whereas it the case of n-cetane, the model over estimates the peak burning velocity by ~5 cm/s at rich equivalence ratios. While not regarded as definitive proof of the values to be indicated by the parent detailed model, the close similarity in burning velocities calculated by several reduced models ranging from 85 to 145 species and 213 to 221 species for each fuel is assuring.

These tests, in addition to those we report previously [3] on model reproduction of the laminar burning velocity are important. The model is shown to reproduce the peak laminar burning velocity of all eight surrogate components of Table 1 to within a maximum deviation of ~10% and does not show a consistent bias to lower or higher burning velocities to the reference experimental determinations. This is shown to be the case for heavily reduced models, even for large molecular weight fuels. For example, Figure 6 shows that a mode comprised of just 86 species can accurately reproduce n-hexadecane burning velocities. This is an important confidence lending feature when reducing models for multicomponent surrogates, as apparent in the following section.

Figure 6 Figure 6. Laminar burning velocities of n-hexadecane (solid triangles, Li et al. (19)) and iso-cetane (hollow diamonds, Li et al. (19)) at 443 K and 1 atm, experiment (symbols) and model calculations with the reduced models of this study lines).

B. Jet-A, Syntroleum S-8 and Sasol IPK Laminar Burning Velocity

Amongst the various determinations of the laminar burning velocity for conventional and alternative aviation fuels, are the data sets of Hui et al. [20] and Ji et al. [21] which have both been obtained with the counterflow flame method. These data sets for equivalence-ratio-in-air mixtures are presented in Figure 11 for the candidate reference fuels that are the subject of this study, Jet-A POSF 4658 and S-8 POSF 4734, where experimentally verified surrogates have been formulated, and for IPK POSF 5642, where the surrogate composition has not been verified by experiment.

Hui et al. [20] contend that the laminar burning velocities of the these fuels ought to show no discernible difference, whereas Ji et al. [21] report that jet propulsion type fuels exhibit a lower rate of flame propagation than various alternative aviation fuels on account of the presence of an aromatic fraction. Ji et al. do not study the particular Jet-A or IPK that are the reference fuels of our work, however they do report data for S-8 POSF 4734. Thus to enable direct comparisons, only this S-8 data set is included in Figure 11. Note that the Hui et al. and Ji et al. experimental data sets of S-8 (both 1 atm counterflow flames, at 400 and 403 K) are inconsistent, particularly at rich equivalence ratios, where the difference approaches ~10 cm/s. The true laminar burning velocity of these fuels may consequently be regarded as uncertain to some extent.

It is viewed as important to test if the overall modeling strategy, through the described five-step procedure, possesses sufficient accuracy to inform this discrepancy. Model calculations, employing reduced models, are also included in Figure 7 resulting from initial conditions of 1 atm and 400 K. First, for S-8, it is apparent that these calculations better approximate the measurements of Ji et al. than those of Hui et al. The calculations of three reduced models, of various degrees, for the S-8 surrogate composition are quantitatively accurate to the data of Ji et al. at all but the richest equivalence ratio. Conversely, comparison of the model calculations are consistently 3-7 cm/s lower than the data of Hui et al.

Hui et al. also determined the burning velocity for the iso-paraffinic kerosene sample studied by Wang and Oehlschlaeger and discussed in this paper. The model calculations for this synthetic fuel are also consistently lower than the recommendations of Hui et al. [20]. Here, the lack of experimental verification of the viability of the suggested IPK surrogate to the IPK target fuel is a recognized source of uncertainty. More generally, by the inclusion of previously reported analysis of the petroleum derive aviation fuel, Jet-A POSF 4658, the model informs the debate above, by suggesting that the burning velocities of these fuel ought to lie in the order of IPKJet-A S-8, in apparent consistency with the recommendations of Ji et al. who state that premixed laminar flames of conventional jet propulsion type fuels should propagate at velocities lower the non-aromatic alternative fuels. However, these differences suggested by the model are small, the peak laminar burning velocities are calculated to differ by at most 7 cm/s (in 60 cm/s).

Figure 7 Figure 7. Laminar burning velocities at 1 atm and 400 K for S-8 (Hui et al. (20), hollow triangles) and 403 K (Ji et al. (21), solid triangles), for Jet-A (Hui et al. (20), hollow circles) and for IPK (Hui et al. (20) hollow squares). Model computations are performed with reduced models of this study and those of (3) (lines), with the S-8 surrogate composition (n-dodecane/iso-octane 51.89/48.11 mole %), the 1st generation (“1Gen_461” (3), n-decane/iso-octane/toluene 42.7/33.0/24.3 mole%) and 2nd generation (“2Gen_425” (3), n-dodecane/iso-octane/1,3,5-trimethyl benzene/n-propyl benzene 40.41/29.48/7.28/22.83 mole %) Jet-A surrogate compositions, and the IPK surrogate composition (30.1/3.5/60.7/5.7 mole % mixture of iso-cetane/n-hexadecane/iso-octane/n-dodecane).

Compact (CFD-appropriate) Model Performance for S-8 as a Prototypical Alternative Aviation Fuel

In addition to high fidelity combustion chemistry models, there is also a practical need for low-dimensional kinetic models for simulation of real fuel combustion chemistry, particularly for the aviation turbine applications we address here. To be useful for parametric computational combustor design and analysis, such models must be sufficiently compact to be used in multi-dimensional, multi-physics, reacting computational fluid dynamics (CFD) simulations. However, they must also retain sufficient complexity to be able to predict combustor temperature distributions; non-equilibrium emissions; and transient combustion behaviors such as lean blow-out, high altitude relight, and flashback [22]. Global and few-step models involving only a handful of species [22,23] or models involving quasi-steady assumptions [24,25] typically lack the feedback coupling of radical/small molecule chemistry with the decomposition of the parent fuel species [22–27]. Even the most severely reduced (e.g., by PFA) models – such as those discussed above with ~100 species – incur prohibitive computational costs when used for complex model-based combustor design and analysis. Compact CFD-appropriate kinetic schemes of the order of 2-3 dozen species (or even fewer) can therefore provide a compromise between predictive fidelity in global combustion behavior and computational costs. By sacrificing (often) unimportant species as well as strict adherence to best-available chemical kinetic constraints, these compact models remain sufficiently detailed to capture the global reacting flow feedback dynamics among fuel, intermediates, pollutant species, and radicals without the excessive computational costs associated with larger models.

A. Formulation of CFD-compact model

In broad terms, the provisional 36 species S-8 surrogate compact model, labeled as “S-8_c_36” (model #17 in Table 2), is developed as follows. First, the identified surrogate formulation is imposed on a conservative model reduction (by PFA), which removes unnecessary fuel and intermediate species from the total 3147 species count of the detailed municipal model. The resulting S-8_473 reduced model is then used to generate transient, zero-dimensional, fuel-air model predictions over a wide, user-specified range of (φ, T, p), similar to the PFA reduction approach discussed above. These benchmark calculations serve as a target database for compact model optimization. Specific targets for optimization are user-specified; for the present example, the compact model seeks to emulate CO, CO2, and H2O mole fraction histories computed from S-8_473 simulations. At fuel-air conditions relevant to aviation combustor applications, these particular species tightly constrain heat release rate (and therefore, temperature evolution), as well as indicate ignition delay time and the radical pool responsible for flame propagation rate and CO/NOx emissions. In other words, these targets are regarded as excellent minimal constraints for global combustion behaviors.

The compact model to-be-optimized (“seed” model) begins as an assumed assembly that includes the previously validated, hierarchically constructed H2/CO core chemistry of the 3147 species detailed model. This core chemistry is not subject to optimization. In this way, the “frozen” core chemistry respects the previous hierarchical construction and validation, as well as reduces the number of degrees of freedom for compact model optimization. Chemistry for intermediate C1-C3 species is added to the frozen core. This chemistry is also in common with the municipal model, but is subject to optimization. Several intermediate species identified as unimportant by PFA reduction of the full detailed model (e.g., HOOCH) are removed from the seed model as an initial step toward reducing the overall species count and optimization computational costs for the compact model. Finally, skeletal and lumped chemistry relevant to the parent fuel components is added to the seed chemistry. The corresponding reaction rate coefficients of this fuel chemistry subset are also subject to optimization.

The complete seed model discussed here involves 36 species describing S-8 combustion, and its inputs are optimized to reproduce the benchmark predictions of the S-8_473 reduced model. To efficiently sample the rate coefficient space that is to-be-optimized, rate coefficients for reactions of the fuel components and intermediates are initially populated using Latin hypercube sampling and user-defined rate coefficient bounds. An evolutionary algorithm applied to these rate coefficients to-be-optimized seeks an optimal solution over the whole discretized (φ, T, P) space previously identified.

B. Compact Model Performance

Exemplar results of the present S-8_c_36 optimization against PFA-reduced models appear in Figures 8 and 9. For ignition delay, Figure 12, the compact model essentially performs as well as the 473 species reduced model over the ≥ 800 K temperature range targeted by the compact model optimization. Also worth noting are the predictions of the (PFA-reduced) S-8_193 and S-8_157 models. Despite a significantly higher species count than the compact model, these models are unable to predict intermediate and low temperature ignition delay times, even qualitatively. This suggests that the mechanistic content of the present compact model seed may be of higher fidelity than that of models produced by aggressive application of PFA or other non-optimization-based methods.

Particularly at fuel rich conditions, the S-8 compact model predictions of laminar burning velocity, Figure 9, appear to deviate from the predictions of larger PFA-reduced models. The maximum deviation from consensus of the more detailed models is ~5-6 cm/s, which is similar to the consistency in burning velocity data sets from independent laboratory determinations as discussed previously and shown in Figure 7. These fuel-rich burning velocity deviations are a target of future investigation and improvement as the CFD-compact model approach continues to develop.

The present demonstration of compact model generation is provisional, and we anticipate significant room for improvement, particularly in the reduction of species from the compact model example discussed here. Initial computations suggest that several species appearing in the compact model (e.g., CH2, C3H3) are unnecessary to achieve the present (or better) agreement with more complex model predictions and optimization targets. Nevertheless, the present preliminary level of fuel-specific model reduction is significant. Using the number of species cubed as a computational figure-of-merit (the cost of simple Jacobian inversion), computations with the present 36 species model may be accelerated by a factor of ~100 compared to those of the S-8_157 reduced model, which has been demonstrated here to fail in predicting ignition below ~1000 K. Relative to the benchmark S-8_473 reduced model, compact model computational times may improve by a factor of ~2000. Future improvements to the compact model generation approach will further improve computation time and predictive accuracy.

Figure 8 Figure 8. Predicted homogeneous, constant volume/internal energy ignition delay times for stoichiometric fuel-in air-mixtures of the S-8 surrogate (n-dodecane/iso-octane 51.89/48.11 mole %) at ~20 atm. Lines are models simulations using the S-8 surrogate composition and the detailed and reduced kinetic models of this study, symbols are calculations with the 36 species compact S-8 surrogate model.

Figure 9 Figure 9. Predicted laminar burning velocities at 1 atm and 400 K for the S-8 surrogate (n-dodecane/iso-octane 51.89/48.11 mole %). Lines are model calculations with PFA-reduced models of this study, symbols are calculations with the 36 species compact S-8 surrogate model

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