Small Skeletal Kinetic Reaction Mechanism for Ethylene–Air

Article pubs.acs.org/EF

Cite This: Energy Fuels 2017, 31, 14138−14149

Small Skeletal Kinetic Reaction Mechanism for Ethylene−Air Combustion Niklas Zettervall,† Christer Fureby,† and Elna J. K. Nilsson*,‡ †

Defense & Security, Systems and Technology, Swedish Defense Research Agency − FOI, SE 147 25 Tumba, Stockholm, Sweden Combustion Physics, Department of Physics, Lund University, Box 118, SE 221 00, Lund, Sweden

‡

S Supporting Information *

ABSTRACT: Ethylene is a fuel considered for high-speed ram- and scramjet combustion applications, mainly because of the short ignition delay time resulting from its high reactivity. Further research and development on these combustion systems would benefit from simulations of large eddy (LES) type, which allow some chemical detail to accurately predict combustion characteristics and pollutant formation. In the present work, a chemical kinetic mechanism suitable for LES is presented, consisting of 66 irreversible reactions between 23 species. The mechanism is extensively validated for combustion characteristics related to ignition and flame propagation over a wide range of pressure, temperature, and equivalence ratios that previously published mechanism of this size have not covered. Agreement with a detailed reference mechanism is good for ignition delay, flame temperature, and laminar burning velocities. In addition, overall concentration profiles of major stable products are in overall good agreement with a reference mechanism. The skeletal mechanism shows an overall good performance in combination with a numerical stability and short computation time, making it highly suitable for combustion LES.

1. INTRODUCTION Ethylene, C2H4, the simplest of the alkenes, is a key intermediate in the oxidation of higher order alkanes and alkenes and thus of importance for combustion of most practical fuels. In addition, it is an important precursor to the formation of soot particles. Ethylene is in itself a highly reactive agent and can, together with methane (CH4), be considered a surrogate for the endothermically cracked military jet propellant JP-7.1,2 Ethylene can be used as fuel in different types of combustors, such as the subsonic, nonpremixed annular combustor by Bauerheim et al.,3 representing a simplified gas turbine combustor, or the high-speed ramjet discussed by Hitch et al.4 and the supersonic ramjet (scramjet).5−18 The use of ethylene as a fuel in the mentioned combustion devices will benefit from an in-depth understanding of ethylene combustion to allow for optimized efficiency and limited emission of hazardous pollutants. Successful combustion research includes experimental as well as computational studies to investigate the combustion process on all scales,19,20 from chemical reactivity on molecular level to physical phenomena governing the turbulent flame. There is a growing interest in using hydrocarbon fuels,1,2,21−28 and especially ethylene,5−18 in ramjet- and scramjet combustors, as the main fuel, as one component of a high-energy density multifuel mixture, or simply as a product of JP-type fuel cracking and decomposition. Most supersonic combustors use hydrogen fuel due to its low ignition time, but hydrocarbon fuels have the advantage of high density and the ease of use and maintenance. A wide range of experimental studies with supersonic combustors utilizing hydrocarbons have been performed,1,2,5−18,21−28 with experiments performed by Driscoll and Micka13,14 being widely recognized. Ethylene is attractive as a fuel in ramjet and scramjet engines because it is © 2017 American Chemical Society

suitable when transitioning from running on pure hydrogen, which is associated with practical challenges in the handling of the fuel,29,30 to hydrocarbons. The main reason for the interest in ethylene use in supersonic combustors is due to its high reactivity, manifested by its short ignition delay time, exemplified by Calcote et al.31 This short ignition delay time is well-demonstrated in the X-51A scramjet engine demonstrator (SED), originally used in the HyTech program,29 where ethylene is used for the initial ignition process, before transitioning to higher-order hydrocarbons. The highly reactive characteristics of ethylene therefore makes it suitable for introduction to hydrocarbon fuels in supersonic combustion. That said, even the high reactivity of ethylene cannot match that of pure hydrogen fuel. Therefore, a flame holding geometry like a cavity flameholder is often needed in scramjet combustors to increase the fuel-residence time,32−35 allowing the buildup of a radical pool and enabling ignition of the fuel. Rapid development in computational capacities in the past decade has enabled the use of large eddy simulations (LES) for a wide range of applications.36,37 However, computational capacities are still a limiting factor, with the cost being dependent on the geometric representation, the simulation model employed, and the complexity and numerical stiffness of the chemistry. A detailed representation of the chemical combustion process is not feasible for use in finite rate LES due to the very high computational cost. Instead, a size-reduced reaction mechanism is needed, as demonstrated by Bulat et al.38 and Zettervall et al.,39 with the latter presenting combustion LES of a full annular combustor. Received: July 17, 2017 Revised: October 11, 2017 Published: November 17, 2017 14138

DOI: 10.1021/acs.energyfuels.7b02078 Energy Fuels 2017, 31, 14138−14149

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Energy & Fuels Table 1. Summary of Experimental Data and Modeling Performed Using the Reference Mechanism40 experiments

reference simulations

p (atm)

T (K)

ϕ

ref

p (atm)

laminar flames

1−5 1 1 1−2

65 66 67 68 70 69 46

300−750

0.5−1.8

1 1−25

0.6−1.7 0.6−1.8 0.6−1.7 0.8−1.6 0.6−1.4 0.5−1.7 0.3−2.0

1−20

flame temperature ignition delay

298 298 298 298 360−470 298 1000−1400

1 1.1−23.6

300 1000−1400

0.5−1.8 0.3−2.0

type

T (K)

ϕ

implemented by Law,19 who first reduced the size of the mechanism to 205 reactions among 33 species and then further simplified it to a final 21 species and 16 lumped reactions assuming a quasi-steadiness for species. A disadvantage with such an approach is that the mechanism is restricted to limited conditions. The time scale for the combustion in high-speed applications is primarily determined by the fuel-air mixing time and the ignition delay time of the fuel itself.50 At highly elevated speeds, the diffusion process is one or more orders of magnitude slower than the fluid-dynamic time scales. This means that the combustion process is less dependent on the laminar flame speed than at low-speed conditions; it is more determined by the ignition process. This is true not only for combustion at supersonic flows but also for combustion at highly subsonic conditions, as is the case for ramjet engines. What this means is that if a kinetic reaction mechanism is to be used for the simulation of combustion under high-speed conditions, it must predict the ignition delay time accurately. Further downstream in the combustion chamber, in cavities or behind flame stabilizers where the residence time could be significantly longer, the accuracy of the laminar flame speed prediction of a mechanism becomes increasingly important. The demands on a skeletal reaction mechanism for use in finite rate chemistry LES is thus to predict the ignition delay time, the laminar flame speed, and flame temperature. It should also capture major species concentrations for emission predictions over a wide range of conditions. To meet the need for a compact ethylene reaction mechanism designed for use in finite rate chemistry LES, we here propose a novel skeletal reaction mechanism designed for ethylene−air combustion. The mechanism is developed to model combustion chemistry over a wide range of conditions with respect to pressure, temperature, and equivalence ratio. Particular attention is paid to ignition behavior because this is of importance in the high-speed combustion applications in which ethylene is considered a suitable fuel. The present paper includes a description of mechanism development and chemical considerations as well as a thorough validation against experimental data and detailed modeling.

Combustion kinetics reaction mechanisms can be of different levels of chemical detail. The most-simplified mechanisms, called global reaction mechanisms, consists of one to six reactions, essentially representing fuel decomposition and final product formation without including any intermediate reaction steps. The detailed reaction mechanisms are designed to capture the full chemical complexity in a combustion process, including hundreds or thousands of reactions. The skeletal reaction mechanisms, also called reduced, are compact versions of detailed mechanisms, disregarding species and reactions of minor importance. In line with detailed mechanisms, the skeletal mechanism can have chemically accurate radical and species oxidation and production description, resulting in accurate species concentration and overall combustion parameter predictions. Because of its considerable smaller size (and, hence, a lower computational cost) compared to a detailed mechanism, the skeletal reaction mechanism can be made suitable for finite-rate combustion LES. Several detailed mechanisms for ethylene combustion are available,40−44 consisting of reaction numbers in the range of approximately 240 to 1550 reversible reactions. Xu and Konnov45 investigated the capacity and reaction routes of four detailed mechanisms and concluded that there are significant discrepancies, meaning that the combustion chemistry of ethylene is not fully understood. Interestingly, Konnov and Xu found that the disagreement between experiments and modeling is most significant at atmospheric pressures. In a thorough experimental and computational study of ethylene ignition in air, Kopp et al.,46,47 reached similar conclusions and made significant updates to improve a mechanism by Metcalfe et al.40 The temperature and pressure range in that study incorporates many of the operating conditions of ram- and scramjet test rigs. Skeletal or reduced reaction mechanisms for ethylene combustion have been developed with detailed mechanisms as a starting point. Zong et al.48 created several reduced reaction mechanisms, of which the smallest one in good agreement with the detailed mechanism that had 115 steps and 24 species. A smaller version with only 19 species and 68 steps did not show satisfactory agreement. Lou et al.49 proposed a reduced mechanism for C1−C3 and NOx, including 50 species and 337 reactions. Albeit being of a reduced format, these skeletal mechanisms are challenging the upper limits of what could be accepted in terms of computational cost when using finite-rate combustion LES for complex real-world applications such as full annular combustors and ram- and scramjets. It is important to note that the mentioned reduced mechanisms were developed and validated to experimental or modeling data over a narrow range of conditions, thus not ensuring that the included chemistry is suitable to accurately predict combustion at the conditions relevant for the applications. An approach to reduce the size of an ethylene mechanism even further was

2. MECHANISM DEVELOPMENT The process of mechanism development starts with the selection of a relevant set of chemical reactions and their corresponding rate parameters. Using experimental data and simulation results from detailed mechanisms, the skeletal mechanism is then tuned by adjustment of the rate parameters. The detailed mechanism, Aramco 2.0 by Metcalfe et al.,40 consisting of 1542 reversible reactions and 252 species, was used as the reference target in combination with experimental data summarized in Table 1. Available data for ignition and 14139

DOI: 10.1021/acs.energyfuels.7b02078 Energy Fuels 2017, 31, 14138−14149

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Energy & Fuels Table 2. Complete Skeletal Reaction Mechanism Z66 (k = A × Tn × exp(−Ea/RT); units of s, mole, cm3, cal, and K A

reaction and no.

n

Ea

ref

1.50 × 10

0

0

21b

4.17 × 10

0

11 030

21

(3)

1.80 × 10

1

9400

a

(4)

12

1.00 × 10

0

48 200

a

5.00 × 1012

0

5000

a

(6)

3.31 × 1012

0

1130

58

(7)

11

1.58 × 10

0

31 180

58

(8)

4.79 × 1012

0

1230

58

C2H3 + H 2O → C2H4 + OH

(9)

12

1.20 × 10

0

14 000

58

C2H4 + CH3 → C2H3 + CH4

(10)

1.00 × 1013

0

13 000

58

(11)

3.02 × 10

0

12 580

58

1.80 × 10

0

44 800

a

2.00 × 10

0

2500

58

7.00 × 10

0

1100

a

1.23 × 10

1

10 360

58

14

C2H5 + H → CH3 + CH3

13

(1)

C2H4 + H + M → C2H5 + M

C2H4 + H → C2H5 C2H4 → C2H3 + H

(2)

12

C2H4 + H → C2H3 + H 2

(5)

C2H4 + O → HCO + CH3 HCO + CH3 → C2H4 + O C2H4 + OH → C2H3 + H 2O

C2H3 + CH4 → C2H4 + CH3

C2H3 → C2H + H 2

10

13 12

(12)

C2H3 + H → C2H 2 + H 2

13

(13)

C2H3 + OH → C2H 2 + H 2O

(14)

C2H 2 + H + M → C2H3 + M

(15)

14 11

2.00 × 10

0

19 000

58

C2H 2 + OH → C2H + H 2O

(17)

8.00 × 1012

0

5000

58b,c

C2H + H 2O → C2H 2 + OH

(18)

5.37 × 1012

C2 H 2 + H → C2 H + H 2

(16)

0

16 360

58

C2H 2 + O → C2H + OH

(19)

3.24 × 1015

0.6

12 000

58c

C2H + OH → C2H 2 + O

(20)

2.95 × 1014

0.6

910

58

1.10 × 109

1

770

58

C2 H + H + M → C2 H 2 + M

(21)

C2H + O2 → HCO + CO

(22)

13

1.00 × 10

0

7000

58

HCO + CO → C2H + O2

(23)

8.51 × 1012

0

138 400

58

8.00 × 1012

0

5000

a

C2H + OH → HCO + CH

(24)

CH4(+ M) → CH3 + H( +M)

54d

(25) 6.30 × 1014 1.00 × 1017

kf kf0

CH3 + H(+ M) → CH4(+ M) kf kf0 CH4 + H → CH3 + H 2

0 0

104 000 86 000 54d

(26) 5.20 × 1012 8.25 × 1014

0 0

−1310 −19 310

(27)

2.20 × 104

3

8750

54

(28)

9.57 × 10

3

8750

54

CH4 + OH → CH3 + H 2O

(29)

6

1.60 × 10

2.1

2460

54

CH3 + H 2O → CH4 + OH

(30)

3.02 × 105

2.1

17 422

54

CH3 + H 2 → CH4 + H

2

CH3 + O → CH 2O + H

(31)

13

6.80 × 10

0

0

54

CH3 + O2 → CH3O + O

(32)

3.00 × 1013

0

25 652

54b

CH3 + OH → CH 2 + H 2O

(33)

7.60 × 106

2

5000

56

CH3O + H → CH 2O + H 2

(34)

2.00 × 1013

0

0

54

13

2.40 × 10

0

28 812

54

3.00 × 1013

0

0

56

(37)

1.13 × 10

2

3000

56b

(38)

13

5.00 × 10

0

3991

54b

1.40 × 1014

0

1100

54b,c

13

5.70 × 10

0

0

56

CH + OH → HCO + H

3.00 × 1013

0

0

56

CH + O2 → HCO + O

13

3.30 × 10

0

0

56

8.40 × 1013

0

200

56

4.00 × 10

0

0

54

CH3O + M → CH 2O + H + M CH 2 + O → CO + H 2

CH 2 + OH → CH + H 2O CH 2O + H → HCO + H 2

CH 2O + OH → HCO + H 2O CH + O → CO + H

(39)

(40) (41)

CH + CO2 → HCO + CO

HCO + H → CO + H 2

(35)

(36)

(42) (43) (44)

7

13

14140

DOI: 10.1021/acs.energyfuels.7b02078 Energy Fuels 2017, 31, 14138−14149

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Energy & Fuels Table 2. continued A

reaction and no.

Ea

ref

1.60 × 10

0

14 700

(46)

1.51 × 107

1.3

−758

54

CO2 + H → CO + OH

(47)

1.57 × 109

1.3

19 800

54,c

14

54

H + O2 → OH + O

(48)

5.00 × 1014

0

16 800

54,b

OH + O → H + O2

(49)

1.20 × 1013

0

690

54,b

O + H 2 → OH + H

(50)

1.80 × 10

1

8826

54

OH + H → O + H 2

(51)

8.00 × 109

1

6760

54

9

10

H 2 + OH → H 2O + H

(52)

1.17 × 10

1.3

3626

54

H 2O + H → H 2 + OH

(53)

6.00 × 109

1.3

18 588

54,b

OH + OH → O + H 2O

(54)

6.00 × 108

1.3

0

54

O + H 2O → OH + OH

(55)

4.00 × 109

1.3

17 029

54,b

2.50 × 1018

−0.8

0

54,e

1.50 × 10

0

1004

54

13

2.50 × 10

0

700

54

2.00 × 1013

0

1000

54

2.00 × 10

0

0

54,b 54

H + O2 + M → HO2 + M H + HO2 → OH + OH

H + HO2 → H 2 + O2

(56)

14

(57) (58)

OH + HO2 → H 2O + O2

(59)

HO2 + HO2 → H 2O2 + O2

(60)

14

H 2O2 + M → OH + OH + M

(61)

1.30 × 10

0

45 500

OH + OH + M → H 2O2 + M

(62)

14

17

9.86 × 10

0

−5070

54

H 2O2 + OH → H 2O + HO2

(63)

1.00 × 1013

0

1800

54

H 2O + HO2 → H 2O2 + OH

(64)

2.86 × 1013

0

32 790

54

OH + H + M → H 2O + M

(65)

2.20 × 1022

−2

0

54

1.80 × 1018

−1

0

54

H + H + M → H2 + M a

n

CO + OH → CO2 + H

(45)

HCO + M → CO + H + M

(66)

b

c

This work. See the text. Pre-exponential factor has been modified compared to the cited reference. Activation energy has been modified compared to the cited reference. dCollisional coefficients: C2H4, 3; CH4, 6.5; CO, 0.75; CO2, 1.5; H2, 1; H2O, 6.5; N2, 0.4; O2, 0.4. eCollisional coefficients: CH4, 6.5; CO, 0.75; CO2, 1.5; H2, 1; H2O, 6.5; N2, 0.4; O2, 0.4.

flame propagation have been reviewed and evaluated by Xu and Konnov.45 The skeletal ethylene reaction mechanism presented here follows a similar mechanism build-up as in previous work done by Larsson et al. on methane51 and Zettervall et al. on propane52 and kerosene.39,53 Following the methodology outlined in the paper describing the kerosene mechanism the presented mechanism is divided into three submechanisms: fuel breakdown, intermediate hydrocarbon oxidation, and base mechanism. The mechanisms constructed using this approach include about 20−25 species and 40−80 reactions. An advantage of the mechanisms is that they have a low numerical stiffness. Because of the interest in applying the mechanism presented here in finite rate chemistry LES of ramjet and scramjet engines, the primary development target was the ignition delay time, and the secondary target was the laminar flame speed. Achieving well-predicted ignition delay times and laminar flame speeds are essential for combustion LES because they represent the link between the chemical kinetics and the fluid flows and a well predicted laminar flame speed also acts as an indicator for well-developed chemistry. Additional targets are concentrations of the major species, defined here as CO2, H2O, CO, and H2. These are the species found in the highest concentrations in the combustion process and they represent the main species of interest in both subsonic and supersonic engines and also indicate if complete combustion has been achieved. The skeletal mechanism presented here contain 23 species and 66 irreversible reactions. The mechanism is from now on

referred to as Z66 and is listed in Table 2. From here on, all reactions are referenced with reaction numbers given in Table 2. Figure 1 show a graphical overview of the main reaction paths for a flame at ambient conditions at peak flame speed. 2.1. Base Mechanism. The underlying H2−O2 and CO− O2 chemistries used here are the same as in previous work by Larsson et al.51 and Zettervall et al.,39,52,53 originating from the 35-step methane−air skeletal mechanism, SG35, of Smooke and Giovangigli54 (reactions 25−32, 34, 35, 38, 39, and

Figure 1. Reaction path diagram for the reduced ethylene−air reaction mechanism for a laminar flame at 300 K, 1 atm, and φ = 1.1. Dashed boxes enclose the three submechanisms: red, fuel breakdown; blue, intermediate hydrocarbon oxidation; and green, the base mechanism. 14141

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Energy & Fuels

previous work by Zettervall et al. for propane52 and kerosene39,53 but with the addition of reactions 12, 14, and 24. The reason for the addition of reaction 12 was its importance for the ignition delay time, significantly reducing it and resulting in a better match with the experimental data for a wide range of pressures and equivalence ratios. The addition of reaction 12 also means that the H and OH radicals are not becoming rate-limiting via reactions 13 and 14 for the oxidation of C2H3. The oxidation of the acetylene (C2H2) produced by reactions 15−17 and 19 occur via reactions with active radicals O, OH, and H. The closing of the intermediate submechanism pathway uses reactions 22 and 24, finalizing the carbon pathway from C2 down to the C1 species and thus coupling to the underlying H/ C1/O mechanism. In the real systems (and detailed mechanisms), C2H3 can undergo several reaction steps: H abstraction by O2 to form C2H2, addition of O2 to form a peroxide radical, or bond scission to mainly form formaldehyde and HCO. The chemistry of oxygenated intermediates is particularly important at low temperatures, and because the present mechanisms focus on higher-temperature applications, the compromise was made to represent the intermediate chemistry subset with nonoxygenated species. C2H3 is thus mainly converted into C2H2 and C2H, such that the latter acts as a simplified representation of the species CH2CHO, an oxygenated intermediate of significant importance for ethylene combustion also at high temperatures. Just like the CH2CHO in the detailed mechanisms, the C2H in the reduced mechanism breaks up in the C1 fragments HCO, CH2O, and CH3.

44−66). The SG35 mechanism has been extensively used in LES, for example in the works by Fureby et al.38 and Ehn et al.,55 and the overall performance of the mechanism is satisfactory at fuel-lean conditions. To improve the SG35 mechanism, a CH2/CH subset of seven reactions (reactions 33, 36, 37, and 40−43) was added on the basis of considerations presented by Glassman et al.56 and implemented and described by Larsson et al.51 The added subset improved the laminar flame speed, the flame temperature, and the CO2/CO and H2 concentration predictions at stoichiometric and fuel-rich conditions, with the improvements in laminar flame speed and flame temperature demonstrated by Larsson et al.51 2.2. Fuel Breakdown Reactions. The small size of the ethylene molecule enables a relatively detailed treatment of the fuel breakdown via its initiation reactions. The initiation of the fuel breakdown start from the thermal decomposition reaction:

C2H4 → C2H3 + H

(4)

initializing the radical pool. Once that radical pool has been formed the fuel is oxidized via reactions with H, O, OH, and CH3. According to work by Glassman et al.,56 the oxidation of the ethylene molecule occurs mainly through the reaction with O, reaction 6, with methyl and formyl radicals as the product species. Reaction 6 creates a bridge directly from the fuel molecule to the underlying base H/C1/O mechanism: C2H4 + O → HCO + CH3

(6)

Apart from reaction 6, all of the reactions involving ethylene oxidations produces C2-intermediate species, either C2H5 or C2H3. C2H5, created via either reaction 2 or reaction 3, C2H4 + H + M → C2H5 + M

(2)

C2H4 + H → C2H5

(3)

3. MODELING DETAILS Modeling of the ignition delay time and laminar flame propagation were performed using the Cantera software v2.3.0.59 The laminar flame speed calculations used adaptive grid refinements, resulting in grids with around 500 grid points. Ignition delay times were simulated using constant pressure assumptions with time steps of 5.0 × 10−8 for lower temperature conditions (1000−1100 K) and 1.0 × 10−8 for higher-temperature conditions. Thermodynamic data were taken from the recent database of Gos et al.60 and transport properties from the San Diego mechanism61 except for the species CH2 (not available in the San Diego mechanism), where the transport properties from the GRI3.0 mechanism62 were utilized. Sensitivity analysis for laminar flames was performed using CHEMKIN PRO.63 For ignition delay times, sensitivity analysis was done in the program Igdelay64 using the “brute force” method, meaning that rate parameters are varied and the model response is recorded. The parameters are then ranked according to their effect on the model response.

connects directly to the base mechanism by resulting in two methyl radicals (reaction 1). As pointed out by Ranzi et al.57 the vinyl radical, C2H3, is of significant importance in ethylene flames as a result of it being produced directly from the fuel by a single step of hydrogen abstraction. This chemistry is represented by reactions 5, 8, and 10. The importance of the vinyl radical requires a C2intermediate submechanism to couple the C2H3 product to the underlying base mechanism. It is important to recognize that hydrogen abstraction from ethylene by oxygen molecules to produce HO2 are important reactions in the early stage of ethylene combustion. The reaction is slow, and the subsequent reactions of the more reactive products are significantly faster, rapidly creating fuel radicals, oxygenated intermediates and a radical pool where OH is the dominating component. To keep the size of the reduced mechanism sufficiently small, the slow reaction with oxygen is not explicitly included, but it is represented by reaction 4, where ethylene decomposes to form the vinyl radical. 2.3. Intermediate Hydrocarbon Chemistry. The C2species reaction subset connects the C2H3 species created by reactions 4, 5, 8, and 10 to the underlying H/C1/O base mechanism. Reactions 13 and 15−23 have been adopted from the work by Sher and Refael.58 The C2 submechanism, handling the C2H3, C2H2, and C2H species, transfers the carbon from the intermediate C2 species down to CH3, HCO, and CO and, hence, coupling the fuel oxidation reactions to the underlying H/C1/O mechanism. The intermediate C2 submechanism is similar to the ones used in

4. MECHANISM VALIDATION The primary mechanism validation targets are the ignition delay time, the laminar burning velocity, and the flame temperature, all for a wide range of equivalence ratios, as specified in Table 1. These laminar burning velocity and the ignition delay time targets have also been simulated for a range of elevated initial gas pressures and temperatures. The Aramco mechanism40 is the reference for all flame parameters, with suitable experimental data included where possible; all data and a full range of simulation parameters are given in Table 1. 14142

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Figure 2. Ignition delay time predictions of Z66 (blue line) and the Aramco mechanism (red line) and experimental data,46 (symbols) for (a) φ = 0.3 and 1.2 atm, (b) φ = 0.5 and 1.2 atm, (c) φ = 1.0 and 1.1 atm, and (d) φ = 2.0 and 1.1 atm.

secondary indicator. As discussed by Xu and Konnov,45 the definition of ignition in ethylene combustion can be ambiguous, and care has to be taken to choose the best way to extract ignition delays from modeling to get results that correspond to the experimental data. An accurate metric that corresponds to the experimental data of Kopp et al.46 is the onset of excited hydroxyl radical production. Because OH* is not included in Z66, the definition used as the indicator of when ignition has occurred was set to 5% of the maximum OH peak. This corresponds to a temperature rise of 200 K to, for some temperatures, in excess of 400 K, showing that the 5% definition represents well the conditions in which ignition can be determined. A total of 5% of the peak of OH also matches the peak in OH* predictions by the Aramco mechanism (which includes both OH and OH* species), further strengthening the definition of the 5% of OH peak as the onset of an ignition process. In the experimental work by Kopp et al.,46 the overall uncertainty of the ignition delay times was about ±15% for all equivalence ratios except for φ = 0.5 at 1, 10, and 20 atm, where the uncertainties were ±30%. These uncertainties are included as error bars on experimental data presented in Figures 2−4. Experimental ignition delay times at pressures close to atmospheric and various equivalence ratios, from Kopp et al.,46 are presented together with modeling in Figure 2. Notice that the experimental data used here has a range of pressures from 1.0 to 1.3 atm. The pressures used in the simulations of the ignition delay times at all pressure ranges are chosen to bestrepresent each interval of pressures presented by the experimental data sets. For fuel-lean conditions, the simulations in panels a and b of Figures 2 predict long ignition delay times compared to the

Ignition delay time simulations were performed at equivalence ratios φ = 0.3, 0.5, 1.0, and 2.0, matching the experimental data sets presented by Kopp et al.46 The range of equivalence ratios for laminar flame speed, flame temperature, and major species concentrations where from φ = 0.5 up to φ = 1.8. To elucidate trends in temperature and pressure, the laminar burning velocity was evaluated for initial gas temperatures of T = 300, 450, 600, and 750 K, all at 1 atm, whereas the initial gas pressures utilized were for p = 1, 5, 10, 15, and 20 atm, all at 300 K. Experimental data is available for a narrower range of conditions.65−68 The work by Law et al.69 provided experimental flame-temperature data at 1 atm and 298 K. Z66 uses roughly 9.5% the number of species present in the Aramco mechanism and 2.1% of the number of reactions, showing the vast mechanism reduction presented by Z66, and gives clear indications of the CPU time saved in a combustion LES. A further indication of the difference in computational time between the skeletal and detail mechanisms is to directly compare simulations of identical cases. For a range of laminar flame speed simulations, from φ = 0.5 to φ = 1.8 with incremental steps of 0.1, the total computational time used by Z66 was roughly 1‰ of the time needed by the Aramco mechanism. Z66 used approximately 2.8 min, which is similar to computational time for the kerosene mechanism developed using the same methodology.53 4.1. Ignition Delay Time. Ignition delay time is an essential combustion characteristic for a kinetic model when simulating supersonic combustion flows. In the experimental study by Kopp et al.,46 a pressure peak was used as the mostconvenient definition of ignition, with additional measurements of excited hydroxyl radical, OH*, and emission used as a 14143

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Figure 3. Ignition delay time predictions of Z66 (blue line) and the Aramco mechanism (red line) and experimental data46 (symbols) for (a) φ = 0.3 and 9.8 atm, (b) φ = 0.5 and 11 atm, (c) φ = 1.0 and 10.2 atm, and (d) φ = 2.0 and 10.1 atm.

from roughly 1.6 times longer ignition for Z66 up to almost 9 times longer, and as with the lower pressures, the largest deviations are occurring at low temperatures. In-depth analysis of the kinetics using the Aramco mechanism by Koop et al.47 reveals that the fate of the H atom is of crucial importance for the pressure dependence because at low pressure, the reaction of H with molecular oxygen is chain-branching, while at higher pressure, it is chainpropagating. This mean that at low pressure, H has a stronger promoting role. This chain-branching reaction appear among the most important reactions as well for the Z66 mechanism; see Figure 5. Other reactions with high sensitivity in the Aramco mechanism are chain-branching and, to some extent, chain-propagation reactions involving C2H4 or C2H3. As mentioned in the mechanism development section, some of this reactivity has been lumped together into decomposition reactions in Z66, reactions that indeed occur among the most sensitive in Figure 5. 4.2. Laminar Burning Velocities and Flame Temperature. The laminar burning velocity, su, is an essential flame characteristic for combustion LES regardless of whether finite rate chemistry modeling or a flamelet approach is utilized. Figure 6 presents data from flames at standard conditions, 1 atm and 300 K, for the laminar burning velocities in panel a and the flame temperatures in panel b. Z66 results are in very good agreement to the experimental su data and the predictions from the Aramco mechanism, matching the experiments and the results from the detailed mechanism for all equivalence ratios. The deviations between the predictions by the two mechanisms

experimental data. At stoichiometric (Figure 2c) and fuel-rich (Figure 2d) conditions, modeling is essentially within uncertainty limits of the experimental data. The Aramco mechanism exhibit an upward bent curve, in agreement with experiments, but this trend is not captured by Z66. The curvature in experiments and Aramco mechanism mean that ignition delay time becomes longer more rapidly than predicted by Z66. Within the relevant temperature range, the discrepancy is small, but it is apparent that at this pressure Z66 likely has worse predictive capacity at lower temperatures. At these lower pressures, the deviation of Z66 to the Aramco mechanism varies from zero to as much as 2.4 times longer ignition for Z66, with the largest discrepancies being at the lower temperatures. Figures 3 and 4 show the ignition delay times for the same equivalence ratios as in Figure 2 but at a pressure of around 10 and 20 atm, respectively. The experimental data are obtained in a pressure range from 8.2 to 13.7 atm and from 18.2 to 24.9 atm. For these elevated pressures, Z66 mostly predict slower ignition than experiments and the reference mechanism, with generally better agreement at the intermediate temperatures and increased divergence toward higher and lower temperatures. Agreement is satisfactory at lean conditions. At the fuellean conditions, the divergence is greatest at the higher temperatures, whereas it is greatest at the lower temperatures at fuel-rich conditions. The deviations between the mechanisms at 10 atm ranges from almost nothing to an ignition as much as four times longer for Z66 compared to the Aramco mechanism, with the largest deviations occurring at fuel-rich conditions and low temperatures. At even-higher pressures, 20 atm, the deviations between the mechanisms grows larger, ranging 14144

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Figure 4. Ignition delay time predictions of Z66 (blue line) and the Aramco mechanism (red line) and experimental data46 (symbols) for (a) φ = 0.3 and 23.3 atm, (b) φ = 0.5 and 23.6 atm, and (c) φ = 2.0 and 21.7 atm.

Figure 5. Sensitivity analysis of ignition delay time for Z66 for (a) lean and (b) stoichiometric conditions at two pressures and a temperature of 1200 K.

including species H, OH, O, CO, O2, and H2 among the most important. Figure 7 present a sensitivity analysis for the flame at 300 K and 1 atm, for lean, stoichiometric, and rich conditions for both mechanisms. It can be seen in Figure 7 that the mostsensitive reactions for the reference mechanism as well as Z66 are indeed involving the mentioned important species. The mechanisms share many of the most-sensitive reactions (for example, reactions 48, H + O2 → OH + O; 46, CO + OH → CO2 + H; and 56, H + O2 + M → HO2 + M). The similarities in sensitivity spectra indicate that the chemistry implemented in

are small, from excellent agreement up to a difference of roughly 8%, with Z66 being closer to the experimental data. For the flame temperature in Figure 6b, Z66 is in agreement with the Aramco, and both mechanisms show a slight underprediction compared to experimental data around stoichiometric conditions. As with the laminar flame speed, the deviations between the two mechanisms are small, up to about 1%. Flame propagation is mainly governed by the small species chemistry included in the base mechanism, with reactions 14145

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Figure 6. (a) Laminar burning velocities and (b) flame temperature at standard conditions of 1 atm and 300 K for Z66 (blue), the Aramco mechanism (red) and experimental data,65−68 and temperature data69 (symbols).

Figure 7. Sensitivity analysis of the laminar flame speed of (a) Z66 and (b) the Aramco mechanism for three equivalence ratios at initial gas mixture condition of 1 atm and 298 K.

Figure 8. Laminar burning velocities for φ = 0.6 (dashed lines), φ = 1.1 (solid lines), and φ = 1.4 (dot−dashed lines), for Z66 (blue) and the Aramco mechanism (red) for elevated (a) initial gas pressures and (b) temperatures. Experimental data in panel a are taken form by Jomaas et al.65 and Hassan et al.;68 those in panel b are from Kumar et al.70 For the experimental data, φ = 0.6 is represented by stars (*), φ = 1.1 by rings (○), and φ = 1.4 by crosses (×).

agree well with experimental data at p = 5 atm. The same trend between the two mechanisms can be observed for the elevated initial gas temperatures in reaction 8b, where Z66 gets a slightly lower response to the changing conditions. For the elevated pressures, the deviations in predictions between both mechanisms ranges from 0% at lower pressures up to 30% at 20 atm and fuel-rich conditions, with the Aramco consistently predicting the higher laminar flame speeds. For the elevated temperature conditions, the deviations ranges from 0% at lower

Z66 is a good representation of the detailed chemistry at these conditions. The laminar burning velocities for elevated initial gas pressures and temperatures for three equivalence ratios (0.6, 1.1, and 1.4) are presented in panels a and b of Figure 8, respectively. For elevated initial gas pressures in Figure 8a, Z66 displays similar behavior as the Aramco mechanism but with lower values. When compared to experimental data, both mechanisms predicts slightly larger values at p = 2 atm but 14146

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Figure 9. Modeling predictions of maximum molar concentrations of major species at (solid lines) 1 atm and (dashed lines) 10 atm and 300 K with (blue) Z66 and (red) the Aramco mechanisms for (a) CO2, (b) CO, (c) H2O, and (d) H2.

the maximum molar concentrations for both pressures investigated.

temperatures up to almost 23%, with the largest deviation occurring at the highest temperature and at fuel-lean conditions. 4.3. Species Concentration in Laminar Flames. Presented below are the comparisons between Z66 and the Aramco mechanism for the predictions of the maximum molar concentrations for the major species at 1 and 10 atm, both at the same range of equivalence ratios as used for the laminar burning velocities and the flame temperatures presented in Figure 6. No experimental data are available and the reference mechanism, with its high level of chemical complexity, is expected to be reliable in its predictions of the stable major species. Figure 9a, showing the maximum molar concentrations of CO2, also shows agreement between the two mechanisms, both for 1 and 10 atm, with a slight deviation at around stoichiometric conditions for the higher temperature. For the CO concentrations in Figure 9b, the Z66 is again in good agreement with Aramco. Apart from a minor divergence at fuelrich conditions, the same could also be said for the water concentrations in Figure 9c, with both mechanisms displaying the same trends when the pressure is increased. The concentrations of H2 in Figure 9d do, however, show slightly more-divergent predictions, with Aramco mechanism having slightly elevated H2 concentrations compareed to Z66, but just like for H2O, the trends between the mechanisms are intact when the pressure is increased. Overall, Z66 shows good agreement with the reference mechanism in the predictions of

5. SUMMARY AND CONCLUSIONS In this work, we have presented a skeletal mechanism for ethylene−air combustion, validated over a wide range of conditions of particular importance in high-speed applications. The simplifications of the chemistry result in that the curved trend in ignition delay time captured by the reference mechanism is not reproduced by Z66. However, the agreement is satisfactory over a wide range of conditions, particularly at the lean, high-temperature, and intermediate-pressure conditions relevant for ramjet and scramjet applications. Sensitivity analysis for both ignition and flame simulations indicate that Z66 has the same chemical species of importance as the reference mechanism. The accuracy of the chemistry is further strengthened by the agreement in profiles of stable species in laminar flames. In comparison to the reduced mechanism available in the literature by Zong et al.48 and Lou et al.,49 the Z66 mechanism was validated over a wider range of conditions, which brings confidence into applying it to CFD simulations of real applications. For the narrow range of conditions in which the validation of the mechanisms coincide, it can be concluded that the present mechanism has the same or better predictions than the other skeletal mechanisms, using fewer reactions. An important difference between the mechanism of Zong et al.48 and Z66 is that the treatment of C2 species, whereas Zong et al.48 has retained the oxygenated species (CH2CO and C2H3O) 14147

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that have been shown to be of importance by detailed modeling, while in Z66, these steps have been replaced by reactions of nonoxygenated C2 species (C2H, C2H3, etc.). The later approach is a step away from the accurate chemical description but seem to be a useful approach for reducing the size of the mechanism while still maintaining a good overall accuracy, just like in the cases of larger fuels in our previous works.39,52,53 Z66 represents a computationally cheap option to larger detailed mechanisms due to a combination of its reduced nature and low numerical stiffness. The present work thus give new possibilities for including a high-performing and chemically sound kinetic mechanism for ethylene combustion in finite rate combustion LES, whether the target combustor represents low Reynolds number premixed flames or scramjet engines.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.7b02078. Mechanism file in CANTERA format. (TXT)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +46-46222-14-03. ORCID

Elna J. K. Nilsson: 0000-0002-8226-3845 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support of the Centre for Combustion Science and Technology (CECOST) is gratefully acknowledged by E.J.K.N. REFERENCES

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