Fuel 234 (2018) 238–246

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Fuel

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Full Length Article A comparison study of cyclopentane and laminar flame speeds at elevated pressures and temperatures T ⁎ ⁎ Haoran Zhao, Jinhua Wang , Xiao Cai, Zemin Tian, Qianqian Li, Zuohua Huang

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

ARTICLE INFO ABSTRACT

Keywords: Laminar flame speeds of cyclopentane/air and cyclohexane/air mixtures were determined at equivalence ratios Laminar flame speeds of 0.7–1.6, initial pressures of 1–5 atm, and initial temperatures of 353–453 K using the spherically propagating Cyclopentane flame method. Four recently published models of cyclopentane and cyclohexane were validated by current Cyclohexane experimental data and showed a reasonable agreement, especially for JetSurF2.0 model and Tian model. A Elevated pressures comparison of cyclopentane/air and cyclohexane/air laminar flame speeds was conducted over wide conditions. Elevated temperatures A comprehensive analysis was conducted through thermal, transport and chemical kinetic effects, and the re- action path analysis and sensitive analysis were employed to further investigate the chemical kinetic effects. The results showed that the laminar flame speed of cyclohexane/air mixture is larger than that of cyclopentane/air and the discrepancy increases with the initial pressure. The discrepancy mainly results from the chemical kinetic effects. Specifically, cyclopentane generates more methyl and allyl intermediates which can consume large amounts of H radicals and induce chain terminating reactions. While, cyclohexane generates a larger amount of ethyl and 1,3- intermediates which can further yield more vinyl, and the later can induce chain branching reactions and increase the overall burning rate. Thus, it is the different distribution of the cracked products in cyclopentane/air and cyclohexane/air flames that leads to the discrepancy of laminar flame speeds.

1. Introduction achieved compared to related low temperature oxidation experiments, such as JSR [5,6] and RCM [13,14]. Later, a detailed kinetic model Cyclic are important components of practical fuels, which JetSurF2.0 was developed, which can not only be used for n-alkanes, can be up to one third or more by weight in diesel [1,2]. It may con- but also for CHX and mono-alkylated CHXs [9]. Based on the previous tribute to the production of aromatics through de-hydrogenation reac- research [8], Serinyel et al. conducted a JSR experiment at tempera- tions and further increase soot formation at high temperatures [3]. With tures ranging from 500 to 1100 K and proposed an optimized compre- the emergence of oil-sand derived fuels, which contains more cyclic hensive oxidation model for CHX including low to high temperature alkanes than conventional fuels [4], cyclic alkanes will become more [10]. Besides the JSR and RCM experiments, which mainly reflect low important in practical fuel chemistry. temperature oxidation of CHX, many evaluated experiments had also Cyclohexane (CHX) is a simple representative of cyclic alkanes with been conducted aimed at high temperature oxidation kinetics. Several a six-membered ring and until now several kinetic models have been ignition delay times have been measured in shock tubes over a wide proposed for it [4–12]. Voisin et al. [5] proposed a low and high range [15–17] and the initial pressure can be up to 61 atm [18]. As for temperature oxidation model for CHX and validated it by the species laminar flame speeds, Davis and Law et al. [19] measured the laminar profiles in a jet stirred reactor (JSR) in the temperature range of flame speeds of CHX at atmospheric pressure and temperature. Ji et al. 750–1100 K and 10 atm. Then Bakali et al. [6] revised this model and [20] and Serinyel et al. [10] conducted relative study of CHX flame validated it through species mole fraction profiles in a JSR at 1, 2 and propagation at atmospheric pressure and temperature from 298 to 10 atm. Ranzi et al. [7] compiled a detailed model for pyrolysis and 398 K. Wu et al. [21] measured the laminar flame speeds of CHX at oxidation of CHX, which was also validated by JSR [6] and ignition 353 K and elevated pressures up to 20 atm with oxygen/helium as delay times in rapid compression machine (RCM) [13]. Silke et al. [4] oxidizer. Although laminar flame speeds of CHX have been measured at proposed an oxidation model of CHX including low and high tem- elevated temperatures, the initial temperature is not high enough and perature oxidation kinetics, and a reasonable agreement had been there still exists some discrepancy among available experimental

⁎ Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (Z. Huang). https://doi.org/10.1016/j.fuel.2018.06.134 Received 13 April 2018; Received in revised form 18 June 2018; Accepted 30 June 2018 0016-2361/ © 2018 Elsevier Ltd. All rights reserved. H. Zhao et al. Fuel 234 (2018) 238–246 results, which is mainly due to the difference of the experimental and 2. Experimental setup and simulation approach data processing approaches. Thus, it is necessary to provide more ar- chival experimental data over broad conditions and investigate the la- Laminar flame speeds were measured with outwardly spherical minar flame speeds of CHX at elevated temperatures and pressures. flame propagation method using a combustion chamber, whose details Adjacent to CHX, cyclopentane (CPT) is another representative of can be found elsewhere [30,31] and only a brief introduction is given cyclic alkanes with five-membered ring, which appears high-octane and here. The chamber is cylindrical with an inner diameter of 180 mm and knock-resistant characteristics. Due to its individual characteristics, a length of 210 mm. Two quartz windows with the diameter of 80 mm CPT has significant influence on the ignition and combustion of gaso- are located on both sides of the chamber for optical access. A 1.5 kW line surrogates, as demonstrated by Sarathy et al. [22]. However, re- heating tape is wrapped around the chamber and the temperature is searches relevant to CPT were much less than CHX. Sirjean et al. [15] monitored by a K-type thermocouple installed in the chamber. Before generated a high temperature oxidation model for CPT using the EXGAS each experiment, the chamber was heated to the experiment tempera- software and investigated the ignition delay time at pressure from 7.3 ture and evacuated by a pump. The fuels CPT (98%) and CHX to 9.5 atm in a shock tube. Later, Daley et al. [18] measured the ignition (99.5%) were injected into the heated chamber using micro syringes delay time of CPT at elevated pressures up to 55 atm. Tian et al. [23] through a valve. To make sure that the liquid fuels had been fully va- conducted a shock tube study at pressures of 1.1–10 atm and in the porized, the real pressure after the injection and vaporization of liquid temperature range from 1150 to 1850 K, and a sub-mechanism was fuels was compared to the theoretical pressure. Then the oxygen added to the JetSurF2.0 mechanism for the kinetic interpretation of (99.999%) and nitrogen (99.999%) were introduced through intake CPT oxidation chemistry. Randazzo et al. [24] investigated the pyr- valves to the required partial pressure, which was monitored by a Ro- olysis of CPT in a diaphragmless shock tube with laser Schlieren den- semount pressure transmitter with a maximum range of 1.03 MPa. At sitometry at nominal post-shock pressures of 35, 70, 150 and 300 Torr least 10 min was awaited before ignited by the centrally located elec- and temperatures of 1472–2074 K. Recently, Rashidi et al. [25] pro- trodes to make sure that the fuels and gases had been mixed completely. posed a conventional oxidation kinetic model for CPT ranging from low A high speed digital camera (Phantom V611) was employed to capture to high temperature. To validate this model, Rashidi et al. [26,27] the spherically propagation flames at the speed of 10,000 frames per conducted a JSR study for low temperature oxidation of CPT and second. fl 0 measured the ignition delay times at pressures of 20 and 40 atm over The unstretched burned ame speed Sb was extrapolated by the the temperature range of 650–1350 K using a shock tube and RCM. nonlinear method of Frankel and Sivashinsky [32], Also, the model was validated by the laminar flame speeds of Davis and 00 Law et al. [19] at atmospheric pressure and temperature. However, SSb =−bb2· SLrb / f (1) until now, there are only the laminar flame speeds of CPT at atmo- where S is the stretched burned flame speed, L is the Markstein length spheric pressure and temperature [19]. As we all know, substantial b b and r is the flame radius. experimental data over broad conditions is necessary to deepen the f Finally, the laminar flame speed S 0 can be determined through a understanding of thermal decomposition and oxidation of CPT. Thus, u simplified continuity equation across the flame front, the relevant study about the laminar flame speeds of CPT is limited and it is necessary to validate these models with laminar flame speeds at 00 SSρρub= ·/bu (2) elevated pressures and temperatures.

Meanwhile, in order to generalize and simplify the oxidation and where ρb and ρu are the burned and unburned gas density, respectively. flame propagation process of large molecular fuels, the investigation of The uncertainty of experimental data in the present study can be similarity between these large alkanes has been conducted through the attributed by various factors, such as mixture composition, initial comparison of laminar flame speeds. Davis and Law et al. [19] mea- temperature, initial pressure, ignition, buoyancy, radiation, instability, sured the laminar flame speeds for n-alkanes from C3 to C7 and found confinement, nonlinear stretch behavior and extrapolation [33]. The that it was nearly identical for the C4–C7 n-alkanes at atmospheric method proposed by Moffat et al. [34] was chosen to evaluate the pressure and temperature. Ji et al. [28] measured the laminar flame overall experimental uncertainty of laminar flame speed, which took speeds of C5–C12 n-alkanes flames at elevated temperatures and the both systematic uncertainty and random uncertainty into consideration. similar results was determined respectively from C5 to C8 and C9 to C12. For the present study, the systematic uncertainty was mainly caused by Later, Kelley et al. [29] extended the experimental condition to ele- equivalence ratio, initial temperature and pressure, and the relationship vated pressures of 10–20 atm and the similar laminar flame speeds still between each factor and laminar flame speed obtained by Cai et al. [35] existed for C5–C8 n-alkanes. However, to the best of our knowledge, the was used here. The relative uncertainty of equivalence ratio was within comparison of C5–C6 cyclic alkanes laminar flame speeds has not been the range of ± (2–3)% mainly induced by the uncertainties in mon- investigated. Cyclic alkanes have an evident difference from n-alkanes itoring the partial pressures of fuel, O2 and N2. The precision of initial in chemical kinetic characteristics because of the existing of ring temperature and pressure were controlled within ± 3 K and ± 3 kPa, structure. Although it is similar in laminar flame speeds for C5–C8 n- respectively. Besides, the random error was taken into consideration alkanes, that of cyclic alkanes is still unknown. Therefore, it is neces- and the experiments were repeated three times for each condition. sary to compare the laminar flame speeds of CPT and CHX and study Accounting for the radiation effect, the deviation due to radiation was the effect of initial pressures and temperatures. also evaluated using the equation of Yu et al. [36]. Flame radius from 9 Thus the objective of this study is to provide the laminar flame to 22 mm were chosen in extracting the laminar flame speeds to avoid speeds of CPT and CHX at initial pressures from 1 to 5 atm and tem- the effects of ignition and chamber confinement [37,38]. And the ef- peratures from 353 to 453 K. Four recently published kinetic models of fects of nonlinear stretch behavior and extrapolation were also included CPT and CHX were validated using the present laminar flame speeds in the overall uncertainty. In total, the uncertainty of the laminar flame over wide experimental conditions. A comparison of CPT and CHX la- speeds was evaluated to be about 1–3 cm/s in this study. minar flame speeds was carried out to investigate the effect of Laminar flame speeds were calculated using the PREMIX model of numbers of ring structure on cyclic alkanes high temperature oxidation Chemkin-PRO software [39]. Simulation was conducted using finite kinetics at various initial pressure and temperature. And a compre- difference method with adaptive grid. Mixture-averaged transport and hensive analysis was conducted through thermal, transport and che- thermal diffusion accounting for Soret effect were used. To ensure the mical kinetic effects to explain the discrepancy between CPT and CHX. accuracy of the calculation, the solution gradient and curvature were both fixed at 0.03 and the total number of points was more than 800. Four recently published kinetic models were validated by the present

239 H. Zhao et al. Fuel 234 (2018) 238–246

80 80

70 CPT 70 CHX P=1 atm P=1 atm 60 60

50 50

40 40 /(cm/s) /(cm/s) L L S 30 S 30 353 K 353 K 20 403 K 20 403 K 453 K 453 K Tian Mech. 10 10 JetSurF2.0 Mech. Rashidi Mech. Battin Mech. 0 0 0.6 0.8 1.0 1.2 1.4 1.6 0.6 0.8 1.0 1.2 1.4 1.6

(a) (a)

80 80

70 CPT 70 CHX T=403 K T=403 K 60 60

50 50

40 40 /(cm/s) /(cm/s) L L

S 30 S 30 1 atm 1 atm 20 2 atm 20 2 atm 5 atm 5 atm Tian Mech. 10 10 JetSurF2.0 Mech. Rashidi Mech. Battin Mech. 0 0 0.6 0.8 1.0 1.2 1.4 1.6 0.6 0.8 1.0 1.2 1.4 1.6

(b) (b) fl Fig. 1. Experimental and calculated laminar flame speeds of CPT/air at (a) Fig. 2. Experimental and calculated laminar ame speeds of CHX/air at (a) T = 353, 403, 453 K, P = 1 atm; (b) T = 403 K, P = 1, 2, 5 atm. T = 353, 403, 453 K, P = 1 atm; (b) T = 403 K, P = 1, 2, 5 atm. laminar flame speeds. For CPT, Tian model [23] and Rashidi model been validated by low to high temperature ignition delay times, JSR fl [25] were used here. Because the complete Rashidi model consists of experimental data and laminar ame speeds [26,27]. However, the fl 1598 species and 6816 reactions, which will cost extremely large laminar ame speeds were only measured at atmospheric temperature fl computational resources, thus we used the model reduced by Rashidi and pressure. Thus, an evaluation with more laminar ame speeds at et al. [26] to calculate the laminar flame speeds of CPT. At the same elevated temperatures and pressures is necessary. It can be seen that time, JetSurF2.0 model [9] and Battin model [10] were chosen for CHX Tian model slightly over-predicts the results at fuel-lean equivalence calculation. ratios and slightly under-predicts the data at fuel-rich conditions, but nearly all of the discrepancies are in the domain of error bars. Rashidi model has a reasonable agreement with the experimental data at at- 3. Results and discussion mospheric pressure, but predicts a little higher than the experimental data near the peak value. Therefore, on the whole, both the models 3.1. Laminar flame speeds of CPT and CHX have a reasonable agreement with the CPT experimental results in the present study. The experimental setup has been validated with many fuels under Fig. 2 presents the measured and simulated laminar flame speeds of different initial conditions [31,40,41], and here we give the experi- CHX at the same experimental conditions as CPT. Also, two kinetic mental and simulation results directly. Fig. 1 indicates the experimental models are selected to calculate the laminar flame speeds of CHX. At and simulated laminar flame speeds of CPT at different initial tem- atmospheric pressure, JetSurF2.0 model predicts fairly well over a wide peratures (353, 403, 453 K) and initial pressures (1, 2, 5 atm) over a range of equivalence ratios, especially at the initial temperature of wide range of equivalence ratios. The models selected to calculate CPT 353 K. Although Battin model predicts well at fuel-lean side, it over- are Tian model and Rashidi model. Until now, Tian model has only predicts the laminar flame speeds at stoichiometric ratio and fuel-rich been validated by ignition delay times [23,26] and has not been vali- side. At elevated initial pressures, JetSurF2.0 model slightly over-pre- dated by any laminar flame speed experimental data. Rashidi model has dict the laminar flame speeds when equivalence ratios are lower than

240 H. Zhao et al. Fuel 234 (2018) 238–246

1.1, but the maximum discrepancy is no more than 3 cm/s, except for 2400 the equivalence ratio of 0.7 and initial pressure of 5 atm, which is in- fluenced a lot by the large ignition energy and voltage. However, Battin model evidently over-predicts the experimental data, especially near 2300 the stoichiometric ratio, which is far beyond the error range. Thus, compared to Battin model, JetSurF2.0 model has a better prediction for the experimental results of CHX in the present study. 2200 Also, it can be seen that for both fuels, several data of laminar flame speeds on fuel-rich side are lacked at the initial pressures of 2 and T=403 K fl 5 atm. For large molecular fuel ame, Le < 1 on the fuel-rich side, so 2100 P=1 atm ff the thermal-di usion instability will occur at this time and be enhanced CHX as the equivalence ratio increases. Besides, with the initial pressure CPT increasing, the flame thickness can be reduced and the hydrodynamic 2000 instability will be enhanced as well. Thus, at these experimental con- Adiabatic Flame Temperature(K) ditions, the onset of the flame front cellular instability appears too early to derive the laminar flame speed. 0.6 0.8 1.0 1.2 1.4 1.6 According to the models evaluated above, JetSurF2.0 model has a better prediction of the present data compared to Battin model, thus (a) JetSurF2.0 model is selected to conduct kinetic analysis of CHX. As for CPT, both Tian model and Rashidi model have reasonable agreements with the experimental data. In consideration of that Tian model is based 0.015 on USC Mech II, which is the same as that of JetSurF2.0 model, thus T=403 K Tian model is selected to analyze CPT in this study. P=1 atm 1/2

] CHX

Le CPT fl ) 0.010 3.2. Comparison of CPT and CHX laminar ame speeds p C

Fig. 3 gives an intuitive comparison of CPT and CHX laminar flame speeds at initial temperature of 403 K and atmospheric pressure. It shows that the laminar flame speeds of CHX are larger than those of 0.005 CPT over all equivalence ratios. The relative minimum discrepancy occurs around the equivalence ratio of 1.1 and the discrepancy in- creases with the equivalence ratio moving to both sides. The relative Diffusion Factor[ maximum discrepancy can be up to 18% at the fuel-leanest or richest condition. It is easy to understand this trend because the absolute dis- 0.000 crepancy nearly doesn’t change with the equivalence ratio while the 0.6 0.8 1.0 1.2 1.4 1.6 laminar flame speed of CPT decreases as the equivalence ratio moves to leaner or richer side, so the division value of them are getting larger (b) with the equivalence ratio moving to both sides. Also, it should be noted that similar results are acquired at other initial temperatures and Fig. 4. Thermal and transport characteristics of CHX/air and CPT/air at pressures. So we can conclude that the laminar flame speeds of CHX are T = 403 K, P = 1 atm: (a) adiabatic flame temperature; (b) diffusion factor. larger than those of CPT at the same condition, which is different from fl that of C5 and C6 n-alkanes, whose laminar ame speeds are similar speed can be expressed by: [19,28,29]. 0 1/2 1/2 According to the research of Law et al. [42], the laminar flame SλcLeERTu ∞−[( /Paad ) ] [exp( /0 )] (3) fi 1.50 where λ is the thermal conductivity, cP is the speci c heat and Le is the 1/2 Lewis number. The term [(/λcP ) Le ] represents transport effect. Tad is T= 403 K fl ff P=1 atm the adiabatic ame temperature and represents thermal e ect. Ea is the activation energy and represents chemical kinetic effect. R0 is the uni- 1.25 versal gas constant. Through the discussion above, it reveals that the laminar flame speed is affected by thermal, transport and chemical kinetic. L(CPT) S / 1.00 3.2.1. Thermal and transport effects L(CHX)

S In order to analyze the thermal effects, the adiabatic flame tem- peratures T of CPT/air and CHX/air flames at 403 K and atmospheric 0.75 ad pressure are calculated and given in Fig. 4(a). It shows that the adia- batic flame temperature of CPT is higher than CHX and the maximum discrepancy is more than 20 K which occurs on the fuel-rich side. Ac- 0.50 cording to the analysis above, the laminar flame speed is positively 0.6 0.8 1.0 1.2 1.4 1.6 correlated to the adiabatic flame temperature, while the laminar flame speeds of CPT are lower compared to CHX. So it is evident that thermal effects are not the main cause for the laminar flame speeds discrepancy Fig. 3. A comparison of laminar flame speeds of CHX/air flames relative to between CPT and CHX. those of CPT/air flames at T = 403 K, P = 1 atm. 1/2 Fig. 4(b) shows the diffusion factor [(/λcP ) Le ] of CPT/air and

241 H. Zhao et al. Fuel 234 (2018) 238–246

CHX, all the CPT firstly undergoes H-abstraction reaction to form cy- -2.7 solid line: CHX Ea=214.1 kJ/mol =0.7 dot line: CPT clopentyl. Then more than 70% of cyclopentyl undergoes ring open -2.8 * reaction to form CH2 eCH2eCH2eCH]CH2 and nearly 26% of cyclo- -2.9 pentyl occurs H-abstraction to form cyclopentene. And then the dif- ference appears between CPT and CHX. Although most

) -3.0 Ea=183.0 kJ/mol * 0 CH2 eCH2eCH2eCH]CH2 still undergoes isomerization and β-scission u

S ff u -3.1 reaction, the distribution of cracked products are di erent from those of Ea=240.5 kJ/mol ( CHX. For CHX, the generated products are ethyl and 1,3-butadiene,

ln -3.2 while the products of CPT are methyl and 1,3-butadiene. Also, a small *e e e ] -3.3 part of CH2 CH2 CH2 CH CH2 directly undergoes cracked reaction to form ethylene and allyl, which is still different from that of CHX. As =1.4 Ea=197.4 kJ/mol -3.4 for cyclopentene, the major of them undergo continuous H-abstraction fi -3.5 and form cyclopentadiene. And nally the cyclopentadiene undergoes ring open reaction and yields acetylene, allyl and 1,3-butadiene. 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 According to the comparison analysis above, we can conclude that ff 1000K/Tad the main di erence between CPT and CHX occurs in the distribution of cracked products. The cracked products of CPT consist of more methyl Fig. 5. A plot of logarithmic mass burning rate over a broad range of at and allyl, while the products of CHX consist of more ethyl and 1,3- ϕ T = 403 K, P = 1 atm, = 0.7 and 1.4. butadiene. In order to validate and extend the results of reaction path

analysis, a calculation of the concentration of major C1–C4 inter- CHX/air at 403 K and atmospheric pressure, which reflects the trans- mediates in the laminar flame reaction zone is also conducted and is port characteristics. On the fuel-rich side, the diffusion factor of CPT is shown in Fig. 7. From Fig. 7(a), it is seen that the mole fraction of nearly equal to that of CHX because the Lewis number of them is equal methyl in CPT flame is higher than that of CHX flame. As we all know, fi ff according to the de nition Le= DT / Di, where DT is the thermal di u- methyl can consume H radical through reaction CH3 + H(+M) → ff fi sivity and Di is the mass di usivity of the de cient reactant. On the fuel- CH4(+M) and generate more methane at the same time. So there is also lean side, the diffusion factor of CPT is slightly smaller than CHX. more methane in the CPT flame. However, the mole fraction of ethyl in However, the maximum discrepancy in diffusion factors is no more than CHX flame is far more than that of CPT, and the ratio of them can be up 0.0005, which is so small and can be neglected reasonably. Besides, the to 10. It was known that ethyl is active and can undergo H-abstraction tiny discrepancy of transport characteristic between C5 and C6 n-al- reaction and yields ethylene. Also, ethylene has high reactivity and can kanes doesn’t result in an evident difference in laminar flame speed. be easily abstracted H to yield vinyl, and the later can undergo chain Thus, transport effects don’t contribute a lot to the discrepancy of la- branching reaction. Thus, more vinyl is formed during this process. At minar flame speeds for CPT and CHX as well. the same time, plenty of H radicals are generated through this process, which can promote the reaction rate and laminar flame speed. Besides, 3.2.2. Chemical kinetic effects as shown in Fig. 7(b), the mole fraction of allyl in CPT flame is more Following Egolfopoulos and Law [43], the global activation energy than twice of that in CHX flame. Allyl is resonantly stabilized and can 0 → Ea can be derived as EaRρST=−2ln()/(1/)0 ∂u u ∂ ad . Because this ex- undergo chain terminating reaction aC3H5 + H(+M) C3H6(+M), traction holds only for sufficiently off-stoichiometric mixtures when the which consumes many H radicals and generates propene. In contrast, reaction rate is controlled by the deficient reactant, Ea of CHX/air and more 1,3-butadiene is generated in CHX flame than CPT, which can also

CPT/air have been calculated at equivalence ratio of 0.7 and 1.4 in the produce ethylene and vinyl through reaction C4H6 +H→ present study, which is given in Fig. 5. Through nitrogen substitution by C2H4 +C2H3. Thus, the results of reaction path analysis have been argon, Tad is varied over a broad range. It can be seen that Ea keeps validated quantitatively. constant over a broad range of adiabatic flame temperature, which To further understand the key reactions related to laminar flame indicates that Ea is independent of adiabatic flame temperature and speed, sensitivity analysis on that of CHX/air and CPT/air is also con- thus chemical kinetic effects can be separated from thermal effects. ducted at initial temperature of 403 K, stoichiometric, and initial Moreover, Ea of CHX is always lower than that of CPT at both lean and pressures of 1 and 5 atm, which is given in Fig. 8. Here, sensitive ffi fl fl 0 rich equivalence ratios, as well as stoichiometric ratio. This indicates coe cient Si re ects the sensitivity between laminar ame speed Su that the global reactivity of CPT is lower compared to CHX, and a de- and elementary reaction rate constant αi, and can be derived as 0 0 tailed analysis will be conducted subsequently to clarify the dis- ∂ ln su αi ∂su Si ==0 . It is evident that both CHX and CPT are mostly ∂ ln αi su ∂αi crepancy in reactivity. sensitive to small intermediates chemistry and the largest sensitive fl fl Fig. 6(a) gives the reaction path ux of CHX/air ames at coefficient reaction is H + O < = > O + OH. Consisted to the ana- ϕ 2 T = 403 K, p = 1 atm and = 1.0. It shows that all the CHX undergoes lysis above, the methyl mainly has an evident negative effect on la- H-abstraction reaction and forms cyclohexyl radicals in the pre-heat minar flame speed, because H radicals are consumed through chain region. Then about 70% of cyclohexyl radicals conduct ring open re- terminating reaction CH + H(+M) → CH (+M). Allyl also has a ne- β ] e e e e * 3 4 action via -scission rule to form CH2 CH CH2 CH2 CH2 CH2 and gative effect on the laminar flame speed of CPT, because allyl consumes nearly one fourth of cyclohexyl radicals continue H-abstraction reaction H radical and generates propene, and the latter is a relatively stabilized ] e e e e * to form cyclohexene. Most CH2 CH CH2 CH2 CH2 CH2 undergoes intermediate. On the contrary, vinyl has a positive effect on the laminar isomerization reaction to yield CH eCH eCH eCH*eCH]CH and 3 2 2 2 flame speed in general. Although the reaction C H +H→ C H +H β 2 3 2 2 2 then generates plenty of 1,3-butadiene and ethyl through -scission indicates negative sensitivity since H radicals are consumed during this rule. And more than 30% of CH ]CHeCH eCH eCH eCH * directly 2 2 2 2 2 process, more evident positive sensitivity can be obtained by the re- undergoes β-scission reaction and finally generates vinyl, ethylene and actions C2H3(+M) → C2H2 + H(+M) and C2H3 +O2 → CH2CHO + O, 1,3-butadiene. As for cyclohexene, most of them conduct ring open both of which produce plenty of active radicals such as H and O. And O reaction and yield ethylene and 1,3-butadiene, while a small part of radical can also be transformed into H radical through the reaction them undergo continuous H-abstraction reaction and finally yields C2H2 +O→ HCCO + H. Thus, vinyl can increase the reaction rate and . laminar flame speed by generates more H radicals. Also, 1,3-butadiene fl A reaction path ux analysis has also been conducted for CPT/air shows relatively high positive effect on flame propagation, because the flames at T = 403 K, p = 1 atm, ϕ = 1.0 and is given in Fig. 6(b). Like

242 H. Zhao et al. Fuel 234 (2018) 238–246

Fig. 6. Reaction path analysis for the stoichiometric CHX/air and CPT/air flames at T = 403 K, P = 1 atm: (a) CHX; (b) CPT.

reaction C4H6 +H→ C2H4 +C2H3 can yield active ethylene and vinyl. and 1,3-butadiene are generated in CHX flame, which induce chain According to the above analysis, it can be concluded that the dis- branching reaction and produce plenty of H radicals, resulting in a crepancy in laminar flame speeds of CHX and CPT would be due to the larger laminar flame speed. Whereas, more stabilized methyl and allyl different distribution of cracked products. In detail, more ethyl, vinyl appear in the CPT flame and undergo third-body chain terminating

243 H. Zhao et al. Fuel 234 (2018) 238–246

0.0025 H+O2<=>O+OH CO+OH<=>CO2+H Solid line: CHX HCO+H<=>CO+H2 Dash line: CPT H+OH+M<=>H2O+M 0.0020 HCO+H2O<=>CO+H+H2O C4H6+H<=>C2H4+C2H3 CH3 HCO+M<=>CO+H+M CH3+H(+M)<=>CH4(+M) CHX 0.0015 C2H3+H<=>C2H2+H2 T=403 K C2H5×10 C2H3+O2<=>CH2CHO+O =1.0 H+O2(+M)<=>HO2(+M) C2H3×10 0.0010 C2H3(+M)<=>C2H2+H(+M) CH3+OH<=>CH2*+H2O 1 atm C2H2+O<=>HCCO+H 5 atm Mole Fraction SAXC4H7(+M)<=>C4H6+H(+M) 0.0005 HO2+H<=>2OH 2CH3<=>H+C2H5 CH3+HO2<=>CH3O+OH O+H2<=>H+OH 0.0000 CH2+O2<=>HCO+OH 0.02 0.03 0.04 0.05 0.06 -0.2 -0.1 0.0 0.1 0.2 0.3 Distance(cm) Logarithmic Sensitivity Coefficient (a) (a)

0.0035 H+O2<=>O+OH CO+OH<=>CO2+H 0.0030 Solid line: CHX H+OH+M<=>H2O+M Dash line: CPT HCO+H<=>CO+H2 HCO+H2O<=>CO+H+H2O 0.0025 HCO+M<=>CO+H+M C4H6+H<=>C2H4+C2H3 CH3+H(+M)<=>CH4(+M) CPT 0.0020 H+O2(+M)<=>HO2(+M) T=403 K C4H6 CH3+OH<=>CH2*+H2O C2H3(+M)<=>C2H2+H(+M) =1.0 0.0015 C2H3+H<=>C2H2+H2 aC3H5×5 C2H2+O<=>HCCO+H 1 atm Mole Fraction 0.0010 C2H3+O2<=>CH2CHO+O 5 atm HCO+O2<=>CO+HO2 O+H2<=>H+OH 0.0005 aC3H5+H(+M)<=>C3H6(+M) OH+H2<=>H+H2O CH2*+O2<=>H+OH+CO 0.0000 O+H+M<=>OH+M 0.02 0.03 0.04 0.05 0.06 -0.2 -0.1 0.0 0.1 0.2 0.3 Distance(cm) (b) Logarithmic Sensitivity Coefficient (b)

Fig. 7. Mole fractions of main C1–C4 intermediates of stoichiometric CHX/air Fig. 8. Sensitivity analysis for the stoichiometric CHX/air and CPT/air flames and CPT/air flames at T = 403 K, P = 1 atm: (a) C1 and C2 intermediates; (b) C3 at T = 403 K, P = 1 and 5 atm: (a) CHX; (b) CPT. and C4 intermediates.

fl reaction, inhibiting the laminar flame speed of CPT. laminar ame speeds between CHX and CPT becomes larger at elevated initial pressures.

3.2.3. The effects of initial pressure and temperature Fig. 9 gives the stoichiometric laminar flame speeds discrepancy 4. Conclusions variation between CHX and CPT with the different initial temperatures (353, 403, 453 K) and pressures (1, 2, 5 atm). It can be seen that the The laminar flame speeds of CPT and CHX were determined at discrepancy seems independent with the initial temperature. However, elevated temperatures (353, 403, 453 K) and pressures (1, 2, 5 atm) the discrepancy increases evidently with the initial pressure increasing using spherically expanding flame method. Four recently published from 1 to 5 atm in the present experimental study. Although there is kinetic models were validated by the present experimental data. For limited experimental data in Fig. 9, the varying trend with initial CHX, JetSurF2.0 model has a better prediction than Battin model. For pressure is obvious. According to the results of sensitivity analysis in CPT, both Tian model and Rashidi model have a reasonable agreement Fig. 8, the sensitivity coefficients of chain terminating third-body re- with the present data, especially at atmospheric pressure. actions CH3 + H(+M) → CH4(+M) and aC3H5 + H(+M) → The laminar flame speed of CHX is larger than that of CPT and the C3H6(+M) become obviously higher at 5 atm compared to those at discrepancy becomes larger with the initial pressure increased. The 1 atm, which is consisted with the Le Chatelier's principle. At the same chemical kinetic effects play the dominant role resulting in the lower time, the reaction C4H6 +H→ C2H4 +C2H3 also has a higher sensi- laminar flame speeds of CPT compared to that of CHX. Specially, CPT tivity coefficient at 5 atm compared to that at 1 atm. However, a dif- flames yield more methyl and allyl, which can induce chain terminating ference occurs in the variation of sensitivity coefficients of the reactions third-body reactions and consume plenty of H radicals. While CHX involving vinyl. For CPT, the reactions involving vinyl have slightly flames yield more ethyl and 1,3-butadiene, which can further produce smaller sensitivity with the pressure increased. While for CHX, the greater amounts of vinyl. The later can generate more H radicals and sensitivity coefficients of the reactions involving vinyl become a little promote the overall burning rate. Besides, the discrepancy in laminar larger at 5 atm than those at 1 atm. Based on the above analysis, the flame speeds becomes more sensitive to the distribution of cracked laminar flame speed becomes more sensitive to the distribution of the products as the initial pressure increases. cracked products with the pressure increased. Thus, the discrepancy in

244 H. Zhao et al. Fuel 234 (2018) 238–246

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