Confined spherically expanding flame method for measuring laminar flame speeds: Revisiting the assumptions and application to C1C4 hydrocarbon flames

Combustion and Flame 212 (2020) 79–92

Contents lists available at ScienceDirect

Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Confined spherically expanding flame method for measuring laminar flame speeds: Revisiting the assumptions and application to C1 –C4 hydrocarbon flames Ashkan Movaghar∗, Robert Lawson, Fokion N. Egolfopoulos Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA

a r t i c l e

i n f o

Article history: Received 21 August 2019 Revised 14 October 2019 Accepted 15 October 2019

Keywords: Laminar flame speed Spherically expanding flames Foundational fuels C1 -C4 n-alkanes and n-alkenes Engine relevant conditions

a b s t r a c t The spherically expanding flame under constant volume method was introduced in 1934 by Lewis and von Elbe as a means to study laminar flame propagation at engine-relevant conditions. Despite its potential, this method has not been utilized extensively due to concerns regarding the underlying assumptions and data uncertainty. In the present study, the intricacies of the experimental approach as well as the models and assumptions involved during data interpretation were reassessed with the aid of direct numerical simulations. Results confirmed that stretch effects are negligible during the compression stage of the experiment for a wide range of Lewis numbers. Additionally, it was shown that the laminar flame speed is sensitive to the flame radius stressing thus the requirement that the modeling of flame radius needs to be done with the highest possible accuracy by accounting properly for product dissociation and thermal radiation from the burned gases. It was also shown, that the equilibrium assumption is valid for modeling the flame radius as a function of pressure and, as expected, the kinetic and transport effects are negligible. Subsequently, laminar flame speeds were measured for methane, ethane, ethylene, propane, propylene, n-butane, 1-butene, and isobutene flames for 8–30 atm pressures and 400–520 K unburned mixture temperatures. A hybrid thermodynamic/radiation model was utilized to interpret the experimental observables and derive the laminar flame speed by accounting for spectrally dependent emission from and absorption by the burned gases as well as product dissociation during compression. The data were found to be consistent with measurements obtained in spherically expanding flame experiments under constant pressure conditions and predictions using a number of current kinetic models. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The availability of fundamental flame data at high pressures is of paramount importance in view of their relevance to power generation and propulsion devices, which operate well above 10 atm. The laminar flame speed (Suo ) is one of the most important fundamental properties of a reacting mixture as it is a measure of the rate of heat release, is essential for testing kinetic models, is used for scaling turbulent combustion observables, and is a key parameter in engine design (e.g., [1,2]). Despite the numerous experimental investigations of Suo over the years, its accurate determination has been and still remains a source of controversy (e.g., [3,4]), which can be attributed largely to the fact that the theoretical freely propagating flame cannot be reproduced in the laboratory. In other words, Suo is not a

∗

Corresponding author. E-mail address: [email protected] (A. Movaghar).

directly measured property and the experimental observables need to be interpreted introducing thus assumptions and associated uncertainties [4,5]. Over the years, Suo has been measured using different experimental techniques including: (1) Bunsen flames (e.g., [6,7]); (2) counterflow flames (e.g., [8,9]); (3) burner-stabilized flames (e.g., [10,11]); (4) spherically expanding flames (SEF) under constant pressure conditions (SEF-CONP) (e.g., [12–15]); and SEF under constant volume (SEF-CONV) conditions (e.g., [16–20]). Among all legacy methods, SEF-CONV was introduced by Lewis and von Elbe in 1934 [16] as a viable method for measurements at engine-relevant conditions that is for pressures (P) well above 10 atm and unburned mixture temperatures (Tu ) as high as 800 K. Application of SEF-CONV to high Tu is possible owing to the fact that during the rapid compression stage of flame propagation, the unburned mixture is heated isentropically to high temperatures in relatively short time scales so that heavy liquid fuels can be sustained in the vapor phase without decomposing to any measurable extent. Furthermore, the Karlovitz number of the

https://doi.org/10.1016/j.combustflame.2019.10.023 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

80

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

resulting flames is very low [4,21] eliminating thus the need for extrapolations, which can introduce large uncertainties in the reported Suo values [22–24]. Recently, the SEF-CONP method was implemented in shock tubes [25], extending thus the applicability of this method to higher unburned temperatures at relatively short time scales. However, the shock tube method is in its early stages of development and further studies are required in order to evaluate its ability to result in Suo data that could be used with confidence as validation targets for kinetic models. Despite the significant potential of the SEF-CONV method for measuring Suo at extreme thermodynamic conditions, it has been under-utilized over the years due to potential sources of error and high uncertainties associated with it. This is in fact manifested through notable discrepancies (as high as 18%) between published Suo s (measured using the SEF-CONV method), as pointed out by Faghih and Chen [26]. Among the major sources of concerns regarding the SEF-CONV method is the requirement of a totally spherical chamber and as a result the absence of optical access that could compromise the sphericity. Thus, the derivation of Suo is based on the experimental pressure-time history and the implementation of analytical models traditionally based on thermodynamic principles. Additionally, the absence of optical access limits the ability to assess the potential development of instabilities (e.g., thermo-diffusive and/or hydrodynamic) that can increase flame surface and as a result the burning rate. In view of these considerations, the first goal of this investigation was to expand the scope of a recently published study by the authors on SEFs [4] by revisiting all assumptions of the SEF-CONV method. To that end, direct numerical simulations (DNS) were carried out that allowed for the assessment of the validity of the underlying assumptions and for the identification of the sources and extent of errors and uncertainties during data interpretation. The main motivation of this first goal was that the literature is rather thin when it comes to much needed Suo data at engine-relevant conditions, which the SEF-CONV method can approach. Upon meeting the first goal, the second one was to apply the improved SEF-CONV method for measuring Suo s of flames of C1 –C4 hydrocarbons, also referred to as foundational fuels, as their oxidation involves numerous rate-limiting steps that control the combustion characteristics of heavier hydrocarbons (e.g., [27–32]). Furthermore, C1 –C4 hydrocarbons are the major constituents of natural gas and key pyrolysis products of practical jet, rocket, gasoline, and Diesel fuels [29,30]. Regarding the availability of high-pressure Suo data for C1 –C4 hydrocarbons, a literature search of nearly 200 published experimental studies was carried out and the references associated with this survey can be found in Section 1 of Supplementary Material 1 (SPM1). It is of interest to note that the majority of the Suo data has been measured at near-atmospheric pressures, while less than 8% of the data correspond to P > 10 atm as shown in Fig. 1 for C1 –C4 n-alkane flames. In the present study, the Suo measurements were carried out for flames of methane (CH4 ), ethane (C2 H6 ), ethylene (C2 H4 ), propane (C3 H8 ), propylene (C3 H6 ), n-butane (n-C4 H10 ), 1-butene (1-C4 H8 ), and isobutene (i-C4 H8 ), for equivalence ratios φ = 0.8, 1.0, 1.3, 8 ≤ P ≤ 30 atm, and 400 ≤ Tu ≤ 520 K. The data are compared with predictions by current kinetic models in order to assess data consistency as well as the models’ performance. However, addressing in depth kinetic issues related to disagreements between data and predictions was beyond the scope of the present study and it will be deferred to future investigations that will be carried out in collaboration with kinetics research groups. Finally, the data are reported along with their uncertainties, which were computed using a rigorous mathematical approach similarly to the previous study [4]. It should be noted that

Fig. 1. Number of published experimental laminar flame speed studies for flames of C1 –C4 n-alkanes depicted with its associated pressure range.

uncertainties of reported laminar flame speed data in many past studies have not been addressed adequately, even though they are required in order to compare meaningfully various experimental methods. Whether the magnitudes of “real” uncertainties are favorable or not, is an issue that the experimentalists need to address using modern tools. 2. Experimental approach Similar to the previous study [4], two facilities were used. First, a cylindrical chamber with optical access was utilized to identify the onset of flame cellular instability for each mixture, as originally proposed by Metghalchi and co-workers [33]. This allows for identifying mixture compositions that result in flames free from thermo-diffusional and hydrodynamic instabilities in the anticipated pressure range, up to 30 atm in the present study. Subsequently, a spherical chamber without optical access was used to measure Suo over the course of the isentropic compression. In doing so, the assumption is that flame stability is not affected to the first order by the shape of the chamber during the compression stage. Additionally, the cylindrical chamber was further utilized to carry out selected Suo measurements under constant-pressure conditions in order to assess the consistency of data obtained in SEFCONV and SEF-CONP experiments, by comparing the results against model predictions. 2.1. Description of experimental facilities Figures 2 and 3 illustrate the schematics of the cylindrical and spherical chambers respectively, both made of 316-stainless steel. The cylindrical chamber is 22 cm long with a diameter of 27 cm, both inner dimensions. The chamber is fitted with two fused quartz windows at both ends limiting thus operation of the chamber to post combustion pressures of less than 80 atm considering a factor of safety. Flame propagation in the cylindrical chamber is imaged using a CMOS Phantom v710 monochrome high-speed camera, with frame rate of 13 kHz in a 600 × 800-pixel window. The spherical chamber inner diameter is 20.32 cm and is capable of withstanding post-combustion pressures up to 240 atm. Arrival of the flame to the spherical chamber wall is signaled through three ionization probes placed in the vicinity of the wall to confirm the flame symmetry and the absence of buoyancy-induced effects. The spherical chamber is housed inside an oven that is capable of preheating uniformly the system to temperatures up to 500 K. Both chambers are equipped with two extended electrodes that allow for central ignition. The implemented ignition system is capable of delivering variable high ignition energy required for igniting mixtures with high He dilution. The partial pressure method is

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

81

Fig. 2. Schematic of the cylindrical chamber.

used for filling both chambers. The partial pressure of each component is measured using various Omega PX-409-A5V transducers with the relevant pressure ranges to reduce uncertainty in mixture composition. A Kistler 601B1 dynamic pressure transducer is mounted on the both cylindrical and spherical chambers to measure pressure-time, [P, t], history over the course of flame propagation. The [P, t] history obtained from the spherical chamber experiments is used as the sole experimental observable for determining Suo given a procedure that will be outlined in the subsequent section. Therefore, the [P, t] signal accuracy is of primary importance in reducing uncertainty of the reported Suo . Hence, the dynamic pressure transducer was calibrated for different pressure ranges of relevance to the experimental conditions to minimize the [P, t] uncertainty during data acquisition. 2.2. Data interpretation and derivation of laminar flame speed 2.2.1. Spherically expanding flames under constant pressure In the few selected SEF-CONP experiments, the temporal variation of flame radius, Rf , was monitored and used for deriving the burned flame speed Sb ≡ (dRf /dt) along with the attendant stretch rate K ≡ (2/Rf )(dRf /dt) [12–15]. Variation of Sb versus K was then extrapolated to zero stretch rate using DNS-assisted extrapolation as proposed by Xiouris et al. [4] to obtain Sbo ; the implementation of DNS-assisted extrapolations is preferred over linear and nonlinear analytical extrapolations which can result in uncertainties as large as 60% as reported by Wu et al. [24] and Jayachandran et al. [23]. Subsequently, Suo was derived from Sbo implementing continuity equation [4]. The data used for extrapolation were restricted to the range of stretch rates in which the effects of ignition and pressure rise is negligible [34]. As a result, the lack of Sb data for a wide range of K contributes to the error arising from extrapolations [35] that cannot be quantified properly. 2.2.2. Spherically expanding flames under constant volume As discussed earlier, the temporal variation of pressure is the sole observable in the SEF-CONV experiments. By assuming a

smooth, symmetric, infinitesimally thin, and buoyancy-free spherical flame that compresses isentropically the unburned mixture, the expression known as Fiock and Marvin equation [16,17] can be obtained for the flame speed with respect to unburned mixture (Su ) (to be distinguished for the time being from Suo ) using conservation of mass:

  −dmu   yields π ρu R3w − R3f & = ρu Su 4π R2f → dt  3  3

mu =

4 3

Su =

dR f − dt

Rw − R f

3R2f γu P

dP dt

(1)

In Eq. (1), P is the thermodynamic pressure, Rf the flame radius, Rw the chamber inner radius, and γ u is the heat capacity ratio of the unburned mixture. The first term represents the velocity of the flame sheet with reference to a stationary observer while the second term represents the velocity of the unburned mixture during compression. Knowing P and Rf as a function of time, one can readily derive Su from Eq. (1). It has been established that the effective compression of the unburned mixture initiates at high values of Rf /Rw ~80% [4,21]. Direct measurements of Rf within the compression zone have been carried out by Metghalchi and Keck [19] using He–Ne laser in order to record the flame arrival time to the laser beam for validation purposes. However, well-resolved near-wall continuous measurements of Rf during compression could be associated with large uncertainties. Therefore, the extraction of Su using the [P, t] trace and appropriate models is at present the most accurate provided that the assumptions of the models are assessed properly. Eq. (1) can be rewritten as



Su =

dR f − dP



R3w − R3f 3R2f Yu

  1 p

×

  dP dP = f Rf , P × dt dt

(2)

and thus Su can be computed by modeling the [Rf , P] relationship and by utilizing the experimental dP/dt trace. The procedure is outlined graphically in Fig. 4 in which Po corresponds to the initial pressure. Several analytical approaches have been implemented over the years to relate Rf , or equivalently burned mass fraction, to the pres-

82

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

Fig. 3. Schematic of the spherical chamber.

Fig. 4. Procedure for extraction of Su in SEF-CONV experiments. Demonstrated case is CH4 /O2 /N2 /He mixture at φ = 0.8, Po = 6 atm, Tu = 298 K (defined as Mixture 2 in Table SPM6).

sure rise in the vessel. Lewis and von Elbe [16] proposed a linear relationship between burned mass fraction and pressure. This relationship, however, does not account for the temperature rise in the burned mixture due to compression and for temperature gradients in the burned region and it is valid only during the initial stages of flame propagation. Regarding the later stages, it has been shown that the maximum temperature difference within the burned gas can be as large as 500 K (e.g., [18,36,37]), which in turn can in-

troduce notable errors when the pressure rise is significant and more accurate analytical relationships have been considered (e.g., [37,38]). Recently Faghih and Chen [26] evaluated the performance of different analytical methods against DNS of SEFs [21,22]. An alternative approach was proposed by Metghalchi and Keck [19,20] in which the [Rf , P] relationship was modeled numerically by solving simultaneously, the mass and energy conservation for a multi-zone model. Metghalchi and co-workers (e.g., [33,39,40])

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

83

further improved this method by taking into account the temperature gradient in the burned gases and thermal boundary layers. Saeed and Stone [36] proposed a principally similar approach in their BOMB program. Despite the significant analytical/numerical strides for computing the burned mass fraction or equivalently Rf as a function of P, only recently has the effect of radiative heat loss been quantified [4] via DNS. Results showed that by employing the adiabatic (ADB) assumption in computing [Rf , P] while using the pressure-time history that is based on optically thin limit radiation model could impose errors as large as 15% in Su . This error has been also shown to be ~17% for the case of low flame speeds for refrigerant/air mixtures [41]. 2.2.3. The hybrid thermodynamic-radiation model In the present study, the evolution of [Rf , P] was modeled using the Hybrid Thermodynamic-Radiation (HTDR) model that was introduced in a previous SEF study by the authors [4]. HTDR is based on a multi-zone method, which accounts for thermal radiation and reabsorption, and has been validated against DNS results. The assumptions are: • The burned gas constitutes a perfectly smooth sphere with the flame representing an infinitely thin sheet separating burned and unburned gas. • The pressure is uniform in space and only varies in time. • The unburned gas is chemically frozen. • The burned gas is always in chemical equilibrium. HTDR is integrated with CANTERA [42] libraries for performing equilibrium calculations. HTDR accounts for ADB conditions as well as for radiative heat loss from burned gases by invoking either the Optically Thin Limit (OTL) or Reabsorption (REAB) models [4]. Regarding REAB, the spectrally dependent emission and absorption of burned gasses are accounted for by implementing RADCAL [43], a radiation subroutine with a statistically narrow-band database for combustion gas properties. The details of the HDTR algorithm are summarized in [4] and the validity and effects of the underlying assumptions are evaluated in the subsequent sections. 3. Modeling approach Suo was computed using the PREMIX code [44] coupled with CHEMKIN [45] and Sandia transport subroutines [46]. The code has been modified to account for thermal radiation of CH4 , H2 O, CO, and CO2 at optically thin limit [47] using Planck mean absorption coefficients provided by Tien [48]. DNS of unsteady propagating spherical flames was conducted using the transient one-dimensional reacting-flow code (TORC) [4,23]. TORC is a low Mach number reacting flow code, which solves the one-dimensional mass, species, and energy equations in spherical coordinates and is integrated with CHEMKIN and Sandia transport subroutines. Upon imposing the proper initial conditions, TORC utilizes the DASPK [49] solver for implicit time integration of the system of equations. More details on the governing equations, boundary conditions and numerical methods of TORC can be found in [4]. For modeling Suo of C1 –C4 flames, the USC-Mech II [50], FFCM 1.0 [51], and ARAMCO 2.0 [52,53] kinetic models were used. The TORC simulations involved a 30 species skeletal model for CH4 developed by Lu and Law [54].

Fig. 5. Variation of Su ( ), Suo ( ), and Ka ( of P/Po for Po = 3 atm and Le = 6.53.

) for the Test Mixture as a function

4.1. Stretch effects in the compression region The Su values obtained using Eq. (1) needs to be distinguished from Suo given that, in principle, its value could be affected by stretch. Recent DNS studies [4,21] have shown that during the late stages of compression, the Karlovitz number (Ka) is of the order of 10−3 implying that Su ≈ Suo . However, those studies were conducted for mixtures with Lewis numbers (Le) (defined based on the deficient reactant) that are close or slightly less than one. Since ( SSuo )2 ln( SSuo )2 = −2MaKa [55], where Ma is the Markstein numu

u

ber, and given that Ma depends strongly on Le, the validity of the Su ≈ Suo assumption for mixtures with Le >> 1 was further investigated; mixtures with Le >> 1 are used typically in high pressure SEF experiments given that He dilution is necessary for suppressing instabilities. Simulations were carried out using TORC in a Rw = 3 cm chamber and the derived Su obtained by implementing Eq. (1) was compared against Suo as computed by the PREMIX code at the identical thermodynamic conditions of the unburned mixture along the isentrope. A φ = 0.8 CH4 /O2 /He mixture (CH4 :O2 :He = 0.8:2.0:9.76 per mole) was chosen with Le = 3.14, with initial pressure Po = 3 atm, initial unburned mixture temperature To = 298 K, and adiabatic flame temperature Tad = 2200 K; this will be referred to as “Test Mixture” hereafter. The original Le = 3.14 value was then artificially increased to Le = 6.53 in the simulations, by replacing the Lennard-Jones parameters of CH4 with those of n-C12 H26 . Figure 5 depicts the variation of Su and Ka as a function of P/Po over the course of flame propagation along with Suo computed values along the isentrope. Results indicate that for P/Po > 2.5, Su deviates from Suo by less than 1%. These results further buttress the negligible effect of flame stretch over the compression region even for mixtures with Le >> 1 and as a result, extrapolations are not required. It is worth noting also that for chambers with Rw > 3 cm the effect of stretch will be even lower given the larger radii that the flames will reach. The reader is advised to refer to Section 2 of SPM1 for an analysis of the effect that different definitions (isotherms) of the flame front have on flame speeds derived using Eq. (1). 4.2. Sensitivity to uncertainties in [Rf ,P]

4. Results and discussion As shown in Section 2.2.2, Su is directly proportional to The assessment of the assumptions involved during data interpretation in SEF-CONV experiments is presented next, followed by Suo results obtained for C1 –C4 hydrocarbon flames at pressures up to 30 atm.

f (R f , P ) = [

dR f dP

−(

R3w −R3f 3 R2 Yu f

) 1p ] in Eq. (2). The two terms that are

subtracted in this expression, are of the same order of magnitude, and thus any uncertainty associated with either one could be mag-

84

Fig. 6. Variation of: (a) Su and b) Su /Su, (R f ) = 1.01(R f )original case ( – ).

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

original

for the Test Mixture as a function of P/Po for the original case (

), (d R f /dP ) = 1.01(d R f /dP )original case (

), and (b)

Figure 6a and b depicts the comparisons of Su and Su /Su, original as functions of P/Po for the original and perturbed cases. It is observed that a 1% increase in (dRf /dP), keeping everything else the same, leads to 2–4% increase in Su resulting in a logarithmic sensidR

tivity coefficient LSC ≡ d(ln Su )/d(ln dPf ) = 2 − 4. Furthermore, 1% increase in Rf , keeping everything else the same, leads to 8–12% increase in Su resulting in LSC = d (ln Su )/d(ln R f ) = 8 − 12. These notably high LSC values of Su to [Rf , P] emphasize the requirement that the Rf vs. P variation needs to be determined with the best possible accuracy. 4.3. Equilibrium assumption The use of any thermodynamic model to determine [Rf , P], implies that equilibrium prevails on the burned side of the flame whose thickness is infinitely small compared to any other spatial scales. This assumption introduces two possible points of concern: Fig. 7. Comparison of Su of the Test Mixture obtained employing [P, t] history from TORC, and [Rf , P] from: the original HTDR model ( ); HTDR-NCID ( ); HTDR-SENKIN using original compression time scale tc ( ); HTDR-SENKIN using tc /10 (); and TORC (- - -).

nified when computing Su . To better illustrate the degree of uncertainty that can be imposed on Su , simulations were carried out for Test Mixture and Rw = 3 cm using TORC, and Su was calculated using Eq. (2). Then, the computed (dRf /dP) and Rf values were perturbed separately by 1% and the effects on Su were determined.

• First, in a flame coordinate system equilibrium is reached at significantly large number of flame thicknesses (δ f ). In other words, it takes time to reach equilibrium. • Second, due to pressure rise during compression the already burned gases will undergo further product dissociation which takes place at a finite rate. Therefore, by assuming equilibrium any relevant time scales associated with dissociation are not accounted for. In order to address the first concern, simulations were carried out for the Test Mixture using both TORC and HTDR, and for a chamber with Rw = 3 cm. Regarding the TORC simulations, the ADB

Fig. 8. Snapshots of flame propagation and onset of cellular instability for the mixture of 0.8n-C4 H10 + 6.5O2 + 7.34N2 + 29.37He, at Po = 6 atm, and To = 298 K (defined as Mixture 32) Cells start to form at P = 30.9 atm.

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

85

Fig. 9. Experimental and predicted laminar flame speeds of φ = 0.8 CH4 /O2 /N2 /He mixture employing (a) SEF-CONP method at Tu = 298 K and P = 3, 5 atm, and (b) SEF-CONV method at Tu,o = = 298 K and Po = 3 atm using HTDR along with OTL (

), REAB (···), and ADB (

) assumptions; (

) modeling results.

Fig. 10. Experimental and predicted laminar flame speeds of CH4 /O2 /N2 /He mixtures for φ = 0.8 (defined as Mixtures 1 and 2 in SPM1) and φ = 1.3 (defined as Mixtures 5 and 6 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

assumption (neglecting radiation heat loss) was invoked for the “Original” case as well as for the “Delayed Equilibrium” case in which the rate constant of CO + OH ⇔ CO2 + H was decreased by a factor of 10 so that the conversion of CO to CO2 would slow down. For both cases, Rf was defined as the location of the maximum heat release rate. HTDR simulations also invoked the ADB assumption to compute [Rf , P]. In the context of these studies the flame propagation speed is defined as Su to be distinguished from Suo that is the actual laminar

) assumptions in HTDR; lines represent numerical results.

flame speed. More specifically, Su is computed using Eq. (2) with dP/dt obtained from the TORC simulations for the “Original” case and [Rf , P] of all other cases stated above. The Su results obtained from HTDR agrees well (within ~0.5%) with Su obtained from the “Original” case of TORC, while a maximum discrepancy of ~1.2% was observed between the Su results of HTDR and the “Delayed Equilibrium” case of TORC. Therefore, the near identical Su results obtained for all the cases during compression (i.e., for P/Po ≥ 2.5) supports the assumption of zero-δ f in [Rf , P] calculations as well as

86

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

Fig. 11. Experimental and predicted laminar flame speeds of C2 H6 /O2 /N2 /He mixtures for φ = 0.8 (defined as Mixtures 7 and 8 in SPM1) and φ = 1.3 (defined as Mixtures 11 and 12 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

the equilibrium assumption associated with the “burning” of each layer. The results are shown in Section 3 of SPM1. Additionally, kinetic and transport effects on [Rf , P] were also assessed using TORC by perturbing the kinetic rates and transport coefficients and the results are shown in Section 4 of SPM1. As expected, [Rf , P] showed no sensitivity to kinetic and transport effects and the influence of reactivity and diffusivity on Su was only manifested through dP/dt. These results are applicable to larger chambers also given that the (δ f /Rf ) will further decrease in the compression region as Rw increases. The effect of the compression-induced dissociation of burned gases on Su was investigated using a modified version of HTDR. As discussed in Section 2.2.3, the original HTDR assumes chemical equilibrium at each computational step. The dissociation of the already burned gases due to subsequent compression is modeled employing re-equilibration of the already burned shells at each computational step in HTDR, neglecting any time scale associated with this process. Given that in reality dissociation happens at a finite rate, HTDR was modified to model the time evolution of the burned gases by employing SENKIN [56] and called HTDR-SENKIN hereafter. The SENKIN calculations for the burned shells require the compression time scale, tc , which was derived iteratively using [P, t] history until reaching convergence. Figure 7 depicts Su results obtained employing [Rf , P] from HTDR, HTDR-SENKIN, and TORC, with the dP/dt obtained from TORC as a function of P/Po for the Test Mixture and for Rw = 3 cm. First, it is observed that Su obtained from the original HTDR is identical to that obtained from HTDR-SENKIN given the proper compression time scale, tc . Additionally, Su was calculated with HTDR-SENKIN but using one tenth of the original compression

) assumptions in HTDR; lines represent numerical results.

time scale (tc /10) instead, and no measurable difference was found compared to the original case. These results indicate that the compression-induced dissociation of burned gases takes place much faster compared to pressure rise in the chamber and estimation of such phenomena as equilibrium is valid for experimental situations of relevance. Note that tc will increase for larger chamber sizes and lower flame propagation speeds, so that similar conclusions are valid for such conditions. It is worth noting that not considering compression-induced dissociation (NCID case), can impose an error as much as 7% in the Su as shown in Fig. 7. 4.4. Sensitivity to heats of formation The effects caused by uncertainties associated with thermodynamic properties were also assessed. To this end, the heat of formation (hf ) for CH4 was perturbed by 2% and [Rf , P] was computed using HTDR for the Test Mixture. The perturbed [Rf , P], were then used along with the dP/dt obtained from TORC (which used the unperturbed hf ) to compute Su . Subsequently the LSC (Su , hf, CH4 ) ≡ ∂ (ln Su )/∂ (ln hf, CH4 ) values were calculated at P/Po = 4 along the isentrope; for comparison reasons the LSC (Suo , h f, CH4 ) ≡ ∂ (ln Suo )/∂ (ln h f, CH4 ) were also computed for the same thermodynamic conditions using the PREMIX code. It was observed that Suo computed using PREMIX is almost 6 times more sensitive to the heat of formation of fuel compared to the Su derived based on HTDR calculations with respective values of LSC (Suo , h f, CH4 ) = +0.36 and LSC (Su , h f, CH4 ) = −0.06. This can be explained as Suo has an exponential dependency on Tad while the dependency of the experimentally obtained Su on Tad is

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

87

Fig. 12. Experimental and predicted laminar flame speeds of C2 H4 /O2 /N2 /He mixtures for φ = 0.8 (defined as Mixtures 13 and 14 in SPM1) and φ = 1.3 (defined as Mixtures 17 and 18 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

only through [Rf , P] modeled using HTDR. Thus, uncertainties in hf affect Su minimally. It is also worth noting that LSC (Suo , h f, CH4 ) and LSC (Su , hf, CH4 ) have different signs. The positive LSC (Suo , h f, CH4 ) is expected as an increase in exothermicity of the mixture will result in an increase in Suo . The counterintuitive negative LSC (Su , hf, CH4 ) can be explained as any increase in the exothermicity of the mixture, leads to a decrease in Rf (P). This is because pressure directly re lates to the heat release to the first order (P = dP dt ∼ Q˙ /cv dt ), dt

and as a result is higher for the same burned mass fraction for more exothermic mixtures, or in other words the same pressure is achieved at lower Rf values.

4.5. Laminar flame speeds of C1 –C4 /O2 /inert mixtures The SEF-CONV method was implemented to measure Suo s of C1 –C4 /O2 /He/N2 mixtures. The experiments were carried out for φ = 0.8, 1.0, and 1.3, Po = 3 and 6 atm, and To = 298 K, and the parameter space is listed in Section 5 of SPM1. The [P, t] history was acquired experimentally, while [Rf , P] was modeled with HTDR employing the ADB, OTL, and REAB models to obtain Suo , with REAB being the most realistic; for the OTL model the Planck mean absorption coefficients of Ju et al. [57] were adopted. Nonetheless, it was observed that the difference between Suo s acquired using the two limiting cases of ADB and OTL lies within experimental uncertainty (±1σ ) for all cases. Ionization probes’ signals for the slowest flame (defined as Mixture 6 in SPM1) of this study is shown in Section 6 of SPM1 revealing that the flames are not influenced by buoyancy effects.

) assumptions in HTDR; lines represent numerical results.

The experimental uncertainty was quantified rigorously utilizing a mathematical error propagation analysis [4] and it involved the combined effects of: (1) mixture preparation; (2) data acquisition; and (3) data post processing. The uncertainty bars shown with all data correspond to ±1σ . The data used to determine Suo were taken for 2.5 < P/Po < 5 so that the effects of stretch and heat loss to the wall were negligible [4]. Based on the results shown in Section 4.1, the lower limit of the pressure range was a conservative estimate ensuring that the stretch effects are negligible for the mixtures of this study with 1 < Le < 4.5. Unlike the lower limit, the upper limit of the pressure range is detectable experimentally with a distinguishable drop in the slope of dP/dt versus P, due to the heat loss to the chamber wall. This slope change is demonstrated in Section 7 of SPM1 for the pressure traces obtained experimentally for Mixture 1 (Po = 3 atm) and Mixture 2 (Po = 6 atm) as defined in SPM1. The upper P/Po limit of 5 in this study was chosen as a conservative value and for consistency between different experiments as none of the experiments in this study showed heat loss effects for P/Po < 6.0. Therefore, Suo was measured for 8 atm < P < 30 atm and 400 K < Tu < 520 K. The values of all Suo along with their associated thermodynamic conditions and uncertainties are listed in Supplementary Material 2 (SPM2); for brevity only the data for φ = 0.8 and 1.3 are presented in the main text; the experimental [P, t] history is provided in Supplementary Material 3 (SPM3). The composition of each mixture was first tested in the cylindrical chamber that allows for optical access to ensure that the flames were smooth and free from cellular instability for the pressure range of interest. Figure 8 depicts snapshots of stable flame propagation and transition from stable to unstable flame

88

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

Fig. 13. Experimental and predicted laminar flame speeds of C3 H8 /O2 /N2 /He mixtures at φ = 0.8 (defined as Mixtures 19 and 20 in SPM1) and φ = 1.3 (defined as Mixtures 23 and 24 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

at P > 30 atm for a lean n-C4 H10 mixture. It is well established in SEF experiments, that using He as diluent delays onset of cellularity because it increases Le and δ f suppressing thus the development of thermal-diffusive and hydrodynamic instabilities respectively [58,59]. Since Le > 1 for all mixtures considered in the present study, the appearance of instabilities during the compression stage, as observed in the cylindrical chamber, are of hydrodynamic nature that depends on the flame thickness, and density jump across the flame [59], with positive stretch (present at the early stages of flame propagation) playing an inhibiting role [60]. At the later stages of compression, flames are nearly stretch-free in both spherical and cylindrical vessels despite the fact that their global topology can be different at the very end due to chamber constraint [61]. Given that the density ratio across the flame and flame thickness for stretch free flames only depend on the unburned thermodynamic conditions, no measurable difference is expected between the onset of instabilities for the flames in cylindrical and spherical chambers. On the other hand, thermo-acoustic instabilities are expected to be more geometry dependent. Al-Shahrani et al. [62] reported that mixtures with positive Ma (Le > 1) are less prone to this mode of instabilities that are evidenced by severe pressure oscillations and burning rate enhancement. More recently, Omari and Tartakovsky [63] reported a clear slope increase of Suo as a function of P at the onset of cellularity using a semi-spherical chamber with optical access. In the present investigation such phenomena have not been observed suggesting that there are no measurable effects from cell formation in the reported data. In order to assess data consistency, similarly to the approach taken by Hinton et al. [64], Suo was measured also in the SEF-

) assumptions in HTDR; lines represent numerical results.

CONP configuration that allows for optical access and direct measurement of the Rf time evolution and the results are shown in Fig. 9a along with predictions using the FFCM 1.0 kinetic model for φ = 0.8 CH4 /O2 /He/N2 mixture at P = 3 and 5 atm. Figure 9b depicts Suo measured in the SEF-CONV configuration method along with predictions using FFCM 1.0 for φ = 0.8 CH4 /O2 /He/N2 mixture and 8 atm < P < 15 atm. Given that the chemical pathways cannot differ significantly between P = 5 atm and P = 8 atm and that the data compare in a similar manner with the predictions in both experiments, the data exhibit consistency and the assumptions invoked in the SEF-CONV method appear to be valid within the overall experimental uncertainty. Additional results are included in Section 8 of SPM1. Data for φ = 0.8 and φ = 1.3 CH4 flames measured using the SEF-CONV method are shown in Fig. 10 along with predicted values employing USC-Mech II, ARAMCO 2.0 and FFCM 1.0 kinetic models. For φ = 0.8, all models result in predictions of Suo within the experimental uncertainty up to P ≈ 15 atm, while USC-Mech II underpredicts the data for P > 20 atm, and ARAMCO 2.0 underpredicts the data for P > 15 atm. For φ = 1.3, only FFCM 1.0 closely predicts the data while both USC-Mech II and ARAMCO 2.0 result in values that are lower by ~10–14% for the entire pressure range. It is also worth noticing the consistency of the data with reference to modeling results at the overlapping P = 15 atm between the experiments performed at Po = 3 and 6 atm (top and bottom panels of Fig. 10). Given the notable discrepancy observed between experimental and predicted Suo using USC-Mech II at rich conditions and higher pressures, sensitivity analysis of Suo on rate constants was conducted and presented in Section 9 of SPM1. In agreement with numerous past studies, H + +O2 ⇔OH and CO+OH⇔CO2 +H

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

89

Fig. 14. Experimental and predicted laminar flame speeds of C3 H6 /O2 /N2 /He mixtures at φ = 0.8 (defined as Mixtures 25 and 26 in SPM1) and φ = 1.3 (defined as Mixtures 29 and 30 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

) assumptions in HTDR; lines represent numerical results.

Fig. 15. Experimental and predicted laminar flame speeds of n-C4 H10 /O2 /N2 /He mixtures at φ = 0.8 (defined as Mixtures 31 and 32 in SPM1) and φ = 1.3 (defined as Mixtures 35 and 36 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

) assumptions in HTDR; lines represent numerical results.

90

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

Fig. 16. Experimental and predicted laminar flame speeds of 1-C4 H8 /O2 /N2 /He mixtures at φ = 0.8 (defined as Mixtures 37 and 38 in SPM1) and φ = 1.3 (defined as Mixtures 41 and 42 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

) assumptions in HTDR; lines represent numerical results.

Fig. 17. Experimental and predicted laminar flame speeds of i-C4 H8 /O2 /N2 /He mixtures at φ = 0.8 (defined as Mixtures 43 and 44 in SPM1) and φ = 1.3 (defined as Mixtures 47 and 48 in SPM1). Symbols represent experimental values employing OTL (

), REAB (···), and ADB (

) assumptions in HTDR; lines represent numerical results.

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

exhibit the highest positive LSCs, while the highest negative sensitivities are exhibited by H + +O2 +M⇔HO2 +M for fuel-lean and CH3 +H + +M⇔CH4 +M for fuel-rich flames. While these reactions have been studied extensively over the years, revisions of their rate constants and chaperon efficiencies may be warranted as reliable flame Suo data at high pressures become available. Suo data for C2 H6 flames are shown in Fig. 11 along with the predicted values using USC-Mech II, ARAMCO 2.0, and FFCM 1.0. Unlike CH4 , all the models predict the data within the experimental uncertainties up to 30 atm except for USC-Mech II that under predicts the φ = 1.3 data for P > 10 atm, beyond the experimental uncertainty (±1σ ). Suo data for C2 H4 flames are shown in Fig. 12. Close agreements are observed between experimental and computed values using USC-Mech II, and ARAMCO 2.0; the predictions of FFCM 1.0 are within experimental uncertainty for the pressure range considered. Suo data for C3 H8 and C3 H6 flames are shown in Figs. 13 and 14, respectively, along with predicted values employing USC-Mech II and ARAMCO 2.0 kinetic models. Both models consistently underpredict the data. The results of sensitivity analysis are shown in Section 9 of SPM1 and indicate that for C3 fuels Suo is sensitive also to fuel-dependent reactions such as those involving H-abstraction. Suo data for n-C4 H10 , 1-C4 H8 , and i-C4 H8 flames are shown in Figs. 15, 16, and 17, respectively, along with predictions using the USC-Mech II, and ARAMCO 2.0 kinetic models. The nC4 H10 data are predicted closely using USC-Mech II for both lean and rich conditions up to P ≈ 20 atm and are underpredicted by ARAMCO 2.0. At P > 20 atm, the data are underpredicted by both models. The Suo data for flames of the butene isomers are under predicted by both models. Sensitivity analysis results for C4 flames at 30 atm (presented in Section 9 of SPM1) revealed the importance of some fuel dependent reactions such as 1-C4 H8 +H⇔C3 H6 +CH3 , 1-C4 H8 +H⇔C2 H4 +C2 H5 , 1 C4 H8 +H⇔C4 H7 +H2 , iC4 H8 +H⇔iC4 H7 +H2 . Sensitivity analysis on transport coefficients was carried out as well for CH4 and n-C4 H10 flames and the results are shown in Section 10 of SPM1. For the experimental conditions of this investigation, Suo exhibits measurable sensitivity to the He⇔N2 , He⇔H2 O, and He⇔O2 binary diffusion coefficients with LSC absolute values ranging approximately between 0.1 and 0.2

91

• As a result, a properly formulated hybrid thermodynamicradiation model can be used for the determination of the relationship between the flame radius and pressure with excellent accuracy. Regarding the hybrid thermodynamic-radiation model it was shown that: • The assumption of equilibrium at each stage of computations is valid for conditions of relevance to typical experimental conditions used in hydrocarbon fuel studies. • Proper accounting of product dissociation during compression as well as radiative heat loss and reabsorption are essential for deriving accurate values of laminar flame speeds. • Uncertainty in the heat of formation of the fuel has a minor effect on the derived laminar flame speed values. Upon meeting the first goal, the second goal was to apply the constant volume method to measure laminar flame speeds of methane, ethane, ethylene, propane, propylene, n-butane, 1butene, and isobutene flames, for various equivalence ratios, pressures from 8 to 30 atm, and unburned mixture temperatures from 400 to 520 K. The kinetics of the C1 –C4 fuels considered in this study, form the foundation for all higher molecular weight hydrocarbon fuels. The data were found to be consistent by comparing them against results obtained using the constant pressure method as well as against predicted values using a variety of current kinetic models. In closing, the authors would like to emphasize that the issue of uncertainty quantification and propagation requires special attention. Meaningful assessments of various experimental methods can only be made if their respective uncertainties have been evaluated from first principle by accounting for the contributions from all controlling parameters. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments

5. Concluding remarks Laminar flame speed measurements under engine-relevant pressures and temperatures for both light and heavy fuels can be measured using the confined spherically expanding flame method. While the method appears to be simple, there is a number of assumptions involved for interpreting the experimental observables given that the experiments are carried out in entirely spherical chambers with no optical access. The validity of these assumptions has not been addressed adequately in the past and this has been among the reasons that this method has been underutilized and as a result laminar flame speeds for engine-relevant thermodynamic conditions and fuels are either scarce or non-existing. The first goal of this investigation was to assess the validity of the underlying assumptions using direct numerical simulations. The results showed that: • The stretch effects on flame propagation are negligible within the compression region for Lewis numbers that are both close to and much greater than one. • The laminar flame speed is highly sensitive to uncertainties in the pressure-flame radius relationship that is primarily dependent on the thermodynamic states of burned and unburned states.

The work was supported by the Air Force Office of Scientific Research (Grant No. FA9550-15-1-0409) under the technical supervision of Dr. Chiping Li. The authors would like to thank Prof. Jagannath Jayachandran, Dr. Vyaas Gururajan, and Dr. Christodoulos Xiouris for fruitful discussions on the topic. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2019.10. 023. References [1] C.K. Law, Combustion physics, Cambridge University Press, 2008. [2] F.A. Williams, Combustion theory, Benjamin Cummins, Palo Alto, CA, 1985. [3] G.E. Andrews, D. Bradley, Determination of burning velocities: a critical review, Combust. Flame 18 (1972) 133–153. [4] C. Xiouris, T. Ye, J. Jayachandran, F.N. Egolfopoulos, Laminar flame speeds under engine-relevant conditions: uncertainty quantification and minimization in spherically expanding flame experiments, Combust. Flame 163 (2016) 270–283. [5] F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C.K. Law, F. Qi, Advances and challenges in laminar flame experiments and implications for combustion chemistry, Prog. Energy Combust. Sci. 43 (2014) 36–67. [6] J. Natarajan, T. Lieuwen, J. Seitzman, Laminar flame speeds of H2 /CO mixtures: effect of CO2 dilution, preheat temperature, and pressure, Combust. Flame 151 (2007) 104–119.

92

A. Movaghar, R. Lawson and F.N. Egolfopoulos / Combustion and Flame 212 (2020) 79–92

[7] N. Bouvet, C. Chauveau, I. Gökalp, S.Y. Lee, R.J. Santoro, Characterization of syngas laminar flames using the Bunsen burner configuration, Int. J. Hydrogen Energy 36 (2011) 992–1005. [8] C.K. Wu, C.K. Law, On the determination of laminar flame speeds from stretched flames, Symp. (Int.) Combust. 20 (1984) 1941–1949. [9] C.M. Vagelopoulos, F.N. Egolfopoulos, C.K. Law, Further considerations on the determination of laminar flame speeds with the counterflow twin-flame technique, Symp. (Int.) Combust. 25 (1994) 1341–1347. [10] L.P.H. de Goey, A. van Maaren, R.M. Quax, Stabilization of adiabatic premixed laminar flames on a flat flame burner, Combust. Sci. Technol. 92 (1993) 201–207. [11] K.J. Bosschaart, L.P.H. de Goey, Detailed analysis of the heat flux method for measuring burning velocities, Combust. Flame 132 (2003) 170–180. [12] D.R. Dowdy, D.B. Smith, S.C. Taylor, The use of expanding spherical flames to determine burning velocities and stretch effects in hydrogen/air mixtures, Symp. (Int.) Combust. 23 (1991) 325–332. [13] D. Bradley, R.A. Hicks, M. Lawes, C.G.W. Sheppard, R. Woolley, The measurement of laminar burning velocities and Markstein numbers for iso-octane–air and iso-octane–n-heptane–air mixtures at elevated temperatures and pressures in an explosion bomb, Combust. Flame 115 (1998) 126–144. [14] S.D. Tse, D.L. Zhu, C.K. Law, Morphology and burning rates of expanding spherical flames in H2 /O2 /inert mixtures up to 60 atmospheres, Proc. Combust. Inst. 28 (20 0 0) 1793–180 0. [15] X. Qin, Y. Ju, Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures, Proc. Combust. Inst. 30 (2005) 233–240. [16] B. Lewis, G. von Elbe, Determination of the speed of flames and the temperature distribution in a spherical bomb from time-pressure explosion records, J. Chem. Phys. 2 (1934) 283–290. [17] E.F. Fiock, C.F. Marvin, The measurement of flame speeds, Chem. Rev. 21 (1937) 367–387. [18] D. Bradley, A. Mitcheson, Mathematical solutions for explosions in spherical vessels, Combust. Flame 26 (1976) 201–217. [19] M. Metghalchi, J.C. Keck, Laminar burning velocity of propane-air mixtures at high temperature and pressure, Combust. Flame 38 (1980) 143–154. [20] M. Metghalchi, J.C. Keck, Burning velocities of mixtures of air with methanol, isooctane, and indolene at high pressure and temperature, Combust. Flame 48 (1982) 191–210. [21] Z. Chen, M.P. Burke, Y. Ju, Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames, Combust. Theor. Model. 13 (2009) 343–364. [22] Z. Chen, On the accuracy of laminar flame speed measure from outwardly propagating spherical flames: methane/air at normal temperature and pressure, Combust. Flame 162 (2015) 2442–2453. [23] J. Jayachandran, R. Zhao, F.N. Egolfopoulos, Determination of laminar flame speeds using stagnation and spherically expanding flames: molecular transport and radiation effects, Combust. Flame 161 (2014) 2305–2316. [24] F. Wu, W. Liang, Z. Chen, Y. Ju, C.K. Law, Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames, Proc. Combust. Inst. 35 (2015) 663–670. [25] A.M. Ferris, A.J. Susa, D.F. Davidson, R.K. Hanson, High-temperature laminar flame speed measurements in a shock tube, Combust. Flame 205 (2019) 241–252. [26] M. Faghih, Z. Chen, The constant-volume propagating spherical flame method for laminar flame speed measurement, Sci. Bull. 61 (2016) 1296–1310. [27] C.K. Westbrook, F.L. Dryer, Chemical kinetic modeling of hydrocarbon combustion, Prog. Energy Combust. Sci. 10 (1984) 1–57. [28] X. You, F.N. Egolfopoulos, H. Wang, Detailed and simplified kinetic models of n-dodecane oxidation: the role of fuel cracking in aliphatic hydrocarbon combustion, Proc. Combust. Inst. 32 (2009) 403–410. [29] H. Wang, R. Xu, K. Wang, C.T. Bowman, D.F. Davidson, R.K. Hanson, K. Brezinsky, F.N. Egolfopoulos, A physics-based approach to modeling real-fuel combustion chemistry – I. Evidence from experiments, and thermodynamic, chemical kinetic and statistical considerations, Combust. Flame 193 (2018) 502–519. [30] R. Xu, K. Wang, S. Banerjee, J. Shao, T. Parise, Y. Zhu, S. Wang, A. Movaghar, D.J. Lee, R. Zhao, X. Han, Y. Gao, T. Lu, K. Brezinsky, F.N. Egolfopoulos, D.F. Davidson, R.K. Hanson, C.T. Bowman, H. Wang, A physics-based approach to modeling real-fuel combustion chemistry – II. Reaction kinetic models of jet and rocket fuels, Combust. Flame 193 (2018) 520–537. [31] Y. Tao, R. Xu, K. Wang, J. Shao, S.E. Johnson, A. Movaghar, X. Han, J. Park, T. Lu, K. Brezinsky, F.N. Egolfopoulos, D.F. Davidson, R.K. Hanson, C.T. Bowman, H. Wang, A physics-based approach to modeling real-fuel combustion chemistry – III. Reaction kinetic model of JP10, Combust. Flame 198 (2018) 466–476. [32] K. Wang, R. Xu, T. Parise, J. Shao, A. Movaghar, D.J. Lee, J. Park, Y. Gao, T. Lu, F.N. Egolfopoulos, D.F. Davidson, R.K. Hanson, C.T. Bowman, H. Wang, A physics-based approach to modeling real-fuel combustion chemistry – IV. Hychem modeling of combustion kinetics of a bio-derived jet fuel and its blends with a conventional Jet A, Combust. Flame 198 (2018) 477–489. [33] K. Eisazadeh-Far, A. Moghaddas, J. Al-Mulki, H. Metghalchi, Laminar burning speeds of ethanol/air/diluent mixtures, Proc. Combust. Inst. 33 (2011) 1021–1027. [34] A.P. Kelly, C.K. Law, Nonlinear effects in the extraction of laminar flame speeds from expanding spherical flames, Combust. Flame 156 (2009) 1844–1851. [35] M. Lawes, G.J. Sharpe, N. Tripathi, R.F. Cracknell, Influence of spark ignition in the determination of Markstein lengths using spherically expanding flames, Fuel 186 (2016) 579–586.

[36] K. Saeed, C.R. Stone, Measurements of the laminar burning velocity for mixtures of methanol and air from a constant-volume vessel using a multizone model, Combust. Flame 139 (2004) 152–166. [37] C.C.M. Luitjen, E. Doosje, J.A. Van Oijen, L.P.H. De Goey, Impact of dissociation and end pressure on determination of laminar burning velocities in constant volume combustion, Int. J. Therm. Sci. 48 (2009) 1206–1212. [38] C.C.M. Luitjen, E. Doosje, L.P.H. de Goey, Accurate analytical models for fractional pressure rise in constant volume combustion, Int. J. Therm. Sci. 48 (6) (2009) 1213–1222. [39] F. Rahim, K. Eisazadeh-Far, F. Parsinejad, R. Andrews, H. Metghalchi, A thermodynamic model to calculate burning speed of methane-air-diluent mixtures, Int. J. Therm. 11 (2008) 151–160. [40] K. Eisazadeh-Far, A. Moghaddas, F. Rahim, H. Metghalchi, Burning speed and entropy production calculation of a transient expanding spherical laminar flame using a thermodynamic model, Entropy 12 (2010) 2485–2496. [41] R. Burrell, J.L. Pagliaro, G.T. Linteris, Effects of stretch and thermal radiation on difluoromethane/air burning velocity measurements in constant volume spherically expanding flames, Proc. Combust. Inst. 37 (2019) 4231–4238. [42] D.G. Goodwin, R.L. Speth, H.K. Moffat, B.W. Weber, Cantera: an object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes,https://www.cantera.org, 2018. [43] W.L. Grosshandler, RADCAL: a narrow-band model for radiation. NIST Technical Note 1402, Calculations in a Combustion Environment, 1993. [44] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, E. Meeks, PREMIX: A FORTRAN program for modeling steady laminar one-dimensional premixed flames, Sandia National Laboratories Report, SAND85-8249, 1985. [45] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical kinetics, SANDIA National Laboratories Report, Livermore, SAND-89-8009, CA, USA, 1996. [46] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, A FORTRAN computer code package for the evaluation of gas-phase multicomponent transport properties, SANDIA National Laboratories Report SAND86-8246, 1986. [47] F.N. Egolfopoulos, Geometric and radiation effects on steady and unsteady strained laminar flames, Symp. (Int.) Combust. 25 (1994) 1375–1381. [48] C.L. Tien, Thermal radiation properties of gases, Adv. Heat Transf. 5 (1968) 254–324. [49] L.R. Petzold, et al., A description of DASSL: a differential/algebraic system solver, in: R.S. Stepleman, et al. (Eds.), Scientific Computing, Amsterdam, North-Holland, 1983, pp. 65–68. [50] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F.N. Egolfopoulos, C.K. Law, USC mech version II. High-temperature combustion reaction model of H2/CO/C1-C4 compounds, http://ignis.usc.edu/USC_Mech_II.htm, 2007. [51] G.P. Smith, Y. Tao, H. Wang, Foundational Fuel Chemistry Model Version 1.0 (FFCM-1), http://nanoenergy.stanford.edu/ffcm1, 2016. [52] Y. Li, C.W. Zhou, K.P. Somers, K. Zhang, H.J. Curran, The oxidation of 2-butene: a high pressure ignition delay, kinetic modeling study and reactivity comparison with isobutene and 1-butene, Proc. Combust. Inst. 36 (2017) 403–411. [53] C.W. Zhou, Y. Li, E. O’Connor, K.P. Somers, S. Thion, C. Keesee, O. Mathieu, E.L. Petersen, T.A. DeVerter, M.A. Oehlschlaeger, G. Kukkadapu, C.J. Sung, M. Alrefae, F. Khaled, A. Farooq, P. Dirrenberger, P.A. Glaude, F. Battin-Leclerc, J. Santner, Y. Ju, T. Held, F.M. Haas, F.L. Dryer, H.J. Curran, A comprehensive experimental and modeling study of isobutene oxidation, Combust. Flame 167 (2016) 353–379. [54] T. Lu, C.K. Law, A criterion based on computational singular perturbation for the identification of quasi steady state species: a reduced mechanism for methane oxidation with no chemistry, Combust. Flame 154 (2008) 761–774. [55] P.D. Ronney, G.I. Sivashinsky, A theoretical study of propagation and extinction of non-steady spherical flame fronts, SIAM J. Appl. Math. 49 (1989) 1029–1046. [56] A.E. Lutz, R.J. Kee, J.A. Miller, SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis, SANDIA National Laboratories Report, SAND87-8248, Livermore, CA, 1990. [57] Y. Ju, H. Guo, F. Liu, K. Maruta, Effects of the lewis number and radiative heat loss on the bifurcation and extinction of CH4 /O2 -N2 -He flames, J. Fluid Mech. 379 (1999) 165–190. [58] J.K. Bechtold, M. Matalon, Hydrodynamic and diffusion effects on the stability of spherically expanding flames, Combust. Flame 67 (1987) 77–90. [59] G. Jomaas, C.K. Law, J.K. Bechtold, On transition to cellularity in expanding spherical flames, J. Fluid Mech. 583 (2007) 1–26. [60] G.I. Sivashinsky, C.K. Law, G. Joulin, On stability of premixed flames in stagnation-point flow, Combust. Sci. Technol. 28 (1982) 155–159. [61] M.P. Burke, Z. Chen, Y. Ju, F.L. Dryer, Effect of cylindrical confinement on the determination of laminar flame speeds using outwardly propagating flames, Combust. Flame 156 (2009) 771–779. [62] A.S. Al-Shahrany, D. Bradley, M. Lawes, K. Liu, R. Woolley, Darrieus–Landau and thermo-acoustic instabilities in closed vessel explosions, Combust. Sci. Technol. 178 (2006) 1771–1802. [63] A. Omari, L. Tartakovsky, Measurement of the laminar burning velocity using the confined and unconfined spherical flame methods – a comparative analysis, Combust. Flame 168 (2016) 127–137. [64] N. Hinton, R. Stone, R. Cracknell, Laminar burning velocity measurements in constant volume vessels–reconciliation of flame front imaging and pressure rise methods, Fuel 211 (2018) 446–457.