Flame Speciation and Laminar Burning Velocity of Tetralin Flames Under Atmospheric Pressure

Abstract

We present a combined experimental and modeling study of premixed atmospheric-pressure tetralin flames. Chemical speciation in near-stoichiometric (φ = 0.8–1.0) tetralin/O₂/Ar flames was characterized by probe-sampling molecular-beam mass spectrometry (MBMS) with soft ionization (12.3–18 eV). Total ionization cross-sections (TICSs) for heavy intermediates were computed ab initio to enable quantitative MBMS processing. Laminar burning velocities (LBVs) of tetralin/air flames were measured in a range of equivalence ratios (φ = 0.75–1.5) on a nozzle burner via the stretch-corrected total area method. This is the first reported LBV data for tetralin/air flames (maximum LBV was 47.3 ± 2 cm/s at φ = 1.1). The experimental mole fraction profiles and LBVs were interpreted using three detailed mechanisms. None of the mechanisms were able to correctly describe the LBV profile, and a number of discrepancies were observed in the mole fraction profiles. Reaction network and sensitivity analyses were performed to identify specific sub-mechanisms requiring refinement. In particular, the subchemistry of naphthalene and indene strongly affects the accuracy of model predictions, whereas the flame speciation data indicate large uncertainties in the simulated concentrations of these species.

1. Introduction

Hydrogenated bicyclic aromatic hydrocarbons (HBAHs) are important constituents of petroleum-derived and alternative fuels such as aviation kerosene, diesel, or SAF. They are commonly included in surrogate fuel blends to reproduce key chemical and physical properties of practical fuels. 1,2,3,4-tetrahydronaphthalene (tetralin) is a representative HBAH and is frequently chosen as a component of real fuel surrogate formulations [1,2,3,4,5,6,7,8,9]. Tetralin is a naphtheno-aromatic compound combining an aromatic ring fused to a partially saturated ring. Beyond surrogate fuel applications, tetralin is of interest in fundamental combustion chemistry because its mixed saturated–unsaturated structure leads to oxidation pathways that differ qualitatively from those of simple aromatics or naphthenes, impacting radical formation, aromatic growth, and soot precursors [10].

The literature on tetralin shows extensive investigations of pyrolysis and oxidation phenomena. Detailed pyrolysis and thermal cracking studies by Bounaceur et al. [11] and Poutsma et al. [12] rationalized product distributions at low temperatures (up to 1000 K) and elucidated the key competing routes of tetralin decomposition, namely dehydrogenation, ring contraction, and ring opening. Later, Li et al. [13] examined low-pressure pyrolysis speciation at 850–1500 K and proposed a new tetralin sub-mechanism. Experimental investigations on oxidation and autoignition kinetics were performed on different rigs: in a motored engine by Yang and Boehman [14], in a jet-stirred reactor by Dagaut et al. [15], in a rapid compression machine by Kukkadapu et al. [16], Wang et al. [9], and Issayev et al. [10], and in a shock tube by Wang et al. [17] and Raza et al. [18]. All these data were obtained from a wide range of temperatures and pressures.

Interest in tetralin chemistry also extends to astrochemistry, where gas-phase kinetics of complex organic molecules are of considerable relevance. In particular, recent ab initio and master equation studies have refined rate constants for OH-initiated channels at 200–2000 K and clarified the combined influence of saturated and unsaturated ring structures on reactivity [19].

Despite this broad base, there is a shortage of flame studies in the literature, preventing validation of the high-temperature radical-driven combustion chemistry of tetralin. The only work on tetralin flame measurements was performed by Li et al. [20]. The authors investigated chemical structure of premixed tetralin flames under low-pressure conditions (~30 Torr) and proposed an updated detailed mechanism of tetralin combustion. To our knowledge, there are no systematic reports of laminar burning velocities (LBVs) for tetralin flames in the open literature. The absence of LBV data is significant, since burning velocity provides a sensitive benchmark for mechanism validation. The dearth of flame measurements likely stems from experimental difficulties specific to tetralin, as follows: its relatively high boiling point (207 °C) and low vapor pressure at ambient temperature complicate stable vapor delivery and promote condensation and liquid carryover in conventional burners, making repeatable premixed flames generation challenging.

Notably, only the mechanism proposed by Li et al. [13,20] was validated against flame and pyrolysis data; however, its performance for atmospheric-pressure flame conditions and for predicting laminar burning velocities is limited. Some of the comprehensive mechanisms, e.g., CRECK [21], include tetralin subchemistry pathways but have not been systematically benchmarked against tetralin-specific flame data.

Given these gaps, the present study aims to (i) obtain new experimental information on flame speciation and LBVs of tetralin premixed flames at atmospheric pressure, and (ii) validate existing kinetic mechanisms of tetralin combustion against these data to identify specific sub-mechanisms that require refinement for accurate description of tetralin combustion under practical conditions.

2. Experiment and Modeling

2.1. Mache–Hebra Nozzle Burner

Laminar burning velocities (LBVs) of tetralin/air flames were measured on a Mache–Hebra nozzle burner [22] using the total area method [23], based on digitized images of flame shadows obtained by CCD shadow photography [24]. High-purity 1,2,3,4-tetrahydronaphthalene (>98% pure, Thermo Scientific) was used as the fuel. The burner consisted of a Pyrex tube (27 cm in length) with an area contraction ratio of 4.7 (over a 3 cm length). The nozzle exit had an inner diameter of 0.9 cm. Gas flows were measured with a mass flow controller (MKS Instruments) calibrated with a high-precision FlexCal-M (Mesa Labs) gas meter with an accuracy of ± 0.5%. The volumetric flow rate of the combustible mixture varied from 29 to 63 cm³/s. Liquid tetralin was fed by a stepper-motor syringe pump into a Pyrex evaporator packed with 3 mm steel beads. The evaporator was maintained at 180 ± 1 °C by an electrical heater with a PID-control system linked with a thermocouple located inside the evaporator. The forming tetralin vapor was mixed with argon and oxygen flows and directed to the burner. The burner temperature was held at 95 ± 1 °C using a water-circulating thermostat.

The accuracy estimation was derived by accounting for (1) the error in measuring the volumetric flow rate of unburned gases (up to ±0.5%), (2) the liquid tetralin flow rate (up to ±0.06%), and (3) the error in determining the flame cone surface area (up to ±3%). The maximum error in measuring the equivalence ratio did not exceed ±1.0%. Correction of the flame propagation velocity for the stretch effect followed the procedure of Mazas et al. [25], resulting in a reduction in the flame propagation velocity by approximately 5−6% compared to the measured value.

2.2. MBMS Setup

The chemical structure of tetralin flames was determined using a probe-sampling molecular-beam mass-spectrometry (MBMS) system. This setup had been previously employed to investigate flame speciation of various fuels [26,27,28,29,30]. Experiments were performed on lean (φ = 0.8) and stoichiometric (φ = 1.0) premixed tetralin/O₂/Ar flames stabilized on a Bota–Spalding burner [31] at atmospheric pressure. The compositions of the unburned mixtures are given in

Table 1. Mole fraction compositions and volumetric and mass flows of the unburned mixtures.

φ	X (Tetralin)	X (O2)	X (Ar)	Qv, cm3/s	Qm, g/(s·cm2)
1.00 ± 0.01	0.0142 ± 0.0001	0.186 ± 0.001	0.800 ± 0.008	25 ± 1	0.020 ± 0.001
0.80 ± 0.01	0.0116 ± 0.0001	0.188 ± 0.001	0.800 ± 0.008	25 ± 1	0.020 ± 0.001

.

The burner comprised a perforated disk 16 mm in diameter with holes of 0.5 mm diameter at a center-to-center spacing of 0.7 mm. The disk was mounted in a brass housing packed with 3 mm steel beads to stabilize the flow and provide thermal homogeneity. The burner was fitted with a cooling jacket incorporated into the housing and it was maintained at 165 ± 5 °C by an oil thermostat to prevent fuel condensation (tetralin boiling point at 207 °C).

The unburned mixture was supplied to the burner via a temperature-controlled electrically heated evaporator similar to the one used for the LBV measurements. The evaporator was an insulated Pyrex cylinder packed with 3 mm steel beads to ensure uniform temperature throughout the volume and to improve mixing of the fuel and carrier gases. Its temperature was held at 165 ± 1 °C to maintain a vapor partial pressure sufficient for delivery while avoiding boiling of tetralin in the capillary. Liquid fuel was fed to the evaporator through a capillary by a stepper-motor-driven syringe pump, providing appropriate dosing accuracy. Oxygen and argon gas flows to the evaporator were controlled by EL-FLOW mass flow controllers (Bronkhorst) calibrated with a FlexCal-M (Mesa Labs) flow calibrator.

The burner was mounted on a movable rig beneath the sampling probe, which was connected to the vacuum system of the MBMS setup. The probe-to-burner distance was adjusted with a micrometer screw and measured using a cathetometer with an accuracy of ±0.01 mm. To account for thermal perturbations introduced by the sampling probe, temperature profiles were measured using an S-type (Pt/Pt + 10%Rh) microthermocouple fabricated from 0.05 mm wire and covered with a thin SiO₂ coating [32]. Measurements were carried out with the probe present in the immediate sampling region. Taking into account radiation corrections [33,34], the accuracy of the temperature measurements was estimated to be no worse than ±80 K.

The sampling probe was a quartz cone with an internal half-angle of 40° and an external half-angle of 60°, with a tip orifice diameter of 0.06 mm. Gas sampling was performed in a three-stage low-pressure system. In the first stage, the sampled gas was expanded to a pressure of 10⁻²–10⁻³ Torr, forming a molecular beam and effectively “freezing” ongoing chemical reactions. The beam then passed through a skimmer with a tip orifice diameter of 0.64 mm into the second stage, which was maintained at ~10⁻⁵ Torr; this stage served to remove the non-collimated fraction of the beam. A modulation system located in the second chamber suppressed background noise in the final signal by extracting the useful component from the modulated signal. After the modulator, the molecular beam entered the third stage (~10⁻⁷ Torr) through a 4 mm collimator, where a quadrupole mass spectrometer (MS-7302, m/Δm~250) was installed together with a custom-built ion source featuring a heated tungsten filament, voltage-compensation system, and dedicated ion optics.

Ionization energies were optimized individually for each species (typically in the range 12.3–18 eV, with an uncertainty of ±0.25 eV) to avoid excessive molecular fragmentation while preserving adequate signal intensity and minimizing contributions from fragment ions at the nominal mass. Ions were detected using a secondary electron multiplier; the output pulses were amplified and shaped by a preamplifier-shaper and subsequently counted by a pulse counter before data treatment. Each obtained mass peak signal was acquired as the average of three consecutive measurements, with automatic background subtraction achieved by modulation of the molecular beam.

The measured mass-signals I_i of i-th species were converted to mole fractions X_i according to the linear relation I_i = S_i(E)·X_i, where S_i(E) is the species- and energy-dependent sensitivity coefficient. S_i(E) was determined for each compound by one of the following procedures, as follows:

−

direct calibration against gas mixtures with known mole fractions of the target species;

−

calibration via the relative ionization cross-section (RICS) method for species that could not be calibrated directly [35,36]; and

−

determination from an elemental material balance (C, O, H, and Ar) for the most abundant species.

The RICS method is based on the direct proportionality between the sensitivity coefficient S_i(E) and the total ionization cross-section σ_i(E), which leads to the relation I_i/I_j = [σ_i(E_i)/σ_j(E_j)][X_i/X_j], where index i denotes an intermediate species and index j denotes the nearest stable species with a known mole fraction. For most light intermediates, total ionization cross-sections (TICSs) at the experimental electron energies were taken from the NIST database [37]. However, for heavy fuel-derived intermediates such data are not available in the literature; therefore, quantum chemical calculations of TICS were performed for the corresponding compounds (see next section).

The complete list of measured compounds, together with the ionizing electron energies used and the chosen calibration method, is given in

Table 2. Measured masses (m/z) and assigned species with ionization energies (IEs), ionizing electron energies (Es), and calibration methods.

m/z	Species	Considered as	IE, eV	E, eV	Calibration Method
15	CH3	Methyl radical	9.8	16.2	RICS
17	OH	Hydroxyl radical	13.0	16.2	RICS
18	H2O	Water	12.6	16.65	Element balance
26	C2H2	Acetylene	11.4	12.3	Direct
28	C2H4	Ethylene	10.5	12.3	Direct
28	CO	Carbon monoxide	14	14.35	Element balance
30	CH2O	Formaldehyde	10.9	11.5	RICS
30	C2H6	Ethane	11.5	12.3	Direct
32	O2	Molecular oxygen	12.0	14.35	Element balance
42	C3H6 +CH2CO	Propene, ketene	9.7	14.35	Direct
44	CO2	Carbon dioxide	13.8	15.4	Element balance
76	C6H4	Benzyne	9.0	15	RICS
78	C6H6	Benzene + fulvene	9.2	15	Direct
92	C7H8 + C6H4O	Toluene + cyclohexadienenone	8.8	15	RICS
94	C6H5OH	Phenol	8.5	15	RICS
102	C6H5C2H	Phenylacetylene	8.8	15	RICS
108	C6H4O2 + CH3C6H4OH + C6H5CH2OH + C6H5OCH3	Benzoquinone + cresols + Benzyl alcohol + anisole	10	15	RICS
115	C9H7	Indenyl radical	8.4	15	RICS
116	C9H8	Indene	8.1	15	RICS
118	C8H6O + C9H10	Benzofuran + indan	8.4	15	RICS
128	C10H8	Naphthalene	8.1	15	RICS
130	C10H10 + C9H6O	Dihydronaphthalene + indenone	8.1	15	RICS
132	C10H12	Tetralin	8.5	18	element balance
143	C10H7O	Naphthol radical	8.1	15	RICS
144	C10H7OH	Naphthol	7.9	15	RICS

. The selection of ionizing electron energies was informed by our previous studies on hydrocarbon flames and by optimization of the signal-to-noise ratio for each species.

Uncertainty values were obtained for each species individually. For reactants and major stable products (e.g., tetralin, O₂, CO_2, and H₂O), the relative uncertainty in the reported mole fraction did not exceed ±5%. For intermediate species, the relative uncertainty was much larger but usually did not exceed ±60%. The overall uncertainty for each species includes the following contributions: (i) statistical uncertainty of the experimental signal at a certain mass peak; (ii) uncertainty in the gas and liquid flow rates at the inlet; (iii) uncertainty associated with subtraction of fragment contributions or overlap from species sharing the same nominal mass; (iv) uncertainty of the sensitivity coefficient S_i determined from direct calibration; (v) uncertainty of the RICS calibration method; and (vi) uncertainty from estimating ionization cross-sections at the experimental ionization energies. Detailed values of all parameters used in the uncertainty analysis for each intermediate, including the ionization cross-sections obtained, are provided in the Supplementary Material.

According to available literature databases, the contributions of tetralin to secondary mass fragments are reported only at an ionization energy of 70 eV, which lies much higher than the experimental range of 12.3–18 eV. In this regard, the fragmentation spectrum of tetralin was measured experimentally and its contributions were subtracted from the corresponding intermediate signals. The influence of heavier intermediates on other mass fragments was negligible since they attained only very low peak concentrations in the flame.

2.3. TICS Calculations

Total ionization cross-sections (TICSs) are essential for the RICS signal processing method; for species not present in the NIST database or elsewhere, TICSs were calculated. The ORCA software (v. 6.0.0) [38] and ChimeraX SEQCROW [39,40] were employed for quantum chemical computations and visualization, respectively. Molecular geometries were optimized using the wB97XD and wB97X functionals [41,42], which have proven effective for TICS calculations [43], along with the def2-TZVP basis set [44]. The TICS values (σ) were computed using the Binary-Encounter Bethe (BEB) method, governed by the following Equation (1) [45].

$$\begin{gathered} {\sigma }_{MO}={\displaystyle \frac{4\pi a_0^{2}N}{\left(t+u+1\right)}}{\displaystyle \frac{R^2}{B^2}}\left[{\displaystyle \frac{\ln t}{2}}\left(1-{\displaystyle \frac{1}{t^2}}\right)+1-{\displaystyle \frac{1}{t}}-{\displaystyle \frac{\ln t}{t+1}}\right] \\ \sigma =\sum _{MO}{\sigma }_{MO}, for B_{MO}\le E \end{gathered}$$

(1)

where t = E/B and u = U/B. Here, E is the energy of the incident electron, N is the number of electrons in the molecular orbital, R is the Rydberg constant, and a₀ is the Bohr radius. ${\sigma }_{MO}$ is the ionization cross-section of a single molecular orbital. B denotes the orbital binding energy, defined as the absolute value of the molecular orbital energy. U is the orbital kinetic energy, computed by applying the kinetic energy operator from the ORCA output file to the molecular orbital wavefunction. Following this approach, TICS values were calculated for the considered 25 compounds (

Table 3. Total ionization cross-section values (σ) calculated using the wB97XD and wB97X functionals for an incident electron energy of 15 eV.

Compound	σ (wB97XD), Å2	σ (wB97X), Å2
Benzene	2.517	2.263
1,2-Dihydronaphthalene	4.348	3.897
α-Cresol	3.266	2.930
o-Cresol	3.032	2.707
m-Cresol	3.109	2.767
p-Cresol	3.101	2.760
Indane	3.596	3.250
Indene	3.886	3.505
Indenyl radical	4.000	3.610
α-Naphthol	4.156	3.743
α-Naphthoxy radical	3.596	3.214
β-Naphthol	4.293	3.869
β-Naphthoxy radical	3.479	3.105
o-1-Phenylyldioxyl radical	2.258	2.026
Phenol	2.661	2.382
Benzyne	2.433	2.201
Cyclohexdienenone	2.163	1.918
p-Benzoquinone	1.655	1.463
o-Benzoquinone	1.794	1.596
Anisole	3.053	2.739
Benzofuran	3.286	2.964
Indenone	3.134	2.805
Naphthalene	4.156	3.749
Phenylacetylene	3.297	2.958
Toluene	2.961	2.647

).

The TICS values computed with the wB97XD functional show better agreement with values from the NIST and PlasmaData [46] databases than those obtained with wB97X. For example, at E = 15 eV, the wB97XD TICS for benzene is 2.517 Ų, compared with 2.567 Ų (NIST) and 2.443 Ų (PlasmaData). For benzyne and phenol, wB97XD yields TICS of 2.433 Ų and 2.661 Ų, respectively, which closely match the PlasmaData values of 2.423 Ų (benzyne) and 2.525 Ų (phenol).

2.4. Kinetic Simulations

Numerical simulations of species mole fraction profiles and laminar burning velocities were performed in the Ansys Chemkin-Pro v.17.0 software package using the PREMIX and Flame Speed modules. The PREMIX code was applied with input data comprising a fixed gas flow rate, initial reactant mole fractions (Table 1), and the experimentally measured temperature profile. The computational mesh was adopted to GRAD = 0.3 and CURV = 0.3, yielding 75–100 grid points; further refinement did not affect the results. For laminar burning velocity calculations, the tetralin/N₂/O₂ mixture (N₂/O₂ = 79/21) was used, with parameters GRAD = 0.05 and CURV = 0.05 and 400–500 grid points, which provided grid-independent results.

Three kinetic mechanisms were employed for tetralin combustion modeling. The first, proposed by Li et al. [20], is the only detailed mechanism of tetralin combustion presented in the literature; it comprises 296 species and 1577 reactions. This model was developed on the basis of low-pressure tetralin pyrolysis and combustion data combined with the subchemistry of ethylbenzene and o-xylene combustion. Two recognized comprehensive models, CRECK [21] and LLNL [47], were also exploited. The TOT_HT CRECK version used in this study contains 368 species and 14,462 reactions. Here, the tetralin subchemistry was considerably based on the investigations of Dagaut et al. [15]. The LLNL semidetailed mechanism of diesel oxidation originally contained 6406 species and 23,656 reactions, but for flame structure calculations it was reduced to a C₁₂ subset comprising 3854 species and 15,003 reactions. This model incorporates recent findings from the work of Issayev et al. [10], who adopted rate rules for the oxidation of allylic, benzylic, paraffinic, and aryl radicals to tetralin oxidation kinetics. Following this step, species not participating in the flame chemistry were removed using a cutoff criterion of peak mole fraction ≤ 10⁻¹⁵. The resulting reduced mechanism contained 1180 species and 6103 reactions and reproduced the flame structure of all measured intermediates identically to the C₁₂ mechanism. This reduced scheme was subsequently employed for laminar burning velocity calculations.

3. Results and Discussion

3.1. Preliminary Analysis

Laminar burning velocity and speciation measurements provide an overall validation of kinetic descriptions as well as species-specific constraints on individual reaction steps. In the following sections, the new experimental data are compared with simulations performed using the three kinetic mechanisms (Li, CRECK, and LLNL). The mole fraction profiles were simulated using the experimentally measured temperature profiles shown in Figure 1. Each temperature profile is the average of three or more independent measurements. Although the temperature gradients within the reaction zone differ between flames, the reaction zone thicknesses are almost equal, measuring about 0.7 mm in height above the burner (HAB). The post-flame temperature differs by approximately 100 K between the cases. Raw data on temperature and mole fraction profiles are available in the Supplementary Materials.

To facilitate the detailed discussion below, Figure 2 summarizes the principal initial fuel consumption networks from the Li (a), CRECK (b), and LLNL (c) mechanisms at the half-conversion point (approximately 0.25 mm and 1100 K). The arrows were derived via the rate of production (ROP) analyses, and each arrow corresponds to a certain component and several reactions. Species whose mole fractions were measured in the present work are highlighted in red.

The mechanisms differ fundamentally in how they treat the initial fuel radical chemistry. The CRECK mechanism lumps all hydrogen abstractions into a single global fuel radical (RTETRALIN), whereas the Li and LLNL models distinguish H-abstraction at the 1- and 2-positions of tetralin, yielding distinct 1- and 2-tetralyl radicals. While the lumped approach of CRECK leads to naphthalene (C₁₀H₈), dihydronaphthalene (C₁₀H₁₀), and indene (C₉H₈) directly, the Li and LLNL models take numerous steps to yield the same intermediates. According to the Li model, about one-third of the 2-tetralyl radical isomerizes to the 1-tetralyl radical, which converts to dihydronaphthalene and then to naphthalene through successive dehydrogenation stages (C₁₀ pool). In contrast, the LLNL model assumes that these intermediates are formed from the 2-tetralyl radical. Fuel radicals also undergo ring opening via β-scission, and due to a lower activation energy for C-C bond cleavage [48], 2-tetralyl radical undergoes ring opening more rapidly than the 1-tetralyl radical. The ring-opening pathways produce monoaromatic intermediates through successive alkyl-chain shortening steps, yielding species such as benzaldehyde, ethylbenzene, and styrene (A1 pool). Not only the reaction pathways but also the exact composition of the C₁₀ and A1 pools differ between the mechanisms. However, the CRECK mechanism generates the A1 pool exclusively via C₁₀ intermediates, and it omits direct ring-opening routes of the tetralyl radicals.

Upon direct decomposition, all mechanisms involve oxygen addition reactions to fuel radicals, but the nature of these reactions is fundamentally different. In the Li mechanism, about 20% of 1-tetralyl radical can attach an O atom in reactions with O and HO_2, yielding oxyradical, which further decompose to benzyl radicals via ring-opening β-scissions. The other two mechanisms assume the decomposition of fuel radicals through the formation of peroxy radicals, which are untypical under flame conditions. It should be noted that the tetralin sub-mechanisms in the CRECK and LLNL models were developed and validated primarily against reactor and pyrolysis data. Consequently, these mechanisms may not correctly represent oxidation kinetics under high-temperature flame conditions with abundant radical pools. In the case of the Li mechanism, many high-temperature kinetic parameters, notably for H-abstractions and β-scissions, were adopted from prior pyrolysis studies [13] or estimated by analogy.

Furthermore, the Li mechanism lacks pressure dependence for a number of fuel-related reactions, which can be important for large molecules like tetralin and their fuel radicals. The 1-tetralyl and 2-tetralyl radicals either undergo rapid β-scission with ring opening or become collisionally stabilized and continue as independent radicals through isomerization, recombination, or further abstractions. The balance between stabilization and decomposition determines whether carbon remains in the C₁₀ pool (naphthalene/dihydronaphthalene) or proceeds to A1 products.

Also, one observation is worth noting. An excessive carbon recirculation (Figure 3) is observed in the Li mechanism, as follows: approximately 65% of benzene recycles back into the heavier C₁₀ radical (H₂A₂-2), which is unexpected under slightly lean flame conditions. By contrast, the CRECK and LLNL mechanisms do not predict such a pronounced shift toward PAH formation.

The reaction networks (Figure 2) can be treated as graphs, where reaction hubs, i.e., the nodes of highest order, can be delineated. In the CRECK mechanism, these hubs are as follows: lumped fuel radical (RTETRALIN), naphthalene (C₁₀H₈), indene (INDENE), phenyl radical (C₆H₅), and phenol radical (C₆H₅O); in the Li model, they are as follows: 1-tetralyl radical (H₄A₂-1), indenyl (C₉H₇), indene (C₉H₈), and toluene radical (C₆H₄CH₃); and in the LLNL scheme, they are as follows: dihydronaphthalene (C₁₀H₁₀), naphthalene (NAPH), naphthoxy radical (NAPHO), phenyl radical (C₆H₅), methylbenzaldehyde radical (CHOC₆H₄CH₂), and methylphenyl radical (C₆H₄CH₃). As can be seen, the number and order of hubs vary greatly from mechanism to mechanism, defining the distribution of carbon flux over C₁₀ and A1 pools toward the light intermediates. Hence, the mechanism validation requires targeted examination of the kinetics around these hubs.

3.2. Validation of Models Against Experimental Data: Chemical Flame Structure

In this section, we refer to the experimentally detected intermediates and to the ROP networks presented above to link network structure with measured mole fraction profiles. Figure 4 and Figure 5 compare the measured mole fraction profiles of reactants (tetralin, O₂) and major combustion products (CO, CO₂, and H₂O) with simulations from the three mechanisms. All models agree well with experiments and reproduce the mole fraction profiles at lean and stoichiometric conditions. The only differences can be observed in the initial stages of tetralin consumption, where the LLNL model predicts slightly lower reactivity, which can be attributed to a slower development of the radical pool.

Figure 6 presents the mole fraction profiles of key C₁₀ intermediates, as follows: naphthalene (C₁₀H₈), dihydronaphthalene (C₁₀H₁₀), and related oxygenates, the naphthoxy radical (C₁₀H₇O) and naphthol (C₁₀H₇OH). Bicyclic hydrocarbons are the most actively formed intermediates during the decomposition of the fuel radical, and their conversion chemistry is fundamental to the predictive capability of the mechanisms, particularly in soot precursor formation. Since C₁₀H₁₀ overlaps in mass with indenone (C₉H₆O), whose mole fraction is not negligible (due to the substantial concentration of indene, see below), Figure 6 displays the summarized mole fraction profile of these two intermediates. It should be noted that the TICS of dihydronaphthalene exceeds that of indanone at the electron energy used. It should also be noted that, for naphthalene, naphthol, and the naphthoxy radical, the predicted contributions from other intermediates sharing the same nominal mass are several orders of magnitude lower and can therefore be regarded as negligible.

Model predictions vary notably, as follows: the CRECK mechanism predicts only C₁₀H₁₀ in this category, whereas the Li model predicts both C₁₀H₁₀ and C₉H₆O to appear with comparable peak concentrations. The LLNL mechanism also includes dihydronaphthalene and indanone, as well as C*CA1C*C radical (smiles: [CH2]CC1=C(C=C)C=CC=C1), but it predicts C₁₀H₁₀ mole fraction two orders of magnitude above the others.

In comparison with the experimental data, the main C₁₀ species, naphthalene, and dihydronaphthalene, were correctly reproduced only in the Li mechanism. Both CRECK and LLNL mechanisms significantly overestimate these intermediates. In the case of CRECK, this is due to a fast direct decomposition of the fuel radical through reactions 2–4.

RTETRALIN => CH₃ + INDENE

(2)

RTETRALIN => H₂ + H + C₁₀H₈

(3)

RTETRALIN => H + C₁₀H₁₀

(4)

The rate parameters of these pathways were adjusted to mimic the JSR data and have not been validated against flame conditions. Moreover, they lack pressure dependence, although ambient pressure can significantly affect radical stabilization. The LLNL mechanism most strongly overpredicts the mole fractions of C₁₀H₁₀ and C₁₀H₈. In contrast to the Li model, most of these intermediates are formed from the 2-tetralyl radical, and the rate constant of its unimolecular decomposition (TETRARS <=> C₁₀H₁₀ + H) is two orders of magnitude higher than in the Li model. Also, LLNL suffers from the slow rates of ring-opening pathways that would consume the 2-tetralyl radical and reduce carbon flux toward the formation of naphthalene and dihydronaphthalene. Sensitivity analysis also shows strong sensitivity to the H-abstraction reactions, which rate parameters, as mentioned earlier, require refinement.

Naphthol and the naphthoxy radical are involved in the conversion chain of C₁₀ intermediates to phenyl (C₆H₅). The CRECK mechanism has a higher formation rate of the naphthyl radical (C₁₀H₇) than LLNL, which yields a larger overestimate of the naphthoxy radical concentration and consequently an overall overprediction of both naphthol and naphthoxy radical. In the Li mechanism, naphthol itself is absent: the naphthol-forming reaction presented in CRECK and LLNL effectively acts as a sink that converts the naphthoxy radical into less reactive intermediates. The absence of this sink in the Li model therefore contributes to the overprediction of the naphthoxy radical. The effect is amplified by the lack of ring-opening pathways for naphthalene in the Li mechanism, which are included in CRECK and LLNL as global conversions of C₁₀H₈ → C₄H₄ + C₆H₅ (CRECK) and C₁₀H₈→NAPHV/NAPH- → C₆H₅ (LLNL).

Figure 7 demonstrates measured and simulated mole fraction profiles of indene (C₉H₈), indenyl (C₉H₇), and the combined profile of indane (C₉H₁₀) + benzofuran (C₈H₆O), both reported by Dagaut et al. [15]. These species mark the transition from bicyclic C₁₀ pool to the subchemistry of A1 pool. The Li and LLNL mechanisms reproduce the indene mole fraction profile most accurately, whereas CRECK substantially overpredicts the peak values. This highlights the importance of additional pathways for fuel radical transformations in the flame, which is substantially reduced in the CRECK. The kinetics of indene is closely linked to those of the indenyl radical, whose mole fraction, in contrast, is reproduced by the CRECK mechanism with the best performance. This can be attributed to the general overprediction of indene, which is converted into indenyl through multiple H-abstraction reactions. The reaction hubs of indene and indenyl differ substantially across all mechanisms and appear to require additional validation and refinement of their kinetic parameters.

The CRECK and LLNL mechanisms do not include indane (C₉H₁₀), whereas the Li model incorporates indane and predicts a quantity comparable with benzofuran. Despite good agreement with the peak mole fraction at 118 m/z, the Li mechanism lacks consumption pathways for benzofuran (see the plateau in Figure 7). Expanding the reaction network responsible for benzofuran consumption should be performed, but it would likely reduce the predicted peak value. In addition to benzofuran, several other non-consuming intermediates were also detected (see Appendix A Figure A1).

The deviation of the Li mechanism from the experimental data is explained by the excessively slow consumption of the naphthoxy radical, resulting in an underprediction of C₉H₇ and an overprediction of the naphthoxy radical (A₂O-2 and A₂O-1). In the CRECK and LLNL mechanisms, discrepancies arise from the rate constants of global reactions involving the indene/indenyl pair and from the overprediction of C₁₀ precursors. In summary, CRECK and LLNL quickly divert C₁₀ intermediates to A1 pool, reducing indene and indenyl. The Li model retains more C₉ intermediates and benzofuran, that is not consumed. The differences trace back to how each mechanism treats the indene and the indenyl radical. In the Li kinetic scheme, indenyl mainly converts by ring opening to oxygenates, whereas CRECK and LLNL assume near-instant conversion of indenyl to C₆H₅, skipping oxygenate steps.

The combustion chemistry of A1 intermediates links the heavy C₁₀ chemistry and the oxidation of light hydrocarbons, exerting a strong control on the concentrations of most radical pools. The measured and simulated mole fractions of the A1 and related species are shown in Figure 8. We were able to register the 108 m/z signal with good accuracy, which corresponds to several possible intermediates. The largest contribution is assumed to come from benzoquinone and cresol isomers, although anisole and benzyl alcohol also share this nominal mass. To interpret this mass peak, we used the averaged value of the calculated TICS.

The Li mechanism largely captures the A1 conversion chemistry well, but it exhibits a serious overprediction of the 108 m/z signal by benzoquinone, which appears to be a bottleneck in the ring-opening and consumption of A1 pool. According to the ROP analysis, the consumption of phenyl derivatives is confined exclusively to benzoquinone (O-C₆H₄O₂), which also serves as the sole precursor for benzene formation. Despite the difficulty in interpreting the 108 m/z signal, it can be clearly stated that the kinetics of benzoquinone formation and consumption need to be clarified in this model. Also, as mentioned above, about 65% of benzene flux is routed through a global reaction producing a dihydronaphthalene radical. This pathway improves agreement for several phenyl-derived species by diverting carbon away from the A1 pool; however, this channel seems to be overpredicted at lean conditions and should be verified.

The LLNL mechanism appears to be correct in many peak concentrations and reproduces the mole fraction profiles of most A1 intermediates satisfactorily, with the notable exceptions of phenol and toluene profiles in the lean flame. It is worth noting that only LLNL was able to correctly describe the 108 m/z signal profile. The CRECK model overpredicts the total A1 pool, which is evidently a consequence of the overestimated concentrations of C₁₀ intermediates.

We also measured a number of key light intermediates, including OH and CH₃ radicals (Figure 9). All tested mechanisms reproduce the experimentally measured OH profile well. The CH₃ mole fraction profile was reproduced less accurately, as follows: for the lean flame, the CRECK and Li predictions lie within the experimental uncertainty, whereas the LLNL mechanism underpredicts CH₃ by roughly 40%. For the stoichiometric flame, none of the mechanisms quantitatively reproduces the peak CH₃ mole fraction within the experimental uncertainty, as follows: CRECK and Li underpredict the peak by 30% relative to the lower value of the experimental error bar, and LLNL underpredicts it by 50%. As expected, the LLNL mechanism is not adapted to account for a significant number of high-temperature H-abstraction reactions, which leads to an underprediction of the mole fractions of key C₁–C₂ intermediates (see below), including CH₃. The shortage of CH₃ radicals in the system indicates the need to refine reactions governing the radical pool, particularly the chain-shortening reactions of heavy primary intermediates.

Figure 10 shows measured and simulated profiles of C₂ intermediates (C₂H₂, C₂H₄, C₂H₆). All mechanisms systematically underpredict these intermediates in the stoichiometric flame, except the Li mechanism, which reproduces C₂H₄ within experimental uncertainty. In the lean flame, models capture C₂H₂ and C₂H₄ reasonably well, but all mechanisms markedly underpredict C₂H₆. This is a consequence of CH₃ underprediction since ethane forms mainly through the recombination of two methyl radicals CH₃ + CH₃(+M) <=> C₂H₆(+M).

We also measured light oxygenates like formaldehyde (CH₂O) and ketene (CH₂CO) (Figure 11). However, the 42 m/z signal corresponds not only to the ketene profile, but to propene (C₃H₆) as well. In this regard, the demonstrated profile is the sum of both species. Although the mole fraction profiles of these intermediates cannot be separated experimentally, the model predictions show strong discrepancies compared with the measurements. Ketene formation is primarily governed by the kinetics of light oxygenated intermediates and aldehydes, whereas propene can be produced during the ring opening of the fuel radicals (e.g., CH₃A1C₃H₅ + H<=>C₆H₄CH₃ + C₃H₆). The kinetic parameters of the latter remain poorly studied and are estimated by analogy.

Overall, the available mechanisms reproduced fewer than half of the measured profiles satisfactorily. As expected, the Li mechanism provided the best agreement, capturing the largest fraction of data within experimental uncertainty. The LLNL mechanism often predicted peak values close to the error bars and rarely exhibited gross deviations from experiment. In contrast, the CRECK mechanism showed the lowest accuracy, underscoring the limited applicability of lumped parameters to tetralin flames. A comparative percentage of accurate predictions across all profiles and the methodology for calculating the error is provided in the Appendix A (see Figure A2 and Equations (A1) and (A2)).

3.3. Validation of Models Against Experimental Data: Laminar Burning Velocity

Figure 11 shows the measured laminar burning velocities (LBVs) of tetralin/air flames at T₀ = 368 K and 1 atm. Despite the relatively limited accuracy of the cone flame method, the obtained data are unique and, to the best of our knowledge, represent the only measurements of their kind. We anticipate that these results will be refined in future work using more accurate LBV measurement techniques.

Simulating the measured LBVs proved challenging due to the size of the detailed mechanisms. Surprisingly, we were unable to obtain a stable solution with the Li mechanism. Numerous attempts were made with the full and reduced versions of this mechanism, but all computations failed because of the excessive stiffness of the system. This suggests that the kinetic parameters of the Li mechanism are poorly balanced and require careful evaluation to reduce system stiffness. Moreover, the mechanism contains a significant number of rate constants (k = A Tⁿ exp(−E/RT)) that have unphysical values, which also complicates calculations. Some of these parameters are presented in

Table 4. Parameters of unphysical chemical reaction constants of the Li mechanism.

Reactions	A 1	n	E, cal/mol
H4A2 = H4A2-1 + H	3.24E + 116	−28.775	151,649.4
H4A2 = H4A2-2 + H	3.24E + 116	−28.775	164,149.4
C9H7 => C7H5 + C2H2	1.526E + 108	−25.979	180,259
o-C6H4 + C3H3 => C9H7	7.46E + 100	−25.035	61,535

¹ depending on the order of the reaction and the value of the parameter n. Units: mole, cm, s, and K.

.

Calculations with the nonreduced CRECK mechanism did not present difficulties. To assess the impact of multicomponent diffusion, we performed simulations under both mixture-averaged and multicomponent transport assumptions (Figure 12, red and purple lines). As demonstrated, only a minor effect is observed in the near-stoichiometric range. For this reason, LLNL-based simulations were carried out using mixture-averaged diffusion. The Soret effect was taken into account in all simulations.

The maximum experimental LBV was 47.3 ± 2 cm/s at φ = 1.1. The CRECK mechanism predicts 43.3 cm/s at the same equivalence ratio, while the LLNL mechanism gives a maximum of 44.6 cm/s at φ = 1.05. Both mechanisms significantly underpredict LBVs in the fuel-rich region. To aid interpretation, LBV sensitivity diagrams for both mechanisms are shown in Figure 13.

Aside from fundamental chain-branching reactions, the CRECK mechanism shows the highest sensitivity of laminar burning velocity to reactions involving the naphthoxy radical (C₁₀H₇O) and the phenylethynyl radical (C₆H₅C₂H). The dependence on equivalence ratio is manifested primarily through H-abstraction reactions, while the remaining transformation channels of C₁₀H₇O and C₆H₅C₂H are almost insensitive to φ. The mismatch between the predicted and measured mole fraction profiles of these radicals therefore confirms the need to re-evaluate the kinetic parameters of the corresponding reactions. At this point, it is important to note several recent works devoted to the fundamental study of C₆H₅C₂H kinetics [49,50].

By contrast, the LLNL mechanism reproduces the experimental profiles of C₁₀H₇O and C₆H₅C₂H more closely, but the corresponding sensitivity analysis indicates that these radicals exert only a moderate influence on the LBV prediction. Instead, the largest positive sensitivity coefficients in LLNL are associated with decomposition reactions of two-ring intermediates (naphthalene and indene derivatives) that yield the phenyl radical (C₆H₅). The largest negative sensitivities are associated with H-abstraction from indene to form indenyl. Thus, the LBV prediction by LLNL depends most critically on the kinetics that control phenyl radical production, which is a key coupling node between the C₁₀, A1, and the light intermediates pools. As in the CRECK model, many of the top sensitivity coefficients are associated with lumped/global reactions. The underprediction of CH₃, C₂H_4, and C₂H₆ can also be interpreted as the result of an insufficient C_xH_y radical pool, which deteriorates LBV predictions with increasing equivalence ratio.

Of course, highly detailed mechanisms such as LLNL are not well suited for routine LBV predictions; nevertheless, sensitivity analysis of such detailed schemes is valuable for identifying reaction sub-networks to enhance reduced or specialized mechanisms, such as the combustion mechanism of tetralin from Li et al. The analysis above suggests that the influence of C₁₀H₇O, C₆H₅C₂H, and C₆H₅ on LBV accuracy is likely to persist in the Li mechanism as well. Taking into account the relatively good agreement for benzene but the discrepancies for the naphthoxy radical, a systematic evaluation of the C₁₀ pool reaction rates and branching ratios is suggested.

4. Conclusions

The chemical structure of premixed tetralin/O₂/Ar flames was investigated experimentally at atmospheric pressure under lean (φ = 0.8) and stoichiometric (φ = 1.0) conditions. Mole fraction profiles of key intermediates, including heavy C₉/C₁₀ species and radicals, were measured by probe-sampling MBMS, and total ionization cross-sections (TICSs) for heavy intermediates were computed ab initio to enable reliable MBMS signal processing. Laminar burning velocities (LBVs) of conical tetralin/air flames at T₀ = 368 K and 1 atm were measured for the first time. Measurements were performed using the total area method with shadow photography, covering the equivalence ratio range φ = 0.75−1.5.

The species profiles and LBVs were simulated using three detailed chemical kinetic mechanisms (Li, CRECK, and LLNL). Comparison between experiments and model predictions revealed notable discrepancies in intermediate concentrations and LBVs. None of the mechanisms reproduces the LBV curve across the full equivalence ratio range, with the largest deviations occurring in fuel-rich mixtures. We were unable to obtain a stable LBV solution with the Li mechanism because of the extreme stiffness of its kinetic system, which apparently originates from its non-physical kinetic parameters.

ROP and sensitivity analyses were used to link the observed discrepancies to specific reactions and chemical network hubs, such as the naphthoxy radical, indene, phenyl radical, and some others. This work identified the principal deficiencies and priorities for refinement. The analysis underscores several critical aspects of tetralin combustion chemistry, as follows:

(1)

The primary decomposition kinetics of tetralin under flame conditions (i.e., those leading to C₁₀ intermediates versus ring-opening reactions) remain poorly understood. These inconsistencies result in different ratios of heavy cyclic hydrocarbons to light hydrocarbon components within the reaction networks. The kinetic parameters of the corresponding pathways should be refined to ensure their accuracy across the full range of temperature conditions, including flames.

(2)

The transition pathways between the C₁₀ and monoaromatic pools are strongly governed by the indene/indenyl subchemistry, which mole fraction profiles were not reproduced properly by the models.

(3)

The C₁₀H₇O, C₆H₅C₂H, and C₆H₅ radicals were identified as the principal fuel-derived intermediates controlling the laminar burning velocity. Taking into account low predictive capability of the models against these intermediates, revising the rate constants and uncertain branching ratios for corresponding H-abstraction and β-scission channels is expected to substantially improve model predictions.

These results provide a quantitative experimental basis and a mechanistic roadmap for improving tetralin combustion models. However, more precise LBV and detailed speciation measurements in fuel-rich tetralin flames are highly desirable for a more comprehensive understanding of the combustion kinetics of tetralin and, more generally, of naphtheno-aromatic compounds.