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. 2024 Sep 4;9(37):38906–38915. doi: 10.1021/acsomega.4c05180

Reduced Kinetic Mechanism for Modeling High-Temperature Ignition and Flames for n-Pentanol

Jaime Tiburcio-Cortés †,*, Juan C Prince †,*, César Treviño ‡
PMCID: PMC11411513  PMID: 39310164

Abstract

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n-Pentanol has emerged as a promising substitute for fossil fuels due to its potential in reducing greenhouse gas emissions. This work presents a reduced combustion mechanism for modeling high-temperature ignition (T > 1000 K) and flames for n-pentanol/air mixtures. The model comprises only 64 species and 282 chemical reactions. As we know, this is the first comprehensive study to include all available experimental data for these phenomena and this specific fuel/oxidizer mixture, reported in the literature. Our approach involves coupling a detailed submechanism for n-pentanol to the San Diego mechanism, a reduced scheme for C1–C4 hydrocarbons, followed by a systematic reduction process, mainly using sensitivity analysis and steady-state approximation. We quantitatively assessed the agreement between experimental data and simulation results using deviation or error indicators along with graphical comparisons. Remarkably, the ignition delay times and flame speeds calculated using the reduced kinetic model exhibit a high agreement with the experimental data reported in the literature.

1. Introduction

The combustion of fossil fuels accounts for more than seventy-five percent of global energy consumption, with the resulting emissions of greenhouse gases playing a crucial role in driving climate change. Consequently, there is a pressing need to prioritize the shift toward alternative energy sources. Developing efficient and environmentally friendly combustion processes has become a paramount concern on the international agenda.1,2 Among the primary alternative fuels for the transportation industry, alcohols with five or more carbon atoms have emerged as significant contenders. These compounds show promise as substitutes or additives to fossil fuels due to their compatibility with advanced internal combustion engine technologies. Additionally, they qualify as biofuels as they can be produced through biological processes.3,4 While the combustion processes of alkanes (gasoline and diesel) have been extensively studied, less is known about oxygenated fuels like alcohols. Therefore, investigating their kinetic combustion mechanisms becomes essential to examine phenomena such as the ignition delay time (IDT) and flame propagation speed.

n-Pentanol is a biofuel with outstanding potential to reduce pollutant emissions from internal combustion engines and presents itself as an attractive energy alternative to mitigate dependency on fossil fuels.5−9 Therefore, a comprehensive understanding of the combustion phenomena associated with n-pentanol is imperative. Owing to its exceptional compatibility with various fuels and biofuels, as well as its distinct physicochemical properties, extensive research has primarily focused on binary mixtures, such as diesel/pentanol and biodiesel/pentanol, as well as ternary mixtures, like diesel/biodiesel/pentanol, in conventional diesel engines.10,11 However, limited investigation has been conducted regarding n-pentanol as a direct substitute for diesel in compression ignition engines. Campos-Fernández et al.12 reported that a 25% n-pentanol/diesel blend effectively replaces 100% diesel in compression ignition engines without necessitating modifications or adjustments while maintaining performance levels. Additionally, Vinod Babu et al.4 concluded that a blend of n-pentanol can potentially substitute up to 45% diesel in compression ignition engines without requiring engine modifications. Furthermore, they also highlighted the feasibility of utilizing pure pentanol under high-pressure conditions in this engine type.

The fundamental tool for simulating and computationally studying combustion chemistry is the kinetic-chemical reaction mechanism, which is invaluable for investigating new fuels. There are two categories of kinetic mechanisms: detailed and reduced. The first provides comprehensive insights into the current understanding of fuel behavior and its conversion into end products. This mechanism determines the kinetic pathways and reaction rates of each step. Similarly, it indicates whether combustion is complete and how much energy, in the form of heat, is supplied to the products. Also, it can predict the extent to which carbon, hydrogen, and oxygen atoms react completely, remain inert, or form toxic byproducts due to incomplete combustion.13 However, detailed mechanisms entail a substantial quantity of species and chemical reactions (ranging from 100 to 10,000).14,15 Therefore, directly coupling these mechanisms with computational fluid dynamics (CFD) codes for internal combustion engine simulations can be technically unfeasible and cost-prohibitive. Reduced kinetic models are needed to enhance computational efficiency while maintaining reliable performance. These reduced mechanisms encompass only the essential species and reactions, reducing the computational requirements. Importantly, they exhibit good agreement with the experimental results, accurately capturing combustion phenomena.16

It is worth noting that a comprehensive discussion on fundamental combustion and alcohol chemistry can be found in the exhaustive review by Sarathy et al.,17 albeit detailed studies specifically focused on pentanol are not extensively covered. Over the past decade, advancements have been achieved in developing kinetic mechanisms for n-pentanol combustion. Detailed mechanisms have been reported by Togbé et al.,18 Heufer et al.,19,20 Köhler et al.,21 Wang et al.,22 Nativel et al.,23 Pelucchi et al.,24,25 and Chatterjee et al.26 Furthermore, reduced kinetic mechanisms for n-pentanol/air mixtures have been proposed by Chang et al.,27 Katoch et al.,28 and Li et al.29 In particular, Liu et al.30 have put forth a combined reduced chemical kinetic mechanism for the oxidation of reference primary fuel blends and C1 to C5 alcohols. In addition, Huang et al.31 have developed two models for diesel/pentanol blends, while Ma et al.32 have focused on diesel/biodiesel/n-pentanol mixtures.

The ignition delay time (IDT) and the laminar flame speed (LFS) are complex combustion phenomena widely employed for validating chemical kinetic reaction mechanisms, as they serve as indicators of reactivity for both fossil fuels and biofuels.33 The IDT represents the time required for a specific fuel mixture to oxidize and release heat under particular pressure and temperature conditions. It is a critical parameter in internal combustion engines, influencing key processes such as preignition, knock, and superknock.34 IDTs of regular fuels range from microseconds at high temperatures to seconds at lower temperatures. In diesel engines, the IDT plays a relevant role in evaluating fuel suitability and efficiency.35 Tang et al.36 performed shock tube (ST) experiments to determine the IDT of the three pentanol isomers: n-pentanol (1-pentanol), iso-pentanol, and 2-methyl-1-butanol. Their findings indicate that activation energy and IDTs of these isomers increase in the following order: n-pentanol, 2-methyl-2-butanol, and isopentanol. Computational simulations were also conducted by these researchers to calculate the IDTs of n-pentanol using the reaction mechanism proposed by Togbé et al.18 at a pressure of 1.0 atm and temperatures ranging from 1100 to 1500 K. The computational results showed good agreement with experimental data at low equivalence ratios (φ = 0.25 and φ = 0.5) and moderate agreement at an equivalence ratio of φ = 1.0. It is important to note that the experimental setup involved mixtures of n-pentanol, oxygen, and argon. Additionally, Heufer et al.19,20 conducted IDT measurements in n-pentanol and air mixtures using both a shock tube and a rapid compression machine (RCM) at φ = 1.0, with pressures of 9.0 and 30.0 bar, respectively, covering a temperature range from 670 to 1250 K. Pelucchi et al.37 conducted experimental measurements of IDT for n-propanol, n-butanol, and n-pentanol in mixtures with air at φ = 1.0, pressures of 10.0 and 30.0 bar, over a temperature range of 704 to 935 K using a RCM. Chatterjee et al.26 performed IDT measurements for the isomers 1-pentanol, 2-pentanol, and 3-pentanol in air. IDTs below 3 ms were measured using a high-pressure shock tube (HPST), while IDTs ranging from 3 to 400 ms were measured in a rapid compression machine. The test conditions included φ = 0.5, 1.0, 2.0, pressures of 15.0 and 30.0 bar, and a temperature range of 600 to 1300 K. It is noteworthy that one of the objectives of these studies was to investigate the differences in the autoignition behavior between alkanes and their corresponding alcohols concerning the carbon chain length and different functional groups.

Laminar flame speed is a crucial parameter utilized to characterize combustion processes, representing the velocity of unburned gases as they traverse the combustion wave in a direction perpendicular to the wave surface.38 It plays a vital role in estimating emissions generated by air–fuel mixtures under varying conditions and provides valuable insights into the reactivity, exothermic nature, and thermal diffusivity of fuels. The LFS of a specific fuel and oxidizer mixture depends on factors such as the initial pressure, temperature of the unburned mixture, and equivalence ratio.38 Several studies in the literature have reported experimental measurements of the laminar flame speed for n-pentanol and air mixtures. Togbé et al.18 conducted measurements at 423 K and 1.0 atm, covering equivalence ratios (φ) ranging from 0.7 to 1.4. Li et al.39,40 presented two studies on n-pentanol and air mixtures, exploring pressure ranges of 1.0–7.5 bar, initial temperatures of 393, 433, and 473 K, and φ values ranging from 0.6 to 1.8. Nativel et al.23 performed experiments on n-pentanol and air mixtures at temperatures of 353, 433, and 473 K, 1.0 bar pressure, and φ values ranging from 0.7 to 1.5. These experimental groups utilized the spherical expanding flame method to measure the laminar flame speed. Katoch et al.28 reported laminar flame speed measurements for n-pentanol/air mixtures at atmospheric pressure and temperatures up to 560 K using a method known as the mesoscale diverging channel. Table 1, summarizes all experimental data on ignition delay times and laminar flame speeds for n-pentanol reported in the literature to date.

Table 1. Experimental Studies on IDT and Flame Speed Measurements for n-Pentanol Simulated in the Present Study.

      test conditions
experimental study combustion phenomena experimental facility temperature range pressure range ϕ
Tang et al.36 IDT ST 1100–1500 K 1.0, 2.6 atm 0.25, 0.50, 1.0
Heufer et al.20 HPST and RCM 670–1250 K 9.0, 30.0 bar 1.0
Chatterjee et al.26 HPST (IDT’s below 3 ms). RCM (IDT’s 3 ms-400). 600–1300 K 15.0, 30.0 bar 0.5, 1.0, 2.0
Togbé et al.18 laminar flame speed outwardly propagating spherical flame 423 K 1.0 atm 0.7–1.4
Li et al.39,40 393, 433, 473 K 0.10, 0.25, 0.50, 0.75 MPa 0.6–1.8
Nativel et al.23 353, 433, 473 K 1.0 bar 0.7–1.5
Katoch et al.28 mesoscale diverging channel 335, 550 K 1.0 atm 0.7–1.3
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Kinetic-chemical modeling studies take into account experimental data obtained from shock tubes, rapid compression machines, jet-stirred reactors (JSR), and various types of flow reactors. These studies can be employed to investigate combustion at temperatures exceeding 1000 K, where reactions with relatively high activation energy barriers are facilitated. Under these conditions, chemical reactions are typically straightforward and frequently involve the unimolecular decomposition of the fuel, hydrogen atom (H) abstraction from the combustible, and the decomposition of the resulting radical species.13 Depending on the availability of sufficient oxidizer, the consumption of fuel and its relatively stable intermediate products directly leads to the formation of smaller intermediate species. Ultimately, these species yield the final products CO2 and H2O. To summarize, high-temperature combustion is insensitive to fuel structure, meaning that all fuels, when pyrolyzed, essentially produce the same set of C1–C3 hydrocarbons, which are subsequently oxidized as well.

It is important to highlight that, based on the literature review and to the best of our knowledge, no reduced mechanisms are available that simultaneously model ignition at high-temperature conditions (T > 1000 K) and flames for n-pentanol/air mixtures across all reported test conditions encompassed in the present work. This study aims to develop a reduced kinetic mechanism for modeling high-temperature ignition (T > 1000 K) and flames of n-pentanol combustion. The model’s effectiveness is assessed by comparing the simulated IDT and laminar flame speeds with experimental data reported in the literature.18−20,23,26,28,36,37,39,40

2. Development of the Reduced Kinetic Model

This work aims to develop a reduced kinetic model for simulating high-temperature ignition and flames of n-pentanol/air mixtures. We utilize the San Diego mechanism (SD mech)41 developed by the University of California, San Diego, which consists of 57 species and 267 reactions for C1–C4 hydrocarbons.42 The SD model is a kinetic model designed to focus on relevant conditions for flames, ignition, and detonations, considering the combustion chemistry of hydrogen and C1–C4 alkane hydrocarbons. This approach seeks to minimize the number of species and chemical reactions to the essential ones needed to describe the systems and phenomena addressed, thereby reducing uncertainties in the applied rate parameters as much as possible.

The development of the present reduced mechanism is described as follows. First, the SD mechanism is taken as a base mechanism, simplifying and enhancing the reduction process for different new fuels. Then, through a comprehensive literature review, key species and reactions of the new fuel are identified. After that, these required species and reactions were taken from some detailed n-pentanol mechanism19,26,27 and integrated into the SD mech, resulting in a semidetailed mechanism comprising 88 species and 462 chemical reactions (see the left part of Figure 1). In this semidetailed mechanism, 31 species and 195 reactions correspond to n-pentanol. Subsequently, a reduction process, primarily involving sensitivity analysis and steady-state approximation, eliminated 24 species and 180 reactions (middle part of Figure 1). The final reduced mechanism includes 64 species and 282 reactions (right part of Figure 1) and was validated against experimental data. In this reduced mechanism, only 7 species and 15 reactions pertain to n-pentanol. It is important to emphasize that the selection of kinetic parameters and reaction rate constants in the reduced mechanism is not arbitrary; rather, they are adopted as reported in the literature. This method has been successfully employed by one of the authors of the present study, achieving precision and alignment with experimental data.42,43,45,46 Additionally, the mechanism developed herein can be used not only for n-pentanol but also for mixtures of n-pentanol with various fuels included in UCSD Mech. Examples of fuel mixtures for various experimental data are presented in ref (44).

Figure 1.

Figure 1

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Development process of a reduced kinetic mechanism for high-temperature ignition (T > 1000 K) and flames of n-pentanol.

The development of the kinetic model and simulations were conducted using the FlameMaster computational code.47 FlameMaster is a software tool that solves the governing conservation equations for both mass (eq 1) and energy (eq 2), providing a detailed understanding of the combustion processes and reaction kinetics.47−49

2. 1
2. 2

T, Yi and ωi represent the temperature, mole fraction, and production rate of species i, respectively. N represents the total number of species, and t corresponds to time. Cp represents the specific heat at constant pressure, ρ denotes the density of the fuel–oxidizer mixture, while hi signifies the specific enthalpy of each i species. The production rate, ωi, of the i species is given by the following expressions

2. 3
2. 4

From eqs 3 and 4, M represents the total number of elementary chemical reactions, and Ci denotes the molar concentration of each species i. Kj and ν’ij are the reaction rate constant and stoichiometric coefficients, respectively, for the jth reaction involving the ith reactant. Aj, bj and Eaj correspond to the frequency factor, pre-exponential factor or Arrhenius factor (A-factor), the constant exponential parameter, and activation energy of the jth reaction, respectively. R represents the universal gas constant. In developing reduced kinetic schemes, prioritizing the elimination of species over reactions offers a greater computational advantage, such as a reduced computational cost or faster simulations, by directly reducing the number of conservation equations that must be solved.

Table 2 presents the reduced mechanism developed in this study, including the 7 new species added to the San Diego mechanism, along with their corresponding reaction parameters. These species are C5H11OH, n-pentanol; PC2H4OH, hydroxyethyl radical; the isomers hydroxypentyl radicals, C5H10OH-11 and C5H10OH-13; NC4H9CHO, pentanal; NC4H9CO, keto-butyl radical and A-C3H5CHO, butenal. The mechanism can be summarized as follows: it begins with the unimolecular decomposition of the fuel n-pentanol, as represented by reactions R1 and R2. The energy required to break the Cα–Cβ and Cβ–Cγ bonds in these reactions ranges from 84.5 to 86.8 and 87.9 to 90.2 kcal/mol, respectively, based on the composite quantum chemistry methods CBS-QB3 and G4.18 Reaction R1 produces butyl (PC4H9) and hydroxymethyl (CH2OH) radicals, while reaction R2 produces propyl (N-C3H7) and hydroxyethyl (PC2H4OH) radicals. The hydroxyethyl radical (PC2H4OH) decomposes in reaction R15, yielding ethene (C2H4) and hydroxyl radical (OH).50 Reactions R3 to R7 involve the attack of n-pentanol by atomic hydrogen (H), hydroxyl radical (OH), and hydroperoxyl radical (HO2), resulting in H-abstraction reactions and the formation of six C5H11O isomers. These reactions produce five isomers of the hydroxypentyl radical n-C5H10OH, and one C5H11O-radical. Diatomic hydrogen, water, and hydrogen peroxide are also formed as products. The formation of the hydroxypentyl radical results in five isomers depending on the C–H bonds broken under the reaction conditions: C5H10OH-11, C5H10OH-12, C5H10OH-13, C5H10OH-14, and C5H10OH-15. The energy required to break the Cα–H bond, resulting in the C5H10OH-11 radical, ranges from 93.0 to 95.1 kcal/mol, while breaking the Cγ–H and Cs–H bonds, leading to the C5H10OH-13 and C5H10OH-14 radicals, requires 97.0 to 99.0 kcal/mol, respectively.19 These energy values are lower than those required to break the Cβ–H and Cp–H bonds, which give rise to C5H10OH-12 and C5H10OH-15 isomers of the hydroxypentyl species. Additionally, H-abstraction can occur at the OH functional group of n-pentanol, forming the C5H11O-radical. However, the energy required to break this bond is higher than the energy needed to break any of the C–H bonds, making the formation of the C5H11O radical extremely unlikely and practically negligible.

Table 2. Set of Chemical Reactions of the Reduced Kinetic Model for n-Pentanol Added into the San Diego Mechanisma.

no. reactions Aj bj Eaj
R1 C5H11OH (+M) ⇔ PC4H9 + CH2OH (+M) 3.020 × 1023 –1.880 8.5710 × 104
low-pressure limit:0.1416 × 10060–0.1193 × 100020.8398 × 10005
TROE centering:0.7646 × 100000.8344 × 100100.7248 × 100030.8214 × 10010
R2 C5H11OH (+M) ⇔ N–C3H7 + PC2H4OH (+M) 5.530 × 1024 –2.230 8.9010 × 104
low-pressure limit:0.6632 × 10060–0.1213 × 100020.8472 × 10005
TROE centering:0.2438 × 100000.7441 × 100030.5000 × 100100.5000 × 10010
R3 C5H11OH + H ⇔ C5H10OH-11 + H2 4.050 × 1005 2.680 2.915 × 103
R4 C5H11OH + H ⇔ C5H10OH-13 + H2 1.300 × 1006 2.400 4.471 × 103
R5 C5H11OH + OH ⇔ C5H10OH-11 + H2O 6.430 × 1003 2.890 –2.291 × 103
R6 C5H11OH + OH ⇔ C5H10OH-13 + H2O 1.141 × 1003 2.870 –2.926 × 103
R7 C5H11OH + HO2 ⇔ C5H10OH-11 + H2O2 2.740 × 10–04 5.260 8.268 × 103
R8 C5H10OH-11 ⇔ CH3CHO+N–C3H7 4.310 × 1012 0.000 2.8700 × 104
R9 C5H10OH-11 + O2 ⇔ NC4H9CHO + HO2 7.670 × 1013 0.000 4.690 × 103
R10 C5H10OH-13 ⇔ CH2O+PC4H9 1.810 × 1033 –7.100 3.2261 × 104
R11 NC4H9CHO + H ⇔ NC4H9CO + H2 4.140 × 1009 1.120 2.320 × 103
R12 NC4H9CO ⇔ PC4H9 + CO 5.780 × 1014 0.000 1.6844 × 104
R13 NC4H9CHO + OH ⇔ A-C3H5CHO + CH3 + H2O 4.670 × 1007 1.610 –3.500 × 10
R14 A-C3H5CHO + OH ⇔ C3H5 + CO + H2O 2.690 × 1010 0.760 –3.400 × 102
R15 PC2H4OH ⇔ C2H4 + OH 1.047 × 1025 –3.990 3.0390 × 104
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a

With the corresponding units, Aj [mol cm s K], Eaj [cal/mol]; “bj” is a dimensionless parameter.

Reaction flow analyses from various studies that model the ignition of n-pentanol/air mixtures reveal that for a stoichiometric ratio (φ) of 1.0, pressures ranging from 10.0 to 30.0 bar, and temperatures between 700 and 1100 K, the primary pathways for the production of hydroxypentyl radical isomers, in order of relevance, are as follows: C5H10OH-11 (38–48%), C5H10OH-14 (17–22%), and C5H10OH-13 (11–17%).19,26,29,51 Our investigation revealed that incorporating the isomers C5H10OH-11 and C5H10OH-13 best reproduced both experimental high-temperature ignition data (T > 1000 K) and laminar flame speeds across a wide range of pressures and equivalence ratios. Consequently, the reduced mechanism developed in this work specifically includes these isomers.

The C5H10OH-11 radical undergoes the following reactions, leading to the formation of two aldehydes. In reaction R8, it decomposes through the β-scission mechanism, producing acetaldehyde (CH3CHO) and the propyl radical (N-C3H7). In the chemically activated pathway of hydrogen abstraction reaction (R9), it reacts to form pentanal (NC4H9CHO) and the hydroperoxyl radical (HO2).26 Under ignition conditions at pressures close to atmospheric and temperatures between 500 and 900 K, as well as flame conditions, the R8 reaction predominates over the R9 reaction, consuming the C5H10OH-11 radical. However, this situation changes for ignition conditions starting from pressures of 9.0 bar and temperatures of 1000 K onward, where R9 becomes the dominant reaction.

The C5H10OH-13 radical decomposes via the β-scission R10 reaction to form formaldehyde (CH2O) and butyl radical (PC4H9). Pentanal reacts with H in reaction R11, resulting in the formation of the keto-butyl radical (NC4H9CO) and H2. Additionally, pentanal reacts with the OH radical in R13, producing butenal (A-C3H5CHO), a methyl radical (CH3), and water. The keto-butyl radical (NC4H9CO) decomposes in reaction R12, generating the butyl radical (PC4H9) and CO, while butenal reacts with OH in R14 to produce the allyl radical (C3H5), CO, and water. Reactions R13 and R14 have been obtained using the steady-state approximation, as these reactions involve two chemical species that are consumed at a rate comparable to their production

3. Sensitivity Analysis

Local sensitivity analysis is the most common method used to assess the responsiveness of model results to one or more input parameters. It involves evaluating the model’s response, Yi, to a finite variation in the nominal value of a specific parameter, Xj, while keeping the other parameters constant. The sensitivity coefficient, ∂Yi/∂Xj, quantifies the relationship between the model’s solution and the modified value of the parameter of interest. To facilitate comparisons, the sensitivity coefficients are normalized as Sj = (Xj/Yi) (∂Yi/∂Xj), making them nondimensional, and independent of both the units of measurement of the model’s solutions and those of the input parameters.16,48 In the present study, we apply local sensitivity analysis to explore how the results of the simulations conducted using the mechanism under investigation vary when a reference parameter is modified. The normalized local sensitivity coefficient, Sj, for each reaction j is calculated as43

3. 5

For ignition sensitivity analysis, the output variable X represents the IDT, while the changing reference parameter is the pre-exponential factor Aj in the Arrhenius equation for each reaction j in the mechanism. Similarly, in the flame sensitivity analysis, output variable X represents the laminar flame speed u. The calculated normalized local sensitivity coefficients in this study demonstrate how the IDT or LFS, as output variables of the proposed kinetic model, change when the pre-exponential factor of each reaction j is doubled while keeping the parameters of other reactions constant. A positive sensitivity coefficient indicates that increasing the reactivity of a specific reaction j amplifies the IDT or LFS calculated by the mechanism. Conversely, a negative sensitivity coefficient implies a decrease in the calculated IDT or LFS. In summary, the magnitude and sign of the sensitivity coefficient determine the significance and influence direction of an individual reaction j’s reactivity on the IDT or LFS values. Sensitivity analysis plots for ignition and flames under various temperature, pressure, and equivalence ratio conditions are presented in Figures SM-1–SM-4, along with detailed explanations and conclusions.

Sensitivity analyses for IDT and LFS performed on the reduced mechanism developed in this work reveal that the H abstraction reaction (R7) exerts the most significant influence on IDT. This reaction, involving the HO2 radical and fuel molecule, leads to the formation of the C5H10OH-11 isomer and H2O2. Furthermore, the unimolecular decomposition of H2O2 (+M) ↔ 2OH (+M) plays a significant role in reducing IDT. This is because it produces OH radicals that are highly reactive. This reaction is a reversible pathway of the 2OH (+M) ↔ H2O2 (+M) equilibrium within the San Diego mechanism. At high temperatures (>900 K), radical production intensifies, promoting inter-radical reactions. The combination of HO2 radicals (2HO2 ↔ H2O2 + O2) further contributes to the H2O2 pool. This elevated H2O2 concentration shifts the equilibrium mentioned above toward the left, resulting in increased OH radical production. These OH radicals subsequently attack the fuel and its decomposition products.53 In contrast, H + O2 ↔ OH + O and CO + OH ↔ CO2 + H reactions exhibit the strongest impact on the flame speed at near-atmospheric pressures, promoting branching and CO oxidation. As observed with IDT, pressure enhances the influence of these bimolecular reactions.

In summary, the sensitivity analysis shows that H radicals exhibit higher reactivity than OH/HO2 radicals at near-atmospheric pressures. However, at intermediate to high pressures (≥9.0 bar), the OH/HO2 reactivity surpasses that of H radicals. This study reinforces the notion that OH/HO2 radicals play a more prominent role in ignition at intermediate and high pressures, while H radicals dominate flame propagation under near-atmospheric conditions. Furthermore, the findings highlight the greater influence of H combustion kinetics on flame speed compared to the n-pentanol submechanism reactions. Additionally, pressure increases the impact of both bimolecular and third-body-mediated unimolecular reactions on flame speed.

4. Results and Discussion

The literature review reveals that comparisons between experimental data and simulation results are typically conducted qualitatively and descriptively. However, the use of statistical measures to quantify agreement is less common. In this study, to address this gap, we employ statistical measures of deviation or error, alongside graphical comparisons. These measures include the mean absolute deviation (MAD), root-mean-square error (RMSE), mean absolute percentage error (MAPE), and mean percentage error (MPE). All these metrics rely on the discrepancies between simulation results and experimental data to assess model accuracy.53,54,55Table SM-1 provides the definitions, main characteristics, and calculation formulas for these statistical measures of deviation. By incorporation of these statistical measures, we aim to evaluate the agreement between simulations and experimental results more rigorously. The reduced mechanism developed herein was compared against all experimental ignition delay time and laminar flame speed data reported in the literature to date, as shown in Table 1. Low-temperature ignition was excluded from the analysis, as it falls outside the scope of this work.37

Figures 2, 3, and SM-5–SM-7 present comparative graphs of experimental and simulated IDTs for n-pentanol/air mixtures under various conditions. The simulations, performed using the newly developed reduced kinetic mechanism implemented within FlameMaster, are compared to experimental data reported by Tang et al.36 and Chatterjee et al.26 These data cover a broad range of pressures (1.0–30.0 bar), temperatures (950–1520 K), and equivalence ratios (φ = 0.25 to 2.0).

Figure 2.

Figure 2

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Experimental data36 and simulation of ignition delay time (IDT, in microseconds) for mixtures of 0.50% n-pentanol at p = 1.0 atm, φ= 1.0, 0.50, 0.25.

Figure 3.

Figure 3

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Experimental data26 and simulation of ignition delay time (IDT, in milliseconds) for mixtures of n-pentanol–21% O2 in N2/Ar, for φ= 0.5 at p = 15.0 and 30.0 atm.

Table 3 presents a quantitative analysis of the statistical measures of variation for the experimental ignition delay time (IDT) data and the corresponding simulation results displayed in Figures 2, 3, and SM-5–SM-7. The term “Combined [reference numbers]” in the table signifies that the calculation of statistical deviation measures incorporates the set of experimental data indicated by the reference numbers within the brackets. This data set also corresponds to the information presented in the referenced figures. To summarize, for high-temperature conditions (T > 1000 K), encompassing 73 experimental IDT measurements (referred to as “All sources combined”), the simulations achieved a MAD of 0.148 ms with minimal bias (|MPE| = 1.5%). These results indicate a high level of agreement between the simulations and the experimental data, with the largest deviations observed for lean mixtures (φ = 0.25) at 1.0 atm pressure (Figure SM-5).

Table 3. Statistical Measures of Deviation of the Simulation Results (This Study) from the Experimental Data Reported in the Literature for the Ignition Delay Time.

experimental data source figure no. experimental facility temperature range pressure ϕ MAD RMSE MAPE (%) MPE (%}
Tang et al. [36] Figure 2 ST 1130–1520 K 1.0 atm 0.50% n-pentanol, 3.75% O2, 95.75% Ar (ϕ ≥ 1.0) 182.48 μs 284.82 μs 24.4 –23.30%
0.50% n-pentanol, 7.50% O2, 92.0% Ar (ϕ = 0.50)
0.50% n-pentanol, 15.0% O2, 84.5% Ar(ϕ = 0.25)
Figure SM-5 1.0 atm 0.25% n-pentanol, 3.75% O2, 96.0% Ar (ϕ = 0.5)
2.6 atm 0.25% n-pentanol, 3.75% O2, 96.0% Ar (ϕ = 0.5)
Heufer et al. [19,20] Figure SM-6 ST & RCM 950–1250 K 9.0 bar 1.0 0.215 ms 0.375 ms 25.8 10.5
30.0 bar 79% N2 and/or Ar and 21% O2 (ϕ = 1.0) 0.038 ms 0.054 ms 19.7 19.7
Chatterjee et al. [26] HPST 0.134 ms 0.148 ms 43.0 43.0
combined [19,20,26]       0.093 ms 0.117 ms 33.2 33.5
Chatterjee et al. [26] Figure 3 HPST 950–1340 K 15 atm 79% N2 and/or Ar and 21% O2 (ϕ = 0.5) 0.122 ms 0.259 ms 15.8 –14.9
30 atm
RCM 15 atm 0.289 ms 0.529 ms 26.1 –25.3
Figure SM-7 HPST 15 atm 79% N2 and/or Ar and 21% O2 (ϕ = 2.0) 0.088 ms 0.131 ms 32.1 29.4
30 atm
combined [19,20,26] Figures 3, SM-6, SM-7     ϕ = 0.5,1.0, 2.0 0.184 ms 0.354 ms 30.9 10.8
all sources combined (73 experimental data) Figures 2, 3, SM-5, SM-6, SM-7   T> 1000 K 1.0–30.0 bar (atm) 0.25 ≤ ϕ ≤ 2.0 0.148 ms 0.246 ms 27.2 –1.5
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Figures 4, SM-8, and SM-9 compare experimental and simulated laminar flame speeds of n-pentanol/air mixtures obtained with the FlameMaster code and the reduced mechanism developed in this study. Figure 4 focuses on p = 1.0 bar and T = 353, 393, 423, and 473 K. The experimental data from Togbé et al.,18 Nativel et al.,23 and Li et al.39,40 were obtained using the spherically expanding flame technique, which necessitates stretching corrections. Consequently, two sets of experimental data (linearized and nonlinearized) are presented for T = 353, 433, and 473 K.23 For all conditions, deviations are larger for the nonlinearized data compared to the linearized data, likely due to stretching corrections and inherent experimental uncertainties, such as measurement errors and variations in experimental conditions.38,52

Figure 4.

Figure 4

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Experimental data18,23,39,40 and simulation for laminar flame speed, n-pentanol/air mixtures, p = 1.0 bar, T = 353, 393, 473, and 423 K (p = 1.0 atm).

Table 4 provides a quantitative analysis of the statistical measures of variation for the experimental laminar flame speed data and the corresponding simulations presented in Figures 4, S8, and S9. Across all data sources (n = 250, referred to as “All sources combined”), the simulations achieved a MAD of 2.73 cm/s with minimal bias (|MPE| = 3.93%). This indicates good agreement between the simulations and the experimental data.

Table 4. Statistical Measures of Deviation of the Simulation Results (This Study) from the Experimental Data Reported in the Literature for the Laminar Flame Speed.

experimental data source figure no. experimental method temperature pressure   MAD (cm/s) RMSE (cm/s) MAPE (%) MPE (%)
Nativel et al. [23] Figure 4 outwardly propagating spherical flame. linear. 353 K 1.0 bar 0.7–1.5 0.695 0.767 1.43 –1.43
outwardly propagating spherical flame. nonLinear. 1.681 1.782 3.55 –3.55
combined (linear and nonlinear)   1.19 1.37 2.5 –2.5
Li et al. [39,40] outwardly propagating spherical flame 393 K 1.0 bar 0.6–1.8 2.56 3.08 6.18 –6.06
Togbé et al. [18] 423 K 1.0 atm 0.7–1.4 9.18 9.52 17.4 –17.4
Nativel et al. [23] outwardly propagating spherical flame. linear. 473 K 1.0 bar 0.7–1.5 0.70 0.92 0.92 0.49
outwardly propagating spherical flame. nonlinear. 1.37 1.54 1.80 –1.27
combined (linear and nonlinear)   1.04 1.27 1.40 –0.39
Li et al. [39,40] outwardly propagating spherical flame 0.6–1.8 5.97 6.88 13.24 –12.1
combined (473 K) [23,39,40]   0.6–1.8 2.98 4.43 6.04 –5.01
Katoch et al. [28] Figure SM-8 mesoscale diverging channel 335 K 1.0 atm 0.7–1.3 3.19 3.41 8.50 –8.50
550 K 8.04 8.38 8.50 –8.50
combined [28] (335 and 550 K)   5.62 6.39 8.48 8.48
Nativel et al. [23] Figure SM-9 outwardly propagating spherical flame. linear. 433 K 1.0 bar 0.7–1.5 0.92 1.55 1.17 1.10
outwardly propagating spherical flame. nonlinear. 1.64 1.94 2.80 –0.66
combined (linear and nonlinear)   1.28 1.76 2.3 0.22
Li et al. [39,40] outwardly propagating spherical flame 0.6–1.8 3.96 4.74 8.68 –8.30
combined (433 K,1.0 bar), [23,39,40]   0.6–1.8 2.52 3.48 5.24 –3.73
Li et al.[39,40] outwardly propagating spherical flame 2.5 bar 0.6–1.8 1.18 1.43 2.44 –0.81
5.0 bar 1.18 1.34 3.72 2.94
7.5 bar 1.17 1.85 5.86 5.86
combined (433 K) [39,40]   1.0–7.5 bar 2.00 2.79 4.62 –1.05
all sources combined (250 experimental data) Figure 4, SM-8, SM-9   335–550 K 1.0–7.5 bar 0.6–1.8 2.73 3.99 5.66 –3.93
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Our simulations exhibited deviations from the experimental data reported by Li et al.39,40 and Togbé18 under specific conditions: T = 393 and 473 K for p = 1.0 bar, and T = 423 K for p = 1.0 atm. These deviations might be attributed to the influence of the O2 content in the test air on laminar flame speeds. Nativel et al.23 observed significant differences at 433 and 473 K, both at 1.0 bar, compared to the data of Li et al.39,40 under identical conditions. Notably, Li et al. did not explicitly report the O2 content, leading Nativel et al. to hypothesize that Li et al.’s experiments likely employed air samples with O2 levels below 21.0%.

Table S2 presents the experimental results reported by Nativel et al.23 Importantly, a difference of 7.4 cm/s is observed between the laminar flame speeds measured at the O2 concentrations of 20.9 and 20.0%, holding all other experimental conditions constant. Similarly, Nativel et al.23 conducted flame speed measurements considering synthetic air (20% O2, 80% N2) under the temperature pressure and φ conditions reported by Togbé et al.18 (Table S3). Confirmation of the composition of this synthetic air is mentioned by ref (23) in discussions with the authors of ref (18). Flame speeds obtained with n-pentanol/synthetic air are lower than those with n-pentanol/air (21% O2). Laminar flame speed measurements (20.9% O2 air) conducted by Nativel et al.23 are plotted in Figure 4, exhibiting good agreement with our simulations (assuming 21.0% O2 air).

5. Conclusions

In this study, we present a reduced combustion mechanism for modeling high-temperature ignition (T > 1000 K) and flames of n-pentanol/air mixtures. This mechanism comprises only 64 species and 282 reactions, offering a more computationally tractable alternative to detailed mechanisms.

Our approach involved combining a detailed submechanism for n-pentanol with the San Diego mechanism, a reduced scheme for C1–C4 hydrocarbons. This combined mechanism was then systematically reduced using sensitivity analysis and the steady-state approximation. The resulting reduced submechanism for n-pentanol kinetics is particularly noteworthy because it includes only 7 species and 15 reactions. Importantly, the chosen reactions and parameters were obtained directly from the literature, without any modifications or adjustments.

To assess the accuracy of our model, we performed a comprehensive validation against a wide range of experimental data available in the literature. This included comparisons with 73 ignition delay time measurements and approximately 250 flame speed measurements. Our simulations show good agreement with the experimental data, confirmed by both graphical inspection and quantitative analysis using statistical measures of deviation. This supports the reliability of our proposed reduced model.

In conclusion, this study presents a new, reliable reduced mechanism for n-pentanol/air combustion at high temperatures, offering a valuable alternative to complex detailed mechanisms. This model simplifies simulations, making it useful for practical applications in combustion system modeling, such as engine design and optimization.

Acknowledgments

The research is sponsored by CONAHCYT and Tecnológico de Monterrey, México.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c05180.

  • Reduced kinetic mechanism for modeling high-temperature ignition and flames for n-pentanol (PDF)

  • Reduced mechanism; thermodynamics parameters and properties information; transport parameters and properties information (ZIP)

The authors declare no competing financial interest.

Supplementary Material

ao4c05180_si_001.pdf (1.2MB, pdf)
ao4c05180_si_002.zip (36.7KB, zip)

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Supplementary Materials

ao4c05180_si_001.pdf (1.2MB, pdf)
ao4c05180_si_002.zip (36.7KB, zip)

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