Multi-stage heat release in lean combustion: Insights from coupled tangential stretching rate (TSR) and computational singular perturbation (CSP) analysis
Introduction
Combustion systems are being constantly pushed towards lower pollutant emissions and higher thermal efficiency. One approach to improve the combustion performance with respect to stringent requirements is to operate under lean (equivalence ratio 0.5–0.9) or ultra-lean (equivalence ratio below 0.5) conditions or increase the dilution ratio. For example, lean premixed combustion, which could be flameless-based, offers the potential for gas turbines with high efficiency and low NOx emissions [1]. Similarly, reciprocating internal combustion engines for ground-based transport can benefit from operating under lean conditions [2].
A common challenge with lean combustion in all the aforementioned applications is combustion instability, which make it challenging to control flame ignition and extinction [3,4], or more simply heat release rates. These problems are exacerbated under ultra-lean conditions. The heat release phenomenon is governed by both fluid mixing and chemical kinetic phenomena. There is a lack of studies on the fundamental chemical kinetics of ultra-lean combustion [5], and this study is concerned with improving our understanding of chemical kinetics governing heat release under lean and highly diluted conditions.
In a recent study, Sarathy et al. [6] showed that heat release under ultra-lean conditions is remarkably different than that at stoichiometric conditions for n-heptane/air mixtures in a homogenous gas phase batch reactor. They discussed the presence of three stages of heat release at equivalence ratios of 0.3, whereas stoichiometric n-heptane/air mixtures displayed only two stages of heat release. The chemical kinetics of three-stage heat release for lean n-heptane/air mixtures were attributed to a delay in high temperature heat release by suppressing CO oxidation (via CO+OHCO2+H), and further elaborated below.
Multiple stages of heat release have been observed in several studies, but the underlying governing phenomena are notably different than those presented in [6]. Intermediate temperature heat release (ITHR) observed in lean homogenous charge compression ignition (HCCI) engine studies [7], [8], [9] is typically attributed to competition between alkylperoxy (RO2) radical chain branching, propagation, and termination pathways. Three-stage oxidation of n-heptane/air mixtures reported by Yamamoto et al. [10] in a micro flow reactor appear to be more similar to the aforementioned ITHR phenomenon in engines. Several HCCI engine studies report delayed high temperature heat release leading to three distinct stage of heat release when burning gasoline fuels containing alkanes and aromatics. Shibata and Urushihara [11,12] stated that dual phase high temperature heat release (HTHR) occurs when CO oxidation is suppressed due to the presence of benzyl radicals derived from toluene in the fuel. Therefore, the separation of heat release stages was attributed to complex interactions within the radical pool [13] generated by alkanes and aromatics in the fuel. Similar trends were reported by Dec [14] and Sjoberg and Dec [15] where the HTHR splits in two stages under extreme dilution conditions in an HCCI engine. This behavior was attributed to suppression of reaction CO-to-CO2 due to bulk-gas quenching at lean conditions. Machrafi and Cavadias [16] compared HCCI engine experiments and chemical kinetic modeling of n-heptane/isooctane and n-heptane/isooctane/toluene mixtures with air to conclusively demonstrate the role of toluene in creating three-stage ignition. Farouk et al. [17] recently reported three-stage burning regime through experiments and simulations of large n-alkane droplet at elevated pressure coupled with helium dilution. The presence of this unique burning behavior characterized as hot, warm, and cool flames was attributed to the competition between heat release rates at low-temperature and NTC kinetic regimes and losses due to radiation and diffusion. To reiterate, the phenomena described in the aforementioned papers are qualitatively different than that presented by Sarathy et al. [6], as the latter showed delayed HTHR in a single fuel (i.e., n-heptane) in the absence of fuel mixture effects and did not attribute the three-stage burning to any transport or radiation phenomena.
A number of studies have also been performed on the heat release phenomena at low temperatures. For example, low temperature auto-oxidation under lean conditions can lead to high oxygenated molecules that decompose to release heat [18], [19], [20]. Thion et al. [21] were the first to show that a highly reactive fuel such as di-n-butylether displays double negative temperature coefficient behavior, which was not reported in earlier studies [22,23]. The team of Ju et al. [24], [25], [26], [27] demonstrated the ability to stabilize cool flames and warm flames by balancing heat release rates and transport phenomenon. Premixed flame studies by Agnew and Agnew [28] with diethylether (DEE) showed multiple luminescent regions, corresponding to heat release and flames; a third yellow luminescent regime was observed under rich conditions, which could be due to soot formation. Similar flame studies [29], [30], [31] utilized spectroscopy to identify cool and hot flames under varying equivalence ratios, albeit three or more stages of heat release were not reported.
The purpose of this work is to extend upon our recent investigation of three-stage heat release observed in n-heptane/air mixtures under constant volume and constant pressure adiabatic batch reactor conditions. We utilize chemical kinetic simulations to further investigate the effects of mixture temperature, pressure, and equivalence ratio to identify regimes under which three-stage heat release can be observed. Furthermore, additional fuels varying in carbon number and molecular structure (normal, branched, and cyclic) are simulated. The influence of the aforementioned parameters on three-stage heat release or delayed HTHR are discussed in detail with the aid of tangential stretching rate (TSR) and computational singular perturbation (CSP) analysis [32,33].
The paper is structured as follows. Sections 2 and 3 provide background knowledge on three-stage heat release and TSR and CSP analysis. Section 4 presents the numerical methodology. Section 5 discusses the results obtained and insights into the effects of fuel type and reactor conditions (e.g., temperature, pressure, equivalence ratio). The conclusions are provided in Section 6.
Section snippets
Background of three-stage heat release and delayed HTHR
The process of three-stage heat release in lean n-heptane/air mixtures was explained by Sarathy et al. [6] using CSP analysis to identify reactions that contribute to the explosive time scale, which according to Tingas et al. [34,35] is the characteristic time scale for auto-ignition. The initial heat release stage follows the same reaction pathways as the low temperature heat release in a typical two stage ignition [36,37]. The ignition is promoted through intra molecular isomerization of RO2
Time scale sensitivity analysis
The tangential stretching rate (TSR) concept, introduced in Valorani et al. [32,33] and Malpica Galassi et al. [38], selects the most active modes of a dynamical system, that is the slow modes with the highest energy content. The TSR is the (reciprocal of the) driving timescale of the system and is evaluated as an average of the system eigenvalues with weights that also depend on the mode amplitudes [33,39]. Note that the TSR can assume both positive and negative values, and in so doing, it is
. Chemical kinetic simulations
The auto-ignition of hydrocarbons was simulated in closed adiabatic homogenous batch reactor in CHEMKIN PRO [44]. The premixed air/fuel charge was allowed to auto-ignite adiabatically at constant volume vessel under predefined initial temperature and pressure. The volumetric heat production rate (HPR) and the evolution of relevant species including CO, CO2, and H2 are monitored simultaneously as the exothermic reaction proceeds. The ignition delay time (IDT) of each heat release stage (i.e.,
n-Heptane ignition
Following our previous work on three-stage auto-ignition of n-heptane [6], we first present a comprehensive analysis on the effect of initial conditions on three-stage heat release. A sweep of different conditions (temperature, pressure, and equivalence ratio) were simulated in a constant volume adiabatic batch reactor. The IDT difference between the third and second heat release (t* = t3-t2), and the heat production rate of the second to third stage (h* = h2/h3) were determined to quantity the
Conclusions
This work investigated an unusual heat release characteristic where the energy of certain fuels is released in three distinct auto-ignition stages. We identified the pressure, temperature, and equivalence ratio conditions where the three-stage ignition is more pronounced by running extensive closed adiabatic homogenous batch reactor numerical simulations. The occurrence of three-stage heat release was then explored in n-alkanes fuels with different chain lengths and different hydrocarbon
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
The simulation work was supported by King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) with funds given to the Clean Combustion Research Center. We acknowledge funding from the KAUST Clean Fuels Consortium and its member companies. MV, PPC, and RMG acknowledge the partial support from the Italian Ministry of University and Research.
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2023, FuelCitation Excerpt :Three-stage heat release behavior of n-heptane/air mixture was later confirmed by Sarathy and co-workers [3] in a rapid compression machine (RCM), but at an ultra-lean equivalence ratio of 0.3 and a much higher pressure (20 bar). Following this, Sarathy and co-workers [4] extended their investigation, though through modeling, from n-heptane to other hydrocarbons including C4–C7 n-alkanes, 2-methylhexane and cyclopentane at a range of temperatures (600–900 K), pressures (10–60 bar), and equivalence ratios (0.3–0.5). With coupled tangential stretching rate and computational singular perturbation analysis, they were able to identify the important chemistries driving the three stages of heat release, in which the first-stage heat release is attributed to the typical low-temperature oxidation chemistries (particularly those related to hydroperoxides), while the second- and third-stage heat releases correlate with the consumption of CH2O (driven by OH radicals from decomposition of H2O2), and the conversion from CO to CO2, respectively.
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These authors contributed equally to this work.