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Chemistry: Autoignition Chemical Kinetics
Since we are purely interested in the phenomenon of turbulent autoignition, we do not want, at least at this initial stage, to complicate matters further by having to consider the two-phase physics of liquid droplet evaporation. We would like to consider the autoignition of gaseous hydrocarbons and hydrogen in air. A preliminary list of desirable fuels includes: (i) methane, CH4, (ii) acetylene, or ethyne, C2H2, (iii) ethylene, or ethene, C2H4, (iv) propane, C3H8, or butane, C4H10, (v) heptane, C7H16, or octane, C8H18, and, (vii) hydrogen, H2. Of these, only heptane and octane are liquid at room temperature and pressure and will have to be pre-vaporized in the experiments. Furthermore, for the purposes of our particular study, the exact choice of fuel within this list is not so relevant, as long as its autoignition chemistry is well known and easy to describe.
The earliest investigations of autoignition, during the late 19th century, were aimed at determining the 'autoignition temperature' of a combustible mixture. From the mid-1950s and following the important finding that there can be no single, absolute 'autoignition temperature', attention was directed towards the 'autoignition delay time' associated with a set of initial conditions for temperature, pressure and composition (e.g. mass fractions). This has remained the 'traditional' form in which autoignition is studied, with the bulk of recent experiments and analyses continuing to be aimed towards understanding the chemical kinetics of oxidation of various fuel-oxidizer systems in homogeneous reactors, whose mixing state by definition collapses to a unique description. Much work is required before it can be claimed that a complete understanding of oxidation kinetics has been attained and the community still struggles to come to a consensus over several issues. Still, knowledge of these chemical processes has been greatly enhanced.
The chemistry statement can be made in a number of ways, with detailed chemistry being more accurate (and complicated) than simplified, reduced elementary reaction mechanisms, which in turn are more accurate (and complicated) than simple, dummy, one-step global 'Arrhenius' reactions. The one-step chemistry model, while capable of producing decent results for most engineering applications including the autoignition of CH4 and H2 at high temperatures, is not in general adequate for calculations of autoignition. Nevertheless, much insight into the physics of autoignition can be gained by taking advantage of this simplification and this is done for a homogeneous mixture in the Autoignition Tutorial.
We turn now to more realistic chemistry scenarios. When simple radicals recombine, the energy released is enough to decompose the product into the original radicals. Usually, a third body is necessary to remove the excess energy and complete the recombination. These elementary reactions are called third-body re-combinations and although their frequency is relatively low (since the probability of three molecules colliding simultaneously is also low) they are crucial in combustion (and autoignition) chemistry. They are the main mechanism for transforming the chemical energy released by the reactions into heat. Nevertheless, there exists a further mechanism for absorbing this energy and allowing the highly exothermic reactions of the radicals to proceed. If the product molecule is large, then it will have a large number of internal (mostly vibrational) degrees of freedom and can thus distribute the energy of formation more efficiently. This mechanism becomes more pronounced for heavier hydrocarbons, as expected by casual consideration of degrees of freedom of these molecules. This is why, for hydrocarbons heavier than propane the simple exponential Arrhenius kinetics are not representative. Experimental Arrhenius plots and plots of autoignition delay time versus initial temperature will show a non-linear dependence. Heavy hydrocarbons will readily exhibit a negative temperature coefficient at temperatures around 700 - 900 K, meaning that the reaction rate will decrease and the autoignition delay time will increase as the temperature increases, which is not intuitive. At these temperatures abstraction reactions become slower than reactions leading to organic acids and other oxygenated intermediates, which are slower to react. The overall process causes a reduction in the rate at which the radicals accumulate to form the pool necessary for autoignition. This implies that the chemistry used in CFD calculations of autoignition must be quite complex, if the autoignition is to be captured accurately. A characteristic of autoignition chemistry is that, unlike flame chemistry, reduced mechanisms require the inclusion of a greater number of intermediate species and elementary reactions.
At present the knowledge of chemical kinetics is just becoming adequate for the analysis of the combustion of most common fuels, yet more work is required for autoignition mechanisms. This is a source of great uncertainty for DNS and theoretical explorations of the turbulent autoignition problem in general. However the chemistry statement for autoignition is made, a successful mechanism should always include a valid representation of the chain branching reactions. They are the steps that mostly determine the rate at which the chain (and overall reaction) continues, but also, directly responsible for the phenomenon of explosion (and hence autoignition).
Hydrogen Chemistry:
One of the reasons why we are interested in hydrogen is because its chemistry is considered a starting point for the more complex hydrocarbon chemistry. Another is that it is considered relatively simple and is easier to describe with fewer elementary reactions, reducing computational cost in numerical investigations. Hence, the autoignition of this fuel has been studied to a considerable extent. The graph below shows the explosion limits of homogeneous, stoichiometric Hydrogen-Oxygen mixtures. Of course, equivalent plots can be obtained for many different mixture compositions. Autoignition limit plots, an example of which is show below, refer to homogeneous mixtures, yet their implications can carry over to the inhomogeneous case.
The general characteristics of such explosion limit plots are:
1. The first and second limits: These are ones that correspond to conditions of very low pressures (up to an absolute pressure of about 0.3 bar) and will not be considered. Our lowest working pressure is atmospheric pressure, 1.01325 bar.
2. The third limit: This follows the trend that one would expect from simple density considerations. As the pressure increases, the initial partial densities of the reactants increase and a lower temperature is necessary for the reactions to become fast enough for explosion. Furthermore, noting the logarithmic axis, we can see that the effect of temperature is much stronger than that of pressure, a trend one would expect and correctly included by the considerations of simplified one-step Arrhenius chemistry used in the Autoignition Tutorial.
It is important to stress that in the autoignition stages of any flame the fuel-oxidizer mixture may follow a low-temperature slow reaction mechanism and in the latter stages an explosive reaction due to the increase in temperature and/or pressure causing the operating point to shift between the regions depicted in graphs such as the one above. Furthermore, for inhomogeneous autoignition, various locations in the flow will exhibit different local mixture compositions. In fact, one of key realizations that must be made in the study of inhomogeneous autoignition is that at any time one will observe both slow (at short lengths or residence times) and fast (at long lengths or delay times) chemistry in the flow. This point is especially significant in hydrocarbon chemistry, because it is in the low-temperature regime that particular pollutant compounds are formed.
We return now to the Hydrogen-Oxygen system. The dissociation energy of H2 is much lower than that of O2 and so the initiation step must be related to the former. Using bold notation to imply radicals, the most likely reaction for this is,
H2 + M ----------> 2 H + M
Under shock tube conditions at lower pressures a different reaction captures the experimental autoignition delay more accurately,
H2 + O2 ----------> HO2 + H
and might be the most probable initiation step. The presence of the hydroperoxy radical, HO2, has been confirmed experimentally by mass spectroscopy and might point towards a different initiation chemistry for shock tube experiments. This point might be significant. It is generally accepted that the effect of the initiation step is simply to provide radicals for the chain reactions and as such, is of less importance in determining the explosive conditions and the resulting products. Yet, the extent of this chemistry variation and its consequences on autoignition, is not established.
The most important chain propagation reactions that follow are possibly,
(2 H + O2 + M ----------> H + M + [HO2) + H2 ----------> H2O2 + H ----------> 2 OH + H]; Chain branching
O + H2 ----------> H + OH; Chain branching
H2 + OH ----------> H2O + H; Chain propagating
O + H2O ----------> 2 OH; Chain branching
Because of the fact that the hydroperoxy radical, HO2, is a relatively stable radical (a 'metastable' species), it does not readily participate in the rest of the necessary chain propagation reactions. The reaction rate of the first chain branching equation above increases at higher temperatures (typically above 900 K) and is dominant for the pressure range of interest (1 - 10 bar). At these high temperatures and for atmospheric pressures the recombinations that make up the terminations steps are,
H + H + M ----------> H2 + M
O + O + M ----------> O2 + M
H + O + M ----------> OH + M
H + O2 + M ----------> HO2 + M
H + OH + M ----------> H2O + M
Active hydrogen atoms can be removed by oxygen molecules in three-body recombination reactions such as that shown in the fourth termination step above. The formation of the hydroperoxy radical, HO2, from this reaction is kinetically favoured at lower temperatures and higher pressures. Consider the chain propagating, branching and recombination reactions outlined above. The fate of HO2 is again significant and must be considered. Since radicals are highly reactive, their concentrations are small and the backward reactions of all the branching and recombination chain steps are usually neglected. The rate of chain branching reactions increases with temperature. On the other hand, since the radical recombination steps require a third body, the rate of these reactions decreases with increasing temperature. The crossover temperature, Tc for hydrogen chemistry is defined as the temperature at which the chain branching and recombination rates of HO2 are the same and is approximately 925 - 930 K at 1 atm. from various sources. At high temperatures, but lower than Tc, the metastable nature of HO2 acts as a barrier for explosion. This is the reason for the relative (to other fuels) difficulty of hydrogen explosion at high temperatures, an observation that at first sight might seem counter-intuitive. As the temperature increases from Tc to even higher temperatures, HO2 continues to abstain from the necessary chain propagation reactions, but chain branching will be increasingly allowed to dominate the overall reaction. This would lead to a rapid increase in the reaction rate and an increased ability for explosive oxidation. Hence, this explains the acceleration in the chemistry at temperatures higher than Tc that has been observed by numerous investigators. For the hydrogen experiments in this work, the temperatures were between 940 - 970 K and were thus in the vicinity of the second explosion limit for the hydrogen-air system and higher, but not considerably so, than Tc.
Hydrocarbon Chemistry:
The importance of the chain mechanism discussed above for the Hydrogen-Oxygen reaction is also apparent for the autoignition of hydrocarbons. Furthermore, explosion considerations of carbon monoxide are also essential to the understanding of hydrocarbon autoignition chemistry because the conversion to carbon dioxide is the highly exothermic part of any hydrocarbon oxidation system. All carbon atoms in alkyl hydrocarbons are converted to carbon monoxide through the radical of formaldehyde, H2CO, called formyl, HCO. All approaches, including the current one, start from the analysis of methane, which is nowadays among the best understood. Of course, methane is a very important practical fuel in itself, with uses including the many natural gas applications. Hydrocarbons heavier than propane oxidize much more slowly than hydrogen and are known to form important metastable molecules. These molecules allow for a qualitative explanation of unique explosion limits of these hydrocarbons, as shown in the figure below.
As can be seen, the larger the molecule the greater the explosion shift towards lower temperatures and pressures, as we would expect. The heavier the hydrocarbon, the easier it is via intermolecular collisions for the larger molecule and its intermediates to break down, forming radical pools that initiate the fast reactions. The shape of propane indicates the effect of branched chain reactions mentioned earlier. The shape of this plot shows how these reactions must vastly differ from the hydrogen case presented above.
Key experimental characteristics relevant to our interests are:
1. Induction intervals are followed by very rapid reaction rates,
2. The formation of formaldehyde, which tends to increase the reaction rates and shorten autoignition times, and,
3. The exhibition of 'cool flames', apart for methane and ethane, which are associated with the shifting explosion limits of the so-called 'multiple ignitions' (two-stage in the case of propane here) and negative temperature coefficients of reaction rates.
The above behaviour can be explained by hypothesizing unstable, but long-lived species that form as intermediates and then undergo different reactions depending on the temperature. Referring to the above figure, for a fuel A, the reaction paths after formation of the unstable intermediate M* can be,
--------> Points 3 to 4 {non-chain branching; higher temperature, larger activation energy}
/
A ----------> M*
\
----------> Points 1 to 2 {chain branching; lower temperature, smaller activation energy}
The negative temperature coefficient from 2 to 3 can be captured by this change in the chemistry. We note, that for lower temperatures, the mechanism for explosion must be a chain propagating one and that the shift from 2 to 3 at higher temperatures requires an increased heat input, explained well by the change of chemistry to a non-chain branching step.
We concentrate now on methane. Although the mechanism presented below is not definitive, it is the simplest scheme of chain reactions that can be used to reasonably explain the low-temperature results.
Chain Initiation:
CH4 + O2 ----------> CH3 + HO2
CH3 + O2 ----------> CH2O + OH
OH + CH4 ----------> H2O + CH3
OH + CH2O ----------> H2O + HCO
CH2O + O2 ----------> HO2 + HCO
HCO + O2----------> CO + HO2
HO2 + CH4 ----------> H2O2 + CH3
HO2 + CH2O ----------> H2O2 + HCO
OH ----------> wall
CH2 ----------> wall
HO2 ----------> wall
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