OOQOOH
3.4 Low Temperature Mechanism of Hydrocarbons Combustion
Step 10. R + O2 addition.
+
The balance of the reaction R + O2 ↔RO2 defines the balance between low and high temperature combustion submechanisms. In many ways, the first addition of O2 to an alkyl radical is the most important reaction for low temperature oxidation, even though it does not determine the overall rate of chain branching. The activation energy of the reverse process is high, and, therefore, the equilibrium constant is highly temperature dependent.
Step 11. R+R’O2 ↔RO+R’O. This reaction between RO2 and R radicals provides two RO radicals. Experimental data are available only for the case, when R is a methyl radical CH3.
+
+
Step 12. RO2 isomerisation to QOOH, where Q is a radical with two radical sites, one of them is connected to the OOH group. Such isomerisation can proceed with different H atoms. As an example one of the possible pathways with a transient formation of a six atom ring for the radical C12H25O2 is shown
transient state
Step 13. RO2+HO2↔RO2H+O2. Due to low concentration of HO2 this reaction is much slower than Step 12. This reaction, when followed by the decomposition of RO2H, converts HO2 to OH radicals, which can accelerate the overall rate of reaction. However, the RO2H species is quite stable, and, at sufficiently low temperature, this reaction terminates chain branching and reduces the overall rate of reaction. Information on this reaction type is available only for the case when R is CH3 [61].
+ +
Step 14. RO2+H2O2 ↔RO2H+HO2. There is little information available for this reaction rate constant except for the case where R is CH3 [62]. Since the RO2H decomposes at lower temperature than H2O2, this process leads to enhancement in overall reactivity. Nevertheless all species are stable and this reaction can be treated as unimportant.
+ +
Step 15. RO2+CH3O2 ↔RO+CH3O+O2. The radicals on the right side decompose faster, and the whole reaction also improves overall reactivity. The situation with reaction rate constants is similar to Steps 13 and 14. Little information exist for radicals R other than CH3 [61].
+ + +
Step 16. RO2+R’O2 ↔ RO+R’O+O2. Information on the reaction rate constants exist only for similar radicals R=R’, where R = CH3,C2H5,C3H7.
+
+ +
Step 17. RO2H↔RO+OH. At low temperature conditions RO2is preferentially isomerises to QOOH. That leads to low concentrations of RO2H radical what makes this process unim-portant.
+
Step 18. RO decomposition. Large alkoxy radicals undergo β−scission producing smaller stable oxygenated species, olefine and an alkyl radical species.
+ +
Step 19. QOOH ↔ Cyclic Ether+OH. The O-O bond brakes and cyclic compound is produced.
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Step 20. QOOH ↔Olefin+HO2. If the radical site is close to the hydroperoxy group, the QOOH can decompose to the olefin and HO2.
+
Step 21. QOOH ↔ Olefin+Carbonyl Radical+OH. This reaction is a β−scission of QOOH molecule.
+ +
Step 22. Addition of QOOH to O2. Due to the absence of the experimental data, this reaction is treated as step 10, under an assumption, that the OOH group doesn’t influence the addition of the O2 to a large molecule QOOH.
+
Step 23. OOQOOH isomerisation to ketohydroperoxide + OH. This reaction provides chain branching and is very important for the modeling of two step ignition phenomena observed in shock tubes, CFR engines (Cooperative Fuel Research, standardized internal combustion engine), and rapid compression machines.
transient state
Step 24. Ketohydroperoxide decomposition.
The further chain branching gives another OH radical and a carbonyl radical:
+
Second, the produced carbonyl radical decomposes further.
+ +
Since this reaction has the highest activation energy among all reactions in the low tem-perature mechanism, it limits the overall reaction rate and therefore it is very important.
Step 25. Cyclic ether reactions with OH and HO2. Due to lack of the data, Curran et al. [59] include only reactions with OH and HO2 and assume that the ring opens leading to the formation of an alkyl-aldehyde or alkyl-ketone and either water or hydrogen peroxide.
The alkyl-aldehyde or ketone is then assumed to undergo β−scission to a stable aldehyde or ketone and a smaller alkyl radical species.
2
+ +
+
Due to the high complexity, lack of data, and relatively low importance reaction steps 11,13-19 and 25 are omitted. For example steps 19 and 25 lead to several isomers of cyclic ethers, description of which would induce a whole new group of additional intermediate species and reactions. Since the final goal of the presented work is to produce a reduced kinetic model for the surrogate fuel this class of reactions is not taken into consideration.
4 Introduction to Reduction of Kinetic Mechanisms
Let us assume that we have a homogeneous system with N species and M reactions. The system of differential equations (3.16) can be rewritten in a vector form:
dc
dt =f(c,k),ct=0 =c0, (4.1) where c is a vector of concentrations, vector f consists of the rates of production (3.18).
Depending on the specific problem other equations for the physical parameters such as temperature, pressure, and mass may be added. For example, a calorimetric bomb reactor with a constant volume is used for modeling the ignition delay experiments in a shock tube.
In that case one has to solve a system of N equations for each substance concentration and an additional equation for temperature, where all reaction enthalpies and all substances’ heat capacities are considered.
In the general case we have to solve a system of differential equations dx
dt =S(x),xt=0 =x0 (4.2)
where x is a vectorx=(c1, ..., cM, T, p, ...).
The numerical solver uses the Jacobian of the matrix f: J = ∂S∂x. Its size is equal to the square of the dimension of vectorx. On the other hand, in CFD modeling the concentrations in millions of cells must be calculated for many time points. For this reason, mechanisms as simple as possible are needed.
The creation of comprehensive reduced mechanisms is a tedious process. It is often pos-sible to delete certain mechanisms from a detailed model with a large number of sub-mechanisms with a relatively small influence on the global accuracy. But further reduction is more difficult. The basic strategy for mechanism reduction is to investigate the mechanism and then reduce species and reactions, which are unimportant for the considered parame-ter range. Therefore, methods stated below are also used for the understanding of complex chemical kinetics processes and the underlying phenomena.