OOQOOH
iC 8 H 18 /air φ =1
5.8 Mechanism of the Surrogate Model Combustion
0,8 0,9 1,0 100
1000
experiment, C 14
H 30
/air, 15 bar, Shen et al.
calculation, C 16
H 34
/air, 15 bar, this work
experiment, C 14
H 30
/air, 40 bar, Shen et al.
calculation, C 16
H 34
/air, 40 bar, this work
IgnitionDelay,s
1000/T, 1/K C
16 H
34 /air
=1.0
Figure 5.33: Comparison of experimental [116] ignition delay times for n-tetradecane/air and calculated ignition delay time for hexadecane/air mixtures. Stoichiometric mixtures.
Pressures approximately 15 and 40 bar. Closed symbols: experiments, open symbols: calcu-lations.
At the moment there is no available data on hexadecane autoignition. But it is a well known fact that large paraffins burn with similar flame velocity and have very similar ignition delays. Since most of the reaction rates are similar to those of the dodecane submechanism, the calculated ignition delays are expected to be very close to those for dodecane. Exper-iments of Vasu et al. [117] for ignition delay times of dodecane and Shen et al. [116] for tetradecane are used for validation of the hexadecane submechanism.
A comparison of experimental [117] ignition delay times for n-dodecane/air and calculated ignition delay times for hexadecane/air mixtures is shown in Figs. 5.30 and 5.31.
A comparison of experimental [116] ignition delay times for n-tetradecane/air and calcu-lated ignition delay times for hexadecane/air mixtures is shown in Figs. 5.32 and 5.33. In the low temperature region there are some deviations with experimental data of Shen et al.
similar to the cases of decane and dodecane.
Generally, the submechanism shows good agreement with experimental ignition delays of C12H26/air and C14H30/air mixtures.
0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 10
100 1000 10000
experiment, 50 bar, Vasu et al., 2008 calculation, 50 bar, this work
experiment, 25 bar, Vasu et al., 2008 calculation, 25 bar, this work
Ignition Delay, µs
1000/T, 1/K
Jet-A = 1.276%
O2 = 20.74%
N2 = 77.98%
φ=1.0
Figure 5.34: Comparison of experimental [118] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Stoichiometric mixture. Pressures approximately 25 and 50 bar. Closed symbols: experiments, open symbols: calculations.
0,90 0,95 1,00
100 1000 10000
Jet-A = 0.615%
O2 = 10%, N2 = 89.38%
φ=1.0
experiment, 18 bar, Vasu et al., 2008 calculation, 18 bar, this work
Ignition Delay, µs
1000/T
Figure 5.35: Comparison of experimental [118] ignition delay times and calculated ignition delay times for a Jet-A/O2/N2 mixture. Stoichiometric mixture. Pressure approximately 18 bar. Closed symbols: experiments, open symbols: calculations.
0,80 0,85 0,90 0,95 1,00 1,05 1,10 10
100 1000 10000
Jet-A = 0.642%
O2 = 20.87%, N2 = 78.48%
φ=0.5
experiment, 20 bar, Vasu et al., 2008 calculation, 20 bar, this work
Ignition Delay, µs
1000/T
Figure 5.36: Comparison of experimental [118] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Lean mixture, φ=0.5. Pressure approximately 20 bar.
Closed symbols: experiments, open symbols: calculations.
0,8 0,9 1,0 1,1
10 100
1000 Jet-A = 1.276%
O2 = 20.74%
N2 = 77.98%
φ=1.0
experiment, 22 bar, Vasu et al., 2008 calculation, 22 bar, this work
Ignition Delay, µs
1000/T, 1/K
Figure 5.37: Comparison of experimental [118] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Stoichiometric mixture. Pressures approximately 22 and 25 bar. Closed symbols: experiments, open symbols: calculations.
0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1
10 100
1000 Jet-A = 0.63%
O2 = 20.87%, N2 = 78.48%
φ=0.5
experiment, 8 bar, Dean et al., 2007 calculation, 8 bar, this work
Ignition Delay, µs
1000/T, 1/K
Figure 5.38: Comparison of experimental [115] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Lean mixture, φ=0.5. Pressure approximately 8 bar.
Closed symbols: experiments, open symbols: calculations.
stoichiometric and lean mixtures, whereas for rich mixtures there is some deviation (see Figs.
5.38-5.40).
On the whole the mechanism of the Jet-A model fuel and experimental data for ignition delay show good agreement over a wide range of parameters. The Fig. 5.41 represents the rate of production analysis. It is performed with the KINALC 2.0 package [119]. The scheme is built for the combustion of 3 paraffins in the surrogate fuel formula: n-hexadecane C16H34, n-dodecane C12H26 and iso-octane C8H18.
Table 14: Aromatic compounds
A2CH3 C11H10
A2 C10H8
Indene C9H8
A1 C6H6
First, the molecules of fuel undergo pyrolysis and react with the oxygen, forming the primary radicals. Then the decomposition of the fuels pro-gresses by pyrolysis or by a reaction with radicals.
As a result a variety of smaller alkyl radicals and olefins emerges. Because of the stochastic charac-ter of bond breaking and radical aided reactions the number of different reaction products grows rapidly with the amount of carbon atoms. A variety of iso-mers of each product make the system even more complex. The fuel components rapidly degrade to the C2H4 and C2H3 molecules. Further decomposi-tion is slow and at high temperatures it creates a
“bottle neck” for the whole process. The strong dependence of the whole process speed on these reactions will be shown later using sensitivity analysis. Figure 5.42 represents the main paths of methylnaphthalene (A2CH31) combustion.
1Notation of cyclic compounds is explained in the Table 14.
0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1
10 100 1000
Jet-A = 1.257%
O2 = 20.745%, N2 = 77.998%
φ=1
experiment, 9 bar, Dean et al., 2007 calculation, 9 bar, this work
Ignition Delay, µs
1000/T, 1/K
Figure 5.39: Comparison of experimental [115] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Stoichiometric mixture. Pressure approximately 9 bar.
Closed symbols: experiments, open symbols: calculations.
0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
1 10 100 1000 10000
Jet-A = 2.48%
O2 = 20.49%, N2 = 77.03%
φ=2.0
experiment, 9 bar, Dean et al., 2007 calculation, 9 bar, this work
Ignition Delay, µs
1000/T, 1/K
Figure 5.40: Comparison of experimental [115] ignition delay times and calculated ignition delay times for a Jet-A/air mixture. Rich mixture, φ=2. Pressure approximately 9 bar.
Closed symbols: experiments, open symbols: calculations.
C8H18
cC8H17
C5H10
34%
C12H26 C12H25
C3H6 C5H11
70%
27% 45% 23%
23%
C16H34 90% C16H33
46%
21%
14%
C4H9 C7H13
C3H5
C2H4
C2H5 C2H3
HCO
CH2HCO
H2O
CH3 CO
HO2 H
22%
14%
51%
16%
C10H21 10%
C4H8
CH2O
C3H7 C7H14
C6H13
C6H12
C5H9
Figure 5.41: Rate of production analysis of the paraffins combustion mechanism. Initial temperature 1192 K. Pressure 27 bar. Calculated ignition delay 93 µs. Analysis shown at t=50 µs.
C10H7CH3 (A2CH3)
C10H7O (A2O)
C10H7CO (A2CO) C10H7HCO (A2CHO)
C10H7CH2 (A2CH2)
C10H7OH (A2OH)
indenyl indene
C6H5C2H2(A1C2H3*)
A1
-C6H5O
C5H5
H2CCCH
C4H6 C10H7(A2-)
C6H5OH 55%
41%
C6H5CCH(A1C2H) 16% 78%
28%
28%
C8H7
51%
42%
83%
16%
CH3HCO C2H3 28%
C8H7 65%
97%
33%
Figure 5.42: Rate of production analysis of the methylnaphthalene combustion mechanism.
Initial temperature 1192 K. Pressure 27 bar. Calculated ignition delay time 93 µs. Analysis shown at t=50 µs.
cyC9H18 cyC9H18E 55%
70% cyC9H18B
25% cyC7H13
C5H9 C2H4
cyC6H11cyC8H14cyC6H10C6H10C7H13C3H7C4H6 C6H11 cyC6H9 cyC6H10OH
75%13% 45% 38% CH2CHO C3H5
94%C3H4O
Figure 5.43: Rate of production analysis of the propyl-benzene combustion mechanism. Initial temperature 1192 K. Pressure 27 bar. Calculated ignition delay 93 µs. Analysis shown at t=50 µs.
Similar to the paraffins the first naphthoxy radicals (A2CH2) are created in reactions with molecular oxygen and when concentrations of radicals O, OH, H, CH3 become significant, methylnaphthalene reacts with them. Then, either through formation of A2CHO or directly from A2CH2 the radical A−2 is produced. Further combustion proceeds through the destruc-tion of one cyclic ring in the A−2 molecule, formation of indene, C6H5O and its decomposition to C2H3 and CH3HCO. The result of the rate of production analysis of propyl-benzene (cyC9H18) combustion is shown on Fig. 5.43.
As expected at high temperatures the concentration of radicals is very sensitive to the rate constants of reactions H + O2 = OH + H and C2H4+ OH = C2H3+ H2O. Fig. 5.44 shows the sensitivity analysis for the H-atom at an initial temperature 1531.8 K, pressure 9.251 bar, φ=1, time 4.4·10−6 s, the calculated ignition delay time is 4.5·10−6 s. Similar dependence is observed for the consumption of the fuel molecules. Fig. 5.45 shows the sensitivity analysis made for the hexadecane at the same conditions as for the H-atom.
At low temperatures the combustion is mainly limited by the creation of the primary radicals. The concentration of H radicals is highly sensitive to the reactionsn−C16H32+OH = C16H33+H2O,n−C12H26+OH = C12H25+H2O, see Fig. 5.46. Also one of the reactions which produces radicals during low temperature combustion is 2OH(+M) = H2O2(+M). Under these conditions this reaction proceeds in the reverse direction. On the other side formation and dissociation of ketohydroperoxides has a large influence on the process. The production of the stable olefins in reactions of the type QOOH= olefin + HO2significantly slows down the ignition. This is reflected in the positive sensitivity of the concentration C16H34 to constants of the reactions C16H32OOH=C16H32+HO2 and C12H24OOH=C12H24+HO2, see Fig. 5.47.
H+O2<=>OH+O C2H4+OH<=>C2H3+H2O C3H5+O2=>C2H2+CH2O+OHC3H5+H(+M)<=>C3H6(+M)CH3+HO2<=>CH3O+OHC2H2+O2<=>CH2O+COCH3+HCO<=>CH4+COnC4H9<=>C2H4+C2H5HCO+M<=>H+CO+M C2H4+O2<=>CH2HCO+OHC3H8+OH<=>nC3H7+H2OCH2O+CH3<=>CH4+HCOO2+CH3<=>CH2O+OHO2+HCO<=>HO2+COnC4H9<=>CH3+C3H6OH+HO2<=>H2O+O2H+HO2<=>H2+O2 aC6H12<=>2C3H6 OH+HO2<=>H2O+O2 C5H10<=>C3H5+C2H5CH2O+H<=>HCO+H2 C7H15<=>C5H10+C2H5 C2H3+O2<=>CH2O+HCOCH2O+OH<=>HCO+H2O C3H6+O<=>C2H5+HCO aC6H12<=>nC3H7+C3H5 CH3+OH<=>CH2(S)+H2O aC6H12+OH<=>C4H8+C2H3+H2OC2H3+O2<=>CH2HCO+OC6H13<=>C3H6+nC3H7C6H13<=>C5H10+CH3H+HCO<=>CO+H2
-0,5 0,0 0,5 1,0 1,5 2,0
Sensitivity
Figure 5.44: Sensitivity analysis for the H atom. T=1531.8 K, p=9.251 bar,φ=1. Calculated ignition delay 4.5 µs. Analysis shown at t=4.4 µs.
H+O2<=>OH+O C3H5+O2=>C2H2+CH2O+OHNC16H34<=>C12H25+nC4H9C2H4+O2<=>CH2HCO+OHC3H5+H(+M)<=>C3H6(+M)C2H2+H(+M)<=>C2H3(+M)C3H8+OH<=>nC3H7+H2OCH2O+CH3<=>CH4+HCOC2H3+O2<=>CH2O+HCOC2H4+OH<=>C2H3+H2OaC6H12<=>nC3H7+C3H5CH3+HO2<=>CH3O+OHC2H2+O2<=>CH2O+COC7H15<=>C5H10+C2H5C6H13<=>C3H6+nC3H7CH3+HCO<=>CH4+COnC4H9<=>C2H4+C2H5C5H10<=>C3H5+C2H5C6H13<=>C5H10+CH3O2+CH3<=>CH2O+OHO2+HCO<=>HO2+COnC4H9<=>CH3+C3H6OH+HO2<=>H2O+O2OH+HO2<=>H2O+O2aC6H12<=>2C3H6H+HO2<=>H2+O2 aC6H12+OH<=>C4H8+C2H3+H2OC3H5+HO2<=>C2H3+CH2O+OHC2H3+O2<=>CH2HCO+OCH2O+OH<=>HCO+H2OC2H4+H<=>C2H3+H2HCO+M<=>H+CO+M
-140 -120 -100 -80 -60 -40 -20 0 20
Sensitivity
Figure 5.45: Sensitivity analysis for C16H34. T=1531.8 K, p=9.251 bar, φ=1.Calculated ignition delay 4.5 µs. Analysis shown at t=4.4 µs.
C16H32OOH<=>C16H32+HO2 C16H32OOH+O2<=>OOC16H32OOHcyC9H18+OH<=>cyC9H17E+H2ONC16H34+OH<=>C16H33+H2ONC12H26+OH<=>C12H25+H2OO2+C2H5<=>C2H4+HO22OH(+M)<=>H2O2(+M) C12H24OOH+O2<=>OOC12H24OOHNC16H34+HO2<=>C16H33+H2O2C12H24OOH<=>C12H24+HO2C2H5+HO2=>CH3+CH2O+OHC16H33<=>C8H17+iC8H16C16H33+O2=>C16H33O22HO2<=>H2O2+O2 OC16H31OOH=>CH2O+2aC6H12+C2H5+CO+OHC12H24OOH=>C7H15+C5H9O+OHNC16H34+C2H5<=>C16H33+C2H6aC6H12+OH<=>C4H8+C2H3+H2OcyC9H18+OH<=>cyC9H17B+H2OiC8H18+HO2<=>cC8H17+H2O2O2RO2H-32<=>ORO2H-32+OHCH3+C2H4(+M)<=>nC3H7(+M)C2H5+HO2<=>CH3CH2O+OHC3H5+O2=>C2H2+CH2O+OHiC8H18+OH<=>H2O+cC8H17C16H33O2<=>C16H32OOHcC8H17<=>C5H10+nC3H7C16H33O2=>C16H33+O2aC6H12<=>nC3H7+C3H5cC8H17<=>aC7H14+CH3CH2O+OH<=>HCO+H2O2HO2<=>H2O2+O2
-150 -100 -50 0 50 100 150
Sensitivity
Figure 5.46: Sensitivity analysis for the H atom. T=880 K, p=25 bar, φ=1. Calculated ignition delay 2350 µs. Analysis shown at t=2300µs.
C16H32OOH<=>C16H32+HO2 C16H32OOH+O2<=>OOC16H32OOHcyC9H18+OH<=>cyC9H17E+H2ONC16H34+OH<=>C16H33+H2ONC12H26+OH<=>C12H25+H2OO2+C2H5<=>C2H4+HO22OH(+M)<=>H2O2(+M) C12H24OOH+O2<=>OOC12H24OOHNC16H34+HO2<=>C16H33+H2O2C12H24OOH<=>C12H24+HO2C2H5+HO2=>CH3+CH2O+OHC16H33<=>C8H17+iC8H16C16H33+O2=>C16H33O22HO2<=>H2O2+O2 OC16H31OOH=>CH2O+2aC6H12+C2H5+CO+OHaC6H12+OH<=>C4H8+C2H3+H2OcyC9H18+OH<=>cyC9H17B+H2OC2H5+HO2<=>CH3CH2O+OHiC8H18+OH<=>H2O+cC8H17C16H33O2<=>C16H32OOHC16H33O2=>C16H33+O2aC6H12<=>nC3H7+C3H5CH2O+OH<=>HCO+H2O C3H5+O2=>C2H2+CH2O+OH iC8H18+HO2<=>cC8H17+H2O2 cC8H17<=>C5H10+nC3H7 CH3+C2H4(+M)<=>nC3H7(+M) C12H24OOH=>C7H15+C5H9O+OHNC16H34+C2H5<=>C16H33+C2H6O2RO2H-32<=>ORO2H-32+OHcC8H17<=>aC7H14+CH32HO2<=>H2O2+O2
-100 -50 0 50 100
Sensitivity
Figure 5.47: Sensitivity analysis for C16H34. T=880 K, p=25 bar, φ=1. Calculated ignition delay 2350 µs. Analysis shown at t=2300 µs.
The sensitivity analysis shows, that at low temperatures the reactions of hexadecane and dodecane are by far the most important. At high temperatures the most important reactions are reactions of the small hydrocarbons presented in the bottom part of the Fig. 5.41. Three other components of the model fuel have little to no influence on the ignition delay times at both high and low temperatures.
6 Automatic Reduction of the Surrogate Fuel Mecha-nism
The produced mechanism is too big for a direct implementation in CFD models. At present the limit on the size of the usable kinetic models for RANS is approximately 50 species.
Considering the constant growth of the computational power it seems to be reasonable to assume that it will be possible to use mechanisms containing 70-80 species in the next few years. For the automatic generation of the reduced model several programs are developed.
6.0.1 KINALC and MECHMOD
The software package KINALC [119] has several mathematical tools useful for mechanism reduction. CONNECT, a subroutine in KINALC, analyzes the effect of the concentration change for a particular species on the rate of production of the selected group of species at certain conditions. CONNECT can be used to determine the group of the most important or, on the contrary, redundant species. This analysis is based on the calculation of an importance index of the substances according to the equation (4.5) as described in subsection 4.5.
Another tool included in the KINALC package is the calculation of the importance of reactions RIMP. This analysis is based on the objective square function (4.8). Both tools will be described in detail in the next two subsections.
The reduced mechanism acquisition proceeds through four steps, which are shown in Fig.
6.1. Initially written by Slavinskaya et al. [120] the programs are further developed and improved. These programs use the KINALC and MECHMOD packages to automatically analyze and reduce the initial mechanism. One of the main improvements is the introduction
RedMaster-S
Model Analysis in time control points, parameter control points.
Species elimination.
Skeletal Mechanism Full Mechanism
RedMaster-R
Model Analysis in time control points, in parameter control points.
Reaction elimination.
Figure 6.1: Mechanism reduction strategy.
of the user defined time points for analysis as fraction of the ignition delay of the corre-sponding experiment, i.e. 0.00001τign, 0.001τign, 0.01τign, 0.001τign and 0.5τign. Taking into consideration different timescales allows a significantly higher reduction with lower deviation of ignition delays from the original mechanism.
6.0.2 RedMaster-R
The program automatically performs ignition-delay calculations with the CHEMKIN II pack-age for selected experimental data. It stores the results in the output file. For the mechanism reduction it reads the output CHEMKIN II files, selects automatically the time points and produces input files for the analysis of the unimportant reactions in the KINALC package.
Then, it selects unimportant reactions common for all chosen time points in each simulation.
After accumulation of the information about all unimportant reactions for all selected exper-imental data it removes the common unimportant reactions simultaneously for all simulated processes. The flow chart of the program is shown in Fig. 6.2.
As input the user provides in the programs directory the kinetic mechanism file, the ther-modynamical data file, the file with the list of experiments and the program control file.
Input Data RedMaster-R
control file
KINALC, RIMP analysis
Delete them from mechanism Choose unimportant reactions common for all tested experiments
and time point
yes All
experiments are tested?
All timepoints are
tested?
no
Take next time point Take next experimental point
no
yes
Save results
Figure 6.2: The flow chart of the RedMaster-R program.
The file with the list of experiments contains all data necessary for ignition delay calcula-tion: temperature, pressure and mixture composition. The program control file contains the numbers of experiments which should be used for the further analysis, calculation data for the Chemkin II package (relative and absolute error, calculation time) and parameters for the unimportant reactions analysis (number of time points at which the analysis is made before and after the autoignition, and reaction importance index TREAC which defines the limit of “unimportance” of reactions. All reactions with TREAC less than a defined value are considered as unimportant.). As output the user obtains the file with calculated ignition delays and a reduced mechanism.
A similar analysis and mechanism reduction can be made for the calculation of flame velocity (1-D flame) or for a mixed calculation of both ignition delays and flames. In this case the user defines a number of x-coordinates, at which the KINALC analysis should be performed. The program automatically defines these points and performs a KINALC analysis.
Since the calculation of 1D flames can be complicated and often needs several attempts with parameter adjustments, the user must provide output files of successful calculations prior to starting the RedMaster-R.
Input data RedMaster-S
control file
KINALC, CONNECT
analysis
Delete them from the mechanism
Choose unimportant species common
for all tested experiments and
time point
All species in the list?
Add new species to the bottom of
list of important
species
no
yes All
experimets are tested?
All timepoints are
tested?
no
Take next time point Take next experimental point
no
yes
yes
Save results
Figure 6.3: The flow chart of the RedMaster-R program.
6.0.3 RedMaster-S
Similar to RedMaster-R the program automatically performs ignition-delay calculations with the CHEMKIN package for selected experimental data. It reads the output CHEMKIN files and selects automatically the time points and produces input files for a CONNECT analysis in the KINALC package as described in subsection 6.0.1. The user defines an initial group of important species (i.e. fuel components). The program finds the species most “connected”
to this group and adds them to the bottom of the initial group of species (list of species). It repeats the iterations until all species are in the list. The final list contains species according to their importance (their connection to the initial group) - most important species on the top, least important species in the bottom part of the list. Then the program produces similar lists for other timepoints and experiments. Then it compares bottom portion of the lists and chooses unimportant species - the species common simultaneously for all collected lists. The bottom portion of the list, which is used in that comparison is a user defined parameter. Then the program removes unimportant species and their reactions from the mechanism. The flow chart of the program is shown in Fig. 6.3.
Similar to RedMaster-R, as input the user provides the kinetic mechanism file, the ther-modynamical data file, the file with the list of experiments, and program control file. The file with the list of experiments contains all data necessary for ignition delay calculation: temper-ature, pressure, and mixture composition. The program control file contains the number of experiments which should be used for the further analysis, calculation data for the Chemkin II package (relative and absolute error, calculation time) and parameters for the unimportant reactions analysis (number of time points at which the analysis is made before and after the autoignition; the initial group of species; theportion of the list of connected species which is taken as unimportant). As output the user gets the file with calculated ignition delays and a reduced mechanism.