Temperature (K) (sec)algobiochem.ntua.gr/Publications/Poster_Budapest_Manias.pdfDimitris M. Manias,...
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Algorithmic identification of the reactions that support or oppose the autoignition of n-heptane/air Dimitris M. Manias, Efstathios Al. Tingas and Dimitris A. Goussis Department of Mechanics, School of Applied Mathematics and Physical Sciences National Technical University of Athens Introduction The dynamics of two-stage autoignition of a homogeneous n-heptane/air mixture is analyzed algorithmically, using tools of the Computational Sin- gular Perturbation (CSP) method. Due to the fast/slow character of this reactive system its dymanics are dominated by the components of the sys- tem that generate explosive scales, which tend to lead the system away from equilibrium [1,2]. The reactions that are responsible for the genera- tion of these time scales and the species that relate with these scales are identified with CSP-tools. The Physical Problem We consider adiabatic autoignition at constant volume of a homogeneous stoichiometric n-heptane/air mixture. The governing equations for the species mass fraction and temperature are: d y dt = 1 ρ W · 2K X k=1 S k R k (1) dT dt = 1 ρc v (-h c · W + RT U) · 2K X k=1 S k R k (2) 10 -2 10 0 10 2 p 0 (atm) 10 -4 10 0 10 4 t ign (sec) p = 30 atm T = 800 K 0 0 Figure 1: Ignition delay time as a function of p o at T o = 800 K. The black bullet indicates the case that will be analyzed. The ignition delays for a wide range of initial pressures p o at T o =800K are shown in Fig 1. The two-stage autoignition occurs in the range of 1 - 100 atm. An extensive analysis of the dynamics of the two-stage ignition of n-heptane for skeletal mechanisms in this region was con- ducted by Peters et al. [3]. A detailed analysis will be performed for the case of p o = 30 atm and T o = 800 K. CSP tools will be employed in order to identify the reactions that generate the explosive time scale τ e,f , the magnitude of which approximates t ign ; i.e. t ign = O(τ e,f ) [4]. An elementary study of the influence of the fast explosive time scale for the two-stage ignition of n-heptane was conducted by Diamantis et al. [5]. Autoignition Dynamics of n-heptane/air Mixture Shown in Fig. 2 are the explosive timescales, τ e ’s, that develop during the autoignition of a stoichiometric n-heptane/air mixture in the case T o = 800 K, p o = 30 atm, along with the temperature profile. 0 10 -6 10 0 10 6 10 12 3000 P 1 P 2 P 3 Temperature (K) time (sec) τ e (sec) 0.0008 0.0006 0.0004 0.0002 2000 1000 τ e,f 0.000796 time (sec) 10 -6 10 -4 τ e (sec) 3000 Temperature (K) P 3 0.000792 2000 τ e,f τ e,s Figure 2: The evolution of the developing explosive timescales. τ e , (red line) and temperature (black line) as a function of time: P o = 30 atm, T o = 800 K and φ = 1. The reactions that generate τ e,f and the variables that are most related to τ e,f will be identified at three points: I P 1 : the initiation of the process I P 2 : right after the first stage I P 3 : right before the explosive stage,where τ e,f gets minimum as shown in Fig. 2. The CSP tools that will be employed are the Time Scale Participation In- dex (TPI) and the CSP Pointer; the first measures the relative contribution of each reaction to τ e,f , while the second measures the relation of each variable to τ e,f . Analysis of the Fast Explosive Mode Values of TPI and Pointer are reported next at the three points during the autoignition process, as indicated by solid black bullets in Fig. 2. C7H15O2-2 => C7H14OOH2-4 C7H15O2-3 => C7H14OOH3-5 C7H15O2-4 => C7H14OOH4-2 C7H15O2-1 => C7H14OOH1-3 C7H14OOH1-3O2 => NC7KET13+OH C7H14OOH2-4O2 => NC7KET24+OH C7H14OOH3-5O2 => NC7KET35+OH 0 0.04 0.08 TPI H2O2(+M) => OH+OH(+M) C2H3+O2 => CH2CHO+O C2H5+HO2 => C2H5O+OH H2O2+O2 <= HO2+HO2 CH2O+OH => HCO+H2O C2H5+O2 => C2H4+HO2 C2H3+O2 => CH2O+HCO -0.05 0 0.05 0.1 TPI H+O2 => O+OH CO+OH => CO2+H OH+H2 => H+H2O H2O2+OH <= H2O+HO2 OH+H2 <= H+H2O H2O2+OH => H2O+HO2 H2O+M <= H+OH+M 0 0.1 0.2 TPI C7H15O2-2 C7H15O2-3 C7H14OOH1-3O2 C7H15O2-1 C7H15O2-4 C7H14OOH2-4O2 C7H14OOH3-5O2 0 0.05 0.1 0.15 Pointer T NC7H16 H2O2 C2H3CHO NC3H7COCH2 C3H6 C2H4 0 0.5 1 Pointer T OH O2 H O C2H2 CO2 0 0.4 0.8 Pointer Figure 3: Top: the reactions with the largest Time scale Participation Indices (TPI). Bottom: the species with the largest CSP Pointers at the three selected points. 1000 2000 3000 0 0.0004 0.0008 10 -15 10 -10 10 -5 y i nC7H16 RO2 QOOH NC7KET-iso Temperature (K) time (sec) 1000 2000 3000 Temperature (K) 0 0.0004 0.0008 time (sec) 10 -15 10 -10 10 -5 CH2O C2H4 C2H3CHO CH3 y i 1000 2000 3000 0 0.0004 0.0008 10 -15 10 -10 10 -5 OH H Temperature (K) time (sec) y i Figure 4: The evolution with time of the temperature and of selected species’ mass fraction during the homogeneous autoignition process. The groups of species’ mass fractions where selected according to the TPI and Pointer results and represent all the stages of the process. p 0 = 30 atm, T 0 = 800 K and φ = 1. At t = 0(P 1 ), it is shown that the major contributors to the generation of τ e,f are: I intramolecular isomerization reactions of RO 2 to QOOH and I reactions of peroxyalkylhydrope- roxides (QOOH - O 2 ) forming ketohyperoxides and OH (R: C n H 2n+1 and Q: C n H 2n groups). The reactions that oppose the generation of τ e,f at t = 0 are dissociation reactions of RO 2 that lead to the formation of Q and HO 2 . When τ e,f re-appears (right before P 2 ), it is generated mainly by the chain branching reaction H 2 O 2 (+M ) → OH + OH (+M ). Since at point P 2 the temperature has already risen around 200 K and keeps rising, it can be con- cluded that this point lies in the thermal runway regime, in agreement with the Pointer which identifies the tempera- ture as the variable related the most to τ e,f . In the vicinity of point P 3 , the highly exothermic H 2 /O 2 -chemistry is domi- nating the generation of τ e,f . Conclusions I As the process evolves, the nature of the reactions related to the characteristic explosive time scale evolves as well. I In the period that leads to the first stage, the reactions promoting τ e,f are heptane isomerization reactions, such as intramolecular isomerization reactions of RO 2 isomers to QOOH isomers and reactions of peroxyalkylhydroperoxides (QOOH - O 2 ) forming ketohyperoxides. I During the second stage, τ e,f is characterized by reactions that relate to the hydrogen chemistry. References [1] Goussis D and Skevis G, Computational Fluid and Solid Mechanics ed Bathe K J, 650 - 653, 2005 [2] Goussis D A and Najm H N, SIAM Multiscale Modeling and Simulations, 5 1297 - 1332, 2006 [3] Peters N, Paczko G, Seiser R and Seshadri K,Combustion and Flame, 128 38 - 59, 2002 [4] Diamantis D J, Kyritsis D C and Goussis D A, Proc. Combustion Institute, 35 267-274, 2015 [5] Diamantis D J, Kyritsis D C and Goussis D A, 2nd Intl. Conference in Model Reduction in Reacting Flows, 2009 Acknowledgments The work of DMM and DAG has been supported by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: “ARISTEIA” 2012-2015. http://www.ecm2015.hu http://algobiochem.ntua.gr
Transcript of Temperature (K) (sec)algobiochem.ntua.gr/Publications/Poster_Budapest_Manias.pdfDimitris M. Manias,...
Algorithmic identification of the reactions that support oroppose the autoignition of n-heptane/air
Dimitris M. Manias, Efstathios Al. Tingas and Dimitris A. GoussisDepartment of Mechanics, School of Applied Mathematics and Physical Sciences National Technical University of Athens
2015GNITEEMNOITSUBMOC
E U R O P E A N
IntroductionThe dynamics of two-stage autoignition of a homogeneous n-heptane/airmixture is analyzed algorithmically, using tools of the Computational Sin-gular Perturbation (CSP) method. Due to the fast/slow character of thisreactive system its dymanics are dominated by the components of the sys-tem that generate explosive scales, which tend to lead the system awayfrom equilibrium [1,2]. The reactions that are responsible for the genera-tion of these time scales and the species that relate with these scales areidentified with CSP-tools.
The Physical ProblemWe consider adiabatic autoignition at constant volume of a homogeneousstoichiometric n-heptane/air mixture. The governing equations for thespecies mass fraction and temperature are:
dydt
=1ρ
W ·2K∑k=1
SkRk (1)
dTdt
=1ρcv
(−hc ·W + RTU) ·2K∑k=1
SkRk (2)
10-2
100
102
p0
(atm)
10-4
100
104
t ign
(sec
)
p = 30 atm
T = 800 K0
0
Figure 1: Ignition delay time as a function of po at To = 800K. The black bullet indicates the case that will be analyzed.
The ignition delays for a wide rangeof initial pressures po at To=800Kare shown in Fig 1. The two-stageautoignition occurs in the range of1 − 100 atm. An extensive analysisof the dynamics of the two-stageignition of n-heptane for skeletalmechanisms in this region was con-ducted by Peters et al. [3].A detailed analysis will be performedfor the case of po = 30 atm and To =
800 K. CSP tools will be employed in order to identify the reactions thatgenerate the explosive time scale τe,f , the magnitude of which approximatestign; i.e. tign = O(τe,f ) [4]. An elementary study of the influence of the fastexplosive time scale for the two-stage ignition of n-heptane was conductedby Diamantis et al. [5].
Autoignition Dynamics of n-heptane/air MixtureShown in Fig. 2 are the explosive timescales, τe’s, that develop during theautoignition of a stoichiometric n-heptane/air mixture in the case To = 800K, po = 30 atm, along with the temperature profile.
010-6
100
106
1012 3000
P1P2
P3
Temperature(K)
time (sec)
τ e(sec)
0.00080.00060.00040.0002
2000
1000
τe,f
0.000796time (sec)
10-6
10-4
τ e(sec)
3000
Temperature(K)
P30.000792
2000
τe,f
τe,s
Figure 2: The evolution of the developing explosive timescales. τe, (red line) and temperature (black line) as a function of time:Po = 30 atm, To = 800 K and φ = 1.
The reactions that generate τe,f and the variables that are most related toτe,f will be identified at three points:
I P1: the initiation of the processI P2: right after the first stageI P3: right before the explosive stage,where τe,f gets minimum
as shown in Fig. 2.The CSP tools that will be employed are the Time Scale Participation In-
dex (TPI) and the CSP Pointer; the first measures the relative contributionof each reaction to τe,f , while the second measures the relation of eachvariable to τe,f .
Analysis of the Fast Explosive ModeValues of TPI and Pointer are reported next at the three points during theautoignition process, as indicated by solid black bullets in Fig. 2.
C7H15O2-2 => C7H14OOH2-4
C7H15O2-3 => C7H14OOH3-5
C7H15O2-4 => C7H14OOH4-2
C7H15O2-1 => C7H14OOH1-3
C7H14OOH1-3O2 => NC7KET13+OH
C7H14OOH2-4O2 => NC7KET24+OH
C7H14OOH3-5O2 => NC7KET35+OH
0 0.04 0.08TPI
H2O2(+M) => OH+OH(+M)
C2H3+O2 => CH2CHO+O
C2H5+HO2 => C2H5O+OH
H2O2+O2 <= HO2+HO2
CH2O+OH => HCO+H2O
C2H5+O2 => C2H4+HO2
C2H3+O2 => CH2O+HCO
-0.05 0 0.05 0.1
TPI
H+O2 => O+OH
CO+OH => CO2+H
OH+H2 => H+H2O
H2O2+OH <= H2O+HO2
OH+H2 <= H+H2O
H2O2+OH => H2O+HO2
H2O+M <= H+OH+M
0 0.1 0.2
TPI
C7H15O2-2C7H15O2-3
C7H14OOH1-3O2C7H15O2-1C7H15O2-4
C7H14OOH2-4O2C7H14OOH3-5O2
0 0.05 0.1 0.15
Pointer
TNC7H16H2O2
C2H3CHONC3H7COCH2
C3H6C2H4
0 0.5 1
Pointer
TOHO2
HO
C2H2CO2
0 0.4 0.8
PointerFigure 3: Top: the reactions with the largest Time scale Participation Indices (TPI). Bottom: the species with the largest CSPPointers at the three selected points.
1000
2000
3000
0 0.0004 0.000810-15
10-10
10-5
yi
nC7H16RO2QOOHNC7KET-iso
Temperature(K)
time (sec)
1000
2000
3000
Temperature(K)
0 0.0004 0.0008
time (sec)10-15
10-10
10-5
CH2OC2H4C2H3CHOCH3
yi
1000
2000
3000
0 0.0004 0.000810-15
10-10
10-5
OHH
Temperature(K)
time (sec)
yi
Figure 4: The evolution with time of the temperature andof selected species’ mass fraction during the homogeneousautoignition process. The groups of species’ massfractions where selected according to the TPI and Pointerresults and represent all the stages of the process. p0 = 30atm, T0 = 800 K and φ = 1.
At t = 0 (P1), it is shown that the majorcontributors to the generation of τe,f are:
I intramolecular isomerizationreactions of RO2 to QOOH and
I reactions of peroxyalkylhydrope-roxides (QOOH − O2)forming ketohyperoxides and OH
(R: CnH2n+1 and Q: CnH2n groups).The reactions that oppose the generationof τe,f at t = 0 are dissociation reactionsof RO2 that lead to the formation of Q andHO2.
When τe,f re-appears (right beforeP2), it is generated mainly by thechain branching reaction H2O2(+M) →OH + OH(+M). Since at point P2 thetemperature has already risen around200 K and keeps rising, it can be con-cluded that this point lies in the thermalrunway regime, in agreement with thePointer which identifies the tempera-ture as the variable related the most toτe,f .
In the vicinity of point P3, the highly exothermic H2/O2-chemistry is domi-nating the generation of τe,f .
ConclusionsI As the process evolves, the nature of the reactions related to the
characteristic explosive time scale evolves as well.I In the period that leads to the first stage, the reactions promoting τe,f are
heptane isomerization reactions, such as intramolecular isomerizationreactions of RO2 isomers to QOOH isomers and reactions ofperoxyalkylhydroperoxides (QOOH − O2) forming ketohyperoxides.
I During the second stage, τe,f is characterized by reactions that relate tothe hydrogen chemistry.
References[1] Goussis D and Skevis G, Computational Fluid and Solid Mechanics ed Bathe K J,
650 - 653, 2005[2] Goussis D A and Najm H N, SIAM Multiscale Modeling and Simulations, 5
1297 - 1332, 2006[3] Peters N, Paczko G, Seiser R and Seshadri K,Combustion and Flame, 128 38 - 59, 2002[4] Diamantis D J, Kyritsis D C and Goussis D A, Proc. Combustion Institute, 35
267-274, 2015[5] Diamantis D J, Kyritsis D C and Goussis D A, 2nd Intl. Conference in Model
Reduction in Reacting Flows, 2009
Acknowledgments
The work of DMM and DAG has been supported by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education andLifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: “ARISTEIA” 2012-2015.
http://www.ecm2015.hu http://algobiochem.ntua.gr
