COMPUTATIONALLY EFFICIENT MODELING OF HYDROCARBON ... · Air, final combustion products Light...
Transcript of COMPUTATIONALLY EFFICIENT MODELING OF HYDROCARBON ... · Air, final combustion products Light...
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COMPUTATIONALLY EFFICIENT MODELING OF HYDROCARBON OXIDATION CHEMISTRY
AND FLAMES USING CONSTITUENTS AND SPECIES
K. G. Harstad* and J. Bellan*,**
*Jet Propulsion Laboratory, California Institute of Technology,Pasadena, CA 90019-8099
**Mechanical Engineering Dept., California Institute of Technology,Pasadena, CA 91125
MACCCR Fuels SummitArgonne National Laboratories
September 20-23, 2011
Sponsored by the Army Research Office under the direction of Dr. Ralph Anthenien
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Outline• Background
• Concept description for chemical kinetics in a constant-volume perfectly stirred reactor
• Fuel pyrolysis in the presence of nitrogen (non-premixed flames)
• Flame model• Premixed• Non-premixed
• Results
• Summary and conclusions
• Future work
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Background
• Necessity to reduce the computational cost of chemistry in simulations of turbulent combustion
• None of the existing chemistry reduction schemes is considered the ultimate solution to the problem of chemical kinetic reduction
• Novel methods of reduction are still sought
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Chemical kinetics: The concept of a base
Species list
Light (we do not decompose) Heavy (we decompose)
Air, final combustionproducts
Light radicals/molecules(e.g. CH3, CH4, H2O2)
Radicals Stable
Constituents
The base = Light species + Constituents(26) (13)
For general alkane or alkene with air:
Remove NOx, C, C2, and N at this preliminary stage, and then,
The base = Light species + Constituents + N2(20) (13) (null rates)
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Kinetic model summary, 1 of 2
∙ n-heptane: 13 constituents, CH2, CH3, CH, C2H3, C2H2, C2, HC2, CO (keto), HCO, HO, HO2, OO, O
N c ≡ ∑ k113 N k
∙ iso-octane, PRF fuels, mixtures of iso-octane and n-pentane or iso-hexane: 14 constituents (C atom added)
N c ≡ ∑ k114 N k
∙ other aspects of the modelN ∗ ≡ Nn2
Nref
≡ T−T0T r,N∗
T r ≡ 2065N ∗0.06 w
w 1.51.3110.711.1 2
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Kinetic model summary, 2 of 2
R i ≡ dNi
dt reac dNi
dt heavies dN i
dt lights
dNi
dt heavies N cKG i − X iKL i
N cC p ,h ∑ i∈lights C p ,iN idTdt
−∑ i∈lights h iR i N cRu T refK h
C p ,h ≡∑ l∈heavies Cp,lN l
Nc
K h ≡ − ∑ l∈heavies h lR l1
R u TrefNc
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Findings from the kinetic model1. Nc exhibits a self-similarity with respect to θ, modulo T0 (600-1200 K), for a wide range of p0 (5-50 bar) and (1/4 to 4)
2. In the cold ignition regime (600-900 K), the self-similarity is independent of T0
3. The molar densities of O2 and H2O exhibit a quasi-linear behavior versus θ
4. Eleven species progress variables: the unsteady light species
5. The capability of the model was assessed from the viewpoints of predicting species, the temperature evolution and the ignition time.
- The species prediction was excellent in all cases, with the exception of the multivalued regions occurring for very rich situations.
- The temperature values were excellently to very well predicted, except for the temperature decrease from the maximum observed for rich mixtures.
- The ignition times were reproduced within percentages of those computed with the full mechanism.
6. The above evaluation was valid for all single fuels and mixtures considered.
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Fuel pyrolysis in counterflow diffusion flames
Non-premixed model- air jet counterflow to fuel/nitrogen jet- need estimate of fuel pyrolysis before mixing with air occurs- calculations performed using LLNL rates with Chemkin II
Results- rates minimal for T ≤ 900 K (≤ 1 s-1)- only 3 light species (H2, CH4, C2H4) are produced having mole fractions
as large as O(10-2); all other mole fractions are much smaller- a single rate form describes the rates of these species
N i N c K i, K i ai 1012 ′0.37 exp−Tp /T
• Tp= 2.9×104 K is the characteristic pyrolysis temperature• ’ is an effective equivalence ratio (air replaced by N2)• aH2,CH4 ≐ 0.35 + 4.25 woct – 2.7 (woct)2 0 ≤ woct ≤ 1 is the octane fraction in the PRF• aC2H4 ≐ 0.78 + 3.9 woct – 4.6 (woct)2
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Interpolation procedure for the rate functions
The reduced rate functions have the general form
where Tm and m are the temperature and at the initial fuel/air mixing; K is in s-1.
-Tables are generated numerically at fixed m and Tm.-The K rates are found by numerical interpolation. Detailed comparisons with the LLNL rates shows that this local interpolation isaccurate using
where s and T* are interpolation parameters.e.g.: s = (ln K2 – ln K1)/(ln m2 – ln m1 )
K f,m , T m , T − T m /T r, T r T rm , N N2
K Kf ms exp−T∗/T
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Flame model, 1 of 3
v r∙
McontinuityR 3
dRdx
momentum ≐ 1 − 1 − L 0
x0 x≠x a
dx / 0
L0 x≠x a
dx x ≡ R0 /Rx
species Ji Ji,light Ji,heavy
J i,light −n X iDT,id ln T
dx∑
j
D ijdXj
dx
J i,heavy −n∑l
D ildX l
dx≡ JH,i
k ∈ ensemble C
l ∈ ensemble H
i, j ∈ ensemble L
JH,i ≐ −nDH,id ln C ave
dx
DH,i ≡ 1n ∑
l
D ilN l ∑l
D ilX l X HD iH
C ave ≡ Ncn ∑
k,l
C klX l
A.
B. 2 1 − k 0x x ′ x
′0
x ′dx ′k determined by BCs; =1 outside the flame; is a cst, model parameter inside the flame chosen to minimize the residue to the momentum eqn.
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Flame model, 2 of 3
species Ji −n ∑j
D ijdX j
dx X HD iH
d ln Cave
dx X iDT,i
d ln Tdx
i and j to the unsteady light species and q to the quasi-steady light species
X u 1 − X H − ∑q
X q m X u
∑i
Yim i
D ia ≡ 1
X u∑
j
D ijX j .
Ji −n ∑j
D ij − D ia m
m j
dY j
dx BT,i
e dTdx
BT,ie ≡ X i
D T,i
T ∑q
D iq − Dia X q
T X HD iHln Cave
T − D ia X H
T
dY i
dx A
∙M
m iR i − ddx
A∙
Mm iJi
R i R i | lights R i |heavies R i |heavies N cK net,i
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Flame model, 3 of 3
energy q ≐ − dTdx− ∑
i
m im H
hH − hi Ji hH 1/X H∑ l X lh l
Cpm
dTdx
ddx
A∙
M dT
dx− A
∙M
dTdx ∑
i
Cp,im i− Cp,H
m Hm iJi ∑
i
h iR i − RuTrefN cK H
equation of state
p Ru Tv PR − bm ix
− am ix
v PR2 2bm ixv PR − bm ix
2
am ix ∑ p ∑ n X p X n apn T bm ix ∑ p X p bp
apn 1 − k ′ pp nn bp 0. 077796
Ru T C,ppC,p
pp T ≡ 0. 457236Ru T C,p 2 1 cp 1 − T red ,p 2/pC,p
cp 0. 37464 1. 54226p − 0. 26992p2
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Computation of Tm and m for non-premixed flames
• The original reduced rate model is based on premixed flow situations where the initial temperature and correspond to the fuel/air being completely mixed.
• For non-premixed situations, mixing occurs continuously through diffusion along fluid paths: the temperature and at which mixing occurs vary according to location.
• An assumption is made that mixing occurs continuously (no ‘puffs’) along the fluid path. This is valid for many, if not most, situations.
• Based on this view, the local mean ‘mixing temperature and ’ are estimated through
T m T T 0 /2
where T0 is the temperature at the first location where either there is non-negligible fuel in the air or non negligible air in the fuel. T0 is a constant for either side of the flow.
• At the location having temperature T the rates correspond to those computed from the tables using the local values of m, θ computed using Tm and m, and Tm.
Lean : m /2; Rich : m 2
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Transport coefficients
• Mass diffusion– need the full matrix of pairwise diffusion coefficients– base the pairwise diffusion coefficients on binary diffusion
coefficient models (Harstad & Bellan 2004a) and all-pressure mixing rules (Harstad & Bellan 2004b)
• Thermal conductivity for the mixture– model from Reid et al.
• Thermal diffusion ratios– based on the all-pressure model of Harstad & Bellan 2004b
• Inviscid fluid: – in principle the viscosity is not needed– in fact it is needed for the modeling of the thermal
conductivity
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Premixed and diffusion flames
• Premixed flames– Version A of momentum equation, large Pé (valid
outside but not throughout the flame); study the influence of diffusion for constant area flow
– Version B of momentum equation, general Pévalues (needed to compute through the flame peak)
• Counterflow diffusion flame– Version B of momentum equation, general Pé
values
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Premixed flames, large Pé
• Defined two parameters
• Based on a large Péclet number approach, i.e. convection dominates diffusion
• The equations are solved using a stiff integrator
i ≡ −m iJi/u0
i′ ≡ − i/Yi uD,i/u0
| i′ | 1
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Initial conditions
• 90% iso-octane and 10% n-heptane• 50% iso-octane and 50% n-heptane• = 1• (ρu)0=0.8 g/(cm2 s)• T0 prescribed• p0 prescribed• Constant area situation
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Premixed flame, large Pé; 1 of 5
90/10; p0 = 30 bar, T0 = 800 K; no diffusion
x (cm)
Nc
(mol
/m3 )
0 0.1 0.2 0.3 0.4 0.5 0.605
1015202530354045505560
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
x (cm)
T(K
)
0 0.1 0.2 0.3 0.4 0.5 0.6
800
1200
1600
2000
2400
2800
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
x (cm)
Noh
(mol
/m3 )
0 0.1 0.2 0.3 0.4 0.5 0.60
0.2
0.4
0.6
0.8
1
1.2
1.4
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
x (cm)
No2
(mol
/m3 )
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
80
90
100
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4x (cm)
0
5
10
15
20
25
Nh2
o(m
ol/m
)3
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
x (cm)
Nco
2(m
ol/m
3 )
0 0.1 0.2 0.3 0.4 0.5 0.60
2
4
6
8
10
12
14
16
18
20
22
p0 = 30 barT0 = 800 Kφ = 1
(Rates only)
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Premixed flame, large Pé; 2 of 590/10; p0 = 30 bar, T0 = 800 K; with diffusion
x (cm)
Nc
(mol
/m3 )
0 0.1 0.2 0.3 0.40
10
20
30
40
50
60
p0 = 30 barT0 = 800 Kφ = 1
x (cm)
T(K
)
0 0.1 0.2 0.3 0.4600
800
1000
1200
1400
1600
1800
2000p0 = 30 barT0 = 800 Kφ = 1
x (cm)
Noh
(mol
/m)3
0 0.1 0.2 0.3 0.40
0.02
0.04
p0 = 30 barT0 = 800 Kφ = 1
x (cm)
No2
(mol
/m3 )
0 0.1 0.2 0.3 0.40
10
20
30
40
50
60
70
80
90
100
p0 = 30 barT0 = 800 Kφ = 1
x (cm)
Nh2
o(m
ol/m
3 )
0 0.1 0.2 0.3 0.40
1
2
3
4
5
6
7
8
9
10
p0 = 30 barT0 = 800 Kφ = 1
x (cm)
Nco
2(m
ol/m
3 )
0 0.1 0.2 0.3 0.40
0.5
1
1.5
2
2.5
p0 = 30 barT0 = 800 Kφ = 1
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Premixed flame, large Pé; 3 of 5
600 700 800 900T0 (K)
0
2
4
6
8
10
12
x fs(c
m)
p0 = 20p0 = 30p0 = 40
p0 in bar, T0 in K
90/10xfs is that at T0+900K
600 700 800 900T0 (K)
100
101
x fs(c
m)
p0 = 20p0 = 30p0 = 40
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Premixed flame, large Pé; 4 of 5
600 700 800 900T0 (K)
50
60
70
80
90
100
110
120
130
140
150U
fs(c
m/s
)p0 = 20p0 = 30p0 = 40
90/10=1
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Premixed flame, large Pé; 5 of 5
50/50
600 700 800 900T0 (K)
10-1
100
x fs(c
m)
p0 = 30
Heptane/Octane=50%/50%
600 700 800 900T0 (K)
60
70
80
90
100
110
120
Ufs
(cm
/s)
p0 = 30
Heptane/Octane=50%/50%
=1
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Premixed flame; general Pé
0 0.1 0.2 0.3 0.4 0.5 0.6X (cm)
30040050060070080090010001100120013001400150016001700180019002000
T(K
)
0
20
40
60
80
100
120
140
160
180
200
220
240
U(c
m/s
)
Ji. C. et al., “Propagation and extinction of premixed C5-C12 n-alkane flames”, Combust. Flame, 157, 277-287, 2010.
The experimental profiles were stated to be for C5-C8 n-alkanes (unburned temperature: 353K), and n-heptane was used .
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Counterflow flame: computation feasibility
0.5 0.75 1 1.25x/L
0
200
400
600
800
1000
1200
1400
1600
1800
2000
T(K
)
0.5 0.75 1 1.25x/L
0
0.05
0.1
0.15
0.2
0.25
Y
Oxygen
Fuel
p = 1 bar, Tjet = 350 K, (ρu)air-jet = 4.8 ×10-2 g/cm2, (ρu)fuel-jet = 4.85 ×10-2 g/cm2, L = 2 cm(ρuYF)fuel-jet / (ρuYO2)air-jet = s
u (@max R) = 56 cm/s
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Summary and conclusions, 1 of 2
• Developed a model of steady quasi-1D flame with variable area, including– Full mass-diffusion coefficient matrix– Thermal diffusion factors– Mixture thermal conductivity– Real-gas EOS
• Preliminary results obtained for premixed flames and constant area flow show that the predictions are qualitatively correct– Ufs varies with the inverse of a power of pressure – The position of the flame initiation depends on T0
– The position of the flame initiation depends of the initial pressure over the entire T0 regime
– Increasing the % heptane in the PRF results in larger Ufs
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Summary and conclusions, 2 of 2
• Limited results were obtained for premixed flow with variable area– Results compare well with experimental data
• The model has been extended to non-premixed flow– Preliminary results are qualitatively correct.– The numerics must be improved as stability problems are still
preventing routine computations and comparisons with experiments.
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Future work
• Solidify the numerical method to enable routine computations
• Investigate whether the same constituents-and-species concept holds for higher alkanes and cycloalkanes