Numerical simulation and parametric sensitivity
study of particle size distributions in a
burner-stabilised stagnation flame
Edward K. Y. Yapp1 , Dongping Chen1 , Jethro Akroyd1 ,
Sebastian Mosbach1 , Markus Kraft1,2 , Joaquin Camacho3 , Hai
Wang3
1 Department
of Chemical Engineering and Biotechnology
University of Cambridge
2 School
of Chemical and Biomedical Engineering
Nanyang Technological University
3 Department
of Mechanical Engineering
Stanford University
3rd July 2015
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Objectives
1
Model soot formation for the burner-stabilised stagnation
flame configuration
2
Perform a parametric sensitivity study
3
Characterise various aspects of soot morphology
4
Discuss implications on mobility sizing experiments
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Burner-stabilised stagnation flame
Stagnation plate/sample probe (Ts)
z
u
vr
Hp
r
Burner (Tb)
• Sample probe integrated into plate1
• Removes need to carry out arbitrary “time or spatial shifting”
1
Abid et al. Combust. Flame, 156 (2009) 1862–1870.
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Experimental conditions
Stagnation plate separation, Hp (cm)
Fuel composition (mol%)
Velocity (STP) (cm/s)
Equivalence ratio (-)
Burner temperature, Tb (K)
Values
0.55, 0.6, 0.7, 0.8, 1.0, 1.2
16.3 C2 H2 , 23.7 O2, 60 Ar
8
2.07
473
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Computational method
Experimental conditions
Mechanism, thermodynamic and transport data
Oppdif
Pre-processing
Temperature
Species
Detailed population balance model
PSDs
Fringe length distributions
TEMs
Post-processing
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Particle representation
Aggregate
Primary particle
PAH
• Connectivity matrix
• Common surface area
• Sintering level
• PAHs rigidly stick
• Edge carbon atoms
• Fringe length
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A; BÞ ¼
K sf ðA; BÞ þ K fm ðA; BÞ
ð4Þ
Particle processes
ere A and B represent particles or PAHs. A and
re particles for a coagulation process, A and B
x ¼ ðq; s; gÞ:
The optimisation consists of two c
steps: a low discrepancy series method
by a quadratic response surface optimi
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Model parameters
(1) Minimum particle inception size
(number of carbon atoms)
(2) Soot density, ρ (gcm−3 )
(3) Smoothing factor, s (-)
(4) Growth factor, g (-)
(5) Critical number of PAHs in a primary
particle before g is applied, ncrit (-)
(6) Sintering model:
- A (sm−1 )
- E (K)
- dcrit (nm)
Value
pyrene dimer
32 carbon atoms
1.4
1.69
0.0263
50
1.1 × 10−14
9.61 × 104
1.58
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Maximum temperature, T
1500
3.5
1000
dT / dH
Temperature (K)
Experiment
ABF
USC
#10 4
3
2.5
2
0
0.01
0.02
H
500
0
0.2
0.4
0.6
0.8
f,max
2000
(K)
Temperature
1
Distance from burner surface (cm)
1.2
2000
1900
1800
1700
1600
1500
0.5
Experiment
ABF
USC
0.6
0.7
0.8
0.9
1
1.1
1.2
Separation distance, Hp (cm)
• Maximum flame temperature increases with separation due to
reduced conductive heat transfer to the stagnation plate
• ABF underpredicts temperature: Larger flame speed, faster
temperature rise and greater heat loss to burner
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Species sensitivity to temperature
−4
5
H mole fraction, XH
−8
x 10
4
Energy equation
Imposed temperature
4
3
2
1
0
0.0
0.2
0.4
0.6
0.8
1.0
Distance from burner surface, H (cm)
1.2
Pyrene mole fraction, XA4
6
x 10
Energy equation
Imposed temperature
3
2
1
0
0.0
0.2
0.4
0.6
0.8
1.0
Distance from burner surface, H (cm)
1.2
• H atoms are critical to radical site generation in PAH
molecules and soot surfaces, and A4 is the gas-phase transfer
species
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Particle size distributions: Base case
10
Energy equation
Imposed temperature
12
Hp = 0.55 cm
1011
1010
109
10
8
10
7
10
6
4
6 810
30 50
Particle diameter, Dp (nm)
1013
dN/dlog(Dp) (cm-3)
dN/dlog(Dp) (cm-3)
1013
1012
Energy equation
Imposed temperature
1011
Hp = 1.2 cm
1010
109
108
107
106
4
6 810
30 50
Particle diameter, Dp (nm)
• PSDs are in qualitative agreement; but quantitatively differ
notably
• Discrepancy is not entirely the consequence of temperature
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Features of the particle size distribution
(b)
Coagulation
peak
dN/dlog(Dp) (cm-3)
(a)
Inception
peak
(c)
Trough
(d)
“Largest”
particle
Particle diameter, Dp (nm)
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dN/dlog(Dp) (cm-3)
1013
12
Base case
X A4 = 2 # 10-9
1011
X A4 = 4 # 10-9
1010
X A4 = 8 # 10-9
10
109
108
107
106
4
6 810
30 50
Particle diameter, Dp (nm)
Pyrene mole fraction, XA4 (-)
Sensitivity to A4 concentration
10
#10-9
A Trough
8
Coagulation !
peak
6
4
2
0
5
10
15
20
25
Particle diameter, Dp (nm)
• Increasing the pyrene concentration leads to a systematic shift
in both the position of the trough and the coagulation peak
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Summary of parametric sensitivity study
(b)
Coagulation
peak
dN/dlog(Dp) (cm-3)
(a)
Inception
peak
(c)
Trough
(d)
“Largest”
particle
Increase in inception size
Increase in coagulation rate
Increase in pyrene concentration
Particle diameter, Dp (nm)
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Soot morphology: PAH evolution
2000
Tf (K)
BC
1500
A
D
E
1000
500
0.0 0.2 0.4 0.6 0.8 1.0 1.2
H (cm)
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% of Fringes
Soot morphology: inception zone
A
D
E
1000
500
0.0 0.2 0.4 0.6 0.8 1.0 1.2
H (cm)
Probability density (−)
BC
Tf (K)
20
0
2000
1500
40
0.8 3.2 5.6 8.0
Fringe Length (nm)
2
10
0
10
−2
10
0.0
0.5
1.0
Sintering level (−)
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% of Fringes
Soot morphology: aggregate formation
A
D
E
1000
500
0.0 0.2 0.4 0.6 0.8 1.0 1.2
H (cm)
Probability density (−)
BC
Tf (K)
20
0
2000
1500
40
0.8 3.2 5.6 8.0
Fringe Length (nm)
2
10
0
10
−2
10
0.0
0.5
1.0
Sintering level (−)
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Implications on mobility sizing experiments
13
13
10
12
p
dN/dlog(D ) (cm−3)
10
11
Hp = 0.55 cm
10
10
10
9
10
8
10
7
10
Original measurement
New measurment
Computed
12
dN/dlog(Dp) (cm−3)
Original measurement
New measurment
Computed
10
11
Hp = 0.80 cm
10
10
10
9
10
8
10
7
10
10
6
6
10
4 6 8 10
30
Particle diameter, Dp (nm)
50
10
4 6 810
30 50
Particle diameter, Dp (nm)
• New measurements repeated at Stanford facility as well as
two other facilities using four different burners2
• Onset of bimodal PSD occurs even at the smallest separation
of 0.55 cm
2
Camacho et al. Combust. Flame (2015) (in preparation).
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Ratio of particle mass to equivalent
collision diameter spherical mass
Implications on mobility sizing experiments
1
0.8
0.6
0.4
Hp = 0.55 cm
0.2
Hp = 0.70 cm
Hp = 1.00 cm
0
4 6 8 10
30
Particle diameter, Dp (nm)
50
• Mobility diameter and the spherical particle assumption
overestimate the particle mass
• Ratio of actual-to-estimated particle was 0.5–0.6 for particles
in the size range of 20–25 nm, and about 0.9 for smaller
particles
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Conclusions
1
Presented a modelling study of soot formation for a laminar
premixed ethylene burner-stabilised stagnation flame.
2
A parametric sensitivity study was performed to understand
the cause of the discrepancies between the experimental and
computed PSDs.
3
Illustrated a dependence of soot morphology upon flame
conditions in the post-flame region.
4
New measurements were made which went some way towards
explaining the discrepancy between the experiment and the
model
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Acknowledgements
CoMo
GROUP
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• E.K.Y.Yapp, D. Chen, J. Akroyd, S. Mosbach, M. Kraft, J.
Camacho, H. Wang, Comb. Flame 162 (2015) 2569–2581
Questions?
22 / 27
Main species profiles
0.2
Energy equation
Imposed Temperature
Mole fractions
CO
0.15
H2O
H2
0.1
CO2
0.05
C2H2
0
0.0
C2H4
0.2
0.4
0.6
0.8
1.0
Distance from burner surface (cm)
1.2
• Concentrations are nearly constant
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Key gas-phase species
−8
3
−4
Pyrene mole fraction, XA4
H mole fraction, XH
4
x 10
3
2
1
Benzene mole fraction, XA1
2
1
0
0.0
0
0.0
3
x 10
0.2
0.4
0.6
0.8
1.0
Distance from burner surface, H (cm)
−4
x 10
1.2
0.2
0.4
0.6
0.8
1.0
Distance from burner surface, H (cm)
1.2
• Flames similar up to 0.2 cm while
length of post-flame region
increases with separation
2
• Low temperature flame: A1
1
increases in post-flame region
• A4 decreases in post-flame region
0
0.0
0.2
0.4
0.6
0.8
1.0
Distance from burner surface, H (cm)
1.2
due to nucleation and
condensation
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dN/dlog(Dp) (cm-3)
1013
Base case
64 carbons
128 carbons
256 carbons
1012
1011
1010
109
108
10
7
106
4
6 8 10
30
50
Minimum particle inception size
Sensitivity to minimum particle inception size
1200
1000
Particle diameter, Dp (nm)
Coagulation !
peak
800
600
400
200
0
0
5
10
15
20
25
Particle diameter, Dp (nm)
• Overall shift in the position of the coagulation peak to larger
diameters
• Increasing the minimum particle inception size increases the
average size of PAHs in a particle
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dN/dlog(Dp) (cm-3)
1013
Base case
coagRate # 2
coagRate # 4
coagRate # 8
1012
1011
10
10
109
108
107
106
4
6 810
30 50
Particle diameter, Dp (nm)
Coagulation kernel factor (-)
Sensitivity to coagulation rate
10
8
A Trough
6
Coagulation !
peak
4
2
0
0
5
10
15
20
25
Particle diameter, Dp (nm)
• Overall shift in the position of the coagulation peak to larger
diameters
• Increasing the coagulation rate increases the number of PAHs
in particle
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Interpretation of mobility diameter
13
10
12
dN/dlog(Dp) (cm−3)
10
Point contact
Sintered
Spherical
11
10
10
10
9
10
8
10
7
10
6
10
4 6 8 10
30
Particle diameter, Dp (nm)
50
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