Numerical simulation and parametric sensitivitystudy 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
1Department of Chemical Engineering and BiotechnologyUniversity of Cambridge
2School of Chemical and Biomedical EngineeringNanyang Technological University
3Department of Mechanical EngineeringStanford University
3rd July 2015
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Objectives
1 Model soot formation for the burner-stabilised stagnationflame 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)
Burner (Tb)
Hp
z
r
u
vr
• Sample probe integrated into plate1
• Removes need to carry out arbitrary “time or spatial shifting”
1Abid et al. Combust. Flame, 156 (2009) 1862–1870.3 / 27
Experimental conditions
Values
Stagnation plate separation, Hp (cm) 0.55, 0.6, 0.7, 0.8, 1.0, 1.2Fuel composition (mol%) 16.3 C2H2, 23.7 O2, 60 Ar
Velocity (STP) (cm/s) 8Equivalence ratio (-) 2.07
Burner temperature, Tb (K) 473
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Computational method
Experimental conditionsMechanism, thermodynamic and transport data
Oppdif
TemperatureSpecies
Detailed population balance model
PSDsFringe length distributions
TEMs
Post-processing
Pre-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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Particle processes
Cða; bÞ ¼Ssphða;bÞ
Sða;bÞ � 2�1=3
1� 2�1=3ð2Þ
where Ssph(a,b) is the spherical surface of the twoprimary particles. Two primary particles are re-placed by one primary particle with the same vol-ume if C(a,b) P 1.
The volume of a particle is calculated as thesum of the volume of the individual primary par-ticles. The surface of the particles incorporates theaverage coalescence level of the individual pri-mary particles and is approximated by
Spart ¼Ssph
ðCavgð1� n�1=3Þ þ n�1=3Þ ð3Þ
where n is the number of primary particles, Ssph thespherical surface of the particle and Cavg the aver-age coalescence level of the particle. This formulainterpolates between the surface of a spherical par-ticle and the surface of a particle where the primaryparticles are in point contact. The inception, coag-ulation and condensation rate is calculated usingthe transition regime coagulation kernel Ktr, multi-plied with the recently determined collision effi-ciency CE for PAHs [28]. The transition regimecoagulation kernel Ktr is the harmonic mean ofthe slip-flow Ksf and free molecular kernel Kfm [30]:
KtrðA;BÞ ¼ Ksf ðA;BÞKfmðA;BÞKsf ðA;BÞ þ KfmðA;BÞ
ð4Þ
where A and B represent particles or PAHs. A andB are particles for a coagulation process, A and B
are PAHs for an inception process and A is a par-ticle and B a PAH for a condensation process.
The collision diameter of a PAH is
dPAHc ¼ dA
ffiffiffiffiffiffiffi2nc
3
rð5Þ
with dA ¼ 1:395ffiffiffi3p
A for a single aromatic ringand nc the number of carbon atoms in the PAH[31]. A fractal dimension Df of 1.8 is used to cal-culate the collision diameter dpart
c of a particle [32]:
dpartc ¼ 6V
S
� �S3
36pnV 2
� � 1Df
: ð6Þ
The different process included in the model aresummarized in Fig. 1.
3. Optimisation
We have selected three free parameters in thePAH-PP model: the soot density q, the growthfactor of the PAHs in a particle g and the smooth-ing factor s (Table 1). The soot density has beenselected as a free parameter because Tottonet al. [10,11] determined recently 1.12 g/cm3 assoot density for nascent particles, which is muchlower then the usually used soot density of 1.8 g/cm3 [33,34].
The parameter vector x is defined as:
x ¼ ðq; s; gÞ: ð7ÞThe optimisation consists of two consecutivesteps: a low discrepancy series method followedby a quadratic response surface optimisation.
Fig. 1. Processes included in the PAH-PP model.
M. Sander et al. / Proceedings of the Combustion Institute 33 (2011) 675–683 677
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Model parameters
Value
(1) Minimum particle inception size pyrene dimer(number of carbon atoms) 32 carbon atoms
(2) Soot density, ρ (gcm−3) 1.4(3) Smoothing factor, s (-) 1.69(4) Growth factor, g (-) 0.0263(5) Critical number of PAHs in a primary 50
particle before g is applied, ncrit (-)(6) Sintering model:
- A (sm−1) 1.1 × 10−14
- E (K) 9.61 × 104
- dcrit (nm) 1.58
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Temperature
Distance from burner surface (cm)0 0.2 0.4 0.6 0.8 1 1.2
Tem
pera
ture
(K
)
500
1000
1500
2000ExperimentABFUSC
H0 0.01 0.02
dT
/ d
H
#104
2
2.5
3
3.5
Separation distance, Hp (cm)
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Max
imum
tem
pera
ture
, T
f,max
(K
)
1500
1600
1700
1800
1900
2000
ExperimentABFUSC
• Maximum flame temperature increases with separation due toreduced conductive heat transfer to the stagnation plate
• ABF underpredicts temperature: Larger flame speed, fastertemperature rise and greater heat loss to burner
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Species sensitivity to temperature
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
1
2
3
4
5
6x 10
−4
H m
ole
frac
tion,
XH
Distance from burner surface, H (cm)
Energy equationImposed temperature
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
1
2
3
4x 10
−8
Pyr
ene
mol
e fr
actio
n, X
A4
Distance from burner surface, H (cm)
Energy equationImposed temperature
• H atoms are critical to radical site generation in PAHmolecules and soot surfaces, and A4 is the gas-phase transferspecies
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Particle size distributions: Base case
Particle diameter, Dp (nm)
4 6 810 30 50
dN
/dlo
g(D
p) (c
m-3
)
106
107
108
109
1010
1011
1012
1013
Hp = 0.55 cm
Energy equationImposed temperature
Particle diameter, Dp (nm)
4 6 810 30 50
dN
/dlo
g(D
p) (c
m-3
)
106
107
108
109
1010
1011
1012
1013
Hp = 1.2 cm
Energy equationImposed temperature
• PSDs are in qualitative agreement; but quantitatively differnotably
• Discrepancy is not entirely the consequence of temperature
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Features of the particle size distribution
dN/d
log(
Dp)
(cm
-3)
Particle diameter, Dp (nm)
(a)Inception
peak
(c)Trough
(b)Coagulation
peak
(d)“Largest” particle
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Sensitivity to A4 concentration
Particle diameter, Dp (nm)
4 6 810 30 50
dN
/dlo
g(D
p) (c
m-3
)
106
107
108
109
1010
1011
1012
1013
Base caseX
A4 = 2 # 10-9
XA4
= 4 # 10-9
XA4
= 8 # 10-9
Particle diameter, Dp (nm)
0 5 10 15 20 25
Pyr
ene
mol
e fr
actio
n, X
A4 (
-) #10-9
2
4
6
8
10A Trough
Coagulation !peak
• Increasing the pyrene concentration leads to a systematic shiftin both the position of the trough and the coagulation peak
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Summary of parametric sensitivity study
dN/d
log
(Dp)
(cm
-3)
Particle diameter, Dp (nm)
(a)Inception
peak
(c)Trough
(b)Coagulation
peak
(d)“Largest” particle
Increase in inception sizeIncrease in coagulation rateIncrease in pyrene concentration
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Soot morphology: PAH evolution
0.0 0.2 0.4 0.6 0.8 1.0 1.2 500
1000
1500
2000
Tf (
K)
H (cm)
A
B C D
E
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Soot morphology: inception zone
0.0 0.2 0.4 0.6 0.8 1.0 1.2 500
1000
1500
2000
Tf (
K)
H (cm)
A
B C D
E
0.8 3.2 5.6 8.0 0
20
40
Fringe Length (nm)
% o
f Frin
ges
0.0 0.5 1.0 10
−2
100
102
Pro
babi
lity
dens
ity (
−)
Sintering level (−)
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Soot morphology: aggregate formation
0.0 0.2 0.4 0.6 0.8 1.0 1.2 500
1000
1500
2000
Tf (
K)
H (cm)
A
B C D
E
0.8 3.2 5.6 8.0 0
20
40
Fringe Length (nm)
% o
f Frin
ges
0.0 0.5 1.0 10
−2
100
102
Pro
babi
lity
dens
ity (
−)
Sintering level (−)
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Implications on mobility sizing experiments
4 6 8 10 30 5010
6
107
108
109
1010
1011
1012
1013
dN/d
log(
Dp)
(cm
−3 )
Particle diameter, Dp (nm)
Hp = 0.55 cm
Original measurementNew measurmentComputed
4 6 810 30 5010
6
107
108
109
1010
1011
1012
1013
dN/d
log(
Dp)
(cm
−3 )
Particle diameter, Dp (nm)
Hp = 0.80 cm
Original measurementNew measurmentComputed
• New measurements repeated at Stanford facility as well astwo other facilities using four different burners2
• Onset of bimodal PSD occurs even at the smallest separationof 0.55 cm
2Camacho et al. Combust. Flame (2015) (in preparation).18 / 27
Implications on mobility sizing experiments
4 6 8 10 30 500
0.2
0.4
0.6
0.8
1
Rat
io o
f par
ticle
mas
s to
equ
ival
ent
colli
sion
dia
met
er s
pher
ical
mas
s
Particle diameter, Dp (nm)
Hp = 0.55 cm
Hp = 0.70 cm
Hp = 1.00 cm
• Mobility diameter and the spherical particle assumptionoverestimate the particle mass
• Ratio of actual-to-estimated particle was 0.5–0.6 for particlesin the size range of 20–25 nm, and about 0.9 for smallerparticles
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Conclusions
1 Presented a modelling study of soot formation for a laminarpremixed ethylene burner-stabilised stagnation flame.
2 A parametric sensitivity study was performed to understandthe cause of the discrepancies between the experimental andcomputed PSDs.
3 Illustrated a dependence of soot morphology upon flameconditions in the post-flame region.
4 New measurements were made which went some way towardsexplaining the discrepancy between the experiment and themodel
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Acknowledgements
CoMoGROUP
21 / 27
• 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
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
0.05
0.1
0.15
0.2
H2
H2O
CO
CO2
C2H
2
C2H
4
Mol
e fr
actio
ns
Distance from burner surface (cm)
Energy equation Imposed Temperature
• Concentrations are nearly constant
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Key gas-phase species
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
1
2
3
4x 10
−4
H m
ole
frac
tion,
XH
Distance from burner surface, H (cm)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
1
2
3x 10
−4
Ben
zene
mol
e fr
actio
n, X
A1
Distance from burner surface, H (cm)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0
1
2
3x 10
−8
Pyr
ene
mol
e fr
actio
n, X
A4
Distance from burner surface, H (cm)
• Flames similar up to 0.2 cm whilelength of post-flame regionincreases with separation
• Low temperature flame: A1increases in post-flame region
• A4 decreases in post-flame regiondue to nucleation andcondensation
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Sensitivity to minimum particle inception size
Particle diameter, Dp (nm)
4 6 8 10 30 50
dN
/dlo
g(D
p) (c
m-3
)
106
107
108
109
1010
1011
1012
1013
Base case64 carbons128 carbons256 carbons
Particle diameter, Dp (nm)
0 5 10 15 20 25
Min
imum
par
ticle
ince
ptio
n si
ze
0
200
400
600
800
1000
1200
Coagulation !peak
• Overall shift in the position of the coagulation peak to largerdiameters
• Increasing the minimum particle inception size increases theaverage size of PAHs in a particle
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Sensitivity to coagulation rate
Particle diameter, Dp (nm)
4 6 810 30 50
dN
/dlo
g(D
p) (c
m-3
)
106
107
108
109
1010
1011
1012
1013
Base casecoagRate # 2coagRate # 4coagRate # 8
Particle diameter, Dp (nm)
0 5 10 15 20 25
Coa
gula
tion
kern
el fa
ctor
(-)
0
2
4
6
8
10
A Trough
Coagulation !peak
• Overall shift in the position of the coagulation peak to largerdiameters
• Increasing the coagulation rate increases the number of PAHsin particle
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Interpretation of mobility diameter
4 6 8 10 30 5010
6
107
108
109
1010
1011
1012
1013
dN/d
log(
Dp)
(cm
−3 )
Particle diameter, Dp (nm)
Point contactSinteredSpherical
27 / 27