Numerical simulation and parametric sensitivity study of

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

1 / 27

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

2 / 27

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

4 / 27

Computational method

Experimental conditionsMechanism, thermodynamic and transport data

Oppdif

TemperatureSpecies

Detailed population balance model

PSDsFringe length distributions

TEMs

Post-processing

Pre-processing

5 / 27

Particle representation

Aggregate Primary particle PAH

• Connectivity matrix • Common surface area • Sintering level

• PAHs rigidly stick • Edge carbon atoms • Fringe length

6 / 27

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

7 / 27

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

8 / 27

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

9 / 27

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



• H atoms are critical to radical site generation in PAHmolecules and soot surfaces, and A4 is the gas-phase transferspecies

10 / 27

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



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


• PSDs are in qualitative agreement; but quantitatively differnotably

• Discrepancy is not entirely the consequence of temperature

11 / 27

Features of the particle size distribution

dN/d

log(

Dp)

(cm

-3)


(a)Inception

peak

(c)Trough

(b)Coagulation

peak

(d)“Largest” particle

12 / 27

Sensitivity to A4 concentration


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


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

13 / 27

Summary of parametric sensitivity study

dN/d

log

(Dp)

(cm

-3)


(a)Inception

peak

(c)Trough

(b)Coagulation

peak

(d)“Largest” particle

Increase in inception sizeIncrease in coagulation rateIncrease in pyrene concentration

14 / 27

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

15 / 27

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 (−)

16 / 27

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 (−)

17 / 27

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 )


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 )


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


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

19 / 27

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

20 / 27

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

23 / 27

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


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


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


• 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

24 / 27

Sensitivity to minimum particle inception size


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


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

25 / 27

Sensitivity to coagulation rate


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


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

26 / 27

Interpretation of mobility diameter

4 6 8 10 30 5010

6

107

108

109

1010

1011

1012

1013

dN/d

log(

Dp)

(cm

−3 )


Point contactSinteredSpherical

27 / 27

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Numerical simulation and parametric sensitivity study of