Title: Stochastic Modelling of Soot Particle Size and Age Distribution in Laminar Premixed Flames
1Stochastic Modelling of Soot Particle Size and
Age Distribution in Laminar Premixed Flames
J. Singh, M. Balthasar, M. Kraft1), W. Wagner2)
2) Weierstrass Institute of Applied Analysis and
Stochastics Berlin
1) Computational Modelling Group Chemical
Engineering University of Cambridge
2Motivation
- Extend the stochastic approach to wider range of
pressures. - Study the ageing effect of the soot particles.
- Establish a functional dependence between
deactivation of surface sites and flame
temperature
3Soot model
Burner
Flame
Condensation of Pyrene molecule, Oxidation by O2,
Oxidation by OH, Addition by C2H2 by HACA mech.
Coalescence of two soot particles termed
coagulation in soot terminology.
Inception by two Pyrene molecules.
4Pressure regimes
5Coagulation kernel
Coagulation Kernel
Knudsen
Regime
10 lt Kn
Free molecular
1 lt Kn lt 10
Transition
0.1lt Kn lt 1
Slip flow
Kn lt 0.1
Continuum
? Mean free path of particles d diameter of
soot particle d1 diameter of a carbon molecule
6Stochastic algorithm
7Flames
8Flame Structure
9Soot particle size distributions
10 Particle ageing
Nucleation
Surface reactions for 2 4 ms
Waiting time 1 ms
Coagulation
(100x6 50x3) (100 50)
5
11Comparisons of Numerical methods with
experimental measurements
12Soot particle size distributions
13Soot particle age distributions
14Active sites definition
- Appel, Bockhorn, and Frenklach introduce an
expression ? for the fraction of reactive
surfaceCF 121122-136 (2000) - The parameters a and b are fitted to be linearly
dependent on flame temperature (based on a set of
8 flames) - ?1 is the first moment of the PSDF obtained from
MoM and introduces a size dependence
15Alpha definition Step function
?p
16Alpha definition Exponential function
?p 0.2 0.8exp(-C Ap)
17Parameter C versus maximum flame temperature
?p 0.2 0.8 exp(-C Ap)
18Conclusions
- Stochastic solution method has been extended to
all relevant pressures. - The particle size and age distributions have been
calculated using a new stochastic simulation
procedure. - A first insight into the ageing of the surface of
the soot particle has been achieved.
19Alpha definition Exponential function
20Operator Splitting (Schematic)
1
Nucleation
?t 1 ms
Surface reactions for 1 ms
Coagulation
21Coagulation kernel
p 10 bar T 1800 K
22Soot particle age distributions
23Efficiency of the majorant
p 10 bar T 1800 K
24High pressure flame model studies
T 1800 K
25High pressure flame model studies
26Extra figures
27Soot Model
- Following events are possible for the soot
formation - Inception by two Pyrene molecules.
- Coalescence of two soot particles termed
coagulation in soot terminology.
- Condensation of Pyrene molecule.
- Oxidation by O2.
- Oxidation by OH.
- Addition by C2H2 by HACA mech.
Flame
- Key points
- Soot particles are spherical.
- Colours in the figure reflect the temperature in
the flame at that position. - Black dots represent the soot particles.
28Active sites
29Reducing computational time
- High computational expense as time scale of
processes are different - Problem High inflow or coagulation rate.
- Remedy Proper choice of Normalization factor.
- Problem High surface reaction rate.
- Remedy Deferred Surface Growth (DSG) algorithm.
30Majorants
Majorant Kernel
Knudsen
Regime
10 lt Kn
Free molecular
1 lt Kn lt 10
Transition
0.1lt Kn lt 1
Slip flow
Kn lt 0.1
Continuum
31Comparisons of Numerical methods with
experimental measurements
32(No Transcript)