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Stochastic Modelling of Soot Particle Size and Age Distribution in Laminar Premixed Flames

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Condensation of Pyrene molecule, Oxidation by O2, Oxidation by OH, Addition by ... Inception by two Pyrene molecules. Flame. Key points. Soot particles are spherical. ... – PowerPoint PPT presentation

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Title: Stochastic Modelling of Soot Particle Size and Age Distribution in Laminar Premixed Flames


1
Stochastic 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
2
Motivation
  • 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

3
Soot 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.
4
Pressure regimes
5
Coagulation 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
6
Stochastic algorithm
7
Flames
8
Flame Structure
9
Soot particle size distributions
10
Particle ageing
Nucleation
Surface reactions for 2 4 ms
Waiting time 1 ms
Coagulation
(100x6 50x3) (100 50)
5
11
Comparisons of Numerical methods with
experimental measurements
12
Soot particle size distributions
13
Soot particle age distributions
14
Active 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

15
Alpha definition Step function
?p
16
Alpha definition Exponential function
?p 0.2 0.8exp(-C Ap)
17
Parameter C versus maximum flame temperature
?p 0.2 0.8 exp(-C Ap)
18
Conclusions
  • 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.

19
Alpha definition Exponential function
20
Operator Splitting (Schematic)
1
Nucleation
?t 1 ms
Surface reactions for 1 ms
Coagulation
21
Coagulation kernel
p 10 bar T 1800 K
22
Soot particle age distributions
23
Efficiency of the majorant
p 10 bar T 1800 K
24
High pressure flame model studies
T 1800 K
25
High pressure flame model studies
26
Extra figures
27
Soot 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.

28
Active sites
29
Reducing 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.

30
Majorants
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
31
Comparisons of Numerical methods with
experimental measurements
32
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