Determining the mean aggregate size of soot particles with the combination of light scattering and two-colour time-resolved LII

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Determining the mean aggregate size of soot particles with the combination of light scattering and two-colour time-resolved LII

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Determining the Mean Aggregate Size of Soot

Particles with the Combination of

Light Scattering and Two-Colour Time-Resolved LII

Sub-Task 3.4S

Gregory J. Smallwood and David R. Snelling

Institute for Chemical Process & Environmental Technology, National Research Council Canada Ottawa, ON, Canada K1A 0R6

International Energy Agency XXIX Task Leaders Meeting on Energy Conservation and Emissions Reduction in Combustion 2-7 September 2007, Gembloux, Belgium

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Motivation/Objective

• Motivation

– details of the morphology of soot/black carbon aggregates are necessary to assess the health and environmental impacts of these nanoparticles

• Objective

– extend the capabilities of LII to include the determination of the mean number of primary particles per aggregate

(4)

Background

• laser-induced incandescence (LII) has become a well established technique for measuring soot concentration and primary particle diameter

• soot aggregate size (number of primary particles per aggregate) distributions are described by a lognormal function whose

distribution width is largely independent of the soot source and the (geometric) mean aggregate size

• due to the relative insensitivity of the distribution width it is

possible to determine mean aggregate size from a combination of absolute LII signals and near forward laser light scattering

(5)

TEM image of soot particles

sampled from a flame

(6)

Primary Particle Size

Distribution

• 385 measurements of primary soot particles • arithmetic mean diameter: D10 = 29.2 nm

• normal distribution fit: dm = 28.3nm and σd = 6.5nm 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 10 15 20 25 30 35 40 45 50 d_p (nm) Pr o b ab il ity

(7)

Aggregate Size

Distribution

• 3400 aggregates measured

• for a lower limit of Np>5: Ng=23.2, σ2g=4.15

1 10 100 1000 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Statistical result for N > 1 Lognormal fitting curve for N >1

Lognormal fitting curve for N > 5

Double lognormal fitting curve for N >1 P ro b a b ili ty

(8)

Approach

• modification of a typical 2-color time-resolved LII system allows simultaneous time-resolved measurement of 2-color LII and single-angle absolute scattering intensity from a 532 nm LII excitation source

• a single measurement can result in estimates of soot volume fraction, the primary particle diameter and the geometric mean aggregate size

• the mean aggregates sizes derived with this method depend on a knowledge of the ratio of the soot absorption and scattering

functions

• this in situ technique is applied to soot in a laminar diffusion flame • an enhanced technique that requires no knowledge of the

absorption or scattering function values, based on the ratio of forward to backward scattering, is also evaluated

(9)

AC-LII / Scattering

Apparatus

35º

(10)

Soot volume fraction

from 2-colour LII

calibration factor T_pe equivalent particle temperature

G amplifier gain w_e equivalent laser width

V potential m refractive index

C centre wavelength E absorption function

• the soot volume fraction (fv) derived from LII (or absorption) is

inversely proportional to the value of E(m) assumed

• the property determined by LII is the product of soot volume fraction and the absorption function

2 ₁ 6

12

1

C pe C EXP v h c k T b EXP C

V

f

c h

m

w G

E

e

(11)

Absolute LII Signals

0 500 1000 1500 2000 1 108 1 109 1 1010 1 1011 1 1012 Time (ns) L II s ig n a l (w a tt/m *3 ·s te ra d ia n ) 400 nm 780 nm 0 500 1000 1500 2000 1 108 1 109 1 1010 1 1011 1 1012 Time (ns) L II s ig n a l (w a tt/m *3 ·s te ra d ia n ) 400 nm 780 nm 400 nm 780 nm

(12)

0 500 1000 1500 2000 1500 2000 2500 3000 3500 4000 4500 Time (ns) T e m p e ra tu re (K )

Real-time Temperature

soot temperature exponential fit

(13)

Soot scattering theory

– I

• based on Rayleigh-Debye-Gans Polydisperse Fractal Aggregate (RDG-PFA) theory

• aggregate differential scattering cross section:

N number of primary particles

d_p primary particle diameter

S(q,R_g) structure factor

• scattering vector, q( ):

• fractal radius of gyration, Rg:

4 6 2 4

,

4

p ag g

d

F m

N

S q R

4 sin

2 q

1 f D g p f

N

R

d

k

(14)

Soot scattering theory

– II

• structure factor is calculated numerically using the confluent

hypergeometric approach of Sorensen, which assumes a Gaussian fractal cut-off

• for a distribution of aggregates the scattering cross section must be integrated over the appropriate distribution function

• lognormal distribution:

N_g geometric mean aggregate size

σg distribution width

• to derive Ng from the ratio of soot scattering to LII intensity and the

known soot scattering and absorption functions we must assume a distribution width σg 2 ln ln exp 2 ln , , ln 2 g g lognorm g g g N N P N N N

(15)

Soot scattering theory

– III

• Sorensen has shown that a self preserving or scaling distribution gives a more accurate description of the higher moments that describe scattering than does a lognormal distribution

• a self preserving distribution is theoretically predicted from solving the aggregate coagulation equations over a wide range of

conditions

• an aggregating system develops a self preserving scaling distribution.

• lognormal distribution moments with a width ~2.5 are in best

agreement with the scaling distribution up to the 3rd _moment

• experimental evidence of flame soot σg ~2.6, used for subsequent

(16)

Volumetric scattering

coefficient

• the soot volume fraction from LII is inversely proportional to the value of

E(m) assumed at the LII wavelengths

• this allows substitution of the requirement to know the relative value of

E(m) from 400 to 780 nm and the ratio F(m)/E(m) at 532 nm for a

knowledge of the absolute values of the coefficients

• the F(m)/E(m) ratio for soot in wide variety of flames has been summarized [3], with F(m₅₃₂)/E(m₅₃₂) = 1.1

• E(m) is assumed constant from 400 to 780 nm

4 6 ₆ 532 2 3 4 2 1 10 , , , 4 exp 0.5ln 6 p _v vol ag ag lognorm g g g p g g d F m _f C N P N N N S q R dN d N 4 6 6 532 2 532 3 4 2 532 1 10 , , , 4 exp 0.5ln 6 p v vol lognorm g g g p g g d F m f E m C P N N N S q R dN d E m N

(17)

Forward and backward

scattering coefficients

• the volumetric scattering coefficient is shown for forward

scattering (35 deg, upper curve) and backward scattering (145 deg, lower curve) for three independent experiments

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 5 104 1 105 1.5 105 2 105 2.5 105

Experimental volumetric scattering coefficient

Fluence (mJ/mm2) V ol u m e tr ic s c a tt e ri n g c oe ff ic ie n t ( /m )

(18)

Forward-to-backward

scattering ratio

• the forward-to-backward ratio gives an independent estimate of aggregate size and requires no knowledge of the scattering

function 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2.5 3 3.5 4

35 deg. to 145 deg. scattering ratio

Fluence (mJ/mm2) F or w a rd t o b a c k w a rd s c a tt e ri n g r a ti o

(19)

Numerical prediction

–

I

– given a primary particle size of 29 nm (from LII and TEM) and an average measured low fluence 35 degree volumetric scattering coefficient/soot volume fraction ratio of 1.91·105_{, the predicted N}

g

~ 18

(20)

Numerical prediction

–

II

• the 145 deg volumetric scattering coefficient/soot volume fraction is insensitive to N_g but varies with d_p

– the measured values of 5.81·104 _{and N}

g=18 gives dp ~ 28 nm, in

good agreement with LII and TEM

(21)

Numerical prediction

–

III

• for a measured experimental forward/backward ratio of 3.25 and

d_p=29 nm, N_g ~19

(22)

Summary of results

• forward scattering and LII soot volume fraction give Ng ~18

• forward to backward scattering ratio gives Ng ~19

• TEM gives Ng ~21

(23)

Conclusions

• an estimate of the mean aggregate size of an assumed lognormal distribution of aggregates can be derived based on the ratio of

laser scattering to LII signal

• these values are in agreement with those obtained from forward to backward scattering ratio and TEM