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The concept of 2D gated imaging for particle sizing in a laminar diffusion flame

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Abstract

In this work, time-resolved laser-induced incandescence (TiRe LII) has been employed to measure primary particle diameters of soot in an atmospheric laminar ethylene diffusion flame. The generated data set complements existing data determined in one single location and takes advantage of the good spatial resolution of the ICCD detection. Time resolution is achieved by shifting the camera gate along the LII decay. One key input parameter for the analysis of time-resolved LII is the local flame temperature. This was determined on a grid throughout the flame by coherent anti-Stokes Raman scattering. The accurate temperature data, in combination with other published data from this flame, are well suited for soot model validation purposes while we showed feasibility of a shifted gate approach to deduce 2D particle sizes in the chosen standard flame.

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Abbreviations

\(\dot{Q}_{\text{int}} = \rho {\kern 1pt} c\frac{{\pi D^{3} }}{6}\frac{{{\text{d}}T_{\text{P}} }}{{{\text{d}}t}}\) :

Change of internal energy of the soot particle

\(\dot{Q}_{\text{abs}} = \alpha_{{\lambda ,{\text{las}}}} \frac{{\pi D^{2} }}{4}q(t)\) :

Rate of energy absorption from the laser pulse

\(\alpha_{{\lambda ,{\text{las}}}} = \frac{4\pi D}{{\lambda_{\text{las}} }}E(m)\) :

Absorption efficiency of soot

\(\dot{Q}_{\text{sub}} = \, - \frac{{\Updelta H_{\text{v}} }}{{M_{\text{v}} }}\frac{{{\text{d}}m}}{{{\text{d}}t}}\) :

Rate of heat loss by soot surface sublimation

\(\dot{Q}_{\text{cond}} = \,h_{\text{cond}} \pi D^{2} \left( {T_{\text{p}} - T_{\text{g}} } \right)\,\) :

Heat conduction to ambient gaseous species due to collisions

\(\dot{Q}_{\text{rad}} = \,\pi D^{2} \int_{\,0}^{\,\infty } {\varepsilon_{\lambda } {\kern 1pt} M_{\lambda }^{0} } {\text{d}}\lambda\) :

Blackbody-like LII radiation

c :

Soot heat capacity

C opt :

Optical function (detection system response)

D 0 :

Primary particle diameter without laser excitation, m

CMD:

Count median diameter of log-normal distribution of primary particle diameters, m

D :

Particle diameter, m

E(m) = 0.232 + 1.2546 × 10+5 λ :

Refractive index function

F :

Laser fluence, W/m2

f v :

Soot volume fraction, ppm

h cond :

Heat transfer coefficient, containing thermal accommodation coefficient α T, W m−2

M 0 :

Blackbody spectral radiation, W m−2 m−1

M v :

Molar mass of soot vapor, kg mol−1

m :

Particle mass, kg

N p :

Number density of the soot particles, m−3

q(t):

Temporal laser intensity profile, W m−2

R :

Particle radius, m

S LII :

LII signal

T p :

Particle temperature, K

T g :

Gas temperature, K

t :

Time, s

U :

Velocity, m/s

V :

Probe volume, m3

α T :

Thermal accommodation coefficient

β :

Mass accommodation coefficient

ΔH v :

Enthalpy of vaporization, J mol−1

ε :

Emissivity of soot, containing E(m)

λ :

Wavelength, m

ρ :

Density, kg m−3 (soot or ambient gas)

σ g :

Geometric width of a log-normal distribution

abs:

Absorption

cond:

Conduction

det:

Detection

sub:

Sublimation

exc:

Excitation

g:

Gas

int:

Internal

las:

Laser

rad:

Radiation

v:

Vapor

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Acknowledgments

The authors acknowledge the support of a Helmholtz/NRC collaborative partnership which made this research possible.

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Authors and Affiliations

  1. Institut de Génie Mécanique, Université Larbi Ben M’Hidi, 04000, Oum El Bouaghi, Algerie

    Redjem Hadef

  2. Institute of Combustion Technology, German Aerospace Center (DLR), Pfaffenwaldring 38-40, 70569, Stuttgart, Germany

    Klaus Peter Geigle & Jochen Zerbs

  3. Measurement Science and Standards, National Research Council of Canada (NRC), 1200 Montreal Road, Ottawa, ON, K1A 0R6, Canada

    Robert A. Sawchuk & David R. Snelling

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  1. Redjem Hadef
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  2. Klaus Peter Geigle
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  4. Robert A. Sawchuk
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  5. David R. Snelling
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Correspondence to Klaus Peter Geigle.

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Hadef, R., Geigle, K.P., Zerbs, J. et al. The concept of 2D gated imaging for particle sizing in a laminar diffusion flame. Appl. Phys. B 112, 395–408 (2013). https://doi.org/10.1007/s00340-013-5507-1

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