Applied Physics B

, Volume 112, Issue 3, pp 395–408 | Cite as

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

  • Redjem Hadef
  • Klaus Peter Geigle
  • Jochen Zerbs
  • Robert A. Sawchuk
  • David R. Snelling


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.


Soot Particle Soot Formation Primary Particle Size Soot Volume Fraction Soot Concentration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


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

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



Soot heat capacity


Optical function (detection system response)


Primary particle diameter without laser excitation, m


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


Particle diameter, m

E(m) = 0.232 + 1.2546 × 10+5λ

Refractive index function


Laser fluence, W/m2


Soot volume fraction, ppm


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


Blackbody spectral radiation, W m−2 m−1


Molar mass of soot vapor, kg mol−1


Particle mass, kg


Number density of the soot particles, m−3


Temporal laser intensity profile, W m−2


Particle radius, m


LII signal


Particle temperature, K


Gas temperature, K


Time, s


Velocity, m/s


Probe volume, m3

Greek symbols


Thermal accommodation coefficient


Mass accommodation coefficient


Enthalpy of vaporization, J mol−1


Emissivity of soot, containing E(m)


Wavelength, m


Density, kg m−3 (soot or ambient gas)


Geometric width of a log-normal distribution
























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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Redjem Hadef
    • 1
  • Klaus Peter Geigle
    • 2
  • Jochen Zerbs
    • 2
  • Robert A. Sawchuk
    • 3
  • David R. Snelling
    • 3
  1. 1.Institut de Génie MécaniqueUniversité Larbi Ben M’HidiOum El BouaghiAlgerie
  2. 2.Institute of Combustion TechnologyGerman Aerospace Center (DLR)StuttgartGermany
  3. 3.Measurement Science and StandardsNational Research Council of Canada (NRC)OttawaCanada

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