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Theoretical study of axisymmeetrical triple flame

by M. Savelieva

(Report number 2002-26)

Abstract
We study the axysymmetrical triple flame, that could be observed at the base of the laminar diffusion lifted flame. The study of this flame has been done by S.Ghosal and L.Vervisch, who applied the two-dimensional approach for the flame that axisymmetrical in fact. The experiments reveal us the necessity to investigate the influence of the radius of the flame base on the behaviour (i.e. such important characteristics as stability and velocity) of the whole structure. Both constant- and variable-density case are considered. Instead of solving a free-boundary problem for the flame surface, we approximate it with a help of parabolic profile, the curvature to be self-consistently determined. This method, called by Ghosal and Vervisch "the parabolic flame path approximation", has shown his validity for planar case, and we would like to expand this result for the axisymmetric flame. The method of matched asymptotic expansions in parabolic-cylinder coordinates will be applied, and the closed expressions for the flame curvature and velocity, as well as the temperature field, will be given. We compare this theoretical results with those J. Boulanger, L. Vervisch, J. Reveillon and S. Ghosal got with by DNS (direct numerical simulations).

Keywords:

@Techreport{S02_312,
  author = {M. Savelieva},
  title = {Theoretical study of axisymmeetrical triple flame},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-26.pdf },
  year = {2002}
}

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