A novel formulation for unsteady counterflow flames using a thermal-conductivity-weighted coordinate Articles uri icon


publication date

  • May 2018

start page

  • 185

end page

  • 201


  • 1


  • 22

International Standard Serial Number (ISSN)

  • 1364-7830

Electronic International Standard Serial Number (EISSN)

  • 1741-3559


  • A general formulation is given for the description of reacting mixing layers in stagnation-type flows subject to both time-varying strain and pressure. The salient feature of the formulation is the introduction of a thermal-conductivity-weighted transverse coordinate that leads to a compact transport operator that facilitates numerical integration and theoretical analysis. For steady counterflow mixing layers, the associated transverse mass flux is shown to be effectively linear in terms of the new coordinate, so that the conservation equations for energy and chemical species uncouple from the mass and momentum conservation equations, thereby greatly simplifying the solution. Comparisons are shown with computations of diffusion flames with infinitely fast reaction using both the classic Howarth-Dorodnitzyn density-weighted coordinate and the new thermal-conductivity-weighted coordinate, illustrating the advantages of the latter. Also, as an illustrative application of the formulation to the computation of unsteady counterflows, the flame response to harmonically varying strain is examined in the linear limit.


  • laminar reacting boundary layers; counterflow; flamelets; boundary-layer transformation; thermal-conductivity weighting