On the evolution of the scalar flux through a planar premixed turbulent flame brush

ABSTRACT

The thermal expansion induced by the exothermicity of chemical reactions taking place in a turbulent flame affects the flow dynamics so deeply that the velocity field can be imposed by chemistry rather than turbulence. Moreover, thermal expansion is known to be responsible for flame-generated turbulence (FGT) as well as non-gradient or counter-gradient diffusion (CGD) phenomena. In the present study, a specific description of the joint probability-density function (PDF) of the progress variable and velocity is introduced. The corresponding PDF accounts for the finite thickness of the local flame. On the basis of this theoretical framework, the evolution of the scalar fluxes is analyzed across a planar premixed turbulent flame brush described as a boundary layer. The corresponding analysis recovers a CGD region in the planar flame brush as well as a region controlled by gradient diffusion (GD) transport at its leading edge. This region, which corresponds to small values of the mean progress variable, is dominated by finite Damköhler number effects. Finally, the dependency of the normalized turbulent scalar flux to classical nondimensional numbers – i.e., the Bray, Karlovitz and Reynolds numbers – is put into evidence. The obtained results provide a relatively simple basis for the development of closure models for the turbulent flux of the progress variable.

KEYWORDS:

• Combustion
• premixed flame
• turbulence
• turbulent transport
• flamelet regime
• leading edge
• flame brush

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ A computer algebra system (CAS) can be used to recover this ODE.

² Notations are simplified to a single velocity component but developments are valid for the velocity vector $v$.

³ Since the conditional PDFs that appear in Equations (36)(36) ${\bar{v}}_u={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}v\tilde{P}(v|c_{min})dv,$(36) and (37(37) ${\bar{v}}_b={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}v\tilde{P}(v|c_{max})dv,$(37) ) are associated to given values of the progress variable (i.e., given values of the density) they can be indiscriminately referred to as standard (i.e., Reynolds) or Favre averaged PDFs.