A new mathematical framework for describing thin-reaction-zone regime of turbulent reacting flows at low Damköhler number Journal article, 2020

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of
an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent
flow in the case of a low Damköhler number. In the cited paper, the theory is also supported by
Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent
premixed combustion is argued. The present work aims at complementing the theory with a new
mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely
thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c(x,t) is considered
to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c(x,t)<1,
where molecular transport plays an important role, and (ii) equilibrium products, c(x,t)=1. The two
zones are separated by an infinitely thin reaction sheet, where c(x,t)=1 and |nabla c| is fixed in order
for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed
of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the
entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable,
its second moment, and instantaneous characteristic functions. Averaging of these equations yields
exact, unclosed transport equations for the conditioned reaction-progress-variable moments and
Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet.
The closure problem for the derived equations is beyond the scope of the paper.

turbulent reacting flows

thin reaction zone regime

probability density function

premixed turbulent combustion

turbulent flame

conditional averaging

Author

ONERA Centre de Palaiseau

Andrei Lipatnikov

Chalmers, Mechanics and Maritime Sciences, Combustion, Förbränning och sprejer

Vol. 5 1-18 109

Driving Forces

Sustainable development

Basic sciences

Subject Categories

Fluid Mechanics and Acoustics

DOI

10.3390/fluids5030109