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

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

### Vladimir Sabelnikov

ONERA Centre de Palaiseau

### Andrei Lipatnikov

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

#### Fluids

Vol. 5 1-18 109

### Driving Forces

Sustainable development

### Roots

Basic sciences

### Subject Categories

Fluid Mechanics and Acoustics

### DOI

10.3390/fluids5030109