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

*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.

premixed turbulent combustion

thin reaction zone regime

probability density function

turbulent reacting flows

turbulent flame

conditional averaging

## Author

### Vladimir Sabelnikov

Office national d'etudes et de recherches aerospatiales (ONERA)

### Andrei Lipatnikov

Chalmers, Mechanics and Maritime Sciences, Combustion and Propulsion Systems, Combustions and Sprays

#### Fluids

Vol. 5 1-18 109

### Driving Forces

Sustainable development

### Roots

Basic sciences

### Subject Categories

Fluid Mechanics and Acoustics

### DOI

10.3390/fluids5030109