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A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

Lookup NU author(s): Professor Nilanjan ChakrabortyORCiD



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2017 The Author(s) The present work aims at modeling the entire convection flux (Formula presented.) in the transport equation for a mean reaction rate (Formula presented.) in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for (Formula presented.) are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, (Formula presented.), and mean, (Formula presented.), convection fluxes is well pronounced, with the turbulent flux, (Formula presented.), showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux (Formula presented.) reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.

Publication metadata

Author(s): Lipatnikov AN, Sabelnikov V, Chakraborty N, Nishiki S, Hasegawa T

Publication type: Article

Publication status: Published

Journal: Flow, Turbulence and Combustion

Year: 2018

Volume: 100

Issue: 1

Pages: 75-92

Print publication date: 01/01/2018

Online publication date: 01/08/2017

Acceptance date: 05/07/2017

Date deposited: 05/07/2017

ISSN (print): 1386-6184

ISSN (electronic): 1573-1987

Publisher: Springer


DOI: 10.1007/s10494-017-9833-y


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Funder referenceFunder name
Chalmers Transport Area of Advance. The second author (VS)
Combustion Engine Research Center (CERC)