Citation: Mohan, V.; Herbert, M.;
Klein, M.; Chakraborty, N. A Direct
Numerical Simulation Assessment of
Turbulent Burning Velocity
Parametrizations for Non-Unity
Lewis Numbers. Energies 2023, 16,
2590. https://doi.org/10.3390/
en16062590
Academic Editors: Monika Rerak,
Tomasz Sobota and Jan Taler
Received: 4 February 2023
Revised: 27 February 2023
Accepted: 6 March 2023
Published: 9 March 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
A Direct Numerical Simulation Assessment of Turbulent
Burning Velocity Parametrizations for Non-Unity
Lewis Numbers
Vishnu Mohan
1
, Marco Herbert
2
, Markus Klein
2,
* and Nilanjan Chakraborty
1
1
School of Engineering, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK;
vishnu.mohan@newcastle.ac.uk (V.M.); nilanjan.chakraborty@newcastle.ac.uk (N.C.)
2
Department of Aerospace Engineering, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39,
85577 Neubiberg, Germany
* Correspondence: markus.klein@unibw.de
Abstract: The predictions of turbulent burning velocity parameterizations for non-unity Lewis num-
ber flames have been assessed based on a single-step chemistry Direct Numerical Simulation (DNS)
database of premixed Bunsen flames for different values of characteristic Lewis numbers ranging
from 0.34 to 1.2. It has been found that the definition of the turbulent burning velocity is strongly
dependent on the choice of projected flame brush area in the Bunsen burner configuration. The
highest values of normalized turbulent burning velocity are obtained when the projected flame brush
area is evaluated using the area of the isosurface of the Reynolds averaged reaction progress variable
of 0.1 out of different options, namely the Favre averaged and Reynolds averaged isosurfaces of
reaction progress variable of 0.5 and integral of the gradient of Favre and Reynolds averaged reaction
progress variable. Because of the axisymmetric nature of the mean flame brush, the normalized
turbulent burning velocity has been found to decrease as the burned gas side is approached, due to
an increase in flame brush area with increasing radius. Most models for turbulent burning velocity
provide comparable, reasonably accurate predictions for the unity Lewis number case when the pro-
jected flame brush area is evaluated using the isosurface of the Reynolds averaged reaction progress
variable of 0.1. However, most of these parameterizations underpredict turbulent burning velocity
values for Lewis numbers smaller than unity. A scaling relation has been utilized to extend these
parameterizations for non-unity Lewis numbers. These revised parameterizations have been shown
to be more successful than the original model expressions. These modified expressions also exhibit
small values of L
2
-norm of the relative error with respect to experimental data from literature for
different Lewis numbers, higher turbulence intensity and thermodynamic pressure levels.
Keywords: turbulent burning velocity; turbulent premixed Bunsen flame; Lewis number; flame
surface area; direct numerical simulations
1. Introduction
Due to threats of climate change, countries and industries are searching for cleaner
and efficient ways of generating energy. Although renewable forms of energy exist, these
have their own drawbacks, such as the intermittent generation of energy for wind and
solar. Unless and until more efficient methods to store such energy are devised, it is very
likely that combustion will remain the principal mode of energy production. Premixed
combustion, in which reactants are homogenously mixed, is a good way to reduce the
emission of pollutants as it limits the chances of incomplete combustion. Moreover, it is
easier to control NOx emissions by optimizing between the peak temperature achieved and
power produced. This can be done by either controlling the temperature or the composition
of the reactants. The emission of greenhouse gases such as CO
2
can also be reduced by
using a premixed combustion of fuels such as hydrogen, ammonia or syngas. Net zero
Energies 2023, 16, 2590. https://doi.org/10.3390/en16062590 https://www.mdpi.com/journal/energies