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