A Direct Numerical Simulation Assessment of Turbulent Burning Velocity Parametrizations for Non-Unity Lewis Numbers

The predictions of turbulent burning velocity parameterizations for non-unity Lewis number 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 projected 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 L2-norm of the relative error with respect to experimental data from literature for different Lewis numbers, higher turbulence intensity and thermodynamic pressure levels.