A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Abstract

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ within turbulent flame brush. Second, negative correlation \documentclass[12pt]{minimal}\begin{document}$\overline{\mathbf {u}^{\prime } \cdot \nabla \Omega ^{\prime }}$\end{document}u′·∇Ω′¯ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and \documentclass[12pt]{minimal}\begin{document}$\overline{\Omega }$\end{document}Ω¯ is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases.