MCE Ph.D. Thesis Seminar

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number premixed flames, which are studied by considering vorticity, ω, and its transport equation.  A series of direct numerical simulations (DNS) of turbulent premixed n-heptane/air flames are performed, whose conditions span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at sufficiently high Karlovitz numbers, enstrophy, ω²=ω∙ω, transport resembles that of homogeneous isotropic turbulence. As a result, enstrophy scales as a function of the kinematic viscosity and dissipation rate alone, supporting the validity of Kolmogorov's first similarity hypothesis for sufficiently high Karlovitz numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration. The isotropy of vorticity is then assessed. It is found that given a sufficiently large value of the Karlovitz number the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching term. In this case, the local dynamics of vorticity in the strain-rate tensor eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence. Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number. This supports the validity of Kolmogorov's first similarity hypothesis and hypothesis of local isotropy under these conditions. This conclusion provides/suggests directions for modeling high Karlovitz number premixed flames using large eddy simulations.