One Dimensional Modeling of Vorticity in high Karlovitz Number Turbulent Premixed Flames

Turbulent combustion involves the interaction of two complex non-linear phenomena: turbulence and chemistry. The current study focuses on modeling the effects of the flame on the turbulence characteristics, more specifically on the vorticity $\omega$, which is characteristic of the smallest turbulent scales. This is performed through an a-priori analysis of high Karlovitz number turbulent premixed flames. The objective is to derive a one-dimensional model equation for the transport of enstrophy, $\omega^{2} = \omega\cdot\omega$. The terms in the enstrophy transport equation are modeled and scaled by a combination of flow properties. Results from a series of previously performed direct numerical simulations(DNS), spanning a range of Karlovitz number(Ka), Reynolds number(Re) and flame density ratios, are analysed to obtain the coefficients in the one-dimensional differential equation for enstrophy and demonstrate their dependence, or lack thereof, on $Ka$ and $Re$. Lastly, the model equation is solved and the results are compared with the DNS results.