Validation of the Turbulent Burning Velocity Based on Asymptotic Zone Conditional Transport in Turbulent Premixed Combustion

영역조건평균에 기초한 난류예혼합 화염 전파 속도식 유도 및 검증

An analytical expression for the turbulent burning velocity is derived from the asymptotic zone conditional transport equation at the leading edge. It is given as a sum of laminar and turbulent contributions, the latter of which is given as a product of turbulent diffusivity in unburned gas and inverse scale of wrinkling at the leading edge. It was previously shown that the inverse scale is equal to four times the maximum flame surface density in the wrinkled flamelet regime [1]. The linear behavior between $U_T$ and u' shows deviation with the inverse scale decreasing due to the effect of a finite flamelet thickness at higher turbulent intensities. DNS results show that $U_T/S^0_{Lu}$ may be given as a function of two dimensionless parameters, $u'/S^0_{Lu}$ and $l_t/\delta_F$, which may be transformed into another relationship in terms of $u'/S^0_{Lu}$, and Ka. A larger $l_t/{\delta}_F$ or a smaller Ka leads to a smaller scale of wrinkling, hence a larger turbulent burning velocity in the limited range of $u'/S^0_{Lu}$. Good agreement is achieved between the analytical expression and the turbulent burning velocities from DNS in both wrinkled and thickened-wrinkled flame regimes.