A Systematic Assessment of Artificial Flame Thickening for Thermodiffusively Unstable Lean Hydrogen Flames in Homogeneous Isotropic Turbulence

The Artificially Thickened Flame (ATF) approach is widely used to render premixed flames resolvable on coarse computational meshes, but thickening alters their interaction with turbulence. While considerable research has focused on the effects of thickening on turbulence-induced flame wrinkling, its influence on the mean local flame propagation speed in turbulent, thermodiffusively unstable hydrogen flames remains poorly understood. More than 200 flame-resolved simulations of premixed flames in homogeneous isotropic turbulence with detailed chemistry and transport are used to systematically isolate and quantify the effects of artificial thickening. Thickening the flame by a factor $F$ increases its effective flame-scale Karlovitz number according to $Ka_{\mathrm{f}}^F = Ka_{\mathrm{f}}\sqrt{F}$, while decreasing its effective Damköhler number according to $Da_{\mathrm{f}}^F = Da_{\mathrm{f}}/F$. In the regime considered here, the former enhances the mean local flame speed, whereas the latter reduces flame wrinkling, resulting in opposing effects on the flame consumption speed; hence, changes in both local flame propagation and flame area must be accounted for. Simulations matched with respect to $Ka_{\mathrm{f}}^F$ and $Da_{\mathrm{f}}^F$ collapse across different thickening factors $F$ until the thickened flame approaches the integral or geometric length scales of the configuration. Based on these scaling relations, a self-consistent efficiency correction is proposed to recover the unthickened flame consumption speed. Since the efficiency factor feeds back on the effective Karlovitz and Damköhler numbers, it must be determined implicitly.