Thermodiffusively-unstable lean premixed hydrogen flames: Length scale effects and turbulent burning regimes

Abstract

This paper presents direct numerical simulations (DNS) of thermodiffusively-unstable lean premixed hydrogen flames in the canonical turbulent flame-in-a-box configuration. A range of reactant (pressure, temperature, and equivalence ratio) and turbulent (Karlovitz and Damköhler number) conditions are used to explore the effects of the small and large turbulent scales on local and global flame response. Turbulence-flame interactions are confirmed to be independent from integral length scale (or equivalently, from Damköhler number) for a fixed Karlovitz number. Furthermore, a recent model that predicts mean local flame speed as a function of an instability parameter and Karlovitz number is also demonstrated to be independent from integral length scale. This model thereby reduces turbulent flame speed modelling for thermodiffusively-unstable cases to predicting surface area enhancement. Flame surface area wrinkling is found to have good agreement with Damköhler’s small-scale limit. There is some scatter in the data, although this is comparable with similar experimental data, and the freely-propagating flame properties have a greater impact on the turbulent flame speed than the flame surface area. It is demonstrated that domain size can have an effect on flame surface area even if the integral length scale remains unchanged; the larger volume into which flame surface area can develop results in a higher turbulent flame speed. This is not accounted for in conventional algebraic models for turbulent flame speed. To investigate the influence of the fuel Lewis number ${\mathrm{Le}}_{\text{f}}$, an additional study is presented where ${\mathrm{Le}}_{\text{f}}$ (alone) is artificially modified to span a range from 0.35 to 2. The results demonstrate that more flame surface area is generated for smaller ${\mathrm{Le}}_{\text{f}}$, but the difference for ${\mathrm{Le}}_{\text{f}}$  $\lesssim$  1 is much smaller than that observed for ${\mathrm{Le}}_{\text{f}}$  $>$  1. A volume-filling-surface concept is used to argue that there is a limit to how much flame surface can develop in a given volume, and so there is only so much more flame surface can be induced by the thermodiffusive response; whereas the thermodiffusive response at high ${\mathrm{Le}}_{\text{f}}$ is to reduce flame surface area. The agreement of the present data (and previous work) with Damköhler’s small-scale limit (even for low-to-moderate Karlovitz numbers) suggests that a distinction should be made between the small-scale limit and the distributed burning regime. Furthermore, it is argued that the distinction between large- and small-scale limits should be made based on Damköhler number. Consequently, the flamelet, thin reaction and distributed regimes should be distinguished by Karlovitz number (as usual), but the two latter regimes both have separate large- and small-scale regimes. Finally, implications for the turbulent premixed regime diagram are discussed, and a modified regime diagram is proposed.

Novelty and significance

This paper: confirms that turbulence-flame interactions at the flame scale are independent of integral length scale (at fixed Karlovitz number), as is the local flame speed model for thermodiffusively-unstable flames (Howarth et al., 2023); demonstrates potential domain size effect not accounted for in turbulent-flame models; flame surface wrinkling agrees with Damköhler’s small-scale limit for thermodiffusively-unstable flames in the thin reaction zone at low Damköhler number; and flame surface wrinkling increases slightly for low fuel Lewis numbers, but decreases significantly at high fuel Lewis numbers. There are significant consequences for the turbulent premixed regime diagram: distinction between Damköhler’s small-scale limit and distributed burning regime; separation of small- and large-scale limit by Damköhler number; application of the $\lambda$-flames concept to thin reaction zone; and exclusive use of Karlovitz and Damköhler number for regime classification and diagram axes.