Premixed flames subjected to extreme levels of turbulence part II: Surface characteristics and scalar dissipation rates

The current work assesses the impact of turbulence on flame surface characteristics and scalar dissipation rates ( χ C ) of piloted premixed methane-air flames. This assessment is facilitated via the application of planar Rayleigh scattering (PRS) to a subset of the flames considered in Part I (13 in total), which possess turbulent Karlovitz, Damkohler, and Reynolds numbers in the range of 1.1 ≤ K a T , P ≤ 144, 0.24 ≤ D a T , P ≤ 5.79, and 1,200 ≤ R e T , 0 ≤ 35,000, respectively. Instantaneous temperature maps are derived from the PRS images with an accuracy that is conservatively estimated to be within ∼ 3%. Additionally, the fidelity of the collected images was enhanced via the application of a combined wavelet-based and edge-preserving guided filtering scheme that allows scales associated with the peak of the dissipation spectra in the modestly turbulent flames considered here to be fully resolved. After such filtering, the temperature images were converted to reaction progress variable maps ( C T ). Two-dimensional isocontours were extracted from these maps and used to assess the flame surface density (FSD; Σ ) and the in-plane curvature ( κ 2 D ) of the flames considered here. Furthermore, scalar dissipation rate ( χ C T ), its density weighted average ( χ C T ˜ ), and other relevant quantities (e.g., the density-weighted variance of C T : C T ″ 2 ˜ and the generalized FSD: | ∇ C T | ¯ ) were derived from the C T -maps. Subsequently, relationships between these quantities were assessed and compared against theoretical models that aim to capture such relationships through simple expressions. The results indicate that the distribution of κ 2 D values broadens with enhanced turbulence, as does the integrated and peak values of FSD. Moreover, each of these parameters exhibit a strong positive correlation with K a T , P , highlighting the role this non-dimensional parameter plays in dictating flame surface wrinkling/area-generation. Relationships between χ C T , C T ″ 2 ˜ , and | ∇ C T | ¯ , are compared to flamelet-type models proposed by Vervisch et al. as well as by Bray, Swaminathan, Kolla, Chakraborty, and coworkers. Overall, despite the fact that the considered flames exhibit substantial preheat zone broadening and are subjected to extreme levels of turbulence, the proposed theoretical relationships between χ C T , C T ″ 2 ˜ , and | ∇ C T | ¯ show favorable agreement to the measurements. While differences between the measured and theoretical results are observed, the two can be reconciled with minor adjustments to the various constants in these models (i.e., changing them by no more than a factor of ∼ 2). Ultimately, such observations provide support for utilizing flamelet-type models to simulate premixed flames even when they are subjected to extreme turbulence levels. Moreover, the wealth of information provided here can help guide the development of robust yet efficient numerical tools for simulating highly turbulent premixed flames, which will aid in reducing the cost of and time to produce robust, efficient, and clean-burning combustion engines.