Direct numerical simulations of laboratory-scale thermodiffusively-unstable piloted Bunsen flames: Flame surface area, turbulent flame speed, and flame height

Direct numerical simulations (DNS) of laboratory-scale Bunsen flames have been conducted to reproduce the Cambridge piloted Bunsen flame, using lean hydrogen-methane blends over a broad range of conditions and thermodiffusive (TD) instability parameter; three nominal Karlovitz numbers (5, 20 and 100), each at four blend fractions (0%, 40%, 70% and 100% hydrogen by volume). The TD response in the Bunsen flames is consistent with previous flame-in-a-box (FIAB) simulations, as is the dual flame nature of TD-unstable blends; hydrogen burns rapidly in positively-curved regions and the methane left behind burns slowly in negatively-curved regions. Isosurfaces from FIAB and Bunsen flames highlight configuration differences, which could be due to two factors: firstly, the jet develops spatially in the streamwise direction (until it interacts with itself due to its inherent limited size), whereas the FIAB develops temporally (until it reaches the largest surface area that can be accommodated in the periodic box); secondly, confinement of dilatation by periodic boundaries in the FIAB may broaden the flame brush. Different measurements of flame surface area are compared; specifically, directly-measured temperature isosurfaces, a binarised flame surface density (FSD) following the experimental approach, and generalised FSD. The binarised FSD is shown to agree well with the direct measurement of isosurface; the experimental approach is valid. The results also demonstrate that 3D statistics can be faithfully inferred from 2D slices from DNS data (with the appropriate correction), even for the most unstable flames considered here. Joint probability density functions of local flame speed and curvature agree well with corresponding turbulent FIAB simulations, despite challenges attributing a single Karlovitz number. Similarly, the mean local flame speeds agree well with the empirical model, but flame surface areas are significantly smaller than the model developed in FIAB. The more local metrics translate well from FIAB, whereas the more global metrics are configuration-dependent. Finally, the models are combined with a shape factor to formulate a model for flame height, which generally presents good agreement with the measurements.