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Thermodiffusive instabilities can have a leading order effect on flamepropagation for lean premixed hydrogen flames. Many simulation studies havebeen performed to study this effect, but almost exclusively in two-dimensional(2D) or domain sizes too small to support the characteristic large-scalefeatures of the instability. The main purpose of this study is to quantify thedifferences of 3D and 2D flames using simulations on sufficiently largedomains. To this end, direct numerical simulations (DNS) of thermodiffusivelyunstable laminar premixed hydrogen flames stabilized in 3D domains wereperformed. The effects of confinement on the flame dynamics are rigorouslyinvestigated by varying the domain size. The flame burning velocity shows astrong dependence on the domain size when the lateral domain width is less than50 laminar flame thicknesses. The characteristic patterns of thethermodiffusively unstable flame are analyzed in detail, including theinstantaneous flame structure, global burning velocity, flame surface area,stretch factor, curvature distribution, and the cell size. The effects of thecomputational setup (2D vs. 3D) on the local flame front curvature and thedistributions of the thermo-chemical quantities are quantified through aconditional analysis. The formation and destruction mechanisms of the distinctcellular structures observed in the 3D domain are analyzed focusing on theinteractions between the flame dynamics and the flow field, and thecontributions of the production of flame surface density, kinematicrestoration, and curvature dissipation are quantified. Compared with thecorresponding 2D simulation, the flame surface area in the cut plane of the 3Dconfiguration is similar, yet the burning velocity and the stretch factor areincreased. The reason for this is the difference in curvature statistics in 2Dand 3D.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain -- Part I: Characteristic patterns