Three-dimensional Simulations of Lean H2-air Flames Propagating in a Narrow Gap: n the Validity of the Quasi-two-dimensional Appoximation

The premixed propagation of lean isobaric H2-air flames (φ = 0.3) in Hele-Shaw cells (i.e. two parallel plates separated by a small distance, h, on the order of the thickness of the planar adiabatic flame, δf ∼ 3 mm) is investigated numerically. Three-dimensional (3D) simulations with detailed chemistry and transport are used to examine the effect of h on the flame dynamics and its overall normalized propagation speed (S T /S L) for a semi-closed system of size 25δf × 25δf × h. To determine the validity of an existing quasi-two-dimensional (quasi-2D) formulation (derived in the limit of h → 0) to capture the 3D dynamics, results for h = 0.1δf , h = 0.5δf , and h = δf are reported. For h = 0.1δf strong cell splitting/merging is observed with associated low frequency/high amplitude oscillations in the temporal evolution of S T /S L (10-17Hz; 6 ≤ S T /S L ≤ 10). Larger values of h exhibit a much smoother evolution. For h = 0.5δf the cell splitting/merging is milder relaxing to a steady propagating speed of S T /S L ∼ 6 after an initial transient; for h = 1δf , the flame dynamics along the h direction starts to play an important role showing two distinct phases: (i) initial symmetric propagation with a linear increase in S T /S L (from 5.3 to 6.8) as early signs of asymmetry are visible, (ii) followed by a fully non-symmetric propagation resulting in an abrupt increase in S T /S L that quickly relaxes to a constant value thereafter (S T /S L ∼ 10). Our preliminary results suggest that for the lean H2-air mixture considered the quasi-2D approximation breaks down for h > 0.1δf .