Effect of backward moving pressure wave on tulip flame formation in premixed hydrogen–air mixture

Flame propagation and tulip flame formation in a premixed hydrogen–air mixture was investigated in a rectangular channel (400 mm length, 40 × 40 mm ² cross-section). High-speed imaging was used to capture the temporal evolution of the flame over an equivalence ratio range from ϕ  = 0.6 to 1.47, with an increment of 0.1. Flame contours extracted from images were used to determine flame position, propagation velocity, and structural transitions, including tulip-flame formation. Time-resolved shadowgraph imaging reveals that a strong upstream-propagating pressure wave interacts with the downstream-moving flame front, causing flame deceleration, local flow reversal, and eventual inversion. This interaction is evident from the pressure gradient appearing within the burnt gases in the shadowgraphs. A detailed instability analysis was performed by evaluating characteristic time scales associated with pressure-wave ( τ _PW ), rarefaction-wave ( τ _RW ), Darrieus–Landau ( τ _DL ), and thermo-diffusive ( τ _TD ) instabilities, along with the Rayleigh–Taylor (RT) instability growth factor ( σ _RT *Δ t ). Although τ _RW is the shortest, its influence is limited due to low wave amplitude. The pressure wave, characterised by a short τ _PW , dominates flame flattening and inversion, while RT instability governs post-inversion distortion. In contrast, τ _DL and τ _TD remain comparatively large, indicating a minor role during rapid transitions. The combined analysis explains the strong dependence of tulip flame formation on equivalence ratio. At rich conditions ( ϕ  = 1.47), multiple inversions occur with peak flame speeds of ∼169 m/s near the wall and ∼137 m/s at the centreline (Mach no. ≈ 0.39 and 0.31), and σ _RT *Δ t > 1. As ϕ decreases, flame speeds and RT amplification reduce significantly, resulting in weaker or no tulip formation for ϕ  ≤ 1.3.