Manifold modeling of flame–flame interactions in turbulent premixed combustion

Whether premixed flame annihilation interactions can be captured by a manifold model for premixed combustion is an open question since flame–flame interactions give rise to local extrema in progress variable dissipation rate ( ⇾ χ ΛΛ ⇾ 0 ) at non-zero/-unity progress variable. This work demonstrates the ability to replicate the local thermochemical state at flame–flame interaction critical points (where ⇾ ∇ Λ ⇾ 0 ) using a manifold model in progress variable Λ by comparing the conditional statistics of Direct Numerical Simulations (DNS) to predictions from the manifold model. A DNS database of turbulent premixed statistically planar hydrogen–air flames in moderate turbulence was generated with conditions that exist firmly in the thin reaction zone regime. Extracting local progress variable dissipation rate profiles at the critical points as a function of progress variable χ ΛΛ ( Λ ) , these profiles are used to close the dissipation rate term in the premixed manifold equations. Furthermore, owing to the influence of differential diffusion, the progress variable curvature κ was extracted from the DNS and closed in the same manner κ ( Λ ) . Good agreement between the manifold model and the DNS for important thermochemical scalars can be achieved but only if the exact progress variable dissipation rate and curvature are enforced in the manifold model, demonstrating that the manifold model is an appropriate framework for modeling flame–flame interactions. A brief perspective is provided for closure of these quantities. Novelty and significance statement: This work demonstrates, for the first time, that a reduced-order, one-dimensional manifold model for premixed combustion can accurately capture the local thermochemical state of turbulent premixed flame–flame interactions. This addresses an “open question” in combustion modeling: annihilation events are a principal mechanism of local extinction but have lacked explicit representation in manifold-based paradigms. The primary scientific advance shows that closing the manifold equations with DNS-extracted profiles for progress variable dissipation rate and curvature yields very close agreement with DNS data. By showing that computationally efficient manifold models can replicate these complex thermochemical states when progress variable dissipation rate and curvature are accurately represented, this study establishes a vital foundation for developing general closure models to enable predictive, low-cost simulations of this critical extinction mechanism.