Modeling of Reaction Dynamics in a Turbulent Hydrogen-Air Slot Flame Using Resolvent Analysis

Abstract: This work applies Resolvent Analysis (RA) to study the dynamics of a hydrogen-air slot flame with a Reynolds number of 5500, a Karlovitz number of 20, and an equivalence ratio of 0.4. Direct Numerical Simulations (DNS) data are analyzed using shifted Spectral Proper Orthogonal Decomposition (SPOD), and the resulting structures are compared with optimal resolvent responses obtained from the linearization of a RANS-EBU reaction rate model. Both SPOD and RA show that the flow dynamics are dominated by Kelvin-Helmholtz wave packets over a broad frequency range, particularly between 300 and 1000 Hz. This behavior is reflected in the resolvent gains and SPOD eigenvalues, which exhibit consistent amplification within this range. The velocity fluctuation mode shapes predicted by RA agree well with the SPOD modes. However, the corresponding mode shapes for the progress variable and heat release show weaker agreement. To address this limitation, the study introduces a generalized active-flame closure calibrated with high-fidelity data, which remains compatible with the linearized framework and improves the agreement with SPOD modes. Overall, the results indicate that thermodiffusive instabilities in turbulent hydrogen flames do not hinder the applicability of the active-flame resolvent approach.