Investigation of Intrinsic Flame Instabilities in Planar Hydrogen Flames with the Linearized Reactive Flow Equations

Lean, premixed hydrogen flames are prone to intrinsic flame instabilities (IFIs). Two mech- anisms primarily contribute to IFIs in lean hydrogen flames: The hydrodynamic instability which is inherently linked to the thermal expansion of the flow across the flame, and the thermodiffusive instability, caused by an imbalance of thermal and diffusion fluxes of the deficient reactant. IFIs in hydrogen flames have predominantly been studied with analytical models and Direct Numerical Simulations (DNS). However, analytical models derived under asymptotic assumptions fail to accurately quantify growth rates in lean hydrogen flames as they are missing higher-order terms. Conversely, while DNS resolves physical scales with a much higher fidelity than analytical models, it is computationally very expensive. To bridge this gap, this thesis applies the Linearized Reactive Flow (LRF) equations to the investigation of IFIs in planar, premixed hydrogen flames in their early, linear regime. With this approach, global linear stability analysis is performed, maintaining the fidelity of physical description comparable to DNS. The LRF equations inherit the linear flame dynamics by design and have been successfully applied to the analysis of thermoacoustic systems. This operator-based framework yields a global eigenvalue problem, which is solved to compute wavenumber-dependent growth rates (i.e. dispersion relations). This thesis develops a numerical framework to compute disper- sion relations with the LRF equations, whereby important insights are gained on the gener- ation of a kinematically stabilized baseflow and the influence of the domain length on com- puted growth rates at low wavenumbers. To model the reaction term, a fuel limited model and a global H2/O2-mechanism are implemented. Dispersion relations generated with the LRF framework are compared against those obtained analytically and by DNS. This comparison shows that growth rates obtained by LRF agree more closely with DNS than analytical models in the high wavenumber limit. These results indicate that the newly established framework successfully computes growth rates in hydrodynamically and thermodiffusively unstable hy- drogen flames, although the degree of accuracy remains to be determined. Finally, physical flow fields are reconstructed from the unstable modes to study two-dimensional effects of the perturbations. Furthermore, an analysis of the adjoint eigenmodes suggests differences in the mechanism of optimal receptivity between hydrodynamically and thermodiffusively unstable flames.