The impact of non-stiff fuel injection on the acoustic response of a partially premixed hydrogen flame

Micro-mix combustion has been proposed to mitigate flashback and maintain low NOx in fuel-flexible gas turbines. In such partially premixed configurations, both velocity and pressure fluctuations can induce equivalence ratio fluctuations near the fuel injector. Once the pressure oscillation reaches a significant level, the assumption of stiff fuel injection will be compromised, resulting in fluctuations in fuel mass flow. This study investigates the influence of non-stiff injection, where the fuel mass flow can be modulated by pressure fluctuations, on the dynamic response of a partially premixed hydrogen flame. A model incorporating the acoustic impedance of a circular aperture in the fuel line is developed to predict the evolution of equivalence ratio fluctuations and validated using time-resolved ultraviolet absorption spectroscopy. The model reproduces the measured gain under non-stiff injection, whereas assuming stiff injection underestimates it. Flame transfer functions (FTF) based on OH* chemiluminescence exhibit gain modulation over frequency, arising from constructive and destructive interferences between velocity- and equivalence ratio-driven oscillations, with Strouhal number scaling effectively collapsing the phase and the positions of peaks and troughs in the FTF gain. However, variations in the FTF gain across different mean flow velocities suggest an additional contribution of pressure-induced equivalence ratio fluctuations. To identify this effect, an alternative FTF is introduced using the fuel injection velocity as the reference input. The resultant collapse confirms the role of pressure-induced equivalence ratio fluctuations. Finally, phase-averaged OH* analysis reveals distinct responses along the flame. These findings offer valuable insights for the design of future hydrogen-fueled combustion systems.