Dynamical Systems Characterization and Reduced Order Modeling of Thermoacoustics in a Lean Direct Injection Hydrogen Combustor

Hydrogen is a promising zero-carbon fuel for decarbonized energy and transportation sectors. While carbon emission is not a concern for hydrogen combustion, its higher adiabatic flame temperature poses challenges of mitigating thermal $NOx$ emissions. The wide flammability limits of hydrogen allow a fuel-lean operation, which can reduce $NOx$ emissions. However, lean operation makes the combustion chamber susceptible to thermoacoustic oscillations. In this study, the thermoacoustic instabilities of partially premixed hydrogen flames in a lean direct injection (LDI) multicluster combustor are characterized using dynamical systems theory. The combustor was operated at a range of bulk velocities (30–90 m/s) and equivalence ratios (0.2–0.6), and time-resolved pressure oscillations and integrated OH* chemiluminescence measurements were taken. The thermoacoustic system reveals a variety of dynamical states in pressure such as period-1 limit cycle oscillation (LCO) with a single characteristic frequency, period-2 LCO with two characteristic frequencies, intermittent, quasi-periodic, and chaotic states as either bulk velocity or equivalence ratio is varied. At a bulk velocity of 30 m/s, as the equivalence ratio is gradually decreased from 0.6 to 0.2, the dynamical behavior follows a sequence from an intermittent state to a period-1 LCO, then to a quasi-periodic state, and eventually reaches a chaotic state. As the equivalence ratio is decreased for a bulk velocity of 60 m/s, the pressure oscillations evolve from a period-2 LCO to quasi-periodic state before flame blows off. The emergence of period-2 and quasi-periodic states indicate the presence of strong nonlinear interactions among the cavity acoustic modes. These modes and their spatial behavior are investigated using a reduced order model which solves the three-dimensional (3D) inhomogeneous Helmholtz equation with an n–tau flame model. The analyses show that the period-2 and quasi-periodic states can arise due to the interaction between the plenum and combustion chamber modes indicating that hydrogen flames may excite a wide range of cavity acoustic modes.