On the Optimum Distribution of Multiple Helmholtz Resonators for Annular Combustors

Abstract The combustors of many modern land-based gas turbines and aero-engines are annular. This kind of combustors often suffer from thermoacoustic oscillations, with the occurrence of mostly the circumferential first-order, second-order, and third-order oscillation modes in the annular combustion chamber. This could cause severe pressure oscillations in the combustor, which may increase noise and NOx emissions, affect the safe operation of the engine and even cause irreversible damages to the structure. To solve this problem, passive control methods are widely used—adding passive acoustic dampers such as Helmholtz resonators (HRs). Depending on the type and number of HRs, and the possible positions over the circumference to install them, there could easily have millions, or even billions, of possible arrangement patterns. Finding a good design is the key to solve this problem. In this paper, we perform a theoretical and numerical study of an annular combustor installed with multiple types of HRs over the circumference. First, a simple annular duct with arbitrary distributions of these HRs is studied analytically by solving the nonlinear eigenvalue problem of a one-dimensional network model. Based on the results of the analytical method, the impact of the HRs on the acoustic modes of the combustion chamber is studied and the optimum arrangement of multiple resonators is obtained. This arrangement usually gives a null (or small) mode splitting strength and a good damping effect. Finally, we apply the optimum arrangement to damp the thermoacoustic modes that have been captured by numerical simulation for a real annular combustor. We use numerical simulations based on solving the three-dimensional Helmholtz equation in COMSOL to verify the feasibility of the optimum arrangement.