Linear and nonlinear modeling of self-excited acoustic oscillations in a T-shaped thermoacoustic engine

Branch tubes are often used in thermoacoustic engines (TAEs) for acoustic power extraction or acoustic field adjustment. Their roles, although critical for the performance of the thermoacoustic system, are not fully understood yet. To address this issue, this study investigates the self-excited acoustic oscillations inside a T-shaped TAE where a branch tube is connected to a classical standing-wave TAE. First, system-level theoretical models based on the linear acoustic and thermoacoustic theories in the frequency domain were established to study the acoustic modes and their stability. System-wide computational fluid dynamics (CFD) simulations were carried out to simulate the evolution of the unstable acoustic modes from the initial start-up to the steady state in the time domain. Second, parametric studies on the coupling position of the branch tube and its length were conducted. The effects of the coupling position and branch length on the natural frequencies and mode shapes of the T-shaped TAE were determined by theoretical derivations and substantiated by CFD simulations. The growth/attenuation rate of each acoustic mode was also examined. The CFD results show that bifurcation in steady-state dynamics occurs when the coupling position is altered or the branch length is increased. The steady-state behavior of the T-shaped TAE can transit from limit-cycle oscillations to quasi-periodic oscillations, or vice versa. The theoretical and CFD methodologies in this work are valuable in comprehending the acoustic/dynamic characteristics of the T-shaped standing-wave TAE, providing useful guidelines for studying the coupling of external loads in traveling-wave thermoacoustic systems that usually have more complex structures but are inherently more efficient.