Different perspectives on predicting the thermoacoustic energy conversion response in a Rijke tube

In this work, six different perspectives on characterizing the thermoacoustic field in an open-ended Rijke tube are considered and discussed. These begin with a three-pronged approach consisting of theoretical, experimental, and numerical investigations of the Rijke tube's time-dependent field. It is followed by a discussion of effective techniques that rely on either Green's function or differential equation models. Finally, a perturbation expansion is introduced that leverages a naturally occurring small parameter in the open tube configuration. This approach is shown to produce accurate predictions of pressure modal shapes and frequencies for an arbitrary specified temperature distribution. It also leads to a set of linear partial differential equations that can be solved in conjunction with a Green's function expression for the thermoacoustic pressure, velocity, and heat oscillations. In this study, the underlying framework is presented and evaluated for the pressure disturbance only. Another fundamental result includes a similarity parameter, coined the Rijke number, which plays an essential role in driving thermoacoustic oscillations, namely, by relating heat-flux fluctuations to the acoustic velocity and pressure. In this context, we find that the peak value of the energy-flux vector modulus, which stands for the modular product of acoustic velocity and pressure, does indeed occur at the heat source location and increases with the heat power input.