The effect of streaming on thermoacoustic systems
Although the current thermoacoustic theory has so far proved successful in allowing us to analyse and understand thermoacoustic systems, there are inherent limitations associated with it. These are related to the fact that this theory is based on linear approximations. As designers search for ways to increase the efficiency and power density of thermoacoustic devices the accuracy of the linear theory decreases significantly, as a variety of non-linear effects start to become important. For example, when the pressure amplitude is increased, in order to increase the power density. This thesis concentrates on the non-linear effect of acoustic streaming.
Acoustic streaming is a steady flow that is superimposed upon the acoustic Oscillations. An expression for the streaming velocity is developed for a parallel plate channel having an arbitrary gap width, so that the solution is valid for both thin and wide boundary layers. The solution includes thermal effects arising from the presence of an axial temperature gradient along the channel, and arbitrary phase between the pressure and velocity. An essential feature of the streaming velocity is the generation of circulating loops, which can cause heat to be convected within the channel.
An expression for the transverse steady state temperature was also derived, for similar conditions as outlined for the streaming velocity. It was found that when an axial temperature gradient is present the magnitude of the transverse steady state temperature increases significantly as the width of the channel increases. The implication of this is that a significant amount of heat can be convected along the channel due to the action of the streaming velocity. When no axial temperature gradient is present, the transverse steady state temperature reduces to a small constant value outside the boundary layer.
A numerical finite difference scheme was developed to model non-linear flow within the two-dimensional channel. The model solves for the conjugate fluid-solid problem enabling the temperature difference induced along the channel to be predicted. The model compared very well to experimental data. It was also found to be in excellent agreement with the analytical solutions for the streaming velocity and the transverse steady state temperature.
The effect of streaming on the energy flux density was examined for a wide channel, having a temperature gradient along its length. A fourth-order expression was developed, which yielded a solution in terms of the transverse steady state temperature and second-order mass flux, which for certain conditions could be of a similar magnitude as the second-order terms.
For a thermoacoustic core, it was proposed that a toroidal flow could form and convect heat from one heat exchanger to the other. To analysis this effect toroidal flow was incorporated into an expression for the temperature difference induced across a thermoacoustic couple. This result was found to be in excellent agreement with experimental data. The effect of toroidal streaming on the thermoacoustic core was also considered. In addition, a second-order expression for the work flux was derived that included a previously ignored term due to acoustic streaming.