| The linear analytical theory of thermoacoustic effects is well developed. However, the literature contains evidence of the presence of nonlinear processes in thermoacoustic devices. The available linear theory is incapable of dealing with these phenomena and its extension to the nonlinear regime does not appear to be easy. Direct numerical simulations that can take into account nonlinearities and multi-dimensional effects are also difficult because of a large disparity in the flow scales existing in thermoacoustic devices.; The focus of this thesis is the study of nonlinear effects which take place in thermoacoustic devices and play an important role already at moderate oscillation amplitudes. Progress in the direction of nonlinear phenomena requires a time-domain formulation. For this purpose, the governing equations are integrated over the cross section of a thermoacoustic device. This procedure leads to a general time-domain, fully nonlinear, quasi-one-dimensional model of thermoacoustic devices. While this model is not exact due to the averaging over the cross section, in the frequency domain and for small amplitudes it reduces to the standard linear theory. The model is substantially simpler than a truly multidimensional one. It is capable of predicting the response of thermoacoustic devices to various design variables such as cross-section area variations, stack position, fluid and solid properties, and others.; A weakly nonlinear theory of thermoacoustic instability in thermoacoustic devices is developed by exploiting the difference between the instability time scale and the period of standing waves. By carrying the expansion to fourth order in the perturbation parameter and using the method of multiple time scales, explicit results for the initial growth, nonlinear evolution, and final saturation are obtained. The dependence of the saturation amplitude upon the temperature difference in the stack, the tube geometry, stack plate spacing, Prandtl number, and other parameters is illustrated.; The second part of the thesis deals with the nonlinear behavior of a layer of bubbly liquid surrounded by clear liquid, and in particular with the use of this arrangement as a parametric array. |
