Nonlinear Behavior of Longitudinal Waves in the Oscillations of Rijke Tube

The Rijke tube device has been employed since its invention in 1859 in the experimental study of many examples of thermo-acoustic phenomena. The device exhibits generation of acoustic oscillations by heat energy supplied to the flow field in the fashion of a selfexcited oscillator. In recent times, the Rijke tube has proved to be a valuable tool in simulation of combustion instability phenomena in rockets and industrial burners. Despite the simplicity of the device, the Rijke tube simulates most important geometrical and physical features that lead to the growth of nonlinear pressure oscillations in combustion chambers. For example it provides a through-flow as in a rocket chamber and is fixed with an energy source that can cause unsteady combustion. The open ends and geometrical simplicity leads to easy accessibility for instrumentation to make measurements that would not be possible in actual combustion chambers. During operation, wave motions are generated by transfer of energy from a heated grid placed at a point within the chamber that can be related to theoretical models for the phenomenon by Rayleigh and other investigators. However, initially, there is exponential growth of these oscillations to high amplitude and transition to a nonlinear limit cycle at a nearly fixed amplitude (usually lasting several seconds) due to natural nonlinearities in the system. The hypothesis advanced in this thesis to explain this nonlinear limiting effect that is the wave steepening occurs in a manner analogous to similar generation of steep wave fronts in rocket motor chambers. The latter proposal is based on: 1) direct observation (using Schlieren techniques) of traveling shock-like waves in axial mode instability, 2) correlation of the observed waves with spectral components similar to that of sawtooth structure, and 3) theoretical calculations showing that the limit amplitude phenomenon is directly related to the cascade of energy from lower frequency standing acoustic modes to higher harmonics leading to characteristic spectrum similar to that of a traveling steep-fronted wave. In prior research, the ‘mechanism’ of initiation of instability in the system has been the main focus. The goal of the research described in this thesis is to measure and to characterize the signal produced during the high- amplitude (nearly steady state) oscillations at the limit cycle. The intent was to demonstrate in a very simple way that the gas motions produced during the limit cycle in the Rijke tube have the same characteristics observed in many years of rocket testing. The observations again verify the great utility of the Rijke tube in seeking better understanding of the analogous rocket instability