An investigation of the open-loop amplification of a Reynolds number dependent process by wave distortion

The response of a constant-temperature hot-wire anemometer to sinusoidal and distorted sinusoidal acoustic oscillations is examined. The output of the anemometer is dependent upon the Reynolds number of the flow over the wire. The response is a measure of the interaction between the anemometer output and the acoustic pressure in the neighborhood of the wire. It is an open-loop prediction of the characteristics of actual closed-loop operation of a system. If the open-loop response is large enough, unstable closed-loop operation is predicted. The study was motivated by a need to investigate the stability limits of liquid-propellant rockets when perturbed by pressure oscillations. The sinusoidal and distorted sinusoidal acoustic oscillations used for this study are the same as those characteristic of unstable rocket combustion. Qualitatively, the results are similar--the response of the system to pure sinusoidal acoustic vibration of the fluid surrounding the wire is small, even when the magnitude of the acoustic pressure is quite large; but the response can be increased by as much as an order of magnitude with respect to the sinusoidal case by the addition of distortion. The amplitude and phase of the distortion component, relative to the fundamental component, are the dominant factors in the increase in the response.