Date of Award
Doctor of Philosophy
Gary A. Flandro
T. Moeller, J. Steinhoff, C. Parigger
Most combustion machines feature internal flows with very high energy densities. If a small fraction of the total energy contained in the flow is diverted into oscillations, large mechanical or thermal loads on the structure can be the result, which are potentially devastating if not predicted correctly. This is particularly the case for lightweight high performing devices like rockets. The problem is commonly known as "Combustion Instability".
Several mechanisms have been identified in the past that link the flow field to the acoustics inside a combustion chamber and thereby drive or dampen oscillations, one of them being vortex shedding.
The interaction between the highly sheared flow behind an obstacle and longitudinal acoustic oscillations inside a solid rocket booster is investigated both analytically and experimentally.
The analytical approach is developed based on modeling of the second order acoustic energy. The energy model is applied to the specific flow conditions just downstream of a single baffle protruding into the flow. The mean flow profile is assumed to be of the form of a hyperbolic tangent, the unsteady acoustic velocities are assumed to be sinusoidally oscillating. Solutions for the unsteady rotational velocities and the unsteady vorticity are derived. The resulting flow field is utilized in stability calculations for a simplified two-dimensional axial-symmetric geometry. This yields to linear growth rates of the (longitudinal) oscillation modes. The growth rates are functions of the chamber geometry, the mean flow properties and the properties of the shear layer created by the flow restriction.
A cold flow experiment is designed, tested and performed in order to validate the analytical findings. Flow is injected radially into a tube with acoustic closed-closed end conditions. A single baffle is installed in the tube, the axial position of the baffle is varied as well as its inner diameter. Frequency spectra of pressure oscillations are recorded.
The experimental data is then compared qualitatively to the analytical growth rates. Those longitudinal Normal Modes, which feature the highest theoretical growth rates, are expected to be most prominent in the experimental data. This behavior is clearly observable.
Blaette, Lutz, "Vortex Driven Acoustic Flow Instability. " PhD diss., University of Tennessee, 2011.