Triglobal Stability Analysis of the Thermoacoustic Field in Rocket Engines
Type of DegreePhD Dissertation
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One of the most daunting problems in the development of a rocket engine is the appearance of coherent oscillatory structures in the flow. Characterized primarily by fluctuations in pressure, these oscillations can sync with a variety of physical mechanisms related to the flow, the combustion process, or geometrical features in the engine itself. In a short period of time, their growth rates can lead to pressure levels that are a significant fraction, or even a multiple, of the mean chamber pressure level. Historically, this problem is addressed primarily through ``guess-and-check'' methods that seek to dampen the unstable behavior through the introduction of baffles, bellows, or geometrical modifications to the engine. While sometimes successful, the experimentally-based approaches greatly increase the time and monetary cost of developing or modifying an engine. This situation has led some engineers to seek other methods for reducing instabilities by developing predictive analytical models. This line of research is successful in uncovering some of the foundational physical mechanisms prompting combustion instabilities, although it remains limited in scope to engines with simple geometries and mean flows. Given the significant computing advances made since the early years of combustion instability studies, computational fluid dynamics (CFD) modeling has begun to dominate the field. However, much like their experimental counterpart, CFD methods are often time consuming, expensive, and limited in their ability to pinpoint specific design parameters responsible for instabilities. The present work seeks to overcome these limitations by creating a linearized framework that allows for the efficient capturing of the acoustics and other unsteady phenomena in a rocket engine. Accordingly, using an energy-based approach, the growth rates of specific physical mechanisms can be calculated for a rocket engine with arbitrary geometry and mean flow. Furthermore, by implementing a triglobal paradigm, fluctuations are allowed to occur arbitrarily in all three spatial directions. In the present study, several verification cases are devised to explore known analytical and experimental results with the aim of assessing the validity and limitations of this model. These include comparisons of the biglobal and triglobal predictions to those obtained using asymptotic solutions or experimental data for burning cylindrical solid rocket motors with internal flow fields that correspond to the Taylor-Culick profile. These comparisons show excellent agreement between the biglobal and asymptotic solutions for the vorticoacoustic modes at several oscillation frequencies and test cases. For the same cases, the triglobal results agree reasonably well, but are constrained in grid resolution due to computational limitations. Lastly, the stability of the first three system modes of a novel bidirectional vortex engine is evaluated using this framework. This allows for an in-depth analysis of the inherent differences between the triglobal and axisymmetric, or biglobal, spatial assumptions when applied to an engine with a non-axisymmetric flow field. The resulting analysis reveals similarities in the acoustic fields of the two approaches, but varying degrees of difference for the vortical and entropic fields. The stability outcome matches reasonably well in the vorticoacoustic and thermoacoustic stability results, though the entropy generation term differs for the first two modes of the biglobal and triglobal formulations. The overall result is that, while the triglobal formulation can more accurately assess stability throughout an entire engine without restriction, the significantly increased computational run-time makes the higher fidelity only desirable for engines exhibiting strong non-axisymmetric behavior. The computational framework developed in the present study has several limitations and computing restraints, including lack of complete combustion model, one-way coupling between the acoustics and unsteady heat release, and the inability to capture nonlinear interactions. Thus, while contextualized within the problem of combustion instability, this framework focuses on establishing the groundwork in the area of rapid, three-dimensional, linear acoustic stability analysis. Building on top of this framework, it is hoped that future studies will increase the fidelity of this predictive tool by incorporating nonlinear and combusting phenomena as well. Nonetheless, by leveraging modern computing power and providing design engineers with specific insight into the sources of unstable behavior, the methodology used in this study has the potential to provide immense savings in resources and time in the development or modification of a rocket engine.