Computational Vorticoacoustic Stability Analysis of the Bidirectional Vortex Engine
Type of DegreeMaster's Thesis
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Since the invention of combustion-based propulsion systems, the presence of resonating, broadband waves has often been associated with the onset of a phenomenon known as "combustion instability." These waves commonly take the form of pressure oscillations in the combustion chamber, reaching amplitudes that can match or even exceed that of the mean chamber pressure. Left unabated, these oscillations can affect the system's overall performance, dramatically increase heat transfer to the chamber walls and injector faceplates, and, in some cases, compromise the structural integrity of the entire propulsion system. Treatment of the problem entails determining potential instabilities during the design phase of the engine. Oftentimes, mitigation efforts lead to program cancellation due to the excessive amount of testing and engine redesigns that follow. Thus, there is a strong need to develop the necessary computational tools to analyze complex propulsion systems that can effectively and accurately determine the stability of large chambers, while also minimizing both computational and financial costs. The present study of a bidirectional vortex engine seeks to illuminate one such tool, which utilizes a linearized, energy-based approach to analyze the acoustic, vortical, and energy fields within the combustion chamber. By computationally discretizing field values across the domain by means of a finite differencing scheme, the tool enables us to return the stability margins of the chamber-specific modes in a relatively short amount of time. The results of this study show that the steep temperature gradient across the shear layer between the primary driving vortices, as well as the high density areas immediately surrounding the inlets, dramatically affect the acoustics of the system. In addition to the primary shear layer, secondary vortex cells can have an appreciable impact on instability. The stability calculations reveal that the first pure tangential mode of 1243 Hz is the most unstable mode, while the first longitudinal mode of 1321 Hz will be stable. Though the thermodynamic nature of this engine creates a unique acoustic environment, the instability of the tangential modes follows suit with traditional, axially-driven liquid rocket engines, where the prevalent modes are often those oscillating tangentially. Thus, while unable to recover the nonlinear, limit-cycle amplitudes of the resonating waves, the presently used linearized approach may be perceived as an efficient method to pinpoint the specific modes and associated physical mechanisms within the chamber that contribute to combustion instability in a rocket engine.