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A method for determining the specific acoustic admittance of the inlet and outlet ports of a combustion chamber is presented. Parameter estimation techniques of Gauss linearization and genetic algorithms are employed to recover the acoustic boundary conditions. These techniques are used with a combination of two resources: dynamic pressure measurements obtained during combustor operation, and a finite element method-based model of the combustion chamber. Results of a theoretical analysis are presented which show that the method is capable of accomplishing its mission. An observation of particular significance is the lack of sensitivity of the pressure mode shape to relatively large changes in the acoustic boundary conditions. / Master of Science

Combustion instability plagues the combustion community in a wide range of applications. This un-solved problem is especially prevalent and expensive in aerospace propulsion and ground power generation. The challenges associated with understanding and predicting combustion instability lie in the flame response to the acoustic field. One of the more complicated flame response mechanisms is the velocity coupled flame response, where the flame responds dynamically to the acoustic velocity as well as the vortically induced velocity field excited by the acoustics. This vortically induced, or hydrodynamic, velocity field holds critical importance to the flame response but is computationally expensive to predict, often requiring high fidelity CFD computations. Furthermore, its behavior can be a strong function of the numerous flow parameters that change over the operability map of a combustor. This research focuses on a nominally two dimensional bluff body combustor, which has rich hydrodynamic stability behavior with a manageable number of stability parameters. The work focuses first on experimentally characterizing the dynamical flow and flame behavior. Next, the research shifts focus toward hydrodynamic stability theory, using it to explain the physical phenomena observed in the experimental work. Additionally, the hydrodynamic stability work shows how the use of simple, model analysis can identify the important stability parameters and elucidate their governing physical roles. Finally, the research explores the forced response of the flow and flame while systematically varying the underlying hydrodynamic stability characteristics. In the case of longitudinal combustion instability of highly preheated bluff body combustors, it shows that conditions where an acoustic mode frequency equals the hydrodynamic global mode frequency are not especially dangerous from a combustion instability standpoint, and may actually have a reduced heat release response. This demonstrates the very non-intuitive role that the natural hydrodynamic flow stability plays in the forced heat release response of the flame. For the fluid mechanics community, this work contributes to the detailed understanding of both unforced and forced bluff body combustor dynamics, and shows how each is influenced by the underlying hydrodynamics. In particular, it emphasizes the role of the density-shear layer offset, and shows how its extreme sensitivity leads to complicated flow dynamics. For the flow-combustor community as a whole, the work reviews a pre-existing method to obtain the important flow stability parameters, and demonstrates a novel way to link those parameters to the governing flow physics. For the combustion instability community, this thesis emphasizes the importance of the hydrodynamic stability characteristics of the flow, and concludes by offering a paradigm for consideration of the hydrodynamics in a combustion instability problem.

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

Velocity-coupled combustion instability is a major issue facing lean combustor design in modern gas turbine applications. In this study, we analyze the complex acoustic field excited by a transverse acoustic mode in an annular combustor. This work is motivated by the need to understand the various velocity disturbance mechanisms present in the flame region during a transverse instability event. Recent simulation and experimental studies have shown that much of the flame response during these transverse instabilities may be due to the longitudinal motion induced by the fluctuating pressure field above the nozzles. This transverse to longitudinal coupling has been discussed in previous work, but in this work it is given a robust acoustic treatment via computational methods in order to verify the mechanisms by which these two motions couple. We will provide an in-depth discussion of this coupling mechanism and propose a parameter, Rz, also referred to as the Impedance Ratio, in order to compare the pressure/velocity relationship at the nozzle outlet to quasi one-dimensional theoretical acoustic approximations. A three-dimensional inviscid simulation was developed to simulate transversely propagating acoustic pressure waves, based on an earlier experiment designed to measure these effects. Modifications to this geometry have been made to account for lack of viscosity in the pure acoustic simulation and are discussed. Results from this study show that transverse acoustic pressure excites significant axial motion in and around the nozzle over a large range of frequencies. Furthermore, the development of Rz offers a defined physical parameter through which to reference this important velocity-coupled instability mechanism. Therefore, this study offers an in-depth and quantifiable understanding of the instability mechanism caused by transversely propagating acoustic waves across a combustor inlet, which can be applied to greatly improve annular combustor design in future low-emissions gas turbine engines.

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

No description available.