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Type of Document	Dissertation
Author	Bres, Guillaume Alain
Author's Email Address	guillaume AT caltech.edu
URN	etd-04262007-095945
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-04262007-095945
Title	Numerical simulations of three-dimensional instabilities in cavity flows
Degree	PhD
Option	Mechanical Engineering
Advisory Committee	Advisor Name Title Christopher E. Brennen Committee Chair Anthony Leonard Committee Member Joseph E. Shepherd Committee Member Timothy E. Colonius Committee Member
Keywords	flow cavity instabilities numerical simulations three-dimensional centrifugal acoustics Rossiter mode
Date of Defense	2007-04-13
Availability	mixed
Abstract Direct numerical simulations are performed to investigate the stability of compressible flow over three-dimensional open cavities for future control applications. First, the typical self-sustained oscillations, commonly referred as shear-layer (Rossiter) modes, are characterized for two-dimensional cavities over a range of flow conditions. A linear stability analysis is then conducted to search for three-dimensional global instabilities of the 2D mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of cavity configurations. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities reported in flows over backward-facing steps, lid-driven cavity flows, and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier-Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. These results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.
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