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Three-dimensional instabilities in compressible flow over open cavities

Brès, Guillaume A. and Colonius, Tim (2008) Three-dimensional instabilities in compressible flow over open cavities. Journal of Fluid Mechanics, 599 . pp. 309-339. ISSN 0022-1120.

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Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one 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 previously 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. The 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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URLURL TypeDescription
Brès, Guillaume A.0000-0003-2507-8659
Colonius, Tim0000-0003-0326-3909
Additional Information:© Cambridge University Press 2008. Reprinted with permission. (Received 26 March 2007 and in revised form 30 October 2007) Published online 6 March 2008. This work was supported by AFOSR under grant F49620-02-1-0362. Computer time was provided in part by the Department of Defense High Performance Computing centres. The authors acknowledge contributions to the linear stability methodology from Professor Vassilis Theofilis, and would like to thank Professor Thierry Faure and his collaborators for allowing us to reproduce their experimental results.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-02-1-0362
Department of Defense High Performance Computing Modernization ProgramUNSPECIFIED
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ID Code:10424
Deposited By: Archive Administrator
Deposited On:04 May 2008
Last Modified:03 Oct 2019 00:09

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