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On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities

Rowley, Clarence W. and Colonius, Tim and Basu, Amit J. (2002) On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. Journal of Fluid Mechanics, 455 . pp. 315-346. ISSN 0022-1120. doi:10.1017/S0022112001007534.

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Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier–Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin–Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin–Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.

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Rowley, Clarence W.0000-0002-9099-5739
Colonius, Tim0000-0003-0326-3909
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 18 November 1999 and in revised form 24 September 2001) Published Online 15 April 2002 This research was supported by AFOSR under grant F49620-98-1-0095 with technical monitor Dr Thomas Beutner. Supercomputer time was provided by the Department of Defense High Performance Computing centers, as well as the National Science Foundation. The first author acknowledges the support of a National Science Foundation Graduate Fellowship. We wish to thank Drs Anatol Roshko, Alan Cain, David Williams, Drazen Fabris, and Edward Kerschen for many helpful discussions on cavity oscillations.
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Air Force Office of Scientific Research (AFOSR)F49620-98-1-0095
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Deposited On:02 Jan 2006
Last Modified:08 Nov 2021 19:08

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