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Research Papers: Fundamental Issues and Canonical Flows

Numerical Analysis on the Start-Up Flow Past a Resonant Cavity

[+] Author and Article Information
Antonio Filippone

School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M60 1QD, UK

J. Fluids Eng 130(10), 101201 (Aug 26, 2008) (12 pages) doi:10.1115/1.2969271 History: Received January 24, 2007; Revised June 03, 2008; Published August 26, 2008

This paper presents the results of a computational analysis on a three-dimensional unsteady flow inside a resonant cavity. The cavity was fully immersed in a channel flow, had a squared cross section, and a spanwise aspect ratio equal to 3. It was partly closed to the inflow by slits upstream and downstream. The lid was 14 of the cavity length. The Reynolds number was Re=8000 based on the freestream velocity. The numerical simulations were carried out for flow times up to 380 units. Results are presented for a symmetric cavity with respect to the normal to the freestream. The analysis shows complex three-dimensional vortex structures, with Taylor–Görtler-type vortices, filament vortices, and other secondary vortices, some having a relatively short life-span. It is shown that the flow is substantially symmetric, with small spanwise instabilities. It is further shown that there is an asymptotic tendency to an unsteady flow with large wavelengths. A primary vortex establishes at the center of the cavity. Most vortex regions disappear and that they depend on the type of geometry and the state of the boundary layer at the inlet.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three-dimensional view of the cavity (computational model)

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Figure 9

Isosurfaces of vertical velocity w, ascending and descending flows, with values w=±0.015, at the times indicated; two-dimensional view in the x-z plane

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Figure 10

Phases in the development of the vertical filament vortex

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Figure 11

Hairpin vortex at the cavity center, time series with flow times as indicated

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Figure 12

Primary vortex core and secondary vortices after the initial transient

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Figure 13

Streamtraces on plane cut x=0.5 (middle of the cavity) at the times indicated; plots show evolution of counter-rotating vortices

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Figure 8

Isosurfaces of total vorticity; two-dimensional view in the x-z plane

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Figure 7

Isosurface of spanwise velocity v, with value v=10−3, at the times indicated; three-dimensional view from the upstream side

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Figure 6

Isosurface of spanwise velocity v, with value v=10−3, at the times indicated; three-dimensional view from the downstream side

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Figure 5

Tracking of v-velocity components over time: (a) point P1 and its symmetric and (b) point P2 and its symmetric

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Figure 4

Cavity model with thick lid

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Figure 3

Comparisons between the present model and the experimental results of Arnal (20) and Kost (21), flow time τ=50

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Figure 2

Comparisons between the present model and the case presented by Guermond (13), flow time τ=12

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