# Self-sustained oscillations of turbulent flows over an open cavity

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- Received:
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- Accepted:

DOI: 10.1007/s00348-008-0510-8

- Cite this article as:
- Kang, W., Lee, S.B. & Sung, H.J. Exp Fluids (2008) 45: 693. doi:10.1007/s00348-008-0510-8

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## Abstract

The mechanism of self-sustained oscillations in laminar cavity flows has been well characterized; however, the occurrence of self-sustained oscillations in turbulent cavity flows has only previously been characterized by direct observation of flows. Here, the quantitative characteristics of vortical structures in turbulent flows over an open cavity were determined, and then statistical properties were examined for evidence of self-sustained oscillations. Specifically, instantaneous velocity fields were measured using PIV and wall pressure fluctuations were determined from microphone data. Cavity geometries of *L*/*D *= 1 and 2, where *L* and *D* are the length and depth of the cavity, respectively, were used under conditions where the incoming boundary layer was turbulent at *Re*_{θ} = 830. Statistical analyses were applied based on the instantaneous velocity fields of PIV data. The spatial distributions of vertical velocity correlations (*v–v*) showed alternating patterns that reflect the organized nature of the large-scale vortical structures corresponding to the modes of *N *= 2 for *L*/*D *= 1 and *N *= 3 for *L*/*D *= 2. These values were consistent with the numbers of vortical structures obtained from a modified version of Rossiter’s equation. Furthermore the numbers of vortical structures determined in the statistical analyses were consistently observed in instantaneous distributions of the swirling strength (*λ*_{ci}). The incoming turbulent boundary layer can give rise to the formation of large-scale vortical structures responsible for self-sustained oscillations.

### List of symbols

*D*depth of the cavity (mm)

*δ*boundary layer thickness (mm)

*δ*_{ω}vorticity thickness (mm)

- Δ
filter width

*f*filter function

*L*length of the cavity (mm)

*L*_{eff}effective length scale (mm)

- Δ
*L*_{l} length of contamination near the leading edge

- Δ
*L*_{t} length of contamination near the trailing edge

*λ*_{ci}swirling strength

*λ*_{x}streamwise wavelength of vortical structure (mm)

*θ*momentum thickness (mm)

*R*_{vv}*v–v*two point correlation coefficient*R*_{θ}Reynolds number based on the momentum thickness

*R*_{D}Reynolds number based on the depth of the cavity

*St*_{L}Strouhal number based on the length of the cavity

- \( \ifmmode\expandafter\bar\else\expandafter\=\fi{u} \)
filtered instantaneous velocity (m/s)

*U*_{c,avg}convection velocity (m/s)

*v*_{rms}root mean square of vertical velocity (m/s)

*x*_{0}streamwise position of reference point (mm)

*y*_{0}vertical position of reference point (mm)