# Three-dimensional centrifugal instabilities development inside a parallelepipedic open cavity of various shape

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- Received:
- Revised:
- Accepted:

DOI: 10.1007/s00348-009-0671-0

- Cite this article as:
- Faure, T.M., Pastur, L., Lusseyran, F. et al. Exp Fluids (2009) 47: 395. doi:10.1007/s00348-009-0671-0

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## Abstract

This experimental study reports flow developments inside a parallelepipedic cavity of variable shape and dimensions. That flow is generated by the interaction between a laminar boundary layer and the cavity, which creates shear-layer oscillations. The aim is to understand the three-dimensional flow morphology varying the Reynolds number and the cavity shape. Flow visualizations are obtained in a plane situated inside the cavity in order to get the dynamical structures. Dimensional analysis of the cavity flow teaches that three dimensionless numbers are necessary for the flow reduction. This is confirmed by experimental results pointing thresholds of appearance of instabilities identified for some combinations of Reynolds number and geometric parameters. The key mechanisms for their existence are centrifugal effects induced by a vortex of spanwise axis with sufficient intensity, and viscous effects due to the wall confinement of the cavity. Their destruction is linked to flow transition to turbulence above a limiting convective velocity generated by the vortex of spanwise axis. These instabilities are generally present in a spanwise row of counter-rotating pairs of vortices, but for some cases, isolated pairs are also identified. Secondary modulations of primary instabilities are also present for particular parameters. Results permit to discriminate the relevant scales associated with the shear layer and the inner cavity flow.

### List of symbols

*A*Plate length upstream of the cavity

*B*Plate length downstream of the cavity

*D*Wind tunnel height

*F*Span ratio

*H*Cavity height

- \( \user1{\mathcal{H}} \)
Helicity

*L*Cavity length

*N*Number of pairs of spanwise vortices

*R*Aspect ratio

*Re*Reynolds number

*S*Cavity span

*t*Time

*U*_{e}External velocity

*U*_{c}Maximum advection velocity inside the cavity

- \( \vec{V} \)
Velocity vector

*W*_{s}Spanwise drift velocity

- (
*x*,*y*,*z*) Cartesian coordinates

*δ*_{2}Momentum thickness of the upstream boundary layer

*λ*Spanwise wavelength of the instabilities

*μ*Dynamics viscosity

*ν*Kinematics viscosity

*ρ*Density

- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\omega } \)
Vorticity