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Unsteady near wake of a flat disk normal to a wall

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Abstract

The unsteady wake of a flat disk (diameter D) located at a distance of H from a flat plate has been experimentally investigated at a Reynolds number Re D  = 1.3 × 105. Tests have been performed for a range of gap ratio (H/D), spanning from 0.3 to 1.75. The leading edge of the flat plate is either streamlined (elliptical) or blunt (square). These configurations have been studied with PIV, high speed PIV and multi-arrayed off-set fluctuating pressure measurements. The results show a progressive increase of the complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D (1.75), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak associated with the vortex shedding events (St = 0.131) – St = fD/U ∞ is the Strouhal number. For lower values of H/D (0.75), the magnitude of the wall fluctuating pressure increases significantly. A large band contribution is associated with the unsteady wake structure and turbulence. A slight increase of the shedding frequency (St = 0.145) is observed. A critical value of the gap ratio (about 0.35) has been determined. Below this critical value, a three-dimensional separated region is observed and the natural vortex shedding process is very strongly altered. These changes induce a great modification of the fluctuating pressure at the wall. Each interaction reacts in a different way to perturbed upstream conditions. In particular, the disk is an overwhelming perturbation for the lowest H/D value studied here and the relative influence of the upstream turbulence on the wall fluctuating pressure below the near wake region is moderate.

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Abbreviations

C p :

Mean pressure coefficient

C p′ :

Fluctuating pressure coefficient

D :

Disk diameter

f :

Frequency

H :

Distance between the disk and the flat plate

p :

Pressure

p′:

Fluctuating pressure

\( \left\langle p \right\rangle \) :

Mean pressure

\( \left\langle {p^{2} } \right\rangle \) :

Variance of the pressure

p ∞ :

Free stream pressure

\( \hat{p}\left( f \right) \) :

Fourier transform of the pressure signal

Re D :

Reynolds number based on disk diameter

St :

Strouhal number

x, y, z :

Cartesian coordinates

U, V, W :

Velocity components with respect to x, y, z

\( \left\langle U \right\rangle ,\left\langle V \right\rangle ,\left\langle W \right\rangle \) :

Mean velocity components with respect to x, y, z

u, v, w :

Fluctuating velocity components with respect to x, y, z

u′:

rms of the axial fluctuating velocity

ξ:

Longitudinal distance from the blunt leading edge

ξR :

Mean reattachment length

U ∞ :

Free stream velocity

δ99 :

Boundary layer thickness

ρ:

Fluid density

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Acknowledgments

The PhD grant of T. Ruiz is financed by PSA Peugeot-Citroen and Renault in the context of a CNRT “Aérodynamique et Aéroacoustique des véhicules terrestres”. The authors thank the scientific committee of the CNRT for scientific discussions. The technical support of M. Rossard, F. Paillé, P. Braud and L. Philippon is warmly acknowledged.

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Authors and Affiliations

  1. Laboratoire d’Etudes Aérodynamiques (LEA), Université de Poitiers, ENSMA, CNRS, Futuroscope Cedex, France

    Tony Ruiz, Christophe Sicot, Laurent E. Brizzi, Janick Laumonier, Jacques Borée & Yves Gervais

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  1. Tony Ruiz
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  2. Christophe Sicot
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  3. Laurent E. Brizzi
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  4. Janick Laumonier
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  5. Jacques Borée
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  6. Yves Gervais
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Correspondence to Tony Ruiz.

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Ruiz, T., Sicot, C., Brizzi, L.E. et al. Unsteady near wake of a flat disk normal to a wall. Exp Fluids 47, 637–653 (2009). https://doi.org/10.1007/s00348-009-0702-x

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  • DOI: https://doi.org/10.1007/s00348-009-0702-x

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