Experiments in Fluids

, 55:1762 | Cite as

Flow characteristics around a wall-mounted spherical obstacle in a thin boundary layer

  • Seyed M. Hajimirzaie
  • Achilleas G. Tsakiris
  • James H. J. Buchholz
  • Athanasios N. Papanicolaou
Research Article

Abstract

The mean wake structures and turbulent flow fields of a wall-mounted spherical obstacle placed in a thin laminar boundary layer, of thickness 14 % of the sphere diameter, were investigated at a Reynolds number of 17,800. Digital particle image velocimetry was used to interrogate the flow in the vicinity of the obstacle, and thermal anemometry measurements were performed to characterize unsteadiness in the wake. Streamwise features observed in the mean wake flow included counter-rotating tip vortices inducing downwash, horseshoe vortices, weak vortices inducing upwash at the top of the near wake, and counter-rotating ‘lobe’ vortices formed by the somewhat unique convex geometry of the sphere near the base. Under the present flow conditions, the sphere base geometry also prevented the roll-up of a horseshoe system upstream of the obstacle. The wake flow field, including lobe structures, is consistent with a vortex skeleton model developed to describe the simpler wakes of low-aspect-ratio wall-mounted semi-ellipsoidal obstacles, with modifications due to the unique junction geometry. Point velocity measurements in the wake identified a weak dominant frequency close to the bed. Cross-spectral analysis of these data at symmetrically located points revealed that, on average, flow oscillations were in phase. The turbulent stress distribution in the wake of the sphere showed a region of high magnitude near the bed not observed for other geometries, and spatially consistent with the lobe structures.

List of symbols

\(f\)

Frequency of velocity fluctuations in the sphere wake (Hz)

\(D\)

Sphere diameter (mm)

\(U_{\infty }\)

Free-stream velocity (m/s)

\(d\)

Flow depth (mm)

\(x\), \(y\), \(z\)

Streamwise, transverse, and spanwise (wall-normal) directions

\(\omega \)

Vorticity (\(\hbox {s}^{-1}\))

\(\omega ^*\)

Dimensionless vorticity, \(\omega ^*= \omega D / U_{\infty }\)

\(\varGamma \)

Circulation (mm2/s)

\(\varGamma ^* = \varGamma /(U_{\infty }D)\)

Dimensionless circulation

\(\tau _{t,p}\)

Turbulent projected shear stress (Pa)

\(Re_D = \frac{U_{\infty } D}{\nu }\)

Reynolds number

\(\nu \)

Kinematic viscosity (\(\hbox {m}^{2}/\hbox {s}\))

\(fD/U_{\infty }\)

Dimensionless frequency

\(St=f_{0}D/U_{\infty }\)

Strouhal number (\( f_{0}\) = dominant frequency)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Seyed M. Hajimirzaie
    • 1
  • Achilleas G. Tsakiris
    • 1
  • James H. J. Buchholz
    • 3
  • Athanasios N. Papanicolaou
    • 1
    • 2
  1. 1.Department of Civil and Environmental Engineering, IIHR - Hydroscience and EngineeringUniversity of IowaIowa CityUSA
  2. 2.Department of Civil and Environmental EngineeringThe University of TennesseeKnoxvilleUSA
  3. 3.Department of Mechanical and Industrial Engineering, IIHR - Hydroscience and EngineeringUniversity of IowaIowa CityUSA

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