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3D reconstruction of the flow and vortical field in a rotating sharp “U” turn channel

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Abstract

Particle image velocimetry experiments have been carried out to obtain visualizations and measurements of the main and secondary flow fields in a square channel with a sharp “U” turn. Both the main and the secondary flow fields have been used to perform a 3D reconstruction of the mean flow and vortical fields in the turn region and in the outlet duct. In order to study the influence of the rotation, tests both in stationary (absence of rotation, Re = 20,000) and in rotating (Re = 20,000 and Ro = 0.3) conditions have been performed. The results show that the Coriolis and centrifugal forces, caused by the rotation, yield strong modifications to the symmetrical flow and vortical fields that are generated, in the static case, only by the abrupt inversion of the flow direction.

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Notes

  1. 1.

    The λ 2-criterion is a vortex identification method based on the eigenvalues of the sum of the strain and rotation square tensor.

Abbreviations

3D:

Three-dimensional

CCD:

Charge-coupled device

LASER:

Light amplification by stimulated emission of radiation

LDA:

Laser doppler anemometry

Nd:YAG:

Neodymium yttrium aluminium garnet

PIV:

Particle image velocimetry

C :

Circuit used to the evaluation of the vorticity components

D :

Channel hydraulic diameter

\( \underline{l} \) :

Direction normal to the planar surface S

Re :

Reynolds number

Ro :

Rotation number

S :

Planar surface bounded by the circuit C

U :

Fluid mean velocity

u, v, w:

Mean velocity components

u′, v′:

Turbulence intensity

u*:

Wall friction velocity

u1, w1:

Mean velocity components obtained from the images acquired with the rotating channel (Re = 20,000, Ro = 0.3)

u2, w2:

Mean velocity components obtained from the images acquired with the rotating channel and the fluid at rest

U2, W2:

Velocity components of V pp

ug, vg, wg:

Mean velocity components relative to the 3D grids

\( \underline{V} \) :

Local velocity vector

V :

Local velocity module

V pp :

Rotation peripheral velocity relative to the generic point of the investigated plane

W 2m :

Spatial average of the mean (in time) velocity component w 2 distribution obtained from the images acquired with the rotating channel and with the fluid at rest

x, y, z:

Cartesian spatial coordinates

xc, zc:

Cartesian spatial coordinates of the channel rotation centre

α :

Rotation angle

λ 2 :

Second eigenvalue of the sum of the strain and rotation square tensor

μ :

Dynamic viscosity coefficient of the fluid

ρ :

Mass density of the fluid

ω :

Channel rotational speed

Ω:

Local vorticity module

Ωl :

Vorticity components relative to the l direction

Ω x , Ω y , Ω z :

Mean vorticity components

References

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Acknowledgments

The authors wish to thank Prof. Giovanni Maria Carlomagno for helpful discussion throughout the course of this work.

Author information

Correspondence to Mauro Gallo.

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Gallo, M., Astarita, T. 3D reconstruction of the flow and vortical field in a rotating sharp “U” turn channel. Exp Fluids 48, 967–982 (2010) doi:10.1007/s00348-009-0776-5

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Keywords

  • Vortex
  • Particle Image Velocimetry
  • Vortical Structure
  • Vortical Field
  • External Wall