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2D PIV measurements in the near field of grid turbulence using stitched fields from multiple cameras

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Abstract

We present measurements of grid turbulence using 2D particle image velocimetry taken immediately downstream from the grid at a Reynolds number of Re M  = 16500 where M is the rod spacing. A long field of view of 14M × 4M in the down- and cross-stream directions was achieved by stitching multiple cameras together. Two uniform biplanar grids were selected to have the same M and pressure drop but different rod diameter D and cross-section. A large data set (104 vector fields) was obtained to ensure good convergence of second-order statistics. Estimations of the dissipation rate \(\varepsilon\) of turbulent kinetic energy (TKE) were found to be sensitive to the number of mean-squared velocity gradient terms included and not whether the turbulence was assumed to adhere to isotropy or axisymmetry. The resolution dependency of different turbulence statistics was assessed with a procedure that does not rely on the dissipation scale η. The streamwise evolution of the TKE components and \(\varepsilon\) was found to collapse across grids when the rod diameter was included in the normalisation. We argue that this should be the case between all regular grids when the other relevant dimensionless quantities are matched and the flow has become homogeneous across the stream. Two-point space correlation functions at x/M = 1 show evidence of complex wake interactions which exhibit a strong Reynolds number dependence. However, these changes in initial conditions disappear indicating rapid cross-stream homogenisation. On the other hand, isotropy was, as expected, not found to be established by x/M = 12 for any case studied.

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Abbreviations

CF:

Correlation function

D :

Rod diameter

M :

Spacing between two nearest parallel grid rods

s x :

Sampling variance

TKE:

Turbulent kinetic energy

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

Time average of *

\(\varepsilon\) :

Average dissipation rate of TKE

η:

Kolmogorov length scale

λ:

Taylor microscale

ν:

Kinematic viscosity

σ:

Grid solidity ratio σ = (D/M)(2 − D/M)

px:

Pixels

\({\bf U} = \left\langle {\bf U} \right\rangle + {\bf u}\) :

Total velocity

\(\left\langle{\bf U}\right\rangle = U{\bf e}_{x} + V{\bf e}_{y} + W{\bf e}_{z}\) :

Mean velocity

u = u e x  + v e y  + w e z :

Fluctuating velocity

\(u' = \sqrt{\left\langle u^{2}\right\rangle }\) :

Root mean square of u

\(U_{\infty}\) :

Free-stream velocity

Re M :

\(\frac{U_{\infty}M}{\nu}\)

Re λ :

\( \frac{u'\lambda}{\nu}\)

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Authors and Affiliations

  1. Engineering Department, Cambridge University, Trumpington Street, Cambridge, CB2 1PZ, UK

    J. I. Cardesa, T. B. Nickels & J. R. Dawson

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  1. J. I. Cardesa
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  2. T. B. Nickels
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  3. J. R. Dawson
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Correspondence to J. I. Cardesa.

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Cardesa, J.I., Nickels, T.B. & Dawson, J.R. 2D PIV measurements in the near field of grid turbulence using stitched fields from multiple cameras. Exp Fluids 52, 1611–1627 (2012). https://doi.org/10.1007/s00348-012-1278-4

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  • DOI: https://doi.org/10.1007/s00348-012-1278-4

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