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Decay of turbulence generated by a square-fractal-element grid

Published online by Cambridge University Press:  17 February 2014

R. J. Hearst  and
P. Lavoie
R. J. Hearst
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6
P. Lavoie*
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6
*
†Email address for correspondence: lavoie@utias.utoronto.ca
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Abstract

A novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing $L_0 = 100\, {\rm mm}$. Measurements were performed in the region $3.5 \le x/L_0 \le 48.5$, which represents a significant extension to the $x/L_0 < 20$ of previously reported square fractal grid measurements. For the region $x/L_0 \gtrsim 24$ it was found that a power-law decay region following $\langle {q}^2 \rangle \sim (x - x_0)^m$ exists with decay exponents of $m = -1.39$ and $-1.37$ at $\mathit{Re}_{L_0} = 57\, 000$ and $65\, 000$, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$). The turbulence in the near-grid region, $x/L_0 < 20$, is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in $m = -2.79$, similar to $m \approx -2.5$ recently reported by Valente & Vassilicos (J. Fluid Mech., vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that $C_\epsilon $ is approximately constant for $x/L_0 \ge 25$, while it grows rapidly for $x/L_0 < 20$. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , pp. 567 - 584
Copyright
© 2014 Cambridge University Press 

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