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

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 $L_0 = 100\, {\rm mm}$L0=100mm. Measurements were performed in the region $3.5 \le x/L_0 \le 48.5$3.5?x/L0?48.5, which represents a significant extension to the $x/L_0 < 20$x/L0<20 of previously reported square fractal grid measurements. For the region $x/L_0 \gtrsim 24$x/L0?24 it was found that a power-law decay region following $\langle {q}^2 \rangle \sim (x - x_0)^m$?q2??(x?x0)m exists with decay exponents of $m = -1.39$m=?1.39 and $-1.37$?1.37 at $\mathit{Re}_{L_0} = 57\, 000$ReL0=57000 and $65\, 000$65000, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$?1?m??1.4). The turbulence in the near-grid region, $x/L_0 < 20$x/L0<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 $m = -2.79$m=?2.79, similar to $m \approx -2.5$m??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 $C? is approximately constant for $x/L_0 \ge 25$x/L0?25, while it grows rapidly for $x/L_0 < 20$x/L0<20. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.

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