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

Abstract

AbstractA 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.