Decay of turbulence generated by a square-fractal-element grid
Journal of Fluid Mechanics
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 mm. Measurements were performed in the region 3.5 x/L 0 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 24 it was found
... L 0 24 it was found that a powerlaw decay region following q 2 ∼ (x − x 0 ) m exists with decay exponents of m = −1.39 and −1.37 at Re L0 = 57, 000 and 65, 000, respectively. This agrees with decay values previously measured for regular grids (−1 m −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 ≈ −2.5 recently reported by Valente & Vassilicos (2011) for space-filling square fractals. It was also found that C is approximately constant for x/L 0 25, while it grows rapidly for x/L 0 < 20. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.