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Journal of Fluid Mechanics , Volume 741, 2014, pp 567- 584. J. Hearst , P. Lavoie.
Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6..
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 L0=100mm. Measurements were performed in the region 3.5≤x/L0≤48.5, which represents a significant extension to the x/L0<20 of previously reported square fractal grid measurements. For the region x/L0≳24 it was found that a power-law decay region following <q2>∼(x−x0)m exists with decay exponents of m=−1.39 and −1.37 at ReL0=57000 and 65000, respectively. This agrees with decay values previously measured for regular grids (−1≳m≳−1.4). The turbulence in the near-grid region, 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, similar to 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 Cϵis approximately constant for x/L0≥25, while it grows rapidly for x/L0<20. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.
© 2014 Cambridge University Press.
Figure: Credit : Journal of Fluid Mechanics / Volume 741 / February 2014, pp 567- 584
