Scalings and decay of fractal-generated turbulence

A total of 21 planar fractal grids pertaining to three different fractal families have been used in two different wind tunnels to generate turbulence. The resulting turbulent flows have been studied using hot wire anemometry. Irrespective of fractal family, the fractal-generated turbulent flows and their homogeneity, isotropy, and decay properties are strongly dependent on the fractal dimension D-f <= 2 of the grid, its effective mesh size M-eff (which we introduce and define) and its ratio t(r) of largest to smallest bar thicknesses, t(r)=t(max)/t(min). With relatively small blockage ratios, as low as sigma=25%, the fractal grids generate turbulent flows with higher turbulence intensities and Reynolds numbers than can be achieved with higher blockage ratio classical grids in similar wind tunnels and wind speeds U. The scalings and decay of the turbulence intensity u(')/U in the x direction along the tunnel's center line are as follows (in terms of the normalized pressure drop C-Delta P and with similar results for v(')/U and w(')/U): (i) for fractal cross grids (D-f=2), (u(')/U)(2)=t(r)(2)C(Delta P)fct(x/M-eff); (ii) for fractal I grids, (u(')/U)(2)=t(r)(T/L-max)(2)C(Delta P)fct(x/M-eff), where T is the tunnel width and L-max is the maximum bar length on the grid; (iii) for space-filling (D-f=2) fractal square grids, the turbulence intensity builds up as the turbulence is convected downstream until a distance x(peak) from the grid is reached where the turbulence intensity peaks and then decays exponentially, u('2)=u(peak)('2)exp[-(x-x(peak))/l(turb)], where u(peak)('2) increases linearly with t(r), x(peak)proportional to t(min)T/L-min (L-min being the minimum bar length on the grid), and l(turb)proportional to lambda U-2/nu (nu being the kinematic viscosity of the air and lambda being the Taylor microscale); lambda remains approximately constant during decay at x > x(peak). The longitudinal and lateral integral length scales also remain approximately constant during decay at x > x(peak). (c) 2007 American Institute of Physics.