A COMPARISON OF THE DECAY OF ENERGY IN THE WAKE OF FRACTAL AND CLASSICAL GRIDS

Abstract

A square-fractal-element grid and two regular grids, all with the same blockage, are used to investigate how the produced turbulence differs. The square-fractal-element grid is made-up of a 12×8 array of small square fractals mounted to a background mesh. For a constant inlet Reynolds number, ReM , it is found that the turbulent kinetic energy powerlaw decay exponent is comparable for all three grids in the far-field, although the fractal-based grid produces an extended non-equilibrium region relative to the other two grids. The normalized dissipation, Cε , is found to be approximately described by ReM/ReL in the non-equilibrium region, becoming approximately constant in the far-field. A correlation is also found between Cε and normalized Reynolds stress, 〈uv〉/u′v′, across both the non-equilibrium region and the far-field. Finally, non-equilibrium and farfield spectra are compared at fixed Reλ across all three grids. It is found that the far-field spectra are reasonably collapsed for all three grids for a given Reλ . However, if a non-equilibrium spectrum at a location where 〈uv〉 6= 0 is compared at a given Reλ to a far-field spectrum where 〈uv〉 ≈ 0, then the non-equilibrium spectrum is nearer to k−5/3. This result appears to be closely related to the existence of 〈uv〉 that is able to penetrate to scales associated with the scaling range.