Decay of homogeneous, nearly isotropic turbulence behind active fractal grids

Abstract

The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results appear to favor power-law decay with exponents between −1.2 and −1.4, approximately. More recently, studies of fractal-generated turbulence with multi-scale passive grids have shown increased Reynolds numbers and exponential or very fast power-law decays following an increase of kinetic energy close to the grid. Other recent studies have confirmed that such non-classical decay is limited to the region near the grid. In order to generate turbulence with multi-scale injection of kinetic energy at more elevated Reynolds numbers and with more spatially homogeneous distributions than available in prior experiments, we use an active-grid consisting of winglets with fractal shapes. We consider various types of fractal winglets, namely, Sierpinski triangle, space-filling squares, and Apollonian gasket type fractal shapes. Regular non-fractal winglets are also considered. Passive fractal grids are studied by keeping the winglets locked in place. Data are acquired using X-wire thermal anemometry and the decay is analyzed between 15 < x/M < 50 (M is the mesh-size). Results exhibit power-law decay with decay exponent approximately between −1.0 and −1.3. The precise values of the decay exponent and the coefficient \documentclass[12pt]{minimal}\begin{document}$C_{\epsilon }=\epsilon \ell /u_{rms}^3$\end{document}Cε=εℓ/urms3 depend on the geometry of the initial condition, although it is not possible to discern systematic or monotonic trends with respect to Reλ, component anisotropy, grid fractal dimension, or blockage ratio.