Relevance of turbulence behind the single square grid to turbulence generated by regular- and multiscale-grids

Abstract

Direct numerical simulations were carried out to study the turbulence generated by a fractal square grid at a Reynolds number of \documentclass[12pt]{minimal}\begin{document}$Re_{L_0}$\end{document}ReL0 = 20000 (based on the inlet velocity Uin and length of the largest grid bar L0). We found that in the near-field region, the fractal square grid can generate much higher turbulence levels and has a better mixing performance than the single square grid. However, the current numerical results show that a single square grid can produce a turbulence intensity and turbulent Reynolds number at the end of the simulation region (i.e., X/L0 ≃ 13) comparable to those of a higher-blockage fractal square grid because the two turbulent flows have quite different energy decay rates. We also demonstrated that for the fractal square grid, the length L0 gives a physical description of the inlet Reynolds number. An examination of the characteristic length scale for the fractal square grid reveals that the unusual high energy decay rates in previous experiments [D. Hurst and J. C. Vassilicos, “Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007); N. Mazellier and J. C. Vassilicos, “Turbulence without Richardson-Kolmogorov cascade,” Phys. Fluids 22, 075101 (2010)] are limited in the near-field (initial decay) region, although this region can last for many meters downstream of the fractal square grids after the production region. Simulation results suggest that the turbulence intensity and energy decay rate of the fractal-generated turbulence may go back to classical values in the region X > 13L0. Additional simulations demonstrate that the fractal square grid can be regarded as an efficient additional turbulence generator in the near-field and can increase turbulent mixing near the grid.