Analysis of non-equilibrium turbulence dissipation downstream of regular and fractal grids in an open channel flow

Abstract

This study investigates the relationship between the turbulence energy dissipation rate coefficient (${\text{C}}_{\epsilon }$) and turbulence Reynolds number (${\text{Re}}_{\lambda }$) in the streamwise and cross-stream directions downstream of four passive grids using a high-resolution particle image velocimetry (PIV) in an open channel. The grids include two regular square grids with 35 % and 48 % blockage ratios and two fractal square grids with 32 % and 41 % blockage ratios. PIV measurements were performed in the production, peak, and decay regions, and the data were analyzed in terms of mean velocity, turbulence intensities, small- and large-scale isotropy, velocity gradient tensor invariants, turbulence length scales, and the energy dissipation rate coefficient. The results in the production region and peak location in the cross-stream direction conform to a non-equilibrium scaling for turbulence energy dissipation rate. It is also shown that the turbulence dissipation rate coefficient (${\text{C}}_{{\epsilon }^{\prime }}$) in the production region and peak location of both regular and fractal grids can be related to a newly proposed local Reynolds number (${\text{Re}}_{\lambda \prime }$) and global Reynolds number (${\text{Re}}_{\text{L}}$) by the relations ${\text{C}}_{{\epsilon }^{\prime }}\propto {\text{Re}}_{\text{L}}^{\text{- 0.4}}/{\text{Re}}_{\lambda \prime }$ and ${\text{C}}_{{\epsilon }^{\prime }}\propto {\text{Re}}_{\text{L}}^{\text{- 0.2}}/{\text{Re}}_{\lambda \prime }$, respectively. This scaling differs from the traditional non-equilibrium equation that relates the local and global Reynolds numbers and energy dissipation rate coefficient (${\text{C}}_{\epsilon }\propto {\text{Re}}_{\text{0}}^{\text{1/2}}/{Re}_{\lambda }$) along the grids$\prime$ centerline.