Turbulent dissipation rate and length-scale anisotropy through passive grid turbulence

This study aims to characterize the range of eddy sizes in grid-generated turbulence within a three-dimensional framework, examining eddy structures arising from interactions between the turbulent flow and a rigid boundary. The study utilizes three-dimensional velocity time-series, processed within a time-averaged framework, to examine both large-scale and small-scale turbulent flow characteristics induced by the passive grid. The integral length scale (in the stream-wise, lateral, and vertical directions) is calculated using the auto-correlation function, while the Taylor length scale (also in the stream-wise, lateral, and vertical directions) is determined using the velocity gradient approach. This approach allows us to capture and compare eddy dynamics across different mesh configurations. The integral and Taylor's length-scale anisotropy are also presented to understand the directional characteristics of the turbulent structures (eddy sizes) at the downstream locations of the grid. The results demonstrate that as the grid's mesh size increases, fluctuations in both the stream-wise and vertical directions, along with turbulence kinetic energy, decrease near the boundary regions. The stream-wise fluctuations significantly increase in both the near-field and far-field regions for all three mesh sizes when compared to that for the no-grid case. The deviations between the surrogates of dissipation rates in the near-field and far-field regions are more pronounced when compared to those in locally isotropic conditions due to increased shear and the resulting anisotropy in the flow. The anisotropy invariant map of the turbulent dissipation rate tensor and Reynolds stress tensor at downstream positions reveals that turbulent fluctuations are predominantly aligned along one direction.