Fractal, Classical, and Active Grid Turbulence: From Production to Decay

The turbulence produced in the wake of fractal grids has been shown to exhibit peculiar decay properties that contrast with expectations for canonical grid turbulence flows. Such flows have been termed `non-equilibrium' turbulence, and feature an unexpectedly high decay rate of turbulent kinetic energy and rapid growth of the normalized dissipation rate relative to canonical grid turbulence flows. The turbulence produced by a square-fractal-element grid, that is known to generate a significant non-equilibrium region in its wake, is compared to the turbulence produced by two regular square mesh grids and an active grid. The three passive grids all have the same blockage, while the blockage of the active grid is transient. The regular grids and active grid are used as benchmarks for comparison because they are known to produce quasi-equilibrium turbulence that matches many of the predictions of Richardson-Kolmogorov equilibrium turbulence phenomenology, save the existence of a $k^{-5/3}$ spectrum in the inertial range.It is found that non-equilibrium and quasi-equilibrium turbulence are two phases of the same turbulence evolution downstream of turbulence generating grids. The flow begins as non-equilibrium turbulence close to the grid, and evolves downstream into quasi-equilibrium turbulence. Evidence for this finding is provided by showing that sufficiently far downstream of the fractal geometry the flow returns to a quasi-equilibrium state with traditional decay rates and constant normalized dissipation scaling. It is found that the non-equilibrium region is characterized by transverse transport of turbulent kinetic energy and turbulent production, both of which are consequences of the mean flow inhomogeneity in the near-grid region. For non-equilibrium turbulence, the production is found to penetrate to wavenumbers inside the inertial range, giving the appearance of a $k^{-5/3}$ spectrum, but this same penetration by production makes non-equilibrium turbulence theoretically incompatible with Kolmogorov's $k^{-5/3}$ prediction. As the homogeneity of the flow improves downstream, the flow reaches a state of approximate equilibrium, although a $k^{-5/3}$ spectrum is never observed behind any grid in this study. This result was absent from previous studies because large fractal geometries limited the observable downstream range in a wind tunnel. This limitation was overcome by using a square-fractal-element grid that was composed of a 12 $\times$ 8 array of small square fractal elements.Ph.D