Influence of an Extended Non-equilibrium Region on the Far-Field of Grid Turbulence

Abstract

The turbulence produced by two regular square mesh grids is compared to that produced by a square-fractal-element grid composed of an array of small square fractals. All three grids have approximately the same blockage. One of the regular grids is designed to have the same mesh length, M, as the fractal element grid, while the other matches the maximum bar thickness of the fractal. The transition of the turbulence from a non-equilibrium to a near equilibrium regime is assessed through the scale-by-scale kinetic energy budget and the velocity derivative skewness. It is found that the turbulence produced by all three grids agrees with many of the predictions for equilibrium phenomenology after approximately 20 M, with the regular grids reaching quasi-equilibrium earlier than the fractal. In the far-field, the fractal grid produces comparable or lower \(Re_\lambda \) than the regular grids in both dimensional and non-dimensional measurements of the streamwise position. This is attributed to an extended rapidly decaying non-equilibrium region in the wake of the fractal grid relative to the regular grids.