Characterization of the Dissipation Tensor from DNS of Grid-Generated Turbulence

Abstract

Grid-generated turbulence is an old but open topic: for instance its spatial decay rate of energy is still being vigorously discussed. It is relevant to turbulence modeling but also related to mechanical and engine design. The influence of grid geometry on the dissipation tensor, in particular on the range and exponent of “self-similar” turbulent energy decay is now studied, using square rods and square grid mesh, via direct numerical simulations by a lattice BGK method at Re M =1400. Four different blockage ratios are compared. A clear picture is obtained concerning the spatial distribution and self-similarity of the dissipation tensor, including anisotropy decay and dissipation rate. The expected axisymmetry is confirmed excellently. The differences in magnitudes of individual dissipation tensor components are only recognizable very close to the grid, where a strong dependence on grid porosity, β, is also found, in terms of anisotropy and dissipation rate. The spatial decay of dissipation rate can be described by a power law with decay exponent ≈3.0 for x/M>10 independent of β. A β-dependent normalization is proposed, which improves dramatically data collapse in that x/M range.