DNS of rotating and non-rotating turbulent flows with synthetic inlet conditions

Abstract

In this paper, direct numerical simulations (DNS) are presented to understand the effects of the inlet conditions on the turbulent energy decay rate of isotropic turbulence. A perfect control of the inlet conditions cannot be achieved in realistic simulations reproducing the effects of a solid grid, which, on the other hand, is possible by adding to a uniform inlet velocity U 0 analytical anisotropic single- or multiple-scale velocity disturbances. The single-scale simulations with different disturbances with a wave number κ show a scaling of the turbulent energy q versus x 1/M with M=2π/κ. The energy decay rate m for multiple-scale disturbances is decreased compared to the case with single-scale disturbances. The transition from anisotropic to isotropic turbulence is analysed through the evolution of the statistics, in particular, those linked to the flow structures. Flow visualisations of the vorticity field and joint of the velocity components at different distances from the inlet illuminate the reasons for the differences between single- and multiple-scale disturbances. The reduction of m, for the latter, indicates the way to generate isotropic turbulence at high microscale R λ. Simulations at different rates of solid-body rotation aligned with the streamwise direction were also performed for the flows with multiple- and single-scale disturbances. Variations of the rotation rate Ω allow to investigate the modifications of the vortical structures for single-scale disturbances. At N Ω=2ΩL/U 0=10, the comparison between single- and multiple-scale disturbances shows a further increase of R λ in the latter flow. One-dimensional energy spectra at different distances from the inlet indicate when the effects of the inlet disturbances disappear. Good agreement, in the inertial and in the exponential decay ranges, between the present spectra and those from the DNS of forced isotropic turbulence demonstrates the quality of the numerical method used.