Novel scaling laws in the nonequilibrium turbulent wake of a rotor and a fractal plate

Abstract

This paper describes an experimental study in which a novel nonequilibrium self-similarity/self-preservation region is found to exist in the wakes of both a rotor and a fractal plate. In this novel nonequilibrium self-similarity region, the ratio of the mean flow length scale to the turbulence length scale and the ratio of the mean flow velocity scale to the turbulence velocity scale are not constant in the streamwise direction. However, in this region, the ratio of the mean flow time scale to the turbulence time scale is approximately constant in the streamwise direction. Using the simplified Reynolds-averaged equation of motion, new scaling laws are derived for this novel nonequilibrium self-similarity region, and these are confirmed by experimental measurements. Significant differences are observed between the rotor wake and fractal plate wake. The rotor wake reaches a self-similarity state much earlier than the fractal plate wake. A transition in the self-similarity state and scaling laws is found to occur in the rotor wake within the measurement region considered in the present study (3 D–20 D, where D is the effective diameter of the wake generator).