An experimental investigation of the turbulent structure in a two-dimensional momentumless wake

Abstract

Mean velocity profiles have been measured in the wake of a two-dimensional airfoil with and without mass injection through a slit along its rear end. In particular, four cases have been documented: (a) a pure wake (no injection), (b) a weak wake (some injection), (c) a momentumless wake (injection adjusted to provide a thrust which exactly cancels the model's drag), and (d) a weak jet (more injection than necessary to cancel the drag). These mean velocity profiles clearly show the difference in momentum deficit for the four cases. When non-dimensionalized, the velocity profiles are self-similar.Smoke-wire flow visualizations are also presented for both the near wake (0 < x/d < 30) and the far wake (45 < x/d < 75). The characteristic geometry of large-scale turbulent vortical structures is easily identifiable for the wake and jet cases, while the structures for the momentumless state are neither wake-like nor jet-like. Beyond about 45 diameters downstream, turbulent structures for the momentumless case become quite weak and can barely be observed.For the momentumless wake at Re = 5400, the axial, lateral, and transverse turbulence intensities as well as the Reynolds stress were measured. Similarity of the axial and the transverse turbulence intensities was observed; the overall shape of those profiles is Gaussian except for the very near-wake region. The mean centreline velocity difference decays much faster (x−0.92) than the axial turbulent intensity (x−0.81). Consequently, the mean shear practically disappears far downstream; the flow becomes nearly isotropic beyond about 45 body diameters from the model. This turbulence behaviour is quite different from that of plane wakes or jets but rather closer to the case of grid turbulence.