Effects of unsteady blowing through a spanwise slot on a turbulent boundary layer

Abstract

The effects of localized periodic blowing on a turbulent boundary layer were investigated by direct numerical simulation. Time-periodic blowing was applied through a spanwise slot by varying the wall-normal velocity in a cyclic manner from 0 to $2A^ + $. Time-periodic blowing was applied at frequencies in the range $0\,{ \le}\, f^ +\,{ \le}\, 0.08$ at a fixed blowing amplitude of $A^ + $ = 0.5. Simulations of a spatially evolving turbulent boundary layer were carried out for two Reynolds numbers, $\hbox{\it Re}_{\theta, in} $ = 300 and 670. Before investigating the effects of periodic blowing, the effects of steady blowing were examined. A new parameter, $\sigma ^ + $, was proposed for describing local blowing; the usefulness of this parameter was that the responses of the flow variables at the two Reynolds numbers were the same for the same $\sigma ^ + $. The effects of varying the blowing frequency were scrutinized by examining the phase- or time-averaged turbulent statistics. For both Reynolds numbers, application of blowing at a frequency of $f^ + $ = 0.035 was found to give the maximum increases in Reynolds shear stress, streamwise vorticity fluctuations and energy redistribution. Analysis of the Reynolds stress budget showed that this effective blowing frequency induced the greatest enhancement of the pressure–strain term, which is closely related to the energy redistribution. Analysis of the phase-averaged stretching and tilting terms revealed that the stretching term is significantly enhanced in the ‘downward’ motion that is induced by the spanwise vortical motion. The correlation between the streamwise vorticity and the stretching term changed in magnitude and length scale as the blowing phase was varied, whereas the correlation between the streamwise vorticity and the tilting term did not.