Effect of streamwise-periodic wall transpiration on turbulent friction drag

In this paper a turbulent plane channel flow modified by a distributed transpiration at the wall, with zero net mass flux, is studied through direct numerical simulation (DNS) using the incompressible Navier–Stokes equations. The transpiration is steady, uniform in the spanwise direction, and varies sinusoidally along the streamwise coordinate. The transpiration wavelength is found to dramatically affect the turbulent flow, and in particular the frictional drag. Long wavelengths produce large drag increases even with relatively small transpiration intensities, thus providing an efficient means for improved turbulent mixing. Shorter wavelengths, on the other hand, yield an unexpected decrease of turbulent friction. These opposite effects are separated by a threshold of transpiration wavelength, shown to scale in viscous units, related to a longitudinal length scale typical of the near-wall turbulence cycle. Transpiration is shown to affect the flow via two distinct mechanisms: steady streaming and direct interaction with turbulence. They modify the turbulent friction in two opposite ways, with streaming being equivalent to an additional pressure gradient needed to drive the same flow rate (drag increase) and direct interaction causing reduced turbulent activity owing to the injection of fluctuationless fluid. The latter effect overwhelms the former at small wavelengths, and results in a (small) net drag reduction. The possibility of observing large-scale streamwise-oriented vortical structures as a consequence of a centrifugal instability mechanism is also discussed. Our results do not demonstrate the presence of such vortices, and the same conclusion can be arrived at through a stability analysis of the mean velocity profile, even though it is possible that a higher value of the Reynolds number is needed to observe the vortices

Auto-generation by interaction of weak eddies

For channel flow, we explore how the interaction of weak eddies produces additional eddies by means of auto-generation. This is done by DNS of two eddies with different initial strengths, initial sizes and initial stream-wise spacing between them. The numerical procedure followed is similar to Zhou et al[1]. The two eddies merge into a single stronger eddy when a larger upstream and a smaller downstream eddy are placed within a certain initial stream-wise separation distance. Subsequently, the resulting stronger eddy is observed to auto-generate new eddies. The non-merging cases with small initial stream wise separation also auto-generate. The auto-generation is characterized by a rapid lift-up of an initial eddy, which blocks the incoming flow and leads to shear- layer roll-up and formation of a new eddy. The same sequence of events is observed in a fully developed turbulent boundary layer[2]