Delaying Transition to Turbulence by a Passive Mechanism

Reducing skin friction is important in nature and in many technological applications. This reduction may be achieved by reducing stresses in turbulent boundary layers, for instance tailoring biomimetic rough skins. Here we take a second approach consisting of keeping the boundary layer laminar as long as possible by forcing small optimal perturbations. Because of the highly non-normal nature of the underlying linearized operator, these perturbations are highly amplified and able to modify the mean velocity profiles at leading order. We report results of wind-tunnel experiments in which we implement this concept by using suitably designed roughness elements placed on the skin to enforce nearly optimal perturbations. We show that by using this passive control technique it is possible to sensibly delay transition to turbulence.

Figure 1

Plane view of the plate used in the experiment. Forty-two cylindrical roughness elements ($\mathrm{\text{diameter}}=4.2\mathrm{mm}$ and $\mathrm{\text{height}}=1.4\mathrm{mm}$) are positioned 80 mm from the leading edge and periodically spaced in the spanwise direction by 14.7 mm. The slot for the TS generation, followed by the one for the smoke injection (330 mm long in the spanwise direction and 0.8 mm wide) are located at $x=190$ and 213 mm, respectively. A CCD camera ($1280\times 1024\mathrm{\text{pixels}}$) is used to record the images in an area of $210\times 168{\mathrm{mm}}^2$ located at $x=1434\mathrm{mm}$.

Figure 2

Smoke flow visualizations from above with flow from left to right. (a) and (b) show the two-dimensional boundary layer, without streaks, with no excitation and with excitation of 201 mV, respectively. The flow in (b) is turbulent, (c) shows the streaky base flow with no excitation. In the presence of streaks with excitation of 450 mV (d), the flow remains laminar; (e) shows a half-streaky boundary layer obtained removing half the roughness elements and without forcing. With a forcing at 157 mV (f), the streaky part of the boundary layer remains laminar while the uncontrolled part undergoes transition.

Figure 3

(a) Evolution of the dimensionless temporal root mean square streamwise velocity fluctuations $U_{\mathrm{rms}}/U_{\infty }$ in the streamwise direction $x$ when TS waves are excited at $f=32\mathrm{Hz}$ and 1000 mV. (b),(c) The time signals at two selected positions ($x=400$ and $x=1650\mathrm{mm}$). Light (red) lines and solid (red) symbols correspond to the two-dimensional boundary layer, without streaks, whereas dark (blue) lines and open (blue) symbols to the boundary layer with the controlling streaks present. In the presence of streaks the flow remains laminar.

Figure 4

(a) Dimensionless temporal root mean square of the streamwise velocity fluctuations $U_{\mathrm{rms}}/U_{\infty }$ and (b) intermittency factor $\gamma$ distributions in the streamwise direction $x$ when a random (white noise) instead of sinusoidal (TS) excitation is used. Solid (red) symbols correspond to the boundary layer without streaks and open  (blue) symbols to the boundary layer with the controlling streaks present. In the presence of streaks, the transition is delayed as indicated by the downstream shift $\Delta x_{\mathrm{delay}}$ of the locations where the levels $\gamma =0.1$ and $\gamma =0.5$ are attained.