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Prediction of turbulence control for arbitrary periodic spanwise wall movement
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View: Figures


Image of FIG. 1.
FIG. 1.

Temporal waveforms of the considered wall oscillation. The following symbols are used throughout the paper for the different waveforms: (a) (○), (b) (♦), (c) (*), (d) (+), (e) (■), (f) (●), (g) (◀), (h) (▶), (i) (▲), and (j) (▼).

Image of FIG. 2.
FIG. 2.

Power consumption rate (top), reduction of pumping power (center), and net energy saving rate as a function of for = 125 (left) and of for (right) for five selected waveforms, see Figure 1 for reference. The sinusoidal case is shown with the empty symbol. The continuous lines in the top plots are .

Image of FIG. 3.
FIG. 3.

Maximum values of net energy saving, , for each pair of (, )-values investigated. Full circles correspond to >, open circles to < 0 while the diameter of the circles reflects the obtained absolute value of . The letter above each circle indicates the waveform yielding the best .

Image of FIG. 4.
FIG. 4.

(Left) Power consumption data for all the simulations versus the analytical prediction based on the Stokes layer assumption, Eq. (5) . The inset plot shows the percentage error. (Right) Turbulent drag reduction as a function of (ℓ ), with ℓ computed from Eq. (7) using a threshold corresponding to = 1.2. Gray symbols are for = 62.5, black symbols for = 125, and open symbols for = 250.

Image of FIG. 5.
FIG. 5.

(Left) Turbulent drag reduction rate, , as a function of for = 125 (black symbols) and = 62.5 (gray symbols). The solid lines are the prediction (8) , with ℓ computed via the first mode, Eq. (10) . (Right) Bi-harmonic waveform (solid line) designed to increase the sinusoidal net energy savings at low values.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Prediction of turbulence control for arbitrary periodic spanwise wall movement