Composite active drag control in turbulent channel flows

A composite drag control (CDC) combining the opposition (OC) and spanwise opposed wall-jet forcing (SOJF) methods is studied in a turbulent channel flow via direct numerical simulation of the incompressible Navier-Stokes equations. A maximum drag reduction of about $33\%$ is obtained for CDC—much higher than that produced by either individual method (namely, 19% for SOJF and 23% for OC). Due to the small power input required for both OC and SOJF methods, a significant net power saving (about 32%) is achieved via CDC. Flow analysis shows that CDC can take advantage of both OC and SOJF methods to better suppress drag producing near-wall turbulent structures—vortices and streaks. In particular, due to the presence of the large-scale coherent swirls generated by SOJF, it is more effective than OC in suppressing the random turbulence. Moreover, due to the OC's role in suppressing random small-scale turbulence, CDC requires weaker large-scale coherent swirls than those using SOJF only—hence decreasing the drag contribution associated with large-scale swirls. In summary, our results suggest prospects of employing composite control strategy for effective skin friction drag reduction, particularly at very high Reynolds numbers.

Figure 1

(a) Schematic of composite drag control (CDC), which combines the spanwise opposite wall-jet forcing (SOJF) and the opposition control (OC); (b) the detailed sketch of OC in the near-wall region [dashed box in (a)].

Figure 2

(a) Drag reduction $\mathcal{R}$ ($\%$) and (b) net power saving $\mathcal{N}(\%)$ as functions of $A_s^{+}$ and $y_d^{+}$ for CDC at ${\mathrm{Re}}_{\tau }=180$. The symbol $+$ indicates simulation data points used for interpolation.

Figure 3

Drag reduction $\mathcal{R}(\%)$ (solid lines) and net power saving $\mathcal{N}(\%)$ (dashed lines) as a function of (a) $y_d^{+}$ and (b) $A_s^{+}$.

Figure 4

${\lambda }_2$ vortical structures associated with the streamwise velocity fluctuations at $y/h=-0.92(y_0^{+}=15)$ on the bottom-half walls for (a) case I; (b) case II; (c) case III; and (d) case IV.

Figure 5

Mean velocity $U\left(y\right)$ for (a) the whole channel, (b) bottom-half, and (c) top-half channel.

Figure 6

Cross-stream (y-z) plane view of the mean velocity field ($\overline{\mathbf{u}}$) with the contours indicating the mean streamwise velocity (normalized by the bulk velocity $U_b$), and the vectors denote the wall-normal and spanwise velocities for (a) case III and (b) case IV.

Figure 7

Root mean square of velocity fluctuations: (a) $u_{rms}^{\prime }$; (b) $v_{rms}^{\prime }$; (c) $w_{rms}^{\prime }$. Note that the dashed lines are $u_{rms}^{\prime \prime }$ and $v_{rms}^{\prime \prime }$ and $w_{rms}^{\prime \prime }$ for cases III and IV.

Figure 8

(a) Total and (b) decomposed weighted Reynolds shear stress (WRSS) distributions for different control cases. The symbols $\circ$ and $\square$ in (b) represent the coherent and random weighted Reynolds shear stress, respectively.

Figure 9

The skin friction decomposition based on (a) FIK and (b) RD identities for different cases.

Figure 10

Energy flux box by (a) Reynolds decomposition and (b) triple decomposition. Abbreviations MKE, TKE, CKE, and RKE represent mean, turbulent, coherent, and random kinetic energies, respectively. All the budget terms have been normalized by the pumping power of the uncontrolled case, and their numerical values for cases I to IV are presented in order.