Scaling of flat plate drag reduction using plasma-generated streamwise vortices

Skin-friction drag reduction (DR) in a turbulent boundary layer (TBL) using plasma-generated streamwise vortices (PGSVs) is governed by plasma-induced spanwise wall-jet velocity $W$ , the distance $L$ between the positive electrodes of two adjacent plasma actuators (PAs) and the friction Reynolds number $Re_\tau$ . It is found experimentally that DR increases logarithmically with the growing maximum spanwise mean velocity $\overline {W}_{max}^+$ but decreases with rising $L^+$ and $Re_\tau$ , where superscript ‘+’ denotes normalization by the inner scales. It is further found from theoretical and empirical scaling analyses that the dimensionless drag variation $\Delta F = g_1 (\overline {W}_{max}^+, L^+, {Re_\tau })$ may be reduced to $\Delta F = g_2 (\xi )$ , where $g_1$ and $g_2$ are different functions and the scaling factor $\xi = [k_{2} \log _{10} (k_{1} \overline {W}_{max }^{+} ) ] / (L^{+} Re_{\tau } )$ ( $k_{2}$ and $k_{1}$ are constants) is physically the circulation of the PGSVs. Discussion is conducted based on $\Delta F = g_2 (\xi )$ , which provides important insight into the physics of TBL control based on PAs.