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Scaling of flat plate drag reduction using plasma-generated streamwise vortices
Published online by Cambridge University Press: 14 March 2025
Abstract
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.
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- © The Author(s), 2025. Published by Cambridge University Press