SCALING OF DRAG REDUCTION IN A TURBULENT BOUNDARY LAYER BASED ON 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) or one pair of PAs, and the friction Rynolds number Reτ. It is experimentally found that DR increases logarithmically with the growing maximum spanwise mean velocity W^̅_max⁺ but decreases with rising L⁺ and Reτ, where superscript + denotes normalization by the inner scales. It is further found from theoretical and empirical scaling analysis that the dimensionless drag variation ∆F = f1 (W^̅_max⁺ , L⁺, Reτ) may be reduced to ∆F = f2 (Г), where f1 and f2 are different functions and the scaling factor Г = [k2log10(k1 W^̅_max⁺ )]/(L⁺Reτ) (k2 and k1 are constants) is physically the circulation of PGSV. Discussion is conducted based on ∆F = f2 (Г), which provides important insight into the TBL control physics.