Experimental assessment of square wave spatial spanwise forcing of a turbulent boundary layer

Abstract

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. SPIV in the streamwise-wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of $\lambda_x^+ = 397$. We confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of $y^+ \approx 100$, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of $A^+ = 12.7$. An extension of the classical laminar Stokes layer theory is introduced, to describe the non-sinusoidal boundary condition that corresponds to the current case. The spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range $2 \leq y^+\leq 5$. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (2009), matching the drag reduction trend with $A^+$, and reaching a maximum of 20%.