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

TL;DR

This paper experimentally demonstrates that square wave spanwise forcing in a turbulent boundary layer can significantly reduce drag by attenuating turbulence stresses and kinetic energy production, with results aligning with extended theoretical models.

Contribution

The study introduces an experimental setup for square wave spanwise forcing and extends classical Stokes layer theory to describe non-sinusoidal boundary conditions.

Findings

Maximum streamwise stress reduction of 45%

Turbulence kinetic energy production reduced by 39%

Drag reduction up to 20% in experiments

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%.