Streamwise variations of turbulence statistics up to maximum drag reduction state in turbulent boundary layer flow due to surfactant injection

Abstract

We investigate streamwise variations of turbulence statistics in the wide range of drag reduction (DR) up to the maximum drag reduction (MDR; DR ≥ 60%) state for the turbulent boundary layer flow due to surfactant injection. One-component laser-Doppler velocimetry (LDV) measurements show that the DR is drastically varied from the low drag reduction (LDR) to the high drag reduction (HDR) regions and is saturated in the MDR region, and such variation is sensitive to the free-stream velocity and dependent on the process of diffusion of injected surfactant solution. Both two-component LDV measurements and particle image velocimetry (PIV) measurements clarify that the mean velocity in wall units agrees with the so-called Virk’s ultimate profile in the MDR region, where both wall-normal turbulence intensity and the Reynolds shear stress with outer scaling are considerably suppressed compared to those in the LDR and HDR regions, while the maximum of streamwise turbulence intensity is comparable with that of water. Such behavior is independent of flow types such as internal and external flows and kinds of additives such as polymer and surfactant. The principal axis angle in joint probability density function of streamwise and wall-normal velocity fluctuations near the wall is the most promising index as the amount of DR based on the LDR, HDR, and MDR. The PIV measurements also show that the sheet-like structures in the HDR and MDR regions expand to around the maximum location of streamwise turbulence intensity, at which spanwise length scales are evaluated.