Comparison of turbulence structures at large and small drag reduction ratios in turbulent boundary layer of surfactant solutions

Abstract

In this study, turbulence structures of drag-reducing turbulent boundary layers in surfactant solutions at the momentum-thickness Reynolds number Re _θ≃800 were compared at large and small drag reduction ratios and 34% at the solution temperature, T=30°C and 35°C. Turbulence statistics and structures were obtained by a two-component laser-Doppler velocimetry (LDV) and particle image velocimetry (PIV) systems for the streamwise and wall-normal (x–y) plane and the streamwise and spanwise (x–z) plane. The quadrant analysis of streamwise and wall-normal velocity fluctuations revealed that at , the positive contribution of sweep and ejection events to the Reynolds shear stress was comparable with the negative contribution of inward-interaction and outward-interaction events, so that the Reynolds shear stress was almost zero. At , the maximum positive contributions of quadrants II and IV and the maximum negative contributions of quadrants I and III were comparable with those of the corresponding water near the wall, but the region of positive contributions in quadrants II and IV became narrower and the region of negative contributions in quadrants I and III became wider, so that the Reynolds shear stress decreased. At , in high activity, the streamwise velocity fluctuations were smaller than those of water but were relatively large even near the center of the boundary layer, in addition to the near-wall region, while in low activity, the fluctuating velocity vectors were almost parallel to the wall. At , the scale of sweep and ejection events was much larger than that of water and the inclination angle of vortex packets at was much smaller than that of water. At , the spanwise turbulence fluctuation was strongly suppressed and vortical structures were not observed on the (x–z) plane, while at , several vortical structures, which seemed to correspond to the cross section of legs of hairpin vortices, were observed near the wall. Under the assumption of frozen turbulence, it was found that for both and 34%, the high- and low-speed regions were aligned laterally, although the low-speed regions at were obscured.

Keywords:

• drag reduction
• turbulent boundary layers
• surfactant
• turbulence structures
• PIV
• LDV

Acknowledgement

This work was partially supported by a Grant-in-Aid for Scientific Research (Nos. 19560170 and 21760126) from the Japan Society for the Promotion of Science. The authors would like to thank Prof. K. Yokota (Graduate School of Engineering, Nagoya Institute of Technology) for useful discussions. The authors also wish to thank S. Takeuchi and E. Junke for their generous assistance with the experimental measurements.