Experimental analysis of a turbulent boundary layer at high Reynolds numbers

Abstract

In this work, time-resolved two-dimensional particle image velocimetry measurements in a zero pressure gradient turbulent boundary layer at high Reynolds numbers (Re _θ = 3940 and 7257, based on momentum thickness) are presented. The boundary layer is obtained on the flat wall of a very large recirculating water channel and is investigated on a streamwise–wall-normal plane. Statistical moments of velocity are determined with the aim to investigate high-Reynolds-number effects in profiles obtained in a direction orthogonal to the wall. A careful analysis of such a profile for the measured average velocity indicates departures from the classical logarithmic law towards the power law or parametric models. Such a departure seems to be independent on the specific parameters used in model laws. On the other hand, instantaneous velocity fields are considered to derive information on the dynamic processes involving near-wall vortical structures. Different vortex eduction methods are implemented including Reynolds decomposition, vorticity, invariants of velocity gradient tensor and wavelet tools and compared. The agreement between these methods is rather good, so all of them are used to derive information on wall dynamics. At both Reynolds numbers, packets of vortical structures are observed to form and to evolve aligned more or less at an angle of 30° to the wall. In order to quantify the importance of such ‘coherent’ phenomena over the entire range of turbulent structure, probability density functions of vortical structure size (obtained from wavelet analysis) are determined. The results show the existence of a hierarchical relation between coherent vortices, the average vortex size being almost equal to 1/10 of the boundary layer displacement thickness. The measured data are consistent with the formation of about seven large ‘children’ vortices from each ‘parent’ vortex.

Keywords:

• turbulent boundary layer
• wall dynamics
• law of the wall
• high Reynolds number
• PIV

Acknowledgements

The authors would like to thank Alessandro Dolcini for his contribution in the measurements tests.