Evolution of eddies and packets in turbulent boundary layers.

Abstract

The objective of this study was to improve understanding of the population distribution and evolution of eddies and eddy packets in turbulent boundary layers using experimental methods. To effectively identify vortical structures, an advanced vortex identification algorithm was developed based on swirl strength, and the real eigenvector of the velocity gradient tensor as an indicator of eddy orientation. The new method applied on the streamwise/spanwise plane had a good performance on vortex identification, which was tested by two Direct Numerical Simulation (DNS) of channel flow at Re#28; = 590 and 934, and one Dual-Plane Particle Image Velocimetry (PIV) data set of boundary layer at Re#28; = 2480. The effect of spatial resolution was studied. Although it was found that relatively coarse resolution of 24.5 wall units (Dual-Plane PIV) caused underestimation of velocity gradients, which resulted in underestimated magnitudes of several derived variables, such as swirl strength, vorticity and circulation, the statistical results of vortex population distribution had a good agreement between DNS and Dual-Plane PIV data sets. A new method of scaling the swirl was proposed based on the invariants of the characteristic equation of the velocity gradient tensor, which could minimize the effects of data resolution among different data sets. A volumetric PIV technique, Tomographic PIV (TPIV), was applied to investigate vortical structures. Although the TPIV resolution was too coarse to resolve the smallest eddies accurately, it worked very well for identifying larger eddies and packets. Population distributions of eddy orientation, size, circulation and convection velocity in the logarithmic region were obtained from both numerical and experimental data. It was found that the elevation angle and size of eddies increased with increasing wall-normal distance, while the eddy circulation decreased with increasing wall-normal distance. The mean convection velocity of eddies was normally #24;97% of the local mean. Joint PDFs of eddy radius and circulation yielded a peak fitting curve of an exponential function a(r+)b. The exponent b was found equal to 2.2 for all data sets in the logarithmic region, while the coefficient a was proportional to the mean magnitude of vorticity which was dependent on the resolution. The difference between vorticity vector and the real eigenvector was documented, and this was thought to be caused by the local shear motion. The volumetric data from TPIV gave strong support for the local shear hypothesis showing that the eigenvector is a better indicator of eddy orientation. Eddy packets and flow evolution were studied using flying TPIV data in the lower (z+ = 100 #24; 300) and upper (z+ = 300 #24; 500) logarithmic region for Re#28; = 2480. Long slow regions (> 0:6#14;) surrounded by eddy pairs were often seen in both locations (#24;10% of all instantaneous fields). The width of the long slow regions was #24;400-500 viscous units (#24;0.16-0.2#14;) at z+ #25; 200 and #24;650- 750 viscous units (#24;0.26-0.3#14;) at z+ #25; 400. Pairs of hairpin legs propagated mostly at velocity of 0.92U+ for both wall-normal locations. The streamwise spacing of vortex pairs in the packets was about 300 viscous units at z+ #25; 200 and 150 viscous units at z+ #25; 400. The spanwise spacing of two long slow regions was typically larger than 0.5#14;. One case at the lower wall-normal location showed that a long slow region stably lasted at least #1;t+ #25; 2300 and traveled about 15.5#14;, while one long slow region lasted #1;t+ #25; 1500 and traveled about 11.5#14; at the upper location. Deforming, meandering, merging, and breaking of these long slow regions was observed. Interaction of neighboring eddies was also observed. Oscillation of hairpin legs in the spanwise direction showed that, whenever they became closer, they appeared to become stronger, and vice versa. Eddies with strong circulation showed greater stability over time. The eddies with less than 10% circulation variation over #1;t+ = 78 had mean circulation of 500 at the lower location and 350 at the upper location.