Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

Abstract

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/δ = 0.15 and 0.89. The Reynolds number based on momentum thickness Re θ = 34 000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of lowspeed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5δ), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wallnormal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5δ distance from the DC peak) and along the 45 • diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise-streamwise organization of the coherent structures in a fully turbulent boundary layer.

Three-dimensional evolution of flow structures in transitional circular and chevron jets

“…Moreover, the temporal resolution of the phenomenon allows addressing the growth and development of the coherent flow structures along with their mutual interaction. TR-TOMO PIV is a suitable technique for the diagnostics of complex three-dimensional flows, as shown by recent applications on turbulent boundary layers 48,49 and wake flows. 50,51 The application to circular and chevron jets has been demonstrated feasible in the visualizations obtained by Scarano et al 52 The use of time-resolved experiments to determine the sound produced by the early transition stage due to vortex pairing 42 has been extended to the natural transition case by Violato et al 53 With direct numerical simulations tailored on the latter experiment, Moore et al 54 showed that the experimental approach is also a valuable tool to provide a comparison based on unsteady flow properties to numerical simulations.…”

Spatial–spectral characteristics of momentum transport in a turbulent boundary layer

“…The filter replaces the value measured experimentally in a certain point of the domain, with the value obtained in the same point by least-square fitting a polynomial function of the second order in x (streamwise direction) and y (wall-normal direction), and of the first order in the third dimension (time), in a 5×5×3 neighborhood around the point. Details on this regression filter are given by Elsinga et al (2010). From these filtered velocity vector fields we obtained the instantaneous RSS fields (uv).…”

Experimental study on the role of spanwise vorticity and vortex filaments in the outer region of open-channel flow

“…On the other hand, there is three-dimensional visualization evidence for hairpins and hairpin packets in the work of Elsinga et al (2010) and Dennis and Nickels (2011), and if one interprets the regions of compact transverse vorticity and swirling strength to be consequences of hairpins intersecting the x-y plane, then there is ample evidence for the existence of hairpins. Thus, the resolution of these conflicting observations is important to the progress of turbulence research, and it is desirable to determine the existence and significance of filamentary vortex heads using means other than qualitative visualization.…”