Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers

Abstract

This work can be viewed as a reprise of Head & Bandyopadhyay's (J. Fluid Mech. vol. 107, 1981, p. 297) original boundary-layer visualization study although in this instance we make use of stereo particle image velocimetry (PIV), techniques to obtain a quantitative view of the turbulent structure. By arranging the laser light-sheet and image plane of a stereo PIV system in inclined spanwise/wall-normal planes (inclined at both 45 • and 135 • to the streamwise axis) a unique quantitative view of the turbulent boundary layer is obtained. Experiments are repeated across a range of Reynolds numbers, Re τ ≈ 690-2800. Despite numerous experimental challenges (due to the large out-of-plane velocity components), mean flow and Reynolds stress profiles indicate that the salient features of the turbulent flow have been well resolved. The data are analysed with specific attention to a proposed hairpin eddy model. In-plane two-dimensional swirl is used to identify vortical eddy structures piercing the inclined planes. The vast majority of this activity occurs in the 135 • plane, indicating an inclined eddy structure, and Biot-Savart law calculations are carried out to aid in the discussion. Conditional averaging and linear stochastic estimation results also support the presence of inclined eddies, arranged about low-speed regions. In the 135 • plane, instantaneous swirl patterns exhibit a predisposition for counter-rotating vortex pairs (arranged with an ejection at their confluence). Such arrangements are consistent with the hairpin packet model. Correlation and scaling results show outer-scaling to be the correct way to quantify the characteristic spanwise length scale across the log and wake regions of the boundary layers (for the range of Reynolds numbers tested). A closer investigation of two-point velocity correlation contours indicates the occurrence of a distinct two-regime behaviour, in which contours (and hence streamwise velocity fluctuations) either appear to be 'attached' to the buffer region, or 'detaching' from it. The demarcation between these two regimes is found to scale well with outer variables. The results are consistent with a coherent structure that becomes increasingly uncoupled (or decorrelated) from the wall as it grows beyond the logarithmic region, providing additional support for a wall-wake description of turbulent boundary layers.

Flow in a commercial steel pipe

“…The profiles are consistent with those previously reported for pipe, channel and boundary layer flows (see, for example, [9] and [4]). Most noticeable is the region of negative correlation occurring in approximately the range 0.3 < S/R < 1.3, the most likely source of which would be coherent structures in the form of hairpins or counter-rotating streamwise pairs.…”

“…Figures 12 and 13 show that the correlations, and therefore the very large-scale motions, show little Reynolds number dependence. This aspect of the VLSM's was previously observed over a smaller Reynolds number range by Hutchins et al [4] in boundary layers and by Monty et al [9] for pipe flows. The results in figures 12 and 13 also indicate that the azimuthal scale of the coherent structures in the outer layer is independent of surface roughness, which is in accordance with expectations based on Townsend's hypothesis.…”

Measurement of laminar, transitional and turbulent pipe flow using Stereoscopic-PIV

“…Measurements behind a heart valve mounted in a pipe (Marassi et al 2004), show that it is not trivial to balance these contradicting requirements. Other SPIV measurements with large cross-flow were performed by Matsuda and Sakakibara (2005) in a turbulent jet and by Hutchins et al (2005) in a turbulent boundary layer.…”

Investigation of Coherence behind a Single Foamed Tube

“…Ganapathisuramani et al [21] showed how stream-wise autocorrelation can be used to measure the size of stream-wise structures. Hutchins et al [22,23] used two-point span-wise correlation to obtain statistical information regarding the width and spacing of the coherent structures. In literature, a number of studies can be found in which two-point correlation is used to obtain the shape of the structures inside the wake region [24,25].…”