Characteristics of turbulent boundary layer large scale motions using direct fluctuating wall shear stress measurements

This experimental work studies the impact large scale motions in a zero pressure gradient turbulent boundary layer have on the fluctuating streamwise wall shear stress component using a recently developed $1\times 1{\mathrm{mm}}^2$ floating element differential capacitive shear stress sensor. The sensing system allows for a flat band response with a bandwidth up to 1.8 kHz (based on a $\pm 3\text{−}\mathrm{dB}$ limit). The streamwise velocity is measured using single component hot-wire anemometry. The experimental setup is first verified to have a canonical zero pressure gradient turbulent boundary layer using the mean and fluctuating velocity profiles as well as fits for the mean wall shear stress with respect to the operating Reynolds number. Characteristics of the large scale structure are examined spatially using Taylor's frozen field hypothesis and the lag time of peak levels of correlation between the shear stress and velocity signals. The large scale motion inclination angle is determined to be ${16}^{\circ }$. The coherence between the signals demonstrate that low frequency motions dominate most of the boundary layer except nearest the wall. In addition, conditional sampling of velocity on shear stress provides conditional velocity statistics profiles which reveal information on the entire boundary layer during shear stress events, representing the qualitative features of the bursting-sweeping process.

Figure 1

(a) Schematic of the flat plate model and supports (coloring for clarity) and (b) flat plate model installed with hot-wire mount descending from the traversing ceiling with capacitive shear stress sensor in view.

Figure 2

Fabricated CSSS device with H-bar supporting tethers and interdigitated fingers on either side of floating element, along with hole array on the floating element for pressure rejection. (Figure was adapted from Ref. [24].)

Figure 3

Frequency response of transfer function between CSSS and streamwise aligned wall mounted microphone in PWT. Black circles (lower curve) show the magnitude response in dB showing a $\pm 3$-dB bandwidth limit of 1775 Hz. Red circles (upper curve) show the difference between the measured phase and the theoretical phase.

Figure 4

(a) Unfiltered and low-pass-filtered power spectral density of ${\tau }_x^{\prime }$, with a resonance peak at 2.8 kHz. (b) Normalized histogram simulating the PDF of measured total normalized wall shear stress, alongside a log-normal distribution matching mean and standard deviations of the data.

Figure 5

Premultiplied and normalized power spectral density of unfiltered streamwise velocity for a variety of wall-normal positions.

Figure 6

(a) Mean normalized velocity profile with friction velocity extracted from CSSS and (b) normalized streamwise velocity variance, each compared to their respective profile from the Schlatter-Örlü [5] DNS data for a zero pressure gradient turbulent boundary layer at comparable Reynolds number.

Figure 7

Diagnostic plot formulation for the streamwise turbulence intensity compared to the Schlatter-Örlü [5] DNS data.

Figure 8

For a wall-normal traverse, cross correlation coefficient $R_{\tau u}$ for (a) inner normalized temporal delays $\mathrm{\Delta }{t}^{+}$ and (b) transformed to the spatial domain with Taylor's hypothesis.

Figure 9

Spatial reconstruction of the large scale motion for the wall-normal traverse using the chosen correlation lag value as the lag at the highest correlation peak (red circles) and the expected correlation lag from the wall-normal traverse (black circles).

Figure 10

For a spanwise traverse at $y^{+}=99$, the inner normalized temporal cross correlation coefficient between shear stress and streamwise velocity transformed to the spatial domain in streamwise direction.

Figure 11

Coherence between fluctuating wall shear stress and velocity signals for (a) a wall-normal traverse and (b) a spanwise traverse of the hot-wire probe at $y^{+}=99$.

Figure 12

Mean streamwise velocity profiles conditioned on shear events compared to the measured mean profile and DNS data from Schlatter and Örlü [5], normalized by (a) the measured total mean friction velocity and (b) the conditional mean friction velocity for each threshold.

Figure 13

Streamwise velocity variance profiles conditioned on shear events compared to the measured variance profile and DNS data from Schlatter and Örlü [5], normalized by (a) the measured total mean friction velocity and (b) the conditional mean friction velocity for each threshold.