Fully resolved measurements of turbulent boundary layer flows up to

Abstract

Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range Re τ = 6000-20 000. Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to Re τ = 20 000. Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with Re τ in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers.

Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra

“…At the small-scale end, all spectra are in close agreement (expected per the law of the wall Samie et al 2018;Ganapathisubramani 2018). In particular, the two highest Re τ spectra (Re τ ≈ 13 000 and 19 300, S18: Samie et al 2018) are in excellent agreement with the DNS spectrum (Re τ ≈ 2 000, S13: Sillero et al 2013), since those data correspond to fully-resolved measurements ( § 3.2 and detailed in Samie 2017). Because all spectra collapse for k x z 10 −1 , the roll-offs of the experimental spectra at the low wavenumber-end also collapse because of the Reynolds-number invariant f W .…”

“…Figure 7 reveals an absence of coherence for λ + x 5 000. From now on it is assumed that (4.8) is applicable to a logarithmic region starting at z ∼ O(100ν/U τ ) (see also Agostini & Leschziner 2017), because DNS data evidences a lower limit down to where the inner-spectral peak has a pronounced appearance in the spectrogram and integrated energy, say z + T ≈ 80, see Figure 4 in Baars et al (2017b) and fully-resolved u 2 profiles in Samie et al (2018). Absence of any small-scale coherence in the W data is a topic for future work as it may be caused by differences in temporal (hot-wire) and spatial (DNS) data, frequency modulation effects that become more pronounced with increasing Re τ (and more strongly affect temporal data, Baars et al 2017a), experimental uncertainty in the spanwise alignment of the hot-wire probes at z R and z, etc.…”

“…Filter fL, with zL = 0.15δ, is applied for z zL; fW is applied for z + T z + z + L , while fW is z-invariant for z + z + T and equal to fW (z + T ; λx). Data are from H09: Hutchins et al (2009) and S18: Samie et al (2018), see § 3.2. Note: λx ≡ U (z)/f .…”

Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and

“…A corrected profile for the streamwise TI is superposed in Figure 3(b) with filled diamonds, following the method of Smits et al (2011). Samie et al (2018) confirmed that this correction scheme is valid for Reynolds numbers up to Re τ ≈ 20 000. Because the TI above the near-wall region (say z > z T ) is unaffected by spatial resolution issues, we can proceed our current analysis without hot-wire corrections.…”

“…Peak values of the streamwise TI at z max , as a function of Re τ , are shown in Figure 9. DNS data include the channel flow of Lee & Moser (2015) and TBL flow of Sillero et al (2013) studies performed in Melbourne's boundary layer facility (Marusic et al 2015;Samie et al 2018), UNH's Flow Physics Facility (Vincenti et al 2013) and at Utah SLTEST (Metzger et al 2001). Current data (employed in Figure 7).…”