The inertial subrange in turbulent pipe flow: centreline

The inertial-subrange scaling of the axial velocity component is examined for the centreline of turbulent pipe flow for Reynolds numbers in the range 249⩽Reλ⩽986. Estimates of the dissipation rate are made by both integration of the one-dimensional dissipation spectrum and the third-order moment of the structure function. In neither case does the non-dimensional dissipation rate asymptote to a constant; rather than decreasing, it increases indefinitely with Reynolds number. Complete similarity of the inertial range spectra is not evident: there is little support for the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 32, 1941a, pp. 16–18; Dokl. Akad. Nauk SSSR, vol. 30, 1941b, pp. 301–305) and the effects of Reynolds number are not well represented by Kolmogorov’s ‘extended similarity hypothesis’ (J. Fluid Mech., vol. 13, 1962, pp. 82–85). The second-order moment of the structure function does not show a constant value, even when compensated by the extended similarity hypothesis. When corrected for the effects of finite Reynolds number, the third-order moments of the structure function accurately support the ‘four-fifths law’, but they do not show a clear plateau. In common with recent work in grid turbulence, non-equilibrium effects can be represented by a heuristic scaling that includes a global Reynolds number as well as a local one. It is likely that non-equilibrium effects appear to be particular to the nature of the boundary conditions. Here, the principal effects of the boundary conditions appear through finite turbulent transport at the pipe centreline, which constitutes a source or a sink at each wavenumber

Spectral scaling in boundary layers and pipes at very high Reynolds numbers

ne-dimensional energy spectra in flat plate zero pressure gradient boundary layers and pipe flows are examined over a wide range of Reynolds numbers (2600?Re??72500). The spectra show excellent collapse with Kolmogorov scaling at high wavenumbers for both flows at all Reynolds numbers. The peaks associated with the large-scale motions (LSMs) and superstructures (SS) in boundary layers behave as they do in pipe flows, with some minor differences. The location of the outer spectral peak, associated with SS or very large-scale motions (VLSMs) in the turbulent wall region, displays only a weak dependence on Reynolds number, and it occurs at the same wall-normal distance where the variances establish a logarithmic behaviour and where the amplitude modulation coefficient has a zero value. The results suggest that with increasing Reynolds number the energy is largely confined to a thin wall layer that continues to diminish in physical extent. The outer-scaled wavelength of the outer spectral peak appears to decrease with increasing Reynolds number. However, there is still significant energy content in wavelengths associated with the SS and VLSMs. The location of the outer spectral peak appears to mark the start of a plateau that is consistent with a k?1x slope in the spectrum and the logarithmic variation in the variances. This k?1x region seems to occur when there is sufficient scale separation between the locations of the outer spectral peak and the outer edge of the log region. It does not require full similarity between outer and wall-normal scaling on the wavenumber. The extent of k?1x region depends on the wavelength of the outer spectral peak (?OSP), which appears to emerge as a new length scale for the log region. Finally, based on the observations from the spectra together with the statistics presented in Vallikivi et al. (J. Fluid Mech., 2015 (submitted)), five distinct wall-normal layers are identified in turbulent wall flow

Turbulent pipe flow near-wall statistics

Results from the first experimental campaign in the Long Pipe facility of the CICLoPE laboratory are reported. Single hot-wire profile measurements are presented, taken from the wall up to one third of the pipe radius, with the friction Reynolds number Re\ucf\u84 ranging from 6.5 \uc3\u97 103 up to 3.8 \uc3\u97 104 . Measurements of the pressure drop along the pipe are presented together with an estimation of its uncertainty. Mean and variance of the streamwise velocity fluctuations are examined and compared with the findings from other facilities. The amplitude of the inner-scaled near-wall peak of the variance, after being corrected for spatial resolution effects, shows an increasing trend with Reynolds number, in accordance with low Reynolds number experiments and simulations

Wavenumber dependence of very large-scale motions in ciclope at 4800 \ue2\u89\ua4 Re\ucf\u84 \ue2\u89\ua4 37,000

The present work aims at investigating the very large-scale structures of turbulent pipe flow in CICLoPE at high Reynolds numbers. According to recent studies, some open questions remain to be answered to identify accurate sizes of these turbulent structures in pipe flow. The CICLoPE facility has been therefore utilized, providing an opportunity to approach high Reynolds number flows with high enough resolution in terms of the viscous length scale, allowing us to investigate the behavior of such turbulent structures. Meandering structures, usually referred as VLSM (very large-scale motions), have been identified with claimed extension up to 20R, where R is the pipe radius