A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to 10(4)
Summary (2 min read)
- The degree to which turbulent zero pressure gradient (ZPG) boundary layer and pipe flows can be treated as similar has been a subject of debate for much of the last decade (e.g. see Monty et al. (2009), Jiménez & Hoyas (2008)).
- One way to approach the issue of experimental scatter is to compare DNS results of internal and external flows directly, as in Jiménez et al. (2010) and Chin et al. (2014).
- Both authors asserted that the distribution of velocity fluctuations was most likely the same in the ‘turbulent’ patches of the boundary layer as they are in the pipe.
- Forgoing measurement of two normal gradients (∂u2/∂x2 and ∂u3/∂x3) eliminates the practical requirement for each sub-array to estimate all three components of velocity simultaneously, the merits of which are evidenced by the velocity component variances reported in Zimmerman et al. (2017).
- 3. Calibration Data collected from a two-step in situ calibration procedure are combined to characterize the response of each sensor to a range of flow angles and speeds expected to be encountered in the profile scans.
3. Velocity statistics
- This section presents profiles of the statistical moments (up to kurtosis) of the three velocity components and the Reynolds shear stress.
- Again, this is consistent with the differences between the intermittency in the pipe and boundary layer.
- The same conclusion is reached via inspection of the HRNBLWT data, the difference in profiles is the most pronounced in the outer region x2/δ ≈ 0.2.
- The pipe and boundary layer cases both exhibit a positive peak in the u2 skewness in the wake region, although the magnitude of the boundary layer peak far exceeds that of the pipe.
- As is the case with u2 fluctuations, the point at which the boundary layer and pipe u3 variance profiles intersect is approximately coincident with the point at which the kurtosis profiles rapidly diverge, with both features occurring near x2/δ ≈ 0.6.
- This section presents statistics of all three components of vorticity, as well as the mean enstrophy 1 2 ωiωi.
- This synthetic case corresponds to the least-resolved physical experimental cases (see Table 1), and so all the experimental data is expected to approximately lie between the DNS computations and the synthetic experimental curve in the absence of effects not captured by the synthetic experimental model.
- As with the two zero-mean vorticity components (i.e. ω1 and ω2), the pipe and boundary layer ω3 vorticity RMS profiles closely resemble each other with the exception of the change of concavity observed in the boundary layer wake.
- With the exception of the highest-Reτ boundary layer case, the pipe and boundary layer kurtosis profiles track each other closely.
- The outer peaks observed in the enstrophy ratio profiles coincide with the change-of-concavity discussed above in the context of figures 8 through 10 as well as the outer ‘bumps’ in the boundary layer u2 and u3 variance profiles relative to those of the pipe.
- Two overarching features of the RMS, skewness, and kurtosis profiles are shown in §3 and §4 to consistently differentiate between pipe and boundary layer flow: outer magnitude peaks in the boundary layer skewness and kurtosis cases that emerge at x2/δ ≈ 0.5; and higher RMS/lower skewness and kurtosis magnitude of boundary layer quantities over a domain roughly spanning 0.1 .
- Early studies of this phenomenon even used the departure of the u1 kurtosis from the Gaussian value as a measure of intermittency (Klebanoff 1955).
- Instead, a range of thresholds for instantaneous enstrophy, 1 2 ω̃iω̃i, are used to identify ‘irrotational’ or ‘quasi-irrotational’ flow.
- Magnitude differences between the two Reτ cases, particularly for the lowest thresholds, are most likely influenced by spatial resolution, and thus conclusions drawn from figure 13 should be limited to those based on the relative magnitudes of the pipe and boundary layer, and the dependence of these relative magnitudes on wall-distance.
- The location of the discrepancy between ‘non-turbulent’ time fractions in the two flows roughly corresponds to the outer ‘bump’ in the boundary layer enstrophy relative to pipe enstrophy, the largest differences in Reynolds stresses between the two flows, and the lower magnitudes of boundary layer skewness and kurtosis profiles for a number of quantities as discussed throughout §3 and §4.
- A multi-sensor hotwire probe capable of measuring both the velocity and vorticity vectors has been deployed in a set of three turbulent pipe flows and three zero-pressure- gradient boundary layers with nominally matched inner and outer scales.
- Basic statistical results of these measurements are presented and highlight differences between the two flows and identify the subdomain over which they occur.
- A number of the observed differences in the present study match the observations of several lower-Reτ DNS and experimental studies, including those of Jiménez & Hoyas (2008), El Khoury et al. (2013), and Monty et al. (2009).
- The pipe and boundary layer velocity variances also intersect at approximately x2/δ ≈ 0.6, beyond which the boundary layer variances decay to zero while those in the pipe do not.
- The kurtosis coefficients of the vorticity fluctuations of all three components are super-Gaussian across the flow domain, with the kurtosis of the zero-mean components (ω1 and ω2) tending to increase with distance from the wall.
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Q1. What are the contributions in "A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction reynolds numbers up to 10" ?
This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity from 5000.